Flash floods are among the most dangerous natural hazards with possible significant damages and human casualties. In China, due to the frequently occurred summer rainstorms and the complex topo-geological conditions, flash flood in hilly area is one of the most severe natural hazards in terms of human deaths and economic losses, constituting 87.6% of the deaths in all kinds of flood disasters . During 2011~2015, 758 small-sized and medium-sized flash flood disasters occurred in China, resulting in 1594 deaths and missing . Therefore, flash flood forecasting should be investigated in detail because it can provide early warnings, and thereby is of great significance for flood prevention, disaster relief and public safety.
In general, flash floods are generated by extreme rainfall events with high intensities shortly followed by a strong and fast flow , and usually occur in small catchments with a drainage area of a few hundred square kilometers . The short lead time and small size of such catchments enhance the difficulty for authorities to take measures. Over the past decade, there have been a range of developments in flash flood forecasting, among which the early-warning indexes and flow forecasting models are two effective tools . The rainfall threshold (also known as flash flood guidance) is the most commonly used among the early-warning indexes as it is easily understood by the general public , whereas it has inadequate explanations of the rainfall-runoff process and the spatial heterogeneity of rainfall and underlying surface. However, the hydrological models, which are theoretical representations of a part of the hydrologic cycle, can take into account the complex generation processes of flash flood, as well as their dependency on different factors related to catchment properties and rainfall spatio-temporal variations. They are widely used for the prediction of flood and for issuing timely warnings. The use of a hydrological model is necessary since the use of hydrological measurements can be very limited . Based on the hydrological mechanism analyses and hydrological process calculations, the time, location, scale, damage range and possible losses caused by flash flood are estimated in advance, and then decision support for flood prevention and disaster relief is provided.
A variety of hydrological models have been successfully applied in flash flood simulation and forecasting [8, 9]. Empirical models (e.g., neural network, statistical) are data-driven that use statistical relationships derived from rainfall events and river discharge data to generate flow forecasts. They usually require long-term data records to train or calibrate, and are site-specific. The conceptual model, such as HBV-96 and TOPMODEL, use semi empirical equations and require several hydrological and meteorological data. Kobold and Brilly applied the HBV-96 MODEL for flash flood forecasting in Savinja catchment with a shorter time step of one hour, proving that the HBV-96 MODEL is capable of simulating flash floods and can be used in pre-warning systems . The process-based models, however, can explicitly represent the mechanisms and physical processes in the real system. Oleyiblo and Li examined the applicability, capability and suitability of HEC-HMS for flood forecasting in Misai andWanan catchments in China, obtaining a fairly accurate simulation results in flood events, volume and timing . In addition, a number of studies have applied a mixture of these models and conducted comparative analysis on the applicability of models in flash flood forecasting. Deng et al. evaluated the applicability of TOPMODEL and Xinanjiang (XAJ) model in the Buliu River Basin in the southeast of China ; the two models are comparably efficient, while TOPMODEL is more advisable due to its simple structure and fewer parameters required. Ye et al. applied two widely used hydrological models, i.e., XAJ and Antecedent precipitation index (API) to forecast flash flood in medium and small rivers in humid regions of China . Results indicated that whilst both models perform well, the XAJ model outperformed the API in capturing the peak discharge and deterministic coefficient.
Among hundreds of hydrological models, there is likely no existing a single model that is universally applicable in predicting flash floods for all catchment types. Studies have found that the same model can have completely different applicability in different regions, and the suitability of a hydrological model to a particular catchment depends largely on the local hydro-meteorological characteristics and the conditions of the underlying surface. Kan et al. used the XAJ, mix runoff generation (MIX) and Northern Shannxi (NS) models in three arid catchments ; while only the NS model can obtain acceptable results. Compared with the humid regions, the XAJ model generally performed poorly in semi-arid and arid regions with respect to peak flow, total volume and peak flood time, primarily due to the differences in rainfall characteristics (e.g., intensity, duration, total amount) and runoff generation mechanisms. Thus, it is essential to have a better understanding on the applicability of various models in regions under different climate conditions and underlying features.
