Parameter Uncertainty Analysis of SWMM Based on the Method of GLUE

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1 2016 7th International Conference on Biology, Environment and Chemistry Volume 98 of IPCBEE (2016) DOI: /IPCBEE V Parameter Uncertainty Analysis of SWMM Based on the Method of GLUE Meishui Li 1, Xiaohua Yang 1, Boyang Sun 1, Lei Chen 1 and Zhenyao Shen 1 1 State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing , China Abstract. Uncertainty analysis of hydrological models has attracted more and more attention for researchers nowadays. In this study, the Generalized Likelihood Uncertainty Estimation (GLUE) was applied to quantify the parameters uncertainty of Storm Water Management Model (SWMM) based on a case in Beijing, China. The results showed that the two parameters of the ratio of impervious surface (PctImperv) and the roughness of conduits (Manning) were the most identifiable parameters which have a great effect on the performance of SWMM modeling. The optimal ranges can be obtained by the method of calibration for the two parameters. The study demonstrated that the model established was rather reliable to simulate the process of the rainfall runoff in this area and the method of GLUE is a powerful tool to analyze the parameter uncertainty for SWMM. Keywords: SWMM, parameters, GLUE, uncertainty analysis 1. Introduction Storm water management model (SWMM) has been one of the most popular tools for simulating the hydrological process of rainfall-runoff in urban area [1], [2]. The model is composed of many mathematical equations which can conceptualize this process in each catchment. The calibration is essential for estimating the best values of parameters. However, the various sets of the best parameters may make the equally good performance of the model which is a phenomenon known as equifinality [3]. Consequently, the uncertainty of parameters should be taken seriously in urban hydrological modeling [4]. In this paper, a rainfall runoff simulation model was established with SWMM based on a case in Beijing, China and the method of GLUE was be used to analyze the parameter uncertainty of SWMM. 2. Methods 2.1. GLUE The Generalized Likelihood Uncertainty Estimation (GLUE) is proposed by [5], which is the most widely used methods of uncertainty analysis. The GLUE method consists of several steps: Step 1: definition of the likelihood function. In this study, the Nash-Sutcliffe efficiency (NSE) is chosen as the generalized likelihood function: n ( ) 2 Q Qsim 1 1 obs NSE i n (1) ( Q Q ) 2 i 1 obs obs Where Q obs and Q sim are the measured and simulated flow series, respectively, and n is the total number of data records. The optimal value of NES is 1.0. Corresponding author. Tel.: ; fax: address: xiaohuayang@bnu.edu.cn. 74

2 Step 2: establishment of the feasible space and prior distribution of parameter. Randomly sampling is conducted in the parameter space using the method of Monte Carlo Sampling (MCS) or Latin Hypercube Sampling (LHS) with uniform distribution. Step 3: uncertainty analysis of model parameters. The values of likelihood function for all the parameter sets are calibrated which are compared with the selected threshold value. If the likelihood value is lower than the threshold value, the former is set to zero. The parameter sets with the likelihood value higher than threshold value are called the effective likelihood values and used to analyze the uncertainty. Step 4: uncertainty analysis of model prediction. The effective likelihood values are sorted from small to large. The uncertainty of model prediction could be estimated with a certain significance level. In this study, the 95% confidence interval (95CI) is calculated for flow from outfall through the likelihood function SWMM SWMM [6] is a distributed hydrological-hydraulic model which can simulate the rainfall-runoff process dynamically in urban area. The hydrological process includes precipitation (R), evaporation (E), infiltration (I) and depression (S), which can be simplified into the formula: R=P-E-I-S. In SWMM, each subcatchment is considered as a nonlinear reservoir (Fig. 1, (2-4)). The infiltration can be simulated by Horton method, Green-Ampt method or Curve number method and flow routing in conduits can be modeled by steady flow, kinematic wave or dynamic wave. In this study, the infiltration was modeled by Horton method. The main parameters and ranges are given in Table I. Table I: The main parameters for uncertainty analysis in the SWMM [6], [7]. Parameters Parameters description Unit Range PctImperv Ratio of impervious area % Width Width coefficient of the subcatchment Slope Average percent slope of the subcatchment % N-Imperv Manning coefficient in impervious area N-Perv Manning coefficient in pervious area S-Imperv Depression storage depth in impervious area mm S-Perv Depression storage depth in pervious area mm Manning Manning's roughness coefficient of the conduit PctZero Percent of the impervious area with no depression storage % MaxRate Maximum infiltration rate mm/h Horton method MinRate Minimum infiltration rate mm/h 0-20 Decay Infiltration rate decay constant DryTime Days for a fully saturated soil to dry completely day 2-14 Evaporation Precipitation d Q d p Infiltration Fig. 1: The conceptual structure of the nonlinear reservoir. ds I( t) Q( t) dt (2) Q W ( d d ) 5/3 p S 0 n (3) W k A (4) Where I(t) is the inflows, Q(t) is the outflows, S is the storage volume, Q is the surface runoff, W is the 75

