Elaborating simulations of the effects of flood events

Abstract

Calibrating parameters in distributed hydrological models is challenging because of the large number of parameters involved. In this study, a distributed physical hydrological model known as the Liuxihe (LXH) model was taken as a case study. We employed an automated algorithm-Particle Swarm Optimization (PSO) to calibrate the parameters of the LXH model. Following optimization, we assessed the model efficiency by simulating the flood process in the Beijiang Basin in Guangxi, China. The model outputs were compared with the measured values, and the results were satisfactory. The Nash coefficient and flood error were 83.9% and 17.7%, respectively. The simulated hydrological processes aligned well with the actual trends. The results showed that the PSO algorithm could effectively optimize the parameters of the LXH model. After parameter calibration, the simulations of the LXH model met the requirements for basin flood forecasting and disaster reduction. This method could be applied to automate the parameter optimization process for distributed hydrological models, and the results of this study could serve as a reference for model calibration in other watersheds.

Graphical abstract

Keywords

distributed hydrological modeling / Liuxihe model / Beijiang Basin / particle swarm optimization algorithm

1 Introduction

To date, extreme rainfall events occur frequently around the globe, leading to significant natural disasters, such as large basin floods. These floods severely impact both the safety of lives and property and socioeconomic development. Flood forecasting is a critical nonengineering strategy that can be employed to mitigate the risk of flooding. The application of hydrological modeling to predict floods is essential. The parameters of distributed physical hydrological models are numerous, resulting in a significant computational workload. Consequently, parameter calibration is particularly important, as it strongly influences the accuracy of flood forecasting results and can effectively enhance model performance (Bai et al., 2025). Accurate flood warnings provide essential technical support for flood prevention and mitigation efforts at both regional and basin scales.

Since the introduction of the Sherman unit graph method (Sherman, 1932), which was the first basin hydrological model, numerous hydrological models have emerged worldwide, significantly enhancing the methods and approaches used for flood forecasting. Among these approaches, lumped hydrological models and distributed hydrological models are the focal points of current research. Lumped hydrological models adopt a holistic perspective of the study basin, which fails to capture the true spatial distribution characteristics within the basin. In contrast, distributed models subdivide the basin into refined units with distinct physical characteristics, allowing for yield and sink calculations at the unit level. This approach effectively illustrates the movement of floodwater across side slopes and channels, resulting in improved accuracy in flood forecasting.

Distributed modeling is a prominent area of research in hydrology. Notable representative models include the System Hydrological European (SHE) (Abbott et al., 1986), the Watershed Environmental Hydrology model (WEHY) (Kavvas et al., 2004), the distributed model for predicting the water and energy transfer between soil, plants and atmosphere (WETSPA) (Wang et al., 1996), the distributed hydrology soil vegetation model (DHSVM) (Wigmosta et al., 1994), the high-resolution rainfall Model (VFLO) (Vieux et al., 2004), the easy distributed hydrological Model (EASYDHM) (Lei et al., 2010), the distributed model based on watershed topography TOPMODEL (Beven, 1995), and the Liuxihe model (LXH) (Chen et al., 2010) models. The parameters of distributed models are important physical properties. In contrast, only a limited amount of measured data are needed to optimize the model parameters. This characteristic presents promising potential for application in areas where hydrological information is scarce.

Parameter determination for hydrological models has always been a crucial aspect of hydrological forecasting. The primary automatic parameter optimization methods for hydrological models include the SCE–UA algorithm (Duan et al., 1994), simulated annealing (Kirkpatrick et al., 1983), the AMALGAM approach (Vrugt and Robinson, 2007), the generic algorithm (Goldberg, 1989), the ant colony system (Goldberg, 1989), adaptive random search (Masri et al., 1980), and particle swarm optimization (Eberhart and Shi, 2001). Unlike lumped models, distributed models require parameter calibration for effective flood forecasting. However, because of their more complex physical structures, distributed models introduce significant uncertainty in parameter calibration (Wang et al., 2024). The calibration results strongly influence the model’s flood forecasting performance and can directly affect the accuracy of hydrological forecasts.

