Study on Dynamic Early Warning of Flash Floods in Hubei Province

Abstract

Flash floods are ferocious and destructive, making their forecasting and early warning difficult and easily causing casualties. In order to improve the accuracy of early warning, a dynamic early warning index system was established based on the distributed spatio-temporally mixed model through a case study of riverside villages in Hubei Province. Fully taking into account previous rainfall and assuming different rainfall conditions, this work developed a dynamic early warning threshold chart by determining critical rainfall thresholds at different soil moisture levels (dry, normal, wet, and saturated) through pilot calculations, to support a quick query of the critical rainfall at any soil moisture level. The research results show that of the 74 counties and districts in Hubei Province, more than 50% witnessed higher mean critical rainfall than empirical thresholds when the soil was saturated, and about 90% did so when the soil was dry. In 881 towns, a total of 456 early warnings were generated based on dynamic thresholds from 2020 to 2022, 15.2% more than those based on empirical thresholds. From the perspective of total rainfall, dynamic early warnings were generated more frequently in wet years, while empirical early warnings were more frequent in dry years, and the frequency of two warnings were roughly the same in normal years. There were more early warnings based on empirical thresholds in May each year, but more based on dynamic thresholds in June and July, and early warnings generated based on the two methods were almost equal in August and September. Spatially, after dynamic early warning thresholds were adopted, Shiyan and Xiangyang, both northwestern cities in Hubei Province, witnessed significant increases in early warnings. In terms of the early warning mechanism, dynamic early warning took into account the impact of soil moisture and analyzed the flood discharge capacity of river channels according to the flood stage of the riverside villages. On this basis, the rainfall early warning thresholds under different conditions were determined. This is a refined early warning method that could improve the accuracy of flash flood warnings in Hubei Province.

1. Introduction

Flash floods are abrupt and destructive, and often hit remote mountainous areas with poor transportation and communication, making forecasting and early warning very difficult [1]. There are two common flash flood forecasting and early warning methods: one is based on distributed hydrological models, such as the flash flood forecasting system (HEC-DHM) developed by the University of Maryland based on distributed hydrological models, and the flash flood early warning system developed by Japan International Cooperation Agency (JICA); the other is the dynamic critical early warning method that takes into account initial soil moisture, e.g., the FFG (flash flood guidance) system [2]. With improvements in weather prediction models at a finer spatial scale and prediction reliability, combining WRF with hydrological models can provide useful insights and predict a disaster some days before its occurrence [3,4]. The level and frequency of social risk are determined by the frequency distribution of deaths, and the risk probability of floods and landslides is ultimately described by the Bayesian model [5]. The catastrophe model was used to evaluate outburst floods in mountainous areas around Vienna [6]. From a spatio-temporal perspective, one article [7] proposed a new approach to dynamic risk assessment of mountain hazards, which combines the vulnerability of those affected by hazards with the same comprehensive intensity, frequency, and loss. Based on threshold changes within a probabilistic framework, a multi-stage early warning system was proposed for heavy precipitation events [8]. Another article [9] put forward a risk assessment framework to quantify the reliability of rainfall thresholds in flash flood early warning; the framework should be subject to uncertainties in rainfall characteristics, including rainfall duration, depth, and storm pattern. It was necessary for Toowoomba, an inland city hit by a severe flash flood in January 2011, to improve its flood warning system, as timely communication and decision-making on early warning is vital to the mitigation of flash flood hazards [10]. The mental models study method was also used to study flash flood warning systems and the context of flash flood risk decisions [11].

