Viktor Mikhailovich Stepanenko

Soils are the largest terrestrial reservoir of organic carbon, so even small changes in soil carbon stocks can have significant eff ects on the atmosphere and climate. To select effective strategies to mitigate climate change, predictions of how soils will respond to future changes in climate and land use are needed. Achieving meaningful predictions requires a deep understanding of the highly complex, open, multicomponent soil organic matter system. One of the most effective methods for predicting the dynamics of soil organic matter is mathematical modeling. Process-oriented (physically based) models make it possible to present the basic concepts about the mechanisms that determine the behavior of this system in a mathematically formalized form and conduct a quantitative analysis. The uncertainty of the forecasts depends on the level of development of the theory explaining the dynamics of soil organic matter, the models representing it and their experimental support. This review examines the achievements of the last decade in modeling the role of microorganisms in the stabilization of soil organic matter, the concept of soil saturation with organic carbon, temperature control, as well as the development of reactive transport models describing the dynamics of organic carbon in the soil profile, and the representation of the dynamics of soil organic matter in global climate models. Unsolved problems associated with the high variability in the structure of new generation soil organic matter dynamics models are discussed.

To mitigate the effects of climate change and preserve and enhance soil fertility, considerable attention is being paid to the development of effective land management methods. Reliable forecasts of soil responses to future climate change and anthropogenic impacts are essential for selecting optimal management strategies. Mathematical modeling is a leading method for analyzing and predicting the spatiotemporal variability of soil organic carbon stocks. It is currently being developed in two main directions. The first uses empirical models obtained using digital soil mapping methods. The second direction represents process-based models of the biogeochemical carbon cycle. Each has strengths and weaknesses. Digital soil mapping models are empirical, based only on the analysis of data on soil properties and environmental characteristics, and therefore are limited in explaining the spatial variability of soil carbon stocks. The uncertainty of forecasts based on these models depends on the volume and quality of the training data. They demonstrate the superiority of process-based models in predicting the spatial distribution of soil organic carbon stocks in cases where large, high-quality data sets were used. The advantage of biogeochemical models is that they are based on accumulated soil science knowledge of the processes that determine the carbon cycle, making them effective in studying the mechanisms of soil carbon stock dynamics. However, forecasts using these models, especially at regional and global scales, are characterized by high uncertainty. Currently, ensemble modeling (the integration of various artificial intelligence algorithms used in digital soil mapping with process-based models) is proposed to reduce forecast uncertainty. Effective development of this strategy requires a thorough understanding of the role of key biogeochemical processes in soil organic carbon stock dynamics to improve the conceptual foundations of the models and increase confidence in