Effects of Prior Rainfall and Storm Variables on

Runoff Curve NumberRichard H. Hawkins and Kevin E. VerWeire

Watershed Resources Program

University of Arizona, Tucson, AZ

ASCE Watershed Management Conference

July 20, 2005 Williamsburg VA

ProblemDirect runoff (Q) from rainfall (P)…

….and what else?

• Why the variation?

- Prior rainfall (“antecedent moisture”)

- Intensity? What intensities?

- Storm distribution?

- Storm duration?

5-day table from Ch 4

Antecedent Moisture driven variation

5-day prior rainfall basis

Dormant season Growing Season --------------------------------------------------------------------

AMC I < 0.5 in < 1.4 in

AMC II 0.5 to 1.1 in 1.4 to 2.1 in

AMC III > 1.2 in >2.1 in ---------------------------------------------------------------------

This was included in original NEH-4, but is now considered obsolete, and is no longer endorsed or included. Do not use.

What we did• Got a LOT of event rainfall-runoff data

• Found primary rainfall effects on runoff (Q) by least squares fitting

Q = (P-0.2S)2/(P+0.8S)

• Found deviations

Dev = Qobs-Qcalc

• Related deviations to “secondary effects”

Prior 1, 2, 5 day prior rain(in) Storm duration(hr)

5,10,15,30 minute max intensities (in/hr)

Pattern Index (dimensionless)

Acquire Data• Select 43 ARS watersheds with long-term rainfall-

runoff data sets– Watkinsville, GA (1)– Edwardsville, IL (2)– Coshocton, OH (22)– Stillwater, OK (1)– Riesel, TX (4)– Hastings, NE (12)– Monticello, IL (1)

• Watershed data were processed with the program GETPQ96 to determine storm variables

Determine Watershed CN and Deviations

• Use Least Squares Method

– Fit Q = (P-0.2S)2 / (P+0.8S), for P/S>0.50

For the natural P:Q data. Find best-fit “S”

– Use the fitted S value to calculate the Qcalc

for all observed rainfall P depths using the

CN equation

– Calculate the deviations from the fit line

Deviation = Qobs - Qcalc

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

P (INCHES)

Q (

INC

HE

S)

Q = P

Secondary Effect

42006 Riesel, TX (176 ac.)N = 229

CN = 81.23

R2 = 53.10SE (in) = 0.5979

Qcalc = (P-0.462)2 / (P+1.848)

Multiple Regression Analysis

Regress deviations against storm variables:

– Pattern Index – a measure of distribution

– Rainfall Duration - hr

– Prior rainfall: 1, 2, and 5-day - in– Rainfall intensity: maximum 5, 10,

15, and 30 minute - in/hr

RegressionProcedureSelective stepwise regression using independent

terms Dev= Qobs- Qcalc = Y = bo + b1X1 + b2X2 +b3X3,…etc

 • X1 = Best fit variable from intensity group (in/hr)• X2 = Best fit variable from prior rainfall group (in)• X3 = Storm duration (hr)• X4 = Pattern index (-)

Keep term if b is significantly different than 0 at Pr>|t|<0.05

Regression –more

• Convert to dimensionless deviations, and coefficients are recast as “beta” values.

• The bo constant is eliminated by this

• (Y-μy)/σY = β1(X1-μX1)/σX1 + β2(X2-μX2)/σX2 + ..etc

• Relationship strengths and directions are expressed by β

• Used Stata software

Data summary 43 watersheds

Item Min Med Max

------------------------------------------------------------------

Drainage area (Ac) 0.65 7.59 3490

# Events with P/S>0.5 7 75 229

Min P(in) P/S>0.5 0.74 1.35 2.53

P(in) 0.74 2.07 7.31

Q(in) 0.0001 0.6118 6.8852

Fitted CN 67.0 78.7 87.2

------------------------------------------------------------------

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

P (INCHES)

Q (

INC

HE

S)

Q = P

Secondary Effect

42006 Riesel, TX (176 ac.)N = 229

CN = 81.23

R2 = 53.10SE (in) = 0.5979

Qcalc = (P-0.462)2 / (P+1.848)

Expectations?

• For deviations Qobs - Qcalc

• Positive with intensity (the more intense the more runoff?)

• Positive with prior rain (the wetter the watershed, the the more runoff?)

• Negative with pattern index (late peaking storms have high intensities on on wetter

watersheds)

Results - General

• 8 watersheds with 3 different secondary effects

• 21 watersheds with 2 different secondary effects

• 8 watersheds with 1 secondary effect

• 6 watersheds with NO secondary effects

Results - more Variable Count β range

-----------------------------------------------------------------

imax5 0 NA

imax10 1 0.26 Only positive

imax15 6 -0.59 to -0.25

imax30 10 -0.38 to -0.22

 (imax group) 17 -0.59 to 0.26 16 of 17 -

  

1-day P 3 0.27 to 0.62

2-day P 6 0.25 to 0.70

5-day P 21 -0.21 to 0.50 20 of 21 +

 (P group) 30 -0.21 to 0.70 29 of 30 +

Results - more

  

Variable Count β range Comment

--------------------------------------------------------------------

Duration 22 -0.50 to 0.41 10 <0 12>0

 

Pattern Index 5 -0.15 to 0.13 3<0 2>0

 

Results - more Summary

Variable Count β range Remarks

------------------------------------------------------------------------

Intensity group 17 -0.59 to 0.26 16/17 -

Prior P group 30 0.14 to 0.70 29/30 +

Duration 22 -0.50 to 0.41 mixed

Pattern Index 5 -0.15 to 0.13 mixed

------------------------------------------------------------------------

Total 74

 

Results

-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

BETA

IMAX30

IMAX15

IMAX10

IMAX05

AMC5

AMC2

AMC1

PDUR

PI

0

10

20

30

40

50

60

70

80

90

100

Watersheds

R2 (

%)

Secondary Effects

Primary Effects

Conclusions • Prior rainfall (“AMC?)? dominates - Significant @ 0.05 in 30 of 43 watersheds

- 29 of the 30 were positive effects - 5-day was the most prevalent

• Intensity is a factor - significant in 17 of the 43 watersheds

- 16 of the 17 were negative effects - longer durations are the most important

Conclusions - more

• Storm duration effects were common, but mixed role

• Pattern index effects were sparse, weak and mixed. Not a major player

Discussion …• Prior rainfall - P1, P2, P5

--Meets expectations and intuition ….

• Intensity - imax5, imax10, imax15, imax30 - 16 of the 17 were negative effects? --Departures from the trend line, not primary effects. --Less important than Prior rainfall (All the departures can’t be positive!)

- Longer durations are the most important (becomes more associated with rainfall depth)

Discussion … more

• Storm Duration..

- An interacting surrogate for storm depth(P)?

- Did the CN fitting remove all the rainfall effect?

• Storm Depth (P)

- It alone accounts for most of the variance in Q

- Did the CN fitting remove all the rainfall effect?

Acknowledgements

• USDA - NRCS and Arizona Agricultural Experiment Station, for support

• USDA- ARS, for the data, and cooperation

• Prior workers: including Mark M. Dripchak, Averill Cate, Maria J. Simas, Paul A. Lawrence, P. Deanne Reitz,

Myra A. Price, Ruiyun Jiang

ITEM MIN AVG MAXWatershed Area (acres) 0.65 280.00 3490.00# Events with P/S>0.5 7 75 229

Min P (P/S = 0.5) 0.74 1.39 2.53P 0.74 2.07 7.31Q 0.0001 0.6118 6.8852

CN 67.00 78.80 87.15