Static critical rainfall thresholds were commonly used in China prior to 2012 [12], and flash flood early warning was mainly based on empirical statistics, water level, discharge routing, and hydrological models [13]. The corresponding rainfall, water level, and discharge to the critical state were calculated to analyze early warning thresholds. An early warning was issued when the predicted or measured value exceeded the early warning threshold [14]. Previous soil moisture levels and precipitation patterns have a significant effect on critical precipitation. An increase from 0.20 to 0.50 and 0.80 in soil saturation rate results in a decrease of 13.7–16.2% and 26.8–31.8%, respectively, in critical rainfall [15]. Through the development of the National Flash Flood Disaster Prevention and Control Project (CNFFPP) over more than a decade, China has established a multi-level, multi-stage early warning system for flash flood hazards [16,17]. According to the rainfall data used, the system covers flash flood trend early warning, meteorological early warning, nowcasting and early warning, professional monitoring and warning, and simple community early warning [18]. At present, meteorological early warning of flash flood disasters is the most important means of flash flood early warning using weather forecast data, given its long forecast period and accuracy [19]. With the development of precipitation forecasting techniques and the improvement of forecasting accuracy, meteorological early warning of flash floods based on precipitation forecasting is a future trend. In light of the need for flood risk early warning and real-time dynamic early warning, the requirements and main techniques of dynamic early warning threshold analysis were proposed, and the dynamic early warning thresholds under different pre-rain or soil moisture conditions were analyzed and determined, taking into account the impact of soil moisture on runoff concentration [20]. The authors of [21] proposed new performance criteria coupling time for immediate evacuation, time for evacuation preparation, and time when an emergency occurs, and according to the temporal differences of flash flood early warning, TOPMODEL is actually the best option.

Currently, flash flood early warning in Hubei Province is mainly based on empirical early warning thresholds and target towns. Such rough early warning takes into account neither the impact of previous rainfall on flash floods nor the difference in flood control status between different villages. Focusing on riverside villages in hilly areas in Hubei Province and in response to the need for real-time dynamic early warning of flash flood disasters, this study developed a distributed hydrological model based on the results of flash flood disaster investigation and evaluation, supplementary investigation and evaluation conducted earlier, as well as rainstorm atlas and hydrological handbooks. Then, the model was used to analyze soil moisture and dynamic rainfall warning thresholds in real time and generate dynamic early warnings of flash flood disasters. The aim is to provide data and technical support for improving the accuracy of flash flood early warning and assisting early warning decision-making.

2. Materials and Methods

2.1. Study Area

Hubei Province is located in the middle reaches of the Yangtze River, north of Dongting Lake. Between 29°05′–33°20′ N and 108°21′–116°07′ E, the province spans some 740 km from east to west, and 470 km from north to south, covering an area of 185,900 km², accounting for 1.94% of China’s total territory. Hubei lies in the subtropics, within a typical monsoon zone. Except for mountainous areas, the province enjoys a humid subtropical monsoon climate with abundant light and heat, a long frost-free period, plentiful rainfall, and rain and heat in the same season. The annual average precipitation is around 1200 mm across the province. The precipitation generally decreases from southeast and southwest to the hinterland and northwest of the province, with a regional variation range of 750–2050 mm. Due to the impact of latitudes and mountainous areas, the annual precipitation is unevenly distributed between regions; it is higher in the south than in the north, and higher in mountainous areas than in plain areas at the same latitude. The province’s precipitation is concentrated from May to September, which accounts for 63% of the annual total. From mid-June to mid-July is the plum rain season in Hubei, when there is frequent and heavy rain.

Hubei is often hit by frontal rain, local severe convection rainstorms, and tropical cyclone rainstorms in the flood season, which contribute to intensive, wide-ranging, and long-term concentrated rainfall that easily triggers flash floods. According to flash flood statistics from 2013 to 2015, Hubei Province has witnessed 1544 flash flood disasters since the founding of the PRC, resulting in 6763 people dead, 448 people missing, 1.91 million houses damaged, and direct economic losses of RMB 39.5 billion. Especially in recent years, Hubei has suffered successively from the “98+” flood in 2016, the rarely seen autumn flood in the Hanjiang River in 2017, and the flood accompanied by the COVID-19 outbreak in 2020, putting many parts of the province to the test of extraordinary floods.

2.2. Data Collection

This study mainly collected the dataset of flash flood disaster investigation and evaluation results, historical hydrological data, flash flood rainfall data in Hubei Province between 2020 and 2022, the province’s empirical early warning thresholds, and the early warning records generated by the provincial monitoring and early warning platform using empirical early warning thresholds. The types and purposes of data are shown in

Table 1. Summary of Data Collection.

