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As limited resources, soils are the largest terrestrial sinks of organic carbon. In this respect, 3D modelling of soil organic carbon (SOC) offers substantial improvements in the understanding and assessment of the spatial distribution of SOC stocks. Previous three-dimensional SOC modelling approaches usually averaged each depth increment for multi-layer two-dimensional predictions. Therefore, these models are limited in their vertical resolution and thus in the interpretability of the soil as a volume as well as in the accuracy of the SOC stock predictions. So far, only few approaches used spatially modelled depth functions for SOC predictions. This study implemented and evaluated an approach that compared polynomial, logarithmic and exponential depth functions using non-linear machine learning techniques, i.e. multivariate adaptive regression splines, random forests and support vector machines to quantify SOC stocks spatially and depth-related in the context of biodiversity and ecosystem functioning research. The legacy datasets used for modelling include profile data for SOC and bulk density (BD), sampled at five depth increments (0-5, 5-10, 10-20, 20-30, 30-50 cm). The samples were taken in an experimental forest in the Chinese subtropics as part of the biodiversity and ecosystem functioning (BEF) China experiment. Here we compared the depth functions by means of the results of the different machine learning approaches obtained based on multi-layer 2D models as well as 3D models. The main findings were (i) that 3 rd  degree polynomials provided the best results for SOC and BD (R 2  = 0.99 and R 2  = 0.98; RMSE = 0.36% and 0.07 g cm -3 ). However, they did not adequately describe the general asymptotic trend of SOC and BD. In this respect the exponential (SOC: R 2  = 0.94; RMSE = 0.56%) and logarithmic (BD: R 2  = 84; RMSE = 0.21 g cm -3 ) functions provided more reliable estimates. (ii) random forests with the exponential function for SOC correlated better with the corresponding 2.5D predictions (R 2 : 0.96 to 0.75), compared to the 3 rd  degree polynomials (R 2 : 0.89 to 0.15) which support vector machines fitted best. We recommend not to use polynomial functions with sparsely sampled profiles, as they have many turning points and tend to overfit the data on a given profile. This may limit the spatial prediction capacities. Instead, less adaptive functions with a higher degree of generalisation such as exponential and logarithmic functions should be used to spatially map sparse vertical soil profile datasets. We conclude that spatial prediction of SOC using exponential depth functions, in conjunction with random forests is well suited for 3D SOC stock modelling, and provides much finer vertical resolutions compared to 2.5D approaches.

Comparison of catchment scale 3D and 2.5D modelling of soil organic carbon stocks in Jiangxi Province, PR China