raindrop size distribution retrievals in the tropics … · 2011. 8. 22. · raindrop size...

RAINDROP SIZE DISTRIBUTION RETRIEVALS IN THETROPICS AND MID LATITUDES

Bronwyn K. Dolman, B.Sc. (Hons)

Thesis

submitted for the degree of

DOCTOR OF PHILOSOPHY

at the

UNIVERSITY OF ADELAIDE

School of Chemistry and Physics

Discipline of Physics

May 2010

Dedicated to all students who paid the ultimate sacrifice in times of war, and

never returned to complete their studies.

In their sacrifice was our shelter

Contents

Abstract v

Statement of Originality vii

Acknowledgements ix

List of Figures xvii

List of Tables xxiii

1 Introduction 1

1.1 Early Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Functional Forms of the DSD . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Ground-based DSD Measurement Instruments . . . . . . . . . . . . . 7

1.4 Radars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5 Scope of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Radars 13

2.1 Profilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Profiler Frequency . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.2 Adelaide Profiler . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.3 Darwin Profiler . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Scanning Radars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.2 Weather Watch . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.3 CPOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Profiler Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4 Empirical Relationships . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.1 Z −R Relationships . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.2 D0-ZDR Relationships . . . . . . . . . . . . . . . . . . . . . . 31

2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

ii CONTENTS

3 Dropsize Distribution Retrievals 33

3.1 Retrieval Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.1.1 Finding the Divide . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.2 Clear-Air Peak . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.1.3 Interference Effects . . . . . . . . . . . . . . . . . . . . . . . . 41

3.1.4 Precipitation Peak . . . . . . . . . . . . . . . . . . . . . . . . 43

3.1.5 Deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.1.6 Small-Drop Regime . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2 Code automation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.3 Calculations from the Retrieval . . . . . . . . . . . . . . . . . . . . . 55

3.3.1 Rainrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.3.2 Liquid Water Content . . . . . . . . . . . . . . . . . . . . . . 56

3.3.3 Median Drop Diameter . . . . . . . . . . . . . . . . . . . . . . 56

3.3.4 Heating Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4 Quality Control 59

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2 DSD Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2.1 DSD Procedural Problems . . . . . . . . . . . . . . . . . . . . 61

4.3 Manual Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.4 Quality Control Routine . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.4.1 Threshold procedure . . . . . . . . . . . . . . . . . . . . . . . 75

4.4.2 Threshold Failure . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.4.3 Quality Control of the Vertical Velocity . . . . . . . . . . . . . 79

4.5 Quality Control in Practice . . . . . . . . . . . . . . . . . . . . . . . 80

4.6 Real-Time Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5 Results from Darwin 85

5.1 Monsoon Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.1.1 Microphysics . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.2 Monsoon Rainfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.3 Break Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.3.1 Microphysics . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.4 Break Rainfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

CONTENTS iii

6 Rain Events in Adelaide 141

6.1 South Australian Drought . . . . . . . . . . . . . . . . . . . . . . . . 142

6.2 12 June 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

6.3 21 September 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

6.4 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

7 Discussion 179

7.1 Microphysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

7.1.1 Median Drop Diameter . . . . . . . . . . . . . . . . . . . . . . 181

7.1.2 Equilibrium Distributions . . . . . . . . . . . . . . . . . . . . 186

7.2 Bright Band D0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

7.3 Empirical Relationships . . . . . . . . . . . . . . . . . . . . . . . . . 200

7.3.1 Z-R Relationships . . . . . . . . . . . . . . . . . . . . . . . . 200

7.3.2 D0-Zdr Relationships . . . . . . . . . . . . . . . . . . . . . . . 205

7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

8 Conclusions and Future Work 209

8.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

A Glossary of Terms 213

B Precipitation Microphysics 215

B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

B.2 Cloud Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

B.3 Precipitating Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

B.3.1 Rainfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

B.3.2 Convective Precipitation . . . . . . . . . . . . . . . . . . . . . 219

B.3.3 Stratiform Precipitation . . . . . . . . . . . . . . . . . . . . . 221

B.4 Mesoscale Convective Systems . . . . . . . . . . . . . . . . . . . . . . 225

B.5 Middle Latitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

B.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

C Equilibrium Distributions 233

References 236

iv CONTENTS

Abstract

Weather radar capabilities have improved dramatically over the last 50 years. Fol-

lowing World War II, surplus military radars were turned to the study of weather.

Since then, they have evolved to the modern standard of rainfall estimations avail-

able to the general public in real time. Forecasters rely on weather radars not only

for routine forecasting, but also for tracking rapidly evolving, potentially hazardous,

severe weather events. These storms have the potential to cause flash floods and

hence loss of crops, livestock, and human life.

Most weather radars estimate rainfall by converting the measured reflectivity to a

rainrate via an empirical relationship (Z-R relationship). There are limitations in

the accuracy of the rainfall estimates derived from these scanning radars. Variations

in the raindrop size distribution (DSD), that is, the spread of sizes of raindrops

falling at a given location, affect the measured reflectivity, and thus the rain rate

estimate. The DSD can vary both temporally and spatially, and also with latitude.

Investigation of the DSD and its evolution can be used to investigate the effectiveness

of Z-R relationships in varied meteorological conditions and locations.

Well-established techniques exist for retrieving the DSD using vertically pointing

VHF Doppler radars. These radars can simultaneously detect a clear-air echo due

to fluctuations in temperature and humidity, and a precipitation echo. Mean ver-

tical air motion and spectral width are estimated from the clear air spectrum, and

used to correct the precipitation spectrum through a deconvolution procedure. The

corrected precipitation spectrum is then converted to a size spectrum, and the DSD

calculated. The DSD and associated integral parameters such as rainrate and liquid

water content can then be used to infer the microphysical processes dominating the

cloud and precipitation structure. This knowledge can then be used to investigate

various Z-R relationships.

This thesis presents DSD retrievals from VHF profilers located in Adelaide and

Darwin. Each profiler is installed within the footprint of a scanning weather radar,

allowing direct comparison of the same air space. These radars provide a unique

vi Abstract

opportunity to study the evolution of the DSD with the profiler, and use this to

investigate variations in time and height of the Z-R relationship. The locations of

the radars also permits investigation of the differing nature of DSD evolution in the

tropics compared to the mid-latitudes.

The TWP-ICE field campaign was conducted in Darwin and surrounding areas in

January and February 2006. The campaign involved many instruments, both in-

situ and remote sensing, including a fleet of aircraft and ship. The University of

Adelaide Atmospheric Physics Group installed a VHF wind profiler operating at

54.1 MHz near Darwin airport for the experiment. This radar sampled the same air

space as a C-band polarimetric scanning radar (CPol), which performed horizontal

scans at increasing elevations, along with vertical scans over the profiler site every

10 minutes. Results from 8 events, differing in age, type, dominant microphysical

process and seasonal regime are presented in this thesis.

A VHF profiler permanently located near Adelaide airport provides an observational

capability similar to Darwin, but in the mid-latitudes where the processes dictating

rainfall are vastly different. This radar also operates at 54.1 MHz, and is installed

within the footprint of an operational weather watch radar. Pseudo vertical scans

can be constructed from the successive horizontal scans allowing direct comparisons.

This profiler is the first generation of the profiler in Darwin. It is not as powerful and

cannot detect low intensity rainfall. Due to this and the drought South Australia

experienced between 2006 and 2008, data from Adelaide are limited. Two events

are presented.

Seasonal trends in the tropics, that is break conditions as opposed to the mon-

soon, are compared and contrasted. These trends are then compared to the limited

Adelaide data. By analysing the evolution in both time and height of the DSD,

and the dependence on season and latitudinal location, this thesis leads to a better

understanding of the microphysical processes dictating rainfall in the tropics and

mid-latitudes.

Statement of Originality

This work contains no material which has been accepted for the award of any other

degree or diploma in any university or other tertiary institution to Bronwyn K.

Dolman and, to the best of my knowledge and belief, contains no material previously

published or written by another person, except where due reference has been made

in the text.

I give consent to this copy of my thesis, when deposited in the University Library,

being made available for loan and photocopying, subject to the provisions of the

Copyright Act 1968.

I also give permission for the digital version of my thesis to be made available on

the web, via the Universitys digital research repository, the Library catalogue, the

Australasian Digital Theses Program (ADTP) and also through web search engines,

unless permission has been granted by the University to restrict access for a period

of time.

SIGNED: ..................................................

DATE: .....................

viii Statement of Originality

Acknowledgements

In any undertaking of this magnitude, there will be many people who have contributed

in some way, either directly or indirectly, towards the ultimate realisation of the

original goal. Practical limitations dictate that everyone can not be mentioned here

but the contribution of those omitted is gratefully acknowledged.

Firstly, I need to thank my Dad, for albeit unknowingly, allowing me to plagiarise

the opening paragraph of his own PhD thesis acknowledgements! Since the time

I understood what that blue bound tome that sits amongst the photo albums on

the bookshelf meant, it has been my ambition to do the same. It is a somewhat

surreal feeling to be so close to achieving what feels like a life long goal. While

the language of the opening statement is not what I would choose, the sentiment

rings true, I would not have reached this final stage of writing the acknowledgements

without the support of some wonderful people. This is my opportunity to thank

those people.

Professor Bob Vincent has been an inspiration. Particularly in the final months, Bob

has been an amazing source of knowledge, encouragement and support. His ability

to know when to drop by just to say hi, or deliver his famous “your not trying to

solve life, the universe and everything” speech is amazing. I finish my years as Bob’s

student not only with an instilled passion for science (and improved grammar!) but

an all important appreciation of red wine! I remember my first Friday night drinks

as a grad student when Bob informed me “if your going to be my student, your

going to learn to drink red wine”. It was certainly tough “learning”, drinking a free

glass or two of red every Friday night! Given all that Bob has taught me, I think

its only fair I now make it my mission to teach him a love of brass bands!

I can’t express my gratitude to Dr Peter (Petroneus) May enough. Despite being an

incredibly busy external supervisor, Peter still found the time to have a profound

impact on my candidature. Discounting the time he ignored my plea for help while

stuck on a tiny tropical island with an approaching cyclone (claiming he never

received the email!), he has been an amazing supervisor. His love and knowledge

x Acknowledgements

of science (and sport!) is infectious and one cannot help but be inspired to achieve

when working with him.

The Atmospheric Physics Group has been a great place to “grow up” as a scientist.

In no particular order, to Andrew Heitmann, Alex Dinovitser, Ray Oermann, Octa-

vianus Cakra, Tran Trong, Sujata Kovalum, Daniel McIntosh, Andrew Dowdy - it

has been a pleasure to work with you. A special thanks to those who have shared

the “good or bad” lunch time routine, the beach volleyball extravaganza, and the

occasional over indulgent usually sneaky drinking session, Peter Love, Chris Pietsch

and Jens Lautenbach. I also thank Professor Iain Reid both for useful discussions,

and for providing cake day comic relief! Two group members deserve special thanks.

Joel Younger, an amazing knowledge on all topics, full of humorous stories, and ex-

ceptional drinking talent. Who could want more in a fellow grad student! Time

spent plotting, conniving and mainly drinking has been awesome. In particular,

our student years will forever be exemplified by “that poster session”. Dr Andrew

MacKinnon, not only an inspirational scientist, but also fulfilling the role of com-

puter tech (even if we did lose all of my data!), gaming buddy and most importantly

mentor. You have been a constant source of encouragement, advice, laughter, and

proof that one can safely emerge on the other side of the write up process! Words

cannot express how grateful I am that you were part of my PhD years.

While discussing encouragement, I am also indebted to Dr Christopher Williams.

Despite only three face to face meetings, Chris has taught and inspired me far more

than I’m sure he realises. It was Chris who taught me the foundations of the field,

but more importantly the inner workings of the scientific community and how to

cope with being a grad student. Chris is a brilliant scientist and genuine nice guy,

and without his pep talks early on, I would not be writing my thanks to him.

The Australian Bureau of Meteorology supported this work both through an Aus-

tralian Postgraduate Award scholarship, and through some fantastic people. Dr

Chris Lucas provided the original code on which my work is based, and always

made himself available to talk through problems. Alan Seed provided radar data,

useful discussions, and inevitably a coffee or two when I was in Melbourne. Scott

Collis has also been a source of knowledge and encouragement. Thanks to Ray

Jones, Ken Glasson and particularly Brad Atkinson for their encouragement and

support. Their dedication to drinking in Cairns is a highlight of my PhD years!

At the local bureau office, thanks to Darren Ray for both data and useful discus-

sions on the Adelaide rainfall climate, and John Nairn and Jenny Dickins for help

in interpreting weather patterns. Their help has been invaluable.

Acknowledgements xi

Thanks must go to both the Atmos cake day team, and the Optics BBQ team, both

an excellent source of procrastination on a Friday! In particular I would like to thank

Dr Aidan Brooks, Dr David Hosken and the soon to be Dr Matthew Heintze, all of

whom have been great friends over the years. The write up process is by necessity

a lonely journey, made so much easier by travelling a parallel path to Matt, who

shared the long hours, failures and triumphs. I have lost count of the number of

times Bob caught one of us in the others office and the subsequent “get back to

work” was heard throughout the department!

My candidature has in some ways been overshadowed by outside influences. The

infamous ankle injury near the beginning of my time brought about an abrupt change

in lifestyle, and a more depressed mind set than I care to admit. The realisation

that I would probably never play sport again lead to some of the darkest days of

my life, from which I didn’t think I would recover. While it will never serve as a

full replacement, a rediscovery of music gave me a new focus and outlook on life. I

don’t think it is any coincidence that many of my acknowledgements go to those in

the band world. After all, banding is not a hobby, its a way of life!

To the members of Unley Concert Band, you have only known me as a PhD student,

and have been supportive every step of the way. The band is filled with some

wonderful people, who have shared some amazing experiences. Getting “the lay of

the land” and “making the necessary adjustments” on the Anzac Tour of Belgium

and France, as the dedication of this thesis suggests, was an incredible and inspiring

experience, made so special by the people it was shared with. To the MD Dr Kevin

Cameron, an inspiration both in life and music, I owe a heartfelt thanks. While

we have in your own words a “love-hate” relationship, you always took the time to

listen, encourage, support and mentor when you saw I needed it. In particular, for

talking me into completing this degree, I will be forever in your debt.

To the members of the Hahndorf Town Band, being a small yet busy band its

members become like a family. I can’t thank this family enough for their support

through my PhD years. Particularly during the final months of living and breathing

thesis, the antics of Monday night rehearsals have been the highlight of my week.

To the MD Philip Paine, I think my gratitude can be summed up with “thank you

for the music”!!

To the other bands people I have gotten to know, Dp and TTB, Al and Holdfast, Un-

kie Brent and Payneham, and particularly Veronica and the many other wonderful

people at MCB, thanks for making banding so special.

The person who started me on this banding journey many years ago deserves a spe-

xii Acknowledgements

cial mention. Geoff Bradley has been an amazing source of inspiration, motivation

and most importantly, humor. A man who will question why we can’t just attach

a low pressure system to a plane, and drag rain where we want it, and ask you to

explain the concept of “nothing” but stop you after one word and explain that by

defining it it is no longer nothing is a worthy adversary in the PhD process. Thanks

for all those “lessons” where not a note was played, but the hysterical laughter

brightened my week.

To my wonderful friends who have not only been supportive and encouraging, but

patient and understanding when I declined invitations in favour of thesis writing.

Mim, a great mate, adventures shared with you always bring a smile, including

the aforementioned tropical cyclone! Gabrielle, a travel buddy and “crunch-time”

specialist, you have supported and encouraged more than I am sure you will ever

know. Skye, a great friend and great support, not to mention a damn fine drinker!

Pip, Andy and Andy, probably the most patient in my disappearance from society,

let the drinking team re-unite! The boys, lil bro Scott, Miller, Bernie, Ramsay and

Cass, and also Steph and Val, you are like family and I thank you for your support.

To all of my other wonderful friends, netball teams, tennis friends, kids I coach and

their families, SABA friends, I can’t thank you enough for kindness, encouragement

and support.

A pizza loving massage therapist best mate, who is always ready to go drinking

seems like a pre-requisite to a successful PhD candidature! Nads, you have been

the most amazing understanding friend I could ask for, even when going through a

rough time yourself. You took the time to email me almost every day just to say

hi and brighten my day, drag me out when needed and understood when I wanted

to work. You have been more support than I could ever have asked for, and the

first person I turn to when things go wrong. You, and also Jd, listened and talked

through every problem I had, and I cannot express how grateful I am for your love

and support. I most definitely would not have achieved this goal if it wasn’t for you

mate.

To my partner Jon, who has been so supportive and put up with so much partic-

ularly in the last 12 months. Thank you for always being available to let me vent,

sympathise, or just grab a coffee. Your face appearing in my doorway gasping for

air because you once again forgot the lift was functional was always a highlight.

Your patience, kindness and particularly the encouragement in your own very spe-

cial “Thok” voice is greatly appreciated, and I cannot thank you enough. To the

Whittall family, thank you for making me feel so welcome in your home and being

Acknowledgements xiii

so supportive of these PhD adventures!

The biggest thanks of all of course goes to my family, without whose love and

support I would not have been able to pursue education to this point. To my cousin

Katie, with whom I share so many crazy memories, thanks for all those moments of

hysterical laughter! To my Grandma, who is always there for a chat or a hug or a 3

course meal. Your ability to cope with whatever life throws at you is to be admired.

Thanks for all of the Sunday night dinners, followed by a strong cup of tea to keep

me going, made with water that we are all sure boils much higher than normal! A

special note must also go to my Grandparents who are no longer with us, but have

been no less influential. My brother Bean, a best mate, a drinking buddy, a taxi

service, a source of computer advice, and so much more. I have missed hanging

out with you and hope there are many years of lazy Saturdays drinking beer while

playing games or watching footy. After all, lazy is what you do best! Finally, to

my parents. The people who sacrificed so much to give us the best education and

start in life possible. No words seem adequate to express my gratitude for your love

and support, and allowing us to chase our every ambition. For being so patient,

supportive, and mostly understanding, I will never be able to re-pay you. And I

could never forget my puppy mate Maestro, as always curled up next to me as I

write making the long hours not so lonely.

Finally, I thank my Dad, the man whose inspirational footsteps I walk in as I add

my own tome to the shelves.

xiv Acknowledgements

List of Figures

1.1 Marshall-Palmer distribution for 3 different rainrates. . . . . . . . . . 4

1.2 Gamma distribution with 3 different shape parameters. . . . . . . . . 5

2.1 Layout of the Adelaide and Darwin wind profiler antennas. . . . . . . 17

2.2 Profiler at Adelaide airport. . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Profiler at Darwin airport. . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 PPI example from TWP-ICE. . . . . . . . . . . . . . . . . . . . . . . 22

2.5 RHI example from TWP-ICE. . . . . . . . . . . . . . . . . . . . . . . 23

2.6 Australian Weather Watch radar network. . . . . . . . . . . . . . . . 24

2.7 Scatter plot showing calibration of the Adelaide profiler. . . . . . . . 27

2.8 Scatter plot showing calibration of the Darwin profiler. . . . . . . . . 28

2.9 Z-R relationships with varied values of A and b. . . . . . . . . . . . . 30

3.1 VHF wind profiler simulated spectrum in precipitation conditions. . . 34

3.2 Twice smoothed simulated spectra, and twice smoothed first derivative. 37

3.3 Examples of the clear-air Gaussian fitting routine. . . . . . . . . . . . 39

3.4 Simulated clear-air fit. . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.5 An example of real spectra containing interference from Darwin. . . . 42

3.6 Simulated spectrum with the clear-air peak removed, and an expo-

nential tail added. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.7 Example DSD retrieval. . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.8 D0 calculated from a gamma fit compared to that from the profiler

retrieval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.9 Difference in D0 and average spectral width. . . . . . . . . . . . . . . 50

3.10 D0 correction mapping function. . . . . . . . . . . . . . . . . . . . . . 53

3.11 Profiler D0 corrected via the mapping function. . . . . . . . . . . . . 54

4.1 Time-height cross-section of profiler reflectivity with no quality-control. 60

4.2 Example spectrum with a spike near the centre of the clear-air peak,

and the resulting bad fit . . . . . . . . . . . . . . . . . . . . . . . . . 63

xvi LIST OF FIGURES

4.3 An example of a broad spectrum, and the resulting wide fit to the

“clear-air”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.4 Example of a rectangular shaped spectrum, and the resulting wide fit. 65

4.5 Two examples of poor divide selection. . . . . . . . . . . . . . . . . . 66

4.6 Doubly smoothed spectrum and its doubly smoothed derivative in a

situation where the divide was poorly selected. . . . . . . . . . . . . . 67

4.7 Example spectra where an interference peak effectively masks auto-

matic precipitation detection. . . . . . . . . . . . . . . . . . . . . . . 68

4.8 Example spectrum showing a random fluctuation misinterpreted as a

precipitation echo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.9 Example spectrum where no retrieval is possible due to the clear-air

and precipitation peaks merging. . . . . . . . . . . . . . . . . . . . . 69

4.10 Example spectrum with a spike near the centre of the clear-air peak

with a more accurate fit. . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.11 Example broad spectrum with a more accurate clear-air fit. . . . . . . 71

4.12 Schematic demonstrating QCR comparison pixels. . . . . . . . . . . . 73

4.13 Schematic flow chart of the QCR zero value procedure. . . . . . . . . 74

4.14 Example plot showing the QCR commonly identified flagged retrievals. 77

4.15 Comparison of retrieved reflectivity, manual correction and the QCR

correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.16 Example contour plot, used for vertical velocity quality control. . . . 79

4.17 QCR processed result for the data seen in Figure 4.1. . . . . . . . . . 81

4.18 Manually processed result for the data seen in Figure 4.1. . . . . . . . 81

5.1 TWP-ICE accumulated rainfall over Darwin airport. . . . . . . . . . 87

5.2 MSLP analysis 22 January 2006. . . . . . . . . . . . . . . . . . . . . . 89

5.3 CPOL PPI scans, 22 January 2006. . . . . . . . . . . . . . . . . . . . 90

5.4 Reflectivity cross-sections, 22 January 2006. . . . . . . . . . . . . . . 92

5.5 CPOL differential reflectivity, 22 January 2006. . . . . . . . . . . . . 93

5.6 Profiler-retrieved cross-sections, 22 January 2006. . . . . . . . . . . . 94

5.7 Profiler-retrieved cross-sections, 22 January 2006. . . . . . . . . . . . 95

5.8 Averaged vertical velocity through the second and third rainbands,

22 January 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.9 Heating rate through the second and third rainbands, 22 January 2006. 98

5.10 Averaged reflectivitys through the second and third rainbands, 22

January 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.11 Averaged rainrates through the second and third rainbands, 22 Jan-

uary 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

LIST OF FIGURES xvii

5.12 Averaged liquid water contents through the second and third rain-

bands, 22 January 2006. . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.13 Averaged median drop diameters through the second and third rain-

bands, 22 January 2006. . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.14 D0 PDF through the second rainband, 22 January 2006. . . . . . . . 104

5.15 D0 PDF through the third rainband, 22 January 2006. . . . . . . . . 105

5.16 Averaged vertical velocitys through the heavy and moderate regions,

22 January 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.17 Averaged heating rates through the heavy and moderate regions, 22

January 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5.18 Averaged reflectivitys through the heavy and moderate regions, 22

January 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.19 Averaged rainrates through the heavy and moderate regions, 22 Jan-

uary 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.20 Averaged liquid water contents through the heavy and moderate re-

gions, 22 January 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.21 Averaged median drop diameters through the heavy and moderate

regions, 22 January 2006. . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.22 D0 PDF through the heavy region, 22 January 2006. . . . . . . . . . 113

5.23 D0 PDF through the moderate region, 22 January 2006. . . . . . . . 114

5.24 Build-up D0 comparison. . . . . . . . . . . . . . . . . . . . . . . . . . 119

5.25 Monsoon D0 comparison. . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.26 CPOL PPI 18 February 2006. . . . . . . . . . . . . . . . . . . . . . . 122

5.27 Reflectivity cross-sections, 18 February 2006. . . . . . . . . . . . . . . 123

5.28 CPOL differential reflectivity, 18 February 2006. . . . . . . . . . . . . 124

5.29 Profiler-retrieved cross-sections, 18 February 2006. . . . . . . . . . . . 125

5.30 Profiler-retrieved cross-sections, 18 February 2006. . . . . . . . . . . . 126

5.31 Averaged vertical velocity in the convective and stratiform regions,

18 February 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.32 Heating rate in the convective and stratiform regions, 18 February

2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.33 Averaged reflectivity in the convective and stratiform regions, 18

February 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.34 Averaged rainrate in the convective and stratiform regions, 18 Febru-

ary 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.35 Averaged liquid water content in the convective and stratiform re-

gions, 18 February 2006. . . . . . . . . . . . . . . . . . . . . . . . . . 132

5.36 Averaged median drop diameter in the convective and stratiform re-

gions, 18 February 2006. . . . . . . . . . . . . . . . . . . . . . . . . . 133

xviii LIST OF FIGURES

5.37 Convective core median drop diameter PDF, 18 February 2006 . . . . 134

5.38 Convective core median drop diameter PDF, 18 February 2006 . . . . 135

6.1 Rainfall over Adelaide airport from 1956 to 2008 averaged by month. 142

6.2 Yearly rainfall over Adelaide airport from 1956 to 2008. . . . . . . . . 143

6.3 MSLP analysis 12 June 2008. . . . . . . . . . . . . . . . . . . . . . . 145

6.4 Weather Watch PPI, Adelaide, 12 June 2008 . . . . . . . . . . . . . . 146

6.5 Radiosonde soundings, Adelaide, 12 June 2008. . . . . . . . . . . . . 147

6.6 Weather Watch and profiler reflectivities, Adelaide, 12 June 2008 . . 149

6.7 Profiler-retrieved rainrate and liquid water content, Adelaide, June

12 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

6.8 Profiler-retrieved median drop diameter, and time series at 1 km,

Adelaide, 12 June 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . 151

6.9 Averaged vertical velocity profiles, 12 June 2008. . . . . . . . . . . . . 152

6.10 Averaged heating profiles, 12 June 2008. . . . . . . . . . . . . . . . . 153

6.11 Averaged reflectivity profiles, 12 June 2008. . . . . . . . . . . . . . . 155

6.12 Averaged rainrate profiles, 12 June 2008. . . . . . . . . . . . . . . . . 156

6.13 Averaged liquid water content profiles, 12 June 2008. . . . . . . . . . 157

6.14 Averaged median drop diameter profiles profiles, 12 June 2008. . . . . 158

6.15 Convective region median drop diameter PDF, Adelaide, 12 June 2008159

6.16 Stratiform region median drop diameter PDF, Adelaide, 12 June 2008 160

6.17 MSLP analysis, 21 September 2009. . . . . . . . . . . . . . . . . . . . 161

6.18 Weather Watch PPI, 21 September 2009. . . . . . . . . . . . . . . . . 162

6.19 Radiosonde sounding, 00 UTC 21 September 2009. . . . . . . . . . . 163

6.20 Reflectivity cross-sections, 21 September 2009. . . . . . . . . . . . . . 164

6.21 Profiler-retrieved rainrate and liquid water content, Adelaide, 21 Septem-

ber 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

6.22 Profiler-retrieved median drop diameter, and time series at 1 km,

Adelaide, 21 September 2009 . . . . . . . . . . . . . . . . . . . . . . . 166

6.23 Averaged vertical velocity profile, 21 September 2009. . . . . . . . . . 167

6.24 Averaged heating profile, 21 September 2009. . . . . . . . . . . . . . 168

6.25 Averaged reflectivity profile, 21 September 2009. . . . . . . . . . . . . 169

6.26 Averaged rainrate, 21 September 2009. . . . . . . . . . . . . . . . . . 170

6.27 Averaged liquid water content, 21 September 2009. . . . . . . . . . . 171

6.28 Averaged median drop diameter, 21 September 2009. . . . . . . . . . 172

6.29 Median drop diameter PDF, 21 September 2009 . . . . . . . . . . . . 173

7.1 Median drop diameters in the active monsoon and break periods. . . 182

7.2 Median drop diameters from TWP-ICE classified by rain type. . . . . 183

LIST OF FIGURES xix

7.3 Median drop diameters from all Adelaide results, separated into strat-

iform and convective rainfall. . . . . . . . . . . . . . . . . . . . . . . . 184

7.4 Z vs. D0 for all results. . . . . . . . . . . . . . . . . . . . . . . . . . . 185

7.5 DSD shape, 22 January 2206. . . . . . . . . . . . . . . . . . . . . . . 188

7.6 DSD average shape between 2 and 4 mm, 22 January 2006. . . . . . . 189

7.7 DSD average shape multiplied by diameter cubed, 22 January 2006. . 190

7.8 DSD average shape between 2 and 4 mm, 5 January 2006. . . . . . . 190

7.9 DSD average shape multiplied by diameter cubed, 5 January 2006. . . 191

7.10 DSD shape in the convective region, Adelaide, 12 June 2008 . . . . . 192

7.11 DSD shape in the stratiform region, Adelaide, 12 June 2008 . . . . . 193

7.12 Example of D0 under a bright band. . . . . . . . . . . . . . . . . . . 195

7.13 Stacked spectra showing a drop in clear-air amplitude. . . . . . . . . 197

7.14 3D plot of spectra at 1 time stamp. . . . . . . . . . . . . . . . . . . . 198

7.15 Convective and stratiform rainrate vs. reflectivity, using derived Z−R

relationships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

7.16 Example Z −R relationships in convective and stratiform regions. . . 204

7.17 CPol Zdr versus profiler D0 in stratiform rain. . . . . . . . . . . . . . 206

7.18 CPol Zdr versus profiler D0 in convective rain. . . . . . . . . . . . . . 207

B.1 Schematic depicting the evolution of a convective cloud. . . . . . . . . 220

B.2 Schematic depicting the evolution of a stratiform cloud. . . . . . . . . 223

B.3 Schematic PPI showing the formative stage of MCS development. . . 225

B.4 Schematic PPI showing the maturing stage of MCS development. . . 226

B.5 Schematic depicting a MCS in its mature stage on a RHI display. . . 227

B.6 Schematic PPI showing the decaying stage of the MCS. . . . . . . . . 228

B.7 Schematic depicting airflow trends in a leading convective line with

trailing stratiform precipitation. . . . . . . . . . . . . . . . . . . . . . 229

xx LIST OF FIGURES

List of Tables

2.1 Adelaide airport profiler operating parameters. . . . . . . . . . . . . . 17

2.2 Darwin airport profiler operating parameters. . . . . . . . . . . . . . 20

5.1 Monsoon storm summary. . . . . . . . . . . . . . . . . . . . . . . . . 115

5.2 Monsoon dominant microphysical processes. . . . . . . . . . . . . . . 116

5.3 Monsoon average storm statistics. . . . . . . . . . . . . . . . . . . . . 117

5.4 Monsoon average D0 statistics. . . . . . . . . . . . . . . . . . . . . . 118

5.5 Break storm summary. . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.6 Break dominant microphysical processes. . . . . . . . . . . . . . . . . 137

5.7 Break average storm statistics. . . . . . . . . . . . . . . . . . . . . . . 138

5.8 Break average D0 statistics. . . . . . . . . . . . . . . . . . . . . . . . 139

6.1 Microphysics summary and Z-R relationship coefficients for Adelaide. 174

6.2 D0 characteristics of Adelaide storms. . . . . . . . . . . . . . . . . . . 175

6.3 Average statistics for storms passing over the Adelaide profiler. . . . . 176

xxii LIST OF TABLES

Chapter 1

Introduction

Quantifying rainfall is an integral component of modern meteorology. On a cli-

matological scale, seasonal rainfall prediction is important not only for agricultural

industries, but in estimating water supply in populated areas. In the short term,

weather forecasts are scrutinised daily by millions of people all over the world, and

dictate decisions on whether its too wet to take the bike to work. Rainfall can

also become a hazardous, potentially lethal natural phenomena, with flash floods

periodically wreaking havoc.

At the heart of rainfall estimation is accurate determination of the dropsize dis-

tribution (DSD), which is the number of drops of a given size in a sampled volume

of the atmosphere. Study of the DSD and its subsequent evolution with both height

and time allows great insight into the microphysical processes that dictate rainfall.

Improved knowledge of precipitation microphysics then leads to better quantitative

precipitation estimation (QPE).

In this introductory chapter the earliest studies of rainfall are discussed, followed

by various parameterisations of the DSD shape. Instrumentation developed to mea-

sure DSDs, including the advent of radar in this field is then described. The chapter

concludes with a brief outline of this thesis.

2 CHAPTER 1. INTRODUCTION

1.1 Early Studies

Studies of the size and shape of raindrops date back to 1892 with the publication

of “Raindrops” [Lowe, 1892]. With varied exposure times to precipitation, Lowe

allowed raindrops to fall on sheets of slate, and then copied the pattern onto paper.

