Effects of Prior Rainfall and Storm Variables on Runoff Curve Number

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Effects of Prior Rainfall and Storm Variables on
Runoff Curve Number
Richard H. Hawkins and Kevin E.
VerWeire Watershed Resources Program University
of Arizona, Tucson, AZ ASCE Watershed Management
Conference July 20, 2005 Williamsburg VA
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ProblemDirect runoff (Q) from rainfall (P)
.and what else?

• Why the variation?
• - Prior rainfall (antecedent moisture)
• - Intensity? What intensities?
• - Storm distribution?
• - Storm duration?

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5-day table from Ch 4

• Antecedent Moisture driven variation
• 5-day prior rainfall basis
• Dormant season
  Growing Season
• --------------------------------------
  ------------------------------
• AMC I lt 0.5 in
  lt 1.4 in
• AMC II 0.5 to 1.1 in
  1.4 to 2.1 in
• AMC III gt 1.2 in
  gt2.1 in
• ---------------------------------------
  ------------------------------
• This was included in original NEH-4, but is now
  considered obsolete, and is no longer endorsed or
  included. Do not use.

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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/(P0.8S)
• 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)

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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

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Determine Watershed CN and Deviations

• Use Least Squares Method
• Fit Q (P-0.2S)2 / (P0.8S), for P/Sgt0.50
• For the natural PQ 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

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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

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RegressionProcedure

• Selective 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 Prgttlt0.05

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Regression more

• Convert to dimensionless deviations, and
  coefficients are recast as beta values.
• The bo constant is eliminated by this
• (Y-µy)/sY ß1(X1-µX1)/sX1 ß2(X2-µX2)/sX2
  ..etc
• Relationship strengths and directions are
  expressed by ß
• Used Stata software

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Data summary 43 watersheds

• Item Min Med Max
• --------------------------------------------------
  ----------------
• Drainage area (Ac) 0.65 7.59 3490
• Events with P/Sgt0.5 7 75 229
• Min P(in) P/Sgt0.5 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
• --------------------------------------------------
  ----------------

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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)

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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

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Results - more

• Variable Count ß 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

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Results - more

•   
• Variable Count ß range Comment
• --------------------------------------------------
  ------------------
• Duration 22 -0.50 to 0.41 10 lt0
  12gt0
•  
• Pattern Index 5 -0.15 to 0.13 3lt0
  2gt0
•  

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Results - more

• Summary
• Variable Count ß 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
•  

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Results
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Conclusions

• Prior rainfall (AMC?)? dominates
• - Significant _at_ 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

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Conclusions - more

• Storm duration effects were common, but mixed
  role
• Pattern index effects were sparse, weak and
  mixed. Not a major player

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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
• cant be positive!)
• - Longer durations are the most important
• (becomes more associated with rainfall
  depth)

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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?

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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

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