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Historical Perspective of the NRCS Lag Equation

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Title: Historical Perspective of the NRCS Lag Equation


1
Historical Perspective of the NRCSLag Equation
  • Norman D. Folmar
  • Arthur C. Miller

2
Spring Flood of 1936
  • Rainfall event on top of a snowmelt in the
    eastern US
  • Due to the flood damages, federal agencies were
    called upon to establish methods for hydrologic
    studies
  • These agencies include the US Army Corp of
    Engineers and the Soil Conservation Service

3
NRCS
  • Under Public Law 566, SCS was to construct
    thousands of flood control structures

4
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5
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6
NRCS
  • Under Public Law 566, SCS was to construct
    thousands of flood control structures
  • Victor Mockus then determined a method for
    hydrologic analysis
  • These procedures then would be used by all SCS
    offices for hydrologic analysis
  • The final result was a dimensionless unit
    hydrograph with an equation for Qp and Tp

7
NRCS Dimensionless Unit-Hydrograph
  • Qp 484A/tp
  • A Area of the watershed in square miles
  • tp Time to peak of the hydrograph (hr)
  • The peak discharge is distributed through a
    dimensionless hydrograph

8
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9
NRCS Synthetic Unit-Hydrograph
  • As was shown by the peak flow equation, the peak
    flow prediction is inversely proportional to the
    lag time
  • An under prediction of the lag time will result
    in an over prediction of the peak flow and vice
    versa
  • Therefore the lag time prediction has a strong
    influence on the design discharge

10
SCS lag time
  • Two methods to calculate lag time
  • The lag time equation was the first and is a
    regression based method using watershed
    characteristics (Mockus)
  • The segmental approach is a method used to
    calculate time of concentration and was
    introduced in TR-55

11
Development of the SCS lag equation
  • Calculations done by Mockus

12
Databases
  • Mitchell collection of 58 watersheds ranging
    in size from 10.1 to 3090 mi2
  • Civil Works 153 collection of 32 watersheds
    ranging in size from 21.3 to 2890 mi2
  • ARS - collection of 18 watersheds ranging in size
    from 0.013 to 78 mi2
  • Ramser original data used by Ramser and
    Kirpich, ranged from 0.002 to 0.175 mi2

13
Steps in Mockus Development
  • Examined relationships between watershed
    characteristics and lag time
  • Analyzed existing equations such as the Kirpich
    equation
  • Then performed a regression analysis

14
Length 8800Area0.55
15
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16
Lag L/11,600 gt from combining relationships
Lag 0.76Area 0.55
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19
WS ID State Area (mi2) Database
Fern Canyon 2 Unknown 0.063 Unknown
61-2 Illinois 0.071 ARS
w-23 North Carolina 0.0094 ARS
NA-GE-1 Unknown 21.3 Civil Works 153
Ramser 1 Tennessee 0.032 Ramser, 1927
Ramser 3 Tennessee 0.077 Ramser, 1927
Ramser 4 Tennessee 0.024 Ramser, 1927
Ramser 5 Tennessee 0.175 Ramser, 1927
Ramser 6 Tennessee 0.002 Ramser, 1927
Ramser 7 Tennessee 0.0044 Ramser, 1927
13-2 Virginia 0.032 ARS
15-1 Virginia 0.610 ARS
20
WS ID State Area (mi2) Database
21-1 Iowa 3.01 ARS
26-29 Ohio 0.116 ARS
26-30 Ohio 0.473 ARS
26-36 Ohio 7.02 ARS
27-1 Ohio 0.291 ARS
31-1 Wisconsin 0.517 ARS
33-5 Arkansas 0.030 ARS
34-9 Oklahoma 0.013 ARS
37-2 Oklahoma 0.143 ARS
42-5 Texas 9.16 ARS
45-2 Arizona 1.065 ARS
47-1 New Mexico 0.152 ARS
21
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22
Ratio of observed to predicted lag
23
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24
The Lag Equation
  • The top equation was the original equation
  • Later analysis revealed that the equation led to
    a severe under prediction
  • The equation then was changed based on a
    sensitivity analysis of the curve number

25
Conclusions
  • The initial SCS unit hydrograph theory was solely
    dependent upon the regression based lag estimate
  • Mockus development shows no justification of the
    use of the segmental approach
  • Later SCS personnel implemented the use of the
    segmental approach with the idea that the timing
    estimates would better reflect development

