Use of Rational and Modified Rational Method for ... - CTR Library

More documents

Recommendations

Info

Figure 2.4: The instantaneous unit hydrograph of the rational method (Singh and Cruise, 1992). Figure 2.5: The D-hour unit hydrograph of the rational method for D < T c (Singh and Cruise, 1992). triangular hydrograph (Figure 2.1) when D = T c and the trapezoidal hydrograph (Figure 2.2) when D > T c from the rational method, similar to results presented by Chien and Saigal (1974); Walesh (1975). Guo (2000, 2001) proposed and developed a rational hydrograph method (RHM) that can be applied for continuous nonuniform rainfall events. Furthermore, Guo applied the RHM to extract both the runoff coefficient and the time of concentration from observed runoff events through optimization. Guo considered the time of concentration as the system memory (Singh and Cruise, 1992) and used a moving average window to estimate uniform rainfall intensity for the application of the rational method to determine hydrograph ordinates. If the rainfall is uniform, the RHM will result triangular or trapezoidal hydrographs, similar to those shown in Figures 2.1 and 2.2. Guo’s RHM was used by Hayes and Young (2005) to estimate peak discharge, time of concentration, and runoff coefficient for small basins in central Virginia with observed nonuniform rainfall data. 12
The RHM developed by Guo (2000, 2001) is not strictly a unit hydrograph because it violates the mass conservation principle when applied to nonuniform rainfall distributions. In contrast, the MRM unit hydrograph is mass conservative. However, the RHM is a practical procedure to compute the moving average rainfall intensity for the application of rational formula, and indirectly links the modified rational approaches to unit hydrograph theory. Singh and Cruise (1992) present a systems-based approach for the analysis of the rational formula. Like Smith and Lee (1984), they assumed the watershed is represented as a linear, time-invariant system whose instantaneous unit hydrograph (IUH) is a uniform rectangular distribution of base time equal to the time of concentration of the basin (Figure 2.4). They used the convolution to derive the S-hydrograph and D-hour unit hydrograph for the rational method as shown in Figure 2.5. The unit hydrograph shown on Figure 2.5 represents the unit hydrograph that results from the modified rational method. This unit hydrograph has a symmetric trapezoidal shape when the duration is less than the time of concentration (D < T c ). Extending the original rational method for computing the peak discharge to the modified rational method for developing runoff hydrographs only assumes an ideal watershed with equal time-area histogram and no watershed storage or hydrograph attenuation. Chien and Saigal (1974) state, In all cases, linear variation in the rising limb and the receding limb of the subhydrograph for a sufficiently small drainage basin is assumed. It is recognized that these variations are, in fact, curvilinear; however, in review of the crudeness in predicting the curvilinear variations and linear approximation in observed experimental hydrographs (Morgali 1970; Schreiber and Bender 1972), the assumption of linear variations is considered practical. The linear channel or constant time-area histogram as basic assumption for the modified rational method UH is a simplistic approximation for watersheds, especially when the drainage area becomes large. Watersheds with a nonuniform time-area histogram (those that cannot be represented by a linear channel approximation) will not produce the same unit hydrographs predicted by the MRM even for the uniform rainfall condition. With these caveats in mind, the MRM is a useful tool for appropriately sized watersheds, with the implicit understanding that the runoff coefficient is a volumetric runoff coefficient, and simply serves to convert rainfall into excess rainfall. Many authors suggest the rational method, and especially the modified rational method, requires a uniform rainfall distribution for application. This requirement is incorrect based on the interpretation of the MRM as a unit hydrograph method. The MRM can be used to generate runoff hydrographs for any nonuniform rainfall events using unit hydrograph convolution. The conclusion that the modified rational method is a unit hydrograph (UH) method is fundamentally important and this linkage establishes a continuity of methodology from very small watershed to rather large watersheds. 2.2.1. Modified Rational Method Runoff Coefficient The precise definition and subsequent interpretation of the runoff coefficient in the MRM varies. The value can be defined either as the ratio of total depth of runoff to total depth of rainfall or as 13
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 10 and 11: 4.2 Application of the Modified Rat
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 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 64 and 65: Table 3.4: Countywide values expone
Page 66 and 67: Table 3.4: Countywide values expone
Page 68 and 69: Table 3.5: Comparison of annual pea
Page 70 and 71: LATITUDE, IN DEGRESS 26 30 34 2−y
Page 72 and 73: PEAK DISCHARGE, IN CFS 0 5 10 15 20
Page 74 and 75: Figure 4.1: Subdivision X Drainage
Page 76 and 77:
Figure 4.2: Depth-Duration diagram
Page 78 and 79:
coefficient C as in Equation 4.1. W
Page 80 and 81:
(Row 27) and the excess rainfall in
Page 82 and 83:
Figure 4.6: Modified rational metho
Page 84 and 85:
Figure 4.8: Modified rational metho
Page 86 and 87:
this report to estimate T ∗ . Wit
Page 88 and 89:
5. Summary and Conclusions This sec
Page 90 and 91:
coefficients entirely). The method
Page 92 and 93:
Bibliography Akan, A. O. (2002). Mo
Page 94 and 95:
FHWA (1983). Urban Highway Storm Dr
Page 96 and 97:
Roussel, M. C., D. B. Thompson, X.
Page 98 and 99:
A. Literature Review The rational m
Page 100 and 101:
Intensity (in/hr) 0 1 2 3 4 5 0 20
Page 102 and 103:
storms with durations greater than
Page 104 and 105:
The intent is to estimate the disch
Page 106 and 107:
Figure A.3: Modified Rational Formu
Page 108 and 109:
where L is a characteristic length
Page 110 and 111:
Table A.1: Rational method runoff c
Page 112 and 113:
Table A.1: Rational method runoff c
Page 114 and 115:
Figure A.4: Runoff Coefficients for
Page 116 and 117:
B. Basin Development Factor The bas
Page 118 and 119:
3. Storm drains, or storm sewers
Page 120 and 121:
C. The iPar Program and Parsing of
Page 122 and 123:
The values for C can not be decoupl
Page 124 and 125:
Figure C.2: Screenshot of custom-bu
Page 126 and 127:
Figure C.3: Screenshot of output fo
Page 128 and 129:
logSrhs 0.26969 0.04056 6.650 3.44e
Page 130 and 131:
hook operator provides a compact no
Page 132 and 133:
20 MEDIAN TIME-R (LAG TIME), IN HOU
Page 134 and 135:
1 0.9 0.8 0.7 MEDIAN CR 0.6 0.5 0.4
Page 136 and 137:
# print ( DDF .at.F); # print ( IDF
Page 138 and 139:
the .I
Page 140 and 141:
eturn ( get (x, COUNTY_NAMES ))), M
Page 142 and 143:
mycol25
Page 144 and 145:
D. Modified Rational Method The pur
Page 146 and 147:
100.0 Cumulative Distribution (%) 8
Page 148 and 149:
10000 Modeled Q p (cfs) 1000 100 1:
Page 150 and 151:
10000 Modeled Q p (cfs) 1000 100 1:
Page 152 and 153:
where A is the drainage area in squ
Page 154 and 155:
500 Station: 08048550 DryBranch For
Page 156 and 157:
10000 MRM Gamma 1:1 line Modeled Q
show all

Use of Rational and Modified Rational Method for ... - CTR Library

Create successful ePaper yourself

Delete template?

Save as template?