# Parameter Optimization of SWMM Model Using Integrated Morris and GLUE Methods

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data

^{2}. Urban precipitation is mainly discharged through river networks, nullahs, and culverts across the city. The terrain is flat, with an average slope of 0.29% and an altitude range of 67 to 110 m. As shown in Figure 1, the region is predominated by temperate continental monsoon climate with four distinct seasons and an average annual rainfall of 542.1 mm. Precipitation is unevenly distributed throughout the seasons and mainly concentrated in summer, resulting in severe spring droughts and summer floods. The land cover may be classified into four categories: buildings, roads, vegetation, and bare ground, with an impervious ratio of about 62.08%.

#### 2.2. Methods

#### 2.2.1. SWMM Model

#### 2.2.2. Morris Screening Method

_{i}, from the examined parameters, holding the remaining parameter values fixed, and altering the variable x

_{i}at random within the variable’s value range. The model is then run to acquire the outcomes of various x

_{i}corresponding to the goal function y(x) = y(x

_{1},x

_{2},x

_{3},…,x

_{n}). Finally, the influence value, e

_{i}, is employed to calculate the effect of input parameter changes on model output:

_{i}is the output value of the ith run of the model; Y

_{i}

_{+ 1}is the output value of the i + 1th run of the model; Y

_{0}is the initial value of the calculated result after parameter calibration; P

_{i}is the percentage change in the ith model operation relative to the parameter value after calibration; P

_{i}

_{+ 1}is the percentage change in the i + 1th model operation relative to the parameter value after calibration; n is the number of model runs.

#### 2.2.3. GLUE Method

- Step 1—Selecting the likelihood function for the model simulation calculation.
- Step 2—Selecting the initial range of the model parameters and the prior distribution of parameters. The random combination of parameters is then obtained by Latin hypercube sampling.
- Step 3—Simulating the likelihood values of each combination by running the model to obtain the posterior distribution of the parameters.

#### 2.2.4. Coupling Based on Genetic Algorithm

_{1}); (2) a multi-objective calibration that considers both objectives (Y

_{1}and Y

_{2}).

_{1}and Y

_{2}are the two target minima; Q

_{o(i)}is the observed value at the moment i; Q

_{s(i)}is the simulated value at the moment i; Q

_{ps}is the peak value of the flow simulation process; Q

_{po}is the peak value of the flow observation process.

## 3. Results

#### 3.1. Parameter Sensitivity Analysis

#### 3.2. Uncertainty Analysis of Parameter Value Range

#### 3.3. Parameter Calibration

#### 3.4. Validation Result

## 4. Discussion

## 5. Conclusions

- (1)
- The parameter sensitivity analysis results varied with the different objective functions utilized. The sensitive factors are also observed to change with the rainfall intensity. These indicate that it is essential to consider multiple operating conditions in the parameter sensitivity analysis. In addition, the perturbation analysis of multiple modalities shows that the sensitivity of the parameters is highly susceptible to sudden changes among different modalities, and the results of the screening method for a single perturbation modality possess considerable uncertainty.
- (2)
- Although the GLUE method only reduced the range of the values for two parameters in the research, the peak error was reduced by up to 9%. For the optimization of complex model parameters, using sensitivity and uncertainty analysis in combination with each other, satisfactory model simulation results can be achieved.
- (3)
- When the Genetic Algorithm was used to optimize parameter sets with different combinations, the model parameter optimization process varied with the increase in the number of constraints on the fitness function. Compared with constructing the fitness function using a single-objective constraint, the Genetic Algorithm for multi-objective constraints shows a decreasing trend in the overall peak error of the model simulations.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Flow chart of the research methods. The first step of the red dashed box symbolizes the process of identifying the parameters to be optimized, the second step depicts the process of narrowing the range of sensitive parameter values, and the third step represents the process of automatic model parameter optimization utilizing the Genetic Algorithm.

**Figure 3.**Comparing three sample techniques’ parameter sensitivity using the Morris screening method: (

**a**) Average flow parameter sensitivity for rainfall event 0819; (

**b**) Max flow parameter sensitivity for rainfall event 0819; (

**c**) Average flow parameter sensitivity for rainfall event 0515; (

**d**) Max flow parameter sensitivity for rainfall event 0515. The gray dashed line denotes the parameter sensitivity threshold.

**Figure 4.**Likelihood scatters plot of parameters: (

**a**) Relationship of parameter Nc and NSE; (

**b**) Relationship of parameter Ni and NSE; (

**c**) Relationship of parameter Dc and NSE. The x-axis represents the posterior distribution of the parameters.

**Figure 5.**Parameter probability density plots and cumulative distribution plots: (

**a**) Parameter Nc; (

**b**) Parameter Ni; (

**c**) Parameter Dc. The x-axis represents the posterior distribution of the parameters.

**Figure 6.**Model flow simulation results during the calibration period: (

**a**) Genetic Algorithm with a single-objective for rainfall event 0819; (

**b**) Genetic Algorithm with multi-objective for rainfall event 0819; (

**c**) Genetic Algorithm with a single-objective for rainfall event 0515; (

**d**) Genetic Algorithm with multi-objective for rainfall event 0515.

**Figure 7.**Error charts for single-objective versus multi-objective constraint algorithms in model flow simulation. Each name corresponds to two groups of two bar charts; the group of bar charts on the left corresponds to the top peak of rainfall event 0819, and the group of bar charts on the right corresponds to the top peak of rainfall event 0515. The length of the vertical lines on the bar graphs represents the peak relative error of the model simulation.

