Study of Flood Simulation in Small and Medium-Sized Basins Based on the Liuxihe Model

Abstract

The uneven distribution of meteorological stations in small and medium-sized watersheds in China and the lack of measured hydrological data have led to difficulty in flood simulation and low accuracy in flood forecasting. Traditional hydrological models no longer achieve the forecasting accuracy needed for flood prevention. To improve the simulation accuracy of floods and maximize the use of hydrological information from small and medium-sized watersheds, high-precision hydrological models are needed as a support mechanism. This paper explores the applicability of the Liuxihe model for flood simulation in the Caojiang river basin and we compare flood simulation results of the Liuxihe model with a traditional hydrological model (Xinanjiang model). The results show that the Liuxihe model provides excellent simulation of field floods in Caojiang river basin. The average Nash–Sutcliffe coefficient is 0.73, the average correlation coefficient is 0.9, the average flood peak present error is 0.33, and the average peak simulation accuracy is 93.9%. Compared with the traditional flood hydrological model, the Liuxihe model simulates floods better with less measured hydrological information. In addition, we found that the particle swarm optimization (PSO) algorithm can improve the simulation of the model, and its practical application only needs one representative flood for parameter optimization, which is suitable for areas with little hydrological information. The study can support flood forecasting in the Caojiang river basin and provide a reference for the preparation of flood forecasting schemes in other small and medium-sized watersheds.

1. Introduction

Due to various factors such as climate conditions and topography, floods in small and medium-sized rivers in China occur frequently [1,2]. Flood forecasting and timely implementation of flood control measures for small and medium-sized watersheds are of great significance for protecting the safety of people’s lives and property [3,4]. Most of the small and medium-sized rivers in China are located in mountainous regions. The construction time of a hydrological monitoring system is relatively short, and the distribution of rainfall stations is sparse, which often leads to a lack of adequate flood data. Thus, it is difficult to adopt data-driven hydrological forecasting methods. Therefore, the selection of a suitable flood simulation method is particularly important for flood warning forecasting in areas lacking hydrological data.

At present, the flood forecasting methods for small and medium-sized watersheds in areas lacking hydrological data mainly include lumped models [5,6,7,8,9] and distributed models [10]. Representative models of lumped models are the Stanford model [11], the ARNO model [12], and the Xinanjiang model [13,14]. Among them, the Xinanjiang model is a lumped hydrological model that can reflect the physical process of rainfall runoff formation to some extent. It has been in widespread use in humid and semi-humid areas for many years. It divides the entire watershed into several (n) units, and performs yield–sink calculations for each unit to obtain the outflow process of the unit watershed. The total outflow process of the basin is obtained by superimposing the n outflow processes. Traditional forecasting schemes based on this model have achieved good results in predicting floods in large rivers, but the accuracy of flood forecasting in small and medium-sized rivers is not high. This is mainly for the following reasons: firstly, the lumped hydrological model treats the entire basin as a whole without considering the spatial distribution characteristics within the watershed, which does not reflect the real situation of the topography, soil cover, and land type of the watershed [15,16,17]; secondly, the flood process is highly sensitive to rainfall, and the lumped model uses the average surface rainfall for its calculations, which cannot reflect the spatial changes in precipitation in the watershed [18,19]; finally, due to the strong dependence of the lumped model on regional observation data, it requires long-term measured historical runoff process data to calibrate the model parameters. However, the accumulated measured flood data of small and medium-sized rivers in China is relatively short, which cannot meet the basic data requirements for parameter calibration of the lumped model [20,21]. Therefore, lumped models are difficult to apply in practical applications in small and medium-sized watersheds.

In the past decades, machine learning methods based on big data have been applied to multiple fields of research [22,23,24,25]. Because of their nonlinear mapping capability, some scholars have applied machine learning methods to runoff prediction, which is more commonly used in BP [26] neural network models and SVM [26] support vector regression models [27,28,29]. Machine learning methods for runoff prediction are purely black-box models that ignore complex subsurface conditions and the physical causality between inputs and outputs, making it difficult to predict changes in runoff caused by changes in the watershed itself [30]. The prediction results of machine learning often depend on the size of the sample and are more data dependent [30]. Exploiting the full predictive power of machine learning requires a wide range of data sets [31]. Therefore, machine learning has some limitations in simulating runoff in areas lacking hydrological data in small and medium-sized watersheds.

