Inflow combination forecast of reservoir based on SWAT, XAJ model and Bayes model averaging method Open Access

Hydrological forecast is an applied subject that makes qualitative or quantitative analysis on the future change of hydrological elements using the existing hydrological change law. As a non-engineering water resource management measure, hydrological forecast plays an indispensable role in flood control, fighting against drought, reservoir operation (Jiang et al. 2017a, 2017b), water resources planning and utilization, etc. (Liu et al. 2018; Fang et al. 2019).

Hydrological model is one of the common methods in hydrological forecast. According to the modeling principle, it can be divided into data-driven models (Jiang et al. 2018a) and process driven models (Meng et al. 2019). The latter can be divided into distributed hydrological models and lumped hydrological models based on whether the spatial changes of basin characteristic parameters are considered. Distributed hydrological model fully considered the spatial characteristics of underlying surface and other conditions. In recent years, with the application of 3S technology in hydrological simulation becoming more and more mature (Dile et al. 2016), distributed hydrological model has been rapidly developed and applied. The lumped hydrological model is a kind of conceptual hydrological model (Dwivedi et al. 2019; Jiang et al. 2019a, 2019b), which is suitable for the small watershed. The model structure is simple, and it has the advantages of easy access to the required data and easy operation in the hydrological practical production. It plays an irreplaceable role in the engineering practice.

In the distributed hydrological model, the typical one is the Soil and Water Assessment Tool (SWAT) model proposed by Dr Jeff Arnold, integrating the characteristics of CREAMS, GLEAMS, EPIC, SWRRB and other models (White et al. 2017). Based on the characteristics of different land use patterns, soil types and management measures, this model can simulate the continuous long-term hydrological cycle and physical process in a complex large watershed (Surhone et al. 2010), and its most widely used field is inflow prediction. For example, Fontaine et al. (2002) increased the versatility of SWAT by developing the capability to simulate hydrology of a non-agricultural mountainous region with a large snowmelt component. Di & Arnold (2004) proposed an hourly input-output calibration approach for the SWAT model, and presented for 24 representative storm events occurring in the Blue River watershed. Bouraoui et al. (2005) applied SWAT model to Medjerda river basin to study the potential impact of land management scenarios, and it was predicted that converting all agricultural land to irrigated crop introduced significant changes on nitrate concentration in surface water. Milewski et al. (2009) calibrated the SWAT model against the observed runoff values from Wadi Girafi Watershed and then used it to provide a continuous simulation (1998–2007) of the overland flow, channel flow, transmission losses, evaporation, evapotranspiration, and groundwater recharge for this watersheds. Perazzoli et al. (2013) applied SWAT model to analyze the impacts of climate changes on the flow and sediment production regimes in the Concórdia River drainage basin. Serpa et al. (2015) evaluated the impacts of climate and land use changes on streamflow and sediment export for a humid and a dry Mediterranean catchment, using the SWAT model. Woldesenbet et al. (2017) used an integrated approach comprising hydrological modeling and partial least squares regression to quantify the contributions of changes in individual land use land cover (LULC) classes to changes in hydrological components based on LULC maps and SWAT model.

For the lumped hydrological model, the typical one is Xin'anjiang (XAJ) model, which was first proposed by Professor Zhao of Hehai University, China (Zhao 1984; Yuan et al. 2008). This model divides the study basin into unit basins, calculates the flow of each unit respectively based on the concept of flow generation under saturated conditions, and then calculates the flow process of the outlet section of the basin by river channel confluence curve. The structure of XAJ model is clear, the data needed is easy to obtain, and it has strong applicability in the practical application. Since the model was proposed, many experts and scholars have been committed to the practicability and universality study of XAJ model in various basins (Jiang et al. 2019a, 2019b). Zhu & Zhang (2004) simulated the daily discharge hydrographs for two flooding events based on the continuous five year's daily hydrological observations, using XAJ model in a semi-distributed schemes. Li et al. (2013) developed the XAJ-Haihe model by improving the XAJ model to study the influence of the underlying surface changes of the Haihe Basin on floods. Song et al. (2013) presented a two-step statistical evaluation framework using global techniques for parameter identification and global sensitivity analysis of XAJ model. Han & Wu (2015) improved the XAJ model using the dynamic storage coefficient method in river flood routing, and analyzed the applicability of the improved XAJ model based on the hydrological data of Yingjiang River Basin. In order to add more constraints to the original XAJ model, Fang et al. (2017) developed an energy balance scheme suitable for this model and coupled it with the mass balance scheme of the original XAJ model.