The LXH model is a distributed framework that infers model parameters in a physical context, and, to date, a manual trial-and-error method is used to optimize the parameters. Although this approach has yielded satisfactory results in previous studies, it requires the user to continuously select appropriate model parameters through a repetitive trial-and-error process. Consequently, the parameter optimization process is cumbersome and time-consuming. To explore effective methods for optimizing these parameters, the LXH model was developed in this study on the basis of the Beijiang Basin in Guangxi, China. Flood simulations for the basin were conducted using the LXH model, with the model parameters being calibrated using automated algorithms. The model outputs were compared with the measured hydrological data, which yielded favorable outcomes. The main objective was to quantitatively assess the necessity and effectiveness of automatic parameter optimization for distributed hydrological models. Previous research has shown that the lumped hydrological model needs only generalized parameters to calculate the runoff flow to the outlet of the basin according to the water balance principle (Chen et al., 2007). In contrast, distributed hydrological models are usually complex in structure and have many parameters; thus, calibrating a model with generalized parameters is difficult. Moreover, the greatest shortcoming of generalized parameters is that the obtained parameters lack clear physical definition (Bai, 2025). Parameter optimization for the distributed Liuxihe model has proved to be necessary and efficient. This study is aimed at providing a theoretical basis and technical support for flood forecasting, decision-making, flood prevention and mitigation in the Beijiang Basin. Additionally, the results of this study are expected to facilitate the further development of parameter calibration methods for distributed models.

2 Study area and modeling data

2.1 Study area

Beijiang is in Rongshui Miao Autonomous County, Guangxi, China, and is a component of the Liujiang River system. The Beijiang River has the longest primary stream and the largest number of tributaries of any river in the county. The primary stream is 146 km in length, with a catchment area of 1762 km². The annual runoff is 6.52 billion m³, which represents 22.9% of the total flow in the Liuzhou area. The water production is 128.8 m³ per square kilometer, with 80% of the flow being concentrated between April and September, a period during which outburst flooding frequently occurs. After March of each year, the Beijiang Basin experiences a range of weather systems, including frontal systems, which lead to widespread heavy rainfall. Furthermore, heavy rainfall is intensified by uplift and disruption of the basin’s topography.

The Beijiang Basin is encircled by mountains on all sides, with the elevation of the surrounding peaks ranging from 10002000 m. The primary topography of the basin is characterized by high, steep mountains and narrow, deep valleys, and the topography is highly complex. As a result, the riverbanks are steep, and storm floodwaters rise and fall rapidly. The basin originates from Jiuwan Mountain and has a primary stream length of 146 km. Numerous tributaries are present in the basin that ultimately merge with the Rongjiang River 7.5 km north of the county town. The Beijiang Basin covers an area of 1662 km², and the rivers in the basin have a long-term average flow rate of 83.3 m³/s. The long-term average water level is 115.10 m, the maximum recorded flow is 5790 m³/s, and the highest water level is 127 m. Conversely, the minimum flow is 7.6 m³/s, and the lowest water level is 114.38 m. The difference in water level is 162 m. The basin has a potential hydroelectric resource capacity of 126000 kW, whereas the estimated hydro-power capacity that can be developed is 116500 kW.

There are five rainfall stations in the basin: Shajie, Jiyang, Zhongzhai, Yangdong, and Goutan. The Goutan station functions as a river station (Fig. 1). The rainfall and water level data from each station are automatically measured and reported. The vegetation in the watershed consists of extensive broadleaf evergreen and coniferous forests, whereas the surface vegetation is dominated by scrub forests, cultivated fields, and herbaceous plants.

2.2 Modeling data

Measured data, including hourly rainfall and flow data, were collected for 23 major flood events in the Beijiang Basin between 1965 and 1984. The rainfall data were interpolated to grid cells using the inverse distance weighting method. By calculating a weighted average of the known data points, the values of the unknown points could be estimated to determine the rainfall intensity for each cell. The foundational surface base data included the soil type, land use and DEM. All these data were freely available for download from open databases. DEM data were downloaded free of charge from the public data source of the US Space Shuttle Radar Topographic Mapping Program (available at SRTM website) for the year 2020. The soil type data were initially downloaded free of charge from ISRIC website for the year 2016, with a resolution of 1 km, and subsequently resampled to 30 m. The land use data were downloaded at no cost from Resource and Environmental Science Data Platform website for the year 2020. The spatial resolution of both the land use and DEM data sets was 30 m.

