A Distributed Kinematic Wave–Philip Infiltration Watershed Model Using FEM,GIS and Remotely Sensed Data

Distributed rainfall–runoff modeling is very important in the water resources planning of a watershed. In this study, a kinematic wave based distributed watershed model which simulates runoff on an event basis has been presented here. The finite element method (FEM) has been used to simulate the overland runoff and channel flow. Philip model has been used for the infiltration estimation. To find out runoff at the outlet of the watershed, both overland flow and channel flow models are coupled. The coupled model has been applied to a typical Indian watershed. Remotely sensed data has been used to obtain the land use (LU)/land cover (LC) for the watershed. Slope map of the watershed has been obtained using geographical information systems (GIS). The grid map of the watershed which contains overland flow elements connecting to channel flow elements has been prepared in GIS. The elemental input files such as slope and Manning’s roughness are prepared using the GIS and are directly used in the model. The model has been calibrated using some of the rainfall events and validated for some other events. The model results are compared with the observed data and found to be satisfactory. A sensitivity study of the infiltration parameters, overland and channel flow Manning’s roughness and time step has also been carried out. The developed model is useful for the simulation of event based rainfall–runoff for small watersheds.     

Effects of Urbanization Factors on Model Parameters

This study mainly explores effects of urbanization factors on hydrograph parameters. Urbanization impacts of the developing watershed are evaluated based on rainfall–runoff simulations. A total of 51 rainfall–runoff events occurred from 1966 to 2002. Forty of these were calibrated, and effects of urbanization factors on runoff hydrographs resulting from a simple hydrological model were assessed. The block Kriging method was used to estimate the mean rainfall of the Wu-Tu watershed, and its hourly excesses were calculated by using the non-linear programming method. The remaining 11 cases were used to test the established relationships. The calibration and verification results confirm that the integral methods used in this study effectively illustrate the hydrological and geomorphic conditions in complex urbanization processes. Parameter n responds more sensitively than parameter k to increasing impervious areas and population densities. Additionally, parameter n responds more strongly to imperviousness than to population. Therefore, an impervious area is an important reference for analyzing hydrological changes of urbanization in the Wu-Tu watershed.     

A Multivariate ANN-Wavelet Approach for Rainfall–Runoff Modeling

Without a doubt the first step in any water resources management is the rainfall–runoff modeling over the watershed. However considering high stochastic property of the process, many models are being still developed in order to define such a complex phenomenon in the field of hydrologic engineering. Recently Artificial Neural Network (ANN) as a non-linear inter-extrapolator is extensively used by hydrologists for rainfall–runoff modeling as well as other fields of hydrology. In the current research, the wavelet analysis was linked to the ANN concept for modeling Ligvanchai watershed rainfall–runoff process at Tabriz, Iran. For this purpose the main time series of two variables, rainfall and runoff, were decomposed to some multi-frequently time series by wavelet theory, then these time series were imposed as input data to the ANN to predict the runoff discharge 1 day ahead. The obtained results show the proposed model can predict both short and long term runoff discharges because of using multi-scale time series of rainfall and runoff data as the ANN input layer.     

Development and Integration of Sub-hourly Rainfall–Runoff Modeling Capability Within a Watershed Model

Increasing urbanization changes runoff patterns to be flashy and instantaneous with decreased base flow. A model with the ability to simulate sub-daily rainfall–runoff processes and continuous simulation capability is required to realistically capture the long-term flow and water quality trends in watersheds that are experiencing urbanization. Soil and Water Assessment Tool (SWAT) has been widely used in hydrologic and nonpoint sources modeling. However, its subdaily modeling capability is limited to hourly flow simulation. This paper presents the development and testing of a sub-hourly rainfall–runoff model in SWAT. SWAT algorithms for infiltration, surface runoff, flow routing, impoundments, and lagging of surface runoff have been modified to allow flow simulations with a sub-hourly time interval as small as one minute. Evapotranspiration, soil water contents, base flow, and lateral flow are estimated on a daily basis and distributed equally for each time step. The sub-hourly routines were tested on a 1.9 km² watershed (70% undeveloped) near Lost Creek in Austin Texas USA. Sensitivity analysis shows that channel flow parameters are more sensitive in sub-hourly simulations (Δt = 15 min) while base flow parameters are more important in daily simulations (Δt = 1 day). A case study shows that the sub-hourly SWAT model reasonably reproduces stream flow hydrograph under multiple storm events. Calibrated stream flow for 1 year period with 15 min simulation (R ² = 0.93) shows better performance compared to daily simulation for the same period (R ² = 0.72). A statistical analysis shows that the improvement in the model performance with sub-hourly time interval is mostly due to the improvement in predicting high flows. The sub-hourly version of SWAT is a promising tool for hydrology and non-point source pollution assessment studies, although more development on water quality modeling is still needed.     

