Research on flood forecasting based on flood hydrograph generalization and random forest in Qiushui River basin, China

Flood disasters often cause considerable loss of production and life, resulting in serious consequences. As an important supporting technology for flood control work, real-time flood forecasting plays a critical role in actual flood control. Commonly used real-time flood forecasting methods can be summarized into two types: physical process-driven flood forecasting models and the data-driven flood forecasting models. Both types of models have developed rapidly and have played an important role in production practices.

At present, the use of hydrological models is the main technical approach to real-time flood forecasting. With the vigorous development of computer technology in the mid-1950s, the study of hydrological models also ushered in a new opportunity for development. Conceptual hydrological models, such as the Stanford Basin Model (Crawford & Linsley 1966), the Soil Conservation Service (SCS) Model (McCuen 1982) and the Hec-1 Model (Chem 1947), emerged in this period. In the second half of the 20th century, many multi-parameter and complex conceptual lumped models have been developed in succession by countries all over the world, such as the TANK model (Sugawara 1961), antecedent precipitation index (API) model (Sittner et al. 1969) and Xin'anjiang model (Renjun et al. 1980). These conceptual hydrological models have played an important role in studying hydrological laws and solving practical problems in production. Another conceptual model: distributed hydrological models also have made great progress, such as the Soil and Water Assessment Tool (SWAT) model (El-Nasr et al. 2005), SHE model (Abbott et al. 1986), the Systeme Hydrologique Europeen TRAN (SHETRAN) (Ewen 2000) model and the MIKE Systeme Hydrologique Europeen (MIKESHE) model (Refshaard & Storm 1995), which were developed on the basis of the SHE model. TOPographic Kinematic APproximation and Integration (TOPKAPI) (Ciarapica & Todini 2002) was established by combining the ARNO model with the TOPgraphy based hydrological (TOP) model and fully exploits the potential of the physical mechanisms of distributed models. Other distributed models include the IHDM (Institute of Hydrology Distributed Model) model and Variable Infiltration Capacity (VIC) model (Liang et al. 1994; 1996).

However, the existing hydrological models are more suitable for flood forecasting in humid areas. Our study area, Qiushui River basin, consists of an arid and semi-arid region where the spatial composition of flood sources is complex (Li et al. 2019), the forecast accuracy of hydrological models is often low, which is difficult to meet the needs of flood control and disaster reduction in this area (Li et al. 2018). Hence, there is an urgent need for a flood forecasting method that can not only avoid the direct simulation of physical flood formation processes in arid and semi-arid areas but also meet forecasting accuracy requirements. Another type of the flood forecasting model is the data-driven model. This type of model does not consider the physical mechanism of the hydrological process, regards the hydrological process as a black box and determines the mathematical function according to input and output data. Random forest (RF) is one of a data-driven model which combines the prediction from an ensemble of decision trees (Breiman 2001). RF has become popular in various industries due to its prediction power and the speed of processing (Svetnik et al. 2003; Belgiu & Drăguţ 2016; Dai et al. 2018; Zahedi et al. 2018). In hydrology, Peters et al. (2007) used RF as a tool for ecohydrological distribution modeling. Carlisle et al. (2010) used natural watershed characteristics to predict the value of each runoff metric using RF. Wang et al. (2015) proposed an approach for the flood hazard risk assessment model based on RF. Albers et al. (2015) determined the relative importance of contributing upstream discharges to the main stem during significant flood events. Yang et al. (2017) used RF to predict reservoir inflows for two headwater reservoirs in USA and China. Based on the flood hydrograph generalization method and RF model, this study intends to use advanced intelligent analysis technology to deeply extract knowledge from the data deluge and establish a new real-time flood forecasting method. Compare the new method with the empirical model: the API model, which is currently used in actual work.

