## 5 Conclusions  
We improved the vertical one-dimensional numerical algorithm of reservoir water temperature and completed the compilation of the corresponding program. The improved  
Figure 8: Comparison of precision coefficients for each month. (**a**) Xulong. (**b**) Xiluodu. (**c**) Jiexu. (**d**) Sanhekou.  
Figure 9: The total error of each depth in the vertical direction of the three reservoirs.  
algorithm can not only take factors such as reservoir operation mode, reservoir water level change, inflow water temperature, reservoir geometry, and solar radiation, etc. into account, but it can also predict distribution of the water temperature under the condition of bottom slag at the front of the dam.  
1. The NSE of the water temperature simulation results of the three different reservoirs are all above 0.85, and the average difference is below 1.0 \({}^{\circ}\)C, which has a high reliability. It can be concluded that the algorithm is suitable for predicting the water temperature at the front of the dam for reservoirs in various scales and modes of operation.
2. Compared with the empirical method, this algorithm is more thorough in theory, considers more working conditions, and has more accurate simulation results. Compared with the three-dimensional numerical algorithm, this algorithm is more efficient and easier to use.
3. The model proposed in this paper can be seamlessly embedded in the simulation program for concrete dam temperature control. More accurate temperature boundary conditions are provided for the simulation program without affecting the overall efficiency. The reliability of the simulation results of stress state in the crack-prone areas of the upstream surface is further improved, and it has important engineering significance for the temperature control and crack prevention design of large concrete dams.  
Conceptualization, X.Z., Z.S. and S.Q.; methodology, X.Z., Z.S. and S.Q.; software, X.Z., Z.S. and S.Q.; validation, X.Z., Z.W. and S.Q.; formal analysis, X.Z., Z.S. and S.Q.; investigation, X.Z.; resources, X.Z., Z.W. and M.Y.; data curation, X.Z., Z.W. and M.Y.; writing--original draft preparation, X.Z., Z.W. and M.Y.; writing--review and editing, X.Z., Z.S. and S.Q.; visualization, X.Z., Z.S. and S.Q. supervision, Z.S. and S.Q.; project administration, Z.S. and S.Q.; and funding acquisition, X.Z., S.Q. and M.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant number 52079049 and 51679074, the Fundamental Research Funds for the Central Universities, grant numbers B200203066, the Postgraduate Research & Practice Innovation Program of Jiangsu Province, grant number KYCX20_0479.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
DKYM Dongkanyuan method  
ZBFM Zhu Bofang method  
1D/2D/3D One-dimensional/Two-dimensional/Three-dimensional  
NSE The Nash-Sutcliffe efficiency coefficient  
LBM Lattice Boltzmann method  
THM Thermal-water-mechanical  
I1 DM Improved 1D numerical model