genesis parameters, genesis thresholds, and mid …kuang/davidnolan.pdf · genesis parameters,...
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1
Genesis Parameters, Genesis Thresholds,
and Mid-Level Humidity
Michael G. McGauley and David S. Nolan
Rosenstiel School of Marine and Atmospheric Science
University of Miami
Miami, Florida, USA
This work is supported by the National Science Foundation.
2
I. Background
•A “genesis parameter” is an attempt to correlate large-scale, environmentalvariables with annual or seasonal frequency of TC formation, e.g., Gray (1975):
GP f 5+ Vp
------ 3+ 1–
EOcean
ep
-------- 5+ max
RH 40–30
-------------------- 1
=
3
•Since then, a number of other genesis parameters have been developed, e.g.,
Emanuel and Nolan (2004): GPEN 1053 2 RH
50--------
3 Vpot
70---------
3
1 0.1 Vshear+ 2–=
Figure fromCamargo, Emanuel, Sobel (2007).
They used this GP to diagnose the mechanisms of ENSOinfluence on TC activity.
4
Emanuel (2010) revised the genesis index to:
Tippett, Camargo, Sobel (2011) derived a GP based on a Poisson regression:
GPE10 3 4 3– max Vpot 35– 2 0 25 Vshear+ 4–=
GPT b b bRHRH bR-SSTR-SST bshearVshear coslog+ + + + + exp=
5
II. A New Approach
•Of course, the GP approach reflects a number of assumptions:
* The influence of each parameter is independent of the values of the others
* The number and strength of pre-cursor disturbances does not matter(some evidence for this)
* Mean values can be used a consistent proxy for more favorable conditions(PDF does not vary with location or season)
6
II. A New Approach
•Of course, the GP approach reflects a number of assumptions:
* The influence of each parameter is independent of the values of the others
* The number and strength of pre-cursor disturbances does not matter(some evidence for this)
* Mean values can be used a consistent proxy for more favorable conditions(PDF does not vary with location or season)
But in fact - the shapes of these PDFs can vary substantially:
7
•With the last issue in mind, we have developed an alternate approach:the genesis frequency index:
where each f is the frequency that each parameter is above or below somethreshold value that will permit TC genesis - given that all the other parametersare highly favorable.
•The GFI formula is very flexible: one can remove or add parameterswithout reformulation
•For now we are also neglecting the issue of generating disturbances
GFI fVpot fshear fRH f=
8
•To build the GFI, we need to:
1) Identify a highly favorable but realistic atmospheric environment, where each parameter is in its “most advantageous but realistic” (MABR) state.
2) For each parameter, we adjust it toward a more unfavorable value while holding the other parameters in the MABR state, until TC genesis can not occur.
To identify when genesis is not possible, we use idealized numericalsimulations.
3) Compute from reanalyses the frequency that each of the parameters is above or below the threshold value.
9
III. Constructing the MABR Environment
•The thermodynamic component of the MABR environment is a combination of SST, temperature profile, and humidity profile.
22 24 26 28 30 32 340
5
10
15
20
25
30
35
40
sst (°C)
freq
uenc
y (x
1000
)
−80 −60 −40 −20 0 20 40
0
100
200
300
400
500
600
700
800
900
1000
temperature (°C)
heig
ht (
hPa)
September Atlantic MDR SST Histogram
MABR SST = 30 C
Mean September soundingand +/- one standard deviation
We use the mean sounding
10
•For humidity, we construct a moistened profile as follows:
−0.5 0 0.5
300
400
500
600
700
800
900
1000
heig
ht (
hPa)
(a)
1 2 3 4 5 6 7 8 90
0.1
0.2
0.3
0.4
0.5
0.6
0.7
frac
tion
of to
tal v
aria
nce
(b)
40 60 80 100
300
400
500
600
700
800
900
1000
heig
ht (
hPa)
relative humidity (%)
(c)
0 5 10 15 20
300
400
500
600
700
800
900
1000
qvapor
(g kg−1)
(d)
EOFs ofvariationsin qvapor
Mean RH and mean plus1st and 2ndEOFs
11
•For wind shear, a similar approach:
−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8
0
200
400
600
800
1000he
ight
(hP
a)
(a)
1st EOF2nd EOF3rd EOF4th EOF
0 2 4 6 8 10 12 14 16 180
0.1
0.2
0.3
0.4
0.5
frac
tion
of to
tal v
aria
nce
(b)
−25 −20 −15 −10 −5 0 5
0
200
400
600
800
1000
heig
ht (
hPa)
zonal winds (m s−1)
(c)
Meanmean−1st EOF
12
IV. Finding the Threshold Values
•To find the threshold value where TC genesis cannot occur, we use idealizednumerical simulations with the WRF model:
* Doubly-periodic f-plane at 15 N, domain size 4320km x 4320km
* Nested, vortex-following grids with 18/6/2km resolution.
