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Infilling Radar CAPPIs
Geoff Pegram, Scott Sinclair, Stephen Wesson & Pieter Visser
What we’ve done …
• We can remove ground-clutter and have improved the estimation of rainfall by radar at ground level
• We have refined the merged fields of radar with raingauge data
• We think that the combined fields are good out to 75 km from the radar with a reasonably dense network of gauges, but we’re happy to take advice!
NATIONAL WEATHER RADAR NETWORKsee Deon’s presentation
Existing radars
Radars added (2004)
Planned radars
Problems with Radar CAPPI Data
• Ground clutter contamination can be extensive
• Results in poor quality rainfall estimates
• Parts of radar volume scan where data is unknown
• Rainfall estimates at ground level unknown
Summary of Infilling Strategy
• Choose Rainfall classification algorithm• Devise Bright band correction algorithm• Semivariogram parameters determined by
rainfall type. Climatological semivariograms.• Ordinary and Universal Kriging to extrapolate
rain information. Universal Kriging utilised in mixed zone.
• Cascade Kriging to progressively infill data down to ground.
Rainfall Classification
• Rainfall separated into two zones:
(1) Convective Zone
(2) Stratiform Zone• Criteria of classification set out in table
below.
Examples of Rainfall Classification
Reflectivity Images Classified Images
CLASSIFICATION COLOURNo Data Grey
Ground Clutter BlackStratiform Rain MagentaConvective Rain Red
XX18 km
0 km
18 km
0 km
CROSS SECTION X-X
dBZ
Classification
Characteristics of Classified Rainfall• Stratiform – low average height, low variability
and intensity.• Convective – considerable vertical extent, high
variability and intensity.• Increase of rainfall intensity nearer ground level
Climatological Profiles of Classified Rainfall
0
2
4
6
8
10
12
14
16
18
15 20 25 30 35 40 45 50Reflectivity (dBZ)
He
igh
t (k
m)
Convective Profile Convective+/-Stdev
Stratiform Profile Stratiform+/-Stdev
Corrected Climatological
Profile
New Rainfall Estimate at Ground
Level
CAPPI level affected by bright band
corrected
Climatological Profile Correction
Procedure
Rainfall Estimate at Ground Level
Climatological Profile Affected by Bright Band
with Extrapolation to Ground Level
CAPPI level affected by bright
band
Climatological Profile Affected by Bright
Band
Typical Climatologial
Profile
Bright Band Correction• Bright Band – melting snow & ice crystals• Need to correct bright band to obtain accurate
rainfall estimates at ground level• Proposed correction procedure: pixel by pixel
approach
2 km
Reflectivity (dBZ)
Height (km)
4 km
3 km
1 km
Bright Band Correction
• Testing of bright band correction
• Results: improved rainfall estimates at ground level
Bright Band Adjustment: 17 December 1995 (00:00 to 24:00)
18
20
22
24
26
28
30
32
0:00 6:00 12:00 18:00 0:00
Time
Wei
gh
ted
Mea
n R
efle
ctiv
ity
(dB
Z)
Mean CAPPI 1 Mean CAPPI 2 Mean CAPPI 2: Corrected Mean CAPPI 3
2km CAPPI before bright band correction
2km CAPPI pixels marked which are
affected by bright band
2km CAPPI after bright band correction
Semivariogram Modeling • Semivariogram model parameters
computed for convective & stratiform rain in horizontal & vertical directions
Reflectivity Image
30km
x
Z
Semivariogram of Stratiform Rainfall in Horizontal Direction
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20 25Distance (km)
Sta
nd
ard
ise
d S
em
iva
rio
gra
m
Data Fitted Semivariogram
38.1
31.8exp1)(
hhg
SILL
RANGE
Graphs indicating clustering of alpha and correlation length parameters by rainfall type (15 Rain Events over 4 different years)
H LH (km)
V LV (km)
STRATIFORM 1.53 8.40 1.33 2.56CONVECTIVE 1.85 3.38 1.71 4.11
HORIZONTAL VERTICAL
Table of Average Parameters:
Convective & Stratiform Semivariogram Parameters in Horizontal Direction
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 2 4 6 8 10 12 14 16 18 20Correlation Length (km)
Alp
ha
Convective Stratiform Convective Centroid Stratiform Centroid
Convective & Stratiform Semivariogram Parameters in Vertical Direction
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 1 2 3 4 5 6 7 8
Correlation Length (km)
Alp
ha
Convective Stratiform Convective Centroid Stratiform Centroid
Sensitivity Analysis of Stratiform, Horizontal Parameters
Missing data infilled with different
combinations of α and L that represent the spread of parameter values.
