Abstract: 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.

Key words: spatial interpolation, GIDS, adiabatic rate, multivariable linear regression model, altitude