* No cumulus parameterization, 6-class microphysics
* MABR SST, sounding, and wind shear profiles
* Initial condition: A weak vortex with peak tangential flow of 12 m/s atmid-levels, 6 m/s at surface.
(Same surface pressure anomaly as pre-depression waves in Atlantic.)
13
Finding the threshold: Vpot
•We vary Vpot only by varying SST.
If the pressure does not fall and stay below 1010 hPa, genesis has failed.
From these results, the threshold for Vpot is set to 47 m/s.
0 1 2 3 4 51000
1002
1004
1006
1008
1010
1012
1014
time (d)
min
imum
pre
ssur
e (h
Pa)
30°C − Vpot 82.8 m/s (ideal)28°C − Vpot 64.1 m/s27°C − Vpot 53.3 m/s26°C − Vpot 41.3 m/s
14
Finding the threshold: Wind Shear
−25 −20 −15 −10 −5 0 5 10
0
200
400
600
800
1000
zonal winds (m s−1)
heig
ht (
hPa)
(a)
Shear = 1.4 m/s (ideal)Shear = 8.0 m/sShear = 10.0 m/sShear = 12.0 m/s
0 1 2 3 4 51000
1002
1004
1006
1008
1010
1012
1014
(b)
time (d)
min
imum
pre
ssur
e (h
Pa)
Shear = 1.4 m/s (ideal)Shear = 8.0 m/sShear = 10.0 m/sShear = 12.0 m/s
Thresholdvalue 11 m/s
Shear varied byvarying amplitudeof 1st EOF
15
Finding the threshold: Environmental Vorticity
•Rather than trying to model horizontal wind shear, we useplanetary vorticity as a proxy for environmental absolute vorticity.
The environmental absolute vorticity threshold is set to 2.0x10-5 s-1 (~ 8N).
0 1 2 3 4 51000
1002
1004
1006
1008
1010
1012
1014
time (d)
min
imum
pre
ssur
e (h
Pa)
Lat = 15° (ideal)Lat = 11°Lat = 9°Lat = 7°
16
Finding the threshold: Humidity
•Our method does not work for humidity.
With very low (MABR) shear, convection in the disturbance can easilysaturate the core. Shear is necessary for dryness to prohibit genesis.
All simulationsdevelop, evenfor RH600 --> 0 (!)
17
•We fall back on a purely empirical approach to find the threshold.
Our humidity variable is the normalized saturation deficit: NSDq600 q600–
qSST q1000–------------------------------=
0 0.25 0.5 0.75 1 1.25 1.5 1.75 20
0.33
0.67
1
norm
aliz
ed fr
eque
ncy
(a)
0 0.25 0.5 0.75 1 1.25 1.5 1.75 20
0.33
0.67
1
saturation deficit
norm
aliz
ed fr
eque
ncy
(b)
Histogram of NSD aroundTC genesis events
NSD from randomly sampledlocations in TC genesis regions and seasons
Threshold is mean plustwo standard deviations
18
V. Results: Putting it all together
100 80 60 40 20
10
20
30
40
latit
ude
(°N
)
(a)
0
0.2
0.4
0.6
0.8
1
100 80 60 40 20
10
20
30
40
(b)
0
0.2
0.4
0.6
0.8
1
100 80 60 40 20
10
20
30
40
latit
ude
(°N
)
(c)
0
0.2
0.4
0.6
0.8
1
100 80 60 40 20
10
20
30
40
(d)
0
0.2
0.4
0.6
0.8
1
100 80 60 40 20
10
20
30
40
longitude (°W)
latit
ude
(°N
)
(e)
0
0.2
0.4
0.6
0.8
1
100 80 60 40 20
10
20
30
40
longitude (°W)
(f)
0
0.2
0.4
0.6
0.8
1
July 1969-2008
Shear < 11 Vpot > 47
Lat > 8N > 2.0x10-5
NSD > 1.05 (a) x (b) x (d) x (e) = GFI
19
GFI: Atlantic
100 80 60 40 20
10
20
30
40
latit
ude
(°N
)
(a)
0
0.2
0.4
0.6
0.8
1
100 80 60 40 20
10
20
30
40
(b)
0
0.2
0.4
0.6
0.8
1
100 80 60 40 20
10
20
30
40
latit
ude
(°N
)
(c)
0
0.2
0.4
0.6
0.8
1
100 80 60 40 20
10
20
30
40
(d)
0
0.2
0.4
0.6
0.8
1
100 80 60 40 20
10
20
30
40
longitude (°W)
latit
ude
(°N
)
(e)
0
0.2
0.4
0.6
0.8
1
100 80 60 40 20
10
20
30
40
longitude (°W)
(f)
0
0.2
0.4
0.6
0.8
1
July August
September October
November December
20
GFI: East Pacific
180 160 140 120 100 80
10
20
30
40
latit
ude
(°N
)
(a)
0
0.2
0.4
0.6
0.8
1
180 160 140 120 100 80
10
20
30
40
(b)
0
0.2
0.4
0.6
0.8
1
180 160 140 120 100 80
10
20
30
40
latit
ude
(°N
)
(c)
0
0.2
0.4
0.6
0.8
1
180 160 140 120 100 80
10
20
30
40
(d)
0
0.2
0.4
0.6
0.8
1
180 160 140 120 100 80
10
20
30
40
longitude (°W)
latit
ude
(°N
)
(e)
0
0.2
0.4
0.6
0.8
1
180 160 140 120 100 80
10
20
30
40
longitude (°W)
(f)
0
0.2
0.4
0.6
0.8
1
July August
September October
November December
21
GFI: West Pacific
100 120 140 160 180 160
10
20
30
40
latit
ude
(°N
)
(a)
0
0.2
0.4
0.6
0.8
1
100 120 140 160 180 160
10
20
30
40
(b)
0
0.2
0.4
0.6
0.8
1
100 120 140 160 180 160
10
20
30
40
latit
ude
(°N
)
(c)
0
0.2
0.4
0.6
0.8
1
100 120 140 160 180 160
10
20
30
40
(d)
0
0.2
0.4
0.6
0.8
1
100 120 140 160 180 160
10
20
30
40
longitude (°E)
latit
ude
(°N
)
(e)
0
0.2
0.4
0.6
0.8
1
100 120 140 160 180 160
10
20
30
40
longitude (°E)
(f)
0
0.2
0.4
0.6
0.8
1
July August
September October
November December
22
•An objective assessment of spatial correlations:
* Each basin is divided into n boxes.
