Flash Flood Simulation for Hilly Reservoirs Considering Upstream Reservoirs—A Case Study of Moushan Reservoir

Abstract

With the advancement of society and the impact of various factors such as climate change, surface conditions, and human activities, there has been a significant increase in the frequency of extreme rainfall events, leading to substantial losses from flood disasters. The presence of numerous small and medium-sized water conservancy projects in the basin plays a crucial role in influencing runoff production and rainwater confluence. However, due to the lack of extensive historical hydrological data for simulation purposes, it is challenging to accurately predict floods in the basin. Therefore, there is a growing emphasis on flood simulation and forecasting that takes into account the influence of upstream water projects. Moushan Reservoir basin is located in a hilly area of an arid and semi-arid region in the north of China. Flooding has the characteristics of sudden strong, short confluence time, steep rise, and steep fall, especially floods caused by extreme weather events, which have a high frequency and a wide range of hazards, and has become one of the most threatening natural disasters to human life and property safety. There are many small and medium-sized reservoirs in this basin, which have a significant influence on the accuracy of flood prediction. Therefore, taking Moushan Reservoir as an example, this paper puts forward a flash flood simulation method for reservoirs in hilly areas, considering upstream reservoirs, which can better solve the problem of flood simulation accuracy. Using the virtual aggregation method, the 3 medium-sized reservoirs and 93 small upstream reservoirs are summarized into 7 aggregated reservoirs. Then, we construct the hydrological model combining two method sets with different runoff generation and confluence mechanisms. Finally, after model calibration and verification, the results of different methods are analyzed in terms of peak discharge error, runoff depth error, difference in peak time, and certainty coefficient. The results indicate that the flooding processes simulated by the proposed model are in line with the observed ones. The errors of flood peak and runoff depth are in the ranges of 2.3% to 15% and 0.1% to 19.6%, respectively, meeting the requirements of Class B accuracy of the “Water Forecast Code”. Method set 1 demonstrates a better simulation of floods with an average flood peak error of 5.63%. All these findings illustrate that the developed model, utilizing aggregate reservoirs and dynamic parameters to reflect regulation and storage functions, can effectively capture the impact of small water conservancy projects on confluence. This approach addresses challenges in simulating floods caused by small and medium-sized reservoirs, facilitating basin-wide flood prediction.

1. Introduction

With the development of society, extreme rainfall events occur frequently under the influence of many factors such as climate change, underlying surface conditions, and human activities [1,2,3]. In recent years, extreme heavy rain events have occurred frequently in China, especially in the arid and semi-arid areas in the north, causing serious losses [4]; for example, from 28 July to 1 August 2023, the flood that occurred in the Haihe river region (named “23 · 7” flood by the Ministry of Water Resources, Beijing, China) [5], and on 20 July 2021, the heavy rain [6] that occurred in Zhengzhou, Henan Province, resulting in serious flood disaster losses (namely “7 · 20” flood). In hilly areas, floods are characterized by rapid onset, short response time, steep rise and fall, and high destructive potential. Additionally, many water conservancy projects such as reservoirs, locks, and dams have been usually constructed in river basins for the development of water resources. The construction of reservoirs changes the natural hydrological characteristics of rivers, resulting in changes in the production and aggregation mechanism [7,8,9,10,11], especially for extreme rainstorm events. In addition, most small reservoirs and pond dams in China have no operation facilities and lack a long series of observation data. However, in the process of reservoir flood prediction, not only the precipitation and runoff process but also the influence of the storage and release of upstream reservoirs should be considered. Therefore, in order to improve flood disaster prevention abilities, it is crucial to study flood simulation methods for hilly reservoirs that take into account the impact of upstream water conservancy projects. This will greatly enhance flood forecasting and control efforts while reducing losses.

For flood simulation and prediction, after years of research, domestic and foreign scholars have proposed lumped models such as the HBV model, Tank model, and Xin’anjiang model [12]. With the development of information and computer technology, scholars put forward distributed hydrological models such as Top model, VIC model, SWAT model, and HEC-HMS [13,14,15,16,17,18]. According to different climate zones and watershed characteristics of our country, Chinese scholars established multiple distributed hydrological models adapting to different watershed characteristics [19,20].

As for the impact of human activities, in foreign countries, hydrological models are mainly used to study runoff changes through land use/cover change [21,22,23]. In the study and application of conceptual hydrological models, many domestic scholars considered the impact of small and medium-sized reservoirs on production and confluence. For example, Guo Shenglian et al. [19] converted the interception of small and medium-sized reservoirs in the basin into the water storage capacity of Xin’an River model. Ling Minhua et al. [24] put forward the Xin’an River model considering pond storage to simulate runoff and analyze the impact of pond storage on river runoff. Chen Jian et al. [25] converted small and medium-sized reservoirs in the basin into virtual reservoirs and proposed an improved Xin’an River model.