He collected more than 300 such diagrams, and then analysed the size of drops. This

method was met with some criticism however, as drops impacting slate would spread

out and not retain their fall shape. Soon after, in 1898, Bentley [1904] studied the

size of raindrops by allowing them to fall into a bed of flour. The author collected

approximately 4 seconds of rainfall and then extracted and examined the hardened

“dough pellets”, formed from the interaction of flour and water. Bentley calibrated

this system of droplet measurement by suspending droplets of two sizes on the end

of a broom splint and a glass pipette, allowed the drops to fall into the flour bed

from varied heights, and correlated original dropsize with dough pellet size. After

analysing data from some 70 storms over the course of six years, Bentley found that

smaller drops were most common, with decreasing numbers of drops as the diameter

increased.

Several paramaterisations of the DSD encompassing this finding of many small

drops and fewer large drops in any given rainband have been proposed. In this study,

the DSD is analysed using a method of direct deconvolution, that is without the a

priori assumption of a functional form. This allows examination of both the spatial

and temporal evolution of the DSD, as there is no limitation to a pre-determined

shape. Functional forms of the DSD are nonetheless useful, because they can be

integrated, and incorporated into rainfield models. Progression in the field of DSD

study is therefore continued by way of introducing proposed functional forms.

1.2. FUNCTIONAL FORMS OF THE DSD 3

1.2 Functional Forms of the DSD

Approximately 50 years after Bentley’s pioneering work, Marshall and Palmer [1948]

studied raindrops using a similar method, but with filter paper in place of flour.

They calculated the density of drop diameters, and empirically derived from their

results the first dropsize distribution relationship. Known as the Marshall-Palmer

(M-P) distribution, the number of drops N(D) in the diameter range between D

and D + dD is given by

N(D) = N0e−λD (1.1)

where N0, the intercept parameter, is given by the constant 8 x 103 mm−1. The

exponent is given by λ = 4.1R−0.21 mm−1 where R is the rainrate, suggesting the

DSD is a function of rainrate. Figure 1.1 illustrates the M-P distribution at rainrates

of 5, 15 and 25 mm hr−1. The intercept parameter, N0, is indicated by the point

where the distributions converge. It is clear that as the rainrate intensifies, the slope

of the distribution lessens, allowing for an increased number of larger drops in the

distribution.

Laws and Parons [1943] conducted a similar study to Bentley [1904] using flour,

and later analysis of this work showed that it fit the M-P distribution, but with

λ = 3.8R−0.20 mm−1. In contrast to the M-P distribution, the Laws and Parons data

suggested the intercept parameter was also weakly dependent on rainrate through

N0 = 5.1 x 104R−0.03 [Ulbrich, 1983].

Subsequent studies showed the M-P distribution is a good approximation to the

DSD near the ground for drops with D > 1 mm, where sufficient averaging in space

and/or time is performed [Sekhon and Srivastava, 1971; Ulbrich, 1983]. At altitude,

or when averaging is not appropriate, the exponential form of the Marshall-Palmer

distribution is too restrictive. Specifically, the M-P distribution under-predicts the

small drop regime in light rainfall, and amplifies small drop numbers in heavy rainfall

[Waldvogel , 1974; Konwar et al., 2006].

Investigators such as Ulbrich [1983] and Willis [1984] generalised to a gamma

distribution given by


Figure 1.1: The Marshall-Palmer distribution for rainfall at 5 (blue), 15 (orange)and 25 (red) mm hr−1. The intercept parameter N0 is marked, and shows the pointwhere these three distributions converge.

1.2. FUNCTIONAL FORMS OF THE DSD 5

N(D) = N0Dμe−λD (1.2)

where N0 is again the intercept parameter, λ the slope, and μ the shape parameter. μ

can have any positive or negative value, and in the limiting case of μ = 0 the gamma

distribution becomes exponential. μ entirely dictates the shape of the retrieval,

with positive (negative) values of μ resulting in a DSD with a downwards (upwards)

concave shape, as illustrated in Figure 1.2.

Figure 1.2: The Gamma distribution showing shape parameters of μ = 1 (blue),μ = 0 (orange) and μ = −1 (red). Positive values of μ indicate a concave downwardsshape, while negative values indicate a concave upwards shape. When the shapeparameter is zero, the Gamma distribution becomes the M-P distribution.

The dimensions of the intercept parameter in the Gamma distribution are not

well defined, and it therefore cannot be considered a physical quantity [Testud et al.,

2001]. A “normalised gamma distribution” was suggested by Willis [1984]. Here,

N(D) is expressed as a function of the independent parameters D0, μ and a nor-

malised intercept parameter No∗:

N(D) = N0∗ Γ(4)

3.674

(3.67 + μ)4+μ

Γ(4 + μ)

(D

D0

)μ

exp

[−(3.67 + μ)

D

D0

](1.3)


This distribution overcomes the non-independence of the intercept and shape

parameters [Testud et al., 2000; Willis , 1984]. In the limit of μ = 0, the normalised

shape parameter reverts to the classic N0 [Testud et al., 2000].

Other suggested, but less commonly employed distributions, include the lognor-

mal [Feingold and Levin, 1986] and Weibull distributions [Jiang et al., 1997]. The

lognormal distribution is given by

N(D) =NT√

2π ln σDexp[− ln2(D/Dg)/2 ln2 σ] (1.4)

where NT is the total number of drops, Dg is the geometric mean of the drop

diameter, and σ is the standard geometrical deviation of D. The Weibull distribution

is given by

N(D) = N0η

σ

(D

σ

)η−1

e

[−

(D

σ

)η](1.5)

where N0 is the intercept parameter, and η and σ are functions of the rainfall rate.

Each distribution imparts various advantages and disadvantages, and the most ap-

propriate choice is highly dependent on measurement technique, geographical loca-

tion and rainfall type.

Waldvogel [1974] described several storms which displayed discontinuities in drop-

size spectra. He found that in the transition regions from convective to stratiform

rainfall1 (or the reverse) there was a sudden and dramatic decrease (increase) in

the intercept parameter N0. The author reasoned this change was logical, given the

change in governing precipitation mechanism aloft. Further, he concluded N0 could

not be considered constant, and must be allowed to vary with precipitation type

[Waldvogel , 1974]. Empirical relations were developed relating N0 to λ, but it was

soon noted that variations in these parameters are independent of each other.

1Convective and stratiform rainfall are defined and discussed in Appendix B.

1.3. GROUND-BASED DSD MEASUREMENT INSTRUMENTS 7

1.3 Ground-based DSD Measurement Instruments

Marshall and Palmer [1948] were not the first to use filter paper; one of the first

rainfall measurements was made by Wiesner in 1895 [Waldvogel , 1974]. Many subse-

quent studies also used this method, but the limitation is the manual effort required

to evaluate the many drops collected during a single rainstorm. Various instruments

were thus developed to automatically evaluate the DSD. Mason and Ramandham

[1953] developed a photoelectric raindrop spectrometer, where light scattered by

drops falling through a light beam was analysed. Dingle and Schulte [1962] also

developed a photoelectric device, but with a measurement region that moved with

respect to the rainfield. Optical spectropluviometers were also developed, where the

duration of drops falling through parallel infra-red light beams was used to compute

fallspeed [Salles et al., 1998].

Joss and Waldvogel developed an electrochemical disdrometer (JWD) which is

still widely used today [Tokay et al., 2001]. The JWD is an impact-type disdrometer,

and assumes drops are falling at terminal velocity. Drops falling on the 50-cm2 sur-

face, a thin aluminium layer covering a styrofoam body, are sorted into 20 dropsize

bins, ranging from 0.3 to 5.5 mm, with 30 second averaging. When drops impact

the surface, a voltage is induced in a coil by the downwards motion of the styro-

foam body. The voltage is amplified, and applied to a second coil, resulting in an

electromagnetic force, restoring the body to its initial position. The magnitude of

the displacement is used to sort drops into dropsize bins. Drops larger than 5.5 mm

cannot be resolved and are placed in the largest dropsize bin. In ideal conditions,

the JWD measures the DSD with an accuracy of approximately 5%. In heavy rain-

fall, however, the number of small drops are underestimated due to instrument dead

time, caused by vibrations in the styrofoam cone. The manufacturer supplies a cor-

rection matrix to account for dead time [Sheppard and Joe, 1994], but the correction

matrix can itself cause problems. For example, if there are no drops recorded in a

particular size class, the matrix modifies the DSD rather than adding drops to this

class, increasing parameters such as rainrate considerably. This is such a problem

that in many cases, users choose to accept the dead time rather than implement the

correction matrix [Tokay and Short , 1996].

The JWD requires a small sampling area to avoid errors caused by simultaneous

drop impacts. Illingworth and Stevens [1987] developed an optical disdrometer al-


lowing for multiple drops in the sample volume, provided these drops are not of the

same size, and do not enter and exit concurrently. The disdrometer set-up allows

only a thin annulus of a high intensity light source to be collected at a photo-diode.

The reduction in light level as a drop passes through the instrument’s cylindrical

sampling volume is proportional to the drop’s diameter. As drops enter and exit

the sample volume, two pulses of equal magnitude are generated. Provided drops

do not enter or exit concurrently, pulse-pair identification allows multiple drops to

be analysed simultaneously. The cylindrical sampling area means drops fall through

the same sample volume regardless of horizontal shear, making these instruments

particularly useful in windy conditions.

In the 1990s a disdrometer capable of measuring dropsize, fall velocity, and also

drop shape became commercially available. This two-dimensional video disdrometer

(2DVD) consists of two planes of light. When falling drops occlude these planes they

produce “image shadows”, which are then recorded on two cameras. The planes of

light are separated by approximately 6 mm, and time taken to traverse this distance

is used to calculate the fall speed of the drop. While both optical disdrometers and

2DVDs offer some advantages, the JWD is still considered the “standard” [Tokay

et al., 2001].

Another instrument developed specifically for DSD evaluation is the Precipita-

tion Occurrence Sensor System (POSS) radar [Sheppard and Joe, 1994]. This is a

continuous-wave bi-static radar operating at X-band, which samples a volume ex-

tending less than 2 m above the unit. The transmitter and receiver radomes face

each other, 45 cm apart, with the antennas oriented 20◦ off vertical, such that the

beams intersect at the midpoint between the radomes. As drops pass through the

measurement volume a voltage signal is generated. The frequency of this signal is

proportional to the Doppler velocity, while the amplitude is a function of the drop

diameter. In non-precipitating conditions, POSS measures the ambient Doppler

“noise” spectrum. When precipitation occurs, the most recent noise spectrum is

subtracted from the measured spectrum, so the radar is sensitive to current atmo-

spheric conditions.

DSDs are also determined in situ by aircraft measurements, generally using a

PMS (Particle Measuring Systems Inc.) 2D precipitation probe [Rogers et al., 1993].

These measurements are generally restricted to atmospheric campaigns, due to the

costs involved. The significant limitation with all technology considered above is

1.4. RADARS 9

the limited spatial sampling, and vertically pointing radars provide an attractive

solution. The development of radars capable of measuring the DSD is now discussed.

1.4 Radars

Christian J. Doppler, while studying electromagnetic waves around the 1850s, dis-

covered the shift in frequency caused by moving sources is directly proportional to

the speed of the source [Rinehart , 2004]. It is on this principle that Doppler radars

work, although use of the term “Doppler” is somewhat ambiguous given that radars

do not directly measure the Doppler shift. The invention of the magnetron in 1940

by John Randall and Henry Boot, at the University of Birmingham, allowed the de-

velopment of radars operating at microwave wavelengths [Doviak and Zrnic, 1993;

Rinehart , 2004]. Following World War II, where radars had played a vital role in

enemy detection, surplus military radars became available for civilian use, and were

turned to the study of weather.

Many radar studies of rainfall were conducted with these early vertically pointing

microwave Doppler radars. Fall-speed relations had been derived previously by

investigators such as Gunn and Kinzer [1949] and Foote and du Toit [1969] and hence

the measured velocity spectrum could be converted to a droplet size spectrum. In

the absence of vertical motions, this method is satisfactory, but fails in the presence

of up or downdrafts. Techniques were developed to measure vertical air motions

[Wakasugi et al., 1985; Doviak and Zrnic, 1993, for details] but as discussed in Atlas

et al. [1973], were only accurate to about 1 ms−1 and hence could not determine the

size distributions of small particles.

Fukao et al. [1985] discussed the development of a VHF Doppler radar that could

simultaneously observe the return from vertical air motions and falling hydrome-

teors. This ability then made VHF profilers, primarily designed to measure the

three-dimensional wind vector, a prime candidate in the study of DSDs and asso-

ciated parameters. Interestingly, work on profiler-like radars had begun soon after

the conclusion of World War II, when Peter Harbury constructed an antenna with

a 50 m diameter, wanting to probe the troposphere. Harbury was tragically electro-

cuted while working on the radar modulator, and work in this area was discontinued

[Doviak and Zrnic, 1993].


The abilities of the VHF profiling radar were demonstrated in an investigation

of clear-air and precipitation motions within a cold frontal system [Wakasugi et al.,

1985]. The authors developed a method of directly estimating N(D), mean ver-

tical air velocity and turbulence, and retrieved DSDs using a parametric method

[Wakasugi et al., 1986]. The direct simultaneous measurement of turbulence and

air velocity, meant the DSD retrieval accuracy was not hindered by the errors that

plagued microwave Doppler radars.

The main difficulty with the pioneering work discussed so far is the assumption

of a particular form of the DSD, which precludes any study on the evolution of the

DSD shape. A second problem is the required initial guess of the parameters that

dictate the chosen functional form. To overcome these limitations, Wakasugi et al.

[1987] described a method for retrieving the DSD without assuming any particular

functional form, where the effects of turbulence are removed through a deconvolution

operation. The authors found this method required significant averaging in time,

resulting in a loss of temporal resolution, and thus decided to use a parametric

fit. Sato et al. [1990] used a similar method to that of Wakasugi et al. [1987], but

developed an algorithm to calculate the initial guess of the functional parameters.

Gossard [1988] developed a technique for retrieving the DSD with no assumptions

about shape, but tested it using a profiler operating at 915 MHz. Profilers operating

at this frequency are of limited use in anything other than low rainrate studies,

because the clear-air peak is masked by the precipitation echo.

Rajopadhyaya et al. [1993] used a similar method to that of Gossard [1988], and

tested it on model spectra which incorporated realistic statistical variations. The

authors tested an iterative and a Fourier transform method of deconvolution and

found that although there were side-lobe issues in both the small and large drop

ranges, the Fourier transform method performed better. This Fourier transform

method is employed in the current study.

The development of VHF profilers able to probe the boundary layer [Vincent

et al., 1998] allowed the examination of the DSD throughout its evolution, and many

studies used the techniques discussed above to analyse the precipitation field. As

noted by Rajopadhyaya et al. [1993], VHF profilers are unable to resolve drops with

diameters smaller than 1 mm, because the clear-air signal has a finite spectral width

and dominates the precipitation echo at fall speeds corresponding to small drops.

UHF profilers are limited to low rainrate studies, such as that of Gossard [1988].

1.4. RADARS 11

Currier et al. [1992] developed a technique to estimate the clear-air properties from

a 50 MHz profiler, and used these measurements to correct the clear-air effects in

the precipitation return from a profiler operating at 915 MHz. Maguire II and Avery

[1994] extended this work with further modelling studies, and Rajopadhyaya et al.

[1998] used these modelling results to estimate the rainrate in both low and high

rainfall regions. Results showed excellent agreement when compared with a rain

gauge. Rajopadhyaya et al. [1999] compared the accuracy of the single and dual-

frequency methods, and found that single profilers operating near 50 MHz cannot

resolve median drop diameters (diameter such that half of the water volume lies

above this value, see section 3.3.3 for the mathematical definition) less than 1.25

mm, while the dual frequency technique can retrieve median diameters as small as

0.5 mm. The authors noted that for median drop diameters beyond 2.5-3.0 mm

errors increase dramatically, as the drop fall speed increase is only slight for drops

larger than 4 mm.

Modern radar techniques afford investigators the opportunity to analyse the spa-

tial and temporal evolution of DSDs around the world. Weather radars estimate

rainfall by converting measured reflectivity (Z) to a rainrate (R) via an empirical

relationship (Z − R relationship) (e.g. Campos and Zawadzki [2000] and Prat and

Barros [2009]). Variation in the DSD affects measured reflectivity, and thus char-

acterisation of the DSD is essential in accurate rainfall estimation. Many modern

weather radars now incorporate at least two Z −R relationships for stratiform and

convective rainfall, and implement them as appropriate.


1.5 Scope of Thesis

In the current study, vertically pointing VHF Doppler profilers are used to retrieve

DSDs in Adelaide (South Australia) and Darwin (Northern Territory, Australia).

Each profiler is installed within the footprint of a scanning weather radar (hereafter

called scanning radar), allowing direct comparison of the same air space. Data

from Darwin come from the Tropical Warm Pool International Cloud Experiment

(TWP-ICE) [May et al., 2008], conducted in January and February 2006. Data

from Adelaide are limited for several reasons, discussed in Chapter 6, with just two

events included. The microphysical processes dictating rainfall are examined using

the profiler retrievals, and compared and contrasted in both locations. The primary

aim of this work is the examination of intra-seasonal, and locational differences in

the retrieved DSD, and related integral parameters. Particular emphasis is placed on

the evolution of the DSD in both time and height, and differences in this evolution

in the tropics and mid latitudes. Changes in the DSD and the subsequent effect on

the Z −R relationship is analysed in both locations.

Chapter 2 continues the preliminary discussion on the development of profiling

radars capable of retrieving the DSD, and, in particular, boundary layer (BL) radars.

The particular profilers used in this study are described, followed by a discussion

on the scanning radars. This chapter also includes a brief discussion of Z − R re-

lationships, and median drop diameter estimations. The DSD retrieval technique

employed in this study is discussed in Chapter 3, while Chapter 4 describes a quality

control routine designed during the course of this study, and implemented through

much of the analysis. Chapters 5 and 6 are devoted to results from Darwin and Ade-

laide respectively. These results are further discussed, and compared and contrasted

in Chapter 7. Conclusions of this work are summarised in Chapter 8, including di-

rections for future work.

Chapter 2

Radars

The development of profiling radars capable of simultaneously detecting clear-air and

precipitation echoes significantly advanced the study of DSDs. In this chapter the

introductory discussion on profiler development is continued, with a particular focus

on precipitation detection at VHF and UHF. The particular profilers employed in

the current study are then introduced. Scanning radars have also enjoyed significant

improvements since their inception, and can now operate with dual-polarisations.

Some of the advantages in precipitation detection offered by this next generation of

scanning radars are discussed here.

2.1 Profilers

Vertically pointing Doppler wind profilers were primarily designed to measure hor-

izontal winds in the troposphere. Profilers were identified as excellent tools in pre-

cipitation studies, when Fukao et al. [1985] noted their capabilities in simultaneous

detection of clear-air and precipitation echo. Fundamentally, any radar capable of

measuring a vertical Doppler spectrum sensitive to precipitation is a candidate in

rainfall studies. However, measurement of the clear-air motions is of prime impor-

tance, and as discussed by Atlas et al. [1973], the vertical offset must be estimated

to within ±0.25 ms−1 in order to obtain an accurate retrieval of the DSD. Upwards

motions left un-corrected result in underestimates of the median drop diameter, or

overestimates in the case of uncorrected downdrafts. Correction of spectral broaden-

14 CHAPTER 2. RADARS

ing is also important, as uncorrected spectral widths result in a positive bias in the

median drop diameter, but this effect is secondary in comparison to vertical motions.

Simultaneous clear-air and precipitation detection requirements suggest the use of

low frequency wind profilers, typically operating at VHF (30 - 300 MHz) or UHF

(300 MHz - 3 GHz), and rules out the use of the higher frequency meteorological

radars. The particular frequency chosen comes with its own problems, determining

the limit of the retrievable DSD. The relative advantages and disadvantages of UHF

and VHF profilers are now discussed.

2.1.1 Profiler Frequency

VHF wind profilers typically operate at frequencies around 50 MHz, and can detect

Bragg scatter from clear-air and Rayleigh scatter from precipitation with a rainrate

greater than ∼ 5 mm hr−1. As noted by Rajopadhyaya et al. [1993], VHF profilers

are unable to resolve drops with diameters smaller than 1 mm, because the clear-air

signal obscures the precipitation echo at fall speeds corresponding to small drops.

Examples of previous DSD studies using a VHF radar include Wakasugi et al. [1986],

Wakasugi et al. [1987], Rajopadhyaya et al. [1993] and May and Rajopadhyaya [1996].

UHF wind profilers typically operate at frequencies around 920 MHz, and are

much more sensitive to Rayleigh scattering from precipitation echoes. High sensi-

tivity means these radars can, unlike their VHF counterpart, resolve drops with a

diameter less than 1 mm. In the presence of low rainfall rates or at low altitude,

UHF profilers can also detect Bragg scatter from turbulence. However, in all but

the lightest rainfalls, or above 1.5 km altitude, the precipitation echo completely

overwhelms the clear-air return. This makes UHF profilers an ideal choice for low

rainrate studies such as Gossard [1988] and Rogers et al. [1993], but are not prac-

tical in the study of moderate to heavy precipitation. UHF profilers also have the

advantage that their antennas are physically small, but relatively large compared

to the wavelength, enabling the generation of small beams. Wide bandwidths allow

the generation of narrow pulses at UHF, which results in good height resolution.

UHF radars sometimes encounter interference from birds and bats, which is not a

problem at VHF.

In order to capitalise on the sensitivity of the UHF profiler, while still capturing

2.1. PROFILERS 15

accurate clear-air information, investigators such as Currier et al. [1992], Maguire

II and Avery [1994], Rajopadhyaya et al. [1998], Cifelli et al. [2000] and Schafer

et al. [2002] performed dual-frequency retrievals with co-located profilers. In this

situation, the relative advantages of both systems are exploited, by taking the clear-

air parameters from the VHF system, and applying them to the precipitation echo

from the UHF system.

Rajopadhyaya et al. [1999] discussed the relative accuracy of the single and dual-

frequency methods using both real and simulated data. Simulations showed that,

using a single frequency, median drop diameters (D0) less than 1.25 mm could

not be resolved, while D0 as small as 0.5 mm could be achieved when using dual-

frequencies. Accuracy in retrievals decreases with an increase in spectral width,

but the dual-frequency technique suffers less. The authors noted that for median

drop diameters beyond 2.5 − 3.0 mm errors increase dramatically, as the drop fall

speed increase is only slight for drops larger than 4 mm. Single frequency retrievals

cannot be accomplished when the precipitation echo is weak, or the spectral width is

large, and therefore the dual-frequency technique is superior under a wider range of

conditions. The dual-frequency method has the obvious fiscal drawback of requiring

two co-located profilers.

In the late 1980s and 1990s wind profilers capable of sensing the lowest part of

the troposphere were developed. These boundary layer radars were first developed

at UHF [Ecklund et al., 1988], because VHF radars suffered from long recovery times

after the transmit-receive switch, and ringing in the lowest range gates due to large

antennas. VHF BL radars were deployed when it was shown that the use of small

antennas was possible despite wide beamwidths [Fillol et al., 1997; Vincent et al.,

1998]. Single frequency retrievals using VHF BL radars are performed in the current

study. Descriptions of the Adelaide and Darwin profilers are provided in the next

section.


2.1.2 Adelaide Profiler

The University of Adelaide Atmospheric Physics Group developed a VHF BL radar,

designed specifically to meet the group’s requirements. The major aim was to mea-

sure winds and temperatures to as low as 300 m, and up to approximately 3 km,

to overlap with an existing ST (stratosphere - troposphere) VHF radar operating

at the University’s field site [Vincent et al., 1987]. To enable deployment at remote

field sites, or to be utilized in atmospheric campaigns, the system was designed to be

power efficient and relatively easy to transport. In this manner, the system was also

designed to allow maximum user flexibility in software, so that as many operating

parameters (such as receiver gain, height range and height increment) as possible

were computer controlled.

The radar supposed here operates at a frequency of 54.1 MHz, and runs in spaced

antenna (SA) configuration, utilizing only vertically pointing beams. The array

consists of three groups of nine antennas, as shown in Figure 2.1. Each group of

nine antennas is arranged on the vertices or mid-points of a square, shown as dashed

lines, and the centre of each sub-array forms the vertices of an equilateral triangle.

The triangular shape minimises systematic bias in SA wind measurements [Vincent

et al., 1987]. It is also possible to partially null-out ground-clutter with optimal

spacing of the antennas. All three groups are used simultaneously for transmission,

while each sub-array is connected to a separate receiver. The antennas are three

element Yagis, and are a compromise between making the antennas as small as

possible to minimise ringing, while still being large enough to achieve sufficient

gain.

The complex time series (in-phase and quadrature terms) from the three receivers

are summed to create the raw signal. A Welch window is then applied to the time

series, which reduces spectral leakage from nearby frequencies, and then the power

series is calculated. The retrieval technique, described in the following chapter, is

performed on this power series.

The radar was initially deployed and tested at Buckland Park (BP). It was moved

to Alice Springs in 1998 to participate in CAFE (Central Australian Fronts Exper-

iment) [Reeder et al., 1992], and then to Sydney airport for a month as part of a

trial for a permanent BLR, before returning to BP. The radar was later moved to its

2.1. PROFILERS 17

Figure 2.1: Layout of both the Adelaide and Darwin wind profiler antennas. Threesub-arrays consist of nine antennas each, arranged on the vertices or mid-points ofa square. The centre of each sub-array forms the vertices of an equilateral triangle.The spacing between antennas is 2.77 m. Diagram after MacKinnon [1991].

current location at Adelaide airport (AAP), shown in Figure 2.2, in November 2004,

to be within the footprint of the new Bureau Weather Watch radar. Implementing

one of its design principles, the radar has been run in several different modes to

optimise parameters for the particular requirement and location. While operating

at AAP, the radar was initially operating in one mode only (normal). It was later

configured to alternating low and high mode settings. The operating parameters for

each mode are summarised in Table 2.1.

Parameter Normal Low HighPeak power (kW) 1 1 1PRF (Hz) 20000 20000 10000Pulse length (m) 150 150 600Range (km) 0.1-5.9 0.1-6.1 0.3-10Range sampling (m) 100 100 300Coherent integrations 1024 1024 512Spectral points 1024 1024 1024Dwell time (s) 51.2 52.4 52.4Nyquist velocity ms−1 ±27.7 ±27.7 ±27.7

Table 2.1: Operating parameters of the profiler located at Adelaide airport. Theradar runs at a frequency of 54.1 MHz.

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Text Box

NOTE: This figure is included on page 17 of the print copy of the thesis held in the University of Adelaide Library.


Figure 2.2: The profiler located at Adelaide Airport. Photo courtesy of AndrewMacKinnon.

Data collected at AAP are stored for approximately 30 days before being au-

tomatically deleted. When a rainfall event occurs, the relevant data is moved to

another directory and collected manually from the site. As is discussed in Chapter

6, South Australia experienced drought conditions from 2006 - 2008, and thus very

little suitable rain data was collected. The collected data displayed less than average

spectra, and on investigation in 2009 it was found that one of the three sub-arrays

was not transmitting, thus throttling the transmitted power. As this is a low power

system to begin with, this explains the lack of quality data from AAP.

In November 2000, when the radar was located at BP, the receiver and data ac-

quisition system (RDAS) and transmitter were replaced with a proprietary system1,

increasing the peak power to 7.5 kW. These system changes resulted in significantly

better daily average coverage (or acceptance rates) [MacKinnon, 1991], indicating

the radar is capable of better retrievals with some modifications in the future.

1Atmospheric Radar Systems Pty Ltd (ATRAD), BLR3 radar

2.1. PROFILERS 19

2.1.3 Darwin Profiler

A second VHF BL radar was built following the success of the Adelaide profiler, and

installed in the Tiwi Islands to participate in DAWEX (Darwin Area Wave Exper-

iment) [Hamilton et al., 2004]. This radar uses larger antennas than the Adelaide

system, and also has increased power [Vincent et al., 2004]. This radar was also

intrinsically better in coverage due to its location, because tropical high humidity

enhances refractive index fluctuations. The radar was moved to its present location

in 2005 in readiness to participate in the Tropical Warm Pool International Cloud

Experiment (TWP-ICE) [May et al., 2008]. The radar, shown in Figure 2.3, is lo-

cated next to Darwin airport on an ARM (Atmospheric Radiation Measurement)

mobile site.

Figure 2.3: Profiling radar located on an ARM mobile site next to Darwin airport.Photo courtesy of Andrew MacKinnon.

The radar operates in two modes, low and high. The low mode uses a 750 ns

length pulse, acquiring 100 m height resolution from as low as 300 m up to 3400 m.

The radar is limited by its acquisition system, which cannot handle more than these

30 range gates at this resolution. To obtain higher level clear-air information, the

high mode uses a 4 μs length pulse, sampling between 1900 m and 10000 m, with

600 m resolution, and 300 m of oversampling. The operating parameters of both

the low and high modes are given in Table 2.2.

The array is set out like that shown in Figure 2.1, and operates at a frequency of

54.1 MHz. Data are stored permanently, and shipped to Adelaide as required. Only


Parameter Low HighPeak power (kW) 7.5 7.5PRF (Hz) 20000 8000Pulse length (m) 100 600Range (km) 0.3-3.2 1.9-10.0Range sampling (m) 100 300Coherent integrations 1000 400Spectral points 1100 1100Dwell time (s) 55 55Nyquist velocity ms−1 ±27.7 ±27.7

Table 2.2: Operating parameters of the Darwin profiler. The radar runs at a fre-quency of 54.1 MHz.

the TWP-ICE data set are considered in the current study.

2.2 Scanning Radars

Scanning radars are one of the most important modern weather tools [Rinehart ,

2004]. These radars are a direct result of the intensive effort to improve radar tech-

nology during World War II [Whiton et al., 1998a]. Radar advancement since that

time has proceeded with the current state of the art technology and signal processing

algorithms, such as the fast Fourier transform and microprocessors for digital sig-

nal processing [Whiton et al., 1998b]. Early scanning radars were continuous-wave

(CW) Doppler systems, but the inability of these systems to ascertain the range of

the target essentially prevented operational use. The advent of pulse-Doppler tech-

nology, and thus the ability to resolve mean radial velocity and spectral width, led

to operational capabilities. Initially, costs prevented the use of scanning radars to

all but the military and civil weather services [Whiton et al., 1998a]. As technology

advanced and costs decreased, scanning radars became more widely available, and

were deployed in aircraft and by television stations. Remote displays also made

weather services available in more locations. Modern scanning radars in developed

countries are generally deployed in networks, providing vast coverage, particularly in

regions prone to severe weather. An example is the NEXRAD WSR-88D network,

in which radars provide contiguous coverage for almost all of the United States,

Alaska, Hawaii, as well as several locations outside the U.S. [Crum et al., 1998].

In this section the general characteristics of scanning radars are first discussed,

2.2. SCANNING RADARS 21

that is how they display information and interpret rainfall. The particular scanning

radars utilized in this study are then introduced.

2.2.1 Displays

Scanning radars typically scan a horizontal plane at a particular elevation, before

increasing the elevation by some angle and repeating the process. This information

must then be displayed in a way useful to the forecaster or researcher. Early displays

used oscilloscopes, with a horizontal axis of time and vertical axis of signal intensity

[Rinehart , 2004]. One of the major problems with this display is it gives no indication

of the direction the antenna is pointing at the time of signal reception. Plan Position

Indicator (PPI) displays were invented to solve this problem, and display the full

360◦ of the radar rotation, often overlayed on a map. An example PPI from TWP-

ICE is shown in Figure 2.4. The scanning radar is located at the centre, marked

with a +, and the Darwin profiler, located to the south-west is marked with a �.

The circular cut-off of the signal indicates the maximum detectable range. Echo

intensity is indicated by the colour scale. A map of the Tiwi Islands and parts of

the Northern Territory covered by the radar are depicted by the black outline, and

show areas affected by the storm. Modern displays are also capable of zooming in

to particular regions of interest [Rinehart , 2004].

An alternative display, particularly useful in severe weather, is a range-height

indicator (RHI). Traditionally, RHIs display a distance from the radar on the hori-

zontal axis, and height above the radar on the vertical axis. In this thesis, the term

RHI is used to describe a particular scanning strategy. The radar scans a particular

location in the vertical rather than horizontal plane, thus acting in a similar fashion

to a vertically pointing radar. With each subsequent scan an image is built up,

displaying time on the horizontal axis and echo intensity with height on the vertical.