At present, a single hydrological model is developed to simulate flash floods for a particular catchment, seldom studies attempt to compare the performance of different hydrological models applied to multiple catchments based on available data in hilly area. The selection of the hydrological models is usually done based on the experience of the researchers, which can lead to great randomness. Further, the terrain and climate characteristics vary greatly across China. The properties of small catchments in hilly area distributed in different locations are all unique, the uniqueness will certainly exacerbate the difficulties in hydrological model selection. In short, suitable hydrological model selection for specific catchment remains a difficult challenge that is yet to be solved; the problem is compounded with the fact that monitoring facilities for hydrological data is poor in hilly areas.
In this paper, five widely used hydrological models, varying in runoff mechanism and complexity, are selected for flash flood simulation. Their comparative analysis and applicability in fourteen typical catchments of hilly area across China are summarized. The expected research results could provide guidance for hydrological model selection according to the characteristics of small catchment and available data in flood disaster prevention and control work. The remainder of this paper is organized as follows: section 2 briefly describes five widely used hydrological models, and the model parameter calibration algorithm. Section 3 introduces the study catchments and the data used for simulation. Section 4 consists of results and discussion. Finally, summary and conclusions are drawn in Section 5.
2.1 Brief Description of Hydrological Models
Various hydrological models have been developed around the world with different degrees of complexity, from simple empirical formulae or correlations to the complex mathematical models. In this paper, five frequently used hydrological models were selected from large variety of available models to simulate the hydrologic processes, including three lumped hydrologic models (the Antecedent precipitation index (API), the Xinanjiang (XAJ), the Dahuo-fang (DHF)), a semi-distributed hydrological model (TOP-MODEL), and a distributed hydrological model (HEC-HMS). The hydrological models are briefly described below.
2.1.1 The Antecedent Precipitation Index Model
The Antecedent precipitation index (API) model is a classic lumped hydrological model based on empirical rainfall-runoff relationship, and the concentration process is usually simulated by unit hydrograph. Detailed descriptions of the API hydrological model can be found in relevant literatures [15, 16]. API model uses the average precipitation of multi-field floods and the total runoff, as well as the main flood affecting factors (the most commonly used is antecedent precipitation, Pa) to establish the P~Pa~R curves (P: precipitation, R: runoff). The API model is widely used in humid areas because of its simplicity to understand and use.
For a long time, China’s economy developed very slowly in hilly areas. Therefore, monitoring facilities for hydrological data and investment in these areas are insufficient. Until recent years, China has started to build automatic monitoring system in provinces where serious flash floods occur . As a consequence, small catchments in hilly area in China usually lack long-term observed data, this brings difficulties to obtain standard P~Pa~R curves and limits the application of API model to some degree. In this paper, the traditional P~Pa~R curves are simplified to adapt to the limited observed data. In general, flash floods are characterized by their rapid onset (usually within six hours after rainfall), the period between the flood peak and the rainfall is very short. Therefore, the infiltration process in humid and semi-humid region is not obvious and can be neglected for practical convenience. As it will be shown in this paper, the runoff process is divided into two lines to approximate the smooth P~Pa~R curves, in which the turning point is judged on the occurrence of the whole catchment storage excess runoff. By doing so, we can expand the application of the API hydrological model in hilly areas with less observed data.
2.1.2 The Xinanjiang Model
The Xinanjiang (XAJ) model is a lumped hydrological model which takes the influence of uneven underlying surface to runoff yield area into consideration by using storage capacity curve of the catchment. The concept of runoff formation on repletion of storage is applied to calculate runoff production, which implies that runoff is not produced until the soil water content of the aeration zone reaches its field capacity, and thereafter the excess rainfall becomes runoff without further loss [18, 19]. The total runoff is subdivided into three components, including surface runoff, interflow and groundwater runoff, based upon the free water capacity distribution curve, the surface runoff is the fastest and the groundwater is the slowest in terms of flow velocity. The flooding process is divided into two stages, namely overland flow and the river networks concentrations. The overland flow concentration is calculated by multiple linear reservoirs method. The runoff is then routed down the river channels to the whole catchment outlet using the Muskingum successive routing method . The core of the XAJ model is the concept of storage excess runoff generation mechanism, it has been widely applied in China for decades and has achieved great success in humid and semi-humid areas.