In practical application, the flood forecasting method considering the influence of human activities mainly adds the influence factors of human activities into the lumped model. For example, Cheng Chuntian and Wang Bende [26] estimated the cumulative net rainfall value of each unit at different time periods, as well as the intercepting capacity of the upstream reservoir and paddy field during the growth period based on flood stage and crop irrigation so as to estimate the maximum intercepting capacity and runoff correction coefficient. They then fine-tuned and optimized the parameters through human–computer interaction to obtain the parameters of flow production and the influence of human activities and pointed out that the forecast accuracy was 9% higher than that without considering the influence of human activities for Shitokoumen Reservoir in Jilin Province, reflecting the influence of human activities on the runoff forecast. Guo Shenglian et al. [19] classified the water conservancy projects in the basin according to their storage capacity, converted the cumulative storage capacity of the same type of reservoir into the maximum storage capacity, and added it into the soil storage capacity of the Xin’an River model to put forward a flood forecasting scheme considering the influence of human activities. Sun Xinguo et al. [27] aggregated many water projects in the basin into a virtual reservoir, formulated the water storage and release law of the aggregate reservoir, effectively quantified the impact of reservoir storage and discharge on the flooding process of the basin, and increased the Nash efficiency coefficient of flood prediction in Fengman Reservoir basin by 22%. Aiming at the problem of poor simulation accuracy of floods with rainfall centers distributed in the upper reaches, Yao Shiqian [28] analyzed and evaluated the impact of changes in land use and water conservancy construction on runoff.

The above studies coupled the lumped model with the reservoir module did not fully consider the spatial distribution of water conservancy projects in the basin and did not describe the regulation and storage function of many small and medium-sized reservoirs with insufficient precision. Therefore, some scholars combined the advantages of the lumped model and distributed the hydrological model to establish a grid-based hydrological model considering the influence of water conservancy projects to further improve the accuracy of watershed flood prediction. For example, Yao Cheng et al. [29] established a grid-based new Anjiang River model (Grid-XAJ) to consider the influence of Kutangdam storage and drainage on the process of production and convergence. The water distribution process along the river course is described well.

Domestic flood simulation and forecast studies on the impact of water conservancy projects are mainly in humid or semi-humid areas, whereas studies on arid and semi-arid areas [9,11,28] only consider drought and humid conditions, but do not reflect semi-drought, and do not study flood simulation and forecast under extreme rainstorm scenarios. This paper proposed a flood simulation method for reservoir basins in hilly areas considering the distribution characteristics of upstream reservoirs and their influence on runoff in semi-humid areas. The method was established on the basis of a reservoir flood simulation model, further studied the flood holding capacity and the influence on runoff of many small and medium reservoirs upstream, and simulated the flooding process under different pre-influence rainfall so as to realize the flood forecast of the watershed as a unit and provide the basis for the following flood control scheduling. Firstly, according to the physical geography and hydrological characteristics, the hydrological model of the Moushan Reservoir basin was constructed based on HEC-HMS, in which two different combination methods of runoff generation and confluence, namely, the steady infiltration method with Snyder unit line method (method set 1) and the SCS-CN curve method with SCS unit line method (method set 2), were selected, respectively, in addition to the Muskingum method, which was used for the river flood evolution. Then, the distribution characteristics of the reservoirs in the basin were analyzed, the three medium and 93 small reservoirs in the upper reaches of the basin were generalized into seven aggregated reservoirs and added to the constructed hydrological model using the “Add Reservoirs” module in HEC-HMS. Finally, nine historical floods under different early influence rainfall were simulated and verified, of which six floods were for parameter calibration and three floods were for parameter verification. The peak discharge error, runoff depth error, peak current difference, and certainty coefficient were analyzed; a comparison between the results from different method sets was made with observed floods to verify the applicability and superiority of this approach.

2. Study Area and Data

2.1. Study Area

Moushan Reservoir is situated on the Wenhe River in Weifang City, Shandong Province, and covers a total drainage area of approximately 1262 km². The upstream main stream is 71 km long with an average gradient of 0.00212, as shown in Figure 1. The basin is located in the East Asian monsoon region and has a continental climate. The annual average rainfall is 702.1 mm, and heavy rains mostly occur in mid-summer and early autumn, with obvious seasonality. Because the stone mountain area in the basin accounts for about 58%, the duration of the flood generated by the rainstorm is short, the flooding process line has a steep rise and steep fall, and the larger flooding process is generally 20–30 h.

In order to fully deploy and utilize the water resources, many small and medium-sized reservoirs have been constructed within the basin (can be seen in Figure 1), which have a significant influence on the accuracy of flood prediction. There is 1 large reservoir (Gaoya Reservoir), 3 medium-sized reservoirs (including Daguan reservoir, Yishan reservoir, and Shangzhuang reservoir), and 93 small reservoirs in the area.

In Figure 1, for the water conservancy projects, only the large and medium-sized reservoirs and small (1) reservoirs are marked, and the rest of the small reservoirs and pond dams are not marked.

2.2. Data Source and Processing

For the Digital Elevation Models (DEMs), the Geospatial Digital Elevation Model of version V3 (namely GDEMV3) is used and obtained from the Geospatial data cloud (http://www.gscloud.cn (accessed on 6 April 2024)), the horizontal resolution is 30 m and the vertical resolution is 1 m.

By using the expansion module of ArcGIS 10.5 software HEC-GeoHMS, which was developed by the Hydrologic Engineering Center (HEC) of the US Army Corps of Engineers to simulate the Hydrologic Modeling System (HMS) in a watershed, the scope of the study area was determined, as shown in Figure 2, through depression filling, flow direction calculation, confluence calculation, river network extraction, sub-basin division, and basin outlet definition, and the study area was divided into 22 sub-basins. Then, we calculated the slope, center location, longest flow path, hydraulic parameters of each sub-basin, and set the network elements of the HMS hydrological model to obtain the digital watershed that meets the requirements of the HEC-HMS model, as shown in Figure 2.