An example RHI from around the time the storm was over the profiler in Figure

2.4 is shown in Figure 2.5. The Weather Watch radar in Adelaide, and CPOL in

Darwin, the scanning radars used in this study, are now discussed.


Figure 2.4: An example PPI from TWP-ICE. The radar is located at the centre,marked with a +. The profiler location is marked with a �, to the south-west ofcentre. The scale on the right is in dBZ.


Figure 2.5: An example RHI from TWP-ICE, for the time surrounding the PPIshown in Figure 2.4. The scale on the right is in dBZ.

2.2.2 Weather Watch

The equivalent of the NEXRAD WSR-88D grid in Australia is the Weather Watch

Network. Figure 2.6 shows the location and optimal coverage of radars across Aus-

tralia. Beginning in 2005, the Australian Government Bureau of Meteorology in-

stalled the first of what is now a group of 5 high-resolution Doppler scanning radars.

The first radar was installed in South Australia at BP.

Weather Watch is a forecasting network, that also provides publicly accessible

information and radar displays via the Bureau’s website. Radar displays are updated

every 10 minutes. Because the BP Weather Watch radar is purely operational,

it does not perform a RHI scan. Vertical cross-sections can be constructed by

extracting the elevation data over a particular location. These pseudo RHI scans

are used in this study.


Figure 2.6: Australian Weather Watch radar network optimal coverage. Im-age taken from http://www.bom.gov.au/weather/radar/about/radar coverage

national.shtml

2.2.3 CPOL

Scanning radars such as the Weather Watch discussed above, transmit and receive

with a single horizontal polarisation. Radars capable of both horizontal and vertical

(dual) polarisations offer significant improvements in rainfall estimation [Doviak and

Zrnic, 1993]. Raindrops are not the artistically depicted “tear-drop” shape. Rather,

the smallest drops are almost spherical, and drops become more oblate as their size

increases. Dual-polarisation radars can measure the size of drops through the ratio

of horizontal to vertical polarisations. This size information is vital for accurate

rainfall estimation. The horizontal and vertical reflectivities are defined as

ZHH =λ4

π5|k|2∫

σHHN(D)dD (2.1)

and

ZV V =λ4

π5|k|2∫

σV V N(D)dD (2.2)

a1172507

Text Box



where σHH and σV V are the horizontal and vertical radar cross-sections respec-

tively, λ is the radar wavelength and N(D) is the DSD. k is given by (ε−1)/(ε+1)−1

where ε is the complex relative permittivity. The ratio of horizontal to vertical re-

flectivity, called the differential reflectivity, ZDR, is then defined as

ZDR = 10 logZHH

ZV V

(2.3)

In addition to the radial velocity and spectral width measured with a single po-

larisation, dual-polarisation radars measure the linear depolarisation ratio, zero lag

cross-correlation coefficient and specific differential phase. The linear depolarisation

ratio is the ratio of the reflectivity from the reception of a vertically polarised sig-

nal, to the reception of a horizontally polarised signal, when a single polarisation

(horizontal or vertical) pulse is transmitted [Rinehart , 2004]. This ratio gives an

indication of shape, and is useful to discriminate between varied forms of precipi-

tation such as rain and snow. The zero lag cross-correlation coefficient represents

the correlation between the horizontally and vertically polarised signals, at a single

point in time and space [Rinehart , 2004]. The magnitude of this coefficient depends

on the target in the sample volume, and is useful in differentiating between precip-

itation and non-precipitation targets. The specific differential phase is calculated

from small changes in speed as signal passes through precipitation. Consider a large

raindrop, with an oblate spheroid shape. The horizontal pulse, passing through a

larger volume of water, will be slowed more than the vertical pulse, and over time

the horizontal pulse will begin to lag behind the vertical. Positive values of specific

differential phase then indicate targets are wider than they are tall (like raindrops)

while negative values indicate targets are taller than they are wide (such as conical

graupel) [Rinehart , 2004].

As part of the TRMM (Tropical Rainfall Measuring Mission) ground validation

program, Australia’s first dual-polarisation Doppler radar was developed [Keenan

et al., 1998]. “CPOL” was created from the modification of a standard 1◦ beamwidth

C-band Enterprise Electronics Cooperation (EEC) radar system. CPOL is linearly

polarised, utilizing a dual-waveguide that feeds a centre-fed 4.2 m paraboloid dish,

to transmit horizontal and vertical polarisations, and receive the co- and cross-

polarisations on a pulse-to-pulse basis. The reader is referred to Keenan et al.

[1998] for a complete description of the radar’s development. The final system is a


fully functional and integrated research-quality Doppler radar, which has been the

centre point in numerous atmospheric measurement campaigns.

One such campaign was TWP-ICE. During this campaign, CPOL completed a

volume scan consisting of 17 tilts, at 0.5◦, 1.2◦, 1.9◦, 2.6◦, 3.5◦, 4.4◦, 5.3◦, 6.4◦,

7.8◦, 9.6◦, 11.7◦, 14.3◦, 17.5◦, 21.4◦, 26.1◦, 33◦ and 42◦ elevation [Frederick and

Schumacher , 2008]. Two RHI scans were also performed, one of these being over

the ARM site, and hence the Darwin profiler.

2.3 Profiler Calibration

Both Adelaide and Darwin profilers were calibrated to the larger scanning radars in

terms of power return. Profiler power was plotted against the reflectivity from the

scanning radar at corresponding times and heights throughout the profiler range

(see tables 2.1 and 2.2). A range-squared correction was applied, but no pulse

volume matching was done. A calibration factor was then calculated through a linear

regression. Owing to the limited data in Adelaide the calibration factor cannot be

considered to be as accurate as in Darwin. Extreme outliers were not included in the

Adelaide case. Scatter plots of the profiler power versus scanning radar reflectivity

for Adelaide and Darwin are shown in Figures 2.7 and 2.8 respectively.

The Adelaide profiler measures around 5.5 dB higher than the Weather Watch,

while the Darwin profiler measures around 8.5 dB too low. Both radars were cor-

rected for this difference prior to calculation of rainfall integral parameters. The

Darwin calculation includes the 4 dB offset to the CPol measured reflectivity, dis-

covered after the TWP-ICE campaign [Bringi et al., 2009].

2.3. PROFILER CALIBRATION 27

Figure 2.7: Adelaide profiler power versus Weather Watch reflectivity plotted on alog scale for corresponding times and heights in two rain events. The plot shows alldata points, extreme outliers were rejected in the calculation.


Figure 2.8: Darwin profiler power versus CPol reflectivity plotted on a log scale forcorresponding times and heights throughout TWP-ICE. Points are coloured accord-ing to stratiform or convective type, and seasonal regime.

2.4. EMPIRICAL RELATIONSHIPS 29

2.4 Empirical Relationships

Polarimetric radars afford opportunities for significant improvements in surface rain-

fall estimation, owing to their ability to estimate DSD properties. As polarimetric

radars cannot directly measure the DSD, rainfall and integrated quantities are cal-

culated via empirical relationships. Two examples relate (i) rainrate to reflectivity

(Z-R), and (ii) median drop diameter to differential reflectivity (D0-ZDR). Note

that Z-R relationships do not require dual polarisation, and are a standard meteo-

rological tool on networks such as the Weather Watch.

2.4.1 Z −R Relationships

Many relations have been proposed relating measured reflectivity to rainrate, all

following the form Z = ARb where Z is the reflectivity and R the rainrate. The

power law coefficients A and b depend on the meteorology, climatology and geo-

graphic location of the radar [Prat and Barros , 2009], and thus investigators arrive

at varied Z-R relationships depending on their experimental set-up. There are in

fact approximately 100 Z-R relationships available in the literature for varied rain

types and locations [Prat and Barros , 2009].

Since Z-R relationships are derived extensively in this thesis, it is appropriate to

quantify what differences in the coefficients A and b constitute a new relationship.

Consider Figures 2.9(a) and 2.9(b), depicting Z-R relationships with varied values

of A and b. To simulate convective rainfall, an array of 200 points with a reflectivity

of 50 dBZ was generated, and statistical fluctuations between ±5 dB were added.

A generic relation of Z = 200R1.4 was then solved for R, shown in black in both

plots. The coefficients A and b were then varied by 10 and 0.01 respectively, up to

a maximum of 40 and 0.04 in both directions, to characterise the error.

With reflectivities ranging between 45 and 55 dBZ, the error in A was found to

be ∼ 5% with a difference of ±10 from 200. This error increased to ∼ 20% with a

difference of ±40. Errors in A are slightly less when the value is overestimated, that

is A > 200 estimates rainrate better than A < 200, as can be seen in Figure 2.9(a).

Errors in b, when reflectivities ranged between 45 and 55 dBZ, were slightly less


(a) Z-R relation with varied values of A.

(b) Z-R relation with varied values of b.

Figure 2.9: Z-R relationships with varied values of the coefficients. In (a) A hasbeen modified by a difference of 10, while in (b) b has been modified by 0.01. Thesemodifications result in errors from around 5% up to 20%.


than for A, ranging from ∼ 3% with a difference of ±0.01 up to ∼ 15% with a

difference of ±0.04.

Errors increase if both A and b are simultaneously varied. Errors in A do not

change as the starting reflectivity is decreased from 50 dBZ, but errors in b lessen

with lower reflectivity values. For the purposes of this thesis, two Z-R relationships

are considered different if A or b vary by more than a difference of 10 or 0.01

respectively.

Z − R relationships in this thesis have been derived using a fitting procedure,

utilising a Levenberg-Marquardt least squares minimisation to fit a power law was

used to derive coefficients A and b. A was constrained between 0 and 1200, and

b was constrained between 0.9 and 1.9. These values were chosen based on those

commonly reported in the literature, and by experimentation on values producing

a good fit. A linear least-squares fit was also used to verify accuracy of the results,

and were found to be in good agreement.

2.4.2 D0-ZDR Relationships

Seliga and Bringi [1976] showed the median drop diameter can be related to the

differential reflectivity for an exponential DSD. For non-exponential DSDs, a power

law regression given by D0 = aZDRb, where ZDR is the differential reflectivity, is the

simplest algorithm relating the two variables [Bringi et al., 2002; Gorgucci et al.,

2002]. There are comparatively less D0-ZDR relationships than Z −R, owing to the

requirement of a differential reflectivity measurement. These relations are discussed

further in Chapter 7.


2.5 Conclusion

In this chapter the frequency selection effects of profiling radars was first discussed.

While UHF radars are more sensitive to precipitation, they cannot detect the clear-

air echo in anything other than low rainrates. VHF radars have the advantage of

always detecting the clear-air return, but cannot resolve drops smaller than 1 mm.

Dual-frequency retrievals, capitalising on the advantages of both frequency bands,

offer the most accurate DSD estimation, but require two co-located radars. VHF

retrievals only are performed in the current study. The advantage here is the low

altitude to which the DSD can be evaluated.

Scanning radars are one of the most important tools in modern meteorology. The

properties of the particular radars used in the current study, one being operational,

one designed for research purposes were presented. Dual-polarisation represents the

next generation in scanning radars, and offers significant improvements as discussed.

In the next chapter the VHF radar DSD retrieval technique is presented.

Chapter 3

Dropsize Distribution Retrievals

In the previous chapter the particular radars used in this study were discussed.

Attention is now turned to the technique employed to retrieve dropsize distributions

using vertically pointing Doppler radars operating near 50 MHz. As noted in the

introduction, the accuracy of DSD retrievals is highly dependent on the resolution of

the broadening effects in the clear-air. This makes profiling radars operating at VHF

powerful tools in precipitation studies, because they are can simultaneously detect

the clear-air and precipitation echoes. By fitting a Gaussian curve to the clear-air

echo the contribution due to turbulence can be calculated and used to correct the

precipitation echo. The objective method used to accomplish this is now described.

3.1 Retrieval Technique

The power spectrum in precipitation conditions is the sum of the backscattered

power from both the clear-air turbulence and the falling hydrometeors. A simulated

spectrum of a VHF wind profiler in precipitation conditions is shown in figure 3.1.

The clear-air peak is centred close to 0 ms−1. Deviations from 0 ms−1 are the

result of the mean vertical motion of the atmosphere. This offset can be as great as

±10 ms−1 in convective conditions. The width of the clear-air peak is determined

by the sum of the contribution to radial velocity from different directions due to the

width of the radar beam (beam broadening), and to turbulent motions within the

34 CHAPTER 3. DROPSIZE DISTRIBUTION RETRIEVALS

Figure 3.1: A simulated spectrum of a VHF wind profiler echoes in precipitationconditions. The clear-air peak is centred at 0 ms−1, and the precipitation peak near−10 ms−1.

3.1. RETRIEVAL TECHNIQUE 35

sampled volume of the atmosphere.

The precipitation peak is generally smaller in magnitude, and is centred around

−10 ms−1. The precipitation echo needs to be corrected for clear-air effects, as it is

both broadened by turbulence and shifted due to the mean vertical air motion. The

total returned power (T ), as a function of vertical velocity (v), is the convolution

of the clear-air echo (C) and the precipitation echo (P ), together with the inherent

noise level, (n), is given by

T (v) = C(v − v̄) + C(v)⊗ P (v − v̄) + n (3.1)

where ⊗ denotes the convolution, and v̄ is the mean vertical wind [Wakasugi et al.,

1986; Rajopadhyaya et al., 1993].

To remove this broadening effect, and correct for the shifting due to background

winds, a deconvolution of the precipitation peak with the clear-air peak must be

performed. To do this, the clear-air and precipitation peaks must first be sepa-

rated into distinct functions. The noise level of the complete spectrum is calculated

following Hildebrand and Sekhon [1974].

3.1.1 Finding the Divide

To separate the clear-air and precipitation peaks, the minimum of the merger must

first be located. For example, in Figure 3.1 the minimum merger point is around

−3 ms−1. In this case, the peaks are clearly distinguishable and the divide is easily

picked both by eye, and by the automated routine described below. Ideally, the

peaks should always be separated at a point where the precipitation peak can be

completely isolated. However, the position where falling hydrometeors become the

solitary signal, and not a mixture of precipitation and clear-air scatter, is not always

apparent. If the divide is chosen such that some of the clear-air signal is included

in the retrieval, there will be an overestimation in the number of small drops in the

resulting DSD, leading to unrealistic rainrates and liquid water contents. Conversely,

placing the divide too far into the precipitation echo, such that some of it is missed,

results in an under-representation of the true DSD, and hence low rainrates and


liquid water contents. As Lucas et al. [2004] note, experiments show that finding

the divide location to within ± 0.5 ms−1 is sufficient, and varying the location of the

divide within this bound will not result in dramatic changes in the final retrieval.

An algorithm is implemented closely following Lucas et al. [2004], to find the posi-

tion of the divide by automated routine. The raw power spectrum is first smoothed

twice over a 1 ms−1 velocity interval to eliminate small fluctuations. The first

derivative with respect to velocity is then calculated on this smoothed spectrum,

and the derivative is then twice smoothed. Figure 3.3 shows an example of a twice

smoothed simulated spectrum in precipitation conditions, and the twice smoothed

first derivative.

In all but the most extreme cases, it can be safely assumed the maximum of

the clear-air peak lies between ± 10 ms−1. Taking the spectrum between −10 and

+10 ms−1, this twice-smoothed derivative is scanned in the positive to negative

velocity direction, looking for the first occurrence of a zero crossing with negative

slope, which also corresponds with a spectral amplitude at least 80% of maximum

(marked as 1 in Figure 3.2(b)). This is taken to be the clear-air peak, and serves as

the starting point in the minimum merger search. The first occurrence is taken as

these conditions are also met at the peak of the precipitation signal in heavy rainfall.

Starting from the identified clear-air peak the routine scans towards negative velocity

looking for a zero crossing with positive slope, which is taken to be the minimum

of the merger between the peaks, and the position where they should be separated

(marked as 2 in Figure 3.2(b)).

Observations dictate that the minimum merger point will be within 10 ms−1 of

the identified clear-air peak. If the merger point is outside this limit a second check

is initiated. A second derivative is calculated from the first derivative, which has

been smoothed once. In the second derivative, scanning from positive to negative

velocity, the minimum point is identified, corresponding to the clear-air “maximum”.

The scan continues from this point, looking for the next maximum, which is taken

as the minimum merger point.

As will be discussed in Chapter 4, and as is the case with any automated algo-

rithm, the correct divide is not always selected. The retrieval code allows the user

to manually select the divide in these situations.


(a) Twice smoothed simulated spectra.

(b) Twice smoothed first derivative of the spectra shown in (a).

Figure 3.2: (a) Twice smoothed simulated spectrum in precipitation conditions, and(b) the first derivative of the spectrum shown in (a), itself twice smoothed. The zerocrossing with positive slope, marked as 1, shows the position of the clear-air peak,while the zero crossing with positive slope, marked as 2, shows the location of thedivide.


3.1.2 Clear-Air Peak

Once the division between peaks has been made, the clear-air spectrum is fitted

with a Gaussian function. An algorithm due to Markwardt [2009] is used to find

the optimal fit to the clear-air peak. Since an accurate description of the clear-air

parameters is critical to the retrieval procedure, some effort was expended on deter-

mining the conditions under which the fitting procedure would fail. Refined initial

guesses for the algorithm were then determined based on these failing conditions, in

order to improve the automated fitting routine. Figures 3.3(a) and 3.3(b) show two

examples of simulated Gaussian functions with added noise. In each Figure, the top

plot (shown in red) represents an early version of the fitting procedure, while the

bottom plot (shown in blue) shows the fitting procedure used to calculate retrievals

in this thesis. In Figure 3.3(a) a spike near the centre of the clear-air peak has caused

the early version of the procedure to fit a curve much narrower than required. A

spike has also caused the terrible fit in Figure 3.3(b), where the early version of the

procedure has attempted to fit the Gaussian to the entire spectrum.

In the retrieval procedure, initial guesses on the centre of the peak, the standard

deviation and the area under the curve provide a starting point to the algorithm for

calculation. The floor of the clear-air peak is taken to be the previously determined

noise floor. The clear-air fit to the simulated spectrum shown in Figure 3.1 is shown

in Figure 3.4.

The clear-air echo is then represented by

C(v) = A0 exp

(−(v − v̄)2

σ2

)(3.2)

where A0 denotes the amplitude of the clear-air spectrum, σ the spectral width,

and v̄ the mean vertical air motion. The clear-air vertical velocity and spectral

width (standard deviation) are calculated using this function, and these parameters

are then used to correct the precipitation spectrum. A bad fit to the clear-air peak

obviously has a strong effect on the DSD calculation when the precipitation function

is deconvolved with the clear-air peak. In general, the automated routine finds an

optimal fit for the clear-air spectrum. Occasional problems occur when there is a

significant “spike” near the peak of the spectrum, to which the algorithm attempts


(a) Clear-air Gaussian fitting routine e.g. 1.

(b) Clear-air Gaussian fitting routine e.g. 2.

Figure 3.3: Two examples of an early version of the Gaussian fitting procedure,shown in red, and the procedure used in this thesis, shown in blue. The spectrum isa simulated Gaussian function with added noise. The x-axis shows spectral points,while the y-axis represents magnitude in arbitrary units.


Figure 3.4: Simulated spectra in precipitation conditions, including statistical fluc-tuations. The clear-air peak is centered on 0 ms−1, the precipitation peak on −8ms−1. The dotted green line depicts the Gaussian fitted to the clear-air peak.


to fit a very narrow curve. Problems can also occur in turbulent conditions when the

clear-air spectrum is very broad, with the algorithm either over or underestimating

the spectral width. As in the case of finding the divide, the retrieval code allows the

user to manually set both the peak and spectral width. These problems and their

solutions will be further discussed in the following chapter.

3.1.3 Interference Effects

The Darwin profiler experiences interference from a co-located millimetre cloud

radar. An example spectrum showing the precipitation, clear-air and interference

peaks is shown in Figure 3.5. This interference peak is not always present, and when

present is not always located in the same place, making masking difficult. When it

is located, as shown in Figure 3.5, in the positive velocity region to the right of the

clear-air peak, it is often mistaken as the clear-air echo by the automated procedure.

This forces the procedure into fitting the Gaussian to the interference peak rather

than the true clear-air peak. This problem can be alleviated by replacing the spec-

tral points to the right of the clear-air peak with the noise floor. However, as the

location of the clear-air peak depends on the mean vertical motion, and the spectral

width is variable, some care needs to be taken and the number of replaced spectral

points edited. To avoid manual editing in every case, spectral points with a positive

velocity greater than 15 ms−1, where one can be sure to avoid the clear-air peak,

are replaced with the noise floor. When the interference peak moves inside this 10

ms−1 bound, the number of spectral points replaced is manually edited.

As mentioned above, when locating the divide between the clear-air and precip-

itation peaks, the automated routine assumes the maximum in the clear-air peak

is between −10 and +10 ms−1. When the interference peak moves inside this ve-

locity region, the automated routine is mislead into placing the divide between the

clear-air and interference peaks. The subsequent routines will then proceed to fit

the clear-air Gaussian to the interference peak, and precipitation function to the

clear-air peak. This issue can be resolved by manually specifying the correct divide,

or editing the number of spectral points replaced with the noise floor.

On occasion, the interference peak merges with either the clear-air or precipitation

peaks. In these cases no retrievals are possible.


Figure 3.5: Twice smoothed real spectrum from Darwin, showing an echo due toprecipitation, clear-air and interference.


3.1.4 Precipitation Peak

Once the Gaussian is fitted to the clear-air, the remaining precipitation spectrum

lacks the part that was previously covered by the clear-air peak, such as that shown

in Figure 3.6(a). Following Lucas et al. [2004], an exponential tail is added to the

spectrum to fill in this region, as shown in Figure 3.6(b). This tail is used only to

perform the deconvolution, it is not included in the retrieval, as it represents the

part of the spectrum that we cannot determine. The point at which the spectrum

becomes unknown is termed the “minimum observable diameter”, and varies from

spectrum to spectrum as it is a function of the clear-air precipitation divide.

The “pure” precipitation spectrum is given as

P (v) =1

ZN(D)D6dD

dv(3.3)

where Z is the reflectivity, D is the diameter, and N(D) is the DSD. The factor dDdv

is derived from the Foote and du Toit [1969] fall-speed relation

v(D) = (9.65− 10.3 exp(−600D))

(ρ

ρ0

)−0.4

(3.4)

where ρ and ρ0 represent the density of air at sea level and the height of observa-

tion, respectively. At mean sea level pressure, this relation indicates an asymptotic

maximum fall speed of 9.65 ms−1 for rain drops [May et al., 2002]. Precipitation

echo with a fall-speed beyond this limit is considered to be ice.

The reflectivity (Z), is the backscattered power seen by the radar due to precip-

itation only, and is dependent on the sixth power of the diameter of the drop, and

the density of raindrops in the sample volume [Doviak and Zrnic, 1993]:

Z =

∫ ∞

0

N(D)D6dD (3.5)


(a) Simulated precipitation spectrum with the clear-air peak removed.

(b) Simulated precipitation spectrum with an added exponential tail.

Figure 3.6: Simulated precipitation spectrum with the clear-air peak removed (a),and the same spectrum with an exponential tail added (b).


3.1.5 Deconvolution

To obtain the pure precipitation spectrum and thus perform the retrieval, the precip-

itation function must be corrected first for the effects of turbulence, vertical motion

and spectral broadening. It is here that a choice must be made between parametric

and direct deconvolution techniques. The parametric method involves assuming a

form for the DSD, such as the Marshall-Palmer distribution or a Gamma distribu-

tion, as discussed in 1.2. Varied parameters are input into the assumed form, and

each solution is convolved with the clear-air spectrum. Nonlinear least squares curve

fitting is then used to determine which set of parameters fits the observed spectrum

best. The alternative direct deconvolution technique does not assume a form for the

DSD, but rather takes the clear-air statistics and performs a direct deconvolution

of the spectrum via Fourier transform with the precipitation spectrum. This was

first proposed by Gossard [1988] and used in studies such as Rogers et al. [1993]

and Rajopadhyaya et al. [1993]. Schafer et al. [2002] compared the deconvolution

and parametric techniques using a dual-frequency system, and concluded that the

deconvolution technique results in retrievals as good, or better than, the parametric

technique, particularly in the case of spectral widths greater than 2 ms−1, or median

drop diameters greater than 3 mm.

While analytical forms of the DSD are useful in that they can be easily integrated,

they do not allow study of the evolution of the shape of the DSD. As discussed above,

Schafer et al. [2002] concluded the direct method performs as well or better than

assuming a functional form, and this method is therefore chosen in this study.

Rajopadhyaya et al. [1993] discussed two methods of direct deconvolution, the first

using a Fourier transform (discussed below), and the second an iterative technique.

Briefly, in the iterative technique, following Cooper [1977], population spectra are

estimated by

hi+1 = hi ⊗ g − h|i=0...∞ (3.6)

where h is the observed precipitation echo, g is the clear-air echo, and ⊗ denotes the

convolution operation. The procedure is iterated, with new estimates of hi, allowing

hi+1 to converge to the measured backscattered power spectrum as i approaches


∞. As discussed in Rajopadhyaya et al. [1993], to avoid contamination with high

frequency terms, only a few iterations are appropriate.

Using simulated spectra, Rajopadhyaya et al. [1993] tested both methods of direct

deconvolution. Both methods suffered widening effects of the spectrum when com-

pared to the simulated spectrum, but the effect was greater when using the iterative

technique. The study also found that the retrieved DSD departed further from the

model in the small drop regime than when using the Fourier method. The Fourier

method is therefore used in this study, as described below.

In the Fourier transform (FT) method, if T (f) is the power spectrum, and T (τ)

is its FT, then

T (τ) =H

G(3.7)

where H and G are the the Fourier transforms of the observed precipitation echo

h and clear-air echo g, respectively. Due to the small amplitude of high-frequency

components in the clear-air echo, the equivalent high-frequency components of the

returned precipitation echo are greatly magnified, resulting in a noisy solution. This

is avoided by truncating the precipitation spectrum, and using a low-pass filter in

order to retain only the low frequency components in the solution, as most of the

important information lies in the central part of the series. As discussed in relation

to the iterative technique, Rajopadhyaya et al. [1993] noted that truncation of the

precipitation spectrum is equivalent to the convolution of the spectrum with the

Fourier transform of the truncating window, resulting in the deconvolved spectrum

being broader than the “true” spectrum. This broadening imparts limitations on

the retrieval, particularly in the small and large drop diameter regimes.

Lucas et al. [2004] tested the variation of the solution when retaining varying

numbers of the lowest frequencies. Solutions were compared to a model gamma

distribution, and the technique was tested with simulated spectra, where the precise

answer was known. Lucas et al. [2004] found that if too few frequencies were retained,

the precipitation spectrum became too broad, with broad sidelobes. When too many

frequencies were retained the noise becomes dominant, and the magnitude of the

higher frequency components is overestimated. Strong, narrow, sidelobes are present

in this case. The “best” solution lies in the narrow range between these two cases.


To differentiate between solutions, Lucas et al. [2004] created a “noise parameter”

by integrating the absolute value of the spectral power of the solutions between 0

and +5 ms−1, choosing this region because no precipitation signal is expected in

this range. This parameter evaluates the goodness of the solution, together with the

strength of the sidelobes.

In the case of real data, to choose the solution automatically, 41 solutions of the

pure precipitation spectra are calculated, with between 5 and 45 retained frequen-

cies. The “noise parameter” is calculated for each frequency, and the lowest value

identified. The lowest value solution is then averaged with spectral values within

±2 frequencies to itself. Averaging acts to smooth the final spectrum. This method

is implemented in the current work. After deconvolution, the inverse transform is

performed and equation (3.3) solved for N(D), returning the number of drops at a

given diameter, i.e. the dropsize distribution.

The retrieval from the simulated spectra shown in Figure 3.1 is shown in Figure

3.7. The retrieval shows a large number of small drops, and a decreasing number

of larger drops, with a maximum dropsize near 6 mm. The vertical dashed line

is the minimum observable diameter, as discussed above, and is demonstrated in

the retrieved DSD by the large increase in the number of small drops at D < 1

mm. This increase is typically around 4 orders of magnitude, and is a result of

incomplete deconvolutions, and the D6 dependence. Inclusion of these small drops

in calculations carried out using the retrieval, such as of the rainrate, liquid water

content and median drop diameter, result in inaccurate estimations. The rainrate

and liquid water content estimations are increased, while the median drop diameter

is lowered. For more realistic calculations, only the part of the spectrum greater

than 1 mm is used.

3.1.6 Small-Drop Regime

The fall velocity of small drops is small in comparison to the vertical wind. Despite

the abundance of small drops, they cannot be detected by the profiler because

the relevant part of the precipitation spectrum is obscured by the clear-air peak.

Scatter from these small hydrometeors instead adds to the turbulence component

of the clear-air [Rajopadhyaya, 1994]. The smallest resolvable dropsize is clearly


Figure 3.7: Dropsize distribution retrieval from the spectra shown in 3.1.

dependent on the atmospheric conditions under which the sample was taken. If

the precipitation peak is large compared to the clear-air peak, such as in heavy

convective rainfall, smaller drops can be retrieved than in mild stratiform conditions

where the precipitation echo is smaller.

To estimate the effect the missing small drops have on the median drop diameter

calculation in the current work, a gamma distribution with a shape parameter of

μ = 1 was fitted to all quality-controlled retrievals for which the DSD shape was

available. The shape of the distribution was not included initially in the saved struc-

ture after processing, because the DSD was characterised by D0 only. Regardless,

6912 individual retrievals from 4 separate events were used in this calculation. The

median drop diameter of the full gamma distribution was calculated, and averaged

as a function of height. Comparison to the profiler calculated D0, also averaged as

a function of height, is shown in Figure 3.8. Note that these data are from Darwin

only. Adelaide results displayed a similar trend, but are not included in the overall

average due to differences in range gates.

On average, the profiler-retrieved D0 is 0.25 mm larger than that calculated from

the gamma fit. This is a 16.5% overestimation, for an average spectral width of 0.63


Figure 3.8: Median drop diameter calculated from the profiler retrieval (red), com-pared to the median drop diameter calculated from a gamma fit (blue). The gammafit includes drops less than 1 mm, and thus shows a uniformly smaller D0.


ms−1, which is comparable to values reported by Rajopadhyaya et al. [1999] and

Schafer et al. [2002] in similar conditions, and therefore confidence can be placed

in the presented retrieval procedure. It is interesting to note in Figure 3.8 that the

difference between the profiler-retrieved, and gamma calculated D0 increases with

increasing height. Figure 3.9 shows the difference between the profiler-retrieved and

gamma calculated D0, along with the average spectral width as a function of height.

The difference between D0 calculations increases with increasing spectral width, as

has been previously reported in the literature [Rajopadhyaya et al., 1999; Schafer

et al., 2002].

Figure 3.9: Difference in the median drop diameter calculated from the profiler re-trieval from a gamma fit (red), and the average spectral width (blue). The horizontalaxis represents both mm for the difference in D0, and ms−1 for the spectral width.The difference in D0 increases with increasing spectral width.

The overestimation in median drop diameter is clearly dependent on factors such

as spectral width, which then depends on both the radar in use and meteorological

conditions. To further characterise this overestimation, and attempt to introduce a

correction factor, a modelling study was undertaken. Simulated raw radar spectra in

precipitation conditions were generated. The simulation allowed the user to vary all

parameters related to precipitating spectra, including rainrate, clear-air amplitude

and spectral width, noise level and mean vertical velocity. For a generated spectrum,


the DSD was retrieved using the technique described in this Chapter. A gamma

function was then fitted to the deconvolved spectrum, and the median drop diameter

calculated via the standard equation D0 = 3.67+μλ

[Ulbrich, 1983]. The gamma

distribution was then integrated analytically for both the full distribution, and the

distribution greater than 1mm, and the drop diameter corresponding to the half

liquid water point (that is, the median drop diameter) calculated. Integration of the

full spectrum was carried out only as a secondary check to that calculated via the

equation. This gamma function fit then has two objectives:

1. Does the gamma function provide an accurate description of the deconvolved

distribution?

2. Can a correction factor be applied from the gamma distribution, to account

for the lack of resolvable small drops?

To answer these questions, the model described above was run 6 times, with

each run consisting of 1000 spectra. Input paramaters were randomly selected for

each individual spectrum, and were allowed to vary between bounds characteristic of

stratiform and convective rainfall separately. Three model runs simulated stratiform

rainfall, and three convective, as dictated by the input parameters. For both rainfall

types, the three runs consisted of a gamma fit with (i) μ = 1, (ii) μ = 2 and (iii) μ

constrained to be positive.