SWAT models often have a large demand for data. Due to the lack of some data and the generalization of the model, the accuracy of the model will be reduced (Setegn et al. 2010; Fan et al. 2020). In actual research on SWAT models, different algorithms are often used to improve the simulation effect of SWAT models and reduce the error value of simulation results (Lv et al. 2020). XAJ models use less data in the process of calling. Moreover, the prediction results in the same watershed are close to the SWAT model indicators, but the prediction accuracy in some periods is different (Shi et al. 2011). Considering the characteristics of SWAT model and XAJ model in runoff prediction, hybrid algorithm can be considered to improve the simulation accuracy of the model. In previous studies, there have been cases of using multiple algorithms to improve prediction results and reduce errors, such as: Cao et al. (2021) used the SWAT model to reproduce the data observed in the Yalong River Basin and forecast future runoff changes. In their article, they used the Bayes Model Averaging (BMA) method to synthesize multiple Global Climate Models for joint forecasting, and found that the method of joint forecasting requires prediction better than a single model. Jiang et al. (2017a, 2017b) used the shuffled complex evolution (SCE-UA) method and the shuffled complex evolution metropolis (SCEM-UA) method to calibrate the Xinanjiang (XAJ), hybrid rainfall–runoff (HYB), and HYMOD (HYM) models in the Mishui watershed. After using the BMA algorithm, it is found that the SCEM-UA algorithm and the BMA method have good effects in runoff forecasting and flood forecasting. Lee et al. (2020) used the BMA method to synthesize multiple linear regression models, support vector machines and artificial neural networks based on the tele-correlation relationship between the monthly inflow of reservoirs and climate variables, and found that the model synthesized by the BMA method was more accurate in prediction results. Zhong et al. (2018) used the BMA method to optimize the inflow prediction data obtained by the artificial neural network, and found that the results predicted by the BMA method were better than the original data in terms of probability and certainty. However, there are few papers on the coupling of SWAT model and XAJ model. Therefore, based on the prediction results of SWAT model and XAJ model on the inflow runoff of Jinxi Reservoir in the Yalong River Basin, this study uses the BMA algorithm to synthesize the two models to build a SWAT-XAJ coupling model, and comprehensively studies the impact of this model on the accuracy of the inflow runoff prediction results.

The overall process of the SWAT model is that after the rain and snow brought by precipitation fall to the ground, part of it infiltrates into the soil, and part of it is converted into surface runoff. The water infiltrated into the soil is lost through soil evaporation, plant evapotranspiration, and flow in the soil, and part of it forms shallow ground water, and part forms deep groundwater. The surface runoff flows into the river after the loss in transportation and the adjustment of the reservoir, and the part of the water flowing into the reservoir also flows into the river through the outlet of the reservoir. After the precipitation is converted into water in the river, after a series of losses in evaporation and transport, the runoff flow required by the model is finally obtained.

The processes of inflow simulation in Yalong River Basin by SWAT model can be summarized as follows. (1) Use the ArcGIS to analyze DEM map, and generate the actual river network (Chaplot 2005). (2) Divide the study area into sub watersheds based on the river network. (3) Divide the sub watersheds into smaller hydrologic response units (HRU) based on land use mode and soil type in each sub watershed. (4) Drive the model by meteorological data, collect the flow of each HRU to the outlet of the basin, and obtain the total outflow of the study basin at last.