In Figure 2, W510, W560, W590, W610, W640, W650, W660, W690, W700, W720, W900, W740, W780, W790,W800, W810, W850, W860, W880, W890, W910, and W920 are the 22 sub-basins divided.

The land use-type data and soil-type data were obtained from Data Center for Resources and Environmental Sciences, Chinese Academy of Sciences (https://www.resdc.cn/ (accessed on 6 April 2024)) and China Soil Database (http://vdb3.soil.csdb.cn (accessed on 6 April 2024)), with an accuracy of 30 m. After tailoring and reclassification by ArcGIS, land use types were mainly divided into farmland, forest land, grassland, water body, urban buildings, and undeveloped soil, as shown in Figure 3. Soil types are mainly divided into sandy loam, clay loam, sandy clay, silty clay loam, and loam, as shown in Figure 4.

There are nine rainfall measuring stations in the basin of Moushan Reservoir, including Daguan (R1), Taoyuanzi (R2), Jiangyu (R3), Lijiagou (R4), Liuzhai (R5), Dianzi (R6), Nanwu (R7), Tangwu (R8), and Sujiazhuang (R9), as well as, two rainfall and hydrology stations in Gaoya (R10) and Moushan (R11). The rainfall data of 11 different rainfall stations were provided by Weifang Water Resources Bureau and floods information of the hydrographic station was provided by Moushan Reservoir operation and maintenance center.

Daily water evaporation was obtained from the China Meteorological Data Sharing Service System.

3. Methods

3.1. Flood Simulation Model

The basin of Moushan Reservoir is a semi-arid and semi-humid area with complex underlying surface conditions. There is basically no base flow in the river course, and the flood caused by rainfall is mainly generated by the rainfall of each event, so the influence of base flow is ignored.

In addition, based on the principle of fewer parameters, easy data access, and stable and reasonable simulation results, combined with the topographic conditions, meteorological conditions, soil conditions, and vegetation conditions of the basin of Moushan Reservoir, the methods with better application effects in semi-arid and sub-humid areas [9,10,11] are compared and analyzed, and two sets of methods (shown in

Table 1. Two sets of simulation methods.

Method Set	Method
	Runoff Generation	Slope Confluence	River Channel Evolution
Set 1	initial loss and steady permeability method	Snyder unit line method	Muskingum method
Set 2	SCS-CN curve method	SCS unit line method	Muskingum method

) are selected for simulation calculation.

In Table 1, SCS-CN is the Soil Conservation Service Curve Number model proposed by the United States Department of Agriculture based on practical experience in 1972; CN is the number of runoff curves and has no dimension.

For runoff generation, the initial loss and steady infiltration method has strong applicability in simulating runoff in short-term rainfall scenarios and can accurately simulate the runoff process of short-term rainfall events and for long-term or complex rainfall patterns; the simulation accuracy of this method may be limited. However, the SCS-CN method may show higher simulation accuracy in long-term or complex rainfall patterns and may lead to prediction errors in the case of short-duration heavy rainfall due to simplified assumptions of the model. In the study area, the soil type and distribution are complex, the data are relatively lacking, and short-duration heavy rainfall events commonly occur. Therefore, the above two methods are used to calculate and analyze runoff production, respectively.

For confluence, the SCS unit line method has been widely used worldwide, and its parameters can be adjusted according to different basin characteristics. The combination of the SCS unit line method and SCS-CN current production method significantly improves the accuracy of flood prediction. This combination enables the model to better reflect the geomorphic characteristics of the basin, especially for the small watershed in the hilly area where data are lacking. The Snyder unit line method can reflect the characteristics of the basin well, including the influence of the basin area, topography, and other factors on the runoff process, but the parameter determination may be more complicated, and more field investigation and tests are needed to determine the appropriate parameters. The study area is a hilly area and data are lacking, so the above two methods are used for comparative analysis.

3.1.1. Flow Generation with Initial Loss and Steady Permeability Method

The Thiessen polygon method is used to divide the Thiessen polygon according to the distribution of rain measuring stations, as shown in Figure 5.

For the sub-basin inside the Thiessen polygon, the area rainfall is the rainfall of the rainfall station. For sub-basins spanning multiple Thiessen polygons, the surface rainfall is calculated with the polygon area as the weight listed in

Table 2. The weight calculated for each rainfall station in each sub-basin.

Sub-Basin	Rainfall Station	Weight	Sub-Basin	Rainfall Station	Weight
W510	R5	0.036	W740	R1	0.016
	R8	0.964		R3	0.367
W560	R11	1.000		R4	0.010
W590	R8	0.209		R10	0.549
	R9	0.602		R6	0.059
	R11	0.189	W780	R7	0.695
W610	R4	0.030		R9	0.305
	R5	0.810	W790	R6	0.063
	R10	0.160		R7	0.937
W640	R5	0.213	W800	R6	0.404
	R10	0.434		R7	0.592
	R8	0.341		R9	0.005
	R9	0.012	W810	R10	0.647
W650	R11	1.000		R6	0.169
W660	R7	0.287		R7	0.013
	R9	0.616		R8	0.008
	R11	0.098		R9	0.163
W690	R7	0.638	W850	R2	0.208
	R9	0.054		R3	0.498
	R11	0.308		R4	0.295
W700	R3	0.002	W860	R3	1.000
	R4	0.712	W880	R1	0.553
	R5	0.033		R3	0.447
	R10	0.253	W890	R2	0.781
W720	R10	1.000		R3	0.219
W900	R1	0.653	W910	R1	0.239
	R2	0.206		R6	0.761
	R3	0.140	W920	R6	1.000

. The calculation formula is as follows:

$$\overline{P}=\sum _{i=1}^n\frac{A_i}{F}{P}_i$$

where $\overline{P}$ is the area mean rainfall of sub catchment i, mm. n is the number of rain measuring stations. A_i is the area controlled by the ith rain measuring station in the sub-watershed, km². F is the area of the sub-watershed, km². P_i is the amount of rainfall at the i station, mm.

