Extended Abstract
Introduction: In many geographical and scientific phenomena such as hydrology and meteorology, where sampling is costly, observations are often sparse and pointwise. Selecting an appropriate interpolation method is crucial for water resource management, as it significantly impacts accuracy and cost reduction. Interpolation, utilized across various sciences, primarily aims to predict unknown values through a range of mathematical and statistical models. Ensuring the interpolation method and its correctness saves money and increases the accuracy of decision making. In general, a method that provides an optimal solution in all phenomena and locations is not found. Considering the environmental conditions of the region various methods should be assessed to determine the most optimal approach.
 
Materials and methods: The study area of Gonabad, with an area of 1805.6 km², of which 1048.7 km² are plains and the rest are highlands. In this research, the main goal is to evaluate the common methods of interpolation in the plains of Razavi Khorasan province. The plains of Gonabad and Sarakhs were studied due to their different hydrological and hydrogeological conditions; Also, in this review, inverse distance weighting (IDW) methods, kriging (simple, ordinary), cokriging, radial basis functions, and Thiessen's method were selected as interpolators for the study; and all these methods were evaluated by cross-validation.
 
Results and Discussion: In the present study, two methods of interpolation, IDW and Kriging, produced much more appropriate estimates than the rest of the studied methods. In comparing these two methods, IDW, as a classic method, requires fewer parameters and is simpler to implement. However, since it does not take into account the arrangement of data and the correlation between them, it is less accurate than kriging. On the other hand, geostatistical methods such as kriging, while offering better accuracy, require statistical tests, data transfer, data distribution, and spatial structure analysis due to hypotheses such as normality of data. This complexity and time-consuming nature can lead to errors. In this study, to assess the groundwater level under different conditions, information from two months of the year was utilized in each time period as representative of wet (February) and dry (August) periods. Contrary to previous ideas, due to the dry climate and low rainfall in the plains of the province, no significant difference was observed between these two months. Contrary to previous assumptions, the dry climate and low rainfall in the plains resulted in no significant difference between these two months.
 
Conclusion: Applying interpolation methods to two different time periods was conducted to investigate long-term decline. In the Gonabad Plain, the best methods were identified with RMSE values ​​of 11.96, 14.02 and 14.49 meters for IDW, ordinary kriging and simple kriging, respectively Simple and ordinary kriging methods as well as IDW with RMSE values ​​of 1.41, 1.58 and 11.83 m, respectively, were introduced in the Sarakhs Plain as the most optimal methods. In depicting the zoning of groundwater levels, as illustrated at the end of each plain by the aquifer map and changes in water level, it was found that height fluctuations corresponded to the information available in hydrogeological surveys of each region to a large extent. Analyzing the forecast results during the years 2012 to 2016, the decrease in groundwater level, based on the best and most optimal methods applied in the study plains of Gonabad and Sarakhs, amounted to a negligible four, seven, and five meters. In the province's plains, the Sarakhs Plain aquifer exhibited higher accuracy than others. This was attributed to the correct arrangement and density of sampling stations in this plain.