The remainder of this paper is organized as follows: ‘Study area and data’ introduces the study area and the data used. The flood hydrograph generalization, RF model and rainfall–runoff relation methods are described in detail in the ‘Methods’ section. The results of flood forecasting and comparison of the hybrid model and empirical model are provided in the ‘Results and discussion’ section. Finally, the conclusions obtained from the study are outlined in the ‘Conclusions’ section.

The Qiushui River basin is located in the left bank of the middle of the Yellow River. It is a tributary of the Yellow River and covers an area of 1,989 km². There are more than 20 branch ditches in the basin (the basin area is larger than 10 km²) that are asymmetric pinnate inlets. Among the main branch, ditches are Taiping ditch, Chengzhuang ditch, Yulin ditch, Chegan ditch, Anye ditch, Dayu ditch and Zhaoxian ditch. The Qiushui River control station, named the Linjiaping Hydrological Station, is located in the upper 13 km of the Yellow River mouth, with a control area of 1,873 km². There are nine precipitation stations in the Qiushui River basin, namely, Zhangjiawan, Daipo, Yangposhuiku, Yaotou, Chengjiata, Linxian, Huangcaolin, Chegan and Linjiaping, with a network density of 208 km² per station. Since the Zhangjiawan and Daipo precipitation stations are located in the upper reaches of the Yangpo reservoir, only the other seven stations and Zhaojiagou were used to analyze the precipitation data (Figure 1).

This study uses 23 flood events that occurred during the period 1980–2010, with hourly observations of the discharge of Linjiaping station and the hourly precipitation data of Yangposhuiku, Daipo, Yaotou, Chengjiata, Huangcaolin, Chegan, Zhaojiagou and Linjiaping precipitation station. Eighteen flood events during the period 1980–1996 are used for calibration, while the remaining datasets during the period 1997–2010 are used for validation. According to the characteristics in this basin, the forecast lead time selected for this study is 5 h. Table 1 lists the information of these flood events, including the beginning and ending time.

Flood hydrograph generalization refers to the production of a representative flood hydrograph based on the observed flood hydrograph data of a large number of flood events at a hydrological station. The method flood hydrograph generalization comprises the following steps: first, combine each flood hydrograph into the same drawing, wherein the ordinate represents the ratio of and ⁠, the abscissa represents the ratio of and T. is the peak discharge, T is the total duration of the flood process, and and represent the discharge and time, respectively, at any time. Then, overlap the time of peak discharge in one place, one common hydrograph that summarizes the station flood shape characteristics of an average hydrograph is chosen as the generalized flood hydrograph. In this paper, considering that the flood recession process is long, the flood progress is divided into two parts: the rising and recession processes. Moreover, we assume that the total flood duration is twice as long as the duration of the rising process. The 6-point generalization method is taken as an example to control the hydrograph characteristics, as shown in Figure 2. When the flood hydrograph is calculated by the generalization map, the coordinates of the points in the graph are ⁠, ⁠, ⁠, ⁠, ⁠, ⁠, respectively. Here, is the peak discharge, is the maximum discharge of the recession process, and T is the flood duration.

RF (Breiman 2001) is a machine learning algorithm combining the Bagging ensemble learning theory (Breiman 1996) and the random subspace method (Ho 1998). An RF is a classifier consisting of a collection of tree-structured classifiers ⁠, where are independent identically distributed random vectors, and each tree casts a unit vote for the most popular class at input x (Breiman 2001). RF utilizes bootstrap resampling technology to sample original samples to generate a number of training samples, each of which randomly selects feature attributes through random subspace methods to construct a decision tree. Finally, the optimal result is obtained by the voting or averaging method. Previous studies have found that RF can effectively overcome the problems of noise and overfitting and obtain a high prediction precision (Wang et al. 2015). RF has two main technological aspects: the first is bootstrap resampling technology and out-of-band error estimation; the second is decision tree construction and the random subspace theory (Liang et al. 2017). The main structure of the model is shown in Figure 3.