2.1.3 The Dahuofang Model
The Dahuofang (DHF) model  is a lumped hydrological model which adopts an eight-parameter excess infiltration runoff mode and a double-layer infiltration rate curve for loss reduction calculation . The distributions of surface water storage and subsoil permeability rate are described by the parabolic equation. The convergence part is calculated by a parameter variable-strength, variable-speed empirical unit hydrograph. The model can calculate runoff generation based on the characteristics of each unit and concentrate the outflow of each unit along the river course to the basin outlet to obtain the runoff at the basin outlet . The evapotranspiration component is represented by double-layers mode, in which the surface adopts the average evapotranspiration capacity of the whole catchment and the subsoil begins to evaporate when the water demand in surface is evaporated. The DHF hydrological model is mainly applied in the arid and semi-arid areas in northern China.
2.1.4 The TOPMODEL
The TOPMODEL is a semi hydrological distributed model which uses the relationship between topographic information and runoff generation . It can also be recognized as a variable contributing area conceptual model. The total runoff is generally the sum of two major flow components: saturated excess overland flow from variable contributing areas and subsurface flow from the vadose zone. When the water content in the aeration zone reaches saturated water content, indicating that the water content of the complete gravity drainage is satisfied, the water in the soil becomes free water that flows completely under the action of gravity . It can be used in single or multiple sub catchments using gridded elevation data of the catchment. The major factors considered in the model are the catchment topography and soil transmissivity . The TOPMODEL can be used to predict runoff in data scarce areas because of its parameter parsimony, structural simplicity and explicit interpretation of the physical concepts, which has been proved to have a good performance in wet, semi-humid and semiarid areas [7, 27].
2.1.5 The HEC-HMS Model
The HEC-HMS is a distributed hydrological model that contains three sections HEC-GeoHMS, HEC-DSSVue and HEC-HMS , which play different roles in the model. The HEC-GeoHMS is a GIS companion product used to create catchment and meteorological models by processing the distributed data such as DEM, land use and soil type reflecting the characteristics of the underlying surface. The HEC-DSS is a data management system which can effectively store and update precipitation and runoff data. The HEC-HMS hydrological model simplifies the actual runoff process, without considering the interaction between the river, the ground and underground aquifers, it merges the overland flow and interflow into direct runoff. The model has the advantages of simple structure and comprehensive consideration of climate and underlying conditions, and can choose different calculation methods according to different catchments, data situation or calculation requirements , it has a wide range of adaptability. In this paper, among the loss methods, the simple “Initial and Constant Loss” method is selected for the event-based simulation studies. The method is simple and practical because it requires only three input parameters, i.e., initial loss (mm), constant rate (mm/h) and impervious area (%). Snyder unit hydrograph is selected for flow concentration, and motion wave is selected for flood wave movement in the river. The combination is simple in principle and has few parameters, which is easy to apply or implement in the area with less observed data.
2.2 Hydrological Model Calibration
2.2.1 Calibration Method
To obtain more accurate hydrological model parameters, we used multi-objective optimization algorithm NSGA-II to calibrate the parameters of the hydrological model. NSGA-II is nowadays one of the most widely used multi-objective genetic algorithms, it has three special characteristics, fast non-dominated sorting approach, fast crowded distance estimation procedure and simple crowded comparison operator. NSGA-II can reduce the complexity of the non-dominated sorting genetic algorithm and ensure that excellent individuals in the evolutionary process are not discarded [30, 31], which improves the accuracy of the optimization results and provides more reliable and comprehensive solution in practical application.
2.2.2 Objective Functions
In traditional hydrological model, single objective function was often applied for parameter calibration. However, the practical application of hydrological model shows that the optimization of hydrological model parameters based on a single objective only considers one aspect of hydrological process, thus unable to fully reflect the different dynamics characteristics of hydrological system. In this study/paper we selected four objective functions based on the accuracy of flood simulation and evaluated the simulation results from three aspects: flood volume, flood peak and flood profile. The objective functions are defined as follows:
- Average relative error of runoff depth:where Rsim and Robs are simulated and observed values of runoff depth of a session of flood, respectively, mm; Rrel is the relative error of runoff depth; n is the number of flood events;
is the average relative error of runoff depth of all the flood events.
- Average relative error of peak runoff:where Qsim, Qobs are simulated value and observed value of peak runoff of a session of flood, respectively, m3/s; Qrel is the relative error of peak runoff; n is the number of flood events;
is the average relative error of peak runoff of all the flood events.