For each spectrum, four separate values of the median drop diameter were cal-

culated, (1) the deconvolved distribution, (2) the full gamma distribution via the

equation, (3) the full gamma distribution via analytical integration, and (4) the

gamma distribution greater than 1 mm via analytical integration. Values for (2)

and (3) should be equal, and were used as a check the procedure had worked cor-

rectly. Values for (1) and (4) provide an estimation of how well the gamma fit

represents the deconvolved distribution. The gamma fit was taken as a good rep-

resentation of the deconvolved spectrum if calculated values for (1) and (4) were

within 0.1 mm of each other. In stratiform rainfall, for μ = 1 and μ = 2, approx-

imately 50% of spectra met this criteria, increasing to approximately 80% when μ

was allowed to vary. For convective rainfall, less than 10% of distrubtions met this

criteria, regardless of chosen shape parameter. The allowed difference of 0.1 mm was

relaxed to 0.25 mm, resulting in 20% of cases meeting the criteria, again regardless

of shape parameter.


In answer to question 1 above, these model runs suggest that a gamma fit can

provide a good representation of a deconvolved distribution in stratiform rainfall

only. It must be noted that spectral widths are generally larger in convective rainfall,

making it more difficult to determine the correct position of the divide between

peaks, and therefore the accuracy of the deconvolution is questionable, particularly

at the small drop end.

Question 2 is somewhat more difficult to answer. Calculated values of the median

drop diameter from the profiler deconvolution method are an overestimation of the

true value. In stratiform rainfall, where a gamma fit provides a good estimate of

the deconvolved distribution, corrected D0 values can be corrected by calculating

D0 from a gamma distribution fitted to the deconvolved spectrum. In the case of

convective rainfall, the question becomes what is the lesser error, the overestimate

of the true median drop diameter, or the introduced error from correcting D0 with a

gamma fit which is not a good representation of the deconvolved distribution. Based

on the errors associated with the deconvolution procedure in convective conditions,

mainly the large spectral widths which make accurate determination of the divide

between peaks difficult, the error in the gamma fit is taken as the lesser error in this

work.

A mapping function was created by analytically integrating the gamma function,

holding μ = 1. The most accurate gamma fits to the deconvolved distribution were

obtained by allowing the shape parameter to vary. This is not an option when

calculating a mapping function. However, it may be possible with future modelling

studies to characterise the shape parameter that best fits a particular rainrate, and

apply a correction factor. The mapping function used in this work is shown by the

blue line in Figure 3.10, where the calculated profiler D0 is shown on the horizontal

axis, and the corrected gamma fit D0 on the vertical. The crosses in this figure

represent the model simulation runs for μ = 1 in stratiform rainfall. As expected,

as the median drop diameter increases, and more water is located at the large drop

end of the distribution, the overestimation in the profiler-retrieved D0 decreases.

All median drop diameters presented in this thesis have been corrected via this

mapping function. As an indication of the function, Figure 3.11 shows the 6912

calculated D0 values shown in Figure 3.8, corrected via the mapping function and

averaged as a function of height. The corrected average is a good approximation to

that obtained by fitting a gamma distribution to each individual spectrum.


Figure 3.10: Median drop diameter correction-mapping function, depicted by theblue line. This was created by the analytical integration of the gamma function withμ = 1. The crosses indicate the model runs for stratiform rainfall with μ = 1.


Figure 3.11: Same as Figure 3.8 but with the profiler calculated D0 corrected viathe mapping function shown in light blue.

3.2 Code automation

This rainfall code was originally designed to be used on saved raw radar data in times

of known rainfall. A significant amount of effort in the current work was expended

on automation of this code to perform the inverse process; detect whether rainfall

is present, and calculate retrievals as appropriate. The motivation for this has two

components. Firstly, where it is known precipitation is occurring over the profiler,

the rain event does not always exist through all time-stamps of the collected data

set. Automatic precipitation detection ensures no retrievals are performed at these

times. If this routine was not implemented, regions of no rainfall would appear as

regions of low reflectivity. This would then require the user to examine the spectra

at these times to determine if there was light rainfall, or no rainfall. Secondly,

a DSD retrieval procedure which does not calculate retrievals where there is no

precipitation peak can be run on raw data blocks to determine if rainfall is present.

This is particularly useful in situations where there is no other information readily

available, such as RHI scans or rain gauge data. This is also a necessary first step

in advances towards real-time DSD calculations.

3.3. CALCULATIONS FROM THE RETRIEVAL 55

To automatically determine if a precipitation echo is present in each spectrum,

after the clear-air peak has been calculated the code looks at the remaining spectrum,

and determines how many of the remaining spectral points are greater than 6.5 dB

above the noise level. Threshold values are then implemented for stratiform and

convective precipitation (some manual control is required here). If the threshold is

exceeded, the automated procedure continues as described above. If the threshold

is not met, the code returns only the clear-air parameters, setting all rain-related

values to zero. As will be discussed in the the following chapter, this procedure is

not always accurate, and the code can be manually forced into recognising a rain

peak or otherwise.

3.3 Calculations from the Retrieval

Having obtained the pure precipitation spectrum and subsequently retrieved the

dropsize distribution, useful parameters such as rainrate, liquid water content and

median drop diameter can now be calculated.

3.3.1 Rainrate

The rainrate is the flux of rain through a horizontal surface, and is expressed as

R =π

6

∫ ∞

0

v(D)D3N(D)dD ≈ π

6

∫ ∞

0

D3.67N(D)dD (3.8)

where v(D) is the terminal velocity for a drop of diameter D, and N(D) is the DSD.

The approximation on the right hand side is often quoted in the literature, and is

derived from the power-law fit to the terminal velocity given by Atlas and Ulbrich

[1977]. Rainrate can also be estimated from the reflectivity factor, as discussed in

2.4.


3.3.2 Liquid Water Content

Knowledge of the liquid water content at varied heights gives insight to the degree

of mixing in the atmosphere. Changes in liquid water content are associated with

large energy changes. The liquid water content is defined as

M =πρω

6

∫ ∞

0

D3N(D)dD (3.9)

where ρω is the water density of the drop.

3.3.3 Median Drop Diameter

The median drop diameter D0 divides the DSD such that precisely half of the drops

have a larger drop diameter than D0, and precisely half have a smaller drop diameter

than D0.

The area under the DSD curve is given by

A =

∫ ∞

0

D3N(D)dD (3.10)

and therefore the median drop diameter is the diameter such that

∫ D0

0

D3N(D)dD =

∫ ∞

D0

D3N(D)dD (3.11)

Since raindrops are not spherical in shape, the term “diameter” has no physical

meaning, but rather refers to an equivalent drop diameter, i.e. a diameter that has

been estimated from the mass of the drop. Note that all D0s calculated via this

equation are then corrected with the mapping function discussed in section 3.1.6.

3.3. CALCULATIONS FROM THE RETRIEVAL 57

3.3.4 Heating Rates

Following May and Rajopadhyaya [1996], sensible heating rates, and heating rates

associated with precipitation can be estimated from calculated rainfall properties.

Neglecting a small storage term, the sensible heating rate, Q1, is defined as

Q1 ≈(∇ · sV +

∂w̄s̄

∂p

)(3.12)

where ∇ is the horizontal divergence operator, V is the horizontal wind vector, w̄ is

the vertical motion in pressure coordinates, s is the static energy (s = gz+cpT ) and

p is pressure [Yanai et al., 1973; Frank and McBride, 1989]. Assuming horizontal

gradients are small, Q1 can be approximated by

Q1 ≈ w̄∂s̄

∂p(3.13)

In practice, using a radar which measures the vertical wind w directly, equation

(3.13) reduces to

Q1 ≈ −w(Γd − Γ) (3.14)

where Γd is the dry adiabatic lapse rate, and Γ is the lapse rate estimated from the

radiosonde sounding closest to the rain event. This simplification involves significant

approximations, and should be taken only as a guide. Note also that in convective

conditions the horizontal wind cannot always be neglected, and the approximation

is less accurate in these situations.

The evaporative heating rate, Qp is defined as

Qp = −Lρωπ

6

∂

∂z

[∫ ∞

0

v(D)N(D)D3dD

](3.15)

where L is the latent heat of vaporisation, ρω is the density of water, and v(D) is the

fall speed of a particle with diameter D [May and Rajopadhyaya, 1996]. The negative


sign, which was not shown in May and Rajopadhyaya [1996], is required to ensure

the correct sign for Qp. Here, the integral term in equation 3.15 is approximated by

the flux of the rainrate between successive range gates.

3.4 Conclusion

This chapter has described a method for the retrieval of dropsize distributions us-

ing a VHF vertically pointing Doppler radar. The methodology in locating the

minimum merger point between the clear-air and precipitation echo, the functions

fitted to these echoes, and the deconvolution procedure used to correct the precip-

itation echo for clear-air effects has been discussed. Particular emphasis was given

to the D0 correction procedure, necessary because the profiler cannot retrieve small

drops. In the next chapter, some of the problems and their subsequent solutions in

implementing this procedure are identified.

Chapter 4

Quality Control

4.1 Introduction

In the previous chapter the technique used to calculate the dropsize distribution

from a vertically pointing Doppler profiler, as well as the calculation of related

integral parameters, such as rainrate and liquid water content was explained. While

this technique is designed to run as automatically as possible, there are occasional

incorrect retrievals, as occurs in all automatic routines used to analyse real data.

There are several recurring problems with the routine, which cannot be alleviated

automatically, as discussed below.

A post-analysis quality-control procedure was written and implemented to auto-

matically find most of these problem retrievals. This chapter describes this proce-

dure, and the possibilities in correcting retrievals. The main problems which cause

bad retrievals, and why these cannot be accounted for in the retrieval procedure are

also discussed. Finally, the potential of this code to be implemented in a real-time

operational setting is proposed.

60 CHAPTER 4. QUALITY CONTROL

4.2 DSD Procedure

The DSD code is run on hour-long blocks of raw radar data. At the conclusion of

processing, an overview is obtained of the data with a time-height cross-section, as

illustrated in Figure 4.1.

Figure 4.1: Time-height cross-section of profiler measured reflectivity as processedby the DSD retrieval procedure, with no quality control. The scale shown on theright is in dBZ.

The plot shows light rainfall starts to fall around 13.4 UTC at the lowest heights.

The precipitation gets heavier and extends vertically 10 minutes later, with a heavier

band extending through all heights of observation around 13.8 UTC. Each pixel in

this plot represents the processing of one raw spectrum, that is, a particular range

gate at a particular time stamp. It is obvious from this figure that there are some

incorrect retrievals.

There are some non-zero values between 13.0 and 13.2 UTC, and at the upper

heights between 13.4 and 13.6 UTC. In the first instance, owing to the sparsity

of these points, one can safely assume there is no actual rainfall here, and the

DSD procedure has interpreted noise fluctuations in the spectrum as a precipitation

4.2. DSD PROCEDURE 61

peak and calculated a “retrieval”. Between 13.4 and 13.6 minutes this particular

assumption cannot be made; it is possible that the rainfall seen in the lower range

gates extends upward, but the DSD procedure has not detected the precipitation

peak, and therefore not processed a retrieval. A missed precipitation echo is also

a problem in the main rain band, where pixels are coloured white. Black and red

coloured pixels can also be seen in this rain band. These “bulls eyes” occur when

the DSD procedure miscalculates the parameters that go into the deconvolution, for

example a bad clear-air fit. These are particularly problematic as they cause gross

overestimation of the precipitation field.

From Figure 4.1 we see that problems occur with the automatic DSD procedure

when (i) it identifies a precipitation peak which is not there, (ii) does not find a real

precipitation peak, or (iii) when a retrieval is performed inaccurately. The reasons

for these problems are now addressed.

4.2.1 DSD Procedural Problems

Several issues cause “bulls eye” retrievals, mainly due to an inadequate fit to the

clear air peak. The precipitation spectrum is broadened by turbulence and shifted

due to the mean vertical air motion. As discussed in chapter 3.1, to obtain the true

precipitation spectrum a deconvolution of the precipitation peak with the clear-air

peak is performed. The clear-air spectrum is fitted with a Gaussian function by

an automated process, and the vertical velocity and spectral width calculated from

this function are used to correct the precipitation spectrum. If these parameters are

not calculated correctly, the deconvolution does not result in the true precipitation

spectrum, leading to a false description of the dropsize distribution.

There are three main problems resulting in inadequate clear-air fits. The first

occurs when there is a “spike” in the clear-air spectrum near the peak. Prior to

the Gaussian fitting routine, the clear-air spectrum is checked for “spikes” and then

smoothed over a 2 ms−1 velocity interval. As discussed in section 3.1.2, the fitting

procedure is supplied with the best starting estimates possible to avoid the curve

fitting to a spike. Despite these efforts, spectra such as that shown in Figure 4.2(a)

occur, where the automatic curve fitting procedure is misled, and the procedure

attempts to fit a Gaussian curve to the spike. The automatic procedure resulted in


the fit shown in figure 4.2(b) in this case, resulting in a nonsensical retrieval after

deconvolution.

A second problem resulting in a bad clear-air fit occurs in convective conditions,

when the spectral width is large and the precipitation peak merges with that of the

clear-air, as shown in Figure 4.3(a). In these cases, the DSD procedure inaccurately

interprets the spectra as not containing a precipitation peak, and therefore does

not attempt to calculate a retrieval. Instead, the Gaussian is fitted to the merged

spectrum, as shown in Figure 4.3(b). This is the principle cause of a zero value

within a rain band.

A third problem resulting in an incorrect clear-air fit occurs when the clear-air

spectrum is more rectangular than Gaussian in shape, e.g. Figure 4.4(a). While

spectra such as this occur frequently enough to warrant comment, their random

occurrence at varied times and heights does not suggest an obvious cause. This

rectangular shape could be the result of random statistical fluctuations, or could be

the result of external interference that has a low Doppler shift picked up through a

side lobe. In these cases, the automated procedure results in a fit that is too wide,

as shown in Figure 4.4(b).

Another issue resulting in “bullseye” retrievals occurs when the divide between

clear-air and precipitation is poorly selected. Two examples of this problem are

shown in Figure 4.5. While the fit to the clear-air peak is quite good in both cases,

the precipitation peak is poorly estimated, and does not therefore provide a true

record of the dropsize distribution or associated parameters.

By eye, location of the divide in both cases in Figure 4.5 looks obvious. As

discussed in section 3.1.1, the location of the divide is calculated by doubly smooth-

ing the spectrum over a 1 ms−1 velocity interval, taking the derivative, and doubly

smoothing this. The doubly smoothed spectrum and first derivative for the spectrum

shown in Figure 4.5(a) are shown in Figure 4.6. In this situation, the automated

procedure has mistakenly identified the peak centred on −1 ms−1 as the clear-air

peak, and therefore mistakenly identified the divide as shown.

The rain peak is identified by folding the spectrum in half, subtracting one part

from the other and looking for a peak in the remainder. Section 3.1.3 discusses the

interference in spectra from Darwin caused by the co-located millimetre cloud radar.


(a) Example spectrum with a spike near the centre of the clear-air peak.

(b) Automatic fit to the spectrum seen in (a).

Figure 4.2: (a) An example spectra showing a spike near the centre of the clear-airpeak. The red horizontal line indicates the calculated noise level. The automatic fitproduced by the DSD code is shown in (b) by the green dotted line. This automaticfit is not a true representation of the clear-air peak, and hence produces an erroneousDSD. Note the black background indicates a screen shot.


(a) Example broad spectrum, with the precipitation and clear-air echomerging.


Figure 4.3: (a) An example of a broad spectrum in convective conditions. The redhorizontal line indicates the calculated noise level. The separation point betweenthe clear air and precipitation peaks is not obvious. The automatic fit is shownin (b). The automated process has assumed a very large spectral width, and noprecipitation peak.


(a) Example spectrum resembling a rectangular shape more than a Gaus-sian.


Figure 4.4: (a) An example of a rectangular spectrum. The red horizontal lineindicates the calculated noise level. The automatic fit to this spectra is shown in(b). As the curve fitting procedure attempts to fit a Gaussian curve, it does not fita spectra such as this well, and overestimates the spectral width.


(a) Example spectrum with a poor divide selection, placed too far to theright.

(b) Example spectrum with a poor divide selection, placed too far to theleft.

Figure 4.5: (a) An example of an automatic selection of the divide placed too far tothe right of the true divide, and (b) placed too far to the left of the true divide. Inboth cases the precipitation and clear air peaks can be easily distinguished by eye.


(a) Doubly smoothed spectrum shown in 4.5(a).

(b) Doubly smoothed first derivative of the spectrum shown in (a).

Figure 4.6: The spectrum shown in Figure 4.5(a) doubly smoothed over a 1 ms−1

velocity interval (a) and the first derivative of this spectrum, also doubly smoothedover a 1 ms−1 velocity interval (b).


Problems are sometimes encountered when this interference sits at roughly the same

place as the precipitation peak on the opposite side of the clear air-peak, effectively

cancelling the precipitation peak on the folding of the spectrum. An example of

this situation is shown in Figure 4.7. This is another potential cause of a zero value

within a rainband.

Figure 4.7: An example showing the precipitation and clear air peaks, but also aninterference peak. This latter peak effectively masks the precipitation peak whenthe spectrum is folded. This results in the code assuming there is no precipitationpeak in the spectrum.

This problem also occurs in reverse, where a random fluctuation in the returned

spectrum is interpreted as a precipitation echo, e.g. Figure 4.8. Fluctuations such

as these, result in the non-zero values shown in Figure 4.1 between 13.0 and 13.2

UTC.

Finally, there are cases where it is just not possible to distinguish a rain peak in

precipitation conditions. An example of this is shown in Figure 4.9. This generally

occurs during convective conditions where there are both broad clear-air spectral

widths, and heavy rainfall, resulting in large rain peaks that merge with the clear-

air echo, making it impossible to separate the two.


Figure 4.8: An example of a random fluctuation in the returned radar spectrum,shown at -10 ms−1, which is misinterpreted as a precipitation echo by the automatedprocedure.

Figure 4.9: An example of a radar spectrum during convective precipitation con-ditions. The peaks cannot be clearly distinguished, and therefore no retrieval ispossible.


4.3 Manual Quality Control

The DSD retrieval code allows the user to manually control aspects of the procedure

such as:

• Force the calculation of a retrieval

• Force the “no rain” procedure

• Place the divide

• Specify the width and centre of the clear-air Gaussian

• Judge that the retrieval is impossible

Invoking these procedures corrects the problems described above in most cases.

The fit shown in Figure 4.2(b) can be corrected by specifying the width of the

clear-air peak, as shown in Figure 4.10.

Figure 4.10: The spectrum shown in Figure 4.2(b) with a more accurate clear airfit.

Cases like that shown in Figure 4.3 are corrected by specifying the location of

the dividing point. Since the DSD procedure first finds the divide, and then fits the

4.3. MANUAL QUALITY CONTROL 71

curve to the remaining spectrum, fixing the divide also provides a better clear-air

fit. This spectrum with a better fit is shown in Figure 4.11.

Figure 4.11: The spectra shown in figure 4.3 with a more accurate clear-air fit.

Where the clear-air peak has a rectangular shape, such as that shown in 4.4(b),

a good clear-air fit becomes more difficult for the obvious reason that a Gaussian

function poorly represents the spectral shape. A combination of moving the divide

and setting maximum or minimum spectral widths can sometimes result in a better

fit, but in general, these cases end up with either a slight under- or overestimate

of the true spectral width. Spectra such as these occur only at isolated times and

heights, so they do not present a major problem.

Incorrectly placed divide points between the clear-air and precipitation peaks,

such as those illustrated in Figure 4.5, are corrected easily by specifying the true

divide location by eye. The remaining cases discussed above are corrected by forcing

the code to either identify or not identify a precipitation peak, and specifying the

location of the divide as the case warrants.

The user can therefore correct bad retrievals by specifying different parameters,

and thus all bad points highlighted in the time-height cross-section shown in Figure

4.1 can be corrected by the methods described above. However, this requires the

user to look at the individual spectra of all suspect retrievals, and in this diagram


approximately 100 suspect spectra can be counted. This is approximately 10% of

data points in a single hour that need to be individually corrected, which becomes

time consuming, especially when rainfall events last for many hours.

Inspection of Figure 4.1 reveals poor retrievals occur mainly at individual times

and heights. That is, errors do not propagate either temporally or spatially. It

is possible to identify suspect retrievals by examining the average statistics as a

function of height. How this is accomplished is outlined below.

4.4 Quality Control Routine

The quality control routine (QCR) is designed to run on previously processed hour-

long DSD data blocks. The QCR separately examines the reflectivity, rainrate,

liquid water content and median drop diameter, to ensure all potential problem

retrievals are identified. Beginning with the first time stamp and lowest height,

the QCR works sequentially upwards through all heights before moving onto the

next time stamp, and examining each spectra individually. The first and last time

stamps in any rain period, and the first range gate are treated slightly differently to

the main body of data. This sometimes results in “edge effects” in the post QCR

data, requiring some manual editing. Here the process involved in treating the main

body of data is outlined.

Consider Figure 4.12, which represents 7 time stamps, with 6 range gates of

reflectivity data. The yellow pixel is the spectra under investigation. If this value is

non-zero, it is put through the thresholding procedure described below. If, however,

the value is found to be zero, the QCR must determine whether this is an incorrect

retrieval, or a true zero value. Since some coherence is expected in both time and

height, the QCR answers this question by looking at immediately adjacent pixels,

depicted in red in Figure 4.12.

The QCR assigns a value of 1 to these surrounding boxes if they contain non-zero

values, a value of 0 if not, and calculates a total. A total of 4 indicates the box in

question is surrounded by data points, and is most likely the result of a precipitation

peak which has not been detected and therefore a DSD retrieval not calculated. A

total of 0 indicates the box is entirely surrounded by “non rain” retrievals and is

4.4. QUALITY CONTROL ROUTINE 73

Figure 4.12: Schematic showing the spectrum under examination in yellow, and theadjacent pixels used as a comparison in red.

most likely correct.

The method used to discriminate between absent retrievals and true zero values

is depicted schematically in Figure 4.13. If the total calculated is strictly either 0 or

1, then the value is assumed to be a true zero. A total of 1 is included because both

the box immediately above the one in question, and in the next time stamp have

not been quality controlled, thus we are allowing for one of these boxes to have an

incorrect value. If the total is equal to 2, i.e. precisely half of the values are non-zero,

the QCR looks at the next two available heights beyond what it has already looked

at. If both of these values are non-zero the QCR assumes it is looking at an absent

retrieval and puts the box in question through the threshold procedure. However,

if one or both of these values are zero the QCR assumes the zero value is correct

and continues onto the next height. In the early stages of development of the QCR,

a problem was encountered whereby a value was miscalculated in a low range gate,

and the error was propagated upwards. This is why, when doing this secondary

check on the zero value, the QCR looks at upper heights rather than those below

which have been quality controlled. When the total is strictly greater than 2, the

value is deemed an absent retrieval and put through the threshold procedure.


Figure 4.13: Schematic flow chart of the zero value procedure used by the QCR.


4.4.1 Threshold procedure

In reflectivity time-height cross-sections, (e.g. Figure 4.1), bad retrievals are easily

identified either as “bulls eyes”, zero-values or “speckle”, that is non-zero values

surrounded by zeroes. When retrievals are good, successive range gates show a

level of coherence in both height and time. After analysis of many cross-sections,

a jump of 5 dBZ between range gates was used as a criterion to indicate a poor

retrieval. A value of 5 dBZ, or 3.16 on a linear scale, is a large enough value that

transition regions from stratiform to convective rainfall, or vertical gradients, are

generally accepted, but small enough that “bulls eyes” are identified. On occasion,

transitions from no rain to rainfall are identified as bad retrievals if the data does

not persist through all heights.

The thresholding procedure takes the reflectivity value, x, currently under inves-

tigation, and the reflectivity in the immediately preceding range gate, y. The ratios

x/y and y/x are then calculated, and if either exceed a value of 3.16, the current

reflectivity value, x, is flagged as a problematic retrieval. This ratio procedure was

extensively tested and found to correctly identify problematic retrievals under a wide

variety of meteorological conditions. Both ratios are included to take care of both

absent retrievals and “speckle”. The procedure for dealing with values which fail

the thresholding procedure is outlined in the next section.

Similarly, threshold values have been derived and tested for the rainrate, liquid

water content and median drop diameter. A differencing procedure was first trialed,

whereby an average difference between bad points and surrounding good ones was

calculated. While it was possible to find a threshold value that worked well for a

particular event, the value did not work consistently under varied meteorological

conditions. The ratio procedure is much more robust. This can be explained by

considering the rainrate in the event of light rainfall. “Bulls eyes” will always be

easy to identify, but “speckle” will be near zero values. If we choose a differencing

threshold small enough that these points are identified as bad data points, many

good data points are mistaken for bad points too. If, however, we choose a ratio

procedure these points will be flagged.


4.4.2 Threshold Failure

When retrievals fail the threshold procedure, they are flagged as bad points. These

are retrievals where the automatic algorithms have failed, and some level of manual

input is required. Since reflectivity, rainrate, liquid water content and median drop

diameter have been individually screened, there are four sets of flagged data points.

The QCR allows the user to look at these flagged points in three ways:

• Individually, e.g. flagged points in the reflectivity,

• Common points which were flagged in all four quantities, or

• The set of all flagged points from all four quantities

An example depicting the common points flagged in Figure 4.1 is shown in Figure

4.14. It is up to the user to deal with these flagged points as the desired outcome

warrants. When an accurate characterisation of the microphysics dictating rainfall is

the end goal, the user has no option but to manually inspect the total of all flagged

retrievals. The value of the QCR is not diminished in this case, as its ability to

accurately detect problematic retrievals still saves the user time. Without the QCR

the user must inspect all cross-sections to determine which retrievals require manual

attention. While this task seems simple in nature, consider the region between 13.4

and 13.6 UTC in Figure 4.1. Here, it must be manually determined whether the

precipitation echo can be detected through all range gates; that is, where does the

main rainband start? Since the QCR has been extensively tested and its accuracy

verified, the identified flagged points can be trusted, and the user can jump straight

to the “re-retrieval” process.

Since some coherence is expected in both time and height, to first order the QCR

can apply a “cosmetic fix” to cross-sections. This allows the user to gain an overview

of the rain event, and make a decision on whether the case is interesting and worthy

of further investigation, again saving time. Here, the QCR replaces flagged points

by the average of the two points immediately below the flag, that is, points that have

already been corrected. It must be emphasised that this is a method of data infilling

only, flagged points are not corrected through a re-calculation of the retrieval, but

are smoothed over. Extensive testing of this method revealed it returns a good


approximation to the value in question. This method will potentially fail in regions

such as the bright band or other gradients, and the user needs to be aware of this.

Figure 4.14: Representation of data values which were identified as problematicduring the QCR in the reflectivity, rainrate, liquid water content and median dropdiameter data in Figure 4.1.

Figure 4.15 shows four time series of reflectivity at various heights in Figure

4.1. These data provide a good overview of the strengths and limitations of the

automated quality control procedure. The black line shows the original profiler

retrieved reflectivity, the red line the reflectivity when each retrieval was corrected

manually, and the dotted blue line shows the reflectivity after operation of the QCR

algorithm on the original. In (a), the QCR has successfully removed the “speckle”

early on, but has introduced a zero-value at the 11th data point. In (b) the QCR

behaves perfectly and follows the manually retrieved reflectivity. In (c) the QCR

has very slightly overestimated the reflectivity at the 22nd point by about 1 dB.

While this is not a drastic result, is it not a desirable feature when accuracy in the

retrievals is required. Finally, (d) shows the QCR has missed a real data point at

18, and has overestimated the reflectivity several times.


Figure 4.15: A comparison of the profiler retrieved reflectivity to that correctedmanually, and by the QCR at four heights. The black line is the original reflectiv-ity, the red line the manual corrections, and the dotted blue line shows the QCRreflectivity. Panel (a) is at 0.9 km, (b) 1.3 km, (c) 2.1 km and (d) 2.5 km. The xaxis represents successive time stamps.


4.4.3 Quality Control of the Vertical Velocity

Vertical velocity data are far more likely to display vertical gradients than the rainfall

parameters. For this reason, quality control is carried out manually. A contour plot

of the raw spectra at each time stamp is produced, including the vertical velocity

and spectral width calculations. An example plot is shown in Figure 4.16, where

we see the rain peak (centred on -7 ms−1), the clear-air peak (centred on 0 ms−1)

and an interference peak (centred on 14 ms−1). The automatic routine has selected

the rain peak as the clear-air peak at 2.3 km. Clearly, the centre of the clear-air

peak should sit in the centre of the bright green region, and this can be corrected

manually. Any dubious vertical velocity estimates can be checked and corrected as

needed.

Figure 4.16: Contour plot of raw spectra at one time stamp. Three peaks arevisible, the precipitation peak centred on -7 ms−1, the clear air peak centred on 0ms−1, and an interference peak centred on 14 ms−1. Connected crosses show theprofiler calculated vertical velocity, while the plus signs represent spectral width.

When spectral widths are narrow, it becomes difficult to distinguish points on

these contour plots where the clear-air Gaussian has been fitted to a spike rather

than the peak, such as that shown in Figure 4.2(b). When the curve fitting routine

fits a “spike”, it produces a spectral width with a constant value in all cases. A


secondary quality control routine is implemented to check the spectral width data

for this value, and alert the user to spectral widths of this value when producing the

contour plot.

4.5 Quality Control in Practice

The end result of applying the QCR procedure to the data shown in Figure 4.1 is

shown in Figure 4.17, while the same data retrieved entirely manually is shown in

Figure 4.18.

Comparing Figures 4.17 and 4.18, we see that there are still two speckle points at

the start of the dataset processed by the QCR, and there are no retrievals in the time

stamp near 13.4 UTC. There are also a few other pixels which are missing retrievals.

Other than these, and certainly when comparing the main rain band between 13.7

and 14.0 UTC the quality control procedure has worked well. When compared to

Figure 4.1, it is seen the integrity of the rain structure has not changed. The quality

control routine has not smoothed out vertical or horizontal gradients. This makes

the QCR procedure exceptionally useful in cleaning up bad data points for further

use.

Incorrect retrievals contained in this thesis have been corrected manually. In the

case of convective cores, retrievals were performed entirely manually. In the far

more numerous stratiform regions, the QCR was used extensively. After raw radar

data had been processed by the DSD procedure, it was processed by the QCR.

The “cosmetically improved” reflectivity time-height cross-section was then used

to determine the location of the main rainband, as only time stamps with rainfall

extending through all range gates were analysed. The total set of flagged points,

as identified by the QCR were then re-retrieved manually. The vertical velocity

quality control procedure was then used to identify any remaining spectra with

“spike” retrievals, or poorly selected clear-air peaks like that shown in Figure 4.16.

4.5. QUALITY CONTROL IN PRACTICE 81

Figure 4.17: Reflectivity time-height cross-section for the data shown in 4.1, once ithas been processed by QCR.

Figure 4.18: Reflectivity time-height cross-section for the data shown in 4.1, whenall spectra have been retrieved manually.


4.6 Real-Time Analysis

As shown above, the quality control routine improves the display of processed data.

While this should never be taken as an accurate description of the rainfall, it does

provide a good first order approximation. This process therefore has potential for

real-time analysis.

The QCR utilises one time stamp immediately previous and post the one in ques-

tion. Thus, as radar data are acquired, it can be run through the DSD process, and

then through a segmented version of the QCR, allowing the user to watch the evo-

lution of the rainfield in close to real time. Consider the two movies accompanying

this thesis, titled “animation final.gif” and “qc animation final.gif”. Here we see

time-height cross-sections of profiler retrieved reflectivity, updated one time stamp

at a time. “animation final.gif” shows what the display would look like after raw

data is fed through the DSD code, while “qc animation final.gif” shows the display

having also been processed by the quality control procedure.

From the original movie, one might detect two areas of increased reflectivity near

18.2 and 18.8, but it is certainly not clear. The quality controlled movie on the other

hand suggests a convective band passed over the profiler, with some stratiform rain

following, which either did not pass directly over the profiler, or decayed. If the

user wished to investigate this event further, the quality controlled data suggest the

useful information lies in the time stamps where the convective band is obvious.

While these data are not typical, it demonstrates a potential application of the

QCR. An area of future research is automatic identification of the problem which

caused a flagged point. If a flagged point can be identified as say a poor divide

selection, a secondary routine can then be implemented to better select the divide

and re-calculate the retrieval. Since some coherency in spectra is expected with

height, analysing the spectral width and divide point in the spectra above and

below a flagged point could help identify the problem. Stratiform and convective

rainfall identification algorithms could also be put in place to help identify errors,

for example bad clear-air fits caused by spikes occur almost exclusively in stratiform

rainfall.

