Overview of QPE/QPF techniquesOverview of QPE/QPF techniques and hydrological applicationsy g pp

Siriluk ChumcheanSiriluk ChumcheanDepartment of Civil EngineeringMahanakorn University of Technology

1Typhoon Committee Roving Seminar 2011, Malaysia (20-23 September 2011)

Talk StructureLecture A1: QPE techniques and development

R l ti d i f ll ti tReal-time radar rainfall estimatesCase studies

Lectuer A2: QPF techniques and developmentQPF techniques (Radar-based nowcasting)q ( g)Operation and research development systemsQPF accuracy assessmentCase study : Bangkok rainfall forecasting system

Lecture A3: Hydrological ApplicationsLecture A3: Hydrological Applications Cases studies

2

Real-time Radar Rainfall E i i A O iEstimation – An Overview

3

Why do we need weather radar ?

• Measure rainfall continuously covering l

• Provide fine spatial and

large area

• Provide fine spatial andtemporal resolution

• Can be used to project the storm trajectory, i.e., provide a short-term storm forecast

4

Basic concept of measuring rainfall using radars

r

bZ*K*C bARz =2rZKCp =

where: A,b – radar parameters; Z – reflectivity;

R - rainfall 5

Volume scan data

und (k

m)

und (k

m)

above

grou

above

grou

Heigh

t He

ight

Range from radar (km)

Range from radar (km)

6

Rhine

Pixel 1 km²

Radar site

Intensity class scale (0 – 200 mm/hr)

7

Simplified scheme of radar processing

Measurement of i drain drops

Radar image inReception of the reflectionof the impulse sent out polar coordinates

- continuous values

of the impulse sent out

Transformation

Radar products, e.g. in cartesian coordinates

values in 256 classes- values in 256 classes

8

Polar and cartesian coordinates

Near distance <-> far distance

Due to the radar measurement in polar coordinates, the data near to the radar are denser than far from the radar.When transforming polar data to a cartesian square grid close to the radar several polarsquare grid, close to the radar several polar pixels are used. The spatial resolution of the square grid data is less than that of the originally measured polar data.

Far from the radar, one polar pixel may be the original for several cartesian grid pixels. Here, the density of the data is less andHere, the density of the data is less and therefore measurement errors have a higher impact on the cartesian data.

9

PPIPPI reflectivity map is extracted from the raw reflectivity data

from the beam at a particular elevation angle.

10

CAPPI

Constant Altitude Plan Precipitation Indicator (CAPPI)Constant Altitude Plan Precipitation Indicator (CAPPI)

11

Problems and LimitationsAre parameters measurable?

Are parameters stable?

Does reliability stay constant with distance a a from the radar?distance away from the radar?

What about obstructions (buildings, mountains)? r

bARZ =

mountains)?

What about multiple raindrops and rain-clouds in the path of the beam?

r

ARZwhere

rain clouds in the path of the beam?

What about the effect of the earth’s curvature?

A,b – radar parameters

Z – reflectivityWhat about differences in rain profile on ground versus high elevations?

R - rainfall

12

Problems of using weather radar?g

1 R fl ti it t1. Reflectivity measurement error

• ground clutter• ground clutter

• attenuation

ti l fl ti it fil• vertical reflectivity profile

• beam geometry

2. Reflectivity-rainfall rate conversion error

3. Residual errors when compared with rain gauges

13

Some difficulties …

Ground-clutter bright-band hail attenuation rangeGround clutter, bright band, hail, attenuation, range dependent bias – not so difficult to remove as they can be noticed easilybe noticed easily

PE PE Completescreening

Partialscreening

Noscreening

14

Some difficulties … Distance vs height of gradar beam

7 0 0 0

8 0 0 0

re) [

m] 1 °

5 0 0 0

6 0 0 0

beam

cen

tr

0 ,5 °

3 0 0 0

4 0 0 0

dar

beam

(b

0 °

2 0 0 0

3 0 0 0

ht o

f the

rad

0

1 0 0 0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

Hei

g

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

Dis ta nc e to ra da r loc a tion [k m ]15

Some difficulties …

Increasing uncertainty in measured reflectivity as a function of range

0 8

1.0C

DF)

Increasing

0.6

0.8

tion

Func

tion

(C Increasing range

0.4

ulat

ive

Dist

ribut

Gauge rainfall Measured reflectivity

0.0

0.2

10 5 0 5 10 15 20 25 30 35 40 45 50 55

Cum

mu

-10 -5 0 5 10 15 20 25 30 35 40 45 50 55

Measured reflectivity (dBZ) / Rainfall rate (dBR)

