## 2 Methodology
### Selection of Covariates  
The degree of correlation between the main variables and the covariates affects the accuracy of the cokriging model, so the factors with the higher degree of influence should be selected as the covariates. The influencing factors of dam deformation usually include water pressure, rainfall, temperature, aging, and so on. Taking the earth-rock dam as an example, the deformation of earth-rock dam caused by the change of water pressure is mainly formed by the compression and shear of soil and the displacement of dam foundation. The effect of temperature on the deformation of earth-rock dam is not obvious, and the change of external temperature generally only affects the surface soil. Rainfall infiltration raises water level and changes soil water content, thus affecting dam deformation. The creep of rockfill, the compression and plastic deformation of fissure joints and other weak structures at the bottom of reservoir under the action of water pressure, and the irreversible deformation of dam caused by cyclic loads such as the rise and fall of water level in front of dam also increase with the increase in dam operation life. Generally, three covariates are selected at most, and the more covariates are selected, the more complex and time-consuming the calculation is. Therefore, selecting appropriate covariates is the key to improving the accuracy and computational efficiency of the cokriging spatial model. In this paper, the variable importance for projection method based on the partial least squares regression method [31] was used to identify the influence degree of environmental factors. It can effectively solve the problems of unstable recognition effect and lack of spatial consistency commonly found in the currently used methods such as the mathematical model method, weighted area method, and grey correlation analysis [32]. The central idea of the method is that the explanatory ability of the factor principal component \(t_{h}\) for the component \(x_{j}\) is equivalent to the correlation coefficient \(\text{R}^{2}\) of the linear regression equation of \(x_{j}\) on \(t_{h}\). Since the explanatory effect of \(x_{j}\) on \(y\) is transmitted through the principal component \(t_{h}\), if the explanatory ability of \(t_{h}\) on \(y\) is strong and the effect of \(x_{j}\) on \(t_{h}\) is very significant, it can be assumed that the explanatory ability of \(x_{j}\) on \(y\) is strong. Therefore, the environmental factors such as water pressure, temperature, rainfall, and aging are regarded as independent variables \(x_{j}\), and the effects variables such as dam deformation and seepage are regarded as dependent variables \(y\). Then, the VIP\({}_{j}\) value of the variable importance for the projection index is solved for each environmental factor separately, as seen in Equation (1). Among them, the values of water pressure, temperature and rainfall are directly measured by instruments, and the days from the observation time to the initial observation time are taken as the aging measurement values. \[\text{VIP}_{j}=\sqrt{\frac{k}{\sum\limits_{h=1}^{m}\text{Rd}(y,t_{h})}\sum \limits_{h=1}^{m}\text{Rd}(y,t_{h})w_{hj}^{2}}, \tag{1}\]  
where \(k\) is the number of independent variables; \(t_{h}\) is the principal component extracted from related independent variables; \(\text{Rd}(y,t_{h})\) is the correlation coefficient between dependent variables and principal components, which indicates the explanatory ability of the principal component to \(y\); \(w_{hj}\) is the weight of independent variables on principal components. The VIP\({}_{j}\) value represents the degree of importance of the independent variables to the fit of the dependent variables, so the higher the value of VIP\({}_{j}\), the more significant the contribution of the independent variables to the dependent variables, and the more critical it is in the interpretation. Generally, if the VIP\({}_{j}\) value of the independent variable is less than or equal to 0.8, its explanatory ability for \(y\) can be ignored [33].