Abstract

Accurate and reliable flood forecasting plays an important role in flood control, reservoir operation, and water resources management. Conventional hydrological parameter calibration is based on an objective function without consideration for forecast performance during lead-time periods. A novel objective function, i.e., minimizing the sum of the squared errors between forecasted and observed streamflow during multiple lead times, is proposed to calibrate hydrological parameters for improved forecasting. China's Baiyunshan Reservoir basin was selected as a case study, and the Xinanjiang model was used. The proposed method provided better results for peak flows, in terms of the value and occurrence time, than the conventional method. Specifically, the qualified rate of peak flow for 4-, 5-, and 6-h lead times in the proposed method were 69.2%, 53.8%, and 38.5% in calibration, and 60%, 40%, and 20% in validation, respectively. This compares favorably with the corresponding values for the conventional method, which were 53.8%, 15.4%, and 7.7% in calibration, and 20%, 20%, and 0% in validation, respectively. Uncertainty analysis revealed that the proposed method caused less parameter uncertainty than the conventional method. Therefore, the proposed method is effective in improving the performance during multiple lead times for flood mitigation.

INTRODUCTION

Floods are the most common natural disasters and cause the highest number of casualties and the greatest extent of damage of all natural disasters (Jonkman 2005; Badrzadeh et al. 2015; Xie et al. 2018). Flood disaster mitigation can be achieved by non-structural measures such as hydrological forecasting, which can be used to support warnings and reduce the risk of large damage, and can also be used to provide effective information for water scheduling to achieve sustainable development (Chen & Yu 2007; Pagano et al. 2011; Awchi 2014; Shi et al. 2016; Feng et al. 2017). Accurate and reliable flood forecasting has been recognized as an essential task, and plays an important role in flood control, reservoir operation, and water resources management (Liu et al. 2015; Badrzadeh et al. 2016; Ming et al. 2017).

Flood forecasting models are usually classified into physically based, data-driven, and conceptual models. Physically based models have the potential to incorporate the fundamental mechanisms of the rainfall–runoff process, although they are difficult to develop because of the critical requirement of high resolution input data for complex mathematical formulation (Luk et al. 2000; Garcia-Pintado et al. 2015). Data-driven models are effective and easy to use, but are less able to provide an interpretable representation of processes in the hydrological cycle (Xu & Li 2002; Goswami et al. 2005). In contrast, conceptual models based on hydrological assumptions are deemed to be more credible and have been shown to provide accurate forecasts (Refsgaard & Knudsen 1996; Toth & Brath 2007). Consequently, conceptual models have been widely utilized (Refsgaard 1997; Perrin et al. 2001; Reed et al. 2004; Zhuo et al. 2015).

Various studies using conceptual models have taken advantage of weather-predicting technologies, i.e., quantitative precipitation forecasts and numerical weather predictions, to increase flood forecasting lead times (Krzysztofowicz 1995; Toth & Brath 2007; Mohan & Sati 2016). For example, Bao et al. (2011) coupled ensemble weather predictions with the Grid-Xinanjiang model to evaluate simulation results based on rain gauge observation as a means of achieving advanced early warnings of flood events. Yao et al. (2014) proposed a hybrid XAJ-GIUH model to improve flood simulation in ungauged catchments by further analyzing the topographic characteristics. Nourani et al. (2013) considered the spatial and temporal variability of precipitation by using satellite-derived rainfall data to improve multi-step-ahead forecasting. However, quantitative precipitation forecasts and numerical weather predictions are not always available (Liu et al. 2017), and an alternative approach is to identify robust parameters for the hydrological model used.

It remains a challenge to satisfactorily calibrate parameters for a conceptual model (Jie et al. 2016; Xue et al. 2016). Generally, conceptual model parameters reflect the catchment characteristics and have significant impacts on forecast accuracy (Deng et al. 2016). However, parameters are difficult to measure in the field (Merz et al. 2011). The current approach to obtaining parameters is calibration using optimization algorithms to maximize or minimize an objective function (Xu 2001; Gragne et al. 2015). Various objective functions have been used in flood forecasting, such as the Nash–Sutcliffe coefficient (NSE) and relative volume error (RE). Li et al. (2013) used the NSE as the objective function and obtained parameters that matched a flatter hydrograph. Moussa & Chahinian (2009) adopted RE as the objective function to fit the total volume. However, most of the current objective functions put the emphasis on the accurate simulation of volumes or hydrographs, and seldom address the forecasting lead times.

The parameters in a conceptual model are often calibrated based on hydrological simulation. However, hydrological forecasting differs from simulation (Beven & Young 2013; Nicolle et al. 2014). Forecasting is the process of predicting future situations based on past information and present hydrological data. Simulation is the imitation of a real hydrological process or system. For the purpose of achieving longer forecasting lead times, it is sensible to build an objective function by considering potential future rainfall during lead-time periods. Therefore, the hydrological parameters calibrated by this objective function do not only reflect key characteristics, but also have the ability to further improve forecasts for given lead times.

In this study, a novel objective function, i.e., minimizing the sum of squared errors between forecasted and observed streamflow during multiple lead times, is proposed to calibrate the hydrological parameters. The proposed method is used to improve the forecasting accuracy for longer lead times in the Baiyunshan Reservoir, China.