As shown in Table 1, there are ten soil types in the Beijiang Basin. Among these types, low-activity luvisols and eutric gleysols account for more than 50% of all the soil, whereas cumulative soil, humic acrylic, and iron acid soil collectively account for more than 40% of the total. These five soil types are the primary components of the soil in the Beijiang Basin, with minor quantities of other soil types being present as well.

As shown in Table 2, there are 15 land use types, with evergreen broadleaved forestland and evergreen needle-leaved forestland accounting for more than 80% of the total, making them the dominant vegetation types in the basin. Additionally, there are small proportions of shrubland and cropland. As illustrated in Fig. 2, the Beijiang Basin features the highest elevation at 2092 m and the lowest elevation at 134 m. The basin is characterized by high mountains, deep valleys, and complex topography and tectonics.

3 Model setup and methodology

3.1 Model setup

The LXH model was initially proposed in response to a study of the Liuxihe watershed (Chen et al., 2010). The model was based on the DEM and used to construct multiple grids, with each grid representing a unit watershed. Furthermore, each grid was subdivided into side slope, reservoir, and channel units. Different model parameters were applied to each unit for evapotranspiration, runoff generation and runoff confluence calculations. The model was optimized by generating distinct parameters for each cell type on the basis of a limited set of watershed subsurface data (topography, vegetation cover, and soil type) and meteorological conditions. The LXH model segments a watershed into smaller units, facilitating increasingly accurate simulation and forecasting of watershed runoff. Moreover, the model requires only a minimal amount of hydrological data to establish physically valuable model parameters, making it particularly suitable for watersheds with limited data availability. However, the model necessitates high-resolution data, which are increasingly accessible because of advancements in remote sensing technology. Parameter calibration is crucial for model effectiveness, and an extensive volume of parameter data demands more efficient computational methods. With the ongoing progress in computer technology, these challenges are expected to be addressed. The simulation process of the LXH model is illustrated in Fig. 3. The model comprises 15 primary types of parameters, among which the slope data and flow direction data are directly derived from the DEM and considered nontunable parameters (Fig. 4).

The remaining parameters were adjustable and depended on the meteorological, DEM, soil type, and vegetation cover conditions. Table 3 shows the field capacity, potential evaporation rate, soil attribute data (b), soil layer thickness, wilting percentage, evapotranspiration coefficient, side slope grade, river bottom slope, saturated water content, saturated hydraulic conductivity, slope roughness, river roughness and width of the river bottom. The adjustable parameters were optimized by modifying them within the left and right intervals of their initial values. Table 3 summarizes the 13 adjustable parameters and their physical significance.

Owing to the lack of large reservoirs in the Beijiang Basin, the influence of reservoir units was excluded from the LXH model during flood simulation studies conducted in this area. The side slope unit and channel unit were subsequently divided using the D8 method (O’Callaghan and Mark, 1984), which determined the flow direction of the unit on the basis of the DEM (Fig. 4). Channel units were extracted on the basis of the accumulation flow. The threshold for accumulation flow was set to 11,035, which allowed for the division of the river system into three levels (Fig. 1). The LXH model demonstrated significant success in practical applications such as reservoir flood forecasting (Zhou et al., 2021; Xing et al., 2022; Zhao et al., 2023) and parameter optimization (Chen et al., 2011; Liao et al., 2012; Chen et al., 2016), particularly in karst basins (Li et al., 2021a; Li et al., 2021b).

3.2 Model initial values

The LXH model determines the initial parameters for each watershed unit on the basis of its physical characteristics. The initial value of the potential evapotranspiration rate in the meteorological conditions parameter was uniformly set to 0.23 mm/d, reflecting the climatic conditions of the basin. Slope roughness and the evaporation coefficient are parameters that are associated with land use. The evaporation coefficient is a relatively insensitive parameter that is typically assumed to be 0.7. Slope roughness was determined on the basis of recommendations from the literature (Wang et al., 1996; Chen et al., 2010).

The generally recommended value for the soil attribute data (b) in the LXH model soil type parameter is 2.5. The initial values of the remaining soil type parameters, including Cfc, Cwl, v, Ep, Csat, Zs, Ks, Sslope, n, Bslope, Manning and Bwidth, were derived from the soil hydraulic properties calculator proposed by Arya and Paris (Arya 1981).

