interpolation methods

Due to the interaction of effective factors in soil formation, changes in soil properties from one place to another and even for one type of soil will be obvious. Iran is one of the countries that has many problems in terms of soil erosion, so that every year millions of tons of rich and fertile soil is eroded from its original location due to mismanagement and unprincipled and becomes inaccessible. Continuation of this trend in recent years has led to the creation of acute environmental problems that should be adopted principled and logical solutions to not intensify and continue this trend.

Nomehrud watershed is limited to Noor city from the north and the Caspian Sea from the east to Vazrud watershed from the west to Noorrud watershed and from the south to Haraz watershed. Its area is about 50 square kilometers. The study area is located between the northern latitudes approximately 4014000 to 4027100 and the eastern longitudes approximately 590300 to 597000 (in the utm system). The average annual rainfall is 613 mm. At first, the whole area was divided into one kilometer square networks (1000 meters * 1000 meters) and within each network, according to the conditions of access to different parts of the region and homogeneity in other characteristics (topography, lithology, land use and soil science) two Three soil samples were taken randomly from a depth of 0 to 30 cm. Soil structure was determined directly in the desert. Parameters, percentage of coarse sand (by sieving method), silt + very sandy (by sieving method), organic matter (by walkie-block method), soil structure (in the desert) and soil permeability (using the relationship between soil texture and group Hydrological) was determined and finally the amount of soil erodibility factor was obtained for each sampling site. Finally, the soil erodibility factor was zoned using some interpolation methods.

Due to the existence of land types in the control area, we have a wide range between the minimum and maximum values ​​of the studied parameters and are involved in the soil erodibility factor. The soil structure in the area is mainly spongy grains. Soil permeability is often in the middle to low category, the amount of organic matter between 0.3 to 5.4, silt in the area 4 to 62%, clay 2 to 51%, sand 14 to 72% and erosion factor values ​​between Is set to 0.05 to 0.6. Gaussian model was selected from the fitted models. Considering the accreditation accuracy indicators, it was found that the kriging method has a higher accuracy than other methods. According to the zoning map, soil erodibility factor shows that except for the central parts of the region, which have dense and semi-dense forest lands, other parts of the region are more sensitive to soil erosion, which is mainly due to the reduction. Soil permeability, higher amounts of silt, lower amounts of clay and sand and the presence of formations more susceptible to erosion, etc., which is accompanied by the effect of destructive factors such as overgrazing in pastures (village and upstream lands), destruction of forest areas (Thin) due to the entry and grazing of livestock in these areas and also the unprincipled use of these lands for recreational activities and wood smuggling on the one hand and lack of access to barren and mountainous forest areas on the other(central areas)Be.

Considering the conditions and situation of degradation in the areas of natural resources of the country, estimating and determining the soil erodibility factor and subsequently using it in different models of soil erosion is an important and necessary matter. In general, it can be said that among the various interpolation methods, the kriging method has a special place. According to some researchers, this method works as the best method of interpolation and estimation in non-statistical points in homogeneous regions. This method requires prior calculation and determination of the spatial correlation of field data, which can be done by drawing a toxic experimental variogram and selecting an appropriate mathematical model that can fit its points. One of the advantages of production plans is the quantification of the obtained results, which leads to the ability to reproduce and update the obtained information.

Precipitation is one of the most complicated climatic elements. Moreover, for many applications a climatological atlas of precipitation is needed. Preparing a climatological atlas of precipitation using observed rain gauge data is a challenging task.
In this research six interpolation methods including Inverse Distance Weighting (IDW), Gradient plus Inverse Distance Squared (GIDS), Multiple Linear Regression (MLR), Ordinary Kriging (O-K), Universal Kriging (U-K) and Simple Kriging (S-K) have been used to analyze the monthly, seasonal and annual means of precipitation at 354 synoptic stations over Iran during TIR 1393 to KHORDAD 1394 and the results have been compared.
Comparison of the results showed that the GIDS method gives relatively better performance for most of the times. It is also found that the U-K method has considerably lower errors particularly for the interpolation of precipitation over the regions/seasons with low amounts of precipitation. The final analyzed data agree well with the corresponding observations

Rainfall is one of the most important components of the hydrologic cycle, and its spatial distribution plays an important role in water resources management. Choosing an appropriate interpolation method is one of the main challenges in optimally estimating the values at those locations where no samples or measurements were taken. The purpose of this research is to determine the best interpolation method for precipitation in Mashhad plain as the main agricultural areas in Khorasan Razavi Province. First, rainfall data was collected during the period of 2004 to 2013. A total of 63 stations were selected. Then, five interpolation methods, namely Kriging, co-Kriging, Regression, regression Kriging and Inverse Weighted Distance were used for estimating spatial distribution of precipitation. The Root Mean Square Error and Mean Bias Error was considered to select the best interpolation method. The interpolation approaches were evaluated using a cross-validation method. Results revealed that the most accurate interpolation method is based on the spherical model as the theoretical semivariogram model. The error of method showed that the regression kriging and three-variable regression (x,y,z) methods are the most accurate models with RMSE=5.8541 and MBE=0.3004 and RMSE=7.5888 and MBE=0.3498, respectively to interpolate annual precipitation over the study area. It was also deduced that for seasonal rainfall data, due to poor data correlation, it is better to use the Kriging method to interpolation method. The co-Kriging method was also recognized as the weakest method with least accuracy for rainfall interpolation.