26
Conclusions (cont.)
  • The effect that the segmental approach prediction
    has on the peak flow estimates has never been
    addressed
  • SCS personnel acknowledge this fact, however
    state that the segmental approach provides a
    relative difference between pre and post
    conditions
  • Instead of depending on the segmental approach do
    further research on lag equation especially
    non-urban watersheds

27
Final Comments
  • Through the 50s and 60s, the NRCS has
    constructed over 10,000 flood control structures
  • Currently, these structures are reaching their 50
    year design life
  • From preliminary studies, it is estimated that
    the repair will cost 540 million dollars
  • An accurate hydrologic procedure would be crucial
    to these renovations

28
Questions?
29
Data Collection
  • The watersheds used in this study were obtained
    from the ARS database
  • A total of 39 watersheds were used in this study
    which ranged in size from 29 to 12,000 acres
  • All watersheds have land uses that are a
    combination of agricultural and forested

30
Data Collection (Cont.)
  • The ARS collects continuous rainfall/runoff data
    from their watersheds
  • GETPQ was used to measure the lag time for
    several storm events
  • Approximately 30 storm events were chosen for
    each watershed, totaling in over 1100 storms for
    this study

31
Objectives
  • Compare the predictions made by the lag equation
    and segmental approach to the measured lag time
  • Determine watershed characteristics to where the
    lag equation and segmental approach closely
    predict the measured lag time

32
Determination of Lag time
  • An average lag time was determined for each
    watershed
  • GETPQ measures lag from centroid to centroid
  • After calculating time of concentration and lag
    time, all definitions were adjusted to match

33
Overview
  • The lag time was calculated for each watershed
    using the lag equation and segmental approach
  • Then these calculated lag times were compared to
    the measured lag time

34
Watershed Characteristics vs Measured Lag Time
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36
Watershed slope vs Measured lag
37
Lag Equation Predictions vs Measured Lag Times
38
Lag Equation
Percent Difference (calculated measured)/
measured
39
Lag Equation
40
LHL vs Watershed slope
41
Lag Equation
42
Summary of the Lag Equation
  • The longest hydraulic length and area are the
    better predictors of the measured lag time
  • Slope was also shown to be important, but may not
    be a linear relationship with lag time
  • Perhaps the exponent on slope should vary for
    different ranges

43
Summary (Cont.)
  • The Ohio and Vermont watersheds followed trends
    nicely
  • This is most likely due to these watersheds being
    fan-shaped
  • The lag time for the Georgia watersheds were
    over-predicted due to the low measured slopes

44
Fan-shaped
Non fan-shaped
45
Lag Equation with Land Slopes
  • Previously, the slopes of the three main
    hydraulic lengths were used to determine the
    average slope of the watershed
  • ARS supplies a summary of land slopes found
    within the watershed
  • These slopes then were used to determine the lag
    time with the lag equation

46
Lag Equation Predictions Using Land Slopes
47
Land slopes vs. Measured lag
48
Lag Equation with Land slopes
49
Summary with Land Slopes
  • The land slopes where shown to have less
    correlation with the measured lag time than the
    hydraulic slopes
  • These slopes where generally higher than the
    hydraulic slopes and thus increased the under
    prediction of the lag time

50
Segmental Approach Predictions vs Measured Lag
Times
51
Segmental Approach
52
Segmental Approach increase in n
53
Summary on Segmental Approach
  • This method was found to under-predict by a
    constant amount
  • The under-prediction ranged from 4090 with the
    majority in the 60-90 range
  • An increase in the Mannings n could compensate
    for this under prediction

54
Summary (Cont.)
  • However, the higher Mannings n values were
    much higher than common values of this variable
  • This suggests that there is possibly more delay
    in the travel time than this method is accounting
    for

55
Conclusion
  • The preceding results have shown that there are
    improvements that can be made to NRCS methods of
    obtaining a watershed response time
  • An equation for lag could be developed for
    different slope ranges
  • An adjustment factor could be developed for the
    segmental approach to account for an added delay
    that is occurring in the travel time

56
Conclusions (cont.)
  • In general, the current methods will likely under
    predict the true lag time of a watershed
  • Therefore, this under prediction of the lag time
    will result in an over prediction of the peak
    discharge

57
New Results
  • R2 of 84.8
  • R2 of 85.1

A total of 54 watersheds The parameters (S1) and
slope are not relevant
58
Questions?
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