METHODOLOGY

As shown in Figure 1, the proposed method utilizes the Xinanjiang model to estimate the forecasted streamflow during the lead time. The forecasted streamflow is based on the inputs of precipitation and evaporation, and an assumption of no rainfall during the lead-time periods. In the conventional method, the parameters are calibrated by matching the observed and simulated streamflows. However, in the proposed method, parameters are calibrated using a novel objective function. This function uses the sum of the squared error between the forecasted and observed streamflow within the lead times.

Figure 1

Flowchart of flood-forecasting methods for multiple lead times.

Figure 1

Flowchart of flood-forecasting methods for multiple lead times.

Xinanjiang model

The Xinanjiang model is a conceptual rainfall–runoff model that was developed in the mid-1970s for flow forecasting (Zhao 1992). The model has been the most popular and widely applied model in China for watershed streamflow forecasting in humid and semi-humid regions (Li et al. 2009; Chen et al. 2012a; Lu et al. 2013; Ouyang et al. 2014; Liu et al. 2016). A schematic overview of the model is presented in Figure 2. The main feature of the Xinanjiang model is the concept of runoff generation on the repletion of storage capacity. This implies that runoff is not produced until the soil moisture content of the aeration zone reaches its field capacity, and thereafter the runoff equals the excess rainfall without further loss (Zhao & Liu 1995).

Figure 2

Schematic overview of the Xinanjiang model.

Figure 2

Schematic overview of the Xinanjiang model.

The model involves a total of 15 parameters, including evapotranspiration parameters (WUM, WLM, KE, C), runoff generation parameters (WM, B, IMP), runoff separation parameters (SM, EX, KI, KG), and flow concentration parameters (CI, CG, N, NK) (Lin et al. 2014; Deng et al. 2015b). These parameters represent characteristics of the watershed and are usually obtained by calibration. Their physical meanings and ranges are listed in Table 1.

Table 1

Parameters of the Xinanjiang model and their physical meanings

Parameters Physical meaning Range 
WM Areal mean tension water capacity 80–200 
WUM Areal mean tension water capacity of the upper layer 0.1–0.4 
WLM Areal mean tension water capacity of the lower layer 0.1–0.5 
KE Ratio of potential evapotranspiration to pan evaporation 0–2 
B Exponential of the distribution to tension water capacity 0.1–1.8 
SM Areal mean free water storage capacity 10–80 
EX Exponential of the distribution of free water storage capacity 0.5–2.5 
KI Outflow coefficient of free water storage to the interflow 0.01–0.06 
KG Outflow coefficient of free water storage to the groundwater 0.01–0.07 
IMP Ratio of impervious area to the total area of the basin 0.001–0.1 
C Evapotranspiration coefficient of deep layer 0–0.5 
CI Recession constant of the lower interflow storage 0.2–1 
CG Recession constant of the groundwater storage 0.6–1 
N Number of cascade linear reservoir of Nash model 1–10 
NK Scale parameter of cascade linear reservoir 1–10 
Parameters Physical meaning Range 
WM Areal mean tension water capacity 80–200 
WUM Areal mean tension water capacity of the upper layer 0.1–0.4 
WLM Areal mean tension water capacity of the lower layer 0.1–0.5 
KE Ratio of potential evapotranspiration to pan evaporation 0–2 
B Exponential of the distribution to tension water capacity 0.1–1.8 
SM Areal mean free water storage capacity 10–80 
EX Exponential of the distribution of free water storage capacity 0.5–2.5 
KI Outflow coefficient of free water storage to the interflow 0.01–0.06 
KG Outflow coefficient of free water storage to the groundwater 0.01–0.07 
IMP Ratio of impervious area to the total area of the basin 0.001–0.1 
C Evapotranspiration coefficient of deep layer 0–0.5 
CI Recession constant of the lower interflow storage 0.2–1 
CG Recession constant of the groundwater storage 0.6–1 
N Number of cascade linear reservoir of Nash model 1–10 
NK Scale parameter of cascade linear reservoir 1–10 

Objective functions

In the calibration procedure, the parameter quality is affected by the objective function. The conventional objective function for calibrating hydrological parameters is based on errors between simulated and observed streamflows, i.e.,  
formula
(1)
where is the observed streamflow at time t (t= 1, 2,…, N), is the forecasted streamflow at time t based on the inputs before time t, is the weight coefficient and N is the total number of observations. The use of various weight coefficients takes into account different criteria (Wu et al. 2012), such as goodness of fit of the overall hydrographs, and goodness of fit between simulated and observed high flows.
Equation (1) aims to identify parameters such that the simulated streamflow at t matches the observed streamflow at t. Hence, if the objective is to forecast streamflow over one time-step ahead as close to the observed streamflow as possible, the objective function can be adjusted as follows:  
formula
(2)
where is the forecasted streamflow for time t based on the observed rainfall before t − 1. Because the rainfall forecasts may not be available, the rainfall at time t can be pre-determined as zero (Rogelis & Werner 2018).
Similarly, the objective function, which ensures that the forecasted streamflow over k lead times matches the observed streamflow at time t, is as follows:  
formula
(3)
where is the streamflow at time t that is forecasted at time tk. Because the rainfall forecasts are assumed to be unavailable, the rainfall from tk + 1 to t is zero.
The proposed method involves obtaining reliable forecasted streamflow from 1 to k lead times simultaneously. For these multiple objectives, the calibration problem is as follows:  
formula
(4)
Since trade-offs exist between the different objective functions over various lead times, it is difficult to solve the multiple objectives' problem. Thus, a single objective optimization problem was built by integrating multiple objectives, and is as follows:  
formula
(5)
Equation (5) considers trade-offs between different lead times by adding equal weights. The parameters of the Xinanjiang model were calibrated with three algorithms, i.e., the Genetic, Rosenbrock, and Simplex algorithms (Chen et al. 2012b; Liu et al. 2016). The genetic algorithm is used first and the calibrated parameters are subsequently used as initial values for the Rosenbrock algorithm. The results from the Rosenbrock algorithm are then treated as initial values for the Simplex algorithm, which optimizes the final parameter values.