• (1)
  The water balance should be considered first in the runoff generation and confluence, which can be expressed by the following formula.

  

  (1)

  where, is the moisture content of soil at the end of period, mm. is the initial moisture content of soil in the ith day, mm. is the precipitation in the ith day, mm. is the surface flow in the ith day, mm. E is the evapotranspiration in the ith day, mm. is the infiltration flow and side flow of soil profile, mm. is the return flow in the ith day, mm. t is the time, d.
• (2)
  For the surface runoff calculation in SWAT model, Soil Conservation Service (SCS) curve number method is usually used when the HRU is used as the basic calculation unit to calculate surface runoff (Tessema et al. 2014). SCS curve number equation can be shown as follow.

  

  (2)

  

  (3)

  where, is the surface runoff of current day, mm. is the precipitation of current day, mm. S is the lag parameter, mm. CN is the runoff curve coefficient of SCS.
• (3)
  For soil water calculation, the dynamic storage model is used, which can be shown as follow (Arnold et al. 1998).

  

  (4)

  where, is the flow in soil, mm. is the permeable water volume in the saturated area of soil, mm. K is the saturated hydraulic conductivity of soil, mm/h. is the slope. L_h is the slope length, m. is the total porosity of soil.
• (4)
  For the evapotranspiration, including water surface evaporation, bare land evaporation, and plant evapotranspiration, there are three methods to estimate potential evapotranspiration, namely Hargreaves, Penman-Monteith and Priestley-Taylor in SWAT model, among which Penman-Monteith is the most commonly used, and the calculation formula is as follows (Arnold et al. 1998).

  

  (5)

  where, is the latent heat flux density, MJ/(m²•d). is the daily evaporation, mm/d. is the coefficient of correlation curve between saturated water pressure and temperature, kPa/°C. is the daily net radiation density, MJ/(m²•d). G is the soil heat flux density, MJ/(m²•d). is the air density, Kg/m³. is the maximum vapor pressure at altitude ⁠, kPa. is the water vapor pressure at altitude ⁠, kPa. is the humidity calculation constant, kPa/°C. is air impedance, s/m. is the canopy impedance, s/m.
• (5)

  For groundwater, it is divided into shallow and deep parts in SWAT model, which are calculated by the following formula (Arnold et al. 1998).

Parameter calibration and verification of the model are very important for the accuracy of inflow prediction (Chen et al. 2016). SWAT-CUP is a computer program specially used for parameter sensitivity analysis and calibration of SWAT model (Abbaspour et al. 2007; Singh et al. 2013). Several optimization algorithms, such as PSO, GLUE, ParaSol, SUFI-2 and MCMC, are embedded in this model. In this paper, SUFI-2 algorithm with relatively high efficiency is used for parameter calibration of SWAT model (Guillermo et al. 2015).

SUFI-2 algorithm is a comprehensive parameter optimization algorithm with global search capability. It updates the parameter combination through multiple iterations, fully considering model input, model structure, model parameters and measured data used for calibration and verification (Cao et al. 2018). The specific steps of SUFI-2 algorithm are as follows.

Step 1: Define the objective function and reasonable parameter range. Generally, the Nash efficiency coefficient or certainty coefficient is selected as the objective function to measure the fitting degree between the predicted value and the measured value. The initial parameter range is determined by the initial range recommended in the existing parameter database of SWAT-CUP.

Step 2: Carry out Latin hypercube random sampling to obtain a variety of parameter combinations, and the parameters obtained after sampling are used as the parameter input of SWAT model.

Step 3: Run the model, and use the defined objective function to conduct sensitivity analysis and sequencing for each parameter, evaluate the uncertainty and recommend a new range of parameters.

Step 4: Adjust the parameters range by further sampling and multiple iterations, until the best combination of parameters is obtained.

