The spatial distribution of precipitation is one of the most important climatic variables used in geographic and environmental studies. However, when there is a lack of full coverage of meteorological stations, precipitation estimations are necessary to interpolate precipitation for larger areas. The purpose of this research was to find the best interpolation method for precipitation mapping in the partly densely populated Khorasan Razavi province of northeastern Iran. To achieve this, we compared five methods by applying average precipitation data from 97 rain gauge stations in that province for a period of 20 years (1994–2014): Inverse Distance Weighting, Radial Basis Functions (Completely Regularized Spline, Spline with Tension, Multiquadric, Inverse Multiquadric, Thin Plate Spline), Kriging (Simple, Ordinary, Universal), Co-Kriging (Simple, Ordinary, Universal) with an auxiliary elevation parameter, and non-linear Regression. Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the Coefficient of Determination (R²) were used to determine the best-performing method of precipitation interpolation. Our study shows that Ordinary Co-Kriging with an auxiliary elevation parameter was the best method for determining the distribution of annual precipitation for this region, showing the highest coefficient of determination of 0.46% between estimated and observed values. Therefore, the application of this method of precipitation mapping would form a mandatory base for regional planning and policy making in the arid to semi-arid Khorasan Razavi province during the future.

中文翻译：

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Khorasan Razavi省（伊朗东北部）平均年降水量分布图的多方法分析

降水的空间分布是地理和环境研究中使用的最重要的气候变量之一。但是，当缺乏完整的气象站覆盖时，必须对降水量进行估算才能对较大面积的降水量进行插值。这项研究的目的是找到伊朗东北部部分人口密集的霍拉桑·拉扎维省的最佳降水插值方法。为实现这一目标，我们通过应用该省97个雨量计站20年（1994-2014年）的平均降水量数据，比较了五种方法：反距离权重，径向基函数（完全正则样条，带张力样条，多二次方） ，逆多二次方，薄板样条），克里格（简单，普通，通用），共同克里格（简单，普通，通用），带有辅助海拔参数和非线性回归。均方根误差（RMSE），平均绝对误差（MAE）和确定系数（R ²）用于确定降水插值的最佳方法。我们的研究表明，带有辅助高程参数的普通协同克里格法是确定该地区年降水量分布的最佳方法，在估计值和观测值之间显示出最高的确定系数，为0.46％。因此，这种降水测绘方法的应用将为未来干旱至半干旱的霍拉桑·拉扎维省的区域规划和政策制定提供必要的基础。