عنوان مقاله [English]
SWMM is one of the common models used in hydrologic and hydraulic simulations of surface runoff flow throughout urban drainage networks. As any comprehensive model, SWMM needs a wide range of parameters as its input data, which usually involve measurement inaccuracies and approximations leading to model output uncertainty. The degree of such uncertainty depends on model sensitivity to each input data. This article aims to study SWMM sensitivity to patterns and sub-models used in the simulations process. Therefore, alongside examining the effect of 5 different synthetic precipitation patterns, 4 time steps of rainfall data, 3 infiltration models and 2 routing methods on runoff peak discharge values; the sensitivity of SWMM to these patterns and sub-models was analyzed. Graphical and Correlation Analysis (CA) methods were used to analyze the model sensitivity. According to the results, the model was most sensitive to rainfall time-step in which a change from 15 min to 90 min, increased peak discharge values as 26.5 and 37.5 percent. In the next level, the model was most sensitive to infiltration methods with spearman coefficients close to 1. However, the model degree of sensitivity to rainfall different distribution patterns was variable, depending on the simulation scenarios predefined.
Urban development in the southern coastal cities of Iran and increasing impermeable increases flood discharge, and consequently the likelihood of life and financial losses along with problems such as disruption to urban traffic, flooding of streets and residential areas, diffusion of pollution through runoff. Therefore, urban flood modeling has recently attracted the attention of researchers to identify the flow capacity of different components in a runoff drainage network. SWMM is one of the most widely used hydrological and hydraulic simulation models in urban surface water disposal network. Like any comprehensive model, SWMM requires a wide range of input data which may result in unreliable outputs, due to the lack of accessible measured data or low accuracy in measurements. The degree of such uncertainty depends on the model sensitivity to the input data. In most studies of SWMM sensitivity analysis, the emphasis has been on hydrological coefficients and parameters. The present study focuses on the methods and sub-models used in the model, rather than focusing on coefficients and factors. This study investigates the model sensitivity to: (a) the selected synthetic distribution for a specific rainfall with a predefined duration, (b) the time steps used for defining the rainfall pattern, (c) the infiltration model, and (d) the selected routing method.
The basin to be studied is Abdul-Salam, one of the urban basins of Kangan city. The city has always been exposed to flood hazards and damages, due to heavy rainfall, steep slope, urban development and consequent increase of impermeability and runoff coefficient. In this study, topographic maps with a scale of 1:500 and field surveys were used to define the characteristics of surface water collection system and the gradient of streets, alleys and canals. Three sub-models including Horton, Green-Ampt and SCS are developed in SWMM to calculate water infiltration into the soil and consequently to analyze runoff flow. Rainfall input data were provided based on the distribution functions developed by the US Soil Conservation Authority. Five SCS 6-hour rainfall types including SCS I, SCS IA, SCS II, SCS IIFL and SCS III were selected. On the other hand, in order to investigate the effect of precipitation time steps on model results, four time steps including 15, 30, 60 and 90 minutes were considered for each of the above five distributions. On the other hand, in order to analyze the hydraulic flow in SWMM model, two kinematic wave and steady-state routing methods were used to solve the Saint-Venant equations and thus predict water level in each node, the flow rate and flow depth in each conduit.
In the present study, in order to analyze the sensitivity of SWMM model, two methods of graphical and correlation analysis have been used. In the graphical method the dependence of the variable y on the parameter x is expressed as a derivative of dy / dx. This partial derivative is then normalized to obtain a dimensionless index and presented as a percentage of changes in the results. The slope of such graphs, known as the ratio of variations (ROV), represents the increasing or decreasing trend of output changes with increasing input variables and also shows the rate of relative changes of the output parameter to relative changes of the input. Spearman rank correlation coefficient (r) was used in the correlation analysis (CA) methods to analyze the sensitivity of SWMM to the selected infiltration sub-model, routing method, rainfall distribution and rainfall pattern time steps.
Results and discussion
According to the 5 rainfall distribution patterns, with 4 design rainfall time step, 3 infiltration equations and 2 flood routing methods, a total of 120 hydrographs were obtained for a 6-hour 46.5 mm rainfall event in the studied basin. Based on the results, the hydrograph peak discharge increased with the extension of time step in each rainfall distribution, regardless of the routing method, selected infiltration models. Also, for all the rainfall distribution patterns and the routing methods studied, the values obtained for the peak flow discharge were reduced with SCS models, Green-Ampt and Horton, respectively. On the other hand, regardless of the time step, infiltration model or routing methods, the highest peak flow values were always obtained for SCSII, SCS IIFL, SCS I, SCS III and SCS IA, respectively. It should be noted that the values of peak flow obtained by kinematic wave routing method are significantly higher than those obtained for steady flow method. However, these values follow the same trend for different rainfall patterns, time steps, and infiltration models.
Regardless of rainfall distribution type and routing method, the length of rainfall time steps is directly related to the flow rate. In other words, by choosing longer time steps, the peak runoff flow rate is increased. But this increasing trend has not been the same in different simulation conditions. Thus, the ROV of flow rates with time steps is different in different rainfall distributions. Meanwhile, the SCS IA and SCS I rainfall distribution include the widest range of variations in both kinematic wave and steady flow routing methods. In other words, the model sensitivity to rainfall time steps is at highest when using the SCS IA rainfall distribution pattern.
While choosing the kinematic wave routing method, the model is less sensitive to the changes of rainfall time steps. So that, under the kinematic wave and steady flow routing method, the minimum-maximum relative changes of peak flow with the relative changes of time step were 4.5-26.5 and 7.6-37.6 percent, respectively. The descending trend of ROV curves shows the decrease in maximum flow rates with time, from SCS to Green-Ampt and then Horton methods. So that in all simulation conditions, peak flow rates obtained from SCS and Horton models were the highest and lowest values, respectively. Also, the effect of rainfall distribution on the model sensitivity to the infiltration sub-models did not follow a significant trend. The highest sensitivity of the model to the infiltration sub-models is observed while applying SCS IA rainfall distribution pattern. Subsequently, the model sensitivity to the infiltration sub-models was reduced by using SCS I, SCS III, SCS II and SCS IIFL distributions, respectively.
According to the variable values obtained for r, it can be concluded that the change of time steps, infiltration sub-models and flow routing methods are effective in model sensitivity to the rainfall distribution pattern applied. Their effect, however do follow a significant trend. In contrast, the effect of rainfall characteristics (including distribution pattern and time steps) on SWMM sensitivity to infiltration sub-models model is significant.