Markov chain Monte Carlo (MCMC) method

The MCMC method has been widely implemented to simulate observations from unwieldy distributions in hydrology and in the water resources fields (e.g., Liu et al. 2011, 2014). In this study, the MCMC method was used for parameter uncertainty analysis. Parameter sets of the Xinanjiang model were derived with specific distributions by producing samples.

The likelihood measure used in the MCMC method has a large impact on the estimation of the posterior parameter probability distribution (Tao et al. 2009; Lv et al. 2016). In our study, the likelihood measure links parameters to observations by minimizing the difference between observed and forecasted streamflow, given the uncertain parameters, i.e., using the Nash–Sutcliffe efficiency (NSE). Provided that the forecast errors follow the Gaussian distribution with a zero mean and a constant variance, the NSE is equivalent to a likelihood measure (Cheng et al. 2014). This assumption has been used in many other studies (Alazzy et al. 2015; Nourali et al. 2016). Based on the objective functions of the conventional and proposed methods, the likelihood measures are as follows:  
formula
(6)
 
formula
(7)
where and are the likelihood measures used to analyze uncertainty in the parameters of the conventional and proposed methods, respectively.

Model evaluation criteria

The performance of the forecasting models was evaluated using five criteria. These criteria are commonly used in the Xinanjiang model. The formulae are as follows:

  1. Nash–Sutcliffe efficiency (NSE)  
    formula
    (8)
  2. Root mean square error (RMSE)  
    formula
    (9)
  3. Water balance index (WBI)  
    formula
    (10)
  4. Qualified rate of peak flow (QRF)  
    formula
    (11)
  5. Qualified rate of peak time (QRT).  
    formula
    (12)
    where and are the total volume of the predicted and observed flow, respectively; NF is the number of the qualified flood events about peak flow; NT is the number of the qualified flood events about peak time; and M is the total number of flood events.

These five criteria test model efficiency from different aspects. The NSE compares the residual variance in simulations with observed variance – the closer to unity, the better the forecasting agreement (Nash & Sutcliffe 1970; Patel & Ramachandran 2015). The RMSE measures the residual variance between the forecasted and observed streamflow. When this criterion is near to zero, a perfect fit is indicated (Kisi & Shiri 2012; Deng et al. 2015a). The WBI is used to assess the water balance during a flood event, and a value of zero indicates that the water balance condition is fully satisfied. QRF and QRT are suggested by the Chinese flood forecasting guidelines, and have been successfully used in the works of Chen et al. (2015) and Li et al. (2010). The QRF is the ratio of the number of qualified forecasted peak flows. If the difference between forecasted and observed values is within ±20%, the forecasted value is considered to be qualified. The QRT is the ratio of the number of qualified forecasted peak flows occurrence time. If the difference between forecasted and observed occurrence time is within ±3 hours, the forecasted occurrence time is considered to be qualified. The perfect values of QRF and QRT are 1.

CASE STUDY

Baiyunshan Reservoir

The Baiyunshan Reservoir basin is situated in Jiangxi Province, China, and is a sub-basin of the Fushui River, which is a secondary tributary of the Yangtze River. Flood control, irrigation, and hydropower are the main functions of the reservoir. The reservoir basin has a drainage area of 464 km2 and the reservoir has a total storage capacity of 1.14 million m3. The reservoir lies in a subtropical region and is governed by a tropical monsoon climate. The mean annual precipitation is 1,161.3 mm and the evaporation is 975 mm. The average streamflow, average annual flow volume, and average runoff depth at the dam site are 12.5 m3/s, 3.94 million m3, and 850 mm, respectively. The river floods are caused by frontal weather systems that occur in April–July, or typhoon storms (the northeast Pacific hurricanes) that occur in July–September.

Nine precipitation stations, three evaporation stations, and one water level station have been established in the basin of the Baiyunshan Reservoir (Figure 3). The outlet of the basin is at the Baiyunshan Reservoir. Areal precipitation was calculated by the Thiessen polygon method. The average value of evaporation data from the three stations was used as the areal pan evaporation. In the case study, hourly precipitation, pan evaporation, and streamflow data set during the flood seasons are used. Eighteen flood events from 1994 to 2000 were selected to calibrate and validate the model (Table 2). The first 13 flood events from 1994 to 1998 were used for calibration, and the remaining five events from 1999 to 2000 were used for validation. The warm-up period approach is widely used for the removal of initialization bias (Cole & Moore 2008; Nicolle et al. 2014).

