2.1.4. Precision Evaluation

Because of the large amount of data generated in the interpolation comparison, it would be burdensome to display all the results. The results corresponding to precipitation fitting in July 2008 and May 2013 are representative of the monthly scale data, and the results of precipitation fitting in 2010 and 2012 are representative of the annual scale data. The evaluation of the interpolation models relied on several performance indices, namely the mean absolute error (MAE), mean relative error (MRE), and the root mean square error (RMSE). The smaller the values of MAE, MRE, and RMSE, the better the interpolation effect.

$$MAE = \frac{1}{n} \sum\_{i=1}^{n} \left| Y\_i - \hat{Y}\_i \right| \tag{10}$$

$$MRE = \frac{1}{n} \sum\_{i=1}^{n} \frac{\left| \mathbf{Y}\_i - \mathbf{Y}\_i \right|}{\mathbf{Y}\_i} \tag{11}$$

$$RMSE = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} \left(\mathbf{y}\_i - \mathbf{\hat{y}}\_i\right)^2} \tag{12}$$

in which *n* denotes the sample size, *Yi* represents the ith a sample value, *Y*ˆ *<sup>i</sup>* denots the sample estimates.