Evaluation of three unit hydrograph models to predict the surface runoff from a Canadian watershed

The predictability of unit hydrograph (UH) models that are based on the concepts of land morphology and isochrones to generate direct runoff hydrograph (DRH) were evaluated in this paper. The intention of this study was to evaluate the models for accurate runoff prediction from ungauged watershed using the ArcGIS^® tool. Three models such as exponential distributed geomorphologic instantaneous unit hydrograph (ED-GIUH) model, GIUH based Clark model, and spatially distributed unit hydrograph (SDUH) model, were used to generate the DRHs for the St. Esprit watershed, Quebec, Canada. Predictability of these models was evaluated by comparing the generated DRHs versus the observed DRH at the watershed outlet. The model input data, including natural drainage network and Horton's morphological parameters (e.g. isochrone and instantaneous unit hydrograph), were prepared using a watershed morphological estimation tool (WMET) on ArcGIS^® platform. The isochrone feature class was generated in ArcGIS^® using the time of concentration concepts for overland and channel flow and the instantaneous unit hydrograph was generated using the Clark's reservoir routing and S-hydrograph methods. An accounting procedure was used to estimate UH and DRHs from rainfall events of the watershed. The variable slope method and phi-index method were used for base flow separation and rainfall excess estimation, respectively. It was revealed that the ED-GIUH models performed better for prediction of DRHs for short duration (≤6 h) storm events more accurately (prediction error as low as 4.6–22.8%) for the study watershed, than the GIUH and SDUH models. Thus, facilitated by using ArcGIS^®, the ED-GIUH model could be used as a potential tool to predict DRHs for ungauged watersheds that have similar geomorphology as that of the St. Esprit watershed.     

A Fast Semi Distributed Rainfall Runoff Model for Engineering Applications in Arid and Semi-Arid Regions

A new GIS based rainfall runoff model is developed for engineering applications, achieving a highly automated watershed analysis process starting from watershed delineation and up to the runoff hydrograph calculation. The model can be classified as a semi-distributed time area model that adopts an improved grid based approach for calculation of watershed response. The model deals with each grid cell in the digital elevation model as an independent hydrologic unit. Travel time through each grid cell is estimated using Manning’s formula and a stream power formula that relates the hydraulic radius at the cell to the characteristics of its upstream watershed area and excess rainfall depth. The watershed response at its outlet is estimated by routing the response of each grid cell using a flow path response function that is defined for that cell. The routed responses of all watershed cells are then convoluted to produce the outflow hydrograph. Model advantages include accuracy improvements due to the incorporation of grid-based routing calculations (both translation and attenuation), fully automated model structure, and fast ability to model many watersheds simultaneously. The combination of these advantages constitutes the novelty of the model that makes it very suitable for engineering design as well as for real-time applications. The model was tested using the data of the experimental watershed, Walnut Gulch, Arizona, USA, gauged by 88 rainfall stations and several discharge recording flumes. The results show that the model can accurately predict the runoff hydrograph where suitable input is available.     

紫色土区小流域泥沙输出过程对雨型和空间尺度的响应

以紫色土区3个具有不同集水面积、物理特征和土地利用方式的小流域为研究对象，在1999～2000年间对流域野外自然降雨下泥沙输出过程进行了监测，旨在从小流域尺度阐明径流含沙量过程特征及其空间约束效应。结果表明：天然降雨侵蚀过程中流域径流含沙量时间曲线表现为波浪起伏形、幂函数递减形和抛物线复合形3种类型；峰值径流流量后，含沙量降低，表现为变化幅度小的低含沙量特征。泥沙输出过程对流域空间尺度的响应受降雨型式的强烈影响。均匀型降雨侵蚀下，径流含沙量时间曲线表现为低含沙量的波浪起伏形，并且，随流域面积的增加，次降雨平均含沙量增加；间歇型降雨侵蚀下，随流域面积的增加，径流含沙量曲线从抛物线复合形向幂函数递减形过渡；中大型降雨侵蚀下，径流含沙量时间曲线表现为幂函数递减形，泥沙输出过程对流域空间尺度的响应不敏感。     

