HYDROLOGIC MODELING CONSISTENCY AND SENSITIVITY TO WATERSHED SIZE

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1 HYDROLOGIC MODELING CONSISTENCY AND SENSITIVITY TO WATERSHED SIZE by James C.Y. Guo. Professor, Civil Engineering, U. Of Colorado at Denver, And Eric Hsu, Project Engineer, Parson Brinkerhoff, Quade and Douglas Inc., Las Vegas, Nevada INTRODUCTION Computer applications to storm runoff prediction have revolutionized the watershed modeling techniques. In general, a watershed is modeled as a system with inputs and outputs (Chow 1964). A system can be lumped or distributed, depending upon the spatial and temporal characteristics of the design variables used in the model. A lumped parameter ignores the variability in space. On the other hand, taking the spatial variations into consideration, the system becomes a distributed model (Singh 198). As a rule of thumb, a lump model is applicable to a small watershed characterized by its quick response to rainfall while a distributed model is recommended for large watersheds. For example, in Las Vegas valley, Nevada, the HMS or HEC-1 model is accepted for regional master drainage planning while the Rational method is recommended for local designs (HCDDM, 1999). Although the watershed size dictates the selection of hydrologic model, both methods must be calibrated to warrant a consistency in flood predictions. Flood predictions and storm water designs apply a risk-based approach to model the rainfall and runoff through a watershed. In an urban area, the storm water drainage system consists of micro (BMP controls), minor (-yr event), and major systems (100-year event). It is imperative that all levels of drainage systems be consistently designed with a selected risk level. Consequently, the upstream drainage system can be constructed with its pipe sizes to increase downstream. In practice, a regional master drainage plan is the guidance to warrant a consistent risk among all levels of drainage systems. However, current practice is a two-method approach, including HEC-1 model for large watersheds and Rational method for small watersheds. Without a careful calibration, these two methods cannot produce flood predictions on a consistent basis. This paper presents an investigation regarding the inconsistency between Rational method and HEC-1 method used in Las Vegas Area, Nevada. The methodology derived in this paper is transferable to other regions. HYDROLOGIC LOSS FUNCTIONS Rainfall excess produces storm runoff. To establish a basis of consistency between two prediction methods, it is necessary to understand the relation between their hydrologic loss functions. The hydrologic loss function used by the HEC-1 method is associated with the soil curve number, CN, (McCuen 198). The relationship between a curve number and the initial soil losses, S, is described as: 1000 S = 10 (1) CN According to the SCS (Soil Conservation Service) method, the rainfall excess or direct runoff depth, is defined as: ( P 0.S) P e P S = () 1

2 in which P e = rainfall excess in inches, and P = design rainfall depth in inches. By definition, the value of a runoff coefficient, C, is equivalent to Pe C = (3) P Substituting Eq into 3 yields ( P 0.S) C = (4) P( P + 0.8S) Eq s 1 and 4 provide the mathematical relationship between runoff coefficients and curve numbers. DESIGN RAINFALL IDF CURVE The Rational method is a simplified procedure to predict peak runoff rates by the contributing rainfall only. Kuichling (1889) stated that the peak rate of runoff at a design point is a direct function of the tributary area, and the contributing rainfall amount to the peak runoff is the rainfall depth over the past up to the time of concentration of the catchment. For convenience, the Rational method suggests that the design rainfall distribution be converted into its IDF curve that depicts the highest intensity for the selected duration. For instance, the intensity for duration of 15 minutes represents the most intense rainfall within a period of 15 minutes during the event (Guo 1998, 000b). An I-D-F curve decays with respect to the period of duration and can be described as: I ap = (5) c ( b + ) T d in which P = base value to represent the event frequency such as the 100-yr 6-hr rainfall depth, a, b, and c = empirical constants, and T d = design rainfall duration that is assumed to be the time of concentration of the watershed. T d =T c (6) in which T c = time of concentration. Eq 6 warrants the entire watershed to be the tributary area to the design point. There are many empirical formulas developed to estimate the time of concentration (Kirpitch 1940, McCuen 1984). In this study, the regional formula developed for the metropolitan Denver and Las Vegas areas is used (USWDCM 001). It states: T = L c (7) in which T c = time of concentration in minutes and L = waterway length in feet. Eq 7 assumes that the overland flow time is 10 minutes and the flow velocity on a street gutter is 3 feet per seconds. According to the NOAA (Nation Ocean Atmosphere Administration) Rainfall Atlas II, Volume 9 for Nevada, the IDF curve at the McCarran Airport site can be mathematically described by I N 1.0P = (8) ( T d )