- Error of peak time:where Tsim, Tobs are simulated value and observed value of peak time, respectively, h; ΔT is the error of peak time; if ΔT ≤ 2h, the simulation for flood peak time is considered qualified.
- Nash-Sutcliffe efficiency coefficient: The objective function applied for average deterministic coefficient was the well-known Nash-Sutcliffe efficiency coefficient , as given below:where Qis, Qio are simulated and observed values of runoff for each time step i, respectively, m3/s;
is the mean observed runoff; N is the total number of all the time steps calculated by adding up the durations of all the flood events. It should be noted that NSE is calculated by connecting all flood events, and therefore can represent the performance for the catchment rather than for a single flood event.
3 Study Catchments and Data
Owing to the varying complexity of geological topography and climatic conditions in China, the flash floods on runoff generation and confluence mechanisms demonstrate distinctive regional features. Therefore, to adequately study the performances and applicability of different hydrological models, it’s necessary to choose as many representative small catchments as possible. In this paper, fourteen small catchments in typical hilly areas from seven provinces including Henan, Hebei, Jilin, Gansu, Fujian, Jiangxi and Zhejiang are chosen as study area, as shown in Figure 1. The selected catchments are situated from the south to north of China, covering different climate, hydrological and geographical conditions.
The basic characteristics of the fourteen catchments can be found in Table 1. The drainage area of these catch
Basic characteristics of catchments for simulation and comparison.
|Province||Catchments||Drainage||Mean annual||Density of precipitation||Number of||Elevation (m)||Average||Major soil||Major land|
|area||precipitation||station (km2/||flood||gradient (°)||type||use|
|Luanchuan||343.0||784||49.0||22||733-2082||29||Sandy loam||Forest land|
|Henan||Xiahecun||208.0||600||34.7||16||404-1811||22||Sandy loam||Forest land|
|Peihe||21.6||1313||10.8||16||93-771||34||Sandy loam||Forest land|
|Gansu||Huating||274.9||607||91.6||15||1393-2736||27||Clayey loam||Forest land|
|Siqian||128.3||1864||32.1||27||416-1806||36||Clayey loam||Forest land|
|Fujian||Xiaoanxia||76.2||1700||38.1||7||321-1213||27||Clayey loam||Forest land|
|Yongchun||389.7||1487||55.7||14||395-1358||24||Clayey loam||Cultivated land|
|Zhejiang||Xufan||61.0||1651||20.3||6||81-736||29||Sandy clay||Cultivated land|
ments varies from 21.6 to 527.5 km2, all are characterized as small catchments. The mean annual precipitation varies from 600 mm to 1864 mm in these catchments and eight catchments exceeds 800 mm. The density of precipitation stations varies from 10.8 to 105.5 km2/precipitation station. The number of flood events selected ranges from 5 to 41. The land use of eleven of the selected catchments are dominated by forest and grass, and the major soil types are sandy loam and Clayey loam. All data for runoff simulation, including DEM, land-use type, soil type, precipitation and runoff, were obtained from the China Institute of Water Resources and Hydropower Research (IWHR). According to the historical data, the number of flood events differs among catchments. There are more flood events in Anhe, Dutou, Siqian, and Luanchuan, while Zhouhutun, Xiaoanxia, Xufan, and Wangan have less than 10 flood events.
4 Results and Discussion
The five hydrological models with different runoff mechanisms and levels of complexity were applied for flash flood simulation in the selected fourteen catchments. Comparative analysis were further conducted to assess the applicability of different models in catchments under different climate conditions and geological features, which thus can provide guidance for hydrological model selection in small catchments in hilly areas. In this study, the hydrological models are calibrated using NSGA-II algorithm; the model performances are presented in Table 2.
Model performance for the fourteen catchments.
|Catchments||Hydrological models||Qualified number of time to peak||NSE|
4.1 The Analysis of API Model
The results of the API model are strongly affected by P~Pa~R correlation diagram. For most of very humid small catchments with mean annual precipitation over or closed to 1500 mm in Fujian, Jiangxi and Zhejiang provinces, the soil moisture is usually very high, and the water shortage is very low in vadose zone. The soil water content, therefore, can easily reach its field capacity, the flash floods in these provinces belong to storage excess runoff generation mechanism. The distribution characteristics of measured P~Pa~R points is obvious and easy to fit, thus the API model shows a generally good capability of flash flood simulation in small-scale humid catchments, which is not surprising given the fact that API model is based on storage excess runoff generation mechanism.