The initial loss steady infiltration method has strong practicability in simulating runoff in short-term rainfall scenarios, and the runoff production process of rainfall can be divided into two stages: initial loss and post-loss. The calculation formula is as follows:

$$p_{et}=\left\{\begin{array}{c}0 \sum p_i<I_a\\ P_t-f_c \sum P_i>I_a \mathrm{and} P_t<f_c\\ 0 \sum P_i>I_a \mathrm{and} P_t<f_c\end{array}\right.$$

(1)

where $p_{et}$ is the net rainfall, mm.$P_t$ is the average rainfall over the surface from time t to time t + Δ, mm, where Δ is the time step. $I_a$ is the initial loss of rainfall, mm. $f_c$ is the soil infiltration rate, mm/h.

3.1.2. Flow Generation with SCS-CN Curve Method

The SCS-CN curve method contains only one dimensionless parameter CN value, with few parameters, and the calculation process is relatively simple. However, this value is related to soil moisture, land use type, and soil type in the previous period, and can reflect the comprehensive characteristics of the underlying surface in the study area in a more comprehensive way. The theoretical value range of the CN value is 0–100, and the specific initial value is generally calculated according to the National Engineering Manual of the United States [15]. In actual simulation calculation, the common value range is 40–98 [6,30]. When there are multiple land use types and soil types in the basin, the compound ${\mathit{CN}}_w$ value of the basin is calculated according to the equation as follows:

$${\mathit{CN}}_w=\frac{\sum A_j{\mathit{CN}}_j}{\sum A_j}$$

(2)

where j is the number of land use types and soil types in the basin. $A_j$ is the area of land use type and soil type of mass j. ${\mathit{CN}}_j$ is the CN value of land use type and soil type of mass j.

3.1.3. Confluence Calculation Method—Snyder Unit Line Method

Under ideal conditions, there is the following relationship between the flood peak lag time T_p and the precipitation duration T_r of the unit line:

$$T_p=5.5T_r$$

(3)

Under standard conditions, the relationship between peak flow U_p and peak time T_p of the unit line is as follows:

$$\frac{U_P}{A}=C\frac{C_p}{T_p}$$

(4)

where U_p is peak flow, m³/s. T_p is the peak time, h. A is the catchment area, km². C is the conversion coefficient; for SI units, the value is 2.75. C_p is the unit line peak coefficient with values ranging from 0.4 to 0.8.

When the actual basin is very different from the ideal condition, the following changes should be made for the peak duration of the unit line:

$$T_{pR}=T_p-\frac{T_r-T_R}{4}$$

(5)

where $T_{pR}$ is the expected peak duration of the unit line. $T_R$ is the expected unit line period; that is, the set time step.

In 1992, Bedient and Huber [31] proposed the calculation formula of expected peak duration of unit line as follows:

$$T_{pR}=\mathrm{C}{C}_t{\left(L{L}_c\right)}^{0.3}$$

(6)

where L is the length of the main stream of a basin, Lc is the distance from the basin center to the basin outlet, C is the conversion constant, which is 0.75 in international units, and C_t is the stagnation of the basin coefficient, usually taking 1.8 to 2.2.

3.1.4. Confluence Calculation Method—Unit Line Method

The relationship between peak flow and peak occurrence time of unit line is as follows:

$$U_p=C_1\frac{A}{T_p}$$

(7)

$$T_p=\frac{∆t}{2}+t_{lag}$$

(8)

where $C_1$ is the conversion coefficient; for SI units, the value is 2.08. $∆t$ is net rainfall duration. $t_{lag}$ is the lag time of the basin; that is, the time difference between the peak of the unit line and the location of the net rain center. $t_{lag}$ can be obtained by formula as follows:

$$t_{lag}=\frac{l^{0.8}{(S+25.4)}^{0.7}}{7069.7y^{0.5}} \mathrm{and} S=\frac{25400}{\mathit{CN}}-254$$

(9)

where l is the length of channel, m. S is the maximum possible amount of stagnant water in the basin, mm. y is watershed slope, whose value can be extracted by HEC-GeoHMS tool.

3.1.5. Confluence Calculation Method—The Muskingum Method

The Muskingum method is a channel confluence algorithm based on tank storage equation and water balance equation and widely used in basin routing because of its simplicity, high efficiency, and relatively low data requirement [32]. The segmental Muskingen method, Muskingum–Cunge method with the nonlinear calculus [33,34,35], and the meshing calculus, as well as the Muskingum–Cunge–Todini with variable parameter method [36,37] were proposed successively.

There are two important model parameters in the Muskingum method: slope K of the tank storage curve and specific gravity factor of discharge X. The estimation formulas are as follows [19]:

$$K=\frac{∆L{n}^{0.6}}{1944\lambda S_0^{0.3}{Q}_0^{0.2}}$$

(10)

$$X=\frac{1}{2}-\frac{n^{0.6}{Q}_0^{0.3}}{5.14\lambda S_0^{1.3}∆L}$$

(11)

where $∆L$ is the length of river, m. n is the roughness coefficient. $\mathsf{\lambda }$ is the conversion coefficient. $S_0$ is the gradient of the riverbed. $Q_0$ is steady flow, m³/s.