As geographic information systems (GISs) [32], remote sensing (RS) [33], and supercomputing technologies develop, distributed hydrological models have been rapidly developed and commonly used [34]. Distributed hydrological models use modern technologies such as RS and GISs to extract the terrain, geomorphic features, and various hydrological parameters required by the model, which has become an indispensable strong support for scientific research on water resources in areas lacking data [35,36]. Representative distributed hydrological models include the European system hydrological model (SHE) [37,38], variable infiltration capacity model (VIC) [39], DHSVM [40], WetSpa [41], GBHM [42], WEP [43], WEHY [44], and the Liuxihe model [34,45], etc. The distributed hydrological model divides the entire basin into independent grid units, and the soil type, landuse, and the spatial distribution of rainfall in each cell are different from each other. By being divided into a fine grids, the Liuxihe model fully considers the non-uniformity of the subsurface and the unevenness of the spatial distribution of rainfall. This method can clearly reflect the production and confluence process of the whole basin, which improves the accuracy of flood forecasting.

In addition, distributed models only require a small amount of measured data for parameter calibration, and their parameters are physically meaningful. The Liuxihe model is automatically parameterized by the particle swarm optimization (PSO) algorithm [46]. By using the PSO algorithm in practice, the Liuxihe model only requires one flood’s data to calibrate its parameters and the remaining floods are used for verification. The Liuxihe model has achieved good results in predicting basin floods and warning of mountain flood disasters, so it can theoretically predict floods in small and medium-sized basins with insufficient information.

To assess the feasibility and stability of the distributed hydrological model for flood simulation in small and medium-sized watersheds, this paper constructs the Liuxihe model based on the Caojiang river basin in Maoming City, Guangdong Province and uses the PSO algorithm to optimize the model parameters. Then, we compare the obtained flood simulation results with the Xinanjiang model. This study is expected to provide data support for flood forecasting decisions and implementation of flood control measures in the Caojiang river basin. The study is promising to provide scientific support for the further development of flood forecasting schemes in small and medium-sized watersheds.

2. Methods and Materials

2.1. Liuxihe Model

The Liuxihe model is a distributed physical hydrological model developed by Yangbo Chen [34,45,47], which has achieved good results in flood simulation and prediction many times previously [47]. This model consists of multiple sub-models, such as the watershed subdivision and evapotranspiration calculation, to represent complex water cycle systems and the process of rainfall runoff formation. The Liuxihe model developed a parameter optimization method by employing the PSO algorithm, so if there is reliable observation data, even if there is only little data available, the model parameters can be optimized. The Liuxihe model has been successfully applied in watershed flood forecasting, realizing the leap from scientific research to engineering application of distributed hydrological models. In this paper, the Liuxihe model is used to simulate floods in small and medium-sized watersheds. The overall simulation process of the model is shown in Figure 1.

2.2. Introduction to the Study Area

Caojiang is a first-class tributary of the Jianjiang river, originating in Gaozhou City, Guangdong Province, and flowing through the towns of Magui, Dapo, and Changpo. Caojiang is a hilly and wide valley type, and its upper reaches are located in high mountains. The Jianjiang basin originates in Xinyi City, Guangdong Province, with a total basin area of 9464 km², an average annual precipitation of 1820 mm, and an average runoff of about 87 × 10⁸ m³. The Caojiang river basin belongs to the subtropical monsoon mild-climate region, with a multi-year average temperature above 22 °C, multi-year average annual precipitation of 2037 mm, multi-year average annual diameter depth of 1277 mm, multi-year average annual runoff of 10.05 × 10⁸ m³, and uneven spatial distribution of rainfall. Influenced by the uplift of the terrain, summer rainstorms often occur and are more concentrated in the middle and upper reaches of the river, showing a steep increase and steep decline trend [48]. Located within the Caojiang basin, Dabai hydrological station is the outlet point for the region’s middle and upper watersheds. Dabai station was established in January 1967 in Dabai village, Changpo town, Gaozhou. The basin area of Caojiang river above Dabai is 394 km² and the river length is 67 km. In this paper, the study is carried out in the watershed above the Dabai hydrographic station, hereafter referred to as the Caojiang river basin. The watershed diagram is provided in Figure 2.