No significant difference between Kriging estimates returned for spread of parameter values
Mean Value of Infilled Data: Horizontal Direction, Stratiform Rain
26.0
26.5
27.0
27.5
28.0
28.5
29.0
29.5
30.0
1 2 3 4 5
Mea
n V
alue
(dB
Z)
L, α + σα L, α - σα L, α L + σL, α L - σL, α
Standard Deviation of Infilled Data: Horizontal Direction, Stratiform Rain
0.0
0.5
1.0
1.5
2.0
2.5
1 2 3 4 5
Sta
ndar
d D
evia
tion
(dB
)
L, α + σα L, α - σα L, α L + σL, α L - σL, α
Range of Convective and Straiform Parameters in the Horizontal Direction
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
0 2 4 6 8 10 12 14Correlation Length (km)
Alp
ha
Convective Cluster Stratiform Cluster
Convective Cluster: Lc , c
Stratiform Cluster: Ls , s
Kriging to Infill Missing Rain Data
• KRIGING used to extrapolate/interpolate horizontal and vertical rainfall information to infill unknown data points
• Considered to be the optimal technique for interpolation of Gaussian data
Computational Efficiency & Stability:• Nearest 25 rainfall values used in Kriging• Singular Value Decomposition (SVD) with
trimming of small singular values to ensure computational stability
Summary: Three Rainfall Zones
Stratiform Zone
All controls stratiform.
OK used to infill target point.
Mixed Zone
Controls stratiform & convective.
UK used to infill target point.
Convective Zone
All controls convective.
OK used to infill target point.
-stratiform pixel
-convective pixel
-target pixel
Validation: Universal & Ordinary Kriging
Reflectivity (dBZ) &|Rainrate Errors|
(mm/hr)
0 10050
Reflectivity (dBZ)Reflectivity (dBZ) Rainrate (mm/hr) Rainrate (mm/hr)
Kriging EstimateObserved Rainfall
Convective Rainrate Errors (mm/hr)
Stratiform Rainrate Errors (mm/hr)
Mixed Rainrate Errors (mm/hr)
All Errors Rainrate (mm/hr)
RAINRATE ERROR MAPS
Absolute Error
UK & OK Effectiveness• UK & OK tested on three different rainfall zones on
a variety of instantaneous images• Effectiveness evaluated by comparing mean,
and Σdifference2 of estimated & observed rainfall• UK in mixed zone provides a superior estimate
than OK and reduced Σdifference2
UNIVERSAL KRIGING: Mixed Rainfall
y = 0.79x + 0.44
R2 = 0.78
0
25
50
75
100
125
0 25 50 75 100 125
Observed (mm/hr)
Es
tim
ate
d (
mm
/hr)
Data 1-1 Line Linear (Data)
ORDINARY KRIGING: Mixed Rainfall
y = 0.37x + 1.12
R2 = 0.47
0
25
50
75
100
125
0 25 50 75 100 125
Observed (mm/hr)
Es
tim
ate
d (
mm
/hr)
Data 1-1 Line Linear (Data)
KRIGING directly to Ground Level
• Unexpected problems with CAPPI edges• Higher Kriged values returned than expected
and serious discontinuity also evident• Example: 24 hour accumulation
Rainfall Accumulation (mm)0 10080604020
DiscontinuitiesInflation of Kriged values
Radar Volume Scan Data
Radar Volume Scan Data After Cascade Kriging
3D CASCADE
KRIGING EXAMPLE
CASCADE KRIGING: Ground Clutter
• Ground Clutter contaminates radar volume scan data up to 5km above ground level.