16

Some difficulties …Range dependent errorsg p

17

Some difficulties …Range dependent errorsg p

1st Range 2nd Range1st Range 2nd Range

g 2 Range

1320.02 =GRσ 1320.0)70(0003.0 02 +−= RGRσ

701320.02 =GRσ 1320.0)70(0003.0 0

2 +−= RGRσ

70

( ) ( )[ ] ( ){ }∑=

>−=N

iGRGGR riRiRiR

Ni1

22 loglog1σ=i 1

Anagnostou et al. (1999) 18

Some difficulties … Attenuation examplep

Rainfield without attenuationRainfield attenuated

(up to 6 classes)

Rainfield without attenuation

Marienfeld

Radar Flechtdorf Radar Essen

Einfalt (2004)19

Some difficulties …Bright-bandg

Fabry et al. (1994)20

Some difficulties..Effect of storm types on Z-R relationyp

∫α

Λ 6D ( )∫ ⎟⎞

⎜⎛−

αΛ

34 dDDDNR D

∫ −= Λ

0

6dDDeNZ Do

( )∫ ⎟⎠⎞

⎜⎝⎛= Λ νπ

0 23dDDeNR D

o

Convective Stratiform

Z = 35 dBZ Z = 35 dBZR = 7 mm/h R = 10 mm/h

21

Z-R relationship for each rain-cloudZ-R relationship for each rain-cloud

Parameters ‘a’ and ‘b’ varies on rain drop size

pp

pdistribution.

NimbostratusCumulus Cumulonimbus

22

Z-R relationship of each type of rain-cloud Z-R relationship of each type of rain-cloud (Calibration)(Calibration)

C l i bC

ectiv

ity (d

BZ) Cumulonimbus

ectiv

ity (d

BZ) Cumulus

ectiv

ity (d

BZ) Nimbostratus

Rad

ar re

fle

Rad

ar re

fle

Rad

ar re

fle

Rain gauge rainfall (mm/hr)Rain gauge rainfall (mm/hr) Rain gauge rainfall (mm/hr)

BZ) CumulonimbusBZ) Cumulus

efle

ctiv

ity (d

B Cumulonimbus

efle

ctiv

ity (d

B

Rain gauge rainfall (mm/hr)

Rad

ar re

Rain gauge rainfall (mm/hr)

Rad

ar re

23

Rain gauge rainfall (mm/hr)Rain gauge rainfall (mm/hr)

Chumchean et al. (2009)

Z-R relationship of each type of rain-cloud Z-R relationship of each type of rain-cloud p ypp yp

CumulusCumulus CumulonimbusCumulonimbus NimbostratusNimbostratusZ=29R1 5 Z=55R1 5 Z=208R1 5

•• Rainyseason

Z=29R1.5 Z=55R1.5 Z=208R1.5

Cumulus Cumulonimbus

Z = 30 dBZ Z = 30 dBZ

R = 10.58 mm/h R = 6.90 mm/h

Z = 30 dBZ

R = 2.85 mm/h

• • SummerCumulus

Z=38R1.5Cumulonimbus

Z=90R1.5

Z = 30 dBZ

R = 8.93 mm/h

Z = 30 dBZ

R = 4.99 mm/hChumchean et al. (2009)

24

Some difficulties … 89

t tif

5678

ht (k

m)

stratiform

Variations in Z~R relationships for different t t 1

234

Hei

g

storm types01

0 5 10 15 20 25Reflectivity (dBZ)Reflectivity (dBZ)

789

convective

4567

Hei

ght (

km)

0123H

00 5 10 15 20 25

Reflectivity (dBZ) 25

Some difficulties …

Residual errors – results in a “mean-field-bias”

Exhibits persistence from one time-step to the nextExhibits persistence from one time step to the next

Very important in real-time estimation

Difficult to remove using physical relations

26

Philosophy p y

“Estimated radar rainfall must first be corrected for reflectivity

measurement errors and Z-R conversion errors based on themeasurement errors and Z R conversion errors based on the

physical methods, and then a statistical method will be used to

remove the average difference (mean field bias) between radar

estimates at the rain gauge locations and the correspondingestimates at the rain gauge locations and the corresponding

gauge rainfall amounts”.

27

Real-time radar rainfall estimation methodReflectivity measurements

Record reflectivity field in 3D polar

Z-R conversion

Instantaneous storm

Rain gauge adjustment

i h l dRecord reflectivity field in 3D polarcoordinate at operational temporal

resolution

Instantaneous stormclassification

Estimate hourly gauge-radarbias adjustment factor (AF)based on Kalman filtering

approach proposed by

Exclude reflectivity that aregreater or lower than the

maximum/minimumreflectivity thresholds

Instantaneous convective/stratiform reflectivity

pp p p y(Chumchean et al., 2003)