No.	Description	Purpose	Data Source
1	Riverside village investigation and evaluation results	Critical rainfall analysis, and the development of a dynamic early warning threshold chart	Mountain Flood Disaster Investigation and Evaluation Project
2	Historical rainstorm flood data between 1956 and 2022	Distributed model calibration
3	Rainfall data between 2020 and 2022	Dynamic rainfall warning and calculation	The Monitoring and Warning Platform for Mountain Flood Disasters in Hubei Province
4	Empirical early warning thresholds	Early warning threshold rationality analysis
5	Early warning records between 2020 to2022 from the flash flood monitoring and early warning platform	Early warning threshold rationality analysis

.

The dataset of flash flood disaster investigation results in Hubei Province includes the results of flash flood investigations, topographic surveys, and analysis and evaluation of 12,893 riverside villages. The bankfull stage in each riverside village was surveyed and used as the critical water level, and the corresponding transverse and longitudinal profiles of the riverbed were measured. Figure 1 shows the location of these villages [22].

This study collected and organized the rainstorm flood data between 1970 and 2022 in Hubei Province, including statistical tables of rainstorm parameters at monitoring stations, annual discharge tables at hydrological stations, extracts of hydrological elements of floods, extracts of precipitation, tables of daily surface evaporation, and a list of monitoring stations. From these, 108 rainstorm flood processes in 10 typical small and medium-sized catchments from different hydrological zones throughout the province were selected for rainfall-runoff simulation.

Table 2. Information on Typical Small and Medium-sized Rivers.

Name	River Name	Hydrological Zone	Catchment Area (km2)
ChangXuanLing	SheShui	IV	1313
HuanTan	YunShui	VI	804
JiaJiaFang	TianHe	IX	1281
LiChuan	QingJiang	X	513
MaCheng	JuShui	IV	888
LongGang	LongGangHe	II	550
XingShan	XiangXi	VIII	1851
XuanEn	ZhongJianHe	X	740
YanBa	ZhuXiHe	XI	598
YuYangGuan	YuYangHe	VII	465

shows the information on 10 typical small and medium-sized catchments. Figure 2 shows the distribution of hydrologic stations in each catchment.

The data on rainfall processes from 2021 to 2022 at 2476 flash flood rainfall stations across the province were collected. The empirical rainfall warning thresholds from the province’s flash flood disaster monitoring and early warning platform were collected, mainly including 1 h, 3 h, and 6 h rainfall warning thresholds, and the early warning targeted 881 towns across the province. The early warning dataset developed by Hubei’s flash flood early warning platform using empirical early warning thresholds from 2020 to 2022 was collected.

2.3. Modelling Approaches

2.3.1. Dynamic Rainfall Warning Threshold Analysis Method

The real-time dynamic rainfall warning threshold analysis method basically involves five steps: determining early warning periods, analyzing the soil moisture in a river basin, calculating the critical rainfall, setting early warning thresholds, and a rationality analysis. The critical rainfall was calculated based on flood-stage levels and a designed rainstorm flood to establish the real-time dynamic rainfall warning threshold analysis method [23]. According to the design rainstorm flood calculation method and the typical rainstorm duration distribution, and considering the dynamic change in soil moisture, the design rainstorm in each early warning period when the design flood peak reached the discharge value was calculated, which is the critical rainfall for affected areas. The rainfall warning thresholds were determined based on a combination of the critical rainfall and the early warning response time. Rationality analysis deals with the rationality of the distributed model and of the early warning thresholds. To be specific, the distributed model is the basis of dynamic early warning, and its rationality directly determines the reliability of the early warning thresholds; the rationality of the early warning thresholds needs to be verified by factors such as early warning frequency, the spatial and temporal distribution of early warnings, and typical flash flood disasters. Among these steps, an important tool for analyzing soil moisture in watersheds and calculating critical rainfall is the distributed hydrological model. The distributed model uses a digital elevation model, land use, soil type, rainfall, and evaporation data as input to simulate rainfall-runoff, and hydrological station data with observation data to calibrate the model parameters. The criteria for calibration include flood peak error, water volume error, peak current time error, Nash–Sutcliffe efficiency coefficient, and other indicators. Figure 3 shows the flow chart of the early warning threshold analysis.

