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