If flagged points can be “re-retrieved”, accurate descriptions of the DSD can

4.7. CONCLUSION 83

be obtained in near real time. This allows the profiler to function much like a

disdrometer, but with greater information gains. The profiler could be used to

identify the dominant microphysical process, which is important in determining the

rainfall reaching the ground. For example, if a significant amount of evaporation

occurs, less water will reach the surface. This is also important in the calculation

of Z-R relationships, as the rainfall rate at say 2.5 km, where the scanning radar

reflectivity is used to determine rainrate, may be different to that closer to the

surface. Real time analysis would also allow the user to identify interesting cases at

a glance, rather than searching through archived data.

4.7 Conclusion

In this chapter some of the problems relating to DSD retrievals have been discussed.

These include inadequate clear-air fits, absent retrievals, and poor divide selection.

The manual effort necessary to correct these problem retrievals are considered, and

the procedure designed to automatically identify problems is discussed. A “cos-

metic” fix to these flagged retrievals is described, and it is shown how this can

be useful, although should not be taken as anything more than an approximation.

Finally, the potential application to near real time analysis has been highlighted.

Chapter 5

Results from Darwin

Darwin experiences a well defined monsoon season, which accounts for around 90%

of the region’s annual rainfall. The monsoon cycles through both active and break

periods, defined by the direction of the low level winds [Drosdowsky , 1996]. Ac-

tive monsoon storms are typical of a maritime environment, while storms in the

break period are characteristic of coastal and continental areas. Active monsoon

storms tend to be more widespread, but exhibit generally weaker convection than

break storms. Break storms also have high lightning activity, and are often isolated,

forming on local circulations such as sea breezes. More detailed descriptions of the

Australian monsoon and corresponding cloud characteristics can be found in studies

such as Mapes and Houze [1992], Keenan and Carbone [1992], Cifelli and Rutledge

[1998] and May and Ballinger [2007].

The TWP-ICE campaign was designed to study tropical convection, and how

the characteristics of this convection affect the surrounding atmosphere. An At-

mospheric Radiation Measurement (ARM) remote field site (ACRF - Atmospheric

Cloud and Radiation Facility) has operated in Darwin since 2002, measuring the

surface radiation budget, surface meteorology and vertical cloud profiles [Mather

et al., 1998; Ackerman and Stokes, 2003]. The Australian Government Bureau of

Meteorology also operates permanent instrumentation for both research and oper-

ational use in the Darwin area. Additional ground-based instrumentation deployed

for the campaign included a lightning detection network, an Atmospheric Emitted

Radiance Interferometer (AERI), multi-channel microwave instruments, and wind

and cloud profiling radars. Radiosondes were also launched at 3 hourly intervals

86 CHAPTER 5. RESULTS FROM DARWIN

from five sites surrounding Darwin, providing data on a similar resolution to a

GCM grid box. One of these launch sites was aboard the research vessel Southern

Surveyor, which also carried its own set of instrumentation. Finally, to compliment

ground based observations, 5 research aircraft flew varied patterns through different

storm systems throughout the campaign. A complete description of the TWP-ICE

scientific objectives and instrumentation can be found in May et al. [2008].

The Darwin monsoon season experiences substantial intraseasonal variability.

The TWP-ICE IOP sampled four distinct weather regimes, as a large amplitude

Madden-Julian oscillation (MJO) moved through the region [May et al., 2008]. An

active monsoon period began on January 13, while more suppressed conditions were

experienced from January 26. This was followed by 3 days of clear skies, before

a typical monsoon break began on February 6. Figure 5.1 shows the accumulated

rainfall at Darwin airport for the months of January and February. Here, the active

and suppressed monsoon differences are obvious, with comparatively little rainfall

falling in the suppressed region. Note also the large increase in rainfall on January

23. Late on this day, as the monsoon trough was receding to the north, a large

MCS1 developed, which moved to the west, and developed into an intense tropical

low.

Many profiler studies of vertical velocity and DSD characteristics have previously

been carried out in the Darwin area [Cifelli and Rutledge, 1994; May and Rajopad-

hyaya, 1996, 1999; Rajopadhyaya et al., 1998; Cifelli et al., 2000; May et al., 2001,

2002; Williams and Gage, 2009]. Profilers used in these studies have typically had

their first useable range gate near 1.5 km, with a vertical resolution ranging from

500 m to 1 km. As stated in table 2.2, the BL radar used in the current study

can reliably sample down to 800 m, with a vertical resolution of 100 m, allowing

examination of precipitation to lower heights. The caveat to this increased range

sampling is that the radar spectra tend to have broader spectral widths, due to the

broader beam.

Each event which passed over the profiler during January and February 2006 was

retrieved, quality controlled, and analysed. Particular attention was given to storm

evolution in time and height, as well as changes in the microphysical processes affect-

ing surface rainfall. Understanding the evolution of precipitation below the freezing

1mesoscale convective systems are defined in Appendix B

87

Fig

ure

5.1:

TW

P-I

CE

accu

mula

ted

rain

fall

over

Dar

win

airp

ort.


level is important for modelling, and quantitative precipitation estimation. Events

were first placed in morphological context by examining consecutive CPOL PPI

displays, and RHI scans were inspected to determine echo-top height and vertical

structure, e.g. was there evidence of a bright band. Profiler cross-sections of reflec-

tivity, rainrate, liquid water content, median drop diameter and vertical velocity,

in conjunction with the RHI, were used to classify convective, stratiform or tran-

sitional segments of the storm. Average profiles in time were then taken through

these segments, and examined for evidence of a dominant microphysical process. It

is not possible to discuss each event in as much detail as it was analysed within this

Chapter. One event from each monsoon period (active and break) is presented, and

remaining events are abstracted into tables to provide an overview. The differences

in period trends are then compared and contrasted.

5.1 Monsoon Case Study

The case study chosen from the active monsoon period occurred on 22 January,

2006. This event is of interest as it was not a typical squall line, rather the event

comprised three parallel convective lines, separated by the order of just 10s of kms.

The lines were oriented north-east to south-west, and moved perpendicular to the

shear to the north-west. The active convection decayed into stratiform rainfall near

the profiler site in all three instances, thus data from this day allow the comparison

of three new stratiform rainbands. The storm morphology, followed by the vertical

structure, is discussed before considering the dominant microphysical processes.

The monsoon trough was located to the north-east of the profiler site, shown

in Figure 5.2. Also shown in this Figure is the remarkably clear rotation about

the trough line. Around 0830, two convective cells on the eastern boundary of the

CPOL display, one located near the coast, the other well inland, began to elongate,

eventually forming the second of the three lines to pass over the profiler. Earlier on

this day, several smaller lines with a similar orientation and direction had moved

towards the north-west. Figure 5.3(a) shows the CPOL PPI at 0830, where these

smaller lines are seen approaching the western boundary (marked by arrows), and

the cells elongating into the second line on the eastern boundary (marked by the

red oval).

5.1. MONSOON CASE STUDY 89

Figure 5.2: MSLP analysis 22 January 2006. The monsoon trough is the black linerunning through the middle of the plot. Note the remarkably clear rotation of thewinds about this line.

As this second line approached the profiler, convective elements formed a smaller

line ahead of it. This smaller line was the first line sampled by the profiler, and

which decayed as it passed over. This is therefore the newest stratiform rainfall

sampled on this day. A much larger mature system appeared at the eastern edge of

the CPOL display around 1200, which was the third line to pass over the profiler.

This system consisted of active cells at the leading edge, and was followed by a large

stratiform rain area. Figure 5.3(b) shows these three lines (marked with red lines).

The first band passed over the profiler around this time (∼1130).

The second line reached the profiler around 1340, and was entirely stratiform

rainfall by this time. This line thus represents more mature stratiform rain that

the previous line. The third line reached the profiler around 1630. The portion

of the line which passed over the profiler had largely decayed, although convective

elements were present in other parts of the line, particularly at the southern end, as

shown in Figure 5.3(c). The entire sequence of events from this day can be viewed

in the attached movie “January 22 ppi.gif”. The rotation about the trough line is

clearly seen in this movie.


(a) CPOL PPI, 22 January 2006, 0830 UTC.

(b) CPOL PPI, 22 January 2006, 1120 UTC.

(c) CPOL PPI, 22 January 2006, 1610 UTC.

Figure 5.3: CPOL PPI scans at (a) 0830 (b) 1120 and (c) 1610 UTC, 22 January2006. The profiler location is marked with a �.


To analyse the vertical structure of this stratiform rainfall, the profiler-retrieved

time-height cross-section of reflectivity due to precipitation, and the CPOL RHI

over the profiler site are examined. The plots, shown in Figure 5.4, demonstrate

excellent agreement in the timing and magnitude of the three rainbands described

above. Rainfall is clearly stratiform as reflectivities do not exceed 40 dBZ and the

bright band is clearly evident in Figure 5.4 at an altitude of 5 km. Also evident in

Figure 5.4 are small reflectivity regions of about 15 dBZ, located between the bands

of heavier rainfall. Reflectivities of this magnitude indicate drizzle, with dropsizes

between 0.1 and 0.25 mm in diameter. As discussed in section 3.1.6, the minimum

observable diameter for the profiler is effectively 1 mm, and thus these drops are too

small for the profiler to detect. This sensitivity of the profiler indicates a minimum

detectable reflectivity near 20 dBZ.

The bright band is not as clear in the first band as it is in either the second or

third bands. This is because this band is the newest stratiform rain, and the line

decayed as it reached the profiler. Also note the increase in echo-top height in the

second and third bands, due to the origin of the different storm systems, with more

vigorous convection in the second and third bands.

Figure 5.5 shows the CPOL differential reflectivity over the profiler during this

event. The bright band signature, at 5 km altitude, is clearly evident, as are the

larger drops in the three rainbands sampled by the profiler. It is unclear what

the region of increased differential reflectivity is, near 8 km at about 1200 UTC.

Differential reflectivities around 2.8 dBZ can indicate either large raindrops, high

density ice crystals, or wet melting snow [Doviak and Zrnic, 1993]. Raindrops do

not exist at 8 km altitude, leaving dry ice or melting snow as the likely causes. The

reflectivity at the same time is no greater than 20 dB, which does not indicate either

case more likely. Given this region of increased differential reflectivity is near the

echo top height, it is also possible this is a side lobe effect. This last solution seems

most likely. The bright band is enhanced after 1500 UTC, indicating higher ice

concentrations. Values near 1 dB above the bright band from 1400 UTC onwards

are too high to indicate ice crystals, and we conclude that snow is also falling in

this region. The differential reflectivity between the rainbands of approximately 0.5

dB, is a further indication of drizzle, that is, drops too small to be detected by the

profiler. Calculated via a D0 − ZDR relationship, a differential reflectivity of this


(a) CPOL RHI reflectivity over the profiler site.

(b) VHF reflectivity cross-section.

Figure 5.4: CPOL RHI reflectivity over the profiler site (a) and profiler-retrievedtime-height reflectivity cross-section (b), 22 January 2006. Scales on the right arein dBZ. Note the difference in height scales.


magnitude corresponds to a median drop diameter only slightly greater than 1 mm

[Williams and May , 2008].

Figure 5.5: CPOL differential reflectivity, 22 January 2006. Scale on the right is indBZ.

Figures 5.6 and 5.7 show the profiler-retrieved cross-sections of rainrate, liquid

water content, median drop diameter, and a time series of all profiler-retrieved

parameters through 2 km altitude. It is apparent the first part of the first rainband

had much heavier rainfall than bands 2 or 3, as this band corresponds to recently

decayed convection. This is discussed further when considering average profiles.

To study the effect of these changing conditions above the freezing level on the

resultant stratiform rain, averaged parameters from the profiler are examined. When

calculating average parameters, only echoes which extend through all range gates

are considered, as this avoids biasing with zero values. Prior to averaging, data

are also plotted as a histogram and outliers rejected. While the quality control

routine described in Chapter 4, and subsequent re-processing, ensures there are no

bad retrievals, real statistical fluctuations imply some outliers remain in the sample,

which can bias the average. Rejecting outliers in this way ensures the mean and

median of the sample are similar. Data points which could not be retrieved are

also interpolated over in this routine. Average profiles through the second and third


(a) Profiler-retrieved rainrate.

(b) Profiler-retrieved liquid water content.

Figure 5.6: Profiler retrieved rainrate measured in mm hr−1 (a) and liquid watercontent measured in gm−3 (b), 22 January 2006.


(a) Profiler-retrieved median drop diameter.

(b) Time series of profiler-retrieved parameters at 2 km.

Figure 5.7: Profiler-retrieved median drop diameter measured in mm (a) and a timeseries of profiler-retrieved parameters at 2 km altitude (b), 22 January 2006.


rainbands are first compared.

Figure 5.8 shows weak downdrafts, characteristic of stratiform rainfall, but while

the magnitude is relatively constant with height in the second rainband, it weakens

with descent in the third. The third band represents the most mature storm to pass

over the profiler on this day, therefore this weakening is most likely related to storm

decay.

Heating profiles for these two rainbands are shown in Figure 5.9. In the second

rainband, the sensible heating rate Q1, shown by the red curve, indicates a steady

heating of the atmosphere. For the third rainband, Q1 decreases with height, fol-

lowing the vertical velocity. The heating due to precipitation Qp is essentially a

net of zero throughout the range gates shown here in both rainbands. This is in

contrast to previous studies, where a balance between Q1 and Qp was found [May

and Rajopadhyaya, 1996]. In this context, the term balance refers to Q1 and Qp

values being equal but opposite.

Reflectivities, shown in Figure 5.10, display little variation with height, but are

approximately 1 dB weaker in the third band, indicating a decaying system. The

rainrate and liquid water contents (Figures 5.11 and 5.12) show little change with

height, and are very similar to each other, indicating these two rainbands were very

similar in structure and microphysical process. The similarity in the median drop

diameters, shown in Figure 5.13, further supports this argument. Recall that all

median drop diameters presented in this thesis have been corrected via the gamma

mapping function discussed in section 3.1.6. The implications of these average pro-

files on the microphysics is now discussed.

5.1.1 Microphysics

The liquid water content average profile on 22 January 2006 does not change with

height, and therefore evaporation cannot be occurring. This is also consistent with

the average heating profile, where cooling is expected in evaporation. The consis-

tency of the median drop diameter with height indicates collisional processes and

drop break-up are in balance. These averaged profiles in fact suggest there is no

dominant microphysical process occurring in these rainbands. This implies that,

drops are either falling to the ground without interacting, either with other drops


(a) Second rainband.

(b) Third rainband.

Figure 5.8: Averaged vertical velocities through (a) the second rainband and (b)the third rainband on 22 January 2006. Horizontal lines represent 95% standarddeviation confidence intervals calculated using t-statistics.



(b) Third rainband.

Figure 5.9: Heating rates through (a) the second rainband and (b) the third rainbandon 22 January 2006. The sensible heating rate is shown in red, the evaporative inblue.



(b) Third rainband.

Figure 5.10: Averaged reflectivitys through (a) the second rainband and (b) the thirdrainband on 22 January 2006. Horizontal lines represent 95% standard deviationconfidence intervals calculated using t-statistics.



(b) Third rainband.

Figure 5.11: Averaged rainrates through (a) the second rainband and (b) the thirdrainband on 22 January 2006. Horizontal lines represent 95% standard deviationconfidence intervals calculated using t-statistics.



(b) Third rainband.

Figure 5.12: Averaged liquid water contents through (a) the second rainband and(b) the third rainband on 22 January 2006. Horizontal lines represent 95% standarddeviation confidence intervals calculated using t-statistics.



(b) Third rainband.

Figure 5.13: Averaged median drop diameters through (a) the second rainband and(b) the third rainband on 22 January 2006. Horizontal lines represent 95% standarddeviation confidence intervals calculated using t-statistics.


or the surrounding atmosphere, or that the microphysical processes are in equilib-

rium. In an equilibrium distribution, the rate at which drops coalesce is exactly

balanced by the rate of drop break up, exhibiting no change in the median drop

diameter. Probability distribution functions (PDFs) of the median drop diameter

through these rainbands are used to investigate further.

Figure 5.14 shows the distribution of D0 with height during band 2. Each plot

represents three height levels, with the middle value listed on the far right. Note

that the number density scale, listed on the far left on the bottom plot, is consistent

through all heights. The plot shows some evolution of the median drop diameters,

but it is clear the average value is consistent with height. Figure 5.15, showing the

PDF through band 3, displays less variation, i.e. the shape of the PDF is more

consistent with height. Analysis of these two rainbands therefore suggest the micro-

physical processes may be in equilibrium. The notion of equilibrium distributions is

further discussed in Chapter 7.

The heaviest rainfall on 22 January 2006 fell in the first part of the first band

to pass over the profiler (see Figure 5.4. The rainfall parameters associated with

the second part of this first band, that is after 1200 UTC, displayed very similar

characteristics to bands 2 and 3 described above (plots not shown). It is therefore

appropriate to average through the latter part of this first band, and bands 2 and 3,

to compare with results obtained in the first part of band 1. The region of increased

rainfall in band 1 is termed “heavy”, while the rest of the rain that fell over the

profiler on this day is termed “moderate”.

Figure 5.16 shows the average vertical velocity profiles, and while the heavy region

is more variable than the moderate region, it also exhibits a weak downdraft. Note

that the heavy region is an average through only 5 time stamps (∼10 minutes),

while the moderate average is through 56 time stamps (∼112 minutes), explaining

the broader confidence limits in the heavy region. The heating profiles through these

rainbands are shown in Figure 5.17. In the heavy region, the sensible heating rate

shows large values where the vertical velocity was greatest, and also large positive

values of the heating rate due to precipitation. In the moderate region, values are

more constant, with little change in Qp and a net heating in Q1.

Average profiles of reflectivity, rainrate, liquid water content and median drop

diameter (Figures 5.18-5.21) show little variation with height in the moderate region.


Figure 5.14: Median drop diameter PDF through the second rainband, 22 January2006. The number density scale listed on the far left is consistent with height.


Figure 5.15: Median drop diameter PDF through the third rainband, January 222006. The number density scale listed on the far left is consistent with height.


(a) Heavy region.

(b) Moderate stratiform.

Figure 5.16: Averaged vertical velocities through (a) the heavy region and (b) themoderate stratiform region on 22 January 2006. Horizontal lines represent 95%standard deviation confidence intervals calculated from t-statistics.


(a) Heavy region.


Figure 5.17: Heating rates through (a) the heavy region and (b) the moderatestratiform region on 22 January 2006. Note the x-axis scales are different. Thesensible heating rate is shown in red, the evaporative in blue.


In the heavy region, reflectivity (Figure 5.18) is approximately 3.5 dBZ larger than

the moderate region, with a slight increase in the lower range gates. The rainrate

shows little variation in the heavy region, although it perhaps decreases slightly in

the lower range gates, as shown in Figure 5.19. Figure 5.20, depicting the liquid

water content, shows more variation with height, but does not show a particular

increasing or decreasing trend. The median drop diameter is very similar, showing

more variation with height, but oscillating about a constant value.

The median drop diameter PDFs, shown in Figures 5.22 and 5.23, show some

evolution with height, but it is clear the average value is consistent. Analysis of

both the heavy rainband and the rest of the stratiform rainfall that fell over the

profiler on January 22 indicate the observation of equilibrium distributions. The

notion of equilibrium distributions is further discussed in Chapter 7.


(a) Heavy region.


Figure 5.18: Averaged reflectivities through (a) the heavy region and (b) the mod-erate stratiform region on 22 January 2006. Horizontal lines represent 95% standarddeviation confidence intervals calculated from t-statistics.


(a) Heavy region.


Figure 5.19: Averaged rainrates through (a) the heavy region and (b) the moderatestratiform region on 22 January 2006. Horizontal lines represent 95% standarddeviation confidence intervals calculated from t-statistics.


(a) Heavy region.


Figure 5.20: Averaged liquid water contents through (a) the heavy region and (b)the moderate stratiform region on 22 January 2006. Horizontal lines represent 95%standard deviation confidence intervals calculated from t-statistics.


(a) Heavy region.


Figure 5.21: Averaged median drop diameters through (a) the heavy region and (b)the moderate stratiform region on 22 January 2006. Horizontal lines represent 95%standard deviation confidence intervals calculated from t-statistics.


Figure 5.22: Median drop diameter PDF through the heavy region, 22 January 2006.The number density scale listed on the far left is consistent with height.


Figure 5.23: Median drop diameter probability distribution function through themoderate region, 22 January 2006. The number density scale listed on the far leftis consistent with height.

5.2. MONSOON RAINFALL 115

5.2 Monsoon Rainfall

Four storms were analysed in the active monsoon, as summarised in Table 5.1. Jan-

uary 5 was strictly in the build-up by kinematic definitions of the monsoon [Dros-

dowsky , 1996], but the local storm characteristics were more like typical monsoon

conditions so are included here for comparison. As discussed for the 22 January

case study above, each storm was examined in detail. Storms were first placed in

morphological context, then profiler cross-sections analysed. Based on this analysis,

a classification of each storm is provided in Table 5.1. Note that this classification

is based on the storm sampled by the profiler. Convective, transitional and strat-

iform periods, as identified from the cross-sections, were further analysed through

averaged profiles of the rainfall integral parameters. Particular attention was paid

to the evolution of the microphysics in both time and height. It is not possible

to discuss each storm in as much detail as it was analysed, thus results from the

monsoon period are presented in summary form only.

Date Storm Type05/01/06 Squall line with trailing stratiform precipitation19-20/01/06 Squall line with trailing stratiform precipitation22/01/06 Stratiform rainfall23/01/06 Squall line with trailing stratiform precipitation

Table 5.1: Storms passing over the profiler in the build-up/monsoon period of TWP-ICE.

A dominant microphysical process (if there was evidence of one) was assigned to

each of the storms in this build-up/monsoon period, is listed in Table 5.2. Also in this

table are the derived coefficients for A and b in a Z −R relationship. It is apparent

that convective events are characterised by higher values of A and smaller values of

b, when compared to stratiform events. Z − R relationships are discussed in more

detail in section 7.3.2 The table also shows that evaporation is the dominant process

in the monsoon period in the lowest part of the atmosphere. Results presented here

are discussed in further detail in Chapter 7, and are compared and contrasted to

both results from the break period and from Adelaide.

Table 5.3 lists the average properties of each storm. Values in this table are

calculated by analysis of individual spectra, not time stamps or range gates, and is

intended to provide a broad overview only. Overall, the values shown in Table 5.3

are as would be expected for convective versus stratiform rain events, in the sense


Date Dominant Process A b

Build-upstratiform05/01/06 Evaporation 820 0.90

Build-upconvective05/01/06 Evaporation 1200 0.92

Monsoonstratiform19-20/01/06 Evaporation 290 1.1222/01/06 Equilibrium-like 260 1.1423/01/06 Collision-coalescence 1170 0.90

Monsoonconvective19-20/01/06 Evaporation 868.54 0.9423/01/06 (1) Evaporation 1200.00 0.9123/01/06 (2) None 1200.00 0.94

Table 5.2: Dominant microphysical processes and derived coefficients A and b ina Z − R relationship for storms passing over the profiler in the build-up/monsoonperiod of TWP-ICE. For the 23 January event, (1) and (2) represent two separateconvective cores.

that average reflectivitys, rainrates and spectral widths are larger in the convective

than in the stratiform regions.


Date

Tim

eSta

mps

Max

ZA

vg

ZM

ax

RR

Avg

RR

Max

+ve

wM

ax

-ve

wA

vg

wA

vg

SW

dB

ZdB

Zm

mhr−

1m

mhr−

1m

s−1

ms−

1m

s−1

ms−

1

Build-u

pst

rati

form

05/0

1/06

4732

.29

27.5

63.

861.

211.

523.

38-0

.21

0.72

Build-u

pco

nvect

ive

05/0

1/06

1457

.08

45.7

721

0.58

74.0

95.

135.

31-1

.40

1.32

Monso

on

stra

tifo

rm19

-20/

01/0

645

37.6

331

.31

11.6

03.

141.

091.

110.

100.

6522

/01/

0662

38.0

030

.56

13.0

32.

661.

071.

82-0

.19

0.34

23/0

1/06

115

40.2

032

.22

15.4

42.

991.

822.

36-0

.23

0.60

Monso

on

convect

ive

19-2

0/01

/06

1356

.20

43.9

638

2.19

66.4

09.

253.

690.

741.

2623

/01/

06(1

)14

56.6

149

.87

245.

7811

8.85

11.3

86.

870.

031.

5023

/01/

06(2

)6

47.4

742

.79

72.8

131

.91

0.20

2.89

-1.2

50.

78

Tab

le5.

3:A

vera

gest

atis

tics

ofst

orm

sin

the

build-u

p/m

onso

onper

iod,Jan

uar

y20

06.

Her

e,Z

repre

sents

reflec

tivity,

RR

rain

rate

,w

vert

ical

velo

city

and

SW

clea

r-ai

rsp

ectr

alw

idth

.


Similar “instantaneous” values for the median drop diameter are shown in Table

5.4, which display little change between stratiform and convective events. Where

there is a clear bright band signature in stratiform rainfall, large drops are expected

as large aggregates of ice crystals melt [Cifelli et al., 2000]. Similarity in the median

drop diameter is therefore not surprising in the active monsoon, where many hours

of stratiform rainfall with an associated bright band signature were sampled by the

profiler.

Date Min D0 Max D0 Avg D0 SDmm mm mm

Build-upstratiform05/01/06 0.59 1.96 1.18 0.26

Build-up con-vective05/01/06 0.66 2.10 1.23 0.23

Monsoonstratiform19-20/01/06 0.56 2.32 1.21 0.3022/01/06 0.63 2.12 1.29 0.2623/01/06 0.57 2.31 1.29 0.33

Monsoonconvective19-20/01/06 0.59 2.11 1.17 0.2923/01/06 (1) 0.59 2.09 1.24 0.2623/01/06 (2) 0.76 2.21 1.41 0.30

Table 5.4: Maximum, minimum, average and standard deviation (SD) values of themedian drop diameter from storms in the build-up/monsoon period, January 2006.

Recently, Bringi et al. [2009] published CPOL-derived D0 distributions for the

events on 5 and 19-20 January. Comparisons to their results for the build-up and

monsoon period are shown in Figures 5.24 and 5.25, where their results have been

redrawn. In the case of stratiform rainfall, both the build-up and active monsoon

agree well. This is particularly true in the build-up, where the shape of the distri-

bution measured by the two radars is very similar.

Convective cases do not agree as well as their stratiform counterparts, where the

mode of the profiler retrieved D0 is approximately 0.5 mm lower than that calculated

by CPOL. However, it must be remembered, the CPOL-derived D0 estimates are

from a low-level PPI scan, while the profiler samples only the portion of the storm


(a) Stratiform.

(b) Convective.

Figure 5.24: Comparison of profiler-retrieved median drop diameters in the build-upto those published by Bringi et al. [2009] using CPOL data (plots redrawn).


(a) Stratiform.

(b) Convective.

Figure 5.25: Comparison of profiler-retrieved median drop diameters in the monsoonto those published by Bringi et al. [2009] using CPOL data (plots redrawn).

5.3. BREAK CASE STUDY 121

which passes overhead. The profiler therefore most likely did not sample the most

vigorous convection, and hence the biggest drops, accounting for the differences

observed in these plots. It should also be noted that the CPOL calculation includes

thousands more sample points than the profiler, but the profiler is the more direct

measurement. This result highlights the relative advantages and disadvantages of

both radars. While CPOL can sample the entire storm at a particular elevation,

the profiler observes the fine detail of the part of the storm that passes overhead.

Median drop diameter differences between monsoon periods and latitudinal location

are discussed further in Chapter 7.

5.3 Break Case Study

In contrast to the widespread nature of storms in the monsoon, the majority of

storms which passed over the profiler in the break were isolated convective cells.

There is one example of a tropical squall line with trailing stratiform precipitation,

which occurred on 18 February 2006. This line appeared at the eastern edge of

the CPOL view around 1130, oriented in a north-east to south-west direction, and

moving perpendicular to the shear towards the north-west. The leading line moved

over the profiler site around 1400, with the trailing stratiform region stretching back

to the eastern bound of the CPOL view, shown in Figure 5.26. By this stage, the

leading line was in a very mature to decaying stage of its lifecycle. One large cell split

from the line and moved in a westwards direction, while the remainder of the line

continued to move towards the north-west. The split cell strengthened, and smaller

cells branched out to the north forming a new squall line oriented north-south and

moving to the west. The remnants of the original line continued to move to the

north-west, until decaying entirely into stratiform rainfall. The new convective line

disappeared from the western edge of the CPOL view around 1700, and the last of

the stratiform rainfall passed over the profiler site around 1930. The entire sequence

of events can be viewed in the attached movie “February 18 ppi.gif”.

The vertical structure of this storm is revealed in the CPOL RHI above the profiler

site, along with the profiler-retrieved reflectivity time-height cross-section, shown in

Figure 5.27. The convective line was classified as being in a mature to decaying

stage of its lifecycle from inspection of the PPI display. This is confirmed in Figure


Figure 5.26: PPI from CPOL showing the 18 February tropical squall line as itintersects the profiler, marked with a �.

5.27 where the echo top height of the intense convection is shallow compared to

other storms in the break period. Further, the high reflectivities (i.e. > 40 dBZ)

do not extend downwards through all range gates in either the CPOL or profiler

displays. The timing and magnitude of the convective, transitional and stratiform

rain regions agree well, and the bright band is clearly evident in the CPOL display.

The differential reflectivity RHI for this storm is shown in Figure 5.28. Values

near 1 dBZ between 1400 and 1600 UTC above the freezing level are too large

to indicate ice, and more likely indicate snow. The “fall streak” with a higher

differential reflectivity beginning near the echo top at 1600 UTC then represents

falling snow.


water content, median drop diameter, and a time series of these parameters at 2

km altitude, for the same time interval shown in Figure 5.27. Figure 5.29 shows the

rainrate and liquid water contents peak in the convective region as expected, and

are also stronger in the bright band region than in the transition or decaying stages

of the stratiform region. Figure 5.30 also depicts this in the time series. The largest


(a) CPOL RHI over the profiler site.

(b) VHF reflectivity time-height cross-section.

Figure 5.27: (a) RHI reflectivity from CPOL, showing a leading convective line,transition region and stratiform rainfall on February 18 2006. The profiler-retrievedreflectivity time-height cross-section for the same period is shown in (b). Scales onthe right are in dBZ.


Figure 5.28: CPOL differential reflectivity, 18 February 2006. Scale on right in dBZ.

median drop diameters are seen in the stratiform region, as is clearly seen in Figure

5.30.

5.3.1 Microphysics

Similar to 22 January, vertically averaged profiles are used to deduce microphysical

processes. In this case, the convective region is compared with the stratiform. Figure

5.31 shows the vertical velocity in both regions. A downdraft is shown in both

regions, but with a larger magnitude in the convective region as expected. Both

regions show the same “balloon-like” shape, with the strongest downdraft occurring

around 2 km. Average heating profiles are shown in Figure 5.32. In the convective

region, the approximations made in calculating these values are not met, and the

heating rate due to precipitation is overestimated. In the stratiform region, the

balance between the vertical velocity and evaporation is clearly seen. This is in

agreement with May and Rajopadhyaya [1996].

Figure 5.33 shows reflectivity decreasing with height in both regions. The con-




Figure 5.29: Profiler-retrieved rainrate measured in mm hr−1 (a) and liquid watercontent measured in gm−3 (b), 18 February 2006.



(b) Time series of profiler-retrieved parameters at 2 km altitude.

Figure 5.30: Profiler-retrieved median drop diameter measured in mm (a) and atime series of profiler-derived parameters at 2 km altitude (b), 18 February 2006.


(a) Convective

(b) Stratiform

Figure 5.31: Average vertical velocity in the convective (a) and stratiform (b) re-gions, 18 February 2006. Horizontal bars indicate 95% standard deviation confidenceintervals calculated from t-statistics.


(a) Convective.

(b) Stratiform.

Figure 5.32: Heating rate in the convective (a) and stratiform (b) regions, 18 Febru-ary 2006. Note the scales are different in both plots. The sensible heating rate isshown in red, the evaporative in blue.


vective region is somewhat misleading, in that the vertical core of high reflectivity

did not extend through all range gates. Regardless, above 2 km the reflectivity is

still showing a decreasing trend. The rainrate is somewhat more variable, shown in

Figure 5.34, but shows an overall trend of decreasing with height in both regions.

Similarly, the liquid water content is variable, with an overall decreasing trend, as

shown in Figure 5.35.

Figure 5.36 reveals the median dropsize is larger overall in the stratiform region

than the convective. While this is somewhat surprising, it must be remembered the

convective region is decaying, and can be considered as transitioning to stratiform

rainfall. A bright band signature is also present in the stratiform region, indicating

large aggregates of ice particles are melting, resulting in large drops. The median

drop diameter in the convective region shows a slight decrease with height. In the

stratiform region, an initially fairly constant D0 in the upper range gates begins to

increase from around 2200 m, down to around 1300 m, where a decreasing trend is

seen with decreasing height.