3 subcatchment width, d p is the depression storage, d is the water depth, S 0 is the subcatchment slope, n is the roughness coefficient of surface, A is the area of subcatchment, and k is the coefficient of the subcatchment width. 3. Case Study The case study was conducted at the campus of Beijing Normal University, a typical urban region in Beijing, China. Fig. 2 below depicts the location of the case study and the delineation of its subcatchments. The city of Beijing is a metropolis with a population exceeding 20 million. It has a warm and semi-humid continental monsoon climate with hot, rainy summers and dry, cold winters. Annual mean precipitation is mm, with most of the precipitation (about 72%) occurring in July and August with <2% occurring during the winter [8]. The college is located in the center district of Beijing, Haidian District. The total area of the campus is about ha with an imperiousness ratio of 64.7%. The main land use type is commercial and public facilities, which mainly includes buildings, pavements, grasses and roads. The area of the study occupied about 72.53% of the campus area. The land use types and proportion are enumerated in Table II. Fig. 2: The delineation of subcatchments Table II: Land use categories and proportion in the study area Land use The campus The catchment Area (ha) Percent (%) Area (ha) Percent (%) Pavement Building Grass Road Athletic filed Total The study area was divided into 51 subcatchments with 107 conduits, 108 junctions and 1 outfall (Fig. 2). The specific settings chosen in the model set-up included the dynamic wave theory used to compute flow routing and infiltration for pervious areas calculated by the Horton method. SWMM was to run on a 5 min timestep. The observed rainfall event on 9th August 2014 was selected to quantify uncertainty for the model. The runoff was measured by the equipment of the HACH flow monitoring placed at the outfall (Fig. 2). The LHS method was used to sample in each parameter space, and up to 20,000 parameter sets were established by Python with SWMM running 20,000 times. The parameter sets with likelihood value larger than 0.8 were treated to be behavioral, otherwise they were treated as non-behavioral. 76

4 3.1. Uncertainty Analysis of Model Parameter In this study, the higher threshold was chosen in order to select the behavioral and non-behavioral parameters. Fig. 3 shows the dotty plot of NSE against 13 parameters. It was obvious that the main uncertainty sources of the rainfall runoff modeling of SWMM were the parameters of Width, Slope, N-Imperv, N-Perv, S-Imperv, S-Perv, PctZero, MaxRate, MinRate, Decay and DryTime. Only PctImperv and Manning were the most identifiable parameters which have a great effect on the performance of SWMM modeling. It was indicated that the two parameters were the most sensitive input parameters in this study. This was similar to the conclusions of other researchers [9], [10]. However, the parameter of Width had less impact on the likelihood value of NSE in this study, which was different with other research results [11]. The reason may be that this parameter was affected by other parameters and the effect of this parameter on the NSE was weakened by the common action with other parameters. Higher impervious surface was the most important and notable characteristics in urban area. The high quality data of impervious surface was required in order to simulate the urban environment more accurately. However, due to the diversity of urban land cover and the complexity of local climatology, accurate impervious surfaces mapping is still challenging [10]-[13]. As shown in Fig. 3, the optimal parameter ranges of PctImperv and Manning were within the range [20, 50] and [0.011, 0.020], respectively. The effective simulation results could be obtained by the calibration techniques in these intervals. However, it was difficult to implement the estimation for other parameters due to their multiple peaks against NSE. In each plot, many points of which y value NSE were higher than 0.9 existed (Fig. 3). This is indicated that the large number of parameter sets with high likelihood values was the specific manifestation of equifinality [3]. Fig. 3: The dotty plot of 13 parameters against NSE. Fig. 4: The 95CI of SWMM output and the best simulation against observed flow. 77

