针对梯度距离平方反比法（GIDS）在地形起伏剧烈地区气温插值误差偏大的问题，提出一种基于经验气温垂直递减率的改进梯度距离平方反比法（GIDS-EAR）。该方法在进行温度插值时分别考虑了经纬度和海拔高度对气温的影响特性。首先根据气温垂直递减率经验值确定气温与海拔高度的偏回归系数，并利用偏回归系数对样本点气温值进行修正，再将此气温修正值代入多元线性回归模型解算气温与经纬度的偏回归系数，依据GIDS插值公式计算待插值点的温度值。基于1981-2010年四川省及周边省份219个气象观测站的累年月值温度值，将GIDS-EAR法与普通克里金法（OK）、反距离权重法（IDW）和GIDS法进行分析比较，结果表明，GIDS-EAR法得到的年均MAE和RMSE值较OK法分别降低67.71%和68.15%，较IDW法分别降低67.68%和66.45%，较GIDS分别降低25.65%和30.08%。该结果验证了改进方法的有效性及复杂地形下的适用性。
To reduce the large errors in spatial interpolation of temperature in terrains of salient relief using gradient plus inverse distance squared (GIDS) method, a method of empirical adiabatic rate-based gradient plus inverse distance squared (GIDS-EAR) is proposed in this work. In this method, the influences of horizontal position and altitude on temperature are considered separately in interpolation of temperature. First, the partial regression coefficient of temperature with altitude is determined based on the empirical adiabatic rate, and temperatures of the samples are corrected by using the partial regression coefficients. Next, the corrected temperature is substituted into a multiple linear regression model to calculate the partial regression coefficients of temperature with latitude and longitude. Then, the temperature to be interpolated is calculated using the GIDS method. The GIDS-EAR method is compared with Ordinary Kriging (OK), Inverse Distance Weighting (IDW), and GIDS methods on a dataset of monthly surface observation temperature from 1981 to 2010 from 219 meteorological stations in Sichuan and the surrounding provinces. The results show that the annual average MAE and RMSE values obtained by the GIDS-EAR method are 67.71% and 68.15% lower than those by the OK method, 67.68% and 66.45% lower than those by the IDW method, and 25.65% and 30.08% lower than those by the GIDS method, respectively. The testing results show the effectiveness and the applicability of the proposed method under complex terrain situations.
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