5. Hydrologic Simulation

5.1 Overall sequence analysis

The four machine learning methods, i.e., MLR, SVM, ANN and MLP, were used to simulate the runoff, and the historical observation climate and hydrological data were brought into the model for calibration and verification. In order to fully analyze the simulation accuracy of hydrological models, this part carries out daily and monthly runoff simulation respectively. And the performance of the hydrological simulation in the three basins is illustrated in Table 3 and Table 4.
Daily simulation result of verification period in Xiangxi River shows Pearson correlation coefficient and the Nash of MLP are the highest, meanwhile RMSE and RRSE are the smallest. This means MLP has the best simulation accuracy. And Nash is 0.71, indicating the simulation results are credible. In addition to MLP, the other three hydrological models have similar simulation effects. Simulation results of ANN are slightly lower than MLR and SVM. Compared with daily runoff simulation, simulation accuracy in monthly runoff are significantly improved. The average Spearman correlation coefficient is increased by 48%, and Nash is increased by 53%. Compared with the other three models, ANN has a slightly poorer simulation effect in the monthly runoff simulation.
In Jinghe River, the MLR, SVM and MLP show better daily simulation accuracy than ANN, and MLP is slightly better than the others. Monthly runoff simulation effect is better than the daily. In monthly runoff simulation, there is no significant difference in simulation results of four hydrological models. MLP has smaller simulation bias and slightly better simulation performance, but the correlation between simulated and actual runoff value is slightly lower than the others. In general, the four hydrological models have a general runoff simulation accuracy in Jinghe River. This may be due to the fact that the two climatic factors of precipitation and temperature have little impact on the overall runoff, and the relationship between climatic factors and runoff is not strong.
In daily performance of hydrological simulation in Zhongzhou River, the effects of the four models show strong differences. Simulation effect of MLP is significantly better than the others. In verification period, RMSE in MLP is about 38% of the SVM model. It can be seen simulation accuracy of MLP is significantly higher than the others. Fig. 8 shows the simulation sequence of the daily runoff of SVM and MLP. It can be seen MLP can better restore the runoff condition and simulation of runoff peak also has a higher accuracy. MLR is the best but MLP in hydrological simulation, and it exhibits superior simulation results in daily runoff simulation. This may be due to the fact that precipitation has a greater impact on runoff and presents a strong linear relationship in Zhongzhou River. SVM and ANN behave similarly, and the simulation performance is general. In the monthly runoff simulation, the simulation performance of MLP is slightly higher than the other three hydrological models. In general, MLP has obvious advantages in runoff simulation.
Based on the hydrological simulation above, it can be found runoff simulation accuracy of MLP is better than the other three models. SVM and ANN have similar simulation performance. MLR exhibits excellent simulation effects when there is a strong linear relationship between inputs and outputs, while the overall performance is slightly worse than the SVM and ANN models in opposite cases. In different basins, the simulation effects of hydrological models vary greatly. Simulation accuracy in Zhongzhou River are the best, while in Jinghe River are the worst. This is because there are large differences in the effects of climatic factors, i.e., precipitation and temperature, on runoff in different watersheds. Within the scope of climate factor impact, MLP can more fully explore its potential relationship with runoff.

5.2 Seasonality of Modeling Accuracies

Through overall sequence analysis for hydrological simulation, it can be seen MLP shows its greatest advantage in hydrological forecast in daily runoff forecast at Zhongzhou River. Therefore, this part selects the daily runoff forecast at Zhongzhou River as research object to analyze runoff simulation of four hydrological models during the four seasons. The data sequence is divided into four parts, i.e., spring (from March to May), summer (from June to August), autumn (from September to November), and winter (from December to February). Select simulation results of MLR, the most commonly used method, as baseline. Since Nash has negative value and RRSE is consistent with Nash on certain extent, this part does not analyze Nash. Analysis results in verification period are shown in Fig. 9.
It can be seen from the results that MLP shows the best simulation accuracy in four seasons compared with the others. Simulation performance in spring and summer is significantly higher. RMSE value of MLP in summer is 54.08% lower than that of MLR, and simulation deviation is greatly reduced. SVM and ANN models show a slightly worse simulation performance than MLR, which is consistent with performance of the four models in the hydrological simulation. It can be seen from the seasonal analysis that, compared with the others, the accuracy of MLP for the prediction in summer runoff peaks is significantly improved.

5.3 Streamflow Magnitudes

In order to further understand the simulation effect of hydrological models in each runoff interval, simulation sequence was subjected to magnitudes analysis. The sequence is arranged in ascending order according to observed runoff, and magnitudes are divided into 0-5%, 5-15%, 15-25%, 25-50%, 50-75%, 75-85%, 85-95% and 95-100%. Results of daily runoff simulation in Zhongzhou River are shown in Fig. 10.
From analysis results of Pearson correlation coefficient and RMSE, runoff simulation effects of the four hydrological models are not much different in 0-95% quantile interval. Overall, MLP is slightly better than the others. In 95-100% interval, the difference is significantly increased. MLP has obvious advantages and simulation accuracy is greatly improved. From the results of RRSE analysis, SVM shows the best simulation effect in 0-50% quantile interval. MLP is similar to MLR, while ANN is slightly worse. In 50-100% interval, difference among simulation results of the four models are reduced. Especially in ANN and SVM, and simulation results are almost identical. However, MLP is stable and exhibits better simulation results than the other three models.

5.4 Inter-Annual Variation of Runoff Changes

The RCM-driven hydrological model was used to forecast runoff during the period 2021-2050. MLP was used for runoff forecasting. Corrected RCMs climate prediction results were used as inputs. The forecast was carried out in Xiangxi River, Jinghe River and Zhongzhou River, respectively. Hydrological forecast results were analyzed based on historical hydrological simulation data.
The annual variability is shown in Fig. 11. It can be seen that annual runoff in the three basins all have upward trend in the next 30 years. And this trend is more obvious under RCP8.5 emission scenario. Among them, average annual runoff of Jinghe River is increasing year by year, and the increase is the largest in the three basins. Hydrological forecast results show that average annual runoff in Jinghe River will increase by about 50% until 2050. While the annual average runoff in Xiangxi River is increasing slightly. Under the RCP4.5 emission scenario, the annual average runoff in Xiangxi River reached its highest level in 2036, an increase of 27.04%. The future annual average runoff in Zhongzhou River is more gradual than that of the other two basins, but the overall trend is increased.

5.5 Intra-Annual Variation of Runoff Changes

Like inter-annual variation, based on historical observation data, intra-annual runoff change trend in three basins under two emission scenarios was analyzed. The results are shown in Fig. 12.
It can be seen that monthly average runoff in the three river basins in the next 30 years show different trends. The average monthly runoff in Xiangxi River increased slightly, and the increase mainly occurred in the peak period (from May to August) of the runoff. Like the Xiangxi River, the runoff growth in Jinghe River is mainly concentrated in summer. The increase is significantly larger than that in Xiangxi River, and this trend is more obvious under RCP8.5 emission scenario. In addition, the future winter (December to February) runoff in Jinghe River has also increased significantly, which may improve the winter runoff in the basin. Future monthly average runoff variation trend in Zhongzhou River is different from the others. The runoff growth is mainly concentrated from February to April, while the flow in other months has no obvious change trend. This means that the peak runoff in Zhongzhou River may move forward.