The hybrid model combines the two methods above. First, the generalized flood hydrograph was obtained by the flood hydrograph generalization method. Then, construct correlations between the flood factors and precipitation factors to screen predictors. And the flood factors series and predictors series were as the input to the RF model to forecast flood factors. The RF algorithm is implemented by Matlab. Finally, according to the forecasted flood factors, the forecasted flood hydrograph was obtained through scaling up the generalized flood hydrograph. The main structure of the hybrid model is shown in Figure 4.

Sittner et al. (1969) proposed the API model for computing a groundwater flow hydrograph; the API uses the unit hydrograph (UH) method to develop a model to simulate the flow hydrograph.

The API model is based on the physical mechanism of rainfall and runoff generation in basins and takes the main influencing factors as parameters to establish the quantitative correlation between rainfall and runoff. Some common parameters are antecedent precipitation, seasonal characteristics and precipitation duration.

Considering the long process of flood recession, the flood progress is divided into two parts: the rising and recession processes. The generalization method is used to generalize these two processes. The rising and recession processes of 18 flood events of the calibration period were generalized for each flood hydrograph, and finally, the general flood hydrograph was obtained by averaging the individual flood hydrographs (Figures 5–8).

A correlation analysis between the precipitation factors (peak hourly precipitation (P_m), accumulated 5 h precipitation (AP₅), accumulated 10 h precipitation (AP₁₀), accumulated 15 h precipitation (AP₁₅), precipitation intensity during rising process (PI), time of peak discharge (⁠⁠), time of peak precipitation (⁠⁠) and peak discharge (⁠⁠), duration of the rising process (⁠⁠) and the maximum discharge of the recession process (⁠⁠) were established, respectively, to select the key influential predictors, as shown in Table 2.

The model was built in three steps. In the first step, peak discharge was forecasted. The duration of the rising process and maximum discharge of the recession process were forecasted in the second and third steps, respectively, with the total duration set to twice the duration of the rising process. The predicted flood hydrograph was obtained by substituting the predicted time into the generalized flood process. Eighteen floods were used to calibrate the model, and five floods were used to validate the model.

The forecasting statistics of the RF model in the calibration period are shown in Table 3. Moreover, according to the accuracy requirement of the flood forecasting in the standard for hydrological information and hydrological forecasting in China (GB/T22482-2008), a 20% variation between the observed peak discharge and forecasted peak discharge is taken as the permissible error, and the qualified rate (QR) is calculated.

In the calibration period of the model, the values of the average relative error of the peak discharge of 13 events were less than 20%; thus, QR of forecasting of is 72%. In addition, the average value of in the calibration period was 18.8%. As for the flood duration, there were four flood events with values at 0, which is a considerable result. However, the value of No. 19890722 was relatively large, mainly because the observed value is relatively large. Ten of the 18 flood events had average relative error of less than 20%; therefore, QR of forecasting of is 55.6%. The average value of the of the calibration period was 22.4%. Broadly speaking, however, the accuracy was satisfactory. Table 4 shows the forecasting statistics of the RF model in the validation period.

During the validation period, QR of forecasting of and is 80 and 60%, respectively. The average value of the and in the validation period was 20.4 and 24.2%, respectively. It has to be noted, for the event No. 20100919, the accuracies of forecasting of the peak discharge and maximum discharge of the recession process are both very low. It is mainly because of the peculiarity of the RF model. RF cannot make prediction beyond the range of training set data despite it being a powerful model. Namely, when the maximum and minimum of the peak discharge in the training set is 1,520 and 207 m³/s, the forecasted discharge cannot be greater than 1,520 m³/s or smaller than 207 m³/s. However, the observation of the of No. 20100919 is 2,280 m³/s, which is beyond the maximum value of the training set. Therefore, the effect will be relatively poor in any case. The same is true for ⁠. In general, the model provided acceptable accuracy in both the calibration and validation periods.

The relation graph is shown in Figure 9. The UH was derived in a conventional manner using the selected events, as shown in the figure.