3.3 Parameter optimization

Automatic parameter calibration was performed using the PSO algorithm. This algorithm is a stochastic optimization strategy based on collective intelligence (Kennedy and Eberhart, 1995). Each particle represents a solution that adjusts its speed and direction by recalling and following both the individual optimal position and the group’s optimal position, ultimately achieving optimization. The algorithm intelligently directs global optimization through interparticle cooperation and competition, with each particle having both self-experience and group-sharing characteristics. The transformations of the particle velocity and position were achieved using the following equation:

(1)\{\begin{array}{l}{V}_{i,k}=\omega \times V_{i,k-1}+C_1\times rand\times (X_{i,p\mathrm{B}\mathrm{e}\mathrm{s}\mathrm{t}}-X_{i,k-1})+\\ C_2\times rand\times (X_{i,g\mathrm{B}\mathrm{e}\mathrm{s}\mathrm{t}}-X_{i,k-1})\\ X_{i,k}=X_{i,k-1}+V_{i,k}\end{array},

where \omega is the inertia weight factor and C₁ and C₂ are learning acceleration factors, which range from 0.5 to 2.5; V is the running speed; X is the position; index i refers to the ith particle; index k is the kth moment; X_i,pBest is the current optimal position; X_i,gBest is the global optimal position; and rand is a random number within the range of [0, 1].

The PSO algorithm has a simple structure and high convergence efficiency, and it is easy to program. This algorithm is particularly suitable for distributed hydrological models with complex structures. However, owing to the small population size, this algorithm tends to prematurely enter the local optimum. Chen et al. (2007) optimized the convergence process of the PSO algorithm, and the calculation formula could be expressed as follows:

(2)\{\begin{array}{l}{C}_1=C_{1min}+(C_{1max}-C_{1min})\times \left[1-{\displaystyle \frac{\arccos \left({\displaystyle \frac{-2i}{T}}+1\right)}{\mathrm{\Pi }}}\right]\\ C_2=C_{2min}+(C_{2max}-C_{2min})\times \left[1-{\displaystyle \frac{\arccos \left({\displaystyle \frac{-2i}{T}}+1\right)}{\mathrm{\Pi }}}\right]\end{array},

where T is the maximum number of iterations.

Moreover, to dynamically adjust the inertia weights \text{ω}, we employ the linear decreasing inertia weights strategy (LDIW) proposed by Eberhart and Shi (2001). The formula for calculating this value is as follows:

(3)\omega ={\omega }_{max}-\frac{t({\omega }_{max}-{\omega }_{min})}{T},

where t and T represent the current and maximum number of iterations, respectively. Larger inertia weights at the beginning of the iteration enable the algorithm to sustain a robust global search, whereas smaller inertia weights toward the end of the iteration process promote a more precise local search.

3.4 Model performance and uncertainty assessment methods

When parameter calibration is conducted, a discrepancy often arises between the actual and theoretical values of the parameters. This discrepancy represents the uncertainty of the parameters (Chen et al., 2010). This phenomenon may result in a corresponding bias in the simulation outcomes. Determining the actual values of model parameters is challenging, and parameter optimization is often employed to identify values that closely approximate the true parameters. This method ensures that both the simulation and prediction performance of the model meet practical requirements. To evaluate the results of the optimization simulation accurately, the objective function was transformed into specific and actionable indicators. Five statistical metrics were employed to evaluate the strengths and weaknesses of the simulation results. These five statistical indicators were the correlation coefficient (R), flood peak error (E%), process relative error (PRE), Nash coefficient (NSE) and peak time error (\mathrm{\Delta }H hours). The simulation results were compared on the basis of evaluation criteria (Samantaray and Sahoo, 2024; Samantaray et al., 2025).

The Nash coefficient was used to assess the accuracy of the output results. The parameter provided an intuitive representation of how well the measured and simulated flow processes aligned, reflecting the overall fit.

