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 100875, 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:

2( )11

2( )1

nQ Q

simobsiNSE nQ Q

obs obsi

(1)

Where Qobs and Qsim 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.: ++86-010-58801757; fax: +86-010-58801757.

E-mail address: xiaohuayang@bnu.edu.cn.

2016 7th International Conference on Biology, Environment and Chemistry

Volume 98 of IPCBEE (2016)

DOI: 10.7763/IPCBEE. 2016. V98. 11

74

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.

2.2. 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 % 0-100

Width Width coefficient of the subcatchment - 0.2-5

Slope Average percent slope of the subcatchment % 0.3-2

N-Imperv Manning coefficient in impervious area - 0.011-0.15

N-Perv Manning coefficient in pervious area - 0.05-0.8

S-Imperv Depression storage depth in impervious area mm 1.27-2.54

S-Perv Depression storage depth in pervious area mm 2.54-7.62

Manning Manning's roughness coefficient of the conduit - 0.011-0.024

PctZero Percent of the impervious area with no depression storage % 50-80

Horton method

MaxRate Maximum infiltration rate mm/h 50-200

MinRate Minimum infiltration rate mm/h 0-20

Decay Infiltration rate decay constant - 2-7

DryTime Days for a fully saturated soil to dry completely day 2-14

PrecipitationEvaporation

d

dp

Infiltration

Q

Fig. 1: The conceptual structure of the nonlinear reservoir.

( ) ( )dS

I t Q tdt

(2)

05/3( )

SQ W d d p 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

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subcatchment width, dp is the depression storage, d is the water depth, S0 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

588.1 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 57.88 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 19.22 33.21 13.32 31.73

Building 17.94 31.00 12.94 30.82

Grass 11.80 20.38 9.10 21.68

Road 6.16 10.64 4.02 9.58

Athletic filed 2.76 4.78 2.60 6.19

Total 57.88 41.98

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

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.

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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): 577-585..

[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: 448-457.

[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): 11-29.

[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): 7739-7740.

[5] K. Beven and A. Binley, The future of distributed models: Model calibration and uncertainty prediction. Hydrol.

Process. 1992, 6 (3): 279–298.

[6] L.A. Rossman, Storm Water Management Model User's Manual Version 5.1. U.S. Environmental Protection

Agency. 2015.

[7] L. A. Rossman and W. C. Huber, Stormwater Management Model Reference Manual Volume I-Hydrology

(revised). U.S. Environmental Protection Agency, 2016.

[8] L. Zhu, Y. Chen, R. Yan, T. Shen, L. Jiang, and Y. Wang, Characteristics of Precipitation and Temperature

Changes in Beijing City During 1951-2010. Resources Science. 2012, 34 (7):1287-1297.

[9] A. Palla and I. Gnecco, Hydrologic modeling of Low Impact Development systems at the urban catchment scale. J.

Hydrol. 2015, 528: 361-368.

[10] C. R. Jacobson, Identification and quantification of the hydrological impacts of imperviousness in urban

catchments: a review. J. Environ. Manage. 2011, 92 (6): 1438-1448.

[11] M. F. Chow, Z. Yusop, and S. M. Shirazi, Storm runoff quality and pollutant loading from commercial, residential,

78

and industrial catchments in the tropic. Environ. Monit. Assess. 2013, 185(10): 8321-31.

[12] H. Zhang, H. Lin, Y. Li, Y. Zhang, and C. Fang, Mapping urban impervious surface with dual-polarimetric SAR

data: An improved method. Landscape. Urban. Plan. 2016, 151: 55-63.

[13] L. Zhang and Q. Weng, Annual dynamics of impervious surface in the Pearl River Delta, China, from 1988 to

2013, using time series Landsat imagery. Isprs. J. Photogramm. 2016, 113 (3) 86-96.

[14] A. H. Elliott, S. A. Trowsdale, A review of models for low impact urban stormwater drainage. Environ. Model.

Softw. 2007, 22 (3), 394-405.

[15] J. Sin, J. H. Zhu, C. Yoo, Evaluation of flood runoff reduction effect of LID (low impact development) based on

the decrease in CN: case studies from Gimcheon Pyeonghwa District, Korea. Procedia Engineering, 2014, 70(4):

1531-1538.

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