Effect of Variations in Reflectivity-Rainfall Relationships on Runoff Predictions

Chakradhar G. Malakpet, Emad Habib (*), Ehab A. MeselheDepartment of Civil Engineering,

University of Louisiana at Lafayette, Lafayette, Louisiana(*) habib@louisiana.edu

Ali TokayJoint Center for Earth Systems and Technology,

University of Maryland, Baltimore County, Baltimore, Maryland

Motivation• To use weather radar data in hydrological applications, radar reflectivity (Z)

need to be transformed into surface rainfall estimates (R).

• Estimation of the Z-R relationships is subject to several sources of uncertainties including the storm-to-storm and within the storm variations in raindrop size distributions (DSD).

• Previous studies demonstrated that accounting for temporal/spatial variability in DSD and Z-R relations affect the overall accuracy of rainfall estimates. - (e.g., Uijelenhoet et al. 2003; Lee and Zawadzki 2005)

• Despite the recognized effect of DSD and Z-R variability, less attention has been dedicated to their effect on hydrologic predictions.

• Some early analysis was reported (Winchell et al., 1998) but focused only on total aggregate runoff volumes.

• Most hydrologic modeling studies use a single Z-R relationship.

• It is not well understood how the variability in DSD and Z-R relationships affect the accuracy of the hydrologic predictions.

Overall Objective

• Investigate the effect of intra-storm and inter-storm variability in Z-R relationships on predictions of stream-flow.

Approach• Perform the analysis using high-resolution disdrometer

measurements along with WSR-88D reflectivity data over an experimental watershed.

• Employ a physically-based hydrologic model to ensure the physical representation of rainfall-runoff processes.

Experiment Site:Isaac-Verot Watershed, Southern Louisiana

ÊÚ

ÊÚ

0 100 200 Kilometers

KPOE

KLCH New Orleans

Louisiana

Vermilion watershed

Isaac-Verot Watershed(~35 km2)

Coverage of Closest NEXRAD stations

KLCH = 116 kmKPOE = 143 km

Annual precipitation = 55-60 inches

Data are been continuously collected since early-20042 Km

Watershed Instrumentation

Watershed boundaryNEXRAD polar grid

Dual rain gauge

Discharge gauge

Total weather station

JW Disdrometer & MRR site

Soil moisture

outlet

Hydrologic Model: Gridded Surface Subsurface Hydrologic Analysis (GSSHA)

• GSSHA is a physically-based fully distributed hydrologic model (Ogden and Downer, 2002).

• GSSHA uses finite difference and finite volume methods to simulate different hydrologic processes.

• The modeling setup used in our study included: – two-dimensional diffusive wave for overland flow– one-dimensional explicit diffusive wave method for channel flow– Penman-Monteith equation for evapotranspiration. – Green and Ampt infiltration with redistribution method (Ogden

and Saghafian, 1997) for flow simulation in the unsaturated zone.

– This infiltration method includes soil moisture accounting and allows for a continuous long-term simulation of the selected periods that contain multiple runoff events.

Model Calibration/Validation Results

Time in days since 9/1/2003 00:00

Dis

char

ge(c

ms)

20.5 20.75 21 21.25 21.5 21.75 220

2.5

5

7.5

10

12.5

15

MeasuredSimulated

Time in days since 10/1/2004 00:00

Dis

char

ge(c

ms)

7 7.5 8 8.5 9 9.5 10 10.50

10

20

30

40

50

60

Prior to being used in further analysis, the model was rigorously calibrated and validated.

Produce “reference/true”stream-flow (Qref)

Hydrologic model

Use Z and Rrefto estimate A&b in Z-R

Reflectivity Data (Z)(disdrometer or radar)

Compare

Compare

MethodologyCalibration/Validation of physically-basedHydrologic Model Using Historic Data

Select rainfall/runoff periods containing several events with various rainfall regimes/types.

