Random forest regression kriging modeling for soil organic carbon density estimation using multi-source environmental data in central Vietnamese forests

Abstract Forest soil organic carbon plays a vital role in the terrestrial carbon cycle. Accurately analyzing the spatial distribution of soil organic carbon density (SOCD) is therefore necessary for sustainable forest management and climate change mitigation. Previous studies explored the potential of random forest (RF) in modeling forest SOCD using various environmental data sources. However, how forest SOCD prediction would be affected by using random forest regression kriging (RFRK), which integrates the predictive power of RF in generating deterministic trends and the capability of the ordinary kriging (OK) in handling spatial autocorrelation structure of residuals, based on the environmental data sources and their combinations remains elusive and deserves further exploration. For this purpose, 104 soil samples were collected at a depth of 30 cm in forest ecosystems of Central Vietnam, and 33 environmental covariates were derived from Sentinel-2 (S2) imagery, Advanced Land Observing Satellite-2 Phased Array L-band Synthetic Aperture Radar-2 (AL2) imagery, digital elevation model (DEM), and climatic data. Using a leave-one-out cross-validation procedure to evaluate and compare the model performances, four metrics, including coefficient of determination (R 2 ), mean absolute error (MAE), root mean square error (RMSE), and relative improvement (RI), were calculated. The results showed that enhanced RFRK performance for forest SOCD estimation was found with the inclusion of additional environmental data sources, with RFRK based on all data sources achieving a high accuracy (R 2 = 0.78, MAE = 8.28 t·ha −1 , and RMSE = 10.54 t·ha −1 ). The comparison of the RF and RFRK models exhibited that additionally interpolated residuals by OK were more accurate than only considering the influences of predictor covariates. The relative improvement of the RFRK models over the RF models in forest SOCD estimation was notable, with $$\:{RI}_{{R}^{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:msub> <mml:mrow> <mml:mi>RI</mml:mi> </mml:mrow> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:msub> </mml:mrow> </mml:math> ranging from 8.20 to 65.00%, $$\:{RI}_{MAE}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:msub> <mml:mrow> <mml:mi>RI</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>MAE</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ranging from 8.18 to 21.07%, and $$\:{RI}_{RMSE}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:msub> <mml:mrow> <mml:mi>RI</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>RMSE</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ranging from 6.76 to 18.18%. The result from our case study emphasizes the robustness of RFRK using S2, AL2, DEM, and climatic data in accurately predicting forest SOCD.