افزایش دقت نقشه های هم بارش ماهانه و سالانه با استفاده از متغیر کمکی در استان مازندران

In most of hydrometeorological studies and water resources management, flood and drought forecasting, irrigation planning and climate change studies, access to rainfall data and especially its spatial distribution (precipitation map), are of particular importance. Different models are used for spatial interpolation of rainfall data that generally fall into two categories of statistical and geostatistical methods. In statistical methods, interpolation is based on linear and nonlinear regression between main variable and covariate, but in geostatistical methods such as Kriging, spatial correlation of the sampled points is take in to account. There are many problems with spatial estimation of rainfall data especially in complex topography. Using correlated covariates is one of the answers to overcoming this problem. The altitudinal range of Mazandaran province fluctuates between -61 to 5610 meters, which creates various climates in this province. Besides, presence of the Caspian Sea in the north and Alborz Mountains Range in the south of the province make further complicates in spatial rainfall estimation, especially in the impassable heights of the province, which are a major water resource for large rivers. Since the elevated meteorological station in Mazandaran province is located on 2134 m, no rainfall data is available in area between 2134 to 5610 meters. So, this study was aimed to compare four interpolation methods include inverse distance weighting, Kriging, Co-kriging, and three-dimensional linear gradient. Also in this study, the role of covariates in precipitation estimation was investigated.
Spatial data interpolation methods are used to estimate a variable at a particular point from actual data measured at adjacent points. The Inverse Distance Weighting method obtains the unknown quantity and performs the interpolation, by weighting the data around the estimated point. The interpolation methods use a set of points with known values around points with unknown data to estimate their values. This method is based on a geographical law that each phenomenon is related to other phenomena, but more depended to the close phenomena. Kriging as an advanced interpolation method is suitable for data with locally defined trends. This method can interpolate with the least variance of estimation that its error rate depends on the variogram specification. Co-Kriging is a suitable method when a covariate is present in all parts of network. In 3D Linear Gradient method, it is assumed that there is a linear trend along the length, width, and height of the region. In this study, in order to evaluate different interpolation methods of rainfall (Inverse Distance Weighting, Kriging, Co-Kriging, 3D linear gradient) the data from 25 synoptic and rain gauge stations were used in Mazandaran province. Surveying the statistical period of stations (1991-1991), the data of 2012 used to select the best interpolation method. Since the height of stations in Mazandaran province varies between -2120 and -21 m, precipitation data is not available for altitudes above 2200 meters. Therefore, altitude variable was used as an auxiliary variable in this study to obtain the most accurate estimation of altitude rainfall. In this study GS + and Mini tab software was used to calculate the estimated values of the models, Arc GIS software to prepare maps and Excel software for other calculations. Root Mean Square Error and Mean Bias Error were used to select the best interpolation method in this study. In variographic analysis, 5 types of semivariable models (Spherical, Gaussian, exponential, Linear and Linear to Sill models) were fitted to the data. The coefficient of determination and the ratio of structural changes to total variations were used to select the best half-variance. The best-chosen model has closer amounts of the coefficient and ratio to the number one. P-value and correlation coefficient were used to select the best covariate. Due to the importance of auxiliary variables in spatializing precipitation data, the variables of latitude, longitude, and altitude were used for the three-dimensional gradient equation. In order to better understanding of the studied methods, the map of annual precipitation changes in the province was plotted with different methods; then comparing them, the best rainfall map was selected.
In this study, in order to determine the best interpolation method for monthly and annual precipitation data of Mazandaran province, four interpolation methods (Inverse Distance Weighting, Kriging, Co-kriging and three-dimensional linear gradients) were compared. Examination of Root Mean Square Error and Mean Bias Error revealed that the best interpolation method for long-term monthly precipitation was the 3D linear gradient method. But, the problem with this method and the other investigated methods in this study was overestimation of precipitation in high and low estimation stations in coastal and plain areas of the province. The overestimation was occured due to the lack of the number of station above altitudes of 2000 m in Mazandaran province. Therefore, the estimation of precipitation in the province's highlands had error. The outcomes of the best semicircle model in this study showed that the best models (except for July with low coefficient of determination) were spherical and exponential models. The results also showed that in hot months the spatial structure of precipitation data became weaker. Also, the impact of precipitation data in this province is about 30 km. The outcomes of correlation between monthly and annual precipitation data with latitude, longitude and altitude revealed that the altitude parameter had a significant correlation with other auxiliary parameters (latitude and longitude), in all months except July. Also, the correlation of latitude and longitude variables with precipitation was significant in some months. Therefore, it can be concluded that altitude parameter was the best auxiliary variable among the others to estimate monthly and annual rainfall in Mazandaran province. Distribution graph of annual rainfall variations with altitude along with regression equation indicated relatively good fit of linear equation to altitude rainfall fluctuations. Based on the results, the importance of the role of latitude and longitude variables for spatial precipitation data was determined. Therefore, latitude, longitude, and altitude variables were used for the three-dimensional gradient equation. Survey of annual precipitation maps showed that the three-dimensional linear, Co-Kriging and gradient methods had the most reasonable estimation of the spatial variability of precipitation in the province. According to the rainfall-altitude diagram, the average rainfall in the province is reduced to 500 mm of annual rainfall per 1000 meters. From the annual precipitation map survey with the selected method, it can be seen that only the western coasts of the province experience more than 1000 mm of rainfall per year. The slope of rainfall variations with altitude in the west of the province is more than east and due to the complex topography of the west of the province the west coast has more rainfall than the western altitudes.