Table 2

Information on the 18 flood events used for model calibration and validation

Flood event Peak discharge (m3/s) Duration (h) Volume (104 m3
Calibration 
940,331 125.9 50 965.6 
940,502 680.1 74 5,304.1 
940,531 238.5 31 1,440.6 
940,617 640.6 46 4,170.5 
950,221 101.2 39 1,087.8 
960,802 1060.4 61 5,699.3 
970,609 248.4 58 3,097.1 
970,705 260.2 47 1,871.2 
970,711 540.4 50 5,416.5 
970,810 404.4 45 1,918.9 
980,308 376.3 63 3,955.5 
980,514 417.4 47 2,136.3 
980,619 409.9 44 1,822.1 
Validation 
19,990,417 355.3 51 1,648.8 
19,990,526 630.4 68 3,988.2 
19,990,714 309.1 49 1,879.0 
19,990,826 188.2 38 1,002.2 
20,000,611 289.4 50 2,415.8 
Flood event Peak discharge (m3/s) Duration (h) Volume (104 m3
Calibration 
940,331 125.9 50 965.6 
940,502 680.1 74 5,304.1 
940,531 238.5 31 1,440.6 
940,617 640.6 46 4,170.5 
950,221 101.2 39 1,087.8 
960,802 1060.4 61 5,699.3 
970,609 248.4 58 3,097.1 
970,705 260.2 47 1,871.2 
970,711 540.4 50 5,416.5 
970,810 404.4 45 1,918.9 
980,308 376.3 63 3,955.5 
980,514 417.4 47 2,136.3 
980,619 409.9 44 1,822.1 
Validation 
19,990,417 355.3 51 1,648.8 
19,990,526 630.4 68 3,988.2 
19,990,714 309.1 49 1,879.0 
19,990,826 188.2 38 1,002.2 
20,000,611 289.4 50 2,415.8 
Figure 3

Location of the Baiyunshan Reservoir basin in China.

Figure 3

Location of the Baiyunshan Reservoir basin in China.

RESULTS AND DISCUSSION

Performance of flood forecasting

The conventional and proposed methods were both used for flood forecasting parameter calibration. Note that equal weights are widely used for parameter calibration (Jie et al. 2016) and do not need to be calculated, thereby reducing the computation burden. Hence, is set equal to 1. The conventional method was implemented for 6 h ahead; while the proposed method, using Equation (5), was applied for lead times of 3, 4, 5, and 6 h. The Xinanjiang model was then calibrated to produce five sets of parameters, i.e., one set of parameters for the conventional method, and four sets of parameters for the proposed method. These five sets of parameters were used in the Xinanjiang model to generate runoff during the validation period. The NSE, RMSE, WBI, QRF, and QRT were used as evaluation indicators.

The performances of the conventional and proposed methods are compared in Table 3. As would be expected, the forecasting accuracies decrease with increasing lead-time length. All values of the NSE index exceed 0.60, and are considered sufficiently reliable for practical forecasting. If the NSE was greater than 0.60, a lead time of 6 h was identified as the maximum forecasting time. It can be seen that the NSE values of the proposed method for lead times from 3 to 6 h are slightly less than the NSE values of the conventional method for shorter lead times, but better than the conventional method for longer lead times. RMSE values increase with increasing lead times in calibration and validation. The WBI index values for the proposed method are slightly smaller than those of the conventional method for calibration, indicating that the proposed method is more effective for the water balance criterion. The QRF index values for 4-, 5-, and 6-h lead times for the proposed method are 69.2%, 53.8%, and 38.5%, respectively, while the corresponding values for the conventional method are 53.8%, 15.4%, and 7.7%, respectively, with a 6-h lead time for calibration. Generally, the QRT values are slightly improved by the proposed method as compared with the conventional method. As shown in Table 3, results for the two methods indicate that they are both effective in the practical implementation of 5-h lead-time streamflow forecasting. In contrast, the proposed model has a better performance than the conventional model for 4–6-h lead-time forecasts, and is significantly better than the conventional model for forecasting the values and times of occurrence of the flood peak flows.

Table 3

Performance evaluation of flood forecasting for the conventional and proposed methods