2.3.2. Hydrological Model

The structure of the distributed model is derived from the spatio-temporally mixed model developed by the China Institute of Water Resources and Hydropower Research (IWHR) [24,25,26,27,28,29,30]. The model takes into account both excess storage runoff and excess infiltration runoff, which are integrated on both temporal and spatial scales. The spatio-temporal variable source mixed runoff model mainly includes spatio-temporal variable sources and mixed runoff. Spatio-temporal variable sources refer to the spatio-temporal variation of soil moisture due to both external factors (rainfall infiltration and evaporation) and internal factors (gravity and matrix suction); mixed runoff is the process in which a river basin experiences a spatio-temporal dynamic combination of excess infiltration runoff and excess storage runoff under the spatio-temporal variation of soil moisture.

The runoff calculation process in the model includes interception and filling, basin evaporation, soil evaporation, infiltration, excess infiltration, excess storage, preferential flow, throughflow, and groundwater runoff. The five components of mixed runoff are excess infiltration surface runoff, excess storage runoff, preferential flow, throughflow, and base flow. Among them, excess infiltration surface runoff includes direct excess infiltration surface runoff over the impervious area, and excess infiltration runoff over the permeable area when the rainfall intensity is higher than the infiltration capacity; excess storage runoff includes runoff generated after the upper layer of soil is preferentially filled with water, and runoff generated as the lower layer of soil replenishes the upper layer after it is filled with water; preferential flow is the outflow from the upper layer of soil; throughflow is the outflow from the lower layer of soil; and base flow is the outflow from underground reservoirs. On this basis, the total runoff process at the outlet of a river basin was finally obtained through lake and reservoir confluence, slope runoff concentration, and river confluence. Figure 4 shows the structure of the spatio-temporally mixed model.

The spatio-temporally mixed model mainly played two roles in the research. First, the model was used to determine the critical rainfall; second, it was used to calculate the soil moisture during real-time dynamic early warning. Whether the model was rational or not directly affected the accuracy of early warning. In order to verify the rationality of the model, we selected 10 stations with long-sequence hydrological observation data from different hydrological zones for model parameter calibration and checked the model for flood peak error, flood volume error, and Nash–Sutcliffe coefficient [31,32].

In this study, the Shuffled Complex Evolution algorithm (SCE-UA) was used to calibrate the model parameters [33,34]. Through model calibration testing, the discretization and regionalization of parameters are realized to reflect the characteristics of runoff yield and concentration in different hydrological regions. Dunan et al. proposed the Shuffled Complex Evolution (SCE) global search algorithm in 1994, which is an algorithm based on population evolution. In the SCE algorithm, s solution vectors (the number of sample points) are randomly generated, and through the process of competitive evolution, mixed recombination, and elimination of the worst individuals, the overall evolution of the population is finally completed. In the algorithm, n variables are represented by an n-dimensional vector, which is a sample point. $\theta \in R^n$ is the estimated problem search space. Thus, in each iteration, the SCE algorithm uses s n-dimensional vectors, $x_i={\left[x_{i1},x_{i2},\dots ,x_{im}\right]}^T\in \theta ,i=1,2,\dots ,s$, to represent the entire population, also known as a descendant of the algorithm.

3. Dynamic Warning Threshold Analysis

3.1. Warning Period

Warning periods refer to the most typical rainfall durations used in rainfall warning thresholds. The warning period varied from basin to basin due to factors such as the size and slope of the upstream catchment area in affected areas, mainly depending on the length of the runoff concentration time in small watersheds. Since most of the targets of early warning were located by small and medium-sized rivers in hilly areas, where the runoff concentration time was within six hours, in most cases, the warning periods selected were 1 h, 3 h, and 6 h.