Generally, if the precipitation intensity is large, the peak discharge of UH is higher and the peak time is earlier. However, the peak discharge is lower and the peak time lags behind. When the precipitation center is in the upstream, due to the long confluence path, the peak discharge of UH is lower and the peak time lags behind. However, the peak discharge is higher and the peak time is earlier. Therefore, the UH is classified and compiled according to the location of the precipitation center and the magnitude of the net precipitation. We summarized the flood events into four types of unit hydrographs, as shown in Figure 10. The classification of the flood events is shown in Table 5.

The CC and the RMSE of the hybrid model and empirical model in the calibration period are summarized and shown in Table 6.

It is evident from Table 5 that the hybrid model performs better than the empirical model in the calibration period. Yet, there are two events which have different results. The results of No. 19840701 and No. 19910721 indicate that the empirical model has better values of CC, which is 0.02 and 0.06 higher than the hybrid model. This might be explained by the variance of the antecedent precipitation. When the antecedent precipitation is well distributed in the temporal scale, the empirical model performs well, and when the antecedent precipitation is more concentrated in a short time, the hybrid model is better. However, the real problem of Qiushui River basin is that the spatial and temporal distribution of precipitation is often uneven and expressed in peaks with rising and dropping steeply. Thus, the hybrid model can be more suitable than the traditional model in the study area. Moreover, Table 7 lists the CC values and RMSE values of the hybrid model and empirical model in the validation period. See Figures 11–15 for comparison of observed and forecasted flood hydrographs of the five flood events in the validation period.

During the validation period, the CC values of the hybrid model were all above 0.7 and there were four flood events with CC values above 0.85. However, the CC values of only two events were above 0.8 for the empirical model. In addition, for event No. 19990711, although the CC value of the empirical model is 0.84, Figure 12 shows that the hydrograph forecasted by the empirical model only follows the trend of the observed hydrograph and the difference between forecasted peak discharge and observed peak discharge is relatively large. On average, the values of CC of the hybrid model and the empirical model are 0.85 and 0.62, respectively, and the values of RMSE of the hybrid model and the empirical model are 210 and 347 m³/s, respectively. The comparison indicates that the hybrid model provided a better flood forecasting fit based on observations compared to the empirical model both in the calibration and validation period.

In order to solve the problem of the low forecasting accuracy of hydrological models in arid and semi-arid areas, this paper develops a flood forecast method that combines the flood hydrograph generalization method and RF in the Qiushui River basin. First, selected flood events from 1980 to 2010 were generalized using the flood hydrograph generalization method. Then, the peak discharge and flood duration were forecasted using the RF method, and the flood processes were deduced. The specific findings of this study are as follows:

1. RF cannot make prediction beyond the range of training set data, which may lead to the poor prediction effect when we do the extreme value prediction. The solution for that problem could not be proposed in this study and must be left for future work.

2. Our study found that when the antecedent precipitation is well distributed in the temporal scale, the empirical model performs well, and when the antecedent precipitation is more concentrated in short time, the hybrid model is better. Thus, the accuracy of the current hydrological model is often lower in arid and semi-arid areas with more complex hydrological processes. The Qiushui River basin is an arid and semi-arid area where the spatial and temporal distribution of precipitation is often uneven and expressed in peaks with rising and dropping steeply. In this study, for the hybrid model, the average CC of the calibration period and validation period of the forecasted and observed flood progress were 0.80 and 0.85, respectively. For the empirical model, the average correlation coefficient of the calibration period and validation period of the forecasted and observed flood progress were 0.67 and 0.62, respectively. The results indicate that the hybrid model provides a better flood forecasting performance than the empirical model. Consequently, this study provides a new method for improving the accuracy of flood forecasting.

This work is supported in part by the National Key Research and Development Program of China (2016YFC0402709, 2016YFC0402706), National Natural Science Foundation of China (41730750), and National Natural Science Foundation of China (41877147). In addition, the authors are indebted to the editors/reviewers for their valuable comments and suggestions.

The Supplementary Material for this paper is available online at https://dx.doi.org/10.2166/hydro.2020.147.