Simulating spatial distribution of snow depth using artificial intelligence and linear regression based on feature reduction (Case study: Chalgerd watershed)

Introduction
Snow monitoring and estimation of runoff from snow melting play an important role in controlling and managing watersheds and reservoirs and flood warning systems more efficiently. Given that the Koohrang area is found to be one of the snowy mountains in the country, and thanks to the high volume of runoff from precipitation, and snow melt, it plays a vital role in water supply for drinking, industry, and agriculture, neighboring provinces and even Iran as a whole so that it meets 10 % of total water demands in Iran. Accurate estimation of runoff from snowmelt entails spatial distribution of snow so that spatial variability of snow depth is measured via measuring snow depth in close resolution. On the other hand, the non-availability of gauge stations and extreme sampling conditions in snowy watersheds have caused researchers to think of simple and indirect strategies including regression techniques, interpolation methods, artificial intelligence, data mining, and also the use of satellite images, especially the use of radar interferometric method. Given the importance of snow depth variations and accurate estimation, although many methods have been used, there is an urgent need formore precise calculation and strategic position in this area requires procedures that are more accurate and more effective variables that are used in snow depth estimation. Study of artificial intelligence techniques and linear regression analysis and principal component analysis (PCA) along with geomorphometry parameters and inputs as well as satellite images were used to estimate the snow depth he and the results were compared. Therefore, in this study, unlike previous studies used much more variables to model snow depth, and also, the digital elevation model with the higher spatial resolution was used to model snow depth in a more accurate manner..
 
Methods and Materials
Koohrang region is located in the west and Chaharmahal and Bakhtiari Province with an area of over 3700 km². It is characterized by unique climatology, hydrology, and topography. Climatic characteristics of the region include an average annual temperature of 8.5 C, rainfall of 1430 mm, a frost period of 130 days, and a winter rainfall regime. In this research, using the hypercube technique, first, 100 points were selected for sampling in the Chalgerd area. In addition to these points, 195 other points were randomly collected from the study area. To obtain the data required for this research in field work, sampling was done over three days by the Monte-Rose model sampler. After the collection of snow samples, auxiliary data required for zoning, which includes data related to satellite images and variables derived from the digital elevation model, was extracted in the Saga software environment. The artificial neural network (ANN) was chosen as a new computing system and method to estimate snow depth using morphometric and climatic information related to snow depth. After extraction of the auxiliary variables in the study, between 32 input variables and snow depth, multiple linear regression analysis was conducted to test this model is 295 points. In order to fit the multiple regression equations, snow depth data as the dependent variable and physical variables as independent variables were considered. After obtaining an equation relating to the model was tested on regression test data (20% of data) to determine the accuracy of the model to predict the snow depth. In this study, in order to reduce the number of input data to the ANN and linear regression models, the PCA method was used, and finally, the number of components was chosen to be eight. For model evaluation, the predicted snow depth was evaluated using a linear regression model and ANN followed by calculating RMSE and R².
 
Results and Discussion
By trial and error, we found that a multi-layer neural network with a sigmoid activation function and a hidden layer of snow 1-6-32 for the optimal structure for the network as well as the number of repetitions and the coefficient of torque and 0.7 and 1000 was found. To evaluate and compare the performance of ANN, test data (20%) were used. ANN output values were compared with the corresponding observational values and details on the correlation coefficient were extracted. So as can be seen in the results, ANN and regression accounted for snow depth variation of 62 and 46% respectively and this regression model was significant at a probability level of 5%. The results of the PCA are to reduce the number of entries after the model of 32 to 8, the values in the model ANN and linear regression coefficient was reduced and root mean square error (RMSE) increases, and the 55 and 45 % variations in snow depth have been able to properly modeled. The less R² and RMSE, the more accurate model is. Thus, according to the error criteria value, the ANN model outperforms other ones. According to the results obtained of all variables used in ANN, the most important variables affecting the spatial variability of snow depth in the study area in order of importance, include profile longitudinal curvature, general curvature, gradient, transverse profile curvature, watershed gradient, slope middle position, wind, normalized elevation, geographical directions, and snow normalized difference index. It is worth noting that additional variables with negligible contributions were neglected. Given that prevalent winds blow in west and southwest directions and most of the highlands are nestled in these directions, much more snow accumulation can be found in this direction than those north, east and southward directions.
 
Conclusion
In the present research, to estimate the spatial distribution of the snow, the four models of ANNs, linear regression, PCA, and neural network were considered. After reviewing the methods according to the statistical criteria, the lowest error rate was attributed to ANN (RMSE, 19.57), followed by PCA using ANN (RMSE, 20.86), then linear regression (RMSE, 21.09), and the highest error rate on PCA using linear regression (RMSE, 21.59). Of all variables used in ANN, the most important variables affecting the spatial variability of snow depth in the study area in order of importance, include profile longitudinal curvature, general curvature, gradient, transverse profile curvature, watershed gradient, slope middle position, wind, normalized elevation, geographical directions, and snow normalized difference index. Therefore, digital elevation models with different resolutions in modeling can be used. However, here, variables such as vegetation, geology, solar radiation were not used and therefore it is recommended to use these variables in similar studies and different time resolutions. However, in future research, the most effective variables mentioned here can be promising for accurate zonation of snow depth in snowy watersheds.