Use Z-R to estimate Rest

Produce stream-flow (Qest)

Hydrologic model

Disdrometer DSD data

calculate “reference/true”Rainfall (Rref)

Methodology (You can delete this slide if you like the previous one)

• Select rainfall/runoff periods that contain several events with various rainfall regimes/types.

• Use the disdrometer DSD data to calculate “reference/true”rainfall

• Use the reference rainfall to drive the hydrologic model and produce “reference/true” stream-flow

• Calculate Z from disdrometer DSD• Estimate A and b for Z-R using:

– different scales for the estimation (e.g., climatological, event, storm, sub-storm)

– different estimation methods (e.g., least-squares regression, min RMSE)

• Run the hydrologic model with each of the estimated rainfall to predict runoff

• Assess how estimated rainfall and streamflow compare to the reference values

• Repeat the analysis using Z from radar

Different Time Scales for Estimating Coefficient and Exponent of Z = A Rb

• Climatological:– Estimate A and b using combined long-term disdrometer

data (e.g., one year).• Storm scale:

– Estimate A and b using Z-R data from each storm.• Event scale:

– Estimate A and b for each event with a storm.• Sub-event scale:

– Split the event into convective/stratiform/transitional periods and estimate A and b for each period.

Different Methods for Estimating Coefficient and Exponent of Z = A Rb

• Least Squares Fit (LSF):– Estimate A and b using linear least squares regression

fitting.• Bias corrected LSF:

– Fix b (e.g., 1.2 or 1.4) and estimate A by removing the overall bias.

• BIAS_RMSE:– Estimate A and b by removing the bias and optimization

for minimum RMSE.• Default:

– Z=300 R1.4; Z=250 R1.2

Selected Storms

• June 22-27, 2004:– included of a sequence of high-intensity and short-duration convective

squall line storms.– A total of ~ 7 inches of rainfall accumulations.

• October 7-10, 2004: – includes Tropical Storm Matthew (10 inches of rain). – Storm Matthew resulted in significant runoff as high as 2.6 m3/sec/km2.

• November 17-27, 2004: – An extensively wet period of scattered and squall line storms.– Five distinct rain storms are observed in this period. – A total of ~ 6 inches of rainfall accumulations. – Runoff generated not very high but had consistent response to rainfall.

Julian day of 2004

Rai

nfal

lAcc

umul

atio

n(m

m)

280 281 282 283 2840

50

100

150

200

250

Julian day of 2004

Rai

nfal

lInt

ensi

ty(m

mh-1

)

280 281 282 283 2840

20

40

60

Julian day of 2004

Ref

lect

ivity

Z(d

bZ)

280 281 282 283 28410

20

30

40

50 RadarDisdrometer

October 2004 Storm (TS Matthew)

June 2004 Storm

Julian day of 2004

Rai

nfal

lInt

ensi

ty(m

mh-1

)

174 175 176 177 1780

20

40

60

80

100

Julian day of 2004

Ref

lect

ivity

Z(d

bZ)

174 175 176 177 17810

20

30

40

50

60

RadarDisdrometer

Julian day of 2004

Rai

nfal

lAcc

umul

atio

n(m

m)

174 175 176 177 1780

50

100

150

200

250

Radar Reflectivity Z (mm6 m-3)

Rai

nfal

lrat

e(m

mh-1

)

101 102 103 104 10510-1

100

101

102

event1event2event3zln1zln2zln3

June 2004 Storm (Disdrometer)

Julian day of 2004

Rai

nfal

lInt

ensi

ty(m

mh-1

)

174 175 176 177 1780

20

40

60

80

100

event 1 event 2 event 3

Radar Reflectivity Z (mm6 m-3)

Rai

nfal

lrat

e(m

mh-1

)

101 102 103 104 10510-1

100

101

102

event1event2event3zln1zln2zln3

June 2004 Storm (Radar)

Julian day of 2004

Rai

nfal

lInt

ensi

ty(m

mh-1

)