3.2. Soil Moisture Content

A distributed hydrological model driven by rainfall and evapotranspiration data was established, which was capped by the maximum soil water storage, Wm, and was used to calculate the soil moisture in small watersheds (Pa, 0 ≤ Pa ≤ Wm). On the one hand, the process of dynamic change in soil moisture in small watersheds needs to be stored in a database table; on the other hand, it can be used to generate soil moisture maps, as shown in Figure 5. In the figure, blue areas indicate high soil moisture towards saturation, while red areas imply low soil moisture and dryness.

3.3. Critical Rainfall

From 2013 to 2015, Hubei Province completed the investigation and evaluation of 74 counties (county-level cities and districts), finished the detailed survey and measurement in 12,893 riverside villages, conducted the measurement and sorting of 11,818 longitudinal profiles and 35,318 transverse profiles of the channels by which these villages were located, and investigated and measured the flood-stage levels there.

Through analysis and pilot calculations based on the distributed model, the critical rainfalls were determined for 12,893 riverside villages under different soil moisture conditions. The 1 h, 3 h, and 6 h critical rainfalls for the affected areas in Hubei Province under different soil conditions (dry, normal, wet, and saturated) are shown in Figure 6.

Table 3. Mean Critical Rainfall for Each City.

City	Dry			Normal			Wet			Saturated
	1 h	3 h	6 h	1 h	3 h	6 h	1 h	3 h	6 h	1 h	3 h	6 h
WuHan	94	158	207	80	132	172	68	113	143	57	95	115
HuangShi	12	187	210	102	148	178	80	119	144	66	100	120
ShiYan	95	118	127	81	102	114	70	87	104	61	76	93
YiChang	124	158	181	109	139	159	93	120	140	82	107	125
XiangYang	101	125	156	85	105	131	73	89	111	63	77	93
EZhou	94	146	188	78	123	157	69	109	133	60	91	111
JingMen	112	143	190	93	119	156	79	99	130	64	80	104
XiaoGan	109	148	211	96	133	180	85	118	156	76	109	133
JingZhou	126	168	198	103	139	166	85	114	141	70	97	118
HuangGang	131	181	205	109	154	179	90	133	156	77	109	139
XianNing	112	152	181	94	135	161	81	118	142	71	107	129
SuiZhou	144	208	251	119	178	218	102	152	191	87	133	167
EnShi	92	130	175	83	118	152	74	104	133	67	94	117

lists the mean critical rainfall for 14 prefecture-level cities in Hubei Province under different soil moisture conditions. As shown in Figure 6 and Table 3, northwestern Hubei experiences the lowest critical rainfall and northern Hubei the highest. Among the 14 prefecture-level cities, the lowest critical rainfall occurs in Shiyan and the highest in Suizhou, and the mean critical rainfall in Shiyan is 30–50% lower than that in Suizhou under different soil moisture conditions.

Based on the standard duration warning thresholds for affected areas under four typical soil moisture conditions, namely dry (0.2 Wm), normal (0.5 Wm), wet (0.8 Wm), and saturated (1.0 Wm), and taking into account the impact of upstream runoff generation and concentration processes and dynamic changes in soil moisture, the standard duration critical rainfall under other soil moisture conditions was analyzed and determined through linear interpolation.

In real-time early warning calculations, if the soil moisture was no more than 0.5 Wm, then the rainfall warning threshold corresponding to 0.5 Wm was adopted; if the soil moisture was greater than 0.5 Wm, then the corresponding early warning threshold was obtained through linear interpolation based on early warning thresholds for 0.5 WM, 0.8 WM, and 1.0 Wm. Based on flood simulation results, the study considered the discharge half an hour earlier than the critical rainfall was reached, as the discharge for evacuation preparation, and analyzed the corresponding rainfall threshold for evaluation preparation through pilot calculations. Figure 7 shows the critical rainfall levels for evacuation preparation and immediate evacuation.