XAJ model contains several calculation modules, such as evapotranspiration calculation, flow generation calculation and confluence calculation, etc. The input of the model is rainfall and evapotranspiration, and the output is the discharge process of the outlet section of watershed. In the model calculation, the whole basin is divided into several units according to the Tyson polygon method, and then the flow generation and confluence process of each is calculated, respectively, to get the outlet flow of each unit, and the flow below the outlet of each unit is calculated by the river flood routing. Finally, the flow processes of each unit are superposed linearly to get the total flow process of the whole basin outlet section.

In the process of parameter automatic calibration using PEST, the main steps is summarized as follows (Doherty 1994).

Step 1: Select the parameters that need to be calibrated, and determine the reasonable value range and initial value of each parameter.

Step 2: Prepare the model parameters and parameter group input files, measured data files and control files required by PEST program.

Step 3: After all the documents are prepared, execute the control files to run the PEST.

During the running process, the computer can automatically call the XAJ model according to the path specified in the control file, and then the PEST program optimizes the parameters through continuous iteration based on the objective function.

Different hydrological models have different advantages and disadvantages when forecasting the inflow in the same basin, and the prediction effect of each model is often limited when the forecasting is done separately, so the research of inflow combination forecasting of multiple models has become the development trend of current hydrological forecasting. Combination forecasting can effectively improve the accuracy of forecasting according to the reasonable weighted average calculation after obtaining the forecast results of various single hydrological models (Dai et al. 2016; Zhang et al. 2020).

For the weight determination of combination forecasting, this paper selects the BMA method (Liang et al. 2010). This method first combines the prediction results of each model with the measured results to calculate the posterior probability. Then, the model with better prediction effect gets higher weight, and the final prediction value can be obtained by the weighted average calculation. Its basic principle can be briefly introduced as follows (Dong et al. 2011).

The detailed calculation steps of EM algorithm are as follows (Duan et al. 2007).

• (1)
  Initialization: set iterations Iter = 0.

  

  (13)

  where, n represents the time length of the calibration period. and is the measured value at time i and the predicted value of the kth model, respectively.
• (2)
  Calculate the initial likelihood value:

  

  (14)

  where, represents the initial likelihood value. represents the initial weight of models which are mentioned above. represents the initial normal distribution with mean and variance.
• (3)
  Calculate the hidden variable: set Iter=Iter + 1

  

  (15)

  where, represents the hidden variable in the Iter iterations. represents the normal distribution of the Iter-1 iterations. represents the sum of models' distribution of the Iter-1 iterations. K means num of models used in research. k means order of model.
• (4)
  Calculate the weights:

  

  (16)

  where, represents the weight of kth model in the Iter iteration. n means the total num of measured sequence. represents the sum of hidden variables which is calculated by step (3) of a sequence.
• (5)
  Calculate the prediction error of model:

  

  (17)

  where, represents the prediction error of model k. represents the hidden value of the kth model of the Iter iteration. represents the observation value in the set. represents the prediction value in the set.
• (6)
  Calculate the likelihood value:

  

  (18)

  where, represents the likelihood value of the Iter iteration.
• (7)

  Check the convergence condition: if is less than or equal to the initially set allowable error limit, end the calculation. Otherwise, return to step (3).

The input data of SWAT model includes spatial data and attribute data. Spatial data includes DEM digital elevation data, land use data and soil type data. Attribute data includes meteorological data and measured flow data of hydrological stations (Gashaw et al. 2018). The specific data sources used in this model are shown in Table 1.

• (1)

  Hydro-meteorological data

The meteorological driving data input by the model includes daily precipitation (mm), daily maximum and minimum temperature (°C), daily average wind speed (m/s) and relative humidity (%). In this paper, SWAT model is built over the whole basin of Yalong River. Based on the measured data of main meteorological stations and Jinping hydrological station, the daily inflow forecast of Jinxi reservoir is carried out. Table 2 is the geographic location of the main meteorological and hydrological stations used in this paper. The meteorological data used are actually measured data from 1995 to 2012. The inflow data is the daily inflow data of Jinping station from 2005 to 2012, which is used to verify the prediction effect of SWAT model.