Scheme Lead time (h) Calibration
 
Validation
 
NSE WBI RMSE QRF (%) QRT (%) NSE WBI RMSE QRF (%) QRT (%) 
Conventional method 0.91 0.01 14.71 84.6 100.0 0.88 0.08 13.95 60 100 
0.91 0.03 15.17 84.6 100.0 0.88 0.06 13.99 60 100 
0.87 0.06 17.68 61.5 100.0 0.86 0.03 14.94 60 100 
0.80 0.10 22.20 53.8 92.3 0.80 0.00 17.88 20 100 
0.71 0.13 26.80 15.4 76.9 0.71 0.04 21.34 20 100 
0.62 0.16 30.61 7.7 53.8 0.63 0.07 24.41 80 
Proposed method 3 h 0.91 0.01 15.21 84.6 100.0 0.86 0.12 14.88 60 100 
0.91 0.01 15.21 84.6 100.0 0.86 0.10 14.71 60 100 
0.88 0.04 16.92 76.9 100.0 0.86 0.07 15.08 60 100 
4 h 0.90 0.00 15.90 76.9 100.0 0.85 0.11 15.27 80 100 
0.89 0.01 16.05 76.9 100.0 0.85 0.10 15.31 80 100 
0.88 0.03 16.89 76.9 100.0 0.85 0.07 15.53 80 100 
0.83 0.08 20.34 69.2 100.0 0.81 0.03 17.58 80 100 
5 h 0.89 0.02 16.45 76.9 100.0 0.85 0.15 15.64 80 100 
0.89 0.02 16.61 76.9 100.0 0.85 0.14 15.68 80 100 
0.88 0.01 17.47 69.2 100.0 0.84 0.12 15.93 80 100 
0.83 0.04 20.44 69.2 92.3 0.81 0.08 17.63 60 100 
0.75 0.09 24.86 46.2 84.6 0.73 0.03 20.59 20 100 
6 h 0.89 0.03 16.63 76.9 100.0 0.85 0.16 15.54 60 100 
0.88 0.02 16.79 76.9 100.0 0.85 0.15 15.43 60 100 
0.87 0.01 18.02 76.9 100.0 0.85 0.12 15.60 60 100 
0.82 0.04 21.27 69.2 92.3 0.81 0.08 17.44 60 100 
0.74 0.08 25.29 53.8 76.9 0.74 0.04 20.21 40 100 
0.66 0.11 28.96 38.5 61.5 0.67 0.00 23.01 20 80 
Scheme Lead time (h) Calibration
 
Validation
 
NSE WBI RMSE QRF (%) QRT (%) NSE WBI RMSE QRF (%) QRT (%) 
Conventional method 0.91 0.01 14.71 84.6 100.0 0.88 0.08 13.95 60 100 
0.91 0.03 15.17 84.6 100.0 0.88 0.06 13.99 60 100 
0.87 0.06 17.68 61.5 100.0 0.86 0.03 14.94 60 100 
0.80 0.10 22.20 53.8 92.3 0.80 0.00 17.88 20 100 
0.71 0.13 26.80 15.4 76.9 0.71 0.04 21.34 20 100 
0.62 0.16 30.61 7.7 53.8 0.63 0.07 24.41 80 
Proposed method 3 h 0.91 0.01 15.21 84.6 100.0 0.86 0.12 14.88 60 100 
0.91 0.01 15.21 84.6 100.0 0.86 0.10 14.71 60 100 
0.88 0.04 16.92 76.9 100.0 0.86 0.07 15.08 60 100 
4 h 0.90 0.00 15.90 76.9 100.0 0.85 0.11 15.27 80 100 
0.89 0.01 16.05 76.9 100.0 0.85 0.10 15.31 80 100 
0.88 0.03 16.89 76.9 100.0 0.85 0.07 15.53 80 100 
0.83 0.08 20.34 69.2 100.0 0.81 0.03 17.58 80 100 
5 h 0.89 0.02 16.45 76.9 100.0 0.85 0.15 15.64 80 100 
0.89 0.02 16.61 76.9 100.0 0.85 0.14 15.68 80 100 
0.88 0.01 17.47 69.2 100.0 0.84 0.12 15.93 80 100 
0.83 0.04 20.44 69.2 92.3 0.81 0.08 17.63 60 100 
0.75 0.09 24.86 46.2 84.6 0.73 0.03 20.59 20 100 
6 h 0.89 0.03 16.63 76.9 100.0 0.85 0.16 15.54 60 100 
0.88 0.02 16.79 76.9 100.0 0.85 0.15 15.43 60 100 
0.87 0.01 18.02 76.9 100.0 0.85 0.12 15.60 60 100 
0.82 0.04 21.27 69.2 92.3 0.81 0.08 17.44 60 100 
0.74 0.08 25.29 53.8 76.9 0.74 0.04 20.21 40 100 
0.66 0.11 28.96 38.5 61.5 0.67 0.00 23.01 20 80 

A graphic depiction of the changes in NSE values for the proposed and conventional methods is shown in Figure 4. The proposed method performs similarly to the conventional method for the shorter lead times, but its descending rate of NSE values is distinctly slower than the conventional method, particularly when the lead time is longer than 4 h.

Figure 4

Nash–Sutcliffe efficiency (NSE) of the conventional and proposed methods.

Figure 4

Nash–Sutcliffe efficiency (NSE) of the conventional and proposed methods.

Visual depictions of the relative performance of the proposed method (with lead times of 3, 4, 5, and 6 h) and the conventional method are presented in Figures 5 and 6. Hydrographs of four typical flood events compare the observed with the forecasted streamflows during calibration and validation periods. The thin dashed-line vertical bars represent the selected time of the forecast. The future 6-h flood flows are forecast by considering the precipitation within the forecasting lead times as zero (the thick dashed-lines). Figure 5 indicates that the performance of the proposed method is better than the conventional method, especially for the forecasts of peak flow. It is clear that flood regression becomes much slower with increasing lead times for the proposed method than with the conventional method. The forecasts for the validation period are consistent with the results of the calibration period. It can be inferred that parameters obtained by the proposed method are superior to those of the conventional method for multiple lead-time forecasting.

Figure 5

Observed versus forecasted streamflow for various lead times during the calibration period: (a) flood in June 1994; (b) flood in August 1996.

Figure 5

Observed versus forecasted streamflow for various lead times during the calibration period: (a) flood in June 1994; (b) flood in August 1996.