4. Result and Discussion

This study selects 10 typical small and medium-sized rivers from different hydrological zones throughout the province for 108 rainfall and flood datasets for rainfall-runoff simulation. The selected data span mainly from 1970 to 2022, involving 10 hydrological stations and 105 rainfall stations. The simulation results of the HuanTan station are shown in Figure 8, and the statistical results of all the stations are shown in

Table 4. Statistics of Flood Simulation Results.

Name	Floods Number	Peak Error (%)	Water Error (%)	Peak Time Error (h)	Nash–Sutcliffe Coefficient
ChangXuanLing	18	−14.6	−10.8	4.1	0.77
HuanTan	4	−8.0	−3.3	1.4	0.86
JiaJiaFang	8	−29.4	−22.8	−2.9	0.65
LiChuan	25	−13.1	13.1	1.7	0.80
MaCheng	10	−13.5	−11.6	−6.0	0.72
LongGang	7	18.1	−12.4	−1.2	0.73
XingShan	16	−23.8	15.1	−2.1	0.72
XuanEn	3	−5.6	−27.3	−2.9	0.72
YanBa	5	−21.7	−17.0	−1.2	0.75
YuYangGuan	12	−19.7	−15.8	−1.0	0.74

.

Among the simulation results of 10 stations, 7 had an average flood peak error of no more than 20%, 8 had an average flood volume error of no more than 20%, and 9 had an average Nash–Sutcliffe coefficient of no less than 0.7.

According to the simulation results of the 108 rainstorm floods, 66 had a flood peak error of no more than 20%, accounting for 61.1% of the total; 84 had a flood volume error of no more than 20%, accounting for 77.8%; 30 and 69 had a Nash–Sutcliffe coefficient of no less than 0.85 and 0.7, respectively, accounting for 27.8% and 63.9%. The calculation results suggest strong applicability of the spatio-temporally mixed model in Hubei Province, which is also the prerequisite for accurate calculation of soil moisture and analysis of dynamic early warning thresholds.

The average of empirical warning thresholds currently adopted by the 74 counties in Hubei Province and the mean critical rainfall under different soil moisture conditions were compared, and the results show a great difference.

Table 5. Statistics of the Proportions of Counties and Districts. (Mean Empirical Threshold ≤ Mean Critical Rainfall).

Warning Period (h)	Soil Moisture
	1.0 Wm	0.8 Wm	0.5 Wm	0.2 Wm
1	54.1%	71.6%	82.4%	89.2%
3	58.1%	71.6%	83.8%	90.5%
6	51.4%	58.1%	74.3%	91.9%

provides the results of the comparison between the empirical thresholds and critical rainfall. Table 5 shows that the critical rainfall (Pa = 1.0 WM) was higher than the empirical threshold in over 50% of the counties, and the critical rainfall (Pa = 0.2 WM) was higher than the empirical threshold in about 90% of the counties. This suggests higher critical rainfall than empirical early warning thresholds in most cases. Under the critical rainfall condition of soil moisture of 0.8 WM and a period of 1 h, for example, the critical rainfall was higher than the empirical threshold in 53 counties, accounting for 71.6% of the total. Further statistics show that 15 counties and districts had a difference of less than 5 mm between the two, 23 had a difference of 5–10 mm, 19 had a difference of 10–20 mm, and 15 had a difference of more than 20 mm. When the soil moisture is lower than 0.8 Wm, rainfall warning thresholds will continue to rise as a result of the dynamic early warning mechanism, further increasing the trend that dynamic warning thresholds are higher than static thresholds and making it more difficult to generate an early warning. When the soil moisture is higher than 0.8 Wm, dynamic warning thresholds drop gradually to be lower than static thresholds, making it easier to generate an early warning. See Figure 9 for the mean values of the two by counties and districts.

As the targets of the two types of early warning thresholds are not identical, further comparisons are needed in real-world applications to verify the rationality of the thresholds and gradually improve the early warning index system. We used the rainfall data in 881 towns in Hubei Province from May to September 2020, 2021, and 2022 for simulation, and counted the frequency of early warnings based on empirical and dynamic thresholds, respectively. For the convenience of comparison, all the early warning records in a town within a day were counted as an early warning, and the statistics of the two early warning methods are shown in

Table 6. Statistics of Early Warning Frequency.

