复杂地形区域平均气温空间插值方法研究

Spatial Interpolation Methods of Average Air Temperature under Complicated Terrain

采用反距离权重、克立格、径向基函数法、三维二次趋势面和地理加权回归5种方法,对云南125个站1月、4月、7月、10月和年的30年平均气温进行空间插值并比较分析发现：反距离权重、克立格、径向基函数法3种常规插值方法对地形复杂的云南气温空间分布模拟精度不高;三维二次趋势面和地理加权回归模型对云南气温空间分布模拟较好,交叉检验结果显示前者的平均绝对误差（MAE）为0.43-1.02℃,均方根误差（RMSE）为0.67-1.77℃,其推算的云南气温栅格数据能较好地反映出云南各地气温的分布和差异;GWR模型对气温的交叉验证在5种插值方法中误差最小,插值结果MAE在0.65℃以下,RMSE在0.8℃以下;进而使用“地理加权回归模型插值＋反距离权重残差内插”叠加法对抽取的10个检验站平均气温进行插值检验,64％的插值结果绝对误差在0.5℃以内,74％的插值结果相对误差在5％以内,且实测值与插值估算值回归关系决定系数R2在0.9以上.

By using such five methods as Inverse Distance Weighted （IDW）, Ordinary Kriging （OK）, Radial Basis Function （RBF）, Three-Dimensional and Quadratic Trend Surface, and Geographically Weighted Regression （GWR）, the spatial distributions of the average temperature for 30 years （January, April, July, October and anniversary） in Yunnan Province are interpolated and contrastively analyzed on the basis of the data of 125 weather stations from 1981 to 2010. The results show that the simulation accuracies of the interpolation for three conventional methods （namely IDW, OK and RBF） are unsatisfactory under the condition of complicated geographical environments in Yunnan; the simulation results of three-dimensional and quadratic trend-surface and GWR to interpolate the spatial distribution of temperature are preferable. The mean absolute errors （MAE） of cross check results for three-dimensional and quadratic trend-surface are 0.43 to 1.02 ℃, with the root-mean-square errors （RMSE） being 0.67 to 1.77 ℃. MAE of the interpolation results of GWR models are less than 0.65 ℃ and its RMSE is below 0.8 ℃. The cross check results indicate that the simulation error of GWR model to simulate the spatial distribution of average temperature in Yunnan was the smallest among the five single interpolation methods. Further, by using the superposition method of ＂ GWR interpolation ＋ IDW residual interpolation, ＂ the absolute errors of 64% interpolation results for tested weather stations, including monthly values and annual values, are less than 0.5 ℃ and the relative errors of 74% interpolation results are below 5%. Meanwhile, the determination coefficients （R2） of the regression relation between measured and interpolated values are above 0.9 under the condition of using the superposition method.