In addition, when building the meteorological database, we need to generate the missing solar radiation data according to the software SwatWeather.exe (Jung et al. 2016), using the existing average air pressure, temperature, average wind speed, relative humidity, rainfall, evaporation, sunshine hours and other meteorological data.

• (2)

  Spatial data

• • ① Digital elevation model (DEM) data

The DEM data in this paper comes from the international scientific data service platform. According to the longitude and latitude of the study basin, the grid data with resolution of 90m × 90 m is downloaded. After data splicing, projection conversion, clipping and other operations are completed in ArcGIS, the DEM map of the study area with standard format can be obtained.

• ② Land use data

The scale of land use data used in this paper is 1:100000. Table 3 and Figure 4(a) is respectively the land use distribution table and the land use distribution map after the reclassification of Yalong River Basin. It can be seen that the grassland area in Yalong River basin is the most extensive, a total of 66,050km², accounting for 51.68%. The second is forest land, a total of 44,842km², accounting for 35.09%.

• ③ Soil data

The soil data of this paper comes from the world soil database. The soil distribution map is come from the soil data of the second national land survey compiled by Nanjing Soil Institute, China, with a scale of 1:1,000,000. The soil type distribution map is shown in Figure 4(b).

• (3)

  Drainage system extraction, sub watershed and HRU division

Through DEM data, the study area is divided into 26 sub watersheds, and the final area of the whole study basin is 128,000 km². The sub watershed division map is shown in Figure 4(c). Because the flow generation and confluence are mainly affected by the underlying surface conditions, different land-use methods, soil types and slopes will have an impact on the infiltration, evaporation and slope flow. Therefore, the sub watershed is further divided into the minimum calculation unit HRU before the calculation to ensure the reliability of inflow prediction results. In this paper, the multiple HRUs method in ARCSWAT is used to divide the sub watershed (Das et al. 2013), and 657 HRUs are generated at last.

Taking 1998–2000 as the three-year warm-up period and 2000–2012 as the model simulation period, the model can be operated. The results of parameter calibration and inflow prediction are as follows.

The best parameters are found by SWAT-CUP and multiple iterations, in which the iteration is stopped until the overall difference between the simulated value and the measured value is the smallest. The final value of the calibrated parameters of inflow simulation is shown in Table 4, and the initial range of parameters is also given in Table 4 for comparison.

It can be seen from the results of the SWAT model that the prediction data in the calibration period can simulate the observed data well. It can also be seen from the results in the validation period that the SWAT model can predict the trend of runoff change. However, the simulation results in the validation period from 2011/9/1 to 2011/10/1 are bigger than observation values. Considering the data in the calibration period and validation period, it is speculated that the precision of soil data and soil utilization in this period is affected.

Based on the results of sub watershed division, the evaporation and runoff yield of each sub watershed are calculated respectively, then the water source is divided and the confluence is calculated. In each unit, the outflow process is calculated using the river channel confluence curve, and then it is added with the flow process of the upstream inflow station at the same time, such as Jiagu, Gaizhu, Baji, Jiami and Yangfanggou. Finally, the daily outflow prediction process of the outlet section of watershed can be obtained. The results of parameter calibration of XAJ model by PEST automatic calibration program are shown in Table 6.

Analyzing the results of XAJ model, it can be seen that the predicted data in the calibration period can well simulate the runoff data in the measured period, while the simulation effect in the verification period from 2011/11/1 to 2012/2/1 is relatively large. Considering the land data in the calibration period and the verification period, it is speculated that the impact of water use condition and rainfall data accuracy in this period is affected.

Three statistical indicators, i.e., certainty coefficient R², root mean square error (RMSE) and Nash-Suthcliffe efficiency (NSE), are selected to evaluate the simulation effect of the models (Thavhana et al. 2018).

