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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