(4)\{\begin{array}{l}\mathrm{N}\mathrm{S}\mathrm{E}=1-{\displaystyle \frac{{\text{MSE}}^2}{{F_0}^2}}\\ \mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N{\left(Q_{\text{sim}}^i-Q_{\text{obs}}^i\right)}^2}}{N}}}\\ F_0=\sqrt{{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N{\left(Q_{\text{obs}}^i-\overline{Q_{\text{obs}}^i}\right)}^2}}{N}}}\end{array},

where MSE and F₀ represent the mean squared error of the forecast error and the forecast flow, respectively (both metrics indicate the degree of agreement between the measured and modeled flow process lines); Q_{\text{obs}}^i and Q_{\text{sim}}^i represent the observed and simulated flows, respectively; index i refers to the ith hour; \overline{Q_{\text{obs}}^i} denotes the mean value of the observed flow process; and N represents the total number of time steps in the modeled flood event.

(5)\{\begin{array}{l}R=\frac{N{\displaystyle \sum _{i=1}^N{Q}_{\text{obs}}^i{Q}_{\text{sim}}^i-{\displaystyle \sum _{i=1}^N{Q}_{\text{obs}}^i{\displaystyle \sum _{i=1}^N{Q}_{\text{sim}}^i}}}}{\sqrt{\left[N\sum {\left(Q_{\text{obs}}^i\right)}^2-{\left({\displaystyle \sum _{i=1}^N{Q}_{\text{obs}}^i}\right)}^2\right]}\sqrt{N\sum {\left(Q_{\text{obs}}^i\right)}^2-{\left({\displaystyle \sum _{i=1}^N{Q}_{\text{sim}}^i}\right)}^2}}\\ \mathrm{P}\mathrm{R}\mathrm{E}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N\frac{\left|Q_{\text{obs}}^i-Q_{\text{sim}}^i\right|}{Q_{\text{obs}}^i}}\\ \mathrm{P}\mathrm{B}\mathrm{I}\mathrm{A}\mathrm{S}={\displaystyle \frac{Q{P}_{\text{sim}}-Q{P}_{\text{obs}}}{Q{P}_{\text{obs}}}}\\ \mathit{\Delta }H=H{P}_{\text{sim}}-H{P}_{\text{obs}}\end{array},

where R is utilized to evaluate the degree of correspondence between the output flow and the actual flow; PRE is utilized to evaluate the extent of deviation between the output values and the actual values; PBIAS is the relative error of the simulations (%), which is used to evaluate the concordance between the actual and modeled flood flows; Q{P}_{\text{sim}} and Q{P}_{\text{obs}} are the peak flows of the modeled and observed data, respectively; \mathrm{\Delta }H is the time difference between the observed and modeled flood peaks; {\mathit{H}\mathit{P}}_{\text{sim}} is the time at which the simulated peak flow occurs (in hours); and H is the time at which the peak flow is observed (in hours):

(6)\text{COF}=0.5\text{NSE}+0.5R.

The composite objective function (COF) is composed of the NES and R (Li et al., 2024). To calculate the sensitivity of a specific parameter, that parameter had to be optimized while maintaining the other parameters at constant values. The sensitivity of the parameter could be determined using Eq. (6). A higher value indicated greater sensitivity of the parameter.

4 Results

4.1 Parameter sensitivity results

Parameter sensitivity represents the pattern of change in flood simulation results as parameter values vary, thereby determining whether a parameter is sensitive. In the LXH model, when the simulated flood process undergoes significant or substantial changes as the parameter values vary, the parameter is classified as highly sensitive; when the simulated flood process shows noticeable changes, the parameter is classified as moderately sensitive; and when the simulated flood process exhibits some changes that are not significant, the parameter is classified as insensitive. Optimizing only the moderately and highly sensitive parameters can significantly improve the parameter calibration efficiency. The parameter sensitivity results are listed in Table 4

In Table 4, parameters with sensitivity results above 0.8 are classified as highly sensitive; these include Cfc, Csat, Zs, Ks, and b. Parameters with sensitivity results ranging from 0.5 to 0.8 are categorized as moderately sensitive and include Sslope, n, Manning, and Bwidth. Parameters with sensitivity results below 0.5, including Cwl, v, Ep, and Bslope, are considered insensitive.

