spatial analysis of precipitation with elevation and distance to sea (case study: sistan and baluchestan province)

introduction the knowledge about spatial variability of precipitation is a key issue for regionalization in hydro-climatic studies. measurements of meteorological parameters by the traditional methods require a dense rain gauge network. but, due to the topography and cost problems, it is not possible to create such a network in practice. in these cases the spatial distribution pattern of precipitation can be produced using different methods of interpolation. interpolation could be done only based on the data of the main variable (i.e. through univariate methods) or on the information obtained from both the main and one or more auxiliary variables (i.e. through multivariate methods). the classical interpolation methods such as arithmetic mean and linear regression (lr) methods are independent of the spatial relationship between observations, while geostatistical methods (such as kriging) use the spatial correlation between observations in the estimation processes (isaaks and srivastava, 1989). the previous studies showed that the choice of interpolation method depends on data type, desired accuracy, area of interest, computation capacity, and the spatial scale used. hence, different interpolation methods, including geostatistical methods (ok, sk, sklm, ked, uk and cok), univariate deterministic methods (idw, lpi, gpi and rbf) and linear regression (lr) were compared to estimate monthly and annual precipitation in sistan and baluchestan province. the auxiliary variables used in the multivariate approaches were dem, distance to sea and spatial coordinates.   materials and methods study area sistan and baluchistan province is located in southeast of iran and covers an area of 181471 km2. it is located between the latitudes 25˚03ʹand 31˚27ʹn and the longitudes 58˚50ʹ and 63˚21ʹe. the precipitation data collected from 50 precipitation stations over the same period of 25 years (1988-2012) were used in this study. interpolation methods detailed description of geostatistical interpolation methods used in this study including ok, sk, sklm, ked, uk and cok are provided in the variety of resources, such as goovaerts (1997) and deutsch and journel (1998). in geostatistics the most important tool for investigating the spatial correlation between observations is the semivariogram. in practice, experimental semivariogram is calculated from the following equation: (1)   where  is the experimental semivariogram, n(h) is the total number of data pairs of observations separated by a distance h, z(ui) and z(ui+ h) are the observed values of the variable z in locations ui and ui +h, respectively. after calculating experimental semivariogram, the most appropriate theoretical model is fitted to the data. unknown values are estimated using the semivariogram model and a geostatistics estimator. comparison method and evaluation criteria to assess the accuracy of interpolation methods and the best method for estimating precipitation, cross-validation technique is used (isaaks and srivastava, 1989). evaluation criteria are including the root mean square error (rmse) and the mean bias error (mbe).   results and discussion statistical analysis showed a high coefficient of variation of precipitation in august, september and july. kolmogorov-smirnov test showed that precipitation data are normally distributed over the study area. the precipitation semivariogram was considered isotropic as a little change was seen for different directions. results of autocorrelation analysis showed a high spatial correlation of precipitation in all periods (except for january and february) with a spherical semivarioram model. this confirms the results of previous studies (lloyd, 2005; haberlandt, 2007; mair and fares, 2010). the maximum sill was observed for months january, february and march with a higher amount of mean and variance. the maximum radius of influence was seen for january (511 km) followed by may (205 km). the performance of uk was evaluated using the trend function of the first and the second order polynomial. the evaluation results indicate that the first order polynomial is the more accurate one. the cross validation results showed that the best method for precipitation estimation was linear regression (precipitation versus elevation) for april, ked for may, uk for june and september, rbf for july, august, october, december, january, february and annual precipitation and sk for november and march. the lpi and gpi methods did not perform well in any of the time periods. this could be possibly due to large changes in surface topography of province. rbf method had the highest accuracy in most of the periods. the estimated values in this method are based on a mathematical function that minimizes total curvature of the surface, generating quite smooth surfaces (zandi et al., 2011). geostatistical methods had the highest accuracy for other periods. one of the reasons for good performance of geostatistical methods may be due to the low density of the meteorological stations. it confirms other researchers’ results (creutin and obled, 1982; goovaerts, 2000). the use of elevation as covariate has improved the estimation results only for april and may. however, the distance to sea did not improve the estimation results in any cases. the reasons for little improvement of the precipitation estimation through the multivariate methods could be due to the complex topography, low density of meteorological stations, and low correlation between precipitation and covariates.   conclusion geostatistical interpolation methods, in deterministic and linear regression methods, were evaluated for precipitation data in sistan and balouchestan province. according to the results of cross-validation, linear regression (elevation- precipitation) for april, geostatistical methods for may, june, september, december and march and rbf method for other periods had the highest accuracy. according to the estimation error maps produced by the geostatistical methods, the highest estimation errors were seen in the area with a low density of stations and the boundaries of the province. these areas are recommended for developing the meteorological network in the future. also, due to the variability of climate, distance from oman sea and changes in the surface topography for the precipitation stations, we recommend that the province is divided into more homogeneous regions and the proposed approaches are investigated in each section, separately.