**Figure 8.**Flow simulation results using two sets of parameter during the validation period: (

**a**) Rainfall event 0801; (

**b**) Rainfall event 0730.

Symbol | Parameter | Description | Domain |
---|---|---|---|

Ni | N-imperv | Manning’s n for impervious areas | (0.011, 0.05) |

Np | N-perv | Manning’s n for pervious areas | (0.01, 0.8) |

Di | Destore-imperv | Depression storage for impervious areas (mm) | (0.2, 10) |

Dp | Destore-perv | Depression storage for pervious areas (mm) | (2, 10) |

Zi | Zero-imperv | Percent of impervious area without depression storage (%) | (5, 85) |

Max_r | Maxrate | Maximum infiltration rate (mm.h^{−1}) | (20, 127) |

Min_r | Minrate | Minimum infiltration rate (mm.h^{−1}) | (0.1, 10) |

Dc | Decay-constant | Infiltration attenuation coefficient (h^{−1}) | (2, 7) |

Nc | N-conduit | Manning’s n for conduits | (0.009, 0.024) |

Event | Data | Total Rainfall (mm) | Duration (h) | Time Step (h) | Max Intensity (mm/h) |
---|---|---|---|---|---|

0819 | 19 August 2018 | 41.5 | 13 | 1 | 11 |

0515 | 15 March 2018 | 64.5 | 12 | 1 | 26.5 |

0801 | 1 August 2018 | 63 | 2 | 1 | 60 |

0730 | 30 July 2017 | 34.5 | 12 | 1 | 7.5 |

**Table 3.**Three sampling methods: SA screening sensitive parameters and a combined relatively sensitive parameter.

Group | 0819 | 0515 |
---|---|---|

Calibration value_sr | Nc, Ni | Nc, Dc, Max_r, Ni |

Median value_sr | Nc, Ni, Di | Nc, Ni, Min_r |

Calibration value_dr | Nc, Ni | Nc, Ni, Dc |

Multiple Morris | Ni, Di, Nc, Zi, Max_r, Min_r | Nc, Dc, Ni, Max_r, Min_r, Dp |

**Table 4.**Mean, standard deviation, coefficient of variation, and correlation matrix of the posterior distributions for the parameters.

Parameter | Mean | σ | Cov | Correlation Coefficient, R | ||
---|---|---|---|---|---|---|

Nc | Ni | Dc | ||||

Nc | 0.014 | 0.003 | 23% | 1 | ||

Ni | 0.027 | 0.011 | 40% | −0.32 | 1 | |

Dc | 4.412 | 1.444 | 33% | −0.03 | 0.01 | 1 |

0819 Parameter | Before Calibration | After Calibration | 0515 Parameter | Before Calibration | After Calibration |
---|---|---|---|---|---|

Ni | 0.013 | 0.0207 | Ni | 0.013 | 0.021 |

Di | 2.54 | 5.1 | Dp | 7 | 5.9 |

Zi | 0 | 47.6 | Max_r | 114.4 | 116.4 |

Max_r | 114.4 | 27.5 | Min_r | 3.8 | 1.3 |

Min_r | 3.8 | 0.7 | Dc | 2 | 4 |

Nc | 0.01 | 0.011 | Nc | 0.01 | 0.012 |

**Table 6.**Peak flow relative error of model simulations during the calibration and validation periods.

Rainfall Event | Method | Peak 1 Error (%) | Peak 2 Error (%) | ||
---|---|---|---|---|---|

Single-Objective | Multi-Objective | Single-Objective | Multi-Objective | ||

0819 | Calibration value_sr | 11.42 | 11.26 | 22.66 | 22.61 |

Median value_sr | 12.17 | 11.71 | 22.76 | 22.72 | |

Calibration value_sr | 11.51 | 11.27 | 22.55 | 22.39 | |

Multiple Morris | 5.22 | 3.09 | 8.77 | 3.71 | |

Combine GLUE | 3.77 | 0.36 | 5.36 | 2.18 | |

0515 | Calibration value_sr | 10.30 | 9.44 | 5.14 | 2.17 |

Median value_sr | 12.83 | 9.81 | 15.72 | 12.83 | |

Calibration value_sr | 13.46 | 11.08 | 13.12 | 6.95 | |

Multiple Morris | 11.60 | 10.31 | 4.90 | 1.76 | |

Combine GLUE | 7.40 | 1.49 | 2.40 | 0.57 | |

0801 | 0819 Parameter | 0.89 | |||

0515 Parameter | 7.77 | ||||

0730 | 0819 Parameter | 3.34 | 6.31 | ||

0515 Parameter | 0.66 | 12.46 |

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**MDPI and ACS Style**

Zhong, B.; Wang, Z.; Yang, H.; Xu, H.; Gao, M.; Liang, Q. Parameter Optimization of SWMM Model Using Integrated Morris and GLUE Methods. *Water* **2023**, *15*, 149.
https://doi.org/10.3390/w15010149

**AMA Style**

Zhong B, Wang Z, Yang H, Xu H, Gao M, Liang Q. Parameter Optimization of SWMM Model Using Integrated Morris and GLUE Methods. *Water*. 2023; 15(1):149.
https://doi.org/10.3390/w15010149

**Chicago/Turabian Style**

Zhong, Baoling, Zongmin Wang, Haibo Yang, Hongshi Xu, Meiyan Gao, and Qiuhua Liang. 2023. "Parameter Optimization of SWMM Model Using Integrated Morris and GLUE Methods" *Water* 15, no. 1: 149.
https://doi.org/10.3390/w15010149