4.2 Parameter optimization results

A LXH model based on the Beijiang Basin was constructed, and the PSO algorithm was used for parameter calibration. From the 23 floods recorded between 1965 and 1984, 13 floods were selected as a result of parameter optimization. The flow processes for 6 of the 13 selected floods were plotted and compared with the observed flows to assess the effectiveness of the parameter optimization. The population size of the particle swarm was set to 20. \omega ranged from 0.4 to 0.9, and C ranged from 0.5 to 2.5. The velocity was constrained between −30 and 30, and the iterative termination condition was defined by a maximum of 50 iterations. The flow processes for the six floods are shown in Fig. 5.

The flow processes indicated that the simulation results, after parameter optimization, closely aligned with the actual flow processes. Both the overall flow simulation and the flood peak simulation demonstrated satisfactory performance. Five evaluation metrics, NSE, R, PRE, E, and \text{Δ}H, were assessed for the 13 flood simulation results. As shown in Table 5, the average NSE for the first 13 flood simulations was 86.3%, the average R was 65.2%, the average PRE was 29.7%, the average E was 19.9%, and the average peak time was advanced by 1.5 h.

Among these parameters, the NSE and E were the key indices for evaluating the effectiveness of the simulation. For the majority of the 13 floods analyzed, the Nash coefficient exceeded 75%, and in some cases, it surpassed 90%. The error in the flood peak for most floods was less than 20%, and the error in the timing of flood peak occurrences for most floods was less than three hours. This level of accuracy met the standards for hydrological and water condition forecasting. The simulation of the flood effects was excellent, indicating that the LXH model exhibited enhanced performance after its parameters were calibrated through an automatic algorithm. The optimized parameters provided a realistic representation of the physical conditions in the basin, indicating that the model could be utilized for flood simulations in the Beijiang Basin.

4.3 Model validation

To validate the simulation results, 10 floods were selected from a total of 23 floods collected between 1965 and 1984 for model validation. Additionally, 6 of these floods were chosen to illustrate the flow process. As illustrated in Fig. 6, the simulation results closely aligned with the observed flow process curve, and the flood peak was accurately represented. At the beginning of the flood, the simulation results initially lagged the observed data. However, prompt adjustments were implemented, and within a few hours, the simulation results aligned with the observed data, accurately reflecting the flood peak.

The data in Table 5 indicate that in the last 10 simulations, the average NSE was 80.8%, the average R was 54.7%, the average PRE was 28.1%, and the average E was 14.9%. The peak time was delayed by 1 h. NSE and peak time error performed well in assessing these ten floods. The Nash coefficients for most flood events exceeded 80%. For most flood events, the error in flood peak predictions was less than 18%. There was only one case where the error in the timing of flood peaks exceeded three hours, which met the hydrological and water forecasting standards. In summary, the forecasting scheme developed for the LXH model could be effectively employed to predict floods in the Beijiang Basin.

As shown in Table 5, among the 23 floods analyzed, the total average NSE was 83.9%, the average R was 60.7%, the average PRE was 29%, the average E was 17.7%, and the average \text{Δ}H was 0.348 h. NSE and E were the key indicators used to evaluate the simulation results among the five assessment metrics. The Nash coefficient reached 90% or higher in 7 cases (30%), 80% or higher in 15 cases (65%), and 75% or higher in 20 cases (86.96%). The error in the flood peak was less than 10% in 8 cases (34.78%) and less than 20% in 15 cases (65%). Only 2 cases (8.6%) exhibited a time error of the flood peak exceeding 3 h. In summary, the results of this simulation were outstanding and fully met the established requirements.

5 Discussion

5.1 Analysis of the effects of parameter optimization

On the basis of the distributed hydrological model, 23 floods were simulated using the PSO algorithm. Thirteen (57%) floods were selected as a result of parameter optimization. The flood process curves are illustrated in Fig. 4. The simulated curves align closely with the observed data, demonstrating strong performance in both the flood peak and the overall curve, which closely reflect real-world conditions. The results indicate that this parameter preference approach is effective when applied to the LXH model, and the simulation outcomes meet the specified requirements.

