To allocate cultivable crops via a new multivariate statistical approach assessing spatial distribution of groundwater quality parameters

Due to the correlation between water qualitative indices, their spatial variations are commonly estimated using semivariogram expressed methods, such as Kriging and cokriging. Some studies have tried applying multivariate statistics to identify the effect of various parameters on groundwater spatial variations; however, their estimations are eventually determined by Kriging family of methods. In this study, two multilevel Gaussian factor models (GF1 and GF2) are introduced to jointly model the multivariate data. Such an approach avoids the difficulties of maximum likelihood estimation, incorporating imperfect information to reach an effective decision. Thirty-five agricultural well samples were analyzed for EC and SAR, and other correlated variables over an area of about 1837 Km2 to prepare thematic maps of the groundwater quality classes, based on which administrative crops are suggested for the regional agriculture after selecting the best model for zoning groundwater quality. The GF2 model outperformed the ordinary Kriging in joint modelling of EC and Mg + Ca + Na. Moreover, the best fitting was obtained under Gaussian and Matern covariance functions. EC estimated values by Kriging and the multilevel Gaussian factor model were 2.18-5.17 ds/m and 2.53-4.54 ds/m, respectively. A notable resemblance was found between the spatial variation patterns obtained by the two methods in both EC and SAR variables. Despite relatively larger domains obtained from the Kriging model, such extreme values of EC and SAR covered small and insignificant zones of the study area. The areas estimated by the GF2 model and Kriging for the EC range 3-4.5 ds/m were relatively close (98.4% and 85.6% of the total area, respectively), while the values exceeding this range, covered very small, negligible fractions of total area (1.1% and 7.9%, respectively). Similar results were obtained for SAR estimates. The cultivable area signified by the two models were not significantly different, as shown by the allowable cultivation area maps generated. When GF2 model is applied, the whole study area is cultivable for all recommended crops in 90% and less yield potentials, while the limitations were insignificant, considering Kriging method.