Global and local modeling of soil organic carbon using Thematic Mapper data in a semi-arid environment

This study aimed at comparing the effectiveness of the global aspatial multiple linear regression (MLR) using ordinary least squares (OLS) and local spatial geographically weighted regression (GWR) for producing a map showing the spatial variations in soil organic carbon (SOC) in Amman-Zarqa Basin (about 3,583 km2)—a typical semi-arid watershed in Jordan—using Landsat Thematic Mapper (TM) data. After normalizing the SOC data (the dependent variable) using Box-Cox power transformation and removing the multicollinearity of TM bands 1 to 5 and 7 (the independent variables) by applying principal component analysis, both regression techniques developed maximum likelihood best linear unbiased estimators in which the residuals had close-to-normal and random independent distributions with almost common variances and close-to-zero means. However, the GWR model had smaller Akaike’s information criterion (corrected) (AICc) (2,534.0 versus 2,560.5), larger adjusted multiple coefficient of determination R¯2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left({\overline{\mathbf{\mathcal{R}}}}^2\right) $$\end{document} (0.31 versus 0.22), and larger Pearson’s product moment correlation coefficient (r) between measured and observed values (0.63 versus 0.51). Thus, applying map algebra using the developed GWR model generated a raster map with 30 × 30 m2 cell size. The map showed that SOC composition to 20 cm depth varied from 3.5 to 85.0 metric tons per hectare (ton/ha) with a mean and standard deviation of about 23.9 and 9.3 ton/ha, respectively. The spatial pattern of surface SOC reflected partly the spatial variability of land cover and agricultural management practices in the basin. The results demonstrate the potential and superiority of GWR over MLR as a practical tool for conducting further spatial and temporal analyses of SOC stocks and implementing best land management practices in semi-arid environments using TM data.