[under review]

reflectivity thresholds

Conversion to CAPPI Cartesiancoordinate at altitude below

Z-R conversionZ=ARb

stratiform reflectivity

Final hourly radarbright-band level

Remove the effect of ground Accumulate intoAccount for the

Instantaneous convective/stratiform radar rainfall

Final hourly radarrainfall

=AF × initial radar rainfall

estimatesg and sea clutter

Accumulate intohourly radarrainfall

Account for thestorm movementwithin an hour

Initial hourly radar

estimates

Scaling correction rainfall estimates

Chumchean et al. (2006) 28

Real-time radar rainfall estimation

Scaling correction (to remove range-dependent bias) ( g p )

+St l ifi tiStorm classification

(to remove bias in Z~R relation due to the dominant (storm type)

++Correction of residual mean-field bias

29

DataC-band Kurnell radar

10 minute 1km210-minute, 1km2

resolution

Analysis period November 2000 to April 2001

254 h l254 hourly rain gauges (SWC,SCA,BoM)

30

Correction of range dependent bias due to radar beam geometryradar beam geometry

31

Application of scaling in measured reflectivitypp g y

1 . 0

F)

0 . 8

nctio

n (C

DF

0 - 2 0 k m2 0 - 4 0 k m4 0 - 6 0 k m

0 4

0 . 6

tribu

tion

Fu 6 0 - 8 0 k m8 0 - 1 0 0 k m

0 . 2

0 . 4

mul

ativ

e D

is

0 . 01 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0

M e a s u r e d r e f le c t iv i t y ( d B Z )

Cum

m

Assume simple scaling holds for measured reflectivity

M e a s u r e d r e f le c t iv i t y ( d B Z )

32

Scale transformation function

The proposed scale transformation formula is :

0 8

1 .0

n (C

DF)

0 -2 0 km2 0 -4 0 km

0 .6

0 .8

on F

unct

ion 2 0 -4 0 km

4 0 -6 0 km6 0 -8 0 km8 0 -1 0 0 km

0 .4

ve D

istri

buti

0 .0

0 .2

Cum

mul

ati

1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5T rans fo rm e d re f le c tiv ity (d B Z )

33

Range-dependent bias correctiong p

Using simple-scaling theory1:

2 7 8

Using simple-scaling theory1:

2 6

BZ)

6

l (m

m/h

)

2 5

Ref

lect

ivity

(dB

4

gaug

e ra

infa

ll

2 3

2 4

R

0

2

Rai

n

0 - 2 0 2 0 - 4 0 4 0 - 6 0 6 0 - 8 0 8 0 - 1 0 0R a n g e in t e r v a l ( k m )

M e a s u r e d r e f le c t iv it y T r a n s f o r m e d r e f le c t iv it y R a in g a u g e r a in f a ll

1Chumchean et al, 2004, J Atmospheric and Oceanic Technology34

Effectiveness of scale transformation function in correcting range dependent bias in radar rainfall

2.40

2.60

2.00

2.20

atio

(G/R

)

S lope = 8.9 %

1 60

1.80

2.00

ge-R

adar

ra

S lope = 0.3 %

1.40

1.60

Gau

g

1.200-20 20-40 40-60 60-80 80-100

Range interval (km)

35

Effect of storm types on radar rainfall ypEstimates (Z-R conversion error)

36

Instantaneous pixel classificationInstantaneous pixel classification

Apply Steiner et al.(1995) storm classification method to use for separation of instantaneous reflectivity of each pixel into convectiveeach pixel into convective or stratiform components

Revise the classification criteria to be suitable for

convective

instantaneous reflectivity of the Kurnell radar

37

Parameter for pixel classification (after Steiner et al., 1995 )

convective centrebackground radius

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . background radiusconvective radiusminimum convective

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .x minimum convectivethreshold*maximum stratiform

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum stratiform threshold*

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

convective radiusconvective radiusBackground radius

11 km

* = proposed additional classification parameter 38

Classification results: calibration

Using modified Parameters based on

Using modified pixel based Parameters based on

Steiner et al. (1995)pclassificationapproach

39

Classification results: verification

Using modified Parameters based on

Using modified pixel based Parameters based on

Steiner et al. (1995)pclassificationapproach

40

Verification using VPRVe ification using VPR9

1011

Calibration: 20 Apr 01 at 14:35 UTC

Verification1: 30 Jan 01 at 12:25 UTC

(a) Stratiform

45

678

Heigh

t (km

).. Verification2: 10 Feb 07 at 18:35 UTC

01

23

0 5 10 15 20 25 30 350 5 10 15 20 25 30 35

Reflectivity (dBZ)

9

10

11Calibration: 20 Apr 01 at 14:35 UTC

Verification1: 30 Jan 01 at 12:25 UTC

(b) Convective

5

6

7

8

Heigh

t (km

)..