• (1)
  Certainty coefficient R²

  

  (19)
• (2)
  RMSE

  

  (20)
• (3)
  NSE

  

  (21)
• (4)
  MAE

  

  (22)

  where, is the measured inflow, is the predicted inflow, is the average of the measured inflow, is the average of the predicted inflow, and n is the length of the inflow data series.

• Based on the above three evaluation indicators, the prediction results of the two models in calibration and verification period are shown in Table 7.

From the inflow prediction results in Figures 5,⁶⁷–8, it can be seen that, during the calibration period (2005–2009), the predicted value of SWAT model at the base flow is consistent with the measured value at most of the time, and the predicted value at the large flood peak is close to the measured value, but the simulation effect for the small flood peak is poor. The predicted value of XAJ model at the base flow is basically consistent with the measured value, and it is more accurate for the prediction at the small flood peak, while the predicted value at the large flood peak often deviates from the measured value, which is slightly lower than the measured value, and most of the predicted value will be smaller than the measured value after the flood peak subsides. One of the reasons for this phenomenon is that the SWAT model is built based on the whole Yalong River Basin, and the rainfall data of the main meteorological stations are used as input. The best value of parameter calibration of SWAT is more suitable for the whole basin, while the XAJ model is built based on the divided interval basin of Jinxi reservoir. The result of parameter calibration of XAJ model is better for the inflow prediction of Jinxi reservoir, so it can well reflect the change of small flood peak.

During the verification period (2010–2012), the predicted value of SWAT model at the base flow is smaller than the measured value at most times, and the predicted value at the small flood peak is larger than the measured value, but the predicted value at the large flood peak is relatively close with the measured value, the rising and declining trend of predicted flood is also consistent with the measured value. XAJ model has the highest agreement between the predicted value and the measured value in the rising process of flood, but in the stage of flood fading, the predicted process often lags behind the measured process. The predicted value at the small flood peak is often lower than the measured value, but the prediction effect at the large flood peak is better. The reason for this phenomenon is that the rainfall input of XAJ model is based on the area rainfall calculated by the rainfall stations in each unit according to the Tyson polygon method, and the actual rainfall situation of each rainfall station is different, so the calculated value of area rainfall can only reflect the rainfall situation of the unit in general, resulting in poor fitting effect in the process of flood fading.

From the prediction accuracy, the SWAT model and XAJ model can predict the daily inflow process of Jinxi reservoir well after the optimal parameter value is obtained through parameter calibration. However, because of the difference of model structure and principle, the prediction effect is also different. According to the statistical results in Table 7, it can be seen that the certainty coefficient of XAJ model can reach 90% in both calibration and verification period, which is higher than the 88.77% in the calibration period and the 84.98% in the verification period of SWAT model, indicating that the overall correlation between the predicted values and the measured values of XAJ model is better than that of SWAT model. Through the comparative analysis of RMSE, it is found that the RMSE value of SWAT model is lower than that of XAJ model in the calibration period, while the result is just the opposite in the verification period. From the perspective of NSE, the NSE of this two models can both reach 80%, which shows that the simulation results of the models are consistent with the measured values. But the NSE value of SWAT model is higher than that of XAJ model in both the calibration and verification periods, which shows that the prediction effect of SWAT model is better than that of XAJ model in terms of the overall prediction process.

From this analysis, it can be seen that the results of the two models both have advantages and disadvantages in each of the three evaluation indicators, so it cannot be concluded which model is better in this basin. In order to give full play to the advantages of each model and improve the accuracy of inflow prediction in the basin, the combination forecast is particularly necessary at this time.

The analysis of the results obtained from the BMA algorithm shows that the model simulation effect in the calibration period is good. By integrating the results of the XAJ model and the SWAT model and assigning different weights to the results, the simulation error of the XAJ model and the SWAT model in the period of poor simulation effect in the validation period can be reduced, and the accuracy of the model can be effectively improved.