The PDFs shown in Figure 5.37 of the convective region reveal D0s concentrated

at the small drop end of the distribution. Further, the number of larger drops is seen

to decrease with decreasing height. Distributions such as this were commonly found

in transition regions between convective and stratiform regions in Darwin. This

adds further support to the argument that the convection was decaying. The PDFs

in the stratiform region, Figure 5.38, show a steady distribution with decreasing

height down to around 2100 m, with larger D0 seen beyond this level down to the

ground.

These results show that both evaporation and break-up were occurring in the

convective region. The liquid water content is generally decreasing with height,

which implies evaporation is occurring. Reflectivity is also generally decreasing with

height, indicating either the loss of a large number of small drops, or comparatively

few large drops, due to the D6 dependence. Since D0 also shows a decreasing

trend, the largest drops must be breaking up. Drop break-up is evident in Figure

5.37, where some larger D0 are seen in the upper levels, but a distinct preference

for D0 between 0.8 and 1.2 mm is seen near the surface. Similar PDFs, showing

the majority of D0 between 0.8 and 1.2 mm were found in all transition regions

analysed, adding further support to the argument this convective core was decaying

as it passed over the profiler. Dominant microphysical processes were generally not


(a) Convective.

(b) Stratiform.

Figure 5.33: Average reflectivity in the convective (a) and stratiform (b) regions, 18February 2006. Horizontal bars indicate 95% standard deviation confidence intervalscalculated from t-statistics.


(a) Convective.

(b) Stratiform.

Figure 5.34: Average rainrate in the convective (a) and stratiform (b) regions, 18February 2006. Horizontal bars indicate 95% standard deviation confidence intervalscalculated from t-statistics.


(a) Convective.

(b) Stratiform.

Figure 5.35: Average liquid water contents in the convective (a) and stratiform(b) regions, 18 February 2006. Horizontal bars indicate 95% standard deviationconfidence intervals calculated from t-statistics. Note that the horizontal scale isdifferent in the top and bottom plots.


(a) Convective.

(b) Stratiform.

Figure 5.36: Average median drop diameters in the convective (a) and stratiform(b) regions, 18 February 2006. Horizontal bars indicate 95% standard deviationconfidence intervals calculated from t-statistics. Note that the horizontal scale isdifferent in the top and bottom plots.


Figure 5.37: PDF of the median drop diameter in the convective core, 18 February2006.


Figure 5.38: PDF of the median drop diameter in the stratiform, 18 February 2006.


discernible in other transition regions analysed, indicating that transition regions

are true to their name, and are transitioning to a new rainfall regime.

The microphysics in the stratiform region on 18 January show similar decreasing

trends of reflectivity, rainrate and liquid water content with height. The median

drop diameter shows a slight decrease above 2 km, indicating similar processes to

the convective region, where both evaporation and drop break-up are occurring.

Below 2 km, the median drop diameter shows an increasing trend.

5.4 Break Rainfall

Five storms were analysed during the break period, two of these occurring on one

day. As with the monsoon storms, a classification of each storm type is given in Table

5.5. As expected in the break period, there is more convective activity occurring in

isolation as “convective bursts”, when Tables 5.1 and 5.5 are compared. Like the

active monsoon, break storms were analysed in detail that cannot be presented here.

Results are summarised into tabular form.

Date Storm Type07/02/06 Convective burst with small region stratiform precipitation10/02/06 Stratiform precipitation16/02/06 Convective burst18/02/06 (1) Convective burst18/02/06 (2) Leading convective line with trailing stratiform precipitation

Table 5.5: Storms passing over the profiler in the break period of TWP-ICE.

Table 5.6 lists the dominant microphysical process (if there was evidence of one),

deduced from analysis of the average profiles. This table also lists derived coefficients

for A and b in a Z-R relationship. Evaporation is seen to be almost exclusively

the dominant process controlling the D0 evolution below the melting layer in the

break period. Values for A and b seem similar to those derived in the monsoon in

convection, indicating the possibility of deriving a definitive tropical convection Z-

R relationship. Stratiform coefficients are somewhat more varied. Z-R relationship

values are discussed in more detail in Chapter 7.

Table 5.7 lists the average properties of each storm. Like the active monsoon

equivalent table, values in this table are calculated through analysis of individual

5.4. BREAK RAINFALL 137

Date Dominant Process A b

Break stratiform07/02/06 Evaporation 1110 0.9010/02/06 Evaporation 720 0.9018/02/06 (2) Evaporation/Break-

up500 1.04

Break convective07/02/06 None 1200 0.9516/02/06 Evaporation 1200 0.9318/02/06 (1) Evaporation 1200 0.9718/02/06 (2) Evaporation/Break-

up990 0.90

Table 5.6: Dominant microphysical processes and derived coefficients A and b in aZ-R relationship for storms passing over the profiler in the break period of TWP-ICE.

spectra and are intended as a broad overview. Like the active monsoon, average

reflectivities, rainrates and spectral widths are larger in convection, as expected.

138 CHAPTER 5. RESULTS FROM DARWIND

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5.5. CONCLUSION 139

An overview of the median drop diameter during the break is given in Table 5.8.

These results are discussed in further detail in Chapter 7, in context of monsoon

period and latitudinal location.

Date Min D0 Max D0 Avg D0 SDmm mm mm

Break stratiform07/02/06 0.73 2.38 1.40 0.3710/02/06 0.59 1.99 1.16 0.2418/02/06 (2) 0.50 2.18 1.26 0.35

Break convective07/02/06 0.57 2.26 1.47 0.3516/02/06 0.52 2.39 1.24 0.3118/02/06 (1) 0.67 2.34 1.48 0.3518/02/06 (2) 0.61 1.79 1.05 0.18

Table 5.8: Average median drop diameter during the break period.

5.5 Conclusion

This Chapter has discussed rain events from Darwin which occurred in January

and February 2006 during the TWP-ICE field campaign. These events represent a

good cross-section of rainfall in Darwin and have allowed detailed examination of

varied storm structure. Various microphysical processes were examined, and general

conclusions drawn. Results from Adelaide are presented in the next Chapter, and

the Chapter 7 compares and contrasts results from both locations.

Chapter 6

Rain Events in Adelaide

Adelaide, located in the middle latitudes in South Australia, experiences four seasons

of weather, in contrast to the tropical rainfall presented in the previous chapter. The

majority of rain falls in the winter months, although rain does occur all year round.

This is illustrated in Figure 6.1, showing the average rainfall by month at Adelaide

Airport for the years between 1956 and 2008 inclusive. The winter months are June,

July and August.

Rain events presented in the previous chapter come from an atmospheric mea-

surement campaign. Both the profiler and scanning radar used in this study in

Adelaide are permanent fixtures, and data were collected for several years. How-

ever, due to technical problems with the profiler, discussed in section 2.1.2, only

strong rainfalls were distinguishable from the clear-air echo. The Adelaide data set

therefore consists only of unusually strong convection, and does not provide a true

representation of rainfall in the region. A significant portion of Adelaide’s rainfall

is stratiform cut-off low and frontal events. A second issue was the drought Ade-

laide experienced from 2006 to 2008, discussed further in the next section of this

chapter. These two complications result in just two rain events from Adelaide that

can be used in this analysis. The first occurred on 12 June 2008 and the second

on 21 September 2009. It must be noted these two events do not provide a true

representation of rainfall in Adelaide. Approximately 10 other rainfall events passed

over the profiler between 2006 and 2009, but with weak reflectivities (as seen by the

weather radar), such that profiler retrievals were impossible. Results presented in

this chapter represent only the most extreme events Adelaide has experienced in

142 CHAPTER 6. RAIN EVENTS IN ADELAIDE

Figure 6.1: Rainfall over Adelaide airport from 1956 to 2008 averaged by month ofyear. Most rain falls in the colder months in the middle of the year.

recent years. The South Australian drought is first discussed before results from

these two events are presented.

6.1 South Australian Drought

South Australia experienced three consecutive years of record low rainfall from 2006

to 2008. Figure 6.2 shows the total rain that fell over Adelaide Airport, where the

profiler is located, from 1956 to 2008. The unbroken horizontal line indicates the

median value, while the broken horizontal lines indicate the 2006, 2007 and 2008

total rainfall values.

It is clearly seen that for rainfall over the airport, 2006 was the driest year on

record. 2008 was also amongst the lowest recorded total rainfalls, and while 2007

was slightly better, the total is still well below the median value. There are several

causes of these low rainfall counts.

6.1. SOUTH AUSTRALIAN DROUGHT 143

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2006 was an El-Nino year, known to induce lower than average rainfalls across

the eastern two thirds of Australia [Wang and Hendon, 2007]. An El-Nino event

disrupts the ocean-atmosphere interaction in tropical Pacific regions, bringing warm

water to the eastern Pacific as the trade winds weaken [Lloyd , 2007]. As sea surface

temperatures (SST) rise in the east, rainfall is induced. Conversely, cooler than

usual SSTs in the west result in lower than average rainfalls and even droughts.

A second ocean-atmosphere interaction affecting Australian rainfall is the Indian

Ocean Dipole (IOD). Occurring in the equatorial Indian Ocean, the IOD accounts

for approximately 12% of SST variability in the Indian Ocean [Saji et al., 1999]. The

IOD is characterised by the difference in SST of the western and eastern equatorial

Indian Ocean, with a positive (negative) IOD indicating cooler (warmer) waters in

the east, and warmer (cooler) waters in the west. Previous reports indicate that

positive IOD (pIOD) events induce drought in Australia [Cai et al., 2009b]. An

unprecedented three pIOD events occurred in the years from 2006 to 2008 [Cai

et al., 2009a]. The connection between ENSO (El Nino-Southern Oscillation) and

IOD events is a subject of some debate [Saji and Yamagata, 2003]. The two events

can occur concurrently, such as in 2006, but also independently, as 2007 was a

La-Nina year [Luo et al., 2008]. The combination of El Nino and pIOD events in

2006-2008 is related to lower than average rainfall over South Australia in these

years.

6.2 12 June 2008

A moderate frontal squall line, as defined by the local forecasting office [Jenny

Dickins, private communication, 2010], moved over the profiler on 12 June 2008. The

line formed on a cold front, shown in Figure 6.3, off of the South Australian coast.

The upwards motion required to carry precipitable particles aloft was moderate in

spatial extent, limited to a narrow band aligned with the front. The squall line

moved towards the north-east, and developed a small region of stratiform rainfall

as convective elements decayed and moved rearward relative to the leading edge of

the line. The stratiform region was never separated from, and decayed soon after,

its parent convection. The storm passed over the profiler at 0830, shown in Figure

6.4. The line became indistinguishable around 1120, with very little rainfall present

6.2. 12 JUNE 2008 145

on the radar display an hour later.

Figure 6.3: MSLP analysis, 12 June 2008. A frontal squall line formed on the smallcold front located to the south of South Australia.

This event represents a fairly common winter storm for the Adelaide region. Cold

fronts embedded in eastward moving waves occur regularly, and are a significant

contributor to winter-time rainfall. The 12 June event was fairly moderate on a

climatological scale. Convection was deep but winds were not severe and there was

no associated lightning. Figure 6.5 shows the radiosonde soundings for this day at

00 (blue) and 1200 (red) UTC. The balloon ascended in cloud, and can therefore

not be taken as a true indication of ambient atmospheric conditions, but it is useful

to note the freezing level is near 2 km.

Figure 6.6 shows the pseudo RHI derived from the Weather Watch radar, and

the profiler-retrieved reflectivity for the same period. Recall that, at this time, the

profiler was operating in the normal mode only, sampling at 100 m range gates every

minute. Due to the poorer quality of data from Adelaide compared to Darwin, the

quality control routine became cumbersome, often with the order of 80% of retrievals

flagged. It therefore became more practical to perform retrievals in Adelaide entirely

by hand, specifying the centre and spectral width of the clear-air peak, and the

location of the divide for each spectrum. This allowed trends in the spectra with

height to be followed, rather than inspecting surrounding spectra to correct a flagged

point. Data were retrieved starting at the 500 m range gate, then moving upwards

a1172507

Text Box



Figure 6.4: Weather Watch PPI showing the leading convective line with trailingstratiform precipitation as it passed over the profiler site. Adelaide, 12 June 2008.

a1172507

Text Box


6.2. 12 JUNE 2008 147

Figure 6.5: Radiosonde soundings at 00 (blue) and 1200 (red) UTC, Adelaide, 12June 2008. The atmosphere is fairly saturated and the freezing level is seen near 2km.

a1172507

Text Box



in height until the power return became negligible. Both plots depict a convective

line, transition region, and trailing stratiform region including a bright band near

the freezing level. The timing of the convective core agrees well in both plots, but

data does not extend to the same altitude in the profiler plot due to the low profiler

sensitivity. The increased region of reflectivity at 9.2 UTC under the bright band

on the Weather Watch plot is not observed with the profiler.


water content, median drop diameter, and a time series of all profiler-retrieved

parameters at 1 km altitude. Rainrate and liquid water content are more intense in

the convective region, as expected. The median drop diameter is larger both in the

convective region and under the bright band.

Average profiles are used to examine the microphysics of this rain event. Since

the freezing level is near 2 km, these average profiles are only taken up to 1500 m,

that is 500 m below the freezing layer. Below this level it is assumed all ice has

melted and that echoes are due to water droplets only. Since spectra from Adelaide

were retrieved entirely manually, each spectrum was inspected for a precipitation

echo beyond the asymptotic limit of 9.6 ms−1 for raindrops, discussed in section

3.1.4. Average profiles through the convective and stratiform regions are shown in

Figures 6.9 - 6.14 (note the horizontal scale differences). The convective region is

an average through just 3 time stamps, which partially accounts for the large 95%

confidence intervals. The vertical velocity profiles show weak downdrafts in the

convective region, and weak updrafts turning to downdrafts around 1200 m in the

stratiform. The heating profiles, shown in Figure 6.10, display overestimations in

both the stratiform and convective regions, and can be taken as a guide only.

In the convective region, the reflectivity, rainrate and liquid water content plots

show a slight decrease in the lowest range gates. However, the error bars are large

and this may not be significant. The median drop diameter shows little variation

with height. Overall trends in all parameters in the convective region indicate an

equilibrium distribution, showing very little variation with height. The PDF of the

median drop diameter, shown in Figure 6.15, supports this argument. The lower

three plots of the PDF represent three range gates, while the topmost plot just two.

The 900 m plot shows a slightly unusual result, but referring back to Figure 6.14(a)

the 800 and 900 m averages show large errors, so less confidence can be placed in

this result. Apart from this level, Figure 6.15 shows a fairly consistent D0, with a

6.2. 12 JUNE 2008 149

Figure 6.6: (a) RHI reflectivity from the Weather Watch, Adelaide, 12 June 2008,and (b) time height cross section from the profiler during the same period as thatshown in (a). Note the height range differences between plots. Reflectivity scale onthe right in dBZ.




Figure 6.7: Profiler-retrieved rainrate (a) and liquid water content (b) for the sameperiod shown in 6.6. Scales on right in mm hr−1 and gm−3 respectively.

6.2. 12 JUNE 2008 151



Figure 6.8: Profiler-retrieved median drop diameter (scale on right in mm) (a) anda time series of profiler-retrieved parameters at 1 km altitude (b), Adelaide, 12 June2008.


(a) Convective region.

(b) Stratiform region.

Figure 6.9: Averaged vertical velocities through (a) the convective region and (b)the stratiform region on 12 June 2008. Horizontal lines represent 95% standarddeviation confidence intervals calculated using t-statistics.

6.2. 12 JUNE 2008 153



Figure 6.10: Averaged heating rate through (a) the convective region and (b) thestratiform region on 12 June 2008. The sensible heating rate is shown in red, evap-orative in blue.


mode near 1.1 mm.

Averaged reflectivity, rainrate and liquid water content in the stratiform region

appear to follow a decreasing trend with height. However, this decrease is, for

example, approximately 1 dB in the reflectivity, and with average error bars 2 dB

wide, these values are assumed constant. The median drop diameter appears to

increase down to 1000 m, then decrease on approach to the surface. However, the

difference between minimum and maximum values of D0 is 0.08 mm, which again

is of the same order as the error bars, hence the median drop diameter profile is also

constant. The stratiform region is therefore possibly consistent with an equilibrium

distribution. The PDF of D0, shown in Figure 6.16, displays minimal change with

height, supporting this argument.

6.3 21 September 2009

The synoptic conditions which lead to rainfall on 21 September 2009 are very dif-

ferent to those discussed above on 12 June, and represent an unusual feature for

the Adelaide region. The vertical uplift was broad in extent, forming on the east-

ern edge of a low pressure system, near the border of WA (Western Australia) and

SA (South Australia). The MSLP around the time rainfall was over the profiler is

shown in Figure 6.17. The system moved east-southeastwards, bringing a convective

rainband of approximately 1 hour duration across the state. The storm passing over

the profiler is shown in Figure 6.18. The Figure shows the rainband consists of mod-

erate intensity rainfall with embedded convection, a result of the broad and deep

nature of the upwards motion in this storm. Low pressure systems tracking across

SA at, or to the north of, Adelaide’s latitude are considered occasional phenomena,

and a higher than normal number of these storms can result in higher than average

precipitation for the winter-spring season [Jenny Dickins, private communication,

2010].

Figure 6.19 depicts the radiosonde sounding from 00 UTC on this day. The

freezing level is seen to be near 3 km, that is ∼1 km higher than the previously

discussed event on 12 June 2008, due to the current event occurring in the spring

rather than winter season.

6.3. 21 SEPTEMBER 2009 155



Figure 6.11: Averaged reflectivity through (a) the convective region and (b) thestratiform region on 12 June 2008. Horizontal lines represent 95% standard deviationconfidence intervals calculated using t-statistics.




Figure 6.12: Averaged rainrates through (a) the convective region and (b) the strat-iform region on 12 June 2008. Horizontal lines represent 95% standard deviationconfidence intervals calculated using t-statistics.

6.3. 21 SEPTEMBER 2009 157



Figure 6.13: Averaged liquid water contents through (a) the convective region and(b) the stratiform region on 12 June 2008. Horizontal lines represent 95% standarddeviation confidence intervals calculated using t-statistics.




Figure 6.14: Averaged median drop diameters through (a) the convective region and(b) the stratiform region on 12 June 2008. Horizontal lines represent 95% standarddeviation confidence intervals calculated using t-statistics.

6.3. 21 SEPTEMBER 2009 159

Figure 6.15: PDF of the median drop diameter in the convective region, 12 June2008. The lower three plots represent three range gates, while the topmost plotrepresents two range gates. The height indicated on the far right is the middle levelof the range gates represented in that plot. The horizontal axis depicts the mediandrop diameter size, while the vertical axis depicts the number in each drop size class.Note that this axis is consistent through all plots.


Figure 6.16: PDF of the median drop diameter in the stratiform region, 12 June2008. The lower three plots represent three range gates, while the topmost plotrepresents two range gates. The height indicated on the far right is the middle levelof the range gates represented in that plot. The horizontal axis depicts the mediandrop diameter size, while the vertical axis depicts the number in each drop size class.Note that this axis is consistent through all plots.

6.3. 21 SEPTEMBER 2009 161

Figure 6.17: MSLP analysis, 21 September 2009. A convective rainband, formedfrom a low pressure system near the Western/South Australian border, moved east-southeastwards across South Australia.

On 21 September, the profiler was operating in both high and low modes. The

high mode is used here, as it employs a longer pulse length and therefore higher

power output. The high mode samples every 2 minutes, with 600 m range gates

and 300 m of oversampling. The pseudo RHI constructed from successive PPI scans

and the profiler-retrieved reflectivity cross-section are shown in Figure 6.20. Note

the higher echo top height observed by the Weather Watch compared to that in

Figure 6.6 on 12 June 2008, which is related to the broader vertical ascent in the

latter case. A bright band of sorts is also visible in the Weather Watch plot, where

reflectivities decrease of the order of 10 dB above the freezing level. As stated above,

this rain event consisted of a broad rain band with embedded convection. This mix

of stratiform and convective precipitation is highlighted in the cross-sections (the

visibility of the freezing level indicates stratiform rainfall, while the reflectivities

greater than 40 dB indicate convection).

Figures 6.21 and 6.22 show the profiler-retrieved time-height cross-sections of rain-

rate, liquid water content, median drop diameter, and a time series of all profiler

retrieved parameters through 1.5 km altitude. Like the reflectivity cross-sections,

these parameters show moderate intensity on a broad scale, with embedded convec-

tion.

a1172507

Text Box



Figure 6.18: Weather Watch PPI showing the convective rainband as it passed overthe profiler site. Adelaide, 21 September 2009.

a1172507

Text Box


6.3. 21 SEPTEMBER 2009 163

Figure 6.19: Radiosonde sounding at 00 UTC, Adelaide, 21 September 2009.

a1172507

Text Box



(a) Weather Watch pseudo RHI.

(b) VHF reflectivity cross-section.

Figure 6.20: (a) Pseudo RHI reflectivity from the Weather Watch radar, Adelaide,21 September 2009, and (b) time-height reflectivity cross-section from the profilerduring the same period. Note the difference in height scales. Scale on right in dBZ.

6.3. 21 SEPTEMBER 2009 165



Figure 6.21: Profiler-retrieved rainrate (a) and liquid water content (b), for the sameperiod shown in 6.20. Scales on right in mm hr−1 and gm−3 respectively.




Figure 6.22: Profiler-retrieved median drop diameter (scale on right in mm) (a) anda time series of profiler-retrieved parameters at 1.5 km altitude (b), for the sameperiod shown in 6.20.

6.3. 21 SEPTEMBER 2009 167

To further analyse this mixed rainfall event, averaged profiles are examined. Pro-

files are taken up to 2500 m, that is, 500 m below the freezing level, so melting

processes can be assumed complete. As was the case on 12 June, spectra were re-

trieved entirely by hand, beginning at the lowest range gate and moving upwards

in height until the signal became negligible. Above the 2500 m level, there were a

few examples of spectra with three peaks, the third peak with large velocity, corre-

sponding to falling ice particles. This indicates the profiler is capable of retrieving

ice particle distributions in the future.

The vertical velocity profile, shown in Figure 6.23 shows an updraft that weakens

with descent. The heating profile, shown in Figure 6.24, seems unreliable and is

not taken as real. Reflectivity, rainrate and liquid water content profiles, shown in

Figures 6.25-6.27, all show a trend which increases in the upper two range gates,

then decreases. In contrast, the median drop diameter profile (Figure 6.28), although

showing a slight decrease in the upper range gates, is very consistent with height.

This is also depicted in Figure 6.29, where the number of drops in each drop class

shows very little variation with height.

Figure 6.23: Averaged vertical velocity through the rain event on 21 September 2009.Horizontal lines represent 95% standard deviation confidence intervals calculatedusing t-statistics.


Figure 6.24: Averaged heating profile through the rain event on 21 September 2009.The sensible heating rate is shown in red, evaporative in blue.

Considering the lowest four range gates only, reflectivity, rainrate and liquid water

content show decreasing trends, while the median drop diameter remains constant.

Decreasing liquid water content and reflectivity indicate evaporation. However, D0

would then be expected to increase due to the loss of small drops. Since this is not

observed, drop break-up must also be occurring. Thus small drops evaporate, de-

creasing the total liquid water content and reflectivity. Simultaneously, larger drops

break-up, further adding to the decrease in reflectivity (due to the D6 dependence),

and maintaining a relatively constant D0. Finally, it is noted that there is much

larger error in the Adelaide data, meaning results cannot be taken to be as accurate

as the Darwin counterpart.

6.3. 21 SEPTEMBER 2009 169

Figure 6.25: Averaged reflectivity through the rain event on 21 September 2009.Horizontal lines represent 95% standard deviation confidence intervals calculatedusing t-statistics.


Figure 6.26: Averaged rainrate through the rain event on 21 September 2009. Hor-izontal lines represent 95% standard deviation confidence intervals calculated usingt-statistics.

6.3. 21 SEPTEMBER 2009 171

Figure 6.27: Averaged liquid water content through the rain event on 21 Septem-ber 2009. Horizontal lines represent 95% standard deviation confidence intervalscalculated using t-statistics.


Figure 6.28: Averaged median drop diameter through the rain event on 21 Septem-ber 2009. Horizontal lines represent 95% standard deviation confidence intervalscalculated using t-statistics.

6.3. 21 SEPTEMBER 2009 173

Figure 6.29: PDF of the median drop diameter, 21 September 2009. Each plotrepresents two range gates. The height indicated on the far right is the middle levelof the range gates represented in that plot. The horizontal axis depicts the mediandrop diameter size (mm), while the vertical axis depicts the number in each dropsize class. Note that this axis is consistent through all plots.


6.4 Overview

With only two events analysed, the data set from Adelaide does not allow conclusions

to be drawn in the same manner as for Darwin. Instead, interesting features and

potential trends are highlighted for future research. Table 6.1 summarises the dom-

inant microphysical process on both 12 June 2008 and 21 September 2009, along

with derived coefficients for A and b in a Z − R relationship. While the data is

limited, A does not show great variation and b has assumed a constant. Further,

combining all data from Adelaide results in a Z − R relationship with A = 570

and b = 0.9. These relationships were derived in the same manner as in Darwin,

utilising a Levenberg-Marquardt least squares minimisation to fit a power law, with

A constrained between 0 and 1200, and b constrained between 0.9 and 1.9. Since

b assumed a constant of 0.9 in all cases in Adelaide, this latter constraint was re-

moved, but with no effect on the derived value of b. If the 21 September 2009 event

can be considered convective, its similarity in derived coefficients to the convective

region on 12 June 2008 is striking. The implication for weather radars in calculat-

ing rainrates via a Z-R relationship in the mid latitudes then becomes very simple.

Only two relationships are required, one in convective conditions, and the other in

stratiform rainfall. Alternatively, a single relationship, such as that derived above

using combined data from all available storms could be implemented, and would

still provide more accurate estimations of the rainrate than the Marshall Palmer

relation Z = 200R1.6. Analysis of further events in Adelaide will reveal if the stable

nature of the Z-R relationship is an accurate depiction of Adelaide’s rainfall, or a

coincidence in the limited data.

Dominant Process A bJune 12 C Equilibrium-like 680 0.9June 12 S Equilibrium-like 330 0.9September 21 Evaporation 670 0.9

Table 6.1: Dominant microphysical processes and derived coefficients A and b in aZ-R relationship for storms passing over the Adelaide profiler.

Table 6.3 provides an overview of the storms discussed above. Similar to Darwin,

this table contains “instantaneous” values, that is values are not calculated through

analysis of time stamps or range gates, and the table is intended to provide a broad

overview only. The time stamps column in this table is somewhat misleading, given

the varied modes of operation of the radar. For the June 12 event, when the radar

6.4. OVERVIEW 175

was operating in the normal mode, time stamps were recorded every minute. For

the September 21 event, the radar was interleaving between low and high modes,

and thus time stamps represent 2 minutes of the storm. Of note in Table 6.3 is the

largest updraft is seen in the stratiform region of the June 12 storm. Since this value

is calculated considering individual spectra throughout the June 12 stratiform region

this is not too surprising. Also of note is the smaller spectral width on September

21. This is due to the differing modes of operation of the radar.

Maximum, minimum, and average median drop diameters for the Adelaide storms,

along with the standard deviation are listed in Table 6.2. D0 is larger in the con-

vective regions as expected. These findings are compared and contrasted to those

from Darwin in Chapter 7.

Min D0 Max D0 Avg D0 SDmm mm mm

June 12 C 0.86 1.70 1.17 0.18June 12 S 0.58 1.54 0.88 0.16September 21 0.73 2.17 0.10 0.23

Table 6.2: Maximum, minimum, average and standard deviation (SD) values of themedian drop diameter of storms passing over the Adelaide profiler.

176 CHAPTER 6. RAIN EVENTS IN ADELAIDET

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6.5. CONCLUSION 177

6.5 Conclusion

This chapter has discussed two events which passed over the Adelaide profiler in 2008

and 2009. Data from Adelaide are limited through a combination of the drought

South Australia experienced from 2006 - 2008, and the low power output of the

profiler requiring strong storms. The June 12 event represents a fairly standard

winter storm for the Adelaide region, and future work will include validating re-

sults presented here with analysis of similar storms. The event on September 21 is

not a common event, but provides interesting data, as increased numbers of these

storms often result in increased average rainfall. Results presented in this chapter

indicate it is possible to derive an accurate Z-R relationship for the Adelaide region,

which provides more accurate estimations of the rainrate than the Marshall-Palmer

relation. Adelaide results are compared to those from Darwin in the concluding

chapter.

Chapter 7

Discussion

Chapters 5 and 6 examined results from Darwin and Adelaide, respectively. Further

discussion and interpretation of these results are presented in this Chapter, with

particular emphasis on intra-seasonal, and latitudinal differences. The microphysics

is first discussed, before paying particular attention to equilibrium distributions and

empirical relationships. An analysis of median drop diameters where a bright band

is evident is also included.

7.1 Microphysics

As noted in Chapter 5, the Darwin monsoon season cycles between active and break

periods. Storms during the active period are characteristic of maritime regions,

while break storms are typical of continental areas and are generally more intense.

Illustrated in a comparison of tables 5.1 and 5.5, the storm type/structure varied

between the TWP-ICE-sampled active monsoon and break seasons. Active storms

were typically tropical squall lines with trailing stratiform precipitation, while storms

sampled during the break were typically convective cells. These data therefore

provide a good overview of the Darwin monsoon season. The same cannot be said of

data from Adelaide, where only two storms could be satisfactorily analysed. While

the winter storm observed on 12 June is typical for the Adelaide region, the spring-

time storm of 21 September is not.

180 CHAPTER 7. DISCUSSION

All rain events retrieved in both Adelaide and Darwin were carefully analysed

for evidence of a dominant microphysical process. Where rain events consisted of

variable rainfall type, for example a convective core followed by a trailing stratiform

region, these differing rainfall types were considered individually. In Darwin, Tables

5.2 and 5.6 indicate that evaporation is the dominant process affecting DSD evolu-

tion. This is expected in stratiform regions as evaporation drives the characteristic

weak downdrafts. It is somewhat more surprising in convective regions. This result

is important in modelling both the total water reaching the surface and latent heat

release.

More retrievals are required to draw the same conclusion on an overall dominant

microphysical process in Adelaide. It is possible evaporation is just as dominant

and important in Adelaide as it is in Darwin. However, it is also possible the varied

precipitation initiation mechanisms in the mid latitudes make rainfall over Adelaide

more variable.

It is interesting to note that in transition regions (that is the section of the rain-

band between the convective core and trailing stratiform precipitation), in both the

tropics and mid latitudes, there was no evidence of a dominant microphysical pro-

cess. Transition regions are thus true to their name, and are transitioning from

precipitation caused by intense upwards motions in convective regions to that re-

sulting from melting ice particles aloft in the stratiform. Further, in most cases,

transition regions were characterised by median drop diameters between 0.7 and 1.0

mm. Given transition regions are characterised by regions of low reflectivity, it is

not surprising that only small drops were retrieved here.

Tables 5.3 and 5.7, which summarise the average properties of monsoon and break

storms in Darwin are remarkably similar. This is somewhat surprising given con-

vection is generally considered stronger in the break than the monsoon [May et al.,

2008]. The effective “point sampling” of the profiler is a factor to be considered. The

data set is restricted to only those storms passing directly over the radar. Analysis

of CPOL PPI displays throughout the break indicates the vast majority of the most

intense convection did not pass over the profiler. The most intense storms often

formed near the TIWI Islands to the north of the profiler.

7.1. MICROPHYSICS 181

7.1.1 Median Drop Diameter

Tables 5.4 and 5.8, which summarise minimum, maximum and average median drop

diameters, with the standard deviation for monsoon and break storms are also very

similar. No striking difference between seasons are seen here, and often the largest

D0 for a particular event is seen in the stratiform region. Figure 7.1 shows the

histogram of all results in the break and active monsoon seasons, separated into

stratiform and convective rainfall for each season. For easier comparison, Figure 7.2

compares rainfall types.

Comparing stratiform and convective rainfall in both seasons reveals little dif-

ference. In the monsoon season, there are higher percentages of large drops in the

stratiform rainfall than the convective. This is not surprising, as stratiform rainfall

in the monsoon largely occurred with an associated bright band, where large drops

form from the melting of large ice aggregates. In the break, the mode of D0 for

convective rainfall is 0.2 mm higher than in stratiform. The break season is asso-

ciated with intense convective bursts, and comparatively little widespread rainfall,

which fits with this result. Comparing rainfall type between seasons, larger drops in

stratiform rainfall are seen in the monsoon season, as expected due to the frequent

presence of a bright band in the monsoon. In convection, larger drops were observed

in the break, as expected when storms are more intense.

