The anisotropy and directional variation of spatial attributes is one of the most important challenges in spatial estimation of environmental features. This problem received a suitable response in the realm of stochastic modeling using directional variography; however, there is not any specific solution in the field of deterministic methods. In this research, Moving Least Square (MLS) and Moving Inverse Distance Weighting (MIDW) have been used to assess a moving domain as the remedy; although, there has been no research on the spatial estimation with the MLS method. The methods are evaluated in three case studies, (I) using anisotropic piezometric head data from the Wolfcamp aquifer in Texas, (II) long-term annual average precipitation measurements in Namak Lake Watershed (NLW) located in the central part of Iran, and (III) estimation of annual precipitation with remote-sensing products, TRMM, in NLW as well. To achieve the best performance of the methods, parameters have been optimized using the modified version of shuffled complex evolutionary method. Assessment of statistical metrics, Taylor Diagram, and numerical results showed that spatial interpolation using MIDW and MLS revealed better results, with an improvement of 45.3% on average in terms of Root Mean Square Error (RMSE), in comparison with original IDW as the benchmark evaluation approach. This shows the power of moving data partitioning on the performance of deterministic estimators. Additionally, MLS was more effective than MIDW with an average of 0.55, 10.53, and 17.19% reduction in RMSE of case I, II, and III, respectively.

Accurate estimation of the spatial distribution of precipitation is crucial for hydrologic modeling. To achieve the realistic estimation of precipitation, developing a ground-based observatory system is a costly and time-consuming strategy compared with other solutions such as using a combination of satellite- and ground-based observations. In this paper, to improve the estimation accuracy of spatial precipitation variation, various linear regression methods were used that combine digital elevation model (DEM) data, rain gauge observations, and Tropical Rainfall Measuring Mission (TRMM) products. Specifically, fuzzy cluster-based linear regression (FCLR), local multiple linear regression using historical similarity (LMLR-HS), model tree (MT), and moving least squares (MLS) were used in the proposed methodology based on local data behavior. The results were compared with those obtained from multiple linear regression (MLR) methods including simple multiple linear regression (SMLR), robust multiple linear regression (RMLR), and generalized linear model (GLM) for monthly precipitation estimation. The study area was Namak Lake watershed, one of the largest watersheds in Iran. The results, estimated for wet and dry years (years 1999 and 2003, respectively), show superiority of local linear regression methods over the other linear methods. Based on the statistical metrics used for assessing the quality the results, FCLR and MLS outperformed other tested methods.