Ground Clutter 3km above ground level
Ground Clutter infilled on 3km level
Reflectivity estimation at ground level
Testing: Ground Clutter Infilling
• Tested on 3D Bethlehem ground clutter map
• Ground clutter placed onto known rain
• Tested on three different rain events over 24hr period
Original Reflectivity Image Ground Clutter Map Superimposed
Ground clutter segments to be estimated
Estimated reflectivity data
Convert to rain rate by Marshall-Palmer
equation
Store estimated and observed rain rate
values and proceed to next image in
sequence
• Accumulations over 6, 12 and 24 hours show close correspondence between observed and estimated values
Accumulation Values (00:00 to 24:00): 17 December 1995
y = 0.74x + 10.18
R2 = 0.70
0
10
20
30
40
50
0 10 20 30 40 50
Estimated (mm)
Ob
se
rve
d (
mm
)
Data 1-1 Line Linear (Data)
Accumulation Values (00:00 to 24:00): 25 January 1996
y = 0.84x + 6.01
R2 = 0.81
0
10
20
30
40
50
0 10 20 30 40 50
Estimated (mm)
Ob
se
rve
d (
mm
)
Data 1-1 Line Linear (Data)
Accumulation Values (00:00 to 24:00): 13 February 1996
y = 1.02x + 2.01
R2 = 0.93
0
10
20
30
40
50
60
70
0 10 20 30 40 50 60 70
Estimated (mm)
Ob
se
rve
d (
mm
)
Data 1-1 Line Linear (Data)
Results: Ground Clutter Infilling
Cape TownPort Elizabeth
De AarBethlehem
Irene
Polokwane
Bloemfontein
Testing: Rainfall Estimation at Ground Level
• Extrapolated radar estimates at ground level compared to raingauge estimates
Durban
East London
Ermelo
MRL5 Weather Radar
Bethlehem
Raingauge Locations
Liebenbergsvlei Catchment
2 L
Selection Range
Radar Pixel Locations
1 km
1 k
m
Rainguage Locations
Results: Rainfall Estimation at Ground Level• Two rain events selected
of different rainfall types – 12h & 24 h accumulations
• Results indicate fair estimation of rainfall at ground level
• We’ve got a handle on the errors
12hr Accumulation (24 January 1996): 12:00 to 24:00
y = 0.82x + 3.38
r2 = 0.86
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140 160 180
Radar Accumulation (mm)
Rain
gau
ge A
ccu
mu
lati
on
(m
m)
Data 1-1 Line Linear (Data)
24hr Accumulation (13 February 1996): 00:00 to 24:00
y = 0.74x + 2.00
r2 = 0.78
0
10
20
30
40
50
60
70
0 10 20 30 40 50 60 70
Radar Accumulation (mm)
Rain
gau
ge A
ccu
mu
lati
on
(m
m)
Data 1-1 Line Linear (Data)
The Conditional Merging algorithm
To combine radar and gauge data optimally:– Krige the gauges to give best guess field, MG
– Krige the radar pixels at gauge locations, MR
– If RR is the measured radar rainfield,– Conditional Merged Field is:
RC = RR + MG – MR
which coincides with the gauges and interpolates intelligently
Conditional mergingConditional merging
Simulation experimentSimulation experiment
Mean errors over 1000 realizations
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-4.00 -3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00
Bin (mm\hr)
Fre
qu
en
cy
Simulated Radar Kriged Gauge EstimateMerged Estimate
Simulation experimentSimulation experiment
Mean error variances over 1000 realizations
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35 40 45
Bin (mm^2/hr^2)
Fre
qu
en
cy
Simulated Radar Kriged Gauge EstimateMerged Estimate
A A real cross-validationreal cross-validation field experiment field experiment
• Compare straight Kriging and Conditional Merging on 45 rain gauges on a 4600 km2
catchment
• Use cross-validation – estimation of daily total at each gauge separately using the remaining data
Layout of the Liebenbergsvlei gauge networkLayout of the Liebenbergsvlei gauge network
Bethlehem
Comparison of daily mean errorsComparison of daily mean errors
-10 0 10 20 30 40 50 60
96/01/24
96/01/25
96/01/27
96/02/01
96/02/05
96/02/11
Radar Error Mean Kriged Error Mean Merged Error Mean
Errors with range – how good is the radar?
• 22 new gauges
• 4 different days of accums
Rainfall 9 January 2005
Rainfall ratio between gauges and radar for MRL-5 on 09 January 2005
-1.5
-1
-0.5
0
0.5
1
1.5
0 50 100 150 200 250
Range(km)
Rai
ng
aug
e/R
adar
rai
nfa
ll ra
tio (L
og
)
Rainfall 12 January 2005
Rainfall ratio between gauges and radar for MRL-5 on 12 January 2005
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 50 100 150 200 250
Range (km)
Rai
ng
aug
e/R
adar
rai
nfa
ll ra
tio (L
og
)
Rainfall 13 January 2005
Rainfall ration between gauges and radar for MRL-5 on 13 January 2005
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 50 100 150 200 250
Range(km)
Rai
ng
aug
e/R
adar
rai
nfa
ll r
atio
(L
og
)
Rainfall 21 January 2005
Rainfall ratio between gauges and radarfor MRL-5 on 21 January 2005
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 50 100 150 200 250
Range(km)
Rain
gau
ge/R
ad
ar
rain
fall
rati
o
(Lo
g)
Concluding RemarksConcluding Remarks
• With intelligent extrapolation and climatoloical variograms we can get good ground estimates
• With conditional merging of radar and gauge data we can get good interpolation to adjust for errors in the Z-R formula
• Within 75 km from the radars, we can offer sound areas in varying climates and land cover in our expanding radar and gauge network