Distributed Hydrologic Modeling--Jodi Eshelman

Analysis of the Number of Rain Gages Required to Calibrate Radar Rainfall for the Illinois

River Basin

REU sponsor: Dr. Baxter Vieux

Dr. Fekadu Moreda

Gary Brickley

Jodi Eshleman

Distributed Hydrologic Modeling--Jodi Eshelman

Introduction• Radar rainfall estimates are an important supplement to

rain gage accumulations for modeling river basins.

• Radar estimates can be biased or in error and must be corrected.

Questions:

1. How many rain gages are necessary to correct the radar?

2. What degree of accuracy can be achieved?

3. How do different correction methods compare?

Distributed Hydrologic Modeling--Jodi Eshelman

Background

• Are 10 gages adequate to calibrate the radar for the Illinois River Basin?

• Radar error in estimating rainfall – overshoot cloud tops– Z/R relationship transforms reflectance to rain rate

• Correction of radar by applying some correction based on rain gage accumulation

• Correcting radar estimates provides more accurate spatial estimates of rainfall for river basin simulation.

Distributed Hydrologic Modeling--Jodi Eshelman

WSR-88D or NEXRAD

• Weather Surveillance Radar-1988 Doppler

• Prototyped in Norman at NSSL

• Scans Every 5 or 6 minutes during precipitation

• 150+ installed in US and abroad

0.5°

1.5°2.5°

Distributed Hydrologic Modeling--Jodi Eshelman

Location of Gages

Distributed Hydrologic Modeling--Jodi Eshelman

Presentation Outline

• Test 4 different correction factors– Mean field bias

– Probability density function

– <1mm

– Weighted

• Gage density study• Size and time progression analysis

Distributed Hydrologic Modeling--Jodi Eshelman

Correction Factor Comparison

• Adjustment to rain gage mean

• Average difference after correction

• Simulated discharge volume

Distributed Hydrologic Modeling--Jodi Eshelman

MEAN VALUESStorm Event MFB PDF <1mm MFB <1mm PDF Weighted Raw Mesonet

Jan-95 0.5277 0.4950 0.5992 0.4058 0.4648 0.4302 0.4950Mar-95 0.2004 0.1964 0.1944 0.1933 0.2374 0.1832 0.1964Jun-95 0.6481 0.6413 0.6530 0.6773 0.6688 0.7317 0.6550Nov-96 0.4191 0.4256 0.4218 0.4335 0.4081 0.4312 0.4191

NovDec96 0.1889 0.1746 0.1682 0.1503 0.1700 0.2091 0.1746Apr-96 0.7290 0.7155 0.7289 0.7483 0.7322 0.8370 0.7155

May-96 0.1712 0.1729 0.1622 0.2031 0.1662 0.1956 0.1729Feb-97 0.4472 0.4507 0.4472 0.4581 0.4660 0.4582 0.4507

AVERAGE DIFFERENCE AFTER CORRECTIONStorm Event MFB PDF <1mm MFB <1mm PDF Weighted Raw

Jan-95 17% 16% 25% 21% 16% 18%Mar-95 36% 35% 34% 34% 46% 32%Jun-95 6% 6% 6% 8% 7% 12%Nov-96 10% 10% 10% 10% 10% 11%

NovDec96 27% 24% 24% 23% 24% 32%Apr-96 16% 15% 16% 17% 16% 23%

May-96 10% 11% 10% 23% 9% 20%Feb-97 11% 11% 11% 12% 12% 12%

PDF is closest to Mesonet

Distributed Hydrologic Modeling--Jodi Eshelman

Volume Comparison

Novdec96

Feb97

Jan95

Nov96

May96

Jun95

Apr96

Mar95

Nov96

Jun95

NovDec96Apr96

May96

Mar95

Feb97

Jan95

NOVDEC96FEB97JUN95

APR96

NOV96

JAN95

MAY96

MAR95

0.0E+00

2.0E+07

4.0E+07

6.0E+07

8.0E+07

1.0E+08

1.2E+08

0.0E+00 1.0E+07 2.0E+07 3.0E+07 4.0E+07 5.0E+07 6.0E+07 7.0E+07 8.0E+07 9.0E+07 1.0E+08 1.1E+08 1.2E+08 1.3E+08

Observed Vol (m3)