5 3.2. Uncertainty Analysis of Model Output The uncertainty of model output along with the best simulation is presented in Fig.4. The 95CI identified the 2.5% and 97.5% of the cumulative distribution of output uncertainty from the behavioral parameter sets. The observed values were almost entirely within the 95CI region. Thus, the model established was rather reliable to simulate the process of the rainfall runoff in this area. As it is shown in Fig. 4, there was a relationship between the rainfall amount and the range of the 95CI region. The width of the 95% region was much larger when the rainfall intensity or the peak of outflow was greater. It indicated that the parameter uncertainty would increase with the intensity of rainfall increasing. The NSE of the best estimation could up to 97% which indicated that this was a very successful model constructed to simulate rainfall runoff process in this area. Thus, the model established could be applied to simulate the hydrologic performance of low impact development (LID) by which urban flooding could be mitigated in this area [14], [15]. 4. Conclusion In the background of uncertainty analysis of hydrological models attracted more and more attention, the method GLUE was applied to quantify the parameters uncertainty of SWMM based on a case in Beijing, China. The results showed that the two parameters of PctImperv and Manning were the most identifiable and sensitive parameters which have a great effect on the performance of SWMM modeling. The optimal ranges can be obtained by the method of calibration for the two parameters. Other 11 parameters were all the non-identifiable and non-sensitive parameters which were the main sources of model prediction uncertainty. However, the study demonstrated that the model established was rather reliable to simulate the process of the rainfall runoff in this area and the method of GLUE is a powerful tool to analyze the parameter uncertainty for SWMM. The further research is needed to explore the uncertainty of the water quality parameters for SWMM. The model established will be used in controlling of water quantity and quality by the low impact development (LID) in the context of the climate change. 5. References [1] H. P. Qin, Z. X. Li, and G. Fu, The effects of low impact development on urban flooding under different rainfall characteristics. J. Environ. Manage. 2013, 129C(18): [2] H. Jia, H. Ma, Z. Sun, S. Yu, Y. Ding, and Y. Liang, A closed urban scenic river system using stormwater treated with LID-BMP technology in a revitalized historical district in China. Ecol. Eng. 2014, 71: [3] K. Beven and J. Freer, Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology. J. Hydrol. 2001, 249(1 4): [4] R. A. Sharifan, A. Roshan, M. Aflatoni, A. Jahedi, and M. Zolghadr, Uncertainty and Sensitivity Analysis of SWMM Model in Computation of Manhole Water Depth and Subcatchment Peak Flood. Procedia - Social and Behavioral Sciences. 2010, 2(6): [5] K. Beven and A. Binley, The future of distributed models: Model calibration and uncertainty prediction. Hydrol. Process. 1992, 6 (3): [6] L.A. Rossman, Storm Water Management Model User's Manual Version 5.1. U.S. Environmental Protection Agency [7] L. A. Rossman and W. C. Huber, Stormwater Management Model Reference Manual Volume I-Hydrology (revised). U.S. Environmental Protection Agency, [8] L. Zhu, Y. Chen, R. Yan, T. Shen, L. Jiang, and Y. Wang, Characteristics of Precipitation and Temperature Changes in Beijing City During Resources Science. 2012, 34 (7): [9] A. Palla and I. Gnecco, Hydrologic modeling of Low Impact Development systems at the urban catchment scale. J. Hydrol. 2015, 528: [10] C. R. Jacobson, Identification and quantification of the hydrological impacts of imperviousness in urban catchments: a review. J. Environ. Manage. 2011, 92 (6): [11] M. F. Chow, Z. Yusop, and S. M. Shirazi, Storm runoff quality and pollutant loading from commercial, residential, 78

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