As shown in the five evaluation indicators presented in Table 5, the results (the first 13) indicate that the average NSE exceeds 85%, the average R exceeds 65%, the average PRE is less than 30%, the average E is less than 20%, and the average peak time error is maintained within 2 h. Notably, there is only one flood event with a peak time error exceeding 3 h and a pass rate of 92%. The results indicate that the LXH model, which was derived from the automated algorithm, demonstrates superior performance. Furthermore, the preferred LXH model effectively captures the true characteristics of the watershed. Additionally, the preferred parameter set can serve as a valuable reference for flood simulations by the LXH model in this basin.

5.2 Model validation analysis

Among the 23 floods, 10 (43%) were utilized for model validation purposes. As illustrated in Fig. 6, the simulated flood process curves are satisfactory, and the flood peaks perform equally well, closely aligning with the actual conditions of the basin. The results indicate that the LXH model is highly effective for application in this watershed and that the simulation outcomes fulfill the requirements.

As indicated by the five evaluation metrics presented in Table 5, the model validation results (the last 10) indicate that the average NSE exceeds 80%, the average R exceeds 50%, the average PRE is less than 30%, the average E is 15%, and the average \text{Δ}H is delayed by 1 h. In the results presented above, all the indicators, except for the average correlation coefficient, meet the simulation requirements, and the simulation calculations are satisfactory. When the average correlation coefficient is less than 60%, the primary reason is that the PSO algorithm computes the correlation coefficient on the basis of the variables included within the algorithm itself. This finding results in an excessive number of variables being considered, ultimately leading to a correlation coefficient that falls below 60%. In summary, the LXH model is applicable to the Beijiang Basin and meets the accuracy requirements for real-time flood forecasting. Additionally, this study provides valuable guidance for flood forecasting in this region.

5.3 Uncertainty analysis

In the LXH model, variations in the classification of the numerical hydrological system result in differences in the characteristics of the catchment. These changes, in turn, influence flood formation, flood peaks, and the timing of peak occurrence within the catchment. Similarly, the thresholds established for the division of subbasins significantly influence the results and contribute to the uncertainty of the calculations. This phenomenon may be the primary reason for the extreme values observed in the peak time error. Second, the volume of rainfall is a critical factor influencing flooding severity. An uneven rainfall distribution within the basin may reduce the accuracy of model simulations.

Considering the impact of river system classification on flood forecasting, the Strahler method (Strahler, 1957) was employed to classify the water system during the extraction of the river channel. For different thresholds, the river system was classified differently, and a series of critical values existed. The river system was classified into three levels on the basis of an accumulation flow threshold of 11,035. These three levels of water regimes effectively represent the actual convergence process of flooding in the basin (Chen et al., 2017; Qin et al., 2018).

The quality of rainfall interpolation directly affects the model’s ability to simulate actual surface rainfall values accurately (Zhao et al., 2023). Owing to the extensive area of the Beijiang Basin and the uneven rainfall distribution, the inverse distance weighting method was employed to interpolate the rainfall intensity across the basin’s grid cells. This approach yields rainfall intensity values for each grid cell that relatively accurately reflect the actual surface rainfall conditions in the basin. As a widely used and effective technique for rainfall data interpolation, it partially addresses the problem of uneven rainfall distribution, thereby enhancing the potential application of the LXH model in the Beijiang Basin.

The uncertainty of model parameters is influenced primarily by the inherent physical characteristics of the parameters themselves. The parameter settings of the LXH model are physically valuable, allowing them to accurately represent the actual water cycle processes within the watershed. Furthermore, in this study, all original data for the model were preprocessed to ensure that the input data fully met the model’s requirements, thereby minimizing any potential impact on model performance. Model parameter uncertainty is reflected in parameter sensitivity. In this study, a sensitivity analysis (Gad, 2022) of the parameters of the LXH model was conducted, and an improved PSO algorithm was used for parameter optimization. The optimization process focused exclusively on parameters with medium to high sensitivity (Table 4), as these parameters have the most significant influence on model simulation performance, whereas less sensitive parameters have negligible effects. The parameter sensitivity radar chart is shown in Fig. 7. As shown in Fig. 7, the parameters are ranked in order of sensitivity from highest to lowest: Cfc, Csat, Zs, Ks, b, Sslope, n, Manning, Bwidth, Cwl, v, Ep, and Bslope. Among these parameters, Cfc is identified as the most sensitive parameter in the LXH model and necessitates careful calibration, whereas v is the least sensitive parameter and can be simplified. Highly sensitive parameters significantly influence the model’s response to hydrological processes and are the primary focus of parameter calibration. Moderately sensitive parameters are generally associated with topography and river channels, making them particularly important for simulating complex watershed environments. Insensitive parameters can utilize default or empirical values during calibration, thereby reducing workload and enhancing efficiency. Consequently, optimizing only the medium- to high-sensitivity parameters significantly enhances the efficiency and reduces the uncertainty introduced by the parameters during the optimization process.