3.2. Simulation Method for Regulation and Storage of the Reservoirs in the Upper Reaches

There is 1 large-sized reservoir which is Gaoya reservoir, 3 middle-sized reservoirs including Daguan Reservoir, Yishan Reservoir, and Shangzhuang Reservoir, and 93 small-sized reservoirs in the upper reaches. The projects greatly increase the difficulty of the flood forecast.

3.2.1. Large-Sized Reservoir

For the large upstream Gaoya reservoir, it can be seen from the water level information after the beginning and end of each flood that the maximum water level datum is about 153.0 m. The water storage and discharge rules are simulated by using the top overflow model on a horizontal dam. The water storage capacity of the reservoir is represented by the relation between water level and storage capacity (seen in

Table 3. The relationship between the water level and capacity of the Gaoya Reservoir.

Water level/m	131.6	132	133	134	135	136	137	138	139	140
Capacity/104 m3	0	0.14	2.38	13.29	43.92	100.4	187.1	304.3	446.4	637.8
Water level/m	141	142	143	144	145	146	147	148	149	150
Capacity/104 m3	893.9	1208	1577	1990	2455	2973	3534	4152	4810	5500
Water level/m	151	152	153	154	155	156	157	158	159	160
Capacity/104 m3	6245	7051	7931	8904	9985	11,175	12,478	13,888	15,430	17,080

and Figure 6).

The initial storage capacity is obtained according to the input initial water level conditions of the reservoir. The dam top elevation is set at 153.0 m; when the water level is lower than 153.0 m, all the incoming water is intercepted, and when the water level exceeds 153.0 m, the excess water is discharged and the overflow length of the dam top is set to 40 m.

3.2.2. Small and Medium-Sized Reservoirs

In order to assess the impact of small and medium-sized reservoirs, the concept of virtual aggregation is employed to simulate the influence of water conservancy projects on production and confluence in the basin by creating aggregate reservoirs. The specific steps are as follows:

(1) Aggregation of small and medium-sized reservoirs. The study area is divided into 22 sub-basins; the small and medium-sized reservoirs located in the same sub-basin are aggregated into a virtual reservoir by analyzing the distribution. Those reservoirs upstream are then aggregated into seven virtual reservoirs (AR1, AR2, AR3, AR4, AR5, AR6, and AR7), as shown in Figure 7.

(2) Determination of water level–storage capacity relationship for aggregate reservoir. The “Add Reservoir” module in HEC-HMS is utilized to add those virtual reservoirs using a dam top overflow mode to replace their storage and discharge processes. Since an aggregate reservoir consists of several smaller ones, it can be assumed as a circular platform with its total volume representing the total storage capacity. By establishing this relationship based on a circular platform model (narrow at the bottom and wide at the top), we can obtain the water level–storage capacity curve for the aggregate reservoir, as depicted in Figure 8.

(3) Determine the moisture of the land according to the previous rainfall. If the initial water level is known, the initial storage capacity and interception capacity of the aggregate reservoir can be obtained from Figure 8.

The initial water level is closely related to the previous rainfall amount, evaporation, and water consumption, and the previous rainfall amount is an important factor. Firstly, according to the catchment area and the available storage capacity [11] of small and medium-sized reservoirs, the interception capacity P_t of the aggregate reservoir is calculated, as well as the cumulative rainfall P_1f, P_2f, and P_3f of the 15 days, 30 days, and 60 days before the occurrence of the flood, respectively, are calculated, and the rainfall is divided into three categories including arid, semi-arid, and humid [12] according to the formula as follows:

$$\left\{\begin{array}{cc}\left(P_{3f}<P_t\right)\mathrm{or}\left(P_t\le P_{3f}<2P_t\mathrm{and} P_{3f}>k\times P_{2f}\right)\hfill & \hfill \mathrm{arid}\\ \left(P_t\le P_{3f}<2P_t \mathrm{and} P_{3f}\le k\times P_{2f}\right)\mathrm{or}\left(2P_t\le P_{3f}\le 3P_t \mathrm{and} P_{3f}>k\times P_{2f}\right)\hfill & \hfill \text{semi-arid}\\ \left(P_{1f}\ge 2P_t\right)\mathrm{or}\left(2P_t\le P_{3f}\le 3P_t \mathrm{and} P_{3f}\le k\times P_{2f}\right)\mathrm{or}\left(P_{3f}>3P_t\right)\hfill & \mathrm{humid}\end{array}\right.$$

(12)

where k is the weight coefficient, k ≥ 2. $P_{3f} \le k \times P_{2f}$ indicates that the rainfall is mainly concentrated in the beginning of the flood season to the previous month. $P_{3f} \le k \times P_{2f}$ indicates that the rainfall mainly occurred within one month before the occurrence of rainfall.

(4) Determine the initial water level of the aggregate reservoir. When under arid conditions, assuming the aggregate reservoir water level is zero, the reservoir intercept ability is the strongest. When it is wet, it is assumed that the water level is located at the elevation H of the wide-top weir, and the reservoir is in the full state; at this time, the reservoir has almost no interception effect on the runoff generated by rainfall. In the case of semi-drought, assuming that the level of the aggregate reservoir is H/2, the retention capacity is half of the maximum retention capacity.