3 in which I N = NOAA rainfall intensity, and P 6 = 100-yr 6-hour precipitation depth, i.e., P =.77 inch at McCarran Airport site. Similarly, an IDF curve can also be derived from the SCS 6-hour rainfall distribution, or SDN-3 curve. Figure 1 is the SDN-3 rainfall distribution used in the HEC-1 model to predict storm runoff in the Las Vegas area. For comparison, the SDN-3 curve is further converted to its IDF curve for the most intense 60 minutes as shown in Table SCS SDN-3 RAINFALL DISTRIBUTION Incremental Rainfall Depth in inch Time in minutes Figure 1 SDN-3 or Six-Hour SCS Rainfall Distribution Duration Rainfall Depth Rainfall Intensity Min Inch Inch/hr Table 1 IDF Curve for SDN-3 SCS Rainfall Distribution Aided by Eq 5, the best fitted equation for the SDN-3 IDF curve is found to be: 3

4 I S 6.10P = (9) ( 10 + Td ) As demonstrated in Figure, the NOAA IDF formula for the Las Vegas area tends to produce peak rainfall intensities twice as much as the SDN-3 curve. This discrepancy between Eq s 8 and 9 is the key factor that introduces an inconsistency between the HEC-1 and Rational methods for Las Vegas areas. Comparison of IDF and SDN-3 Las Vegas Area 10 Avg Intensity (inch/hr) Rainfall Duration Td = Tc minutes IDF SDN-3 Figure Comparison of NOAA and SDN-3 IDF Curves MODIFIED RATIONAL METHOD Over 0 years, many major storm water detention systems and flood channels have been already constructed in the Las Vegas area using the SDN-3 rainfall curve while the minor drainage systems have also been designed using the NOAA s IDF curve. It has been long concerned as to how to establish consistency between these two methods. In this study, it is first suggests that the Rational method be modified as: Q = K C I N A (10) in which K = adjustment factor. Aided by Eq 4, Eq 10 is re-arranged as: K Q P ( P + 0.8S) 6 6 = (11) AI N ( P6 0.S) To investigate the value of K, a numerical test was conducted for a series of hypothetical square watersheds with drainage areas ranging from 0.05 to 0.50 square mile. The assumed flow path 4

5 through a square watershed is described in Figure 3. Table is the summary of the hydrologic parameters for the hypothetical watersheds. Flow path Low Point Figure 3 Hypothetic Wat ershed and Flow Path S quare Time Lag I Product Catchment Of Time I*A Area Concentrati on acre m inutes Hours inch/hr Table Hydrologic Parameters for Hypothetical Watersheds In this study, a set of curve numbers ranging from 50 to 90 was applied to each watershed. With an assigned CN, the HEC-1 model was applied to each watershed to produce the 100-year peak flow rate used in Eq 11. The rainfall depth in Eq 11 was set to be the 100-year 6-hr rainfall depth of.77 inches at the McCarran Airport site. Eq 7 is applied to the flow path defined in Figure 3 to calculate the time of concentration. The lag time, T p, required by the HEC-1 SCS method is estimated as: T = (1) p T c With a known T c, Eq 8 is used to calculate the rainfall intensity in Eq 11. Calculations of the value of K for the hypothetical watersheds are summarized in Table 1. The average value for K is approxima tely CN 50 CN 60 CN 70 CN 80 CN 90 Q by K Q by K Q by K Q by K Q by K Area H EC-1 HEC-1 HEC-1 H EC-1 H EC-1 Acres Cfs cfs cfs cfs cfs Table 3 Calculations of the Value of adjustment Factor 5