Figure 6

Observed versus forecasted streamflow for various lead times during the validation period: (a) flood in May 1999; (b) flood in April 1999.

Figure 6

Observed versus forecasted streamflow for various lead times during the validation period: (a) flood in May 1999; (b) flood in April 1999.

The proposed method could be coupled with precipitation prediction to prolong lead-time periods for streamflow forecasting (Ma et al. 2016; Ye et al. 2017). A deeper understanding of the physical mechanism of hydrological processes, and improving the forecasting simulation accuracy of the rainfall–runoff model may be required (Xiong & O'Connor 2002; Ma et al. 2013).

Parameter uncertainty analysis

To further understand the parameters obtained, it is necessary to analyze the parameter uncertainty. As an illustration, the proposed and conventional methods for a 3-h lead time were implemented using the MCMC.

Figure 7 shows scatter plots of the parameter value vs. the NSE (≥0.6), where 10,000 parameter sets were randomly generated from their given ranges and used in flood forecasting for three lead times during 1994 to 1996. It can be observed that the scatter plots of the conventional and proposed methods are similar. Insensitive parameters include WM, X, Y, B, EX, KI, KG, IMP, and C, which have less impact on uncertainty, while sensitive parameters are KE, SM, CI, CG, N, and NK, which have a greater influence on uncertainty.

Figure 7

Scatter plots of Nash–Sutcliffe efficiency (NSE) for selected parameters of the Xinanjiang model using (a) the conventional method and (b) the proposed method.

Figure 7

Scatter plots of Nash–Sutcliffe efficiency (NSE) for selected parameters of the Xinanjiang model using (a) the conventional method and (b) the proposed method.

The posterior distributions of the sensitive parameters are plotted in Figures 8 and 9. For both the conventional and proposed methods, the posterior distributions of KE, SM, N, and NK show a log-normal and unimodal shape (Figure 8), while the posterior distributions of CI are relatively irregular (Figure 9). A slightly bimodal shape is present in the posterior distribution of CG obtained from the proposed model. It can be inferred that the most likely values of KG, NK, and N are better defined by the proposed model because the peaks of their posterior distribution functions are sharper. Only the most likely value of CG is better defined by the conventional model. The conventional model may have a more significant uncertainty effect on the most likely values of the sensitive parameters.

Figure 8

Posterior distributions of sensitive parameters with a log-normal and unimodal shape.

Figure 8

Posterior distributions of sensitive parameters with a log-normal and unimodal shape.

Figure 9

Posterior distributions of sensitive parameters with an irregular shape.

Figure 9

Posterior distributions of sensitive parameters with an irregular shape.

Figure 10 shows the confidence interval of 90% produced by the proposed method and MCMC. The proposed method is able to cover most of the observed streamflow during 1–3-h lead times. With lead times of 1–3 h, the interval remains narrow, indicating good estimation and low uncertainty. However, the observed peak flood is outside the 90% interval in Figure 10(c), and therefore more attention should be paid to uncertainty in peak-flood forecasting.

Figure 10

90% confidence intervals for flood forecasting using the proposed model: (a) 1 h ahead, (b) 2 h ahead, and (c) 3 h ahead.

Figure 10

90% confidence intervals for flood forecasting using the proposed model: (a) 1 h ahead, (b) 2 h ahead, and (c) 3 h ahead.

CONCLUSIONS

The main purpose of this study was to improve the flood-forecasting efficiency of conceptual models for longer lead times. The conventional method compares simulated and observed streamflow, while the proposed method uses a novel objective function, namely, minimizing the sum of the squared errors between the forecasted and observed streamflow during multiple lead times. Both conventional and proposed methods were applied to forecasting the 1–6-h ahead streamflow in the Baiyunshan Reservoir basin. Uncertainty analysis was used to further compare the two methods. The following conclusions can be drawn:

  1. The proposed method significantly outperforms the conventional method when the lead time is longer than 3 h, particularly for flood peak flow in terms of the value and occurrence time.

  2. The efficiency of forecasting decreases with increasing lead times, and 5-h ahead forecasting is recommended for practical use in the Baiyunshan Reservoir.

  3. The proposed method produces less uncertainty in obtained parameters than the conventional method. Implemented with MCMC technique, the proposed method can provide a robust probabilistic forecast over multiple lead times.

The proposed method is reliable when providing multiple parameter sets for forecasting with different lead times, and may be used to achieve accurate and longer lead-time basin forecasts for flood disaster mitigation. A flood-forecasting model incorporated with weather prediction can increase forecast lead times from a few hours to a few days. With advanced precipitation forecasting technologies, longer forecasts could be considered that couple accurate rainfall data with the proposed model and thereby increase hydrological forecasting lead times. Future research is recommended to address these issues.

ACKNOWLEDGEMENTS

This study was supported by the National Key R&D Program of China (2017YFC0405900), the National Natural Science Foundation of China (51579180, 51861125102), and the Innovative Research Groups of the Natural Science Foundation of Hubei, China (2017CFA015). The authors would like to thank the editor and the anonymous reviewers for their comments that helped improve the quality of the paper. The authors declare that they have no conflict of interest.

