Performance Evaluation of Geo-Statistical Methods to Estimate the Spatial Distribution of Snow Depth and Density in Mountainous Areas (Case Study: Gush Bala Watershed, Mashhad)

Introduction One form of precipitation is snow. Due to the long-lasting process of its transformation into runoff, it is different from other ingredients of the water budget. In most permanent rivers whose basins are covered with snow, it plays a little role in water resource's studies. This case study is the Gush Bala mountain watershed, which is located in the eastern part of Mashhad in Khorasan-Razavi province.
Materials and methods In this study, 11 measured samples were used to map the depth and density of snow. Using Minitab software, the normality of the gathered data of snow was assessed through Kolmogorov-Smirnov test. The probability of more than 0.05 was considered as a criteria for the normality of the distribution of the data. If it does not have a normal distribution, they are normalized, through using modified shapes, in regard to their skewness. After testing the normality, the point data was transformed to regional data through Geo-Statistics such as Inverse Distance Weighting (IDW), Radial Basis Function (RBF), Kriging, and Cokriging. Geo-statistical estimation consists of two phases. Its first phase involves identifying and modeling spatial structure that can be studied by means of half-changing facade and estimation which can be the best linear unbiased estimation. The mutual assessment method was utilized to choose the most appropriate Geo-Statistical method. In this method, for each step, one observed point was crossed out and its value was estimated. After that, the estimated value was compared with the observed one.
Results and discussionThe most vital criterion was Root Mean Square Error (RMSE).The comparison of the RMSE of different methods like IDW, RBF, Kriging, and Cokriging showed that the most and the least values were for simple cokriging and simple kiriging methods whose values were respectively 0.518 and 0.023. Therefore, the simple kriging revealed better results than the other methods. Overall, less values of RMSE led to a better performance of a spatial semi-variogram for depth and density. Because the values of RMSE for 11 functions including Circular, Spherical, Tetra spherical, Penta spherical, Exponential, Gaussian, Quadratic Rational, Hole Effect, K-Bessel, J-Bessel, and Stable for simple Cokriging for depth and simple kriging for density were respectively 0.518 and 0.023, the interpretation Variogram for 11 functions was needed in the case of simple cokriging for depth and simple kriging for density.
The criteria which were used were Nugget and Nugget to sill ratio. Generraly, if they are less, their results are better super structure. The value with simple cokriging method for the depth of the snow for J-Bessel and sill ratio were respectively 0.795 and 0.95 which experienced better super structure. The value with simple kriging method for the density of the snow for J-Bessel and sill ratio were respectively 0.806 and 0.9 which showed an optimum method compared to other methods. All values that are obtained from interpolating kriging and cokriging methods must be evaluated with variogram structure, especially Nugget and Nugget to sill ratio. If the values of Nugget and Nugget to sill ratio increases, the predictability of the variogram decreases. In the variogram which was related to the depth and density data, the piece effect showed high levels. Furthermore, the ratio of nugget to sill was more than 0.75, which revealed a weak super structure between values in various distances. These findings demonstrated the heterogeneity of the data. On the other hand, considerable oscillations between nugget in depth data and density was shown on high values for nugget.
Conclusion The results of the predictions assessment done with simple cokriging for depth and simple kriging for density showed the higher accuracy of the aforementioned methods to other methods. One reason for this high accuracy can be ascribed to the influence of these parameters. In general, when the environment is more homogeneous, the Mardr small scale's results will be better than conventional statistical analysis. Thus, it seems that the sampling method with homogeneous units using satellite and aerial images could result in the homogeneity of the data. In addition, as a result, the spatial vacillations of the data went down and the ability of Geo-Statistics to predict and estimate will improve.