Figure 7.3 compares the median drop diameter in stratiform and convective rain-

fall in Adelaide. Note that the 21 September event has been considered convective.

It is clear from this plot that the average drop size in the middle latitudes is much

smaller than in the tropics. There are few drops larger than 1.5 mm in the Adelaide

data, which is clearly not the case in Darwin. It is also interesting to note, particu-

larly in stratiform rainfall, that most drops are contained within a narrow range of

sizes. It must be remembered however, that these data come from two events only,

and further analysis is required to validate these results.

An alternative way to examine and compare data is presented in Figure 7.4,

where the median drop diameter has been plotted against reflectivity for all results

presented in this thesis. Data have been separated according to rainfall type. The

difference in drop sizes between the tropics and mid latitudes is clear in this plot,

where mid latitude drop sizes are concentrated at the small drop end. This Figure


(a) Active Monsoon.

(b) Break.

Figure 7.1: All median drop diameters from the active monsoon (a), and break (b)seasons during TWP-ICE.


(a) Stratiform.

(b) Convection.

Figure 7.2: All median drop diameters in stratiform (a), and convective (b) rainfallduring TWP-ICE.


Figure 7.3: Median drop diameters from all Adelaide results, separated into strati-form and convective rainfall.

highlights an important implication for QPE. A range of median drop diameters

correspond to any given measured reflectivity. This is true both in the tropics and

mid latitudes, and means that, according to these data, the median drop diameter

cannot be related to measured reflectivity via an empirical relationship. Z − R

relationships are an important tool to the weather forecaster, and a characterisation

of D0 through measured reflectivity would provide even more information. However,

this is not possible with these data, and measurements of median drop diameter via

scanning radar must be left to those with polarimetric abilities. It is also interesting

to note that based on these parameters, population sorting is due to rainfall type

rather than location.

Average storm statistics from Adelaide are presented in Table 6.3. The convective

region on 12 June is found to be weaker than convection in Darwin. Analysis of

further convective regions would indicate whether this result provides an accurate

description of rainfall in Adelaide, or is a unique case. The result is not surprising,

however, because tropical regions are well known for severe storms, whereas severe

weather occurs less frequently in the mid latitudes.


Figure 7.4: Reflectivity plotted against median drop diameter for all results pre-sented in this thesis. Results are separated according to both location and rainfalltype. T=topical, ML=mid latitudes, C=convection and S=stratiform.


In terms of the median drop diameter, results from Adelaide indicate smaller

drops than those found in Darwin. The stratiform region on 12 June contains the

smallest D0 of all events analysed in this study. Further analysis of rainfall in

Adelaide will indicate whether this is unique to this case, or typical in the mid

latitudes.

7.1.2 Equilibrium Distributions

Evidence of equilibrium rain dropsize distributions, where there is a balance in the

microphysical processes, were observed in both Adelaide and Darwin. This is a

somewhat controversial issue, and worthy of further discussion. A brief literature

review on this topic is given in Appendix C. Briefly, modelling studies indicate

equilibrium distributions can form in either cold or warm rain processes, although

the time taken to reach equilibrium is longer in cold processes. Equilibrium DSDs

have been observed in warm rain only, where updrafts are thought to act as a drop-

sorting mechanism.

For an equilibrium distribution to exist, three criteria must be met:

1. A balance in the microphysics; i.e. reflectivity, rainrate, liquid water content

and median drop diameter must not vary with height.

2. The shape of the distribution must not change.

3. The exponent in the derived Z −R relationship must approach unity.

In the course of this study, data potentially consistent with equilibrium distribu-

tions were observed in Darwin on 22 January 2006, and in Adelaide on 12 June 2008,

where the rainfall parameters showed little or no variation with height. The Darwin

case occurred in stratiform rainfall, and therefore is not consistent with observa-

tions most commonly reported in the literature, of equilibrium distributions formed

in the updraft of warm rain. As noted by other authors however, when the freezing

level is sufficiently high, as is the case in tropical regions, there is enough time for

collision-coalescence and breakup processes to come into equilibrium. In Adelaide,

equilibrium distributions were found in both the convective and stratiform regions.

The freezing level was only ∼ 2 km above ground on this day, although there was a


narrow, intense updraft seen immediately prior to the convective core, which could

have acted to sort drops.

To further investigate these two equilibrium like situations, the shape of the DSD

was examined. Figure 7.5 shows DSDs retrieved 13-1400 UTC, 22 January, during

the second rainfall band. Each plot represents data from three range gates, with the

central height listed on the far right. Overlaid in each plot is the average shape for

that height range.

The upper range gates show some consistency, i.e. there is little difference between

the steepest and flattest distributions. The lowest range gates show far greater

variability. This suggests that the distribution evolved with height. To illustrate

this point further, Figure 7.6 shows the averaged distributions, i.e. the colour overlay

in Figure 7.5, for D between 2 and 4 mm. This dropsize region is chosen because it

avoids contamination from clear-air echo in the small drop region, and the limited

resolution in the large drop region caused by small changes in fall velocity. The

distributions do not conform to a particular shape, i.e. they are not parallel, and

they cross over each other at multiple points. For example, at the 3 mm point, there

is a 45% difference between the minimum and maximum distributions.

An alternative examination of the same data is shown in Figure 7.7, where the

DSD has been multiplied by the cube of the diameter, and plotted as function of

diameter. This indicates where the water lies in each distribution. Evolution of the

DSD is clearly seen here, particularly when comparing the top-most to bottom-most

range gate.

By way of comparison, Figure 7.8 shows the averaged distributions between 2

and 4 mm for a stratiform rainband on 5 January 2006, where evaporation was the

dominant process. This plot shows far more consistency in the shape, particularly

at the small drop end, and at the large drop end distributions are parallel, and

do not cross over each other, like those on 22 January. At the 3 mm point, there

is a 40% difference between the maximum and minimum averaged distributions.

After inspecting the plot, there is one distribution that lies well above the others.

Excluding this outlier, the difference reduces to 25%. Figure 7.9 shows this same

data multiplied by diameter cubed. This plot shows a clear evolution with height,

with less water located particularly at the large diameter end in the lowest range

gates.


Figure 7.5: Shapes of the DSD, 13-1400 UTC, 22 January 2006. The colour overlayrepresents the average shape. The x-axis represents drop diameter in mm, and thedashed vertical line the cut off at 1 mm. The y-axis shows number density on alogarithmic scale.


Figure 7.6: Averaged shapes from Figure 7.5 between 2 and 4 mm. The x-axis showssize in mm, while the y-axis shows number density on a logarithmic scale.

Figure 7.10(a) shows the shape of the DSD in the convective region of the 12 June

2008 Adelaide event, with a colour overlay of the averaged distribution. The lower

three plots represent three range gates, while the topmost plot represents only two.

The central height is listed on the far right. The averaged distribution (the colour

overlay in 7.10(a)) is shown in Figure 7.10(b), for D between 2 and 4 mm. The

shape of the averaged distributions appear to at least assume the same shape, but

at the 3 mm point there is a 100% difference between the maximum and minimum

distributions. This difference reduces to 50% if the 600 m outlier is excluded, but

this is still a greater difference than seen in non-equilibrium cases.

The shape of the DSD in the stratiform region of the 12 June 2008 event is shown

in Figure 7.11(a), with a colour overlay of the averaged distribution. As was the case

in the convective region, the lower three plots represent three range gates, while the

topmost plot represents only two. The central height is listed on the far right. The

distributions display a much sharper cut-off at the large drop end compared to both

convection in Adelaide, and all events from Darwin. The distributions also seem to

converge at the large drop end. At the 3 mm point, there is just a 9% difference

between maximum and minimum averaged distributions. However, while in all other


Figure 7.7: Averaged shapes from Figure 7.5 multiplied by the diameter cubed, andplotted as a function of diameter. The y-axis shows the log of the number density,multiplied by the diameter cubed.

Figure 7.8: As for 7.6 but for 5 January 2006.


Figure 7.9: As for 7.5 but for 5 January 2006.

cases, the 3 mm size has represented a convenient mid-point, in this case 3 mm is

closer to the largest dropsizes seen in the sample. At the 2 mm size point, which is

closer to the middle of the distribution, this difference increases to 62%. Plotting

the DSD multiplied by the diameter cubed revealed a similar evolution with height

as that shown in Darwin (plots not shown).

The analysis of the DSD shapes presented above do not indicate the microphysical

processes are in equilibrium. Despite little variation in the rainfall integral param-

eters (criteria 1), a rainfall event cannot be considered to be in equilibrium if the

distribution is not constant (criteria 2). The third criteria is now considered. As

stated in Equation C.2, the exponent b approaches unity in an equilibrium distribu-

tion. For the event in Darwin on 22 January, where equilibrium-like distributions

were observed in both the second and third rainbands, exponents of b = 1.34 and

b = 1.20, respectively, were derived. Similarly, in Adelaide where equilibrium-like

distributions were observed in both the convective and stratiform regions of the 12

June 2008 event, an exponent of b = 0.90 was derived in both cases. Referring to

section 2.4, a difference in b of just 0.04 produces an error of 15%. Given the closest

derived values of b shows a difference of 0.1 from unity, these Z-R relationships


(a) DSD shape in the convective region.

(b) Colour overlay from (a).

Figure 7.10: (a) DSD shape in the convective region, 12 June 2008. The x-axis rep-resents drop diameter in mm, and the dashed vertical line the cut off at 1 mm. They-axis shows number density on a logarithmic scale. The colour overlay representsthe average distribution at that height. This average distribution between 1 and 4mm is shown in (b), where the y-axis shows number density on a logarithmic scale.


(a) DSD shape in the stratiform region.

(b) Colour overlay from (a).

Figure 7.11: As for 7.10 but in the stratiform region.


cannot be considered representative of true equilibrium distributions.

Regardless of the method by which a distribution may come to equilibrium, the

three criteria listed above must be satisfied. While criterion 1 was satisfied in both

cases, neither criteria 2 or 3 were met. The conclusion must be therefore that equi-

librium distributions are not observed in the lowest 3 km of the natural atmosphere.

Rather, in these cases, it is the average of the distributions which is stable, not the

individual distributions themselves. The term “microphysically stable” rather than

“equilibrium” is therefore preferred for the observations of 22 January and 12 June.

There are several caveats to this conclusion. The first is that conditions under

which equilibrium distributions were observed are different to those previously re-

ported in the literature [Atlas and Ulbrich, 2000; Ulbrich and Atlas , 2007]. Previous

equilibrium distributions were generally observed in updrafts in warm rain processes,

where the updraft was theorised to act as a drop-sorting mechanism, allowing only

a narrow distribution of drops to reach the ground [Atlas and Ulbrich, 2000]. It has

been noted that when the freezing level is high enough to allow collision-coalescence

and break-up processes to come into balance on the fall to the surface, equilibrium

distributions may exist in cold rain, regardless of other microphysical processes above

the freezing level. This is therefore possible in Darwin, where the freezing level is

at ∼ 5 km, but less likely in Adelaide where the freezing level on 12 June was near

2 km. There was an intense updraft near the beginning of the Adelaide case, which

may have acted to sort drops in the convective core. The same cannot be said of

the stratiform region on this day.

Results in this thesis do not preclude the existence of equilibrium distributions.

However, if they were as common as has been reported in the literature it can

be argued that they would have been observed in this moderate sized sample set.

There are two counterarguments here. Firstly, the argument of frequently occurring

equilibrium distributions is based on warm rain, and there are no good examples of

purely warm rain in data contained in this thesis. Secondly, the profiler takes only

point-like samples of the atmosphere. If the equilibrium distribution is observed only

near the updraft, this requires the storm to initiate in the vicinity of the profiler.

The location of both the Adelaide and Darwin profilers is such that much of the

sampled convection is aged, and accompanied by downdrafts. With these arguments

in mind, the study of the existence or otherwise of equilibrium distributions remains

a direction for future research for a larger data set.

7.2. BRIGHT BAND D0 195

7.2 Bright Band D0

An increase in D0 under a bright band, associated with the melting of large aggre-

gates of ice particles has been noted by many authors (e.g. Cifelli et al. [2000]).

This increase in D0 was observed in the TWP-ICE data set. However, on four sep-

arate occasions, the increase was not evident in the topmost profiler range gates,

as illustrated in Figure 7.12. For the rainband centred on 3 UTC, where there is

a bright band (not shown), larger values of D0 below the melting level were not

observed until near 2.4 km.

Figure 7.12: Example of median drop diameter in stratiform rainfall under a brightband signature. The characteristic increase in D0 is not seen until near 2.4 kmaltitude.

The four cases occurred on 5, 20 and 23 January, and 18 February 2006 in Darwin.

There was also a bright band signature on both 22 January and 10 February, but

the effect was not observed on these occasions, nor was it seen in Adelaide. The

four storms for which this effect was observed were all tropical squall lines with

trailing stratiform precipitation, while the storms of 22 January and 10 February

were not. Observations in 3 out of 4 of these storms indicated that evaporation

was the dominant microphysical process, while that of 23 January was collision-


coalescence.

It was first thought these missing large drops were a result of noise in the spec-

trum. Much the same as the smallest drops are masked by the clear-air peak, the

largest drops may be masked by noise. The signal-to-noise (SNR) ratios in the re-

gions where this effect was observed were investigated. While the SNR decreased

with increasing height as expected, the drop-off in affected regions was no different

to non-affected regions. Further, a modelling study was conducted to determine the

noise level at which the large drops could not be retrieved. The model simulated

radar spectra, allowing the user to specify all parameters. The average rainrate,

mean vertical velocity and spectral width for the cases in which the bright band

effect was observed were input, and the DSD retrieved. With no noise, the model

returned a median drop diameter of ∼1.2 mm, which is close to those values seen

in the bright band affected regions. This gives confidence in the model providing

an accurate description of the processes occurring here. The average change in D0

where this effect occurred was of the order of 1 mm. To cause this large a change

in the calculated D0 in the model, so much noise was added that the precipitation

peak was no longer distinguishable. In these cases, the automated DSD code did not

perform a retrieval until manually forced. This is therefore clearly not the problem

here.

In the course of investigating the properties of the storms where this effect was

observed, an issue with the clear-air amplitude was discovered. Figure 7.13 shows

spectra at a particular time stamp stacked on top of each other. These spectra

have been smoothed such that only the general trend is shown. The clear-air and

precipitation echoes are both strong in the lower range gates, but in the top 10 range

gates the clear-air amplitude is much weaker. This is particularly evident in the 7th

range gate from the top, where the clear-air echo is entirely missing. Another plot

representing the same information in 3D is shown in Figure 7.14, where the drop-off

in clear-air amplitude in the upper range gates is clearly seen.

Using the model described above to investigate the effect of increasing noise levels

in masking the large drops, the effect of decreasing clear-air peak amplitude was

examined. With rainrate, spectral width and mean vertical velocity held constant

according to the average values in the affected regions, the median drop diameter

was found to decrease with decreasing clear-air amplitude. Fluctuating clear-air

amplitudes above ∼ 2.5 km were found in all four cases of decreasing D0 under the


Figure 7.13: Stacked spectra from 1 time stamp on 20 January 2006. The clear-airand precipitation signals are clearly seen in the lower range gates, while the clear-airsignal diminishes in the upper range gates. This is particularly obvious in the 7th

range gate from the top, marked with an arrow.


Figure 7.14: Same data as shown in Figure 7.13 but shown in 3D. The z-axis repre-sents dBZ.

bright band, thus explaining this effect. It is a consequence of the deconvolution

operation, rather than a real microphysical process.

Atmospheric echoes are the result of scattering from inhomogeneities in the re-

fractive index, n. For VHF radars, n can be expressed as

n− 1 =0.373e

T 2+

77.6× 10−6p

T− Ne

2Nc

(7.1)

where e is the partial pressure of water vapour (hPa), T is the absolute temperature

(K), p is the atmospheric pressure (hPa), Ne is the number density of electrons,

and Nc is the critical plasma density [Gage and Balsley , 1980]. Subtraction by 1

on the left-hand side of this equation is done for convenience, as the expression

is only slightly greater than unity. The three terms on the right of equation 7.1

represent the contribution from water vapour/humidity (first), dry air (second) and

free electrons (third). The third term is negligible below 50 km, and is therefore not

considered here.


Variations in the radio refractive index are defined by the vertical gradient of the

potential refractive index given by

M = Md

[1 +

15500q

T

(1− 1

2

∂ ln q/∂z

∂ ln θ/∂z

)](7.2)

where q is the specific humidity, given by q = e/1.62P , θ is the potential tempera-

ture, given by θ = T (1000/P )0.286 [VanZandt et al., 1978]. Md is the clear-air term,

and is given by

Md = −77.6× 10−6P

T

(∂ ln θ

∂z

)(7.3)

Atmospheric echo is therefore returned from fluctuations in temperature, humid-

ity and pressure. The strength of this return is proportional to M2. For there to

be no clear-air return in the region discussed above directly below the bright band,

there must be no gradients in these variables. The effect is observed in the top ∼ 1

km of the profiler data, that is between ∼ 2.5 and 3.5 km. Melting processes are

complete by this level. The conclusion is made that no microphysics occurred in

this layer, therefore maintaining constant humidity and temperature. If evaporation

does not occur, there is no heat exchange, and no change in liquid water content,

and a null gradient in temperature and humidity. The closest agreeing radiosonde

soundings to these events show adiabatic ascent between 2.5 and 3.5 km approx-

imately half of the time. However, sonde data is generally considered unrealiable

in rain, because the parcel ascends through cloud and does not therefore provide

a true reading of the ambient atmosphere. Further profiler observations under a

bright band signature are required in the future to determine whether this effect

is consistent. If it is a real phenomenon, previous profiler studies are unlikely to

have observed it due to limited sampling. Williams [2002] developed a technique

to perform retrievals using only a UHF profiler. It is possible if this effect is found

to be real and consistent a similar metholodology could be employed in the upper

range gates.


7.3 Empirical Relationships

It is important to generalise profiler measurements to scanning radars, as profilers

measure only the portion of the storm passing directly overhead. Two such rela-

tionships, first discussed in section 2.4, relate the measured reflectivity to rainrate,

and measured differential reflectivity to median drop diameter. These relationships

are now discussed, incorporating the results presented in the previous two chapters.

7.3.1 Z-R Relationships

Derived coefficients of the Z − R relationships in the monsoon and break seasons

in Darwin are listed in Tables 5.2 and 5.6 respectively. In convective storms, there

is little difference seen between seasons. The convection in both seasons was char-

acterised by A near 1200 and b of the order of 0.9. Stratiform regions were more

variable, often with A much closer to the Marshall-Palmer value of 200, but with

somewhat lower values of b. These values are somewhat different to those previously

reported in the literature, where A varies between 100 and 300 and b between 1.1

and 2.0 [Doviak and Zrnic, 1993]. However, as noted by Ulbrich and Atlas [2007],

when rainfall is partitioned into convective, transition and stratiform regions, as was

done in this study, the value of A becomes much larger and b much smaller than

previously reported values. It is also possible these relations are different because

they are derived from a composite volume rather than a surface measurement. The

values presented in this work agree well with those presented by Ulbrich and Atlas

[2007] for varied times and geographical locations.

Derived coefficients from Adelaide are shown in Table 6.1. While the data are

limited, A does not show great variation and b has become constant. If the 21

September 2009 event can be considered convective, its similarity in derived coeffi-

cients to the convective region on 12 June 2008 is striking. Analysis of further events

in Adelaide will reveal if the stable nature of the Z − R relationship is an accurate

depiction of Adelaide’s rainfall, or a coincidence due to the limited data available.

As noted in section 2.4, for the purposes of deriving coefficients, relationships

were considered different if A varied by a value of 10 or more, or b varied by a value

of 0.01 or more. Given this difference, there are not two derived relationships that


are the same in all data presented in this thesis. However, there are some strong

similarities and it is possible to divide data into four categories

1. Tropical convection

2. Tropical stratiform

3. Mid latitude convection

4. Mid latitude stratiform

It is not necessary, based on rain events analysed in this work, to consider the

season when choosing an appropriate Z−R relationship. This may not be true in the

mid latitudes, and this remains a topic of future work when more data are available.

Combining all tropical rain events together, separated into stratiform and convective

classifications, results in values of A = 460 and b = 1.05 for stratiform rainfall, and

A = 1200 and b = 0.92 for convective. Figure 7.15 shows profiler-derived reflectivity,

plotted on a log scale, against the rainrate calculated from these derived relations,

also on a log scale, for stratiform and convective rain events throughout TWP-

ICE. The plots show both relations have been derived satisfactorily. Comparing

these relations to those listed in Tables 5.2 and 5.6, the overall relations provide

a very good approximation to those derived for individual events, particularly in

convection. Note that similar overall trends have not been performed for Adelaide

due to the limited amount of data.

The implication for weather radars in calculating rainrates via a Z−R relationship

therefore becomes quite simple. Only two relationships are required per region, one

in convective conditions, and the other in stratiform rainfall. While these relations

are not perfect, they would still provide more accurate estimations of the rainrate

than the Marshall Palmer relation Z = 200R1.6. To demonstrate this feature, Figure

7.16 shows rainrate calculations in the convective and stratiform regions separately.

In each plot, the profiler-measured rainrate at 1.8 km altitude on 18 February 2006

in Darwin is shown with the broken line. This height level was not chosen for any

particular reason other than it provided a good variety of rainrate values. The

purple line in both plots depicts the rainrate calculated from the profiler-derived

reflectivity via a Z−R relationship, with the coefficients listed above for convective

and stratiform regions. For comparison, the blue line depicts the Marshall-Palmer


(a) Convective.

(b) Stratiform.

Figure 7.15: Reflectivity vs. rainrate calculated from the Z−R relationships derivedfor convective (a) and stratiform (b) rainfall during TWP-ICE. Both quantities areplotted on a log scale. The dashed line shows the 1-to-1 relationship.


Z−R relationship, also calculated from the profiler-derived reflectivty. Note that the

profiler-derived quantities have not been calibrated. It is obvious in both plots that

the Marshall-Palmer is an underestimation of the true rainrate. In the stratiform

region, the derived Z − R relationship shows excellent agreement to the measured

rainrate. In the convective example, agreement is not as good as in the stratiform,

but the derived relation still provides a much improved approximation to the rainrate

over the Marshall-Palmer relation.

Referring to Table 5.6, for the stratiform region, the derived coefficients on 18

February (A = 500 and b = 1.04) are similar to those derived in the overall relation,

that is a difference in A of 40 and a difference in b of 0.01. In the convective region,

the coefficients are somewhat different (A = 990 and b = 0.90), that is a difference in

A of 210 and a difference in b of 0.02. This explains why the stratiform region shows

much greater agreement, when the overall relationship is much closer to that derived

for that region. The convective region still provides a much improved approximation

compared to the Marshall-Palmer relation, but it is apparent that for best accuracy,

coefficients must be derived for individual events.

The Australian Weather Watch radar network currently utilises only the Marshall-

Palmer relation when calculating rainrates [Jenny Dickins, private communication,

2010]. The above analysis indicates that this relation does not provide a satisfactory

estimate of rainfall. Far greater accuracy in rainrate estimation would be obtained

if two relationships were implemented, one for stratiform and one for convective

rainfall. This comes with the obvious caveat of then having to differentiate between

these rain types in near real-time, however a broad differentiation based on reflec-

tivity would provide better rainfall estimates than the current Australian standard.

Chapter 4 included some discussion on profiler analysis of rainfall in near real-

time. Essentially, with appropraite quality control algorithms, the profiler can func-

tion as a disdrometer, but with greater information gains due to greater sampling. A

profiler analysing the DSD in near real-time then also permits the calculation of Z−R relationships in near real-time. The animation “derived rainrate animation.gif”

shows the same convective region of 18 February 2006, with a Z − R calculated

rainrate using increased lengths of time averaging. The profiler-calculated rainrate

at 1.8 km is shown with the broken line, while the blue line depicts the rainrate

calculated via a Z − R relationship. Using only a few timestamps, the approxima-

tion to the profiler measured rainrate is overestimated. However, from around the


(a) Convective.

(b) Stratiform.

Figure 7.16: Examples of Z − R relationships in convective (a) and stratiform (b)regions on 18 February 2006. Broken lines indicate the profiler-measured rainrate at1.8 km altitude. The purple line is the rainrate calculated via a Z −R relationshipwith coefficients derived from rainfall during TWP-ICE. The blue line shows therainrate calculated via the Marshall-Palmer relation.


11th timestamp the approximation becomes quite good. Given the operation of the

Darwin profiler, 11 timestamps represents ∼ 22 minutes of the rain event. This is a

proof-of-concept that the profiler can be used to derive the coefficients of a Z − R

relationship after the profiler has sampled ∼ 30 minutes of data. The disadvantage

here is that storms must pass directly over the profiler. However, a useful application

would be in a situation where the weather patterns are somewhat predictable. For

example, the majority of Adelaide’s storms come from either the south or west of

the city. Considering storms moving eastwards, if a profiler was located to the west

of the city such that at least 30 minutes of profiler samples could be taken before

the storm reached the city, an accurate depiction of the rain event would have been

formulated. Analysis of precipitating weather patters would indicate an appropriate

position for the profiler. This system would be particularly useful in the advent of

severe storms.

7.3.2 D0-Zdr Relationships

Modern, dual-polarisation scanning radars offer significant opportunities to gain

more information on precipitation than is possible with single frequency radars.

Significant research effort has therefore been dedicated to characterising the DSD

using these radars. As discussed in section 2.4, the median drop diameter can be

related to the differential reflectivity via an empirical relationship.

Williams and May [2008] derived a D0 −Zdr relationship using a dual frequency

profiler system and CPOL, during three stratiform rain events from December 2001

and January 2002. Their relation is given by D0 = 1.430Zdr0.40. Figures 7.17 and

7.18 show the median drop diameter derived from the University of Adelaide pro-

filer, against the CPOL measured differential reflectivity at corresponding times and

heights. Figure 7.17 shows results derived from stratiform rain events, while Figure

7.18 shows results from convective events. Events are coloured according to sea-

son. The stratiform events show some agreement to the relation, but the convective

events do not. This is not at all surprising given the relation was derived from strat-

iform events. The agreement with both a different profiler and different stratiform

data lends support to the relation, and suggests that, like Z − R relations, this

power law must vary with varying precipitation to accurately describe the median

drop diameter.


Figure 7.17: CPOL differential reflectivity versus profiler retrieved median dropdiameter for corresponding times and heights in stratiform rainfall events duringTWP-ICE. Points are coloured according to seasonal regime. The solid line is givenby the relation D0 = 1.430Zdr

0.40, the dashed lines represent the uncertainties, givenby D0 = 1.430Zdr

0.40 ± 0.172Zdr−0.60.

7.4. CONCLUSION 207

Figure 7.18: As for Figure 7.17 but for convective rainfall events during TWP-ICE.

7.4 Conclusion

This Chapter has discussed the results from Darwin and Adelaide presented in the

previous two chapters. Results from Darwin where somewhat surprising in that av-

erage storm properties did not vary greatly between the active monsoon and break

seasons. This is an important result for modeling studies, as in terms of precipita-

tion, intra-seasonal variations need not be considered. Results from Adelaide were

disappointing due to the lack of data. While one event was typical of the Adelaide

region, it cannot be placed in any context without comparison. The concept of

equilibrium distributions was explored, with the conclusion made that there were

no observations of such a distribution in this study. Observation conditions were

different to those previously reported in the literature, where equilibrium distribu-

tions were observed in the updraft of convection. Further observations are therefore

required to fully explore this possibility. The increase in median drop diameter

from approximately 2.5 km downwards under a bright band signature, which was

observed on four occasions, was discussed. The conclusion was made that a lack of

clear-air signal caused the false description of D0. Finally, empirical relationships

were examined. In convection values of A were larger, and b were smaller than pre-


viously reported in the literature. However, this is due to previous investigators not

discriminating between rainfall types. In this study rainfall was separated into con-

vective, transition and stratiform regions and Z − R relations derived accordingly.

A D0 − Zdr relation was also examined with the present data set from Darwin. In

the concluding Chapter to this thesis, a summary is provided along with directions

for future work.

Chapter 8

Conclusions and Future Work

This thesis has discussed the retrieval of rain dropsize distributions in the tropics

and mid latitudes. Retrievals were calculated using a direct deconvolution method,

therefore not assuming an a priori shape of the DSD, allowing examination of the

evolution of the DSD in both space and time. Chapter 1 overviewed the development

of rainfall research, from the early flour bed/filter paper methods, to purpose-built

instrumentation such as disdrometers, and finally profiling radars capable of simulta-

neously measuring echo due to clear-air and precipitation. Chapter 2 continued the

discussion on profiling radars, and summarised the relative advantages of VHF and

UHF profilers. The profilers and scanning radars used in this study were introduced

in this chapter, including an overview of scanning radar displays. The increased

capabilities of dual-polarisation scanning radars, representing the next generation

in scanning weather radars, was also discussed.

Chapter 3 introduced the DSD retrieval technique, detailing the procedure used

to separate the clear-air and precipitation peaks, fit a Gaussian to the clear-air, a tail

to the precipitation echo, and deconvolve the functions. Dealing with interference

in the spectra was discussed, as well as the procedure for automating this code.

Automation involved detecting if a precipitation peak was present in any given

spectrum, allowing the code to be run on any data without prior knowledge of

there being any rainfall. This is a necessary first step in real-time calculations of

the DSD. Chapter 4 discussed the problems with the automation of this retrieval

procedure, and introduced the quality control routine written to identify problematic

retrievals. To provide a first order approximation to the “true” rainfall parameters

210 CHAPTER 8. CONCLUSIONS AND FUTURE WORK

calculated from the retrieval, the quality control routine replaces flagged retrievals

with the average of the two spectra immediately below the flagged one. This chapter

demonstrated how this quality control routine can potentially be implemented in a

near real-time setting.

Chapters 5 and 6 presented two case studies each of rain events in Darwin and

Adelaide respectively. Data from Darwin were collected during the TWP-ICE, and

in total 9 rain events were retrieved and analysed. Data from Adelaide are limited to

just two events, largely owing to a drought experienced in South Australia between

2006 and 2008. Results from both locations are compared and contrasted in Chapter

7. Evaporation was found to be the dominant microphysical process affecting the

DSD, and vertical motions in the tropics, in both active monsoon and break periods.

Data from Adelaide was too limited to draw any conclusions on microphysics. In

terms of the median drop diameter, little difference was found between convective

and stratiform rain regions in either the active monsoon or break. When comparing

stratiform/convective rainfall between seasonal periods, larger drops were found

in the active monsoon for stratiform rainfall, and during the break for convective

rainfall. Results from Adelaide showed larger drops in convection than in stratiform

rain, but overall drops were much smaller in Adelaide, largely concentrated below 1

mm. This characterisation of the median drop diameter has important implications

when modelling rainfall, where location in latitude must be considered. Further,

median drop diameters for all results presented in this thesis were plotted against

reflectivity. Here it was shown that a measured reflectivity cannot be correlated to

median drop diameter. This means that a single empirical relationship cannot be

derived for standard Australian scanning weather radars, and must be left to the

next generation of dual-polarisation radars.

The concept of equilibrium distributions was discussed, and found to not be ob-

served in these data, despite several instances of apparently balanced microphysics.

There are no observations of warm rain dominated systems in these data, where pre-

vious observations of equilibrium distributions have been made. Empirical relation-

ships were also discussed, particularly the Z − R relationship. Here it is concluded

that for best results, Z − R relationships must be derived for individual events.

Very good approximations can be made however, utilising just two relationships per

location, one for stratiform and one for convective rainfall.

8.1. FUTURE WORK 211

8.1 Future Work

The lack of results from Adelaide make comparisons of the tropics to mid latitudes

difficult. A data set of similar size and quality of data from the mid latitudes to

that obtained during TWP-ICE would make comparisons more reasonable. This

then, is first and foremost in directions for future research. The Adelaide radar was

built as a prototype, and is in need of maintenance. In the first instance, fixing

the sub-array which is not transmitting would be appropriate, however as stated

in section 2.1.2, the radar enjoyed superior height coverage when operating with a

proprietary RDAS and transmitter. Since height coverage is important in observing

the DSD and its natural evolution, this would be the ideal solution. An improved

radar however, does not improve the weather, and therefore it is potentially more

advantageous to look at multiple profiling radar sites in the mid latitudes to collect

this data set.

The Darwin radar has also recently been improved, and now routinely returns

reliable data down to 300 m. Collecting more data from Darwin is therefore another

direction for future work, to observe the DSD throughout almost its entire fall range.

At 100 m range resolution, the Darwin system is limited by the acquisition system.

An improved acquisition system would allow collection of rainfall data from 300

m above the ground up to the freezing level with excellent resolution. This would

provide the most accurate information possible from a VHF profiling radar with

some relatively minor improvements to the system.