Deterministic Insight into ANN Model Performance for Storm Runoff Simulation

The artificial neural network (ANN) theory has been widely applied to practical applications in hydrology. Since watershed rainfall–runoff processes are nonlinear and exhibit spatial and temporal variability, the ANN model, which considers watershed nonlinear characteristics, can usually but not always obtain satisfactory simulation results. The training of an ANN network is based completely on the reliability of the available hydrologic records. The objective of this study was to provide deterministic insight into the limitations of storm runoff simulation when using ANN. Hydrologic records of 42 storm events from two watersheds in Taiwan were adopted for analysis. A deterministic runoff model was used to classify the hydrologic records into “usual” and “unusual” storm events. The analytical results show that the ANN model could provide good simulation results for “usual” storm events; however, its performance was poor when it was applied to “unusual” storm events because no consistent hydrologic characteristics could be extracted from the storm event records using ANN. The success of the ANN model in usual storm discharge simulations may be mainly due to the input vectors including the previous observed discharge. Moreover, the number of past periods of rainfall that were set as the input vectors of the ANN model was found to be highly correlated with the watershed time of concentration. It can be used to efficiently determine the ANN network structure instead of using iterative network training.     

基于径流侵蚀功率的流域次暴雨输沙模型研究——以岔巴沟流域为例

流域次暴雨侵蚀产沙模型研究是国内外土壤侵蚀研究的重点领域之一。提出了基于径流深和洪峰流量模数两个流域次暴雨洪水特征参数的径流侵蚀功率的概念;利用岔巴沟曹坪水文站1959至1990年间历年实测的次暴雨洪水径流泥沙资料,系统研究了该流域次暴雨径流侵蚀功率与流域输沙模数之间的相关关系,建立和验证了基于径流侵蚀功率的岔巴沟流域次暴雨输沙模型。结果表明,岔巴沟流域次暴雨径流侵蚀功率与流域输沙模数之间具有极显著的幂函数相关关系;模型验证期的次暴雨输沙模数模拟值与实测值之间具有较好的一致性。     

Management of Upstream Dams and Flood Protection of the Transboundary River Evros/Maritza

The flood frequency and the dikes overtopping at the downstream part of transboundary (Bulgaria–Greece–Turkey) river Evros/Maritza has increased dramatically in the last 13 years. It is not clear if the increase of flood frequency is due to climatic changes or to inappropriate management of Bulgarian dams. This fact raises the question of modeling the flood routing through the many dams in the Bulgarian territory (upstream), which receive the runoff of the 38% of the area of the Evros watershed in Bulgaria, in a way to protect the downstream countries from flooding. The basic objective of this paper is the development of a new management tool (software) for the simulation of the rainfall–runoff and routing process taking into account the existence of many dams and mainly their operation not only from a hydrologic viewpoint, but also from the administrative, with emphasis on the “energy–economic” exploitation of the reservoirs. The developed software (named Evrofloods) models the rainfall–runoff, the routing of runoff through the various Evros river tributaries taking in account various scenarios of the runoff through the artificial reservoirs with the aim of optimal management of the water released from the dams spillways and turbines. The “optimal management” is related with the finding for a given rainfall distribution, the appropriate combination of actions at many reservoirs (“reservoirs management”) in order to prevent or mitigate the floods downstream, aiming at the same time to minimize hydroelectric energy loss. Although Evrofloods software is basically dedicated to the large Evros basin, it can be easily used to determine the management of large transboundary rivers with many artificial reservoirs to avoid floods downstream. Recent European legislation on floods encourages the good cooperation of neighbor countries, to avoid floods.     

