A new approach for sensitivity analysis of the StormWater Management Model applied in an airport

In recent years, flood safety has become a prominent problem in urban development. The frequent occurrence of sudden torrential rain leads to more and more frequent flood disasters at airports, resulting in greater and greater losses. In the airport, the area of impervious ground, such as buildings, cement concrete, and asphalt concrete floors, accounts for a large proportion. This leads to an increase in the coefficient of rainwater runoff. In the face of sudden heavy rainfall, the drainage capacity of the airport is insufficient, even resulting in water accumulation in the apron, taxiway, and other areas. This seriously affect the take-off, landing, skidding, and docking of aircraft, resulting in large-scale flight delays and other losses (Peng et al. 2020). Many airports in China and other countries are affected by heavy rainfall and water accumulation, which seriously affects the safety and normal operation of aircraft. The Beijing Daxing International Airport of China was affected by heavy rain on July 31, 2023. The apron of the airport was heavily flooded and the depth of the water had submerged half of the car's tire. A large number of inbound flights were diverted and a large area of outbound flights were delayed or canceled. Zhengzhou was affected by a once-in-a-millennium rainstorm disaster on July 20, 2021, and the cumulative rainfall at the Zhengzhou Xinzheng International Airport reached 217.8 mm in 24 h, exceeding the recorded extreme. A total of 422 inbound and outbound flights were canceled and 234 were delayed, including 64 flights delayed for more than 4 h. New Delhi in India was affected by a heavy rain on September 11, 2021, the part of runway and apron and the outside road of the New Delhi International Airport were seriously flooded. As a result, three flights were canceled and five flights scheduled for New Delhi were forced to land at airports in surrounding cities.

Urban flood numerical simulation technology is the core component of flood warning and forecast, and an accurate and efficient forecast result is especially important for urban flood control and disaster reduction (Zhang et al. 2023). In response to the flood problem, scholars in China and other countries have conducted a lot of research and developed a variety of flood models, such as one-dimensional river/pipe network models, two-dimensional surface models, and coupling models (Sidek et al. 2021; Son et al. 2023). The development of new models that combine artificial intelligence (AI) models with flood processes has also become a new research direction (Yan et al. 2023). Urban flood models generally include storm runoff generation module, surface confluence module, and pipeline confluence module. According to the different modes of rainfall–runoff generation and confluence, it can be divided into hydrologic urban flood model and full hydrologic urban flood model. The StormWater Management Model (SWMM) is a dynamic model that can simulate urban stormwater runoff (Ma et al. 2022). After multiple updates, the SWMM has become more robust, with a more user-friendly interface. The SWMM is capable of simulating and analyzing the rainfall–runoff, infiltration, and drainage systems in the study area. Additionally, compared to other models, the SWMM offers advantages such as easier parameter acquisition, simpler usage methods, superior simulation performance, and being a non-commercial model, which contribute to its widespread practical application. Therefore, this paper will utilize the SWMM for the related research (Li et al. 2022; Tansar et al. 2023).

Scholars in China and other countries have carried out a lot of research on the sensitivity analysis of parameters. To accurately identify sensitive parameters, both the modified Morris method and mutual information (MI) method were used to conduct sensitivity analysis from local and global perspectives (Liao et al. 2022). A quantitative analysis using the modified Morris screening method and MI method was conducted to assess the sensitivity of model parameters to the peak flow at the drainage outlet and the average runoff coefficient of the basin under design rainstorms with return periods of 1 year, 10 years, and 50 years (Xiang et al. 2020). The impact of the Generalized Likelihood Uncertainty Estimation (GLUE) on the uncertainty analysis of a two-dimensional hydrodynamic model was evaluated in the Daqing River Basin downstream of the Dawen River. They also utilized the MI method to analyze the sensitivity of model parameters and boundary conditions to the prediction results (Sun et al. 2020). An integrated approach was proposed that combines the Morris screening method with the GLUE method, utilizing a Genetic Algorithm for parameter optimization. The results demonstrate the superior applicability of this integrated method across different rainfall intensities and rain-type events (Zhong et al. 2022). Du et al. investigated the feasibility of utilizing the dynamic system response curve (DSRC) method for parameter optimization, offering a solution to the nonlinear challenges encountered by current widely used optimization methods (Du et al. 2023). A reliable framework for setting up and calibrating the SWMM by integrating multiple automated tools was proposed to address some issues (Zhuang et al. 2023).

During the sensitivity analysis of parameters in airport flood models, several issues often arise, such as a large number of sampling parameters, extensive computational requirements, and nonlinear correlations between input parameters and output variables. In order to explore these problems, this paper proposed a new correlation analysis approach combining MI method and heat maps. The Latin hypercube sampling of model parameters applied MATLAB software and the inp files was filed by Python programming, then the multi-group sampling results were obtained. The type, strength, and order of sensitive parameters to the four outputs (Average Depth, Hour of Maximum Flooding, Total Inflow, and Time to Peak) are analyzed using proposed approach in this paper. The study can improve the accuracy of the airport flood simulation model and provide theoretical guidance for the application of SWMM software in airport flood simulation and parameter calibration.