2.3. Data Collection and Processing

2.3.1. Land Use and Soil Type Data

In this study, the three basic data types of DEM, soil type, and land use type are mainly used to construct the Liuxihe model. The DEM data in this paper is from the Shuttle Radar Topography Mission (SRTM). The SRTM data are obtained from the public database (http://srtm.csi.cgiar.org/ (accessed on 17 January 2023)) with a spatial resolution of 90 m × 90 m. The land use type data are freely available for download from the United States Geological Survey’s Global Land Cover database (http://landcover.usgs.gov (accessed on 17 January 2023)) with a spatial resolution of 1000 m × 1000 m. The soil type data are freely available for download from the International Food and Agriculture Organization (http://www.isric.org/ (accessed on 17 January 2023)) with a spatial resolution of 1000 m × 1000 m. In this paper, the three base data types need to be resampled to 90 m × 90 m spatial resolution for analysis. The results are shown in Figure 3.

2.3.2. Hydrological Data

There are five rainfall stations and one hydrological station in the Caojiang river basin, which are Houyuan, Magui, Baima, Dapo, and Haipiao, a total of five rainfall stations, and the Dabai hydrological station, with an average of one station deployed per 65.67 km² (Figure 2). This article collected flood data for 7 rainfall and flow events at each station from 2010 to 2018, all with a 1 h time interval. We used the Thiessen polygon method [49,50,51] to spatially interpolate the rainfall data from the rainfall stations, which obtained the rainfall strength of each grid unit.

2.4. Evaluation Methods for Model Performance

We used four statistical metrics to assess the simulation performance of the Liuxihe model. These four metrics are the correlation coefficient, R, the Nash–Sutcliffe Coefficient, S, the flood peak error, E (%), and the flood peak present error, $∆H$ (hours).

$$R=\frac{N\sum _{i=1}^N{Q}_{obs}^i{Q}_{sim}^i-\sum _{i=1}^N{Q}_{obs}^i\sum _{i=1}^N{Q}_{sim}^i}{\sqrt{\left[N\sum {\left(Q_{obs}^i\right)}^2-{\left(\sum _{i=1}^N{Q}_{obs}^i\right)}^2\right]}\sqrt{\left[N\sum {\left(Q_{obs}^i\right)}^2-{\left(\sum _{i=1}^N{Q}_{sim}^i\right)}^2\right]}}$$

(1)

where $Q_{sim}^i$ = simulated flow at time $i$, $Q_{obs}^i$ = observed flow at time $i$, while $N$ = total time steps in the simulation process of the flood event.

$$S=1-\frac{{MSE}^2}{F_0^2}$$

(2)

$$MSE=\sqrt{\frac{\sum _{i=1}^N{(Q_{sim}^i-Q_{obs}^i)}^2}{N}}$$

(3)

$$F_0=\sqrt{\frac{\sum _{i=1}^N{(Q_{obs}^i-\overline{Q_{obs}^i})}^2}{N}}$$

(4)

$$E=\frac{{QP}_{sim}-{QP}_{obs}}{{QP}_{obs}}$$

(5)

where ${QP}_{sim}$ = simulated peak flow, while ${QP}_{obs}$ = observed peak flow.

$$∆H={HP}_{sim}-{HP}_{obs}$$

(6)

where ${HP}_{sim}$ = time (hours) of occurrence of flood peak flows during the simulation process, while ${HP}_{obs}$ = time (hours) of occurrence of flood peak flows during the observation process.

3. Model Construction

3.1. Liuxihe Model Setup

The Liuxihe model divides the whole watershed into grid units with separate physical mechanisms based on the DEM data. The grid units include river slope units, channel units, and reservoir units. Since this paper is a small and medium-sized river flood forecasting study based on the Caojiang river basin, the effect of the reservoir cells is not considered in this modeling with the Liuxihe model. We use the D8 [45] flow direction method to divide the cells into side slope cells and river cells. By setting a suitable cumulative flow threshold, we select the cells larger than the cumulative flow threshold as river cells and the remaining cells as side slope cells. We use the Strahler [52] method to classify the extracted river channels into appropriate classes based on flow accumulation (FA0). The FA0 value can divide the river channels into up to six levels. By changing the cumulative flow threshold multiple times, we found that the level 1 and 2 river divisions should not be selected as the corresponding tributaries were not fully divided. Through observation of Google Earth remote sensing images, we found that the river divisions were too dense and difficult to estimate the cross-sectional size of the river after being classified into level 4, 5, and 6 rivers. Therefore, this study compares and calculates the river cross-sections for level 3 channels. The Liuxihe model specifies a range of FA0 values to be used to generate third-order river channels. The threshold size can be reasonably adjusted within the range through several attempts. We generated the SHP (shapefile) files for the level 3 river systems with adjustable thresholds and imported the SHP files into remote sensing images for comparison to determine the deviation from the real river systems. After several attempts, we found that a threshold setting of 300 was reasonable in this study. The final number of level 3 river cells was 1719 and of slope cells was 46,929. Figure 4 shows the result of dividing the river channels into three levels.