A Threshold Based Wavelet Denoising Method for Hydrological Data Modelling

This work developed a novel framework for considering wavelet denoising in linear perturbation models (LPMs) and simple linear models (SLMs). Rainfall and runoff time series data were decomposed using wavelet transforms to acquire approximate and detailed rainfall and runoff signals, respectively, at various resolution levels. At each resolution level, threshold quantifications were performed by setting the values of a detailed signal below a certain threshold to zero. The denoised rainfall and runoff time series data were obtained from the approximation at the final resolution level and processed detailed signals using threshold quantification at all resolution levels of rainfall and runoff, respectively, by wavelet reconstruction. The data were then applied to the SLM and regarded as the smooth seasonal mean employed in the LPM. The noise, i.e., original time series value minus denoised time series value, was employed as the perturbation term in the LPM. Moreover, a linear relationship between input and output noise was assumed. The denoised runoff and estimated noise of runoff were summed to estimate overall runoff in the LPM. To verify the accuracy of the proposed method, daily rainfall–runoff data were analyzed for an upstream area of the Kee-Lung River. The analytical results demonstrate that wavelet denoising enhances rainfall–runoff modelling precision for the LPM.     

流域初始状态对环境同位素法划分流量的影响

在使用同位素示踪剂划分流量时,流域初始状态会对事件水和事件前水分割产生影响。为研究流域初始状态对环境同位素法划分流量的影响,以和睦桥流域2015—2016年间4场降雨事件为研究对象,根据稳定同位素含量(δ¹⁸O)确定其在流域出口断面径流的不同水源组成比例,着重分析流域不同初始流量和前期土壤含水量对流量过程线划分的影响。结果表明:流域出口径流总量中事件前水占优,洪峰流量以事件水为主;流域不同初始状态下同位素分割结果不同,表明该流域存在多种产流机制,流域初始流量与总径流系数及事件水贡献比例呈负相关;前期土壤含水量与事件水贡献比例的影响模式复杂多变,但在前期土壤含水量较高或前期降雨较多的情况下,总径流中事件水贡献比例将降低。     

Flood Intensification due to Changes in Land Use

The non-stationarity in runoff regime may be attributed to various causes such as climate change, land use change, and man-made runoff control structures. Degradation of land use can induce significant impact on infiltration and surface roughness leading to higher flood discharges. This study aims at quantifying possible effects of land use changes and identifying flood source areas for future flood control planning in the Golestan watershed located northeast of Iran. A preliminary trend analysis on the annual maximum flood record of three stations inside the watershed showed that two stations were subject to anthropogenic change. This is while no trend could be detected in the annual maximum rainfall records in the region. Using a calibrated event-based rainfall-runoff model, flood hydrographs corresponding to land use conditions in 1967 and 1996 were simulated and relative changes in the peak flow of the two subsequent conditions were determined for different return periods. The results showed that the impact of land use changes on the flood peak discharge is considerably greater in some subwatersheds. Two limiting land use scenarios were also considered to investigate the envelope of future flood peaks in the watershed. By successively eliminating subwatersheds from the simulation process in a method titled "unit flood response”, the contribution of each subwatershed to the outlet flood peak was quantified. Contribution, per unit area, to the outlet flood peak was the basis to rank the subwatersheds in terms of their flood potential.     

WetSpa Model Application for Assessing Reforestation Impacts on Floods in Margecany–Hornad Watershed,Slovakia

The spatially distributed hydrologic model WetSpa working on a daily or hourly time scale combines elevation, soil and landuse data within GIS, to predict flood hydrographs and spatial distribution of hydrologic characteristics in a watershed. The model is applied to the Margecany–Hornad river basin (1,131 km²) located in Slovakia. Daily hydrometeorological data from 1991 to 2000, including precipitation data from nine stations, temperature data from four stations and evaporation data measured at one station are used as input to the model. Three base maps, i.e., DEM, landuse and soil types are prepared in GIS form, using 100×100 m cell size. Results of the simulations show good agreement between calculated and measured hydrographs at the outlet of the basin. The model predicts the daily/hourly hydrographs with good accuracy, between 75–80% according to the Nash–Sutcliff criteria. For assessing the impact of forests on floods, the calibrated model is applied for a reforestation scenario using the hourly data of the summer of 2001. The scenario considers a 50% increase of forest areas. The model results show that the reforestation scenario decreases the peak discharge by 12%. Investigation of peak discharges from the whole simulation period, shows that the scenario results are reduced by 18% on average. Also, the time to peak of the simulated hydrograph of the reforestation scenario is 14 h longer than for the present landuse. The results show that the effect of land cover on flood is strongly related to storm characteristics and antecedent soil moisture.     