174 175 176 177 1780

20

40

60

80

100

event 1 event 2 event 3

Julian day of 2004

Hei

ght (

km)

175.45 175.5 175.55 175.6 175.65 175.7 175.75 175.82

4

6

8

5

10

15

20

25

30

35

40

45

Vertical Profile of ReflectivityJune 2004

dBZ

June event 1, 2004 (Disdrometer)

Julian day of 2004

Rai

nfal

lInt

ensi

ty(m

mh-1

)

174 175 176 177 1780

20

40

60

80

100

event 1

Radar Reflectivity Z (mm6 m-3)

Rai

nfal

lrat

e(m

mh-1

)

101 102 103 104 10510-1

100

101

102

convstrtrnsconvftdstrftdtrns

ConvectiveStratiformtransitional

June event 1, 2004 (Radar)

Reflectivity (mm6 m-3)

Rai

nfal

lrat

e(m

mh-1

)

101 102 103 104 10510-1

100

101

102

convecstrfmtrsnlconvlnstrlntrsnln

ConvectiveStratiformtransitional

Julian day of 2004

Rai

nfal

lInt

ensi

ty(m

mh-1

)

174 175 176 177 1780

20

40

60

80

100

event 1

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 50 100 150 2000

50

100

150

200

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 50 100 150 2000

50

100

150

200

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 50 100 150 2000

50

100

150

200

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 50 100 150 2000

50

100

150

200

(LSF estimation method)

BIAS_RMSE estimation method

June 2004 Storm (Disdrometer)

event scaleSub-event

scalestorm scale

climatologial

scale

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 1000

20

40

60

80

100

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 1000

20

40

60

80

100

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 1000

20

40

60

80

100

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 1000

20

40

60

80

100

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 1000

20

40

60

80

100

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 1000

20

40

60

80

100

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 1000

20

40

60

80

100

Reference rainfall rate (mm h-1)

Est

imat

edra

infa

llra

te(m

mh-1

)

0 20 40 60 80 1000

20

40

60

80

100

(LSF estimation method)

BIAS_RMSE estimation method

June 2004 Storm (radar)

event scaleSub-event

scalestorm scale

climatologial

scale

Julian day of 2004

Run

off(

m3 /s

ec)

175 176 177 178 1790

10

20

30

40

50ReferenceClimatologicalStormEventPhy Process

Julian day of 2004

Run

off(

m3 /s

ec)

175 176 177 178 1790

10

20

30

40

50ReferenceClimatologicalStormEventPhy Process

June 2004 (Disdrometer)

LSF

BIAS_RMSE

Sub-event

Sub-event

Julian day of 2004

Run

off(

m3 /s

ec)

175 176 177 1780

10

20

30

40

50 ReferenceDefaultStormEventPhy Process

Julian day of 2004

Run

off(

m3 /s

ec)

175 176 177 1780

10

20

30

40

50 ReferenceDefaultStormEventPhy Process

June 2004 (Radar)

LSF

BIAS_RMSE

Sub-event

Sub-event

Conclusions• Z-R parameters show strong dependence on the estimation time

scale and on the method of estimation.

• Use of least-squares fitting resulted in relatively inaccurate rainfall estimates and poor runoff predictions especially when coarse estimation time scales were used (e.g., storm or event).

• The least-squares fitting method gives improved results only when the estimation is performed on a sub-event time scale that accounts for convective/stratiform classification.

• Estimation based on bias removal and minimization of random differences (BIAS_RMSE) shows superior accuracy even when using coarse estimation time scales.

• Estimation time-scales that account for variations in the sub-event rainfall physical processes do not necessarily result in significant improvements in runoff predictions.

• A simple estimation method based only on bias removing and selection of a climatological representative exponent has resulted in acceptable runoff predictions.

Thank You!

For further questions contact Emad Habib

(habib@louisiana.edu)