The design of airport's drainage system must take into account numerous factors such as airport safety, operational efficiency, and environmental impact. It is essential to prevent the accumulation of water within internal areas of the airport, including roads, runways, and aprons. Furthermore, measures must be implemented to ensure that the surrounding areas, such as roads and rivers, remain unaffected. In order to study the influence of rainfall beyond design standard on airport safety and operation, we selected the case of a 50-year rainfall recurrence period to study in this paper.

In the process of parameter sensitivity analysis of the SWMM, there is often a nonlinear correlation between input parameters and output variables. The linear sensitivity analysis method cannot accurately obtain nonlinear results, but a more satisfactory result can be obtained by using the nonlinear sensitivity analysis method. This study proposed a new correlation analysis approach – a method of analysis combining the MI method and heat maps.

The MI method is a nonlinear sensitivity analysis method, which can be used to analyze whether the input parameters have a nonlinear correlation with the output results and the strength of the nonlinear. The correlation between two random variables is a measure of the interdependence between the variables. Correlation indicates the amount of shared information between two or more variables and is an indicator of the degree of interdependence between random variables in information theory.

If the variables X and Y are independent of each other, then ⁠, and the correlation has symmetry, namely ⁠. When the variables X and Y are completely correlated, then = 0.5[H(x) + H(y)].

The MI method is based on the concept of information theory. Between two random variables X and Y, the mutual information I (X; Y) represents the reduction of the uncertainty measure for x by observing Y. The greater the MI value, the stronger the correlation between Xand Y, both linear independence and nonlinear independence. The value of the MI I does not indicate linear independence or nonlinear independence. The value of I gives the degree of difference between two probability distributions and does not directly reflect the type of relationship between variables. Other statistical methods or indicators, such as heat maps, scatter plots, and regression analyses, are often used to determine linear independence or nonlinear independence between variables. A new method of analysis combining the MI method and heat maps is proposed in this paper. On the basis of MI method analysis, heat maps are used to analyze the linear independence or nonlinear independence between variables and the strength of correlations.

Due to the common use of the R value as a correlation coefficient, it is more intuitive compared to the I value. When the R value is close to 1, it indicates a strong correlation between two variables; when the R value is close to 0, it indicates no correlation between the variables. The intuitive nature of the R value makes it easier for people to understand the degree of correlation between variables. Therefore, this study focuses on exploring the correlation of variables using the R value.

Latin hypercube sampling is a classic parameter sampling technique used for experimental design or parameter sensitivity analysis. It generates sample points in multi-dimensional space, enhancing sampling efficiency by making full use of the parameter space. The main idea of Latin hypercube sampling is to uniformly divide the possible value range of each parameter into multiple intervals and ensure that only one sample point appears in each interval (Li et al. 2023). This means that the sample points are uniformly distributed on each parameter dimension, allowing for a more even distribution of sample points throughout the entire parameter space. First, determine the possible range of parameter values. Then, divide the value range of each parameter uniformly into an equal number of intervals. Finally, select one sample point from each interval of each parameter, ensuring that each sample point is unique on each parameter dimension. This method reduces the variance of sample points, avoids duplicate points, maintains the independence and randomness of samples, and greatly improves sampling efficiency.

The parameters of the SWMM can be divided into four main types: sub catchment parameters, pipe segment parameters, infiltration parameters, and water quality parameters. These parameters can be divided into two types according to different ways of obtaining them. The first way is through the actual survey, construction drawings, land types, and other design data, such as sub-catchment parameters including area, slope, percentage of impervious area, and pipe segment parameters including pipe type, slope, length, and so on. The second way is to set the parameters empirically, such as impermeability roughness factor, permeability roughness coefficient, impermeable depression water storage, and pipe section roughness factor. In the model manual, these parameters are given a range of values, which will vary according to the land type, climate characteristics, vegetation types, soil types, and so on. There are 14 hydrological and hydraulic parameters in the SWMM, including catchment, slope, and impervious percentage, which can be obtained by the first way, and the parameter setting has greater certainty. Therefore, this paper focuses on the selection of the second way to obtain the parameters. Table 1 shows the selected parameters and ranges of values, which are determined according to the SWMM application manual, related research, and regional actual conditions (Li et al. 2014; Li & Yang 2020).

