Geographically Weighted Regression Effects on Soil Zinc Content Hyperspectral Modeling by Applying the Fractional-Order Differential

Biao Jin,Jinming Sha,Jiali Shang,Yang-Yi Sun,Xue Lin,Yung-Chih Su,Xiaomei Li,Jianwan Ji

doi:10.3390/rs11060636

Abstract

With the development of remote sensing techniques and the increasing need for soil contamination monitoring, we estimated soil heavy metal zinc (Zn) content using hyperspectral imaging. 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, whereas the regression parameters of an OLS model are global and aspatially-varied. The objectives of this study were: (1) To find the possible relationships between hyperspectral data and soil Zn content, and (2) to investigate the existence of their spatial heterogeneity. In this study, 67 soil samples collected from Pingtan Island, Fujian Province, China, were 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 differential operations were 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 Zn content. To find 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 the correlation coefficients with Zn content in one type of spectral data and by employing Variance Inflation Factors. Since a modeling sample size of 46 is insufficient to construct the appropriate OLS and GWR models, four methods are proposed using all 67 samples to choose explanatory variables. 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 R2 (Rv2) was used as an indicator. The results show that GWR stepwise regression is the most effective method to select better variables. As the mean Rv2 converges toward the OLS value when the bandwidth of the 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 studied models, which had a mean Rv2 value that is 44.6% higher than the OLS model constructed using OLS stepwise regression.

Highlights

With intensified human activity, an increasing amount of heavy metals has entered the soil and is posing serious threats to human and animal health, and the environment
For the Geographically weighted regression (GWR) model, the stepwise regression method used was the same as that used for the ordinary least squares (OLS) model except the indicator, for which the average |t| of one explanatory variable was used because the t-values vary with location
To better predict new samples and obtain accurate variations in regression coefficients, the mean Rv2 of a random process was used as an indicator to assess the models

Summary

Introduction

An increasing amount of heavy metals has entered the soil and is posing serious threats to human and animal health, and the environment. Accurate and timely measurements of heavy metal content in the soil are urgently needed. Conventional investigations into heavy metal pollution have been mainly based on field sampling and chemical analyses in laboratories, which is time- and labor-consuming, and cannot satisfy the dynamic needs over large areas. We completed a modeling investigation using 67 soil samples with heavy metal Zn contents and their hyperspectral measurements. The study was conducted to offer a reference for heavy metal content retrieval from satellite-based and aerial hyperspectral data for large-scale and highly-efficiency quantitative monitoring. Many researchers have attempted to use hyperspectral remote sensing technology to retrieve soil heavy metal content [1,2,3]. It will be even harder to retrieve soil heavy metal content. In addition to metal type and metal concentration, other factors, such as soil organic matter, moisture content, and the state of the metals (e.g., ions or in compound) create challenges for the retrieval processes

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Conclusion