Contextual spatial modelling in the horizontal and vertical domains.

Multi-scale contextual modelling is an important toolset for environmental mapping. It accounts for spatial dependence by using covariates on multiple spatial scales and incorporates spatial context and structural dependence to environmental properties into machine learning models. For spatial soil modelling, three relevant scales or ranges of scale exist: quasi-local soil formation processes that are independent of the spatial context, short-range catenary processes, and long-range processes related to climate and large-scale terrain settings. Recent studies investigated the spatial dependence of topsoil properties only. We hypothesize that soil properties within a soil profile were formed due to specific interactions between different features and scales of the spatial context, and that there are depth gradients in spatial and structural dependencies. The results showed that for topsoil, features at small to intermediate scales do not increase model accuracy, whereas large scales increase model accuracy. In contrast, subsoil models benefit from all scales-small, intermediate, and large. Based on the differences in relevance, we conclude that the relevant ranges of scales do not only differ in the horizontal domain, but also in the vertical domain across the soil profile. This clearly demonstrates the impact of contextual spatial modelling on 3D soil mapping.

On the interpretability of predictors in spatial data science: the information horizon.

Two important theories in spatial modelling relate to structural and spatial dependence. Structural dependence refers to environmental state-factor models, where an environmental property is modelled as a function of the states and interactions of environmental predictors, such as climate, parent material or relief. Commonly, the functions are regression or supervised classification algorithms. Spatial dependence is present in most environmental properties and forms the basis for spatial interpolation and geostatistics. In machine learning, modelling with geographic coordinates or Euclidean distance fields, which resemble linear variograms with infinite ranges, can produce similar interpolations. Interpolations do not lend themselves to causal interpretations. Conversely, with structural modeling, one can, potentially, extract knowledge from the modelling. Two important characteristics of such interpretable environmental modelling are scale and information content. Scale is relevant because very coarse scale predictors can show nearly infinite ranges, falling out of what we call the information horizon, i.e. interpretation using domain knowledge isn't possible. Regarding information content, recent studies have shown that meaningless predictors, such as paintings or photographs of faces, can be used for spatial environmental modelling of ecological and soil properties, with accurate evaluation statistics. Here, we examine under which conditions modelling with such predictors can lead to accurate statistics and whether an information horizon can be derived for scale and information content.

The relevant range of scales for multi-scale contextual spatial modelling.

Spatial autocorrelation in the residuals of spatial environmental models can be due to missing covariate information. In many cases, this spatial autocorrelation can be accounted for by using covariates from multiple scales. Here, we propose a data-driven, objective and systematic method for deriving the relevant range of scales, with distinct upper and lower scale limits, for spatial modelling with machine learning and evaluated its effect on modelling accuracy. We also tested an approach that uses the variogram to see whether such an effective scale space can be approximated a priori and at smaller computational cost. Results showed that modelling with an effective scale space can improve spatial modelling with machine learning and that there is a strong correlation between properties of the variogram and the relevant range of scales. Hence, the variogram of a soil property can be used for a priori approximations of the effective scale space for contextual spatial modelling and is therefore an important analytical tool not only in geostatistics, but also for analyzing structural dependencies in contextual spatial modelling.

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

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 3rd degree polynomials provided the best results for SOC and BD (R2 = 0.99 and R2 = 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: R2 = 0.94; RMSE = 0.56%) and logarithmic (BD: R2 = 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 (R2: 0.96 to 0.75), compared to the 3rd degree polynomials (R2: 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.

Impacts of species richness on productivity in a large-scale subtropical forest experiment.

Biodiversity experiments have shown that species loss reduces ecosystem functioning in grassland. To test whether this result can be extrapolated to forests, the main contributors to terrestrial primary productivity, requires large-scale experiments. We manipulated tree species richness by planting more than 150,000 trees in plots with 1 to 16 species. Simulating multiple extinction scenarios, we found that richness strongly increased stand-level productivity. After 8 years, 16-species mixtures had accumulated over twice the amount of carbon found in average monocultures and similar amounts as those of two commercial monocultures. Species richness effects were strongly associated with functional and phylogenetic diversity. A shrub addition treatment reduced tree productivity, but this reduction was smaller at high shrub species richness. Our results encourage multispecies afforestation strategies to restore biodiversity and mitigate climate change.