The total catchment area of the small and medium-sized reservoirs is 329 km² and the total storage capacity is 43.61 million m³. The interception capacity of the aggregate reservoirs can be calculated to be 132.6 mm. According to the above classification methods, the nine floods selected for simulation research are classified as shown in

Table 4. Classification for the floods selected for simulation research.

Flood Number	P1f (mm)	P2f (mm)	P3f (mm)	Classification
22 August 1998	104	211.4	400.4	wet
11 October 2003	13.5	24.8	258.4	arid
11 August 2011	140.4	173.9	330.5	wet
6 July 2017	60.5	63.5	90.2	arid
2 August 2017	38	200.9	263.4	wet
23 July 2018	6	236.1	263.7	semi-drought
18 August 2018	41	169.4	405.5	wet
10 August 2019	95	110.5	147.5	semi-drought
23 July 2020	40.4	101.1	144.7	semi-drought

.

3.3. Parameter Calibration

Two methods are used to automatically adjust the model parameters. The first is the Nelder–Mead algorithm, proposed by Nelder and Mead, for finding the extreme value of a multidimensional function, and the second is the Percent Error Peak function, one of the seven optimization objective functions provided in HEC-HMS. The automatically obtained parameter values would often ignore the actual physical meaning of the parameters, resulting in unreasonable values. Then, the unreasonable values are fine-tuned according to the actual meaning of parameters to obtain the calibration values of model parameters. The parameter calibration process is shown in Figure 9, the optimization results of flow-producing and confluence parameters in the method set 1 and set 2 are shown in

Table 5. Optimization results of flow-producing and confluence parameters.

Method Set 1					Method Set 2
Sub-Basin	Ia/mm	Stable Permeability fc/(mm/h)	Time Lag of the Basin tpR/min	Peak Coefficient Cp	Area/km2	CN Value	Time Lag of the Basin tpR/min
W510	14.2	2.96	228	0.51	43.5	70	179.6
W560	13.6	2.48	272	0.75	66.5	72	158.2
W590	12.4	2.59	449	0.51	148.5	75	335.4
W610	13.2	1.94	341	0.22	104.6	79	212.5
W640	14	2.66	197	0.55	32.2	76	127.9
W650	11.2	2.98	93	0.68	10.4	77	46.9
W660	11.1	2.07	324	0.61	72.2	74	260.6
W690	14.1	3.34	356	0.59	139.4	80	264.2
W700	13.4	2.35	192	0.43	57.8	66	161.7
W720	13.1	2.30	80	0.40	5.1	69	60.6
W740	11.8	2.68	218	0.37	42.3	66	192.6
W780	14.4	2.70	124	0.42	12.2	74	83.0
W790	11.5	3.31	195	0.54	60.7	76	148.2
W800	13.8	2.54	161	0.59	26.1	73	128.2
W810	12.8	2.85	186	0.15	60.7	71	139.2
W850	13.6	2.35	202	0.39	60.2	65	167.0
W860	11.8	3.00	157	0.78	10.9	63	137.0
W880	11.5	2.14	142	0.63	37.8	69	108
W890	13.1	2.72	176	0.50	48.1	70	136.9
W900	11.9	2.35	199	0.83	96.9	71	167.3
W910	14.9	2.63	192	0.77	50.4	71	164.8
W920	14.4	2.13	145	0.69	63.3	72	110.7

, and the optimization results of river confluence are shown in

Table 6. The optimization results of river confluence.

Channel Number	K	X	Channel Number	K	X
R10	0.1	0.11	R240	2.1	0.22
R60	1.7	0.23	R250	1.3	0.1
R80	0.3	0.21	R260	0.5	0.26
R110	1	0.16	R270	1.2	0.13
R120	1.3	0.15	R330	0.7	0.15
R130	1.4	0.12	R340	1.8	0.29
R150	0.6	0.2	R350	1.1	0.27
R220	0.6	0.19	R360	1.8	0.19

.

4. Results and Discussions

4.1. Simulation Results

Nine flooding processes were selected for simulation, among which six floods were used to determine model parameters and three floods were verified and analyzed. The simulation results of six floods used to calibrate the model parameters are shown in Figure 10, Figure 11, Figure 12, Figure 13, Figure 14 and Figure 15. The model parameters obtained by the above calibration are used to verify the three floods, and the simulation results are shown in Figure 16, Figure 17 and Figure 18.

As can be seen from Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18, the flooding processes simulated by the two method sets are consistent with the measured ones. The errors in flood peak discharge Q and runoff depth H, difference in peak time $∆t$, and certainty coefficient C of the simulation results were compared and analyzed, as shown in

Table 7. The flood results simulated by the method set 1.

Flood Event	Flood Peak Discharge Q/m3/s			Runoff Depth H/mm			Difference in Peak Time Δt/h	Certainty Coefficient C
	Measured Value	Simulated Value	Error	Measured Value	Simulated Value	Error
22 August 1998	1375.8	1409.5	2.4%	73.84	72.11	2.3%	1	0.91
11 October 2003	368.9	424.2	15%	22.86	23.1	1.0%	1	0.83
11 August 2011	538.2	551.6	2.5%	38.19	44.33	16.1%	3	0.86
6 July 2017	1169.4	1222.8	4.6%	54.78	63.21	15.4%	2	0.92
18 August 2018	4150.4	4019.2	3.2%	185.51	200.2	7.9%	0	0.89
10 August 2019	2025	2155.5	6.4%	132	132.07	0.1%	3	0.92
2 August 2017	896.4	840.1	6.3%	57.74	61.11	5.8%	3	0.90
23 July 2018	1047.4	981.6	6.3%	40.81	41.58	1.9%	1	0.92
23 July 2020	890.5	926.2	4%	33.5	34.27	2.3%	2	0.87

,

Table 8. The flood results simulated by the method set 2.