REFERENCES

REFERENCES
Badrzadeh
H.
,
Sarukkalige
R.
&
Jayawardena
A. W.
2015
Hourly runoff forecasting for flood risk management: application of various computational intelligence models
.
Journal of Hydrology
529
,
1633
1643
.
Badrzadeh
H.
,
Sarukkalige
R.
&
Jayawardena
A. W.
2016
Improving ANN-based short-term and long-term seasonal river flow forecasting with signal processing techniques
.
River Research and Applications
32
(
3
),
245
256
.
Bao
H. J.
,
Zhao
L. N.
,
He
Y.
,
Li
Z. J.
,
Wetterhall
F.
,
Cloke
H. L.
,
Pappenberger
F.
&
Manful
D.
2011
Coupling ensemble weather predictions based on TIGGE database with Grid-Xinanjiang model for flood forecast
.
Advances in Geosciences
29
,
61
67
.
Beven
K.
&
Young
P.
2013
A guide to good practice in modeling semantics for authors and referees
.
Water Resources Research
49
(
8
),
5092
5098
.
Chen
S. T.
&
Yu
P. S.
2007
Real-time probabilistic forecasting of flood stages
.
Journal of Hydrology
340
(
1–2
),
63
77
.
Chen
H.
,
Xiang
T. T.
,
Zhou
X.
&
Xu
C. Y.
2012a
Impacts of climate change on the Qingjiang Watershed's runoff change trend in China
.
Stochastic Environmental Research and Risk Assessment
26
(
6
),
847
858
.
Cole
S. J.
&
Moore
R. J.
2008
Hydrological modelling using raingauge- and radar-based estimators of areal rainfall
.
Journal of Hydrology
358
(
3–4
),
159
181
.
Deng
C.
,
Liu
P.
,
Liu
Y.
,
Wu
Z.
&
Wang
D.
2015b
Integrated hydrologic and reservoir routing model for real-time water level forecasts
.
Journal of Hydrologic Engineering
20
(
9
),
05014032
.
Deng
C.
,
Liu
P.
,
Guo
S.
,
Li
Z.
&
Wang
D.
2016
Identification of hydrological model parameter variation using ensemble Kalman filter
.
Hydrology and Earth System Sciences
20
(
12
),
4949
4961
.
Feng
M.
,
Liu
P.
,
Guo
S.
,
Gui
Z.
,
Zhang
X.
,
Zhang
W.
&
Xiong
L.
2017
Identifying changing patterns of reservoir operating rules under various inflow alteration scenarios
.
Advances in Water Resources
104
,
23
36
.
Garcia-Pintado
J.
,
Mason
D. C.
,
Dance
S. L.
,
Cloke
H. L.
,
Neal
J. C.
,
Freer
J.
&
Bates
P. D.
2015
Satellite-supported flood forecasting in river networks: a real case study
.
Journal of Hydrology
523
,
706
724
.
Goswami
M.
,
O'Connor
K. M.
,
Bhattarai
K. P.
&
Shamseldin
A. Y.
2005
Assessing the performance of eight real-time updating models and procedures for the Brosna River
.
Hydrology and Earth System Sciences
9
(
4
),
394
411
.
Gragne
A. S.
,
Sharma
A.
,
Mehrotra
R.
&
Alfredsen
K.
2015
Improving real-time inflow forecasting into hydropower reservoirs through a complementary modelling framework
.
Hydrology and Earth System Sciences
19
(
8
),
3695
3714
.
Jie
M.-X.
,
Chen
H.
,
Xu
C.-Y.
,
Zeng
Q.
&
Tao
X.-E.
2016
A comparative study of different objective functions to improve the flood forecasting accuracy
.
Hydrology Research
47
(
4
),
718
735
.
Krzysztofowicz
R.
1995
Recent advances associated with flood forecast and warning systems
.
Reviews of Geophysics
33
,
1139
1147
.
Li
H. X.
,
Zhang
Y. Q.
,
Chiew
F. H. S.
&
Xu
S. G.
2009
Predicting runoff in ungauged catchments by using Xinanjiang model with MODIS leaf area index
.
Journal of Hydrology
370
(
1–4
),
155
162
.
Li
X.
,
Guo
S.
,
Liu
P.
&
Chen
G.
2010
Dynamic control of flood limited water level for reservoir operation by considering inflow uncertainty
.
Journal of Hydrology
391
(
1–2
),
126
134
.
Li
Z.
,
Xin
P.
&
Tang
J.
2013
Study of the Xinanjiang model parameter calibration
.
Journal of Hydrologic Engineering
18
(
11
),
1513
1521
.
Liu
P.
,
Li
L.
,
Chen
G.
&
Rheinheimer
D. E.
2014
Parameter uncertainty analysis of reservoir operating rules based on implicit stochastic optimization
.
Journal of Hydrology
514
,
102
113
.
Liu
P.
,
Li
L.
,
Guo
S.
,
Xiong
L.
,
Zhang
W.
,
Zhang
J.
&
Xu
C.-Y.
2015
Optimal design of seasonal flood limited water levels and its application for the Three Gorges Reservoir
.
Journal of Hydrology
527
,
1045
1053
.
Liu
Z.
,
Guo
S.
,
Zhang
H.
,
Liu
D.
&
Yang
G.
2016
Comparative study of three updating procedures for real-time flood forecasting
