## 2 Data and Methods
### Methods  
In this paper, we used crop-water model variables as independent variables and investigated their correlations with population redistribution. Of course, there are discussions about migration and climate change, such as climate migration [23; 51; 52]. However, it is difficult to get reliable net migration data. In addition, either the mechanical growth of the population (through migration) or the natural growth is likely to be affected by climate change. Therefore, it was reasonable to use population redistribution as a dependent variable. The reason for using these variables was that crop and water models do not include any changes in human management, such as growing areas. There is no feedback from population to crops and water. As for validation data or observed data on crop yields, both climate change and socioeconomic change have impacts on the results; however, perhaps the latter is more important and significant. In addition, the population redistribution also affects crop yield output (such as changes in labor input), thus forming a circular argument. For our purposes, it was preferable to use simulation data over observed data. To reduce the influence of model simulation errors on regression results, two different sets of modeling data on crop production and water discharge distributed by ISIMIP were adopted: Lpjml_Gswp3 and Lpjml_Princeton. The two sets of data were obtained by using the agricultural and water resources model LPJmL, which was driven by two different observational climate datasets (GSWP3 and Princeton Global Forcing data PGFv2) to assess the effects of the choice of climate data on the results. Considering the availability of population data, correlation and regression analyses are performed for the two eras of the 1990s and the 2000s. Environmental variables, including crop yield deviation (MeanYield), water flow deviation (MeanFlow), maximum number of consecutive years below median crop yield (ConsecLowYield), and maximum number of consecutive years below median water flow (ConsecLowFlow) were included as independent variables. Built-up area (Built-up) and population (Pop) were included as control variables. These two control variables are factors that have significant impacts on population redistribution and can objectively reflect the demographic characteristics in the two countries. Pearson's correlation coefficients between the dependent variable (PopReDist), independent variables (MeanYield, MeanFlow, ConsecLowYield, and ConsecLowFlow) and control variables (Built-up and Pop) were calculated with the water-crop modeling data for each of the periods the 1990s and the 2000s. OLS (ordinary least squares) regression was then conducted to investigate the influences of the independent variables. Three different models were considered in the OLS regression. OLS Model 1 examined the impacts of four environmental variables on population redistribution. OLS Model 2 explored the impacts of environmental variables on population redistribution while controlling for the impact of urbanization level. OLS Model 3 included Pop as control variable; it explored the impacts of the environmental change variables on population redistribution while controlling for population density. VIF (Variance inflation factor) was used to assess the degree of multicollinearity among the independent variables. Formal studies of population redistribution tended to focus on identifying patterns that are presumed to hold universally [4; 53; 54]. The global regression assumes that the relationships between the variables are homogeneous across space. However, spatial dependences often are not homogeneous across large geographical regions [55]. We were more concerned about areas where spatial redistribution is sensitive to climate change. In addition, GWR can be used to statistically avoid the influence of multicollinearity.