The literature describes numerous methods for the transfer of point data to spatial data. Li and Heap (2008) present a broad overview of spatial interpolation methods in environmental science and their application in numerous studies. Babak and Deutsch (2009) stated that IDW interpolation and its modifications are the most frequently applied deterministic methods (without the authors citing any evidence for this). A number of publications compare IDW and Kriging as methods for the spatial interpolation of hydrochemical groundwater characteristics using various water quality parameters and scales (Elumalai et al. 2017; Gong et al. 2014; Mirzaei and Sakizadeh 2016; Mueller et al. 2004; Rostami et al. 2019; Zimmerman et al. 1999). For sample datasets with semi-variograms that did not indicate the presence of spatialautocorrelation, Mueller et al. (2004) conclude that IDW is a better choice than Ordinary Kriging. When performing an IDW procedure, the methodological problems are regularly discussed. Above all, it is not possible to derive measures of uncertainty from deterministic methods in addition to the estimates (Ohmer et al. 2017). When a deterministic criterion is used, the measures of optimality are chosen arbitrarily (Borga and Vizzaccaro 1997). IDW is very sensitive to the amount of data used in interpolation and to the exponent value (Kravchenko et al. 1999). Only very few studies deal with the interpolation of nitrate concentrations in groundwater using IDW. For a 4545 km2 district in India, Kriging outperformed IDW and other techniques to interpolate the spatio-seasonal variation of nitrate in the aquifers (Mukherjee and Singh 2021). The optimal IDW exponent values range between 1.30 and 1.54 for the interpolation of nitrate concentration in 41 groundwater sites in Greece (Charizopoulos et al. 2018). Of the six methods investigated, IDW shows the greatest mean absolute error in the interpolation of a vertical transect of nitrate concentration (Bronowicka-Mielniczuk et al. 2019). For the arsenic concentration in groundwater in Texas (USA), the correlation coefficient between the measured and estimated values with IDW was higher than with Kriging interpolation (Gong et al. 2014). The results of the interpolation of soil fertility data were better with determination of the IDW exponent based on an independent dataset instead of estimating IDW exponents by means of the minimization of cross-validated errors (Mueller et al. 2005). The large influence of data and sampling characteristics on the interpolation accuracy of IDW was highlighted by Zimmerman et al. (1999). The authors stated that the effect of certain data characteristics (such as the level of noise or the strength of spatial correlation) on interpolation accuracy can only be systematically evaluated with synthetic data.
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