.
Water Resources Management
30
(
7
),
2111
2126
.
Lu
H. S.
,
Hou
T.
,
Horton
R.
,
Zhu
Y. H.
,
Chen
X.
,
Jia
Y. W.
,
Wang
W.
&
Fu
X. L.
2013
The streamflow estimation using the Xinanjiang rainfall runoff model and dual state-parameter estimation method
.
Journal of Hydrology
480
,
102
114
.
Lv
Z.
,
Liu
X.
,
Tang
L.
,
Liu
L.
,
Cao
W.
&
Zhu
Y.
2016
Estimation of ecotype-specific cultivar parameters in a wheat phenology model and uncertainty analysis
.
Agricultural and Forest Meteorology
221
,
219
229
.
Ma
Z.
,
Li
Z.
,
Zhang
M.
&
Fan
Z.
2013
Bayesian statistic forecasting model for middle-term and long-term runoff of a hydropower station
.
Journal of Hydrologic Engineering
18
(
11
),
1458
1463
.
Ma
F.
,
Ye
A.
,
Deng
X.
,
Zhou
Z.
,
Liu
X.
,
Duan
Q.
,
Xu
J.
,
Miao
C.
,
Di
Z.
&
Gong
W.
2016
Evaluating the skill of NMME seasonal precipitation ensemble predictions for 17 hydroclimatic regions in continental China
.
International Journal of Climatology
36
(
1
),
132
144
.
Merz
R.
,
Parajka
J.
&
Bloeschl
G.
2011
Time stability of catchment model parameters: implications for climate impact analyses
.
Water Resources Research
47
,
W02531
.
Mohan
M.
&
Sati
A. P.
2016
WRF model performance analysis for a suite of simulation design
.
Atmospheric Research
169
,
280
291
.
Nicolle
P.
,
Pushpalatha
R.
,
Perrin
C.
,
Francois
D.
,
Thiery
D.
,
Mathevet
T.
,
Le Lay
M.
,
Besson
F.
,
Soubeyroux
J. M.
,
Viel
C.
,
Regimbeau
F.
,
Andreassian
V.
,
Maugis
P.
,
Augeard
B.
&
Morice
E.
2014
Benchmarking hydrological models for low-flow simulation and forecasting on French catchments
.
Hydrology and Earth System Sciences
18
(
8
),
2829
2857
.
Nourali
M.
,
Ghahraman
B.
,
Pourreza-Bilondi
M.
&
Davary
K.
2016
Effect of formal and informal likelihood functions on uncertainty assessment in a single event rainfall-runoff model
.
Journal of Hydrology
540
,
549
564
.
Ouyang
F.
,
Lu
H. S.
,
Zhu
Y. H.
,
Zhang
J. Y.
,
Yu
Z. B.
,
Chen
X.
&
Li
M.
2014
Uncertainty analysis of downscaling methods in assessing the influence of climate change on hydrology
.
Stochastic Environmental Research and Risk Assessment
28
(
4
),
991
1010
.
Pagano
T. C.
,
Wang
Q. J.
,
Hapuarachchi
P.
&
Robertson
D.
2011
A dual-pass error-correction technique for forecasting streamflow
.
Journal of Hydrology
405
(
3–4
),
367
381
.
Reed
S.
,
Koren
V.
,
Smith
M.
,
Zhang
Z.
,
Moreda
F.
,
Seo
D.-J.
&
Participants
D. M. I. P.
2004
Overall distributed model intercomparison project results
.
Journal of Hydrology
298
(
1–4
),
27
60
.
Refsgaard
J. C.
&
Knudsen
J.
1996
Operational validation and intercomparison of different types of hydrological models
.
Water Resources Research
32
(
7
),
2189
2202
.
Rogelis
M. C.
&
Werner
M.
2018
Streamflow forecasts from WRF precipitation for flood early warning in mountain tropical areas
.
Hydrology and Earth System Sciences
22
(
1
),
853
870
.
Xie
A.
,
Liu
P.
,
Guo
S.
,
Zhang
X.
,
Jiang
H.
&
Yang
G.
2018
Optimal design of seasonal flood limited water levels by jointing operation of the reservoir and floodplains
.
Water Resources Management
32
(
1
),
179
193
.
Xiong
L. H.
&
O'Connor
K. M.
2002
Comparison of four updating models for real-time river flow forecasting
.
Hydrological Sciences Journal-Journal Des Sciences Hydrologiques
47
(
4
),
621
639
.
Xu
Z. X.
&
Li
J. Y.
2002
Short-term inflow forecasting using an artificial neural network model
.
Hydrological Processes
16
(
12
),
2423
2439
.
Xue
X.
,
Zhang
K.
,
Hong
Y.
,
Gourley
J. J.
,
Kellogg
W.
,
McPherson
R. A.
,
Wan
Z.
&
Austin
B. N.
2016
New multisite cascading calibration approach for hydrological models: case study in the Red River basin using the VIC model
.
Journal of Hydrologic Engineering
21
(
2
),
05015019
.
Zhao
R. J.
1992
The Xinanjiang model applied in China
.
Journal of Hydrology
135
(
1–4
),
371
381
.
Zhao
R. J.
&
Liu
X. R.
1995
The Xinanjiang model
. In:
Computer Models of Watershed Hydrology
(
Singh
V. P.
, ed.).
Water Resources Publications, Colorado
, pp.
215
232
.