According to the construction method of the Liuxihe model, we set up virtual nodes in the Caojiang river basin and divided the river into virtual river sections by observing and analyzing the changes in river network structure and channel bottom slope. The Liuxihe model assumes that the channel section is trapezoidal, and estimates the channel bottom width, channel bottom slope, and side slope.

3.2. Initial Model Parameters

Based on the physical mechanisms of each watershed unit, the initial parameters of the Liuxihe model can be divided into four categories: topography, land use, meteorology, and soil. Flow direction and slope are topographic parameters of the Liuxihe model, which are non-adjustable parameters and can be directly calculated by DEM (Figure 5). The parameters characterizing land use type are mainly the evaporation coefficient and roughness coefficient, where the initial value of the roughness coefficient of the slope unit is determined according to the method of the runoff model. Since the evaporation coefficient is a non-sensitive parameter, we empirically set it to 0.7 for all types of land use data [45] (

Table 1. Parameters of land use types.

Land Use Type	Evaporation Coefficient	Roughness Coefficient
Needleleaved evergreen forest	0.7	0.4
Broadleaved evergreen forest	0.7	0.6
Bush	0.7	0.4
Sparse woods	0.7	0.3
Slope grassland	0.7	0.1
Farmland	0.7	0.15

). In this paper, the potential evapotranspiration has to be determined empirically on the basis of the climatic conditions of the watershed, with one value (0.23 mm/h) [45] applied to the entire basin. This study empirically set the groundwater recession coefficient at 0.995. The soil parameters include the field water holding rate, wilting water content, saturation water content, saturation hydraulic conductivity, soil thickness, and soil properties.

Table 2. Parameters of soil types.

ID	Thickness of Soil Layer (mm)	Saturated Water Content	Field Moisture Retention	Saturated Hydraulic Conductivity	Soil Porosity Characteristics	Wilting Moisture Content
CN10033	1000	0.451	0.300	8.64	2.5	0.176
CN10171	810	0.447	0.300	7.81	2.5	0.182
CN30045	990	0.477	0.354	4.73	2.5	0.213
CN30063	1080	0.466	0.359	7.76	2.5	0.181
CN30109	1000	0.443	0.274	12.09	2.5	0.160
CN30139	1140	0.485	0.343	7.69	2.5	0.179
CN30147	1000	0.447	0.242	21.61	2.5	0.126

provides the empirical thickness values for different soil types in the Caojiang basin. The soil porosity characteristic parameter, b, is uniformly assigned a value of 2.5 [45] based on the literature, and the remaining parameters are obtained by the soil hydraulic characteristic calculator proposed by Arya et al. [53] (http://www.bsyse.wsu.edu/saxton (accessed on 17 January 2023)).

3.3. Model Parameter Optimization

The Liuxihe model uses the PSO algorithm for parameter optimization. The PSO algorithm simulates the migratory behavior of a flock of birds during foraging, and the flock shares and learns from each other to find the optimal search strategy based on the experience gained during the search process, which is widely cited in various industries due to its simple and efficient global search capability. In the flood forecasting model, the PSO algorithm requires only one typical flood event from the flood data of previous years for parameter optimization. We selected flood 2018091600 to optimize the parameters and used the remaining floods for validation of the model simulation results.

The PSO algorithm is essentially an intelligent optimization strategy. The transformation relationship between particle velocity and position follows the following principles:

$$V_{i,k}=\omega \times V_{i,k-1}+C_1\times rand\times \left(X_{i,pBest}-X_{i,k-1}\right)+C_2\times rand\times (X_{gBest}-X_{i,k-1})$$

(7)

$$X_{i,k}=X_{i,k-1}+V_{i,k}$$

(8)

where $C_1$ and $C_2$ are learning factors, also known as acceleration constants; $rand$ is a random number within the range [0, 1], increasing the randomness of particle’s flight; $k$ refers to the number of iterations; $\omega$ is the inertia weight; $V_{i,k}$ is the velocity of the ith particle at the kth iteration; $X_{i,k}$ is the position of the ith particle at the kth iteration; $X_{i,pBest}$ is the optimal position of individual particle i at the kth iteration; and $X_{gBest}$ is the global optimal position of all particles at the kth iteration.