Year	Month	Monthly Average Rainfall (mm)	Warning Times
			Empirical Threshold	Dynamic Threshold
2020	5	90	4	2
	6	290	64	100
	7	324	103	130
	8	134	42	46
	9	129	1	1
2021	5	172	31	13
	6	112	19	18
	7	194	50	65
	8	246	65	63
	9	80	2	8
2022	5	42	9	0
	6	81	0	6
	7	116	1	4
	8	19	3	0
	9	25	2	0

and Figure 10.

Table 5 shows that, in May, the early stage of the flood season, soil moisture stayed at a relatively low level, and more early warnings were generated based on empirical thresholds; in June and July, usually, more dynamic early warnings were generated, and, in August and September, early warnings based on the two methods were almost equal. On the whole, more early warnings were generated after dynamic early warning thresholds were adopted than when empirical thresholds were used. Hubei Province has an annual average rainfall of about 1200 mm, of which 760 mm occurs from May to September, accounting for 63% of the annual total. According to the statistics in Table 5, the cumulative rainfall from May to September 2020 was 967 mm, 27% higher than the annual average, indicating a wet year, when 214 early warnings were generated based on empirical thresholds and 279 based on dynamic thresholds, with the latter 30.4% more than the former. The cumulative rainfall from May to September 2021 was 804 mm, indicating a normal year when 167 early warnings were generated each in the two cases; the cumulative rainfall from May to September 2022 was 283 mm, 63% less than the annual average, indicating a dry year, when 15 early warnings were generated based on empirical thresholds and 10 based on dynamic thresholds, with the latter 33.3% less than the former. From 2020 to 2022, 396 early warnings were generated based on empirical thresholds, and 456 based on dynamic thresholds, with the latter 15.2% more than the former.

Table 7. Statistics of Early Warnings in Different Cities.

City	Empirical Threshold			Dynamic Threshold
	2020	2021	2022	2020	2021	2022
WuHan	1	0	0	8	6	0
HuangShi	7	10	0	15	9	0
ShiYan	3	2	0	23	39	1
YiChang	54	45	6	43	14	3
XiangYang	17	13	2	28	26	2
EZhou	6	0	0	10	1	0
JingMen	12	8	1	23	10	2
XiaoGan	11	11	0	11	9	0
JingZhou	6	4	1	4	3	1
HuangGang	56	27	3	46	13	1
XianNing	16	21	0	22	11	0
SuiZhou	0	0	1	2	1	0
EnShi	25	26	1	43	24	0
ShenNongJia	0	0	0	1	1	0
Total	214	167	15	279	167	10

and

Table 8. Statistics of Early Warnings in Different Hydrological Zones.

Hydrological Zones	Empirical Threshold			Dynamic Threshold
	2020	2021	2022	2020	2021	2022
I	19	12	4	31	10	2
II	7	11	0	15	10	0
III	43	18	0	48	13	0
IV	21	21	1	28	18	1
V	9	7	1	0	5	0
VI	24	16	1	26	18	0
VII	31	31	3	26	11	2
VIII	29	25	4	31	12	4
IX	4	4	0	19	29	0
X	26	22	1	47	24	0
XI	1	0	0	8	17	1
Total	214	167	15	279	167	10

show the numbers of early warnings in different cities and hydrological zones in Hubei Province from 2020 to 2022. It can be seen from Table 5 that more dynamic early warnings were generated than empirical early warnings in Wuhan, Huangshi, Shiyan, Xiangyang, Ezhou, Jingmen, Xianning, and Enshi; more empirical early warnings were generated than dynamic early warnings in Yichang and Huanggang, and empirical and dynamic early warnings were almost the same in Xiaogan, Jingzhou, Suizhou, and Shennongjia. Figure 11 shows the number of early warnings in different cities and hydrological zones from 2020 to 2022. Spatially, more dynamic early warnings were generated than empirical early warnings in northwestern Hubei, especially in Shiyan and Xiangyang, which witnessed a significant increase in the number of early warnings after dynamic early warning thresholds were adopted. There may be two reasons for the high frequency of early warnings in Shiyan and Xiangyang. On the one hand, the rainstorm atlas used in this study is too old, which may be different from the actual situation. On the other hand, the flood-stage levels determined by the analysis and evaluation may be too conservative, leading to lower critical rainfall than normal.