Wang et al. (2025) proposed a parameter calibration framework for a distributed hydrological model that integrates MPR and LSTM. Using this framework, the scholars simulated the VIC model and optimized it using the SCE–UA algorithm, resulting in enhanced simulation performance. Distributed hydrological models possess complex structures and should be coupled with additional algorithms and models for parameter calibration to improve accuracy. In this study, an improved PSO algorithm was employed for the parameter optimization of the LXH model, which led to a moderate improvement in the model performance. In future research, scholars should explore the combination of various methods to further increase the efficiency of parameter calibration. Additionally, Li et al. (2021a) modified the structure of the LXH model to facilitate its application in karst environments. Modifying a model’s structure is a complex process, and we have not addressed the structural changes or analyzed the uncertainties associated with such modifications. Future research will be focused on refining the LXH model to increase its applicability in more complex watershed environments.

6 Conclusions

In this study, the LXH model is applied to simulate flooding. The overall results are promising, with the simulation results indicating that the LXH model demonstrates strong hydrological simulation performance, effectively meeting the real-time flood simulation requirements of the Beijiang Basin. Additionally, the model offers valuable technical and theoretical support for early flood warnings and for flood security systems in the region. The following conclusions are drawn in this study.

1) Owing to the complex characteristics of distributed hydrological models, multiparameter calibration presents the greatest challenge in their application. The primary function of a distributed physical model is to simulate and predict floods. The LXH model was initially employed to adjust the model parameters through a manual trial-and-error method. This method requires experienced researchers who possess in-depth knowledge of the model to achieve optimal parameter calibration, a process that is both time-consuming and labor-intensive. Automatic parameter optimization has emerged as an essential development trend, and the automatic optimization of multiple parameters is crucial for enhancing the computational efficiency of models.

2) An automated algorithm is employed to calibrate the parameters. The results of this optimization are utilized to test the simulations, yielding satisfactory outcomes. The lowest average correlation coefficient exceeds 60%. The average NSE is 83.9%, the average PRE is 29%, the average E is 17.7%, and the average \text{Δ}H is 0.348 h. The results indicate that an automated algorithm can effectively calibrate the parameters. The calibrated model complies with the relevant specifications for hydrological and water forecasting. This model enables real-time flood forecasting within a river basin.

3) The implementation of automated algorithms can greatly increase computational efficiency. In the PSO algorithm, the optimal parameters are obtained by executing 50 iterations of population evolution, resulting in robust global optimization capabilities and rapid convergence speed. Compared with manual trial-and-error methods for optimization, the efficiency of the PSO algorithm is improved by more than 5-fold.

4) This approach offers an additional method for parameter optimization and is versatile, with the potential for application in other distributed hydrological models and other basins. The performance of this method in simulating complex watershed environments is satisfactory. Importantly, the parameters of the distributed model increase multiplicatively with the size of the watershed. The PSO algorithm still requires considerable computational time when addressing excessively large watersheds. Moreover, an excessive number of parameters may introduce bias in the calculation of correlation coefficients, thereby increasing uncertainty. The next phase of research will be concentrated on enhancing the computational efficiency of the algorithms within the model and reducing the computation time. We aim to closely integrate distributed hydrological models with information technology and geographical tools to improve the stability and applicability of these hydrological models and our understanding of hydrological dynamic processes. In addition, further coupling with other algorithms will enhance both the computational efficiency and accuracy of the results while minimizing errors. Compared with other models, the LXH model can be combined with various optimization algorithms to explore its advantages and disadvantages. Additionally, this approach can be applied to more complex watershed environments, such as karst regions. Future research will be concentrated on enhancing the performance and applicability of the model to ensure its effective implementation in practical settings.

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