Multi-scale digital soil mapping with deep learning.

We compared different methods of multi-scale terrain feature construction and their relative effectiveness for digital soil mapping with a Deep Learning algorithm. The most common approach for multi-scale feature construction in DSM is to filter terrain attributes based on different neighborhood sizes, however results can be difficult to interpret because the approach is affected by outliers. Alternatively, one can derive the terrain attributes on decomposed elevation data, but the resulting maps can have artefacts rendering the approach undesirable. Here, we introduce 'mixed scaling' a new method that overcomes these issues and preserves the landscape features that are identifiable at different scales. The new method also extends the Gaussian pyramid by introducing additional intermediate scales. This minimizes the risk that the scales that are important for soil formation are not available in the model. In our extended implementation of the Gaussian pyramid, we tested four intermediate scales between any two consecutive octaves of the Gaussian pyramid and modelled the data with Deep Learning and Random Forests. We performed the experiments using three different datasets and show that mixed scaling with the extended Gaussian pyramid produced the best performing set of covariates and that modelling with Deep Learning produced the most accurate predictions, which on average were 4-7% more accurate compared to modelling with Random Forests.

Predicting reference soil groups using legacy data: A data pruning and Random Forest approach for tropical environment (Dano catchment, Burkina Faso).

Predicting taxonomic classes can be challenging with dataset subject to substantial irregularities due to the involvement of many surveyors. A data pruning approach was used in the present study to reduce such source errors by exploring whether different data pruning methods, which result in different subsets of a major reference soil groups (RSG) - the Plinthosols - would lead to an increase in prediction accuracy of the minor soil groups by using Random Forest (RF). This method was compared to the random oversampling approach. Four datasets were used, including the entire dataset and the pruned dataset, which consisted of 80% and 90% respectively, and standard deviation core range of the Plinthosols data while cutting off all data points belonging to the outer range. The best prediction was achieved when RF was used with recursive feature elimination along with the non-oversampled 90% core range dataset. This model provided a substantial agreement to observation, with a kappa value of 0.57 along with 7% to 35% increase in prediction accuracy for smaller RSG. The reference soil groups in the Dano catchment appeared to be mainly influenced by the wetness index, a proxy for soil moisture distribution.

Approximation and spatial regionalization of rainfall erosivity based on sparse data in a mountainous catchment of the Yangtze River in Central China.

In densely populated countries like China, clean water is one of the most challenging issues of prospective politics and environmental planning. Water pollution and eutrophication by excessive input of nitrogen and phosphorous from nonpoint sources is mostly linked to soil erosion from agricultural land. In order to prevent such water pollution by diffuse matter fluxes, knowledge about the extent of soil loss and the spatial distribution of hot spots of soil erosion is essential. In remote areas such as the mountainous regions of the upper and middle reaches of the Yangtze River, rainfall data are scarce. Since rainfall erosivity is one of the key factors in soil erosion modeling, e.g., expressed as R factor in the Revised Universal Soil Loss Equation model, a methodology is needed to spatially determine rainfall erosivity. Our study aims at the approximation and spatial regionalization of rainfall erosivity from sparse data in the large (3,200 km(2)) and strongly mountainous catchment of the Xiangxi River, a first order tributary to the Yangtze River close to the Three Gorges Dam. As data on rainfall were only obtainable in daily records for one climate station in the central part of the catchment and five stations in its surrounding area, we approximated rainfall erosivity as R factors using regression analysis combined with elevation bands derived from a digital elevation model. The mean annual R factor (R a) amounts for approximately 5,222 MJ mm ha(-1) h(-1) a(-1). With increasing altitudes, R a rises up to maximum 7,547 MJ mm ha(-1) h(-1) a(-1) at an altitude of 3,078 m a.s.l. At the outlet of the Xiangxi catchment erosivity is at minimum with approximate R a=1,986 MJ mm ha(-1) h(-1) a(-1). The comparison of our results with R factors from high-resolution measurements at comparable study sites close to the Xiangxi catchment shows good consistance and allows us to calculate grid-based R a as input for a spatially high-resolution and area-specific assessment of soil erosion risk.