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4.2 Application of the Modified Rational Method Parameterized by the Unified Rational Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2.1 Non-Uniform Rainfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.2 Characteristic Time Assessment . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3 Regression Equation Adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5 Summary and Conclusions 74 5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.3 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.3.1 Additional Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.3.2 Implementation of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 A Literature Review 84 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 A.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 A.2.1 Modified Rational Method — Background . . . . . . . . . . . . . . . . . . . . 87 A.3 Rational Method Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 A.3.1 Modified Rational Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 A.3.2 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 A.4 Characteristic Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 A.5 The Runoff Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 A.5.1 Standard Rational Runoff Coefficients . . . . . . . . . . . . . . . . . . . . . . 95 A.5.2 Runoff Coefficients Based on Water Budgets and Long-Term Basin Scale Studies 99 A.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 B Basin Development Factor 102 C The iPar Program and Parsing of Rainfall and Runoff Events 106 C.1 Inverting the Rational Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 C.1.1 The Rational Method for Real Storms . . . . . . . . . . . . . . . . . . . . . . 107 C.1.2 Regression of Time-R (Lag Time) . . . . . . . . . . . . . . . . . . . . . . . . 111 C.1.3 Distribution of C R and Relation between C R and Drainage Area and Basin- Development Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 C.2 Algorithms of the Unified Rational Method Appendix . . . . . . . . . . . . . . . . . 121 D Modified Rational Method 130 D.1 Modified Rational Method for Texas Watersheds . . . . . . . . . . . . . . . . . . . . 130 D.2 Runoff Coefficients and Time of Concentration . . . . . . . . . . . . . . . . . . . . . 130 D.3 Estimated Runoff Hydrographs Using the MRM . . . . . . . . . . . . . . . . . . . . 132 D.4 Comparison of MRM Results and Other Unit Hydrograph Methods . . . . . . . . . . 137 ix
List of Tables 3.1 Countywide values of mean-annual precipitation and OmegaEM parameter. . . . . . 30 3.2 Countywide values of scale factor for unified rational method in Texas. . . . . . . . . 34 3.3 Countywide values of exponent on drainage area for unified rational method. . . . . 41 3.4 Countywide values of exponent on dimensionless main-channel slope. . . . . . . . . . 48 3.5 Comparison of Dickens County example peak streamflow frequency estimates. . . . . 54 A.1 Rational method runoff coefficients for various land uses (Standard C std ). . . . . . . 96 D.1 Runoff coefficients used in the modified rational method. . . . . . . . . . . . . . . . . 133 x
Page 2 and 3: NOTICE The United States Government
Page 4 and 5: This page intentionally left blank.
Page 6 and 7: AUTHOR’S DISCLAIMER The contents
Page 8 and 9: Acknowledgements A project of the m
Page 12 and 13: List of Figures 2.1 The MRM hydrogr
Page 14 and 15: D.5 Modeled and observed peak disch
Page 16 and 17: The modified rational method extend
Page 18 and 19: 2. Technical Aspects of the Rationa
Page 20 and 21: unoff, with a negligible amount of
Page 22 and 23: 2.1.4. Summary and Important Implic
Page 24 and 25: If the storm duration is equal to t
Page 26 and 27: Figure 2.4: The instantaneous unit
Page 28 and 29: the ratio of peak rate of runoff to
Page 30 and 31: in these cases strictly converts th
Page 32 and 33: 3. A Proposed Unified Rational Meth
Page 34 and 35: with the middle of the C-value rang
Page 36 and 37: 10. The intercepts of β and expone
Page 38 and 39: Limits of the Unified Rational Meth
Page 40 and 41: T ⋆ as a “travel time” is ten
Page 42 and 43: 5. Determine IU ⋆ using T L ⋆ b
Page 44 and 45: Table 3.1: Countywide values of mea
Page 46 and 47: Table 3.1: Countywide values of mea
Page 48 and 49: Table 3.2: Countywide values of sca
Page 56 and 57: Table 3.3: Countywide values of exp
Page 58 and 59: Table 3.3: Countywide values of exp
Page 60 and 61:
Table 3.3: Countywide values of exp
Page 62 and 63:
Table 3.4: Countywide values of exp
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Table 3.4: Countywide values expone
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Table 3.4: Countywide values expone
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Table 3.5: Comparison of annual pea
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LATITUDE, IN DEGRESS 26 30 34 2−y
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PEAK DISCHARGE, IN CFS 0 5 10 15 20
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Figure 4.1: Subdivision X Drainage
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Figure 4.2: Depth-Duration diagram
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coefficient C as in Equation 4.1. W
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(Row 27) and the excess rainfall in
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Figure 4.6: Modified rational metho
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Figure 4.8: Modified rational metho
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this report to estimate T ∗ . Wit
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5. Summary and Conclusions This sec
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coefficients entirely). The method
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Bibliography Akan, A. O. (2002). Mo
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FHWA (1983). Urban Highway Storm Dr
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Roussel, M. C., D. B. Thompson, X.
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A. Literature Review The rational m
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Intensity (in/hr) 0 1 2 3 4 5 0 20
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storms with durations greater than
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The intent is to estimate the disch
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Figure A.3: Modified Rational Formu
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where L is a characteristic length
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Table A.1: Rational method runoff c
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Table A.1: Rational method runoff c
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Figure A.4: Runoff Coefficients for
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B. Basin Development Factor The bas
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3. Storm drains, or storm sewers
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C. The iPar Program and Parsing of
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The values for C can not be decoupl
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Figure C.2: Screenshot of custom-bu
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Figure C.3: Screenshot of output fo
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logSrhs 0.26969 0.04056 6.650 3.44e
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hook operator provides a compact no
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20 MEDIAN TIME-R (LAG TIME), IN HOU
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1 0.9 0.8 0.7 MEDIAN CR 0.6 0.5 0.4
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# print ( DDF .at.F); # print ( IDF
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the .I
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eturn ( get (x, COUNTY_NAMES ))), M
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mycol25
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D. Modified Rational Method The pur
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100.0 Cumulative Distribution (%) 8
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10000 Modeled Q p (cfs) 1000 100 1:
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10000 Modeled Q p (cfs) 1000 100 1:
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where A is the drainage area in squ
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500 Station: 08048550 DryBranch For
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10000 MRM Gamma 1:1 line Modeled Q
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