Flood Event	Flood Peak Discharge Q/m3/s			Runoff Depth H/mm			Difference of Peak Time/h	Certainty Coefficient
	Measured Value	Simulated Value	Error	Measured Value	Simulated Value	Error
22 August 1998	1375.8	1331	3.3%	73.84	62.96	14.7%	2	0.88
11 October 2003	368.9	414.3	12.3%	22.86	25.41	11.2%	1	0.78
11 August 2011	538.2	507.4	5.7%	38.19	34.89	8.6%	3	0.84
6 July 2017	1169.4	1225.3	4.8%	54.78	49.97	8.8%	2	0.92
18 August 2018	4150.4	4293.1	3.4%	185.51	203.7	9.8%	2	0.79
10 August 2019	2025	2071.3	2.3%	132	109.52	17%	2	0.87
2 August 2017	896.4	942.5	5.1%	57.74	59.5	3.0%	2	0.89
23 July 2018	1047.4	1107.7	5.8%	40.81	48.27	18.3%	0	0.88
23 July 2020	890.5	968.5	8.8%	33.5	40.08	19.6%	1	0.87

and

Table 9. Comparison and analysis of the simulation results from two method sets.

Period	Flood Event	Method Set 1				Method Set 2
		Error of Q/%	Error of H%	Δt/h	C	Error of Q/%	Error of H%	Δt/h	C
Calibration period	22 August 1998	2.4	2.3	1	0.91	3.3	14.7	2	0.87
	11 October 2003	15.0	1.0	0	0.85	12.3	11.2	1	0.77
	11 August 2011	2.5	16.1	3	0.86	5.7	8.6	3	0.8
	6 July 2017	4.6	15.4	2	0.92	4.8	8.8	2	0.91
	18 August 2018	3.2	7.9	1	0.87	3.4	9.8	2	0.79
	10 August 2019	6.4	0.1	3	0.91	2.3	17.0	2	0.87
Validation period	2 August 2017	6.3	5.8	2	0.9	5.1	3.0	2	0.89
	23 July 2018	6.3	1.9	1	0.92	5.8	18.3	0	0.88
	23 July 2020	4.0	2.3	2	0.87	8.8	19.6	1	0.78
Mean value		5.63	5.87	1.67	0.89	5.72	12.33	1.67	0.84

.

As can be seen from Table 9,

(1) The flood peak errors simulated by method set 1 are between 2.4% and 15%, with an average error of 5.63%, and those simulated by method set 2 are between 2.3% and 12.3%, with an average error of 5.72%. Except the floods on 11 October 2003 and 10 August 2019, the flood peak error of the other seven fields simulated by method set 1 is smaller than those simulated by method set 2. The simulated runoff depth errors of method set 1 are between 0.1% and 16.1%, with an average value of 5.87% and those of method set 2 are between 3.0% and 19.6%, with an average value of 12.33%. It can be seen that the accuracy of the simulation results of the two method sets meets the requirements of Class B accuracy of the “Water forecast Code” [38]; that is, the two simulation method sets can be used for the flood forecast of the Moushan Reservoir basin, and method set 1 shows better simulation results compared to method set 2.

(2) The average simulation certainty coefficient of method set 1 and set 2 are both greater than 0.7, which meets the accuracy requirements of Class B and can be used for flood forecasting. The average simulation certainty coefficient of method set 1 is 0.89 and that of method set 2 is 0.85, which also shows that the simulation effect of method set 1 is better than that of method set 2.

(3) According to Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18, considering the regulation and storage function of small and medium-sized reservoirs, both methods have better simulation effects, and the simulated flooding process is more consistent with the actual flooding process, which solves the difficult problem of flood simulation and provides a reference for other river basin flood simulations.

(4) By using the reservoir module of HEC-HMS, the initial water level of the aggregate reservoir is determined by considering the three initial states of “drought, semi-drought and wet”, ensuring accurate flood holding capacity to accommodate incoming flooding process curves and improve flood forecasting accuracy.

4.2. Discussions

To test the validity of the model proposed, some discussions about the model are presented below.

(1) The generalization of rainfall data results in differences between simulated and measured values. The distribution of rainfall stations in the study area are not uniform, and the areal rainfall of each sub-watershed is generalized by the Thiessen polygon method, but the areal rainfall calculated by the weight of the control area of each rainfall station in the sub-watershed is too average, ignoring the influence of the rainstorm center. The rainstorm center has an obvious peaking effect, which has a great influence on the flood peak and the confluence time, so there are differences between the simulated values and the measured values.

(2) The setting of the aggregation reservoir causes the difference between the simulated values and the measured values. In this paper, there are some shortcomings in considering the influence of small and medium-sized reservoirs. The uneven spatial distribution of small and medium-sized reservoirs is not taken into account in the model, and the storage capacity of small reservoirs is only a quantitative estimate. Therefore, with the reinforcement of small reservoirs and the increase in monitoring stations in the basin overcoming the lack of data at present, a distributed hydrological model should be established to simulate the influence of a large number of upstream water conservancy projects on the downstream hydrological process, and the accuracy of watershed flood simulation could improve.