Karst Spring Discharges Analysis in Relation to Drought Periods,Using the SPI

Based on the long hydrological time series, the correlation between karst spring discharge series and rainfall has been analysed, using the Standard Precipitation Index (SPI). Analysis has been focused on the drought periods. Data come from a large karst system (Campania, Southern Italy), in an area characterised by a distribution of the precipitation prevalently during autumn-winter period. Insufficient recharge due to poor rainfall results in flat spring hydrographs (with no peak during spring season) that indicate a continuously decreasing discharge. Specifically, it has been found that 12 months cumulative rainfall, expressed by SPI₁₂, and spring discharge have similar trend. When SPI₁₂ will be equal or less that − 1, springs reduce the discharge, and a flat spring hydrograph will be produced when SPI reaches value less than − 1.5. In these cases, the prolonged shortage of accumulated rainfall causes a reduction in spring discharge also during the following year as well, pointing out a memory effect of the karst aquifer, and more complex rainfall–discharge relationship is observed.     

Application of Muskingum routing method with variable parameters in ungauged basin

This paper describes a flood routing method applied in an ungauged basin, utilizing the Muskingum model with variable parameters of wave travel time K and weight coefficient of discharge x based on the physical characteristics of the river reach and flood, including the reach slope, length, width, and flood discharge. Three formulas for estimating parameters of wide rectangular, triangular, and parabolic cross sections are proposed. The influence of the flood on channel flow routing parameters is taken into account. The HEC-HMS hydrological model and the geospatial hydrologic analysis module HEC-GeoHMS were used to extract channel or watershed characteristics and to divide sub-basins. In addition, the initial and constant-rate method, user synthetic unit hydrograph method, and exponential recession method were used to estimate runoff volumes, the direct runoff hydrograph, and the baseflow hydrograph, respectively. The Muskingum model with variable parameters was then applied in the Louzigou Basin in Henan Province of China,and of the results, the percentages of flood events with a relative error of peak discharge less than 20% and runoff volume less than 10% are both 100%. They also show that the percentages of flood events with coefficients of determination greater than 0.8 are 83.33%, 91.67%, and 87.5%,respectively, for rectangular, triangular, and parabolic cross sections in 24 flood events. Therefore,this method is applicable to ungauged basins.     

Runoff and Sediment Yield Modelling for a Treated Hilly Watershed in Eastern Himalaya Using the Water Erosion Prediction Project Model

The Water Erosion Prediction Project (WEPP) watershed model was calibrated and validated for a hilly watershed treated with graded bunding and water-harvesting tank in high rainfall condition of eastern Himalayan range in India. The performance of the model for the treated watershed was unacceptable with percent deviation of −45.81 and −38.35 respectively for runoff and sediment yield simulations when calibrated parameter values for the nearby untreated watershed were used. This was possibly due to differences in soil properties and average land slope. When soil parameters were calibrated for the treated watershed, the model performance improved remarkably. During calibration, the model simulated surface runoff and sediment yield with percent deviations equal to +6.24 and +9.02, and Nash–Sutcliffe simulation coefficients equal to 0.85 and 0.81, respectively. During validation period, the model simulated runoff and sediment yield with percent deviations equal to +8.56 and +9.36, and Nash–Sutcliffe simulation coefficients equal to 0.81 and 0.80, respectively. The model tended to slightly under-predict runoff and sediment yield of higher magnitudes. The model performance was quite sensitive to soil parameters namely, rill erodibility, interrill erodibility, hydraulic conductivity, critical shear stress and Manning’s roughness coefficient with varying levels. The WEPP model picked up the hydrology associated with bund and water-harvesting tank, and simulated runoff and sediment yield well with overall deviations within ±10% and Nash–Sutcliffe simulation coefficients >0.80. Simulation results indicate that in high slope and high rainfall conditions of eastern Himalayan region of India where vegetative measures are not adequate to restrict soil loss within the permissible limit, the WEPP model can be applied to formulate structure-based management strategies to control soil loss and to develop water resources.     