However, as shown in Table 2, the performance of the API model in Yongchun catchment is obvious worse than all the other hydrological models. This is mainly due to the obvious inaccuracy of the calculated Pa, caused by discontinuous rainfall data and incomplete observed runoff data before flash flood begins. It can be found from Figure 2a that the P~Pa~R curves fitted to Yongchun catchment is poor with some flood points obvious deviated from P~Pa~R curves, which seriously affects the accuracy of flash flood simulation. Similarly, in Xiaoanxia catchment, due to the lack of antecedent rainfall data before flash flood, and insufficient flood events used for fitting P~Pa~R curves, the P~Pa~R curves are unreliable thus resulting in negative NSE in Xiaoanxia catchment, and meanwhile, the result of Zhouhutun catchments is also significantly worse than other hydrological models, as shown in Figure 2b~c and Table 2. The coexistence of storage excess runoff generation mechanism and infiltration excess runoff generation mechanism is an important feature in the semi-humid and semi-arid catchments, especially under the condition of excessive rainfall in short duration, the infiltration excess-based flash floods are prone to occur. Furthermore, the measured P~Pa~R points for these catchments are mostly at the stage of unsaturation excess runoff, therefore the accuracy of the API model is limited. For example, the API model is obviously inferior to the other models in Xiahe-cun, Wangan, and Huating catchments, where the NSEs are negative.
Overall, as a typical excess storage model, the API model is not applicable to all small humid catchments because of its high requirements for observed data. Uncontinuous precipitation and runoff data or insufficient flood events can lead to poor fitting of P~Pa~R curves and result in poor forecasting capability of the API model.
4.2 The Analysis of XAJ Model
In this paper, the mean annual precipitation for most selected small catchments in hilly area is over 800 mm. Considering the storage excess runoff generation, the XAJ model seems very suitable to these humid catchments. In addition, the parabola distribution is adopted in the tension water storage capacity and surface free water capacity curves in the XAJ model, which can effectively account for the spatial distribution characteristics of the underlying surface. Even under the condition of dry soil, part of the catchment will still yield runoff when rainfall occurs. Therefore, as seen from Table 2, the XAJ model performs well for most humid small catchments in hilly area.
However, for Xiaoanxia and Zhouhutun catchments where the antecedent observed data is lacking, the performance of the XAJ model is poor in terms of the runoff production evaluation index
Figures 3 and 4 present the typical flash flood events of Xiaoanxia and Zhouhutun catchments. The mean average tension water storage capacity (Wm) is an important parameter controlling the total runoff production. Generally, lower Wm usually results in higher total runoff production because the soil has little power to contain water for a single flood event. However, even when the parameterWm for both catchments is about 100 mm,which is obviously lower than the normal range of 120~200mm,the simulation results are severely underestimated. For Yongchun catchment, where the precipitation data in the pre-flood period is also lacking, the accuracy of the XAJ model is similar to other models especially the
4.3 The Analysis of DHF Model
Based on infiltration excess runoff generation mechanism, the DHF model has been successfully applied in arid and semi-arid catchments in northern China. Since most of the selected catchments in this study have high vegetation coverages (from 80% to 95%) and well developed hydrographic networks, the flash flood simulation by the DHF model is relatively poor compared to other hydrological models. However, the performance of the DHF model on peak runoff and peak time simulation is prominent.
4.4 The Analysis of TOPMODEL
It can be seen from Table 2 that TOPMODEL is successfully applied in almost all the humid catchments but its performance is not competitive with other hydrological models in some semi-humid, e.g. Huating, Wangan and Xitaiyu catchments. This is due to the fact that runoff simulated by TOPMODEL is directly related to the groundwater level, therefore the shallower groundwater level will generally produce higher simulated runoff. Meanwhile groundwater is unlikely to rapidly rise and recess. In small humid catchments, the base flow is usually at a relatively high level and the groundwater level is shallow, most of the flash floods rise more slowly than in arid area, so the TOPMODEL behaves well in humid catchments with
Figure 5 shows four typical flash flood events, before which no precipitation occurred for a long period of time, hence the initial runoff is very low around 1 m3/s. The initial groundwater depth is determined by the initial flow in TOPMODEL, so it is assumed that the initial groundwater levels of all the four flood events are very deep. The results show that the simulated peak runoff of this type of flash flood is far lower than observed data. Huang et al. analyzed the simulation results of TOPMODEL model in semi-humid and semi-arid catchment, and concluded that the average depth of groundwater in these catchments are too deep so it is difficult to simulate the flood peak well by TOP-MODEL .