In this paper, the key research parameters of the SWMM are first determined, and the statistical sampling of sample data is carried out by Latin hypercube sampling, and the data extraction and processing are carried out by MATLAB software and Python programming. Finally, a new correlation analysis approach combining MI method and heat maps is applied to the sensitivity analysis of parameters. The sensitivity and ranking of parameters for the four outputs (Average Depth, Hour of Maximum Flooding, Total Inflow, and Time to Peak) are studied, and the detailed findings are shown in Table 2. From Table 2, we can see the value of correlation coefficient R for each parameter clearly. The value of R is between 0 and 1. The closer the value is to 1, the stronger the correlation is. The parameter sensitivity of each output is sorted from high to low. The closer the value of R is to 1, the stronger the correlation between the variables. Similarly, the closer the value of R is to 0, the weaker the correlation between the variables. The parameter sensitivity of each output is sorted from high to low.

Heat map is a valuable tool for intuitively displaying large amounts of data and information on a two-dimensional plane. This paper utilizes a 10 × 10 grid heat map for data analysis. The x-axis divides the subject values into 10 gradients and the y-axis does the same for corresponding parameter values. In heat maps, frequency percentages are used to explore the relevance of the subject to the corresponding parameter, and color changes represent the proportion of a particular value in the entire data set. Blue indicates a low frequency percentage, and red indicates a high frequency percentage. According to the color and shape distribution of the heat map, the correlation between x and y can be intuitively seen.

The SWMM has been widely applied for urban rainfall–runoff simulations. Sensitivity analysis of urban flood model parameters is important for efficient and accurate flood simulation. Due to the influence of special land types, functional zoning and use requirements of airports, there are many problems in parameter sensitivity analysis of the airport flood model, such as large sampling parameters, large amount of calculation, and nonlinear correlation between input and output variables. This study proposed a new correlation analysis approach combining the MI method and heat maps. The Latin hypercube sampling of model parameters was applied using MATLAB software and the inp files were filed by Python programming, then the multi-group sampling results were obtained and the sensitivity analysis was carried out using proposed approach. The type, strength, and order of parameter sensitivity to the four outputs (Average Depth, Hour of Maximum Flooding, Total Inflow and Time to Peak) are analyzed in this paper. The detailed results are as follows.

1. For Average Depth, the R value of Manning-N is the largest, reached 0.715, and its distribution shown in Figure 4 is forming a straight line. Manning-N has a strong linear correlation with the Average Depth, and special attention should be paid to the parameter setting of the airport flood model. The second sensitive parameter is Conductivity. The distribution of Conductivity in Figure 4 is divergent, and it has a medium nonlinear correlation with the Average Depth.

2. For Hour of Maximum Flooding, the R value of Manning-N is the largest, reached 0.676, and its distribution shown in Figure 5 is forming a straight line. Manning-N has a strong linear correlation with the Hour of Maximum Flooding. The second and third more sensitive parameters are Conductivity and N-perv, and their distribution in Figure 5 is divergent, and there are certain nonlinear correlations with the Hour of Maximum Flooding. The other parameters have smaller R values, ranging from 0.183 to 0.242, the sensitivity is not obvious.

3. For Total Inflow, the R values of each parameter are between 0.021 and 0.534. There are no most sensitive parameters, the more sensitive parameters are Conductivity, N-perv, and Initial Deficit, and the R values are 0.534, 0.418, and 0.399, respectively. The arrangement of Conductivity almost forms a straight line in Figure 6, and it has a medium linear correlation with Total Inflow. The distribution of N-perv and Initial Deficit is divergent, and they have a medium nonlinear correlation with Total Inflow.

4. For Time to Peak, the R value of Manning-N is the largest, reached 0.721, and it is the most sensitive parameter. The distribution of Manning-N in Figure 7 is forming a straight line, and it has a strong linear correlation with the Average Depth. The second and third more sensitive parameters are N-perv and N-Imperv. The other parameters have smaller R values, ranging from 0.180 to 0.205. The distribution of N-perv and N-Imperv in Figure 7 is divergent, and there are certain nonlinear correlations.

This study quantitatively analyzed the influence of multiple input parameters on the output results in the airport flood model and the correlation between them under the influence of special land types, functional zoning, and usage requirements in the airport airfield area. The sensitive parameters and their ranking are effectively identified, which can greatly improve the accuracy of the airport flood simulation model. Since this paper only analyzes a rainstorm in 50 years, the application of other sensitivity analysis methods under different rainfall return periods should be studied in the future.

The authors wish to thank the anonymous reviewers for their comments and suggestions and people who have supported this study.

This research was funded by the Enterprise Science and Technology Commissioner Project of Tianjin Technology Innovation Fund [grant number: 22YDTPJC00430] and Research Centre for Environment and Sustainable Development of Civil Aviation Administration of China Open Fund [grant number: 2022YB03].

J.P. conceptualized the study; prepared the methodology; did software analysis; supervised the study; wrote, reviewed, and edited the article. H.Z. did data curation; prepared and wrote the original draft; visualized the study; investigated the study; did software analysis. Z.L. validated the study; wrote, reviewed, and edited the article. J.O. guided the study. L.Y. collected resources and did software analysis.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.