Verification2: 10 Feb 07 at 18:35 UTC

1

2

3

4

H

00 5 10 15 20 25 30 35

Reflectivity (dBZ)41

Correcting for mean field biasCorrecting for mean field bias in real-time radar rainfall

estimates usingestimates using Kalman

?Filtering techniques

?Rain gauge rainfall (G) = AF x Radar rainfall (R)

AF = adjustment factor or mean field biasAF adjustment factor or mean field bias

42

Advantage of Kalman filtering technique over the

1) It accounts for the “noise” in the measurements when updating

simple G/R) p g

the mean bias.

2) It id ti t f th i th t d bi2) It provides an estimate of the error in the computed bias.

3) It combines an estimate of the bias and its error variance3) It combines an estimate of the bias and its error variancemade an hour earlier with the current measurementsand its estimated measurement error variance to compute anupdated bias estimate and new forecast for the next hour.

Time update-tP and ˆ −

tβ

Measurement update

tP and ˆtβ

43

Residual mean-field bias correction1

Logarithmic Mean ∑ ⎟

⎞⎜⎛n

tiG ,l1βg

Field Bias (β)Assumed β exhibits

∑=

⎟⎟⎠

⎜⎜⎝

=i ti

tit Rn 1 ,

,10logβ

βMarkovian dependence (Kalman 5

6Kalman Filter

Observed (G/R)p (process model assumed AR1)

3

4

Bia

s)

Kalman measurement error model specified 0

1

2

pas function of range2 -1

0 100 200 300 400 500 600

Time step (hours)

2Chumchean et al, 2003, Physics and Chemistry of the Earth, 28(3), 27-39.

1Chumchean et al, 2006, Journal of Hydrology, 44

Radar rainfall error variance model

Chumchean et al. (2003)

14.0015.02,

+×−= ttiY Gσ for ri ≤ 55 km ;( ) 14.05513.0 015.02

,+

−×+×−=

prG i

ttiYσ ; for ri > 55 km 45

Comparison of observed G/R and the Kalman-filter estimated bias (Calibration)

5

6Kalman FilterObserved (G/R)

lag 1 correlation coefficientof innovation sequence

3

4= 0.047

2

3

Bia

s

0

1

18 Dec 0012 Dec 00 30 Jan-1 Feb 01 19-22 Apr 013 Nov 00

-10 20 40 60 80 100 120 140 160 180 200 220 240

Ti t (h )

12 Dec 00 30 Jan 1 Feb 01 19 22 Apr 01

Time step (hours)

46

Comparison of observed G/R and the Kalman-filter estimated bias (Validation)

5

6Kalman Filter

Observed (G/R)

lag 1 correlation coefficientof innovation sequence = 0.08

4

( )

2

3

Bia

s

0

1

-1

0

0 100 200 300 400 500 600

Time step (hours)

47

Applicationpp

Stepwise application of error correction strategiesBase reflectivity data free of effects of ground-clutter, y gbright-beam, hailTotal rain gauges - 260Total rain gauges 260Cross-validation performed by leaving fraction of rain

t l t di ti t i tgauges to evaluate predictive uncertaintyPerformance statistic - Root Mean Square Error (RMSE)

48

Results

Climatological Z-R parameters of convective and stratiform rainfall

(Z = AR1.5)

A parameter

No scaling correction Scaling correction Calibration strategies

Convective Stratiform Convective Stratiform

No-classification 128 146

Hourly pixel classification 150 93 172 100

49

Results

3 90

4.10GHNBO

3.70

3.90

m) .

GHNBO+SCGHNBO+SC+ZR

3.30

3.50

RM

SE (m

m

2.90

3.10

2.70Without bias adjustment Kalman Filtering Sample G/R

G b d dj h dGauge-based adjustment methods

‘GHNBO’ – Base data‘SC’ – Scaling correctiong‘ZR’ – Storm classification

50

Resultsa) No bias correction

GHNBO GHNBO+SC GHNBO+SC+ZR

b) sample G/R

GHNBO GHNBO+SC GHNBO+SC+ZR

c) Kalman filtering

GHNBO GHNBO+SC GHNBO+SC+ZRGHNBO GHNBO+SC GHNBO+SC+ZR

51

Conclusions

A stepwise decrease in RMSE with added levels of error correction

Correcting mean-field bias more important that correcting the other sources of errors

Storm classification relatively more important than the correction of range dependent biascorrection of range dependent bias

Kalman filtering much better than use of sample G/R ti ti l l h lib ti icorrection, particularly when calibration rain gauges are

few

52

Conclusions

Range dependent bias and storm-classification, though small, are certainly not insignificant

Complete model (after mean-field bias correction) explains more than 50% variance of gauge rainfallexplains more than 50% variance of gauge rainfall

This may be the best we will ever have – remember weThis may be the best we will ever have remember we are comparing 1kmx1km grid averages to rainfall at a point! p

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