From Table 8, it can be seen that the R² of BMA is 95.15% in calibration period, and that is 92.14% in verification period, which are both larger than that of the previous two models. The effective increment of R² of BMA in calibration and verification period is 2.87% (compared with the 92.28% of XAJ) and 1.19% (compared with the 90.95% of XAJ), respectively. In terms of NSE, the NSE of BMA is higher than any single model in both calibration and verification period. The effective increment of NSE of BMA in calibration and verification period is 2.24% (compared with the 89.12% of SWAT) and 6.80% (compared with the 84.42% of SWAT), respectively. In terms of RMSE and MAE, the RMSE and MAE of BMA is the smallest compared to the previous two models. The effective decrement of RMSE of BMA in calibration and verification period is 50.19 (compared with the 383.08 of SWAT) and 82.00 (compared with the 413.09 of XAJ) and the effective decrement of MAE of BMA in calibration and verification period is 55.17 (compared with the 234.30 of XAJ) and 65.23 (compared with the 266.55 of SWAT), respectively. These results show that BMA method can effectively improve the prediction effect of the whole inflow series. Besides, it also shows that the combination forecast can combine the advantages of different forecast models, overcome the shortcomings of single hydrological model, and make the forecast results more accurate and reliable.

The error between the predicted results and the measured results obtained above was calculated. The data time of the calibration set has 1826 data from 2005 to 2009, and the data time of the validation set has 1096 data from 2010 to 2021. The percentage relative error of the calibration set and the validation set of each model was calculated as follows:

Based on the introduction of principle, structure and parameter calibration method of SWAT model and XAJ model, this paper studied the inflow forecast of Jinxi reservoir in Yalong River basin by SWAT model, XAJ model and the BMA based combination forecast model, and evaluated the forecast results by three evaluating indicators, i.e., certainty coefficient, RMSE and Nash efficiency coefficient. The advantages and disadvantages of different models in Jinxi reservoir inflow prediction are analyzed and compared. The following conclusions are summarized:

• (1)

  When the conventional single hydrological model is used for inflow forecasting, due to the differences in the structure, modeling principle and application scope, there will be different advantages and disadvantages for different models even if the inflow forecasting is carried out in the same research area.

• (2)

  Based on the prediction results of SWAT and XAJ model, it is found that XAJ model is better than SWAT model in terms of certainty coefficient, but SWAT model is more accurate than XAJ model in terms of RMSE and Nash efficiency coefficient.

• (3)

  Based on the inflow prediction results of the two models, the BMA method is used to carry out the combination forecast in this paper, which can effectively combine the prediction advantages of different single models and greatly improve the overall prediction accuracy of basin. Compared with the SWAT and XAJ model, the maximum effective increment of certainty coefficient of combination forecast is 2.87%, the maximum effective decrement of RMSE is 82.00, and the maximum effective increment of NSE is 6.80%, so the effect of combination forecast is significant.

• (4)

  Based on the error between the predicted value and the measured value, it can be concluded that the XAJ model and SWAT model have a good prediction effect on the Yalong River Basin, and the prediction accuracy can be further improved after the synthesis of BMA method.

It can be concluded from the points mentioned above that inflow forecast effect of the XAJ model and the SWAT model in the Jinxi reservoir is good. Then use the BMA method to combine the two kinds of comprehensive physical model; the purpose of this technique is to combine two kinds of physical model to overcome their limitations, in particular, the prediction error value reduced to some extent. According to the current results, there is some error between the predicted data and the measured data in the verification period when the inflow is large, and the prediction effect is good in the rest of the flow. In order to better improve the prediction effect, further research on the physical model is needed. This work can provide a certain reference for the flood control and operation technology of cascade reservoirs in Yalong River Basin. In the future, this technology can be used to improve the inflow prediction accuracy and establish a more accurate flood control and operation system when the inflow prediction of cascade reservoirs in Yalong River Basin is carried out.

This study was financially supported by the Natural Science Foundation of China (52179016), Natural Science Foundation of Hubei Province (2021CFB597). The authors are grateful to the anonymous reviewers for their comments and valuable suggestions.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.