4.5 The Analysis of HEC-HMS Model
The HEC-HMS model generates good simulation results in all 14 catchments, as a simple corollary of our assessment of model performance, HEC-HMS model outperforms other models in simulating flash floods. In semi-humid and semi-arid catchments, the initial loss parameters adopted in runoff production mode effectively consider the vegetation interception and ground filling and other losses. Further, the constant loss parameters represent the maximum infiltration capacity of catchments. Overall, the selected method belongs to infiltration excess runoff generation mechanism and is more suitable for flash flood under the condition of short duration. Therefore, the simulation results are superior to other hydrological models especially in Luanchuan, Wangan and Xiahecun catchments, where most of floods are in short duration under high intensity rainfall. Wang et al. compared the simulation results in semi-humid and semi-arid catchments of TOP-MODEL, HEC-HMS and XAJ model, and concluded that the HEC-HMS model behaved best . In small humid catchments, the initial losses can be described as the initial storage deficit and the constant losses indicate the infiltration rate of saturated soil. Moreover, the runoff generation losses in humid areas is larger than semi humid and semiarid area, which reflects storage excess runoff generation mechanism to a certain extent , thus HEC-HMS model achieves similar simulation results.
As a typical distributed hydrological model, HEC-HMS model can effectively consider the different spatial distribution of rainfall and shows a satisfactory capability when the spatial distribution of rainfall is uneven. Taking the "20050817" flood event in the Luanchuan catchment for example (shown in Table 3), the average total rainfall in the
Performances of the “20050817” flood in Luanchuan catchment.
5 Summary and Conclusions
We have successfully applied five frequently used hydrological models in fourteen typical small catchments to study the hydrological model applicability in hilly areas of China. Overall the simulation for flash flood in hilly area is very difficult, since there is not a single hydrological model that can perform well for all the catchments.
Among five hydrological models, the DHF hydrological model performs worst in general. Although the flood peak simulation is relatively good, the DHF model shows a poor capability for other indices in catchments in hilly area. However, according to NSE results in Table 2, API seems to be worse than DHF in most catchments.
In small humid catchments, the HEC-HMS, API, XAJ, TOPMODEL hydrological models overall generate satisfactory simulation results. However, the API and XAJ models have higher requirements on the length of observed data, and the TOPMODEL showed some limitations in simulating the floods with flow rising up and going down rapidly. Therefore, the simple models like API and the XAJ model can be selected preferentially only when the historical observed data is sufficient. For data insufficient catchments, the HEC-HMS distributed hydrological model can obtain some parameters from underlying surface data rather than using hydrological data to calibrate parameters, thus it is more suitable to be used in small ungagged catchments.
In small semi-humid and semi-arid catchments, under the condition of short duration and high intensity rainfall, the storage excess-based floods are dominant. HEC-HMS model produces best results among the five hydrological models. Despite all this, HEC-HMS model still cannot simulate flash floods well in some catchments, mainly limited by the model structure to capture such complex rainfall-runoff processes in hilly areas and the data availability. For future study, understanding the temporal and spatial conversion mechanism of the mix runoff generation mechanism in semi-humid and semi-arid catchments, and improving the understanding of basic theory of rainfall-runoff process are two important tasks to be studied for developing a hydrological model that can be applied to both semi-humid and semi-arid catchments.
Author Contributions: Zhuohang Xin analyzed the data and wrote the manuscript; Ke Shi designed the study and revised the manuscript; Chenchen Wu performed the experiments and assisted with the result; Lu Wang provided a feedback on the structure of the manuscript and reviewed the manuscript; Lei Ye assisted with the data collection and preprocessing.
This study was jointly supported by the National Key Research and Development Program of China (No.2017YFC0406001), and the National Natural Science Foundation of China (No.91647201, No.91747102, No.51579027).
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