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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
53