Part of this work involved automating the DSD retrieval procedure, such that

the code recognised if a rainfall echo present in any given spectrum. This results

in the ability to retrieve and display DSDs on a near real-time basis, effectively al-

lowing the profiler to function as a disdrometer. The profiler is superior technology

to the disdrometer however, firstly because the disdrometer collects data only on

a 50-cm2 surface, and secondly because the profiler samples the DSD throughout

its fall. The retrieval, for varied reasons discussed in Chapter 4, is sometimes inac-

curate. The QCR was developed to identify these inaccuracies, and provide a first

order approximation to the true value, based on two range gates immediately be-

low the inaccurate retrieval. In a real-time setting, these first-order approximations

are accurate enough to provide an overview of the current microphysical processes

dictating rainfall.

212 CHAPTER 8. CONCLUSIONS AND FUTURE WORK

A more accurate quality control routine could be developed, if some measure

of determining the problem with the retrieval could be created. Some level of co-

herency, both spatial and temporal, is expected in the location and spectral width

of the clear-air peak. It therefore seems simple enough to both determine if the

clear-air fit is the problem, and implement a solution, by comparison to adjacent

spectra. Since QCR is useful in flagging suspect spectra, a secondary check could

compare the location and spectral width of the flagged spectra with surrounding

spectra. If the spectral width of the flagged spectrum is much smaller or larger than

those surrounding, the code has either fitted the Gaussian to a spike, or produced a

broad-fit. In these cases, a new initial guess to the parameters of the Gaussian can

be calculated from the values surrounding the flagged spectrum, and the retrieval

re-calculated. If the location of the clear-air peak differs from surrounding spectra,

the code has mistaken the interference peak for the clear-air. This can be alleviated

by replacing the peak with the noise floor, and re-calculating the retrieval. A similar

method could be employed with regard to the location of the divide between the

clear-air and precipitation echoes, as some coherency is also expected here. Prob-

lems which cause the code to calculate a retrieval when there is no precipitation

peak do not require re-calculation, as the QCR successfully flags these and replaces

them with zero values.

Heating rates during stratiform rainfall, where Q1 does not balance Qp were ob-

served in Darwin. This indicates evaporation is not driving the downdraft. Further

investigation of the heating rates, and the cause of the downdraft, whether it be

precipitation drag on another mechanism is an interesting area of future research.

It was found, particularly in Darwin, Z-R relationships are specific to individual

rain events. If the retrieval code and any necessary re-calculations can be imple-

mented in near real-time, Z-R relationships can subsequently be calculated for each

event. This would then improve the accuracy of scanning radar rainfall estimations.

Appendix A

Glossary of Terms

ARM atmospheric raditation measurement

BL boundary layer

BP Buckland Park

CPOL C-band polarimetric radar

CW continuous wave

DSD drop size distribution

ENSO El Nino-Souther Oscillation

IOD Indian Ocean dipole

JWD Joss-Waldvogel disdrometer

MCS mesoscale convective system

M-P Marshall-Palmer

PDF probability distribution function

pIOD positive Indian Ocean dipole

POSS precipitation occurrence sensor system

PPI plan position indicator

PRF pulse repetition frequency

RHI range height indicator

SA spaced antenna

SST sea surface temperature

ST stratosphere-troposhere

TRMM tropical rainfall measuring mission

TWP-ICE tropical warm pool international cloud experiment

UHF ultra-high frequency

VHF very-high frequency

214 APPENDIX A. GLOSSARY OF TERMS

QCR quality control routine

QPE quantitative precipitation estimation

QPF quantitative precipitation forecasting

RDAS reciever and data acquistion system

2DVD two-dimensional video disdrometer

Appendix B

Precipitation Microphysics

B.1 Introduction

“The most readily observable parameter that indicates the detailed three-dimensional

structure of the cloud system below the cloud top is the precipitation, which can be

scanned by radar. The radar has both broad coverage and high resolution, and the

spatial pattern of the radar reflectivity of the precipitation is a sensitive tracer of

storm organisation.” Houze [1993]

In this chapter we explore the basics of the microphysics associated with a precipi-

tating cloud, in order to better understand the results presented in chapters 5 and

6. This is not intended to be an in-depth discussion, but rather an overview of the

cloud structure and dynamics relevant to this study. For a more detailed analysis

the reader is referred to texts such as Houze [1993] and Rogers and Yau [1989]. It

should be noted that we present this information in an idealised form, unlikely to

occur so neatly in the real atmosphere. The discussion starts with the formation of

clouds in the atmosphere and the conditions under which clouds begin to precipi-

tate. We then discuss the characteristics of convective and stratiform rain processes

in the tropics and mid latitudes individually, before considering them in connection

in a mesoscale convective system.

216 APPENDIX B. PRECIPITATION MICROPHYSICS

B.2 Cloud Formation

Water vapour condensing in the atmosphere will only form a cloud droplet if its

radius exceeds a critical threshold. The supersaturation required for drops to con-

dense purely from vapour, and exceed this critical survival radius does not occur in

the natural atmosphere. Instead, aerosol particles act as cloud condensation nuclei.

Molecules of water vapour condense on aerosol particles forming spherical caps in a

process of heterogenous nucleation, and the combined radius of aerosol and water

cap has a much greater chance of exceeding the critical radius. Assuming the crit-

ical radius is achieved, the newly formed cloud droplet grows as vapour is diffused

towards it. Growth of individual cloud particles ceases when there are too many

drops competing for available vapour. The cloud is then fully formed and in a stable

state.

Aerosol particles are both omnipresent and abundant in the atmosphere. Particles

come in many and varied forms; natural constituents such as dust and sea salt, ash

from bushfires, and human introduced factors such as industrial by products. The

aerosol concentration of an atmospheric region has an enormous effect on the size

distribution of particles in a cloud. The larger the formed nucleus, that is the more

the radius exceeds the critical threshold, the better the chance that drop has of

survival. Nuclei also have a better chance of survival if the aerosol particle is soluble

in water, hence vapour molecules in a forming cloud tend towards the largest, most

soluble aerosol particles first. The growth rate of formed particles is also dependent

on the concentration and type of aerosols. Droplets which form on larger aerosols

develop, at least initially, at a faster rate than droplets formed on smaller aerosols.

Clouds form in regions of adiabatic ascent, where moist air is cooled and relative

humidities approach 100%. The development after this formative stage, and in

particular whether the cloud will precipitate or not, is dependent not on the internal

properties or structure of the cloud, but on large scale phenomena in the surrounding

environment, such as updraft speed and moisture supply.

Thus far, only warm clouds have been considered, where the temperature is every-

where greater than 0oC. If the cloud continues to ascend, its top may be cooled

to temperatures below 0oC, and the water droplets become supercooled. Whether

water drops freeze depends on whether they come into contact with a suitable nu-

cleating surface.

B.2. CLOUD FORMATION 217

In cold clouds, the formation of ice crystals is not as simple as water droplets because

ice particles do not form readily on many particles found in the atmosphere. As is

the case with vapour condensing to liquid, ice crystal formation is enhanced by the

presence of a nucleating surface, because formed crystals then have an increased

chance of exceeding the critical radius of survival. The difference in the case of cold

clouds, is that the probability of heterogeneous nucleation is highly dependent on

the molecular structure of the nuclei. Ice exhibits a crystal lattice structure, and

nucleates most readily on surfaces with a similar structure. In this respect, ice itself is

the most effective nucleating surface. Some clay materials found in certain soil types

and bacteria in decayed plant leaves have similar structures to that of ice, and can

provide alternative nucleation surfaces, but are of low concentration in the natural

atmosphere. The probability of ice particle nucleation increases with decreasing

temperature, and ice crystals tend to appear in clouds in appreciable numbers when

the temperature drops below -15oC. Observations of cold clouds confirm that, with

decreasing cloud top temperature, the concentration of ice crystals increases [Rogers

and Yau, 1989]. When the temperature drops to -40oC homogeneous nucleation

becomes possible and any liquid drops present freeze spontaneously.

The occurrence of ice crystals in a cloud is related to the cloud type, temperature

and age. Clouds are unlikely to consist of any ice particles at all until cloud top

temperatures decrease to -5oC, and clouds are unlikely to be free of ice when tem-

peratures decrease to -20oC. Ice is more common in decaying cumulus clouds than

in newly forming clouds. Ice is more common and more important in stratiform

clouds than in cumulus clouds with the same cloud top temperature. Since nucle-

ating surfaces are rare, when the first ice crystals in a forming cloud appear they

find themselves in an environment with an abundance of vapour available for rapid

growth by diffusion and deposition. The conditions will remain favorable to rapid

growth provided there are liquid droplets present to evaporate. The ambient con-

ditions in which an ice particle forms dictate not only its growth rate, but also the

shape the crystal assumes.

Once formed, clouds exist in a stable state, composed of an assembly of tiny droplets

with a radius around 10 micrometres, and a density of several hundred per cubic

centimetre [Rogers and Yau, 1989]. As cloud drops form and grow they are subject

both to the force of gravity and the frictional force of the surrounding environment.

Cloud droplets grow to a maximum radius of approximately 0.1 mm [Houze, 1993].

At these sizes, fall speeds are negligible and we consider these drops to remain


suspended in air indefinitely. However, if a drop has grown beyond this threshold

size it will fall towards earth with a terminal fall speed dependent on its radius. We

now discuss precipitating cloud.

B.3 Precipitating Clouds

Cloud populations becoming unstable leads to precipitation. When water drops

become too large to remain suspended the cloud is considered unstable and drops

begin to fall. Clouds are also considered unstable if an ice particle exists within a

population of supercooled water droplets. In this case, the ice crystal will grow by

diffusion of vapour towards its, at the expense of the evaporation of water droplets.

In parity with water drops, once the ice crystal has grown to an appreciable size in

comparison to the surrounding population of droplets, it begins to fall.

As precipitation particles fall, they can either grow or diminish in size through sev-

eral different processes. As we have already discussed, a water drop will continue to

grow by process of condensation if vapour diffuses towards it, or conversely diminish

if vapour diffuses away through evaporation. The diffusional growth rate of a drop is

dependent on both the temperature and humidity of its surrounding environment,

and also on the radius of the drop [Houze, 1993]. An ice particle can also grow

as vapour is diffused towards it by process of deposition, and diminish if vapour

is diffused away by sublimation. The shape of an ice crystal which is growing by

vapour diffusion is influenced by both the temperature and supersaturation of the

surrounding atmosphere.

Water drops can grow by collision-coalescence as they fall, where colliding droplets

merge to form a larger droplet. Usually, a large droplet will “capture” a smaller

one, as larger droplets fall at faster speeds. Ice crystals can also grow by collisional

processes; forming snowflakes, graupel or hail depending on the collision being with

other ice crystals or water droplets. Collisions in a cold cloud are termed aggregation

if ice particles collect other ice particles, or accretion/rimming in the case of ice

particles collecting water drops. Water drops freeze on contact with the ice particle

in this case. Aggregation is strongly dependent on environmental temperature, as

ice particles become “sticky” at temperatures higher than -5oC, thus increasing the

chances that colliding particles will fuse. Certain ice crystal shapes are also more

prone to aggregation than others.

B.3. PRECIPITATING CLOUDS 219

Riming is dependent on the liquid water mixing ratio. Riming can occur to any

extent, but when it is so heavy the ice particle shape is no longer distinguishable,

the new particle is known as graupel [Houze, 1993]. Extreme riming results in

the formation of hailstones, formed when either graupel or frozen raindrops collect

supercooled cloud droplets. Ice particles can also simply melt as they descend into

regions with temperatures greater than 0oC.

As water drops become larger, their shape changes from spherical to oblate spheroid.

If drops grow too large, beyond 6 mm they become unstable and break up into

smaller drops.

B.3.1 Rainfall

Raindrops are defined as those drops large enough to fall from cloud base to ground

before evaporating. The dividing line between cloud and raindrops is a radius of

approximately 0.1 mm. Rainfall is broadly classified into two categories, stratiform

and convective. Stratiform precipitation is defined as a precipitation process in which

the vertical velocity of air does not exceed the terminal fall velocity of ice crystals and

snow, typically 1− 3 ms−1 [Houze, 1993]. Convective precipitation is much heavier

and associated with severe weather. Convective drops typically fall with speeds

exceeding 3 ms−1, and can fall as fast as 10 ms−1. Another distinction between

stratiform and convective processes is the time taken for precipitation particles to

form. In convective clouds the time scale can be short as 20 minutes, while the

process is much longer in stratiform clouds typically taking 1 - 3 hours. We will now

discuss convective and stratiform cloud formation and precipitation.

B.3.2 Convective Precipitation

Convective, or cumuliform clouds occur when moist air becomes less dense than the

surrounding environment in a localised region, typically of the order of 0.1−10 km in

horizontal extent. The buoyancy of this air then accelerates in an updraft of 1− 10

ms−1 magnitude, which equals or exceeds the terminal fall speed of precipitable

particles. In this study we are concerned mostly with cumulonimbus clouds; that

is those that produce the characteristic anvil shape closely associated with severe

storms.

As a result of the rapid lifting in the buoyancy driven updraft a large liquid water


content evolves. It is here that precipitable particles are grown by accretion of

liquid water. This accretional growth can lead to the formation of hailstones in

extreme cases. Consider Figure B.1 showing a schematic sketch of the evolution

of a cumulonimbus cloud. These clouds begin life as small cells, very often at

temperatures warmer than 0oC. The intense updraft within these cells allow them

to grow vertically in a “tower” shape. A, in Figure B.1, shows a cell in this formative

stage, where particles are carried aloft. Note that the cell is already characterised

by high reflectivities.

Figure B.1: Evolution of a convective cloud. A shows the cell in its formation stage,as particles are lifted in the intense updraft. B depicts the cloud growing into the“tower” shape, with particles still being carried upwards, growing by accretion. ByC, particles have become large enough to overcome the updraft and fall. D showsthe cloud in its fully formed, precipitation stage. The cloud top has reached thetropopause and begun to spread out, and ice particles have melted and are fallingto the ground as heavy rainfall. Convective clouds are characterised by maximalreflectivity’s throughout their formative and mature stages. Schematic adaptedfrom Houze [1993]

Cumulonimbus clouds continue to grow vertically with particles growing through

accretion in the updraft (B in Figure B.1). Eventually particles grow to large enough

sizes that they can overcome the updraft and fall, as shown in C in Figure B.1. Due

to the intensity of rainfall in convective cores, precipitation particles can initiate

downwards acceleration by dragging air downwards as they fall. Melting of particles

as they pass the freezing level and possible evaporation may also contribute to the

establishment and sustention of this downdraft. Rapidly moving up and downdrafts

are very turbulent, leading to the entrainment of surrounding environmental air,

modifying the cloud dynamics and microphysics.

Cumulonimbus clouds, provided the updraft continues, continue to grow vertically


until they reach the tropopause, where their tops spread out and form the charac-

teristic anvil, as depicted by D in Figure B.1. By this stage of the clouds formation,

precipitation particles which grew through the early updraft depicted in A in Figure

B.1 are beginning to reach the ground. Note that convective clouds are characterised

by vertical cores of maximal reflectivity at all stages.

Convective clouds are associated with heavy precipitation, thunder and lightning,

and produce strong outflow winds. They are also the source of cyclones if in-cloud

rotation develops. Convective clouds are also closely connected with stratiform

clouds as we will now discuss.

B.3.3 Stratiform Precipitation

Stratiform rain falls from nimbostratus clouds, primarily associated with widespread

continuous clouds of mesoscale convective systems, hurricanes and extra-tropical cy-

clones. Nimbostratus clouds occur extensively in both the tropics and mid latitudes.

They typically have a base near 4 km, and tops near the tropopause. Ice particles

play an important role in stratiform rainfall; all precipitation that reaches ground

began life as an ice crystal in the upper levels of a nimbostratus cloud. In contrast

to convective rainfall discussed above, precipitating particles in stratiform clouds

grow from the top down.

As inferred previously, nimbostratus clouds always occur in association with convec-

tive cloud, and it is the convective updrafts that provide the source of ice crystals in

the upper levels of the nimbostratus. Numerical simulations show that without the

influx of ice particles from convection virtually no rain reaches the surface [Houze,

1993]. This process can occur either as a shallow layer of convection embedded in

the upper levels of the nimbostratus, as ice particles in the upper regions of deep

convective towers are advected to neighbouring nimbostratus, or as cumulus clouds

decaying into nimbostratus clouds, leaving ice particles aloft.

When convective cells form in a shallow layer of potentially unstable air they can

become “feeder cells” to a developing nimbostratus cloud. The weak convective cells

sitting on top of the nimbostratus cloud deck have strong updrafts, that allow rapid

growth of precipitable ice particles. The particles then fall into the upper levels of

the nimbostratus layer.

Convective cores evolve into nimbostratus as they decay, leaving ice particles aloft to


grow through stratiform processes. New convective cells can develop simultaneously,

leading to a mixture of cumulonimbus and nimbostratus cloud. As the new con-

vection decays, it will also evolve into nimbostratus, and this process can continue

for many hours leading to vast regions of stratiform rainfall. Gentle ascent through

the upper levels of nimbostratus formed in this way allows sustainability for many

hours. The cause of this ascent is dependent on the meteorological context.

Alternatively, ice particles can be introduced to the top of a nimbostratus cloud

through advection from a well established convective core, if in the presence of

shear of the horizontal wind. Particles grown in the updraft of the convective core

are advected horizontally into the nimbostratus cloud. If the upper level shear is

strong, the stratiform and convective regions can become separated, and appear as

isolated systems, which is not the case.

The method by which ice particles arrive in the upper levels of nimbostratus is

dependent on the meteorological context. Combinations of the methods described

above can also occur. For example, decaying cumulonimbus may retain small cells

that remain relatively active, acting as feeder cells above the nimbostratus, while the

majority of nimbostratus comes from the decay of the convective cloud. Convective

cores may also decay in the presence of shear, resulting in the nimbostratus consisting

partly of ice crystals from decaying convection, and partly from advection.

Regardless of the method of introduction, the microphysics of stratiform rainfall from

this point is largely dictated by the vertical motions. The updraft in the upper levels

of nimbostratus is important. Numerical simulations show that without particles

grown in the gentle uplift, the total mass of rain reaching the surface is reduced by

a factor of four [Houze, 1993]. The time available for growth of the ice particles

falling from nimbostratus cloud top is approximately 1− 3 hours, based on the time

it takes a particle falling at approximately 1− 3 ms−1 to descend 10 km.

Consider Figure B.2, depicting a simplistic radar reflectivity pattern as seen in

stratiform rainfall. We assume that ice crystals are present in the upper regions of

this cloud. In the top layer (A), upwards air motion exists, of the order of a few

tens of centimetres per second. For ice crystals to grow, this upwards motion must

maintain a delicate balance. It must be large enough to maintain supersaturation

by condensing vapour, but small enough to not exceed the terminal fall speed of ice

crystals. As ice crystals fall through this layer they grow by vapour deposition. The

height from which ice particles fall dictates the amount of growing that can occur


due to vapour deposition. Because particles in this region are small, and deposition

is a slow growth process, this region is characterised by low radar reflectivities.

Figure B.2: Precipitation growth in a stratiform cloud. Ice particles, introducedby a convective element, grow by vapour deposition in layer A. Aggregation beginsin layer B, and becomes more dominant as drops approach the freezing level. Iceparticles melt in layer C, known as the radar bright band. Layer D depicts raindropsfalling to earth. Schematic adapted from Houze [1993].

When ice particles fall to within 2.5 km of the freezing level (B in Figure B.2), par-

ticles begin to aggregate and form large irregularly shaped snowflakes. Aggregation

becomes more frequent as drops approach the freezing level. Riming can also occur

here, when vertical motions are strong enough to support a few liquid water drops in

the presence of falling ice particles. No mass is added to the falling particles in the

action of aggregation, but instead concentrates the falling ice particles into larger

clumps. These large clumps produce sharp increases in the radar reflectivity.

Characteristic of stratiform rainfall is the radar bright band, a region of increased

reflectivity near the freezing level (C in Figure B.2). The bright band is a com-

plex region of the stratiform cloud, and the subject of many studies. An example

is Stewart et al. [1984], where aircraft were flown through the melting region of

stratiform clouds. Such experiments lead to the following explanation. As ice par-

ticles approach the freezing level, melting occurs on the surface first, so the particle


takes on the appearance of water, but does not collapse until the melting process is

complete. Because the dielectric constant of water is greater than that of ice, and

particles have not yet diminished in size, there is an increase of approximately 5 dB

in this level. This effect does not fully explain the increases in reflectivity seen at

this level, and it is concluded that aggregation continues to occur here.

Below the bright band (D in Figure B.2) particles have collapsed to form raindrops.

Reflectivity decreases in accordance with decrease in diameter of the drops. The fall

speed of drops also increases in this level, from approximately 1-3 ms−1 for snow to

5-10 ms−1 for raindrops [Houze, 1993]. The mean concentration of rain water at any

given level decreases due to the increase in fall speed, which further acts to reduce

reflectivity.

The microphysics that occurs in this level is dictated by the meteorological context.

In the simplest case, precipitation will fall to the ground at a constant rate. If

an updraft exists in this layer, and potentially another level of cloud, drops will

continue to grow by vapour diffusion, and potentially collection of cloud droplets.

In contrast, if drops fall into a layer of dry air they will evaporate and the flux of

drops reaching the surface will be less than that which fell from the melting layer.

The dry air will be cooled by the evaporation, and downdrafts will likely develop.

Updraft-downdraft couplets, that is an updraft above the freezing level, downdraft

below, are common and quite characteristic of stratiform rainfall in the tropics [May

and Rajopadhyaya, 1996].

This lowest layer is the region of interest in this study. The microphysical processes

and meteorological context which dictate the evolution of the drop size distribution

through this layer have important feedbacks on cloud dynamics and sustainability

of precipitation. Understanding these mechanisms allows for better nowcasting in

severe storms and QPE.

B.4. MESOSCALE CONVECTIVE SYSTEMS 225

B.4 Mesoscale Convective Systems

Mesoscale convective systems (MCS) are responsible for a large portion of the pre-

cipitation that falls to earth in both the tropics and mid latitudes, and hence are

an important part of the current study. All MCS are associated with a large area of

precipitation, including both stratiform and convective components. Houze [1993]

defines a MCS as “a cloud system that occurs in connection with an ensemble of

thunderstorms and produces a contiguous precipitation area 100 km or more in

horizontal scale in at least one direction”.

MCS were first recognised as distinct meteorological phenomena in 1945 [Gamache

and Houze, 1982], but were not extensively studied for another 35 years when the

technology became available. For example, amongst the first studies of MCS include

Zipser [1969], using a composite of satellite, airborne and surface meteorological data

during the Line Islands experiment. Many studies have been conducted since this

time, leading to a vast of knowledge of MCS structure. Following is a description of

the lifecycle of a MCS.

In the formative stage of development, a MCS consists only of isolated cells, such

as those depicted by A in Figure B.1. Figure B.3 shows a schematic of the the PPI

display in this formative stage.

Figure B.3: Isolated convective cells on a PPI display. Schematic adapted fromHouze [1993].


As the storm intensifies, individual cells grow and merge, forming a single contiguous

rain area. Within this rain area are one or more intense cores of precipitation,

interconnected by lighter rainfall. The PPI in this case is shown in Figure B.4.

Figure B.4: Isolated cells interconnected with a contiguous rain area on a PPIdisplay. Schematic adapted from Houze [1993]

The MCS reaches its mature stage when a large stratiform area develops from the

decaying older cells. If new cells continue to form, the MCS stays in this mature

stage, consisting of active cells, weakening cells and stratiform precipitation. Con-

sider the schematic shown in Figure B.5, depicting a MCS in this mature stage.

Cloud and precipitation are detrained from the top of active cells, and if the upper

level winds carry the condensate away from the rain area, an overhang of radar echo

can form, as shown in this schematic. Alternatively, the winds carry the condensate

back towards the centre of the rain area, where it combines with the stratiform

clouds and precipitation formed from the old cells. We see in this figure an active

convective cell, characterised by a vertical core of high reflectivity. The updrafts

in active convective cells are sometimes so vigorous the cloud top breaks through

the tropopause and continues to extend vertically, as seen in this schematic. To

the left of the active cell is a decaying convective cell, and to the left of this is a

region of stratiform rainfall with a characteristic bright band. These elements are

interconnected with lighter rainfall.

The MCS reaches its dissipating stage when the formation of new convective cells

B.4. MESOSCALE CONVECTIVE SYSTEMS 227

Figure B.5: Schematic of a Mesoscale Convective System in its mature stage. Thesystem consists of an active convective call (far right) characterised by a verticalcore of maximal reflectivity, decaying convective cell (middle) and a stratiform regioncharacterised by a radar bright band. These elements are interconnected with lighterrainfall. Schematic adapted from Houze [1993]


ceases, and the system consists of weakening stratiform precipitation, such as shown

on the PPI in Figure B.6. Although the rainrate in the stratiform region is con-

siderably less than in the convective, the great area covered by the stratiform rain

implies a large total fallout of water mass over the whole region. It is typical for the

stratiform rain to account for 25-50% of the total rain integrated over the lifetime

of a MCS.

Figure B.6: Decaying stratiform rainfall on a PPI Display. Schematic adapted fromHouze [1993]

A commonly occurring MCS, seen in both the tropics and mid latitudes, is a leading

convective line (squall line) with trailing stratiform precipitation. These systems

have been extensively studied due to their relative simplicity in comparison to other

mesoscale convective systems.

Figure B.7 shows the general trends of airflow in an idealised convective line with

trailing stratiform precipitation. Two concurrent trends of motion are seen, inter-

acting with the storm from the front and rear. Beginning in the boundary layer

intense upwards motion is seen. This persists through the convective region, and

into the stratiform, where it levels out to become more horizontal and is known as

the ascending front-to-rear flow [Houze, 1993]. Entering the storm from the rear, the

descending current, known as the descending rear inflow, moves under the base of the

stratiform cloud, entering the stratiform region above melting level and descending

to interact with the back of the convective region at low levels. This interaction rein-

a1172507

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B.5. MIDDLE LATITUDES 229

forces convergence and overturning at the leading line. The arrows in the stratiform

region falling away from the rear inflow depict the descending cold pool, associated

with precipitation fallout and evaporation. Decaying convective cells and some ice

particles are advected rearward to maintain the stratiform region.

As already discussed, within the convective core we see an intense updraft, pene-

trating the top of the cloud shield and allowing the cloud to grow vertically in this

localised region. We also see the formation of a downdraft in mid levels, associated

with the precipitation drag and possibly evaporation.

Figure B.7: Schematic showing the general airflow trends in a leading convectiveline with trailing stratiform precipitation. Schematic adapted from Houze [1993]

B.5 Middle Latitudes

Initiation of cloud formation in the middle latitudes is somewhat different to the

tropics, and is largely dictated by baroclinic processes. Strong horizontal tempera-

ture gradients, usually associated with an upper level jet stream, exist in the mid

latitudes. This is in contrast to the tropics, where the horizontal thermal variation

is negligible. A baroclinic wave can develop when the wind at a given pressure

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Text Box



level blows parallel to these temperature gradients. Mid latitude synoptic systems

generally develop from infinitesimal perturbations on this baroclinic wave. These

small perturbations can then amplify exponentially, drawing potential energy from

the mean flow [Holton, 1972].

Such a perturbation causes the ascent necessary in cloud formation. Meridional

motions of the perturbation distort the original temperature gradients, forcing cold

air to the north (in the southern hemisphere) and warm air to the south, resulting

in a trough. Since cold air has been forced into a warmer environment on one side

of the trough it sinks, while the warm air forced into a cold environment rises, thus

providing a suitable environment for cloud formation.

The manifestation of a small perturbation on a baroclinic wave tends to form a

closed cyclonic shape, in a process known as cyclogenesis [Houze, 1993]. When

air streams of varied temperatures and vertical circulations which result in clouds

come together on a small scale in the low levels the process is termed frontogenesis.

Other causes, such as the release of latent heat, can trigger synoptic systems in

the mid latitudes, however observational evidence and numerical models suggest

cyclogenesis and associated frontogenesis, is the primary developmental mechanism

of cloud formation and hence precipitation in the extra-tropics.

We will now look at the evolution of a precipitation field in the context of a mesoscale

convective system, and the associated radar patterns. We will also further discuss

the symbiotic nature of convective and stratiform precipitation.

B.6 Conclusion

In this chapter we have briefly examined the microphysics concerning cloud forma-

tion and precipitation. We have looked at the difference between stratiform and

convective precipitation, and the dependence of nimbostratus cloud on convective

activity. We discussed precipitation types in the context of a mesoscale convective

system, and looked at the dynamics of the air motion. We have seen the many and

varied processes droplets can undergo on their descent to earth.

It is very important for quantitative precipitation estimation to understand which

processes are dictating the drop size distribution. We discuss seasonal trends, storm

evolutionary stage and latitudinal location in relation to microphysics in Chapters

B.6. CONCLUSION 231

5 and 6.

Appendix C

Equilibrium Distributions

The central idea behind an equilibrium distribution is a balance of the microphysical

processes. This idea was first identified in modelling studies conducted to understand

the evolution of rainfall from cloud base to the surface. List and Gillespie [1976]

described a scenario where collisions of small and large drops were likely to cause

the larger drop to fragment into smaller drops, thus reducing the overall population

of large drops. Over short integration times, this DSD approaches a steady shape

with a steep slope. Gillespie and List [1978] proposed all DSDs will develop into

equilibrium distributions, regardless of the initial spectrum given sufficient time.

Further, the authors suggested all equilibrium distributions attain the same shape,

and are only different in the sense of a factor proportional to the rainrate. List et al.

[1987] showed equilibrium distributions could take some time to evolve, especially in

low rainfall rates, but the main features of the distribution became obvious within

5 - 10 minutes. Further, the authors reported that while evaporation preferentially

removes small drops, collisional processes rapidly mix the remaining liquid water

across the whole spectrum, allowing the observation of equilibrium distributions.

These modelling studies consider warm rain only, where drops grow by collisional

processes in updrafts until they are massive enough to overcome the updraft and

fall out. Large raindrops are associated with cold rain processes, where large drops

form from melting ice particles. List [1988] argues that in the case of warm rain,

distributions can be considered never far from equilibrium. In the case of cold rain,

the author argued an equilibrium distribution could be achieved. However, fall times

available may not be sufficient to observe an equilibrium.

234 APPENDIX C. EQUILIBRIUM DISTRIBUTIONS

Hu and Srivastava [1995] approximated “showery” precipitation with a spatially

homogeneous model, and stratiform rainfall with a 1D vertical column. Considering

coalescence and break-up only, both models showed the DSD tended towards an

universal shape. For the spatially homogeneous model, the magnitude of the shape

was found to be proportional to the water content, and time taken to reach the dis-

tribution inversely proportional to water content. The vertical model also showed

DSDs become steady at any given height after a certain time has lapsed. The time

taken increases with fall distance. This model also considered vertical motions, and

found that in a downdraft results were similar, except the fall distance to reach equi-

librium increased. They also considered evaporation in both models, and concluded

equilibrium distributions were still achieved, with the evaporation acting to smooth

out the shape [Hu and Srivastava, 1995].

Experimental observations of equilibrium DSDs have also been reported in the lit-

erature, but in general these observations occur when the rainrate is > 50 mm h−1

[Atlas and Ulbrich, 2000]. Based on observations of warm rain, Atlas and Ulbrich

[2000] proposed a conceptual model whereby updrafts act to sort drops by size.

The authors hypothesise that small drops, with a fall speed less than the updraft

are carried upwards and lost in the divergent flow above the updraft. Large drops

descend through the updraft, and reach the surface in a narrow DSD with a large

D0. Further observational studies indicate the major growth of droplets occurs in

the region where drops are approximately balanced by the updraft, which extends

the time available for collisional processes to occur [Atlas and Williams , 2003]. Us-

ing disdrometer data measured in tropical continental storms, Ulbrich and Atlas

[2007] argued equilibrium DSDs could also occur in cold rain processes, when there

is sufficient time below the freezing level for the collision-coalescence and breakup

processes to come into equilibrium.

Equilibrium distributions, like all changes in the DSD, impact the Z-R relationship.

Atlas et al. [1999] showed that the exponent b depends on the relation between the

median drop diameter and rainrate such that

b =ΔdBZ

ΔdBR(C.1)

= 1 + 23.3

(Δ log D0

RΔdB

)(C.2)

235

Thus when D0 attains a constant value, b approaches unity, and reflectivity becomes

proportional to the rainrate. Ulbrich and Atlas [2007] also showed that A increases

with D0 for equilibrium distributions in convection.

236 APPENDIX C. EQUILIBRIUM DISTRIBUTIONS

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