5. Conclusions

In this study, the spatio-temporally mixed model of Hubei Province was constructed; combined with the investigation and evaluation result datasets, the critical rainfall of villages along the river was determined, and a comprehensive comparative analysis was conducted with the empirical threshold. The main results are as follows:

(1)

A total of 108 rainstorm flood processes in 10 typical small and medium-sized rivers were selected from different hydrological zones across Hubei Province for rainfall-runoff simulation. The data selected span from 1970 to 2021, involving 10 hydrological stations and 105 rainfall stations. According to the simulation results of the 108 rainstorm floods, 66 had a flood peak error of no more than 20%, accounting for 61.1% of the total; 84 had a flood volume error of no more than 20%, accounting for 77.8%; 30 and 69 had a Nash–Sutcliffe coefficient of no less than 0.85 and 0.7, respectively, accounting for 27.8% and 63.9%. This suggests the strong applicability of the spatio-temporally mixed model in Hubei Province, which also lays a solid foundation for the calculation of soil moisture and the analysis of dynamic early warning thresholds.

(2)

Through analysis and pilot calculations based on the distributed model, the study determined the critical early warning thresholds for 12,893 riverside villages under different soil moisture conditions and analyzed the 1 h, 3 h, and 6 h critical rainfall thresholds under different soil moisture conditions in affected areas in Hubei Province. The lowest critical rainfall threshold was observed in northwestern Hubei and the highest was in northern Hubei. Among the 14 prefecture-level cities, the lowest critical rainfall threshold occurs in Shiyan and the highest in Suizhou, and the mean critical rainfall in Shiyan is 30–50% lower than that in Suizhou under different soil moisture conditions.

(3)

Both empirical and dynamic thresholds were used for early warning calculations. The results show that, from 2020 to 2022, 396 early warnings were based on empirical thresholds and 456 based on dynamic thresholds, with the latter 15.2% more than the former. Compared with empirical thresholds, dynamic thresholds were relatively high in May, with fewer early warnings; they were relatively low in June and July, making it easier to generate an early warning; the two were almost the same in August and September. From the perspective of total rainfall, more frequent dynamic early warnings were generated in wet years, while more frequent empirical early warnings were generated in dry years, and the two were roughly equally frequent in normal years. Spatially, after dynamic early warning thresholds were adopted, early warnings increased significantly in northwestern Hubei Province, especially in Shiyan and Xiangyang. Dynamic early warning considers the influence of previous soil moisture on the formation of flash floods, uses different flood-stage levels based on the profile survey results in each riverside village, and analyzes the flood discharge capacity of river channels. On this basis, the rainfall warning thresholds under different conditions were formulated. Due to the short sample sequence time, it is currently impossible to clearly infer that the dynamic rainfall warning threshold is better than the empirical threshold, but it can provide valuable reference for similar research.

(4)

The determination of early warning thresholds is a long-term process, as these thresholds need to be corrected from time to time in the process of application. In the future, on the one hand, it is essential to integrate supplementary investigation and evaluation data and the results of dynamic inventory management of hazardous areas, and complete the analysis of dynamic early warning rainfall thresholds for a larger range of hazardous areas; on the other hand, it is necessary to conduct an ongoing analysis of the rationality of dynamic rainfall warning thresholds based on flash flood disasters. The verification of rainfall warning thresholds is a long-term endeavor, which requires the correction of early warning thresholds at regular intervals in light of the data on floods that take place from time to time. It is recommended to carry out the practical application after 2–3 years of review.