Mod

el V

ol (

m3)

MFB

PDF

RAW

Weighted

Linear (MFB)

Linear (PDF)

Linear (RAW)

Linear(Weighted)

Distributed Hydrologic Modeling--Jodi Eshelman

Presentation Outline

• Test 4 different correction factors– Mean field bias

– Probability density function

– <1mm

– Weighted

• Gage density study• Size and time progression analysis

Distributed Hydrologic Modeling--Jodi Eshelman

Gage Density

2

22

d

stn

Statistically estimating the mean with prescribed accuracy

Where:

n=number of gages requireds2=Varianced=Allowable margin of error (5-30% mean)=% Confidence (60-90%)

Distributed Hydrologic Modeling--Jodi Eshelman

Calibration Comparison

555 55530

18

69

69

4

20 8076 50 2829

5

0.5

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350Number of Gages Needed to Calibrate

Allo

wab

le M

arg

in o

f Err

or

(% m

ean

)

49.545

20.321

0.499

29.915

68.781

80.343

28.172

4.264

68.921

17.789

29.23

5.259

76.008

Total Mean Depth (mm)

Distributed Hydrologic Modeling--Jodi Eshelman

Standard Error Approach

# gauges Variance S.E.(X) S.E.(X)% Avg. Difference X

10 1085.99 10.42 28.5 32%9 1080.25 10.39 29.1 32%8 989.36 9.95 27.6 38%7 1042.69 10.21 27.2 45%6 1045.36 10.22 27.6 48%5 1087.81 10.43 26.6 58%4 1110.16 10.54 27.0 59%3 1086.94 10.43 25.4 54%2 978.62 9.89 25.0 49%

Distributed Hydrologic Modeling--Jodi Eshelman

Presentation Outline

• Test 4 different correction factors– Mean field bias

– Probability density function

– <1mm

– Weighted

• Gage density study• Size and time progression analysis

Distributed Hydrologic Modeling--Jodi Eshelman

Mean Total Accumulation

May96

Mar95

NovDec96

Jun95

Jan95

Apr96Feb97

Nov96

y = 1.0368x

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100

Mesonet (mm)

Un

co

rre

cte

d R

ad

ar

(mm

)

Distributed Hydrologic Modeling--Jodi Eshelman

Time Progression

First 6-Hour Period

miam

cook

jayx

tahl

pryo

w estw ebb

y = 1.5943x

0

5

10

15

20

25

30

35

40

0 10 20 30 40

Mesonet (mm)

Ra

da

r (m

m)

06/08 18-23

Second 6-Hour Period

sall

w ebb

tahl cooktull

w est

y = 0.487x

0

24

68

10

1214

1618

20

0 5 10 15 20

Mesonet (mm)

Ra

da

r (m

m)

06/08 23-09 05

Seventh 6-Hour Period

miam

jayx

pryo

tahl

tull

y = 1.0587x

0

10

20

30

40

50

60

70

0 20 40 60

Mesonet (mm)

Ra

da

r (m

m)

06/10 05-11

Final 6-Hour Period

cook

tahl

west

webbsall

tulljayx

wist

miampryo

y = 0.5172x

0

1

2

3

4

5

6

0 2 4 6

Mesonet (mm)

Ra

da

r (m

m)

06/11 11-17

Distributed Hydrologic Modeling--Jodi Eshelman

Conclusions

• PDF correction factor is most effective– Mean adjustment is closer to Mesonet– Average difference is less than MFB

• Weighted PDF – – Weighting gages close to the basin improve discharge

volume simulations

• Gage density study– 10 gages are sufficient for 30% of the mean and 90%

confidence– Due to large variance, smallest storms are negligible– little consideration for flooding