The Geographically Weighted Regression (GWR) method was used to interpolate climate characteristics at station level to spatial grids, generating both the interpolated value and the standard error estimation at each grid point. It is a localized regression based method widely used for spatial interpolation, accounting for the spatial inhomogeneity with spatially varying slopes and intercepts. At each prediction location, the GWR picks up nearby training data points and constructs a weighted linear regression model of the dependent variable based on explanatory variables. There exists a set of options for determining whether a training point is included and its corresponding weight for constructing the linear model at a prediction location (Fotheringham
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A series of topographical facets were generated at different scale levels, following the methodology described by (Daly et al., 1994). At each prediction location, the customized GWR tries to first select stations sitting in the same facet at the finest level. If the number of selected stations does not meet the requirement of minimum number of stations (MIN_STA), the algorithm goes to the upper level facet and selects stations sitting in the same facet, until fulfilling the requirement. Considering topographical facet in the procedure of selecting neighboring stations helps to utilize the dependency of precipitation on topographical features (Daly et al., 1994). The whole algorithm was implemented in cython (www.cython.org) with Gnu Scientific Library (GSL) (http://www.gnu.org/software/gsl/).
4.6 Calculation of regional level climate characteristics
Regional mean value of each climatic characteristics was calculated for each climatic region (CR), elevation range (ER) and elevation range within climatic region (ERCR) as simple arithmetic mean of all interpolated values within the calculation region. Considering only spatial autocorrelation between two grid points within a calculation region, the uncertainty of the calculated regional mean was estimated using a simplified method based on uncertainty propagation with the following formula:
SE=√(∑_(i=1)^N▒〖se_i^2+ ∑_(i,j)▒〖〖2*ρ〗_(i,j)* se_i* se_j 〗〗)/N
A series of topographical facets were generated at different scale levels, following the methodology described by (Daly et al., 1994). At each prediction location, the customized GWR tries to first select stations sitting in the same facet at the finest level. If the number of selected stations does not meet the requirement of minimum number of stations (MIN_STA), the algorithm goes to the upper level facet and selects stations sitting in the same facet, until fulfilling the requirement. Considering topographical facet in the procedure of selecting neighboring stations helps to utilize the dependency of precipitation on topographical features (Daly et al., 1994). The whole algorithm was implemented in cython (www.cython.org) with Gnu Scientific Library (GSL) (http://www.gnu.org/software/gsl/).
4.6 Calculation of regional level climate characteristics
Regional mean value of each climatic characteristics was calculated for each climatic region (CR), elevation range (ER) and elevation range within climatic region (ERCR) as simple arithmetic mean of all interpolated values within the calculation region. Considering only spatial autocorrelation between two grid points within a calculation region, the uncertainty of the calculated regional mean was estimated using a simplified method based on uncertainty propagation with the following formula:
SE=√(∑_(i=1)^N▒〖se_i^2+ ∑_(i,j)▒〖〖2*ρ〗_(i,j)* se_i* se_j 〗〗)/N