6 CASE STUDY A series of small urban watersheds ranging from 0 to 00 acres were selected from Pittman Watershed in the City of Handerson, Nevada. The 100-year storm runoff peak rates for the sample watersheds are simulated by HEC-1 using the 100-year SDN-3 SCS curve. Similarly, the modified Rational method was also used to predict the 100-year peak flow rates for the selected sample watersheds. Table 4 lists the input parameters for both methods and their results for comparison s. R ational HEC1 Catchment Catchment 6-hr CN Tc CIA Model ID Area P Q Q sq mile Inch min cfs cfs A A A C D A C C B C C A A B C B D F D F F F Table 4 Comparison of Predictions by Rational and HEC-1 Methods Figure 4 is the plot of Table 4 with the drainage area up to 550 acres. Using the adjustment factor of two, the Rational method produces compatible 100-year peak flood flows with HEC-1 until the watershed area increases to 150 acres. A similar conclusion was also reached for the 10-year flood flow predictions. In addition, another 30 some small urban watersheds in the City of North Las Vegas, and Mesquite areas were also examined for both 10- and 100-year floods. Similar conclusions to the Pittman watershed were observed. 6

7 Consistency Between Rational Method and HEC1 Model For the Las Vegas Areas 1000 Peak Discharge in CFS Watershed Area in Acres Rational HEC-1 Figure 4 Comparison Between Modified Rational and HEC-1 Methods Based on the investigation on 50 some sample urban watersheds in the Las Vegas area, it is suggested that the modified Rational method be applicable to watersheds up to 150 acres. For any watershed greater than 150 acres, the HEC-1 model shall be employed. CONCLUSION Various hydrologic methods were developed for various hydrologic conditions and applicable ranges. As a result, each method has its own limitations and requirements on the design information. The conclusions for this study include: (1) For the Las Vegas area, the NOAA IDF curve used in the Rational method produces rainfall intensities twice as much as the SCS SDN-3 curve used in the HEC-1 method. () The Rational method is applicable to small urban watersheds. With significant depression and storage effects, the Rational method needs a modification. This study indicates that the inconsistency between the HEC-1 and Rational methods mainly results from the different design rainfall distributions. The hypothetical watersheds used in this study suggest that the value of the adjustment factor in Eq 10 be two. (3) More than 50 urban watersheds outlined in the master drainage study published for the Las Vegas area were further investigated to confirm the consistence between the predictions from the HEC-1 and modified Rational methods. The comparison suggests that the modified Rational method is applicable up to 150 acres. 7

8 ACKNOWLEDGMENT The method developed in this paper has been adopted by Hydrologic Criteria and Drainage Design Manual published by Clark County Flood Control District, Las Vegas, Nevada. The task of Rational Method Modification was executed by a technical review committee. The authors like to express his thanks to Kevin Eubank, Stephen Roberts, Randy Fults, Allen Bell, Lenny Badger, John Clark, Steve Mano, and many others for their contributions. REFERENCES Chow, V.T. (1964). "Handbook of Applied Hydrology", McGraw-Hill Book Company, New York. Guo, James C.Y. (001) "Rational Hydrograph Method for Small Urban Catchments", ASCE J. of Hydrologic Engineering, July/August, Vol 6, No.4, July/August. Guo, James C.Y. (1998). "Overland Flow on a Pervious Surface", International Journal of Water,Volume 3, No, June, pp Guo, James C.Y. (000a). "A Semivirtual Watershed Model by Neural Networks", J. of Computer- Aided Civil and Infrastructure Engineering, Vol 15, pp Guo, James C.Y. (000b). "Storm Hydrographs From Small Urban Catchments", International Journal of Water, No 3, September, HEC-1 Flood hydrograph Package (1985), published by the Hydrologic Engineering Center, U.S. Army Corps of Engineers, Davis, California. HCADDM (Hydrologic Criteria and Drainage Design Manual) (1999), published by Clark County, Las Vegas, Nevada. Kirpich, Z.P., (1940). "Time of Concentration for Small Agricultural Watersheds," Civil Engineering, ASCE, Vol 10, No 6, June, pp 36. Kuichling, E. (1889). "The Relation between Rainfall and the Discharge of Sewers in Populous Districts," Trans. ASCE, Vol 0, pp McCuen, R. (198) "A Guide to Hydrologic Analysis Using SCS Methods", Prentice-Hall, Inc., Englewood Cliffs, New Jersey. McCuen, R. H., Wong, S. L., and Rawls W. J. (1984). "Estimating Urban Time of Concentration", J. of Hydraulic Engineering, ASCE, Vol 110, No. 7, July. Singh, V.P. (198) "Hydrologic Systems: Rainfall-Runoff Modeling", Volume I, Prentice-Hall, Inc., Englewood Cliffs, New Jersey. USWDCM (Urban Storm Water Design Criteria Manual), (001), published by Urban Drainage and Flood Control District, Denver, Colorado. 8

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