Initial Soil Water Content as Input to Field-Scale Infiltration and Surface Runoff Models

Evidence is given of the role of initial soil moisture content, θ _i , in determining the surface runoff hydrograph at field scale, that is a crucial element when distributed models for the estimate of basin response to rainfall have to be formulated. This analysis relies upon simulations performed by a model that, because of the necessity of representing the infiltration of surface water running downslope into pervious saturated or unsaturated areas, uses a coupled solution of a semi-analytical/conceptual approach for local infiltration and a nonlinear kinematic wave equation for overland flow. The model was applied to actual spatial distributions of θ _i , earlier observed over different fields, as well as to a uniform value of θ _i assumed equal to the average value or to the value observed in a site characterized by temporal stability. Our results indicate that the surface runoff hydrograph at a slope outlet is characterized by a low sensitivity to the horizontal heterogeneity of θ _i , at least in the cases of practical hydrological interest. In fact, in these cases the correct hydrograph can be simulated with considerable accuracy replacing the actual distribution of θ _i by the corresponding average value. Moreover, the surface hydrograph is sufficiently well reproduced even though a single value of θ _i , observed at a site anyhow selected in the field of interest, is used. In particular, this extreme simplification leads to errors in magnitude on peak runoff and total volume of surface water with values typically within 10% and 15%, respectively.     

Derivation of Probabilistic Thresholds of Spatially Distributed Rainfall for Flood Forecasting

“Rainfall threshold” is considered as one of the evolving flood forecasting approaches. When the cumulative rainfall depth for a given initial soil moisture condition intersects the corresponding moisture curve, the peak discharge is expected to be equal or greater than the threshold discharge for flooding at the target site. Besides the total rainfall depth, spatial and temporal distribution of rainfall can influence the peak discharge and the time to peak. In the few past studies on the extraction of rainfall threshold curves for flood forecasting, the rainfall assumed to be uniform in space whereas the temporal distribution was subjected to certain assumptions. In the present study, the spatial distribution of rainfall was simulated with the Monte Carlo (MC) method and the mean Huff pattern for all rainfall durations was imposed for the temporal distribution. For each of the MC run, the random weight assigned to every sub-watershed follows the pdf of weights in historical rainfall events. The HEC–HMS model with two different infiltration methods namely SCS–CN and Green–Ampt and Muskingum river routing were adopted as the hydrologic model. After the calibration and validation of the model for Madarsoo watershed in Golestan province in Northeastern Iran, the MC simulations were performed for 1, 2, 6 and 12 h durations. The outputs from the SCS–CN method exhibit only a slight increase in threshold values with respect to duration and was not in the range of our expectations from watershed response, i.e. the rainfalls with greater durations should be greater in depth to produce a specific peak discharge. For the Green–Ampt infiltration method, the rainfall thresholds with 50% probability associated with the critical discharge under dry soil moisture condition were 44.5, 49.0, 64.2 and 94.6 mm for 1, 2, 6 and 12 h durations, respectively. Results for July 2001 flooding revealed that the cumulative rainfall intersected all 10%, 50% and 90% rainfall threshold curves but for July 2005 flooding the 10% curve was only intersected by the cumulative rainfall curve. The advantage of MC-derived rainfall threshold curves in real-time operations is that decision-makers have the flexibility to adopt a curve more consistent with flood observations in the region.     

Influence of Rainfall,Model Parameters and Routing Methods on Stormwater Modelling

Quantification of the uncertainty associated with stormwater models should be analyzed before using modelling results to make decisions on urban stormwater control and management programs. In this study, the InfoWorks Integrated Catchment Modelling (ICM) rainfall-runoff model was used to simulate hydrographs at the outfall of a catchment (drainage area 8.3 ha, with 95% pervious areas) in Shenzhen, China. The model was calibrated and validated for two rainfall events with Nash-Sutcliffe efficiency >0.81. The influence of rainfall, model parameters and routing methods on outflow hydrograph of the catchment was systematically studied. The influence of rainfall was analyzed using generated rainfall distributions with random errors and systematic errors (± 30% offsets). Random errors had less influence than systematic errors on peak flow and runoff volume, especially for two rainfall events with larger depths and longer durations. The Monte Carlo simulations using 500 parameter sets were used to verify the equifinality of the nine model parameters and determine the prediction uncertainty. Most of the monitored flows were within the uncertainty range. The influence of two routing methods from rainfall excess to hydrograph was studied. The InfoWorks ICM model incorporating double quasilinear reservoir routing was found to have a larger effect on the simulated hydrographs for rainfall events having larger depths and longer durations than using the U.S. EPA’s Storm Water Management Model nonlinear reservoir routing method did.