Summary This study introduces a hybrid spatial modelling framework, which accounts for spatial non‐stationarity, spatial autocorrelation and environmental correlation. A set of geographic spatially autocorrelated Euclidean distance fields (EDF) was used to provide additional spatially relevant predictors to the environmental covariates commonly used for mapping. The approach was used in combination with machine‐learning methods, so we called the method Euclidean distance fields in machine‐learning (EDM). This method provides advantages over other prediction methods that integrate spatial dependence and state factor models, for example, regression kriging (RK) and geographically weighted regression (GWR). We used seven generic (EDFs) and several commonly used predictors with different regression algorithms in two digital soil mapping (DSM) case studies and compared the results to those achieved with ordinary kriging (OK), RK and GWR as well as the multiscale methods ConMap, ConStat and contextual spatial modelling (CSM). The algorithms tested in EDM were a linear model, bagged multivariate adaptive regression splines (MARS), radial basis function support vector machines (SVM), Cubist, random forest (RF) and a neural network (NN) ensemble. The study demonstrated that DSM with EDM provided results comparable to RK and to the contextual multiscale methods. Best results were obtained with Cubist, RF and bagged MARS. Because the tree‐based approaches produce discontinuous response surfaces, the resulting maps can show visible artefacts when only the EDFs are used as predictors (i.e. no additional environmental covariates). Artefacts were not obvious for SVM and NN and to a lesser extent bagged MARS. An advantage of EDM is that it accounts for spatial non‐stationarity and spatial autocorrelation when using a small set of additional predictors. The EDM is a new method that provides a practical alternative to more conventional spatial modelling and thus it enhances the DSM toolbox. Highlights We present a hybrid mapping approach that accounts for spatial dependence and environmental correlation. The approach is based on a set of generic Euclidean distance fields (EDF). Our Euclidean distance fields in machine learning (EDM) can model non‐stationarity and spatial autocorrelation. The EDM approach eliminates the need for kriging of residuals and produces accurate digital soil maps.
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.
Soil organic C (SOC) and soil moisture (SM) affect the agricultural productivity of soils. For sustainable food production, knowledge of the horizontal as well as vertical variability of SOC and SM at field scale is crucial. Machine learning models using depth-related data from multiple electromagnetic induction (EMI) sensors and a gamma-ray spectrometer can provide insights into this variability of SOC and SM. In this work, we applied weighted conditioned Latin hypercube sampling to calculate 25 representative soil profile locations based on geophysical measurements on the surveyed agricultural field, for sampling and modeling. Ten additional random profiles were used for independent model validation. Soil samples were taken from four equal depth increments of 15 cm each. These were used to approximate polynomial and exponential functions to reproduce the vertical trends of SOC and SM as soil depth functions. We modeled the function coefficients of the soil depth functions spatially with Cubist and random forests with the geophysical measurements as environmental covariates. The spatial prediction of the depth functions provides three-dimensional (3D) maps of the field scale. The main findings are (a) the 3D models of SOC and SM had low errors; (b) the polynomial function provided better results than the exponential function, as the vertical trends of SOC and SM did not decrease uniformly; and (c) the spatial prediction of SOC and SM with Cubist provided slightly lower error than with random forests. Hence, we recommend modeling the second-degree polynomial with Cubist for 3D prediction of SOC and SM at field scale.
The soil organic carbon (SOC) pool of the Northern Hemisphere contains about half of the global SOC stored in soils. As the Arctic is exceptionally sensitive to global warming, temperature rise and prolonged summer lead to deeper thawing of permafrost-affected soils and might contribute to increasing greenhouse gas emissions progressively. To assess the overall feedback of soil organic carbon stocks (SOCS) to global warming in permafrost-affected regions the spatial variation in SOCS at different environmental scales is of great interest. However, sparse and unequally distributed soil data sets at various scales in such regions result in highly uncertain estimations of SOCS of the Northern Hemisphere and here particularly in Greenland. The objectives of this study are to compare and evaluate three controlling factors for SOCS distribution (vegetation, landscape, aspect) at two different scales (local, regional). The regional scale reflects the different environmental conditions between the two study areas at the coast and the ice margin. On the local scale, characteristics of each controlling factor in form of defined units (vegetation units, landscape units, aspect units) are used to describe the variation in the SOCS over short distances within each study area, where the variation in SOCS is high. On a regional scale, we investigate the variation in SOCS by comparing the same units between the study areas. The results show for both study areas that SOCS are with 8 kg m -2 in the uppermost 25 cm and 16 kg m -2 in the first 100 cm of the soil, i.e., 3 to 6 kg m -2 (37.5%) higher than existing large scale estimations of SOCS in West Greenland. Our approach allows to rank the scale-dependent importance of the controlling factors within and between the study areas. However, vegetation and aspect better explain variations in SOCS than landscape units. Therefore, we recommend vegetation and aspect for determining the variation in SOCS in West Greenland on both scales.
<p>Over the last decades, a progressive glacier melting has been detected induced by climate change which cause a rapid enlargement of ice-free areas in glacier forelands in Arctic, Antarctic and Alpine regions. These recently deglaciated areas represent highly dynamic environments in terms of vegetation development and soil formation. Tundra plant communities of glacier forelands mainly consist of cryptogamic species forming biological soil crusts (BSCs) on the surface. These BSCs are known to promote the accumulation of aeolian particles and organic material being relevant to soil formation. It is important to understand both BSC development and soil formation in glacier forelands as fundamental to future development of mature tundra which contributes to an increase in soil organic carbon (SOC) and nitrogen (N) stocks in soil. The heterogeneous terrain of glacier forelands affects the spatial variation in both soil and vegetation characteristics which are additionally influenced by the distance to the glacier terminus. This study focuses on the spatial variation in soil and BSC characteristics in Arctic glacier forelands of Svalbard using multi-scale contextual soil mapping (CSM) and Euclidean distance fields (EDF). The data set comprises of soil (SOC, N, texture) and BSC characteristics (species composition, percent cover) from 168 sampling locations as well as terrain covariates (elevation, slope, aspect, curvature) at several scales using CSM and spatial covariates (EDF). Random forests (RF) are used to analyse the relationships between the covariates and soil and BSC characteristics, respectively.</p><p>Preliminary results show a good quality of the RF models (R&#178;/RMSE) which is similar for SOC (0.41/6.19) and N (0.44/0.22). Elevation, curvature and slope at large scales are the most important covariates to explain the spatial variation in SOC and N. On large scales, these covariates represent the distance to the glacier terminus and generally explain the increase in SOC and N with increasing distance from the glacier terminus.&#160; Additionally, elevation at small scales represents relevant issues of predominant geomorphologic features signature (e.g. moraine topography) to soil formation and BSC development. Analyses of the spatial variation and interrelationships of soil and BSC characteristics are still ongoing and further results will be presented at EGU 2020.</p>
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