Spatial Assessment of Soil Organic Carbon Using Bayesian Maximum Entropy and Partial Least Square Regression Model

Abstract

There has been great interest in the estimation of soil carbon over the last decade to address critical environmental, agronomic, and sociopolitical issues. Soil proximal sensing has shown much potential for soil carbon assessment. Visible/near-infrared diffuse reflectance spectroscopy (VNIRS) has been introduced as a complementary data source in digital soil mapping due to its cost effectiveness. However, in many studies, the uncertainty in soil modeling using VNIRS has not been explicitly taken into account. Bayesian maximum entropy (BME) is a modern geostatistical method that incorporates auxiliary/soft data within a theoretical sound framework. Our objective was to employ VNIR data and BME to spatially estimate soil organic carbon (SOC). Another objective was to compare the performance to estimate SOC using BME to classical geostatistical methods. A total of 1012 soil samples from Florida, USA, were employed from a database that included pairs of SOC measurements derived by dry combustion and hyperspectral data with 1-nm resolution in the VNIR spectral range (350–2500 nm). Partial least square regression (PLSR) was used to model the relationship between VNIR data and SOC. For spatial estimations of SOC, we employed BME using “hard” (SOC measurements from the laboratory) and interval “soft” data (predictions of VNIR–PLSR model). For the purpose of comparison, ordinary kriging (OK) was used with only the hard data set (OK1) and the SOC estimates derived from the VNIRS–PLSR model (OK2) at point locations. Both BME and OK2 show distinctly different pathways of assimilating vague (“soft”) data into the spatial modeling process. The three spatial estimation methods (BME, OK1, and OK2) were examined using the independent validation set by calculating bias, root mean square error (RMSE), residual prediction deviation (RPD), and ratio of performance to inter-quartile distance (RPIQ). The preliminary results show that BME performed generally as well as OK1, which may be due to the data splitting effects. However, both BME and OK1 were better than OK2. As BME can take advantage of data from the PLSR model, it offers the possibility to reduce the amount of laboratory-measured samples to map across a region. OK2 performed worse than OK1, which showed that using vague data into kriging leads to higher uncertainties. In this case, data from the VNIRS model may not help to improve the performance of predictions in kriging. These results underpin the potential of the BME approach in digital soil mapping.