Journal of Spatial Analysis

Assessment of the measurement statistics of model accuracy and the appropriate
use of them (Case study: Interpolation of Precipitation in Fars province)
Abstract
In many scientific researches, error measurement statistics are often used without taking notices into account
when selecting a model or method for the spatial analysis of environmental hazards. In order to assess the
accuracy of precipitation interpolation methods in Fars province, the performance of widely used error
measurement statistics and some comments were implemented. Spatial interpolation of precipitation was
accomplished using inverse distance weighting, kriging, co-kriging, and radial basis functions methods with 161
weather stations (22 synoptic and 139 rain gauge stations) for 2018 as a rainy year. The results of MBE statistic
evaluation indicated that the researcher may have chosen the incorrect interpolation method in certain cases
where the sum of the positive and negative values became zero. In addition, this statistic is limited to indicating
overestimation or underestimation and should not be used for assessing accuracy or selecting interpolation
techniques. Regarding the coefficient of determination (r 2 ), the results revealed that due to the lack of
compatibility in the magnitude of the range of this coefficient (0 to 1) with error values (100 to 400 mm for the
interpolation of precipitation in Fars province), its use in evaluation of the accuracy of a method is not
recommended. In terms of NRMSE, the results showed that samples with a small number of observations (n=3),
its value increased excessively (NRMSE=0.35) when compared to samples with a bigger number of data (n=20,
NRMSE=0.097). Therefore, it is not advised to use this statistic. In conclusion, since MAE and RMSE statistics
provide a more realistic error value, it is advised to use them for assessing the accuracy of interpolation
methods.
Keywords: Precipitation, Error evaluation statistics, Interpolation methods, Fars province