* In each basin, ,
where (indexi) and (TCcounti) are normalized by maximum valuesin all basins for all seasons.
10 10
score = indexi TCcounti– 2
i 1=
n
n
1 2
month month
ATL EPAC WPAC NIND SIND SPAC
23
VI. Applications
•As in the development of the GPs, we have neglected the frequency ofinitiating disturbances.
If we had a good count, we could simply attach it to the end of the GFIto get a prediction of actual TC numbers.
Assuming the GFI is perfect, we can back out the number of disturbances:
GFI fVpot fshear fRH f=
100 80 60 40 205
10
15
20
25
30
35
40
longitude (°W)
latit
ude
(°N
) 20
20
40 60
8080
60
40
20
20
20
4060
80
60
4020
2040
60
60
20
40
60
20
20
2020
60
80
40
20
40
60
2040
60
2040
60
80
20
40
20
40
40
60 80
24
As in Camargo et al. (2007) and Vecchi and Soden (2007), the GFI could be usedto diagnose changes due to ENSO and/or climate change.
25
All details and further discussion can be found in our publication:
26
VII. Ongoing Work
•Both statistical analyses and idealized simulations show that:
1) A sufficient environmental vorticity is needed for genesis, but
2) Increasing beyond that value does not further favor genesis.
•What physical processes are limiting development - on either side of the threshold?
Tippett et al. (2011)
27
GFI: Northern Indian
0 20 40 60 80 100
10
20
30
40
latit
ude
(°N
)
(a)
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100
10
20
30
40
(b)
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100
10
20
30
40
latit
ude
(°N
)
(c)
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100
10
20
30
40
(d)
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100
10
20
30
40
longitude (°E)
latit
ude
(°N
)
(e)
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100
10
20
30
40
longitude (°E)
(f)
0
0.2
0.4
0.6
0.8
1
July August
September October
November December
28
GFI: Southern Indian
40 60 80 100 120
40
30
20
10
latit
ude
(°S
)
(a)
0
0.2
0.4
0.6
0.8
1
40 60 80 100 120
40
30
20
10
(b)
0
0.2
0.4
0.6
0.8
1
40 60 80 100 120
40
30
20
10
latit
ude
(°S
)
(c)
0
0.2
0.4
0.6
0.8
1
40 60 80 100 120
40
30
20
10
(d)
0
0.2
0.4
0.6
0.8
1
40 60 80 100 120
40
30
20
10
longitude (°E)
latit
ude
(°S
)
(e)
0
0.2
0.4
0.6
0.8
1
40 60 80 100 120
40
30
20
10
longitude (°E)
(f)
0
0.2
0.4
0.6
0.8
1
January February
March April
May June
29
GFI: Southern Pacific
140 160 180 160 140
40
30
20
10
latit
ude
(°S
)
(a)
0
0.2
0.4
0.6
0.8
1
140 160 180 160 140
40
30
20
10
(b)
0
0.2
0.4
0.6
0.8
1
140 160 180 160 140
40
30
20
10
latit
ude
(°S
)
(c)
0
0.2
0.4
0.6
0.8
1
140 160 180 160 140
40
30
20
10
(d)
0
0.2
0.4
0.6
0.8
1
140 160 180 160 140
40
30
20
10
longitude (°E)
latit
ude
(°S
)
(e)
0
0.2
0.4
0.6
0.8
1
140 160 180 160 140
40
30
20
10
longitude (°E)
(f)
0
0.2
0.4
0.6
0.8
1
January February
March April
May June