The parameters used in the PSO algorithm are the overall size of the particle swarm, the number of iterations, the total number of computations, the inertia factor, and the learning acceleration factor. The number of particles is set to 20, the number of iterations is set to 200 and the total number of computations is set to 1000. C1 and C2 are run dynamically and iteratively according to the inverse sine acceleration algorithm in the range of [0.5, 2.5]. The results of the parameter optimization of the Liuxihe model based on the PSO algorithm are shown in Figure 6.

The model objective function maintains a gradually decreasing trend. After 49 calculations, the model objective function tends to be stable and the model parameters tend to converge to their optimal values. The performance of the parameters optimized by the PSO algorithm is better than the initial parameters, which indicates that the parameter optimization of the Liuxihe model based on the PSO algorithm enhances the rate of convergence.

4. Results and Analysis

4.1. Model Performance Evaluation

This paper mainly collected and compiled a total of seven actual floods measured during 18 years from 2000 to 2018. We bring the rainfall obtained from the Thiessen polygon method interpolation into the model for calculation, and the flood 2018091600 was selected for parameter optimization. The final simulation results are listed in

Table 3. Flood simulation results.

Flood Number	Nash–Sutcliffe Coefficient	Correlation Coefficient	Process Relative Error	Flood Peak Error	Water Balance Coefficient	Flood Peak Present Error
2010092023	0.64	0.839	0.501	0.097	0.864	−1
2013081420	0.815	0.936	0.28	0.107	0.973	1
2013111000	0.702	0.93	0.395	0.073	0.705	0
2015100400	0.858	0.961	0.294	0.059	1.058	0
2017062200	0.724	0.924	0.3	0.024	1.026	0
2018081100	0.613	0.855	0.449	0.006	1.189	2

, and the flow process line is shown for floods other than the 2018091600 flood (Figure 7). The results show that the Nash–Sutcliffe coefficients of all six floods are high. Among them, there are four floods with Nash–Sutcliffe coefficients above 70%, accounting for 66.67% of the total number of floods. Combined with the results in Figure 7, the forecast results and the actual measured runoff process are more closely matched. Therefore, the simulation of the flood process by the model was relatively satisfactory.

According to the specifications of hydrological water forecasting, the rainfall runoff forecast takes 20% of the actual measured flood flow as the permitted error and the flood peak present time takes 3 h as the permitted error. Among the above results, except for flood 2018091600, the flood peak errors of the other six floods were less than 20%, and the pass rate was 100%. It is worth noting that four of them had flood peak errors less than 8%. In addition, all the flood peak present errors were within 3 h, and the passing rate was 100%. Therefore, this shows that the model can simulate the flood flow and peak present time satisfactorily. In conclusion, it shows that the Liuxihe model has strong applicability for the Caojiang river basin.

4.2. Analysis of the Results of Model Parameter Optimization

In this study, the PSO algorithm can obtain the optimal parameters after 49 times of population evolution in the optimization of the model parameters. It has the characteristics of a strong global optimization ability and fast convergence speed. We simulated six floods using initial and optimized model parameters to verify the performance of the model after parameter optimization by the PSO algorithm.

Table 4. Statistical indicators of the flood simulation results before and after parameter optimization.

Parameter	Average Nash–Sutcliffe Coefficient	Average Correlation Coefficient	Average Process Relative Error	Average Flood Peak Error	Average Flood Peak Present Error
Before optimization	0.12	0.81	0.85	0.70	−4.6
After optimization	0.73	0.90	0.37	0.061	0.33

shows the average metrics of the simulation results. The model simulated flood flow process after parameter optimization is closer to the actual flow process than the model simulated flood flow process at the initial parameters, with the average Nash–Sutcliffe coefficient increasing from 12% to 73%, the average correlation coefficient increasing by 9%, the average process relative error reducing by 48%, and the average flood peak error reducing by 64%. Thus, the results show that the PSO algorithm can significantly reduce the uncertainty in the flood simulation and forecasting performance of the distributed model. This approach only requires the selection of classical flood types for parameter optimization for use in practice and validates the performance of the model with the effects.

4.3. Comparison of Simulation Results of Different Models

At present, the traditional flood forecasting scheme in China mainly adopts the Xinanjiang model. We used the Xinanjiang model to simulate floods other than 2018091600, with four being used for calibration and two for validation. We compared the flood simulation results of the Xinanjiang model with the Liuxihe model. The results are listed in

Table 5. Comparison of simulation results of different models.

Flood Number	Model	Nash–Sutcliffe Coefficient	Correlation Coefficient	Flood Peak Error	Flood Peak Present Error
2010092023	Liuxihe model	0.64	0.839	0.097	−1
	Xinanjiang model	0.6	0.886	0.593	−1
2013081320	Liuxihe model	0.815	0.936	0.107	1
	Xinanjiang model	0.834	0.923	0.114	1
2013111000	Liuxihe model	0.702	0.93	0.073	0
	Xinanjiang model	0.906	0.969	0.0978	−1
2015100400	Liuxihe model	0.858	0.961	0.059	0
	Xinanjiang model	0.624	0.89	0.144	0
2017062200	Liuxihe model	0.724	0.924	0.024	0
	Xinanjiang model	0.334	0.932	0.654	−1
2018081100	Liuxihe model	0.613	0.855	0.006	2
	Xinanjiang model	0.409	0.932	0.0104	0

, and the floods’ flow process lines are shown in Figure 8.

The results from Table 5 show that there were four floods with Nash–Sutcliffe coefficients greater than 70% in the Liuxihe model, accounting for 66.67%. The passing rate of flood peak error and peak present error are both 100%. There were three floods with Nash–Sutcliffe coefficients greater than 70% in the Xinanjiang model, accounting for 50%. The passing rate of flood peak error and peak present error in the Xinanjiang model were 66.67% and 100%, respectively. In the Xinanjiang model, the simulation results of peak flow were overall lower than measured flow, with the flood errors of 2010092023 and 2017062200 both exceeding 50%, and the peak present time for the flood was overall more accurate. From Figure 8, compared with the Xinanjiang model, the flow process lines calculated by the Liuxihe model were more consistent with the measured flow process lines, indicating that the results were more consistent with the actual situation.

In conclusion, compared with the Xinanjiang model, the flood simulation effect of the Liuxihe model in the Caojiang river basin is more stable and accurate. The reason may be that the representative historical flood data in the Caojiang river basin were less, and the distribution of stations was sparse. However, the Xinanjiang model needed more fields with different magnitudes of flood data for model parameter calibration to obtain better simulation results. Therefore, the historical flood data of the Caojiang river basin is insufficient to support the parameter calibration of the Xinanjiang model. The Liuxihe model is a distributed model with a certain physical mechanism. Furthermore, the Liuxihe model usually needs only one representative flood for parameter optimization, which helps it to perform better simulations in areas lacking hydrological data. Therefore, compared with the Xinanjiang model, the Liuxihe model offers more possibilities for flood forecasting in areas lacking hydrological data. Future research can discuss the applicability of different models.

This paper achieved good simulation results for the floods in the Caojiang river basin. The Caojiang river basin is a small and medium-sized watershed located in a humid and semi-humid region. Interestingly, when the basin area is large or the climate conditions of the basin is arid or semi-arid, the applicability of the Liuxihe model needs further discussion. This paper selects too few traditional hydrological models. We only used one model to compare with the Liuxihe model, which is not enough. Future studies should compare simulation results with multiple lumped hydrological models to enhance the persuasiveness.

5. Conclusions

Based on the Caojiang river basin, this paper used the Liuxihe model to simulate flooding in the basin and used the PSO algorithm to optimize the parameters. Then, we analyzed it and compared it with traditional forecasting schemes. The results indicate that:

(1)

According to the simulation results of the Liuxihe model, out of the six floods, there were four floods with a Nash–Sutcliffe coefficient of over 70%, accounting for 66.67%. The peak error of all of the floods was less than 20%, and the qualification rate reached 100%. The pass rate of the flood peak present error reached 100%. The Liuxihe model established in this paper had strong applicability in the Caojiang river basin and could be used for flood forecasting in the Caojiang river basin.

(2)

The PSO algorithm markedly enhanced the flood simulation and prediction performance of the flood prediction model in the Caojiang river basin. In practical applications, the PSO algorithm only used one flood to optimize the parameters, which effectively improved the simulation accuracy of the model.

(3)

Compared with the Xinanjiang model, the flood simulation results of the Liuxihe model in the Caojiang river basin are more stable and accurate. Due to the lack of measured hydrological data in the Caojiang river basin, the Liuxihe model may have stronger flood simulation capability in areas lacking hydrological data, and more use of the model needs to be further discussed.