(3) The difference in runoff depth between simulated results and measured values. The flood control standards of small reservoirs in the basin are not high, and this paper does not consider the phenomenon of a sudden increase in water intake in the reservoir caused by dam break and dam collapse under extreme circumstances. In addition, there are a large number of small reservoirs in the study area. This paper generalizes these reservoirs and greatly improves the accuracy of flood simulation. However, the generalized treatment results are different from the actual situation, especially the small water storage buildings such as ponds and dams, which will partially intercept flood waters, resulting in the simulated runoff depth generally being slightly larger than the actual situation.

(4) Calculation accuracy of storage capacity of small and medium-sized reservoirs. The model of the aggregation reservoir established in this paper only considers the influence of small and medium-sized reservoirs on flooding, and the storage capacity of aggregation reservoirs is mainly calculated according to the soil water content in the early stage. However, actually, the influencing factors of hydraulic engineering should generally be considered in addition to the upstream small and medium-sized reservoirs, as well as ponds and dams, farmland, and water blocking projects on rivers, etc., and the influencing factors for the impaction of reservoirs are not only the soil water storage in the early stage. So, in future studies, the influence of other hydraulic projects and other indicators affecting storage capacity can be added to further improve the model.

Despite the analysis of the above shortcomings, the simulation results of the established model still meet the accuracy requirements and can provide more accurate forecast information for defense decisions such as flood control scheduling, according to the result analysis in 4.1. Of course, aiming at the above shortcomings, the following research plan will further improve accuracy.

(5) Further research plans for flash flood simulation methods. The above analysis and discussion results show that the rainfall center and the setting of the aggregate reservoir have an important influence on the flood simulation accuracy. Therefore, it is planned to carry out studies on the regulating effect of rainfall distribution and reservoir aggregation methods on the confluence process of small and medium-sized reservoirs; for example, calculating the water storage capacity of both upper and lower soil layers in the basin by developing a model to simulate and rate various types of floods and then determine the soil water content over the first 30 days using the Thiessen polygon method to weight the rainfall of each sub-region and calculate the preliminary filling rate and storage capacity of the aggregate reservoir to improve the calculation accuracy of flood peak discharge and peak time.

(6) The focus of this paper is how to consider the impact of upstream water conservancy projects and simulate the flooding of hilly reservoirs under extreme rainstorm conditions. The impact of climate change on rainfall and flood simulation is not taken into account. Although climate change is recognized as a key factor affecting the frequency and intensity of extreme weather events [39], studies have shown that there is a significant correlation between temperature and rainfall for the Northeastern Himalayas [40], and climate change affects the spatial distribution of precipitation and heavy precipitation [41], potentially increasing the risk of flash floods in the basin [42,43]. Therefore, research on predicting changes in climate and environmental factors and their impact on rainfall is beneficial for simulating floods in hilly area reservoirs.

5. Conclusions

This paper takes the basin of Moushan Reservoir as the research object, considers the influence of small and medium-sized reservoirs in the upstream of the basin, and summarizes them as aggregate reservoirs. HEC-HMS is used to construct the hydrological model of the basin, and two kinds of flow generation and confluence simulation methods are developed. The effects of the two method sets in the flood simulation of the basin of Moushan Reservoir are compared in terms of peak flow, runoff depth, and peak occurrence time and certainty coefficient. The main conclusions are as follows:

(1) Based on HEC-HMS, the hydrology model of the Moushan Reservoir basin is constructed by using two different production–confluence combination method sets. Both methods are suitable for flood simulation and forecast of the basin. The simulated flood peak errors of method set 1 are between 2.4% and 15%, and those of method set 2 are between 2.3% and 12.3%. The errors of simulated runoff depth in method set 1 are between 0.1% and 16.1%, and those in method set 2 are between 3.0% and 19.6%. The accuracy of the simulation results of the two method sets can meet the requirements of Class B accuracy of the “Water Forecast Code”.

(2) Of the models established by the two method sets, method set 1 can better simulate the flood in the basin of Moushan Reservoir. The average flood peak error simulated by method set 1 is 5.63%, and that simulated by method set 2 is 5.72%. The average errors of runoff depth simulated by method set 1 and method set 2 are 5.87% and 12.33%, respectively. The simulated average certainty coefficient of method set 1 is 0.89, and that of method set 2 is 0.85. Therefore, the simulation effect of the first method is better than that of the second method in the Moushan Reservoir basin in terms of the certainty coefficient, the precision of the peak discharge, and the precision of the runoff depth.

(3) Many small and medium-sized reservoirs in the basin are summarized as aggregate reservoirs and dynamic parameters are used to reflect the regulation and storage functions under the three scenarios of drought, semi-drought, and humid, which can better reflect the influence of small water conservancy projects on confluence, solve the problem of flood simulation difficulties caused by small and medium-sized reservoirs, and facilitate the realization of flood prediction for the basin. It provides the basis for the next flood control operation and has certain reference significance for other related river basins.

(4) In order to enhance the accuracy of basin flood simulation and forecasting, further research on the impact of climate change on rainfall distribution and intensity is crucial for addressing the precision issue caused by above-average area rainfall. As well, for calculating the aggregation and storage capacity of small and medium-sized reservoirs, more factors should be taken into account. It is necessary to improve the model or establish a watershed-distributed hydrological model so as to better reflect the impact of small and medium-sized reservoirs on the basin flooding process.