Investigation Of The Geographically Weighted Regression On Soil Zinc Content Hyperspectral Modeling By Applying The Fractional-order Differential

With the development of remote sensing techniques and the increasing requirement for soil contamination monitoring,an investigation on soil heavy metal Zinc(Zn)content estimation by hyperspectral imaging was carried out.Geographically weighted regression(GWR),an extension of the ordinary least squares(OLS)regression framework was proposed.By estimating a set of parameters for any number of locations in a study area,GWR can probe the spatial heterogeneity in data relationships,while the regression parameters of an OLS model are global aspatially-varied.The objectives of this study are two folds:1)to find the possible relationships between hyperspectral data and soil Zn content,2)and to investigate existence of their spatial heterogeneity.In this study,67 soil samples collected from Pingtan Island,Fujian Province,China are used to conduct laboratory hyperspectral modeling for soil Zn content estimation.Four transformations of square root,logarithm,reciprocal of logarithm and reciprocal as well as the fractional-order(FO)differential operations are applied to increase the amount of reflectance data,in which the effective variables for modeling might be involved,and to enhance the spectral characteristics of soil Zinc content.To find the sensitive variables and to remove redundancy and multicollinearity in the spectra,a data sifting process was applied by selecting wavelengths with local maximum in the absolute values of correlation coefficients with Zn content in one type of the spectral data and by employing the Variance Inflation Factors(VIFs).Since a modeling sample size of 46 is insufficient to construct the appropriate OLS and GWR models,four methods using all of the 67 samples to choose explanatory variables are proposed.A random process to select 57 samples for modeling and 10 samples for validation was applied to assess model performance,in which the mean verification R~2(R_v~2)was used as an indicator.The results show that the GWR stepwise regression is most effective to select better variables.Because the mean R_v~2 converges towards the OLS value when the bandwidth of GWR model increases,the four variables selected by the GWR stepwise regression were used to establish the representative OLS and GWR models.The representative OLS model has the best mean verification effect among all models studied,which is enhanced by 44.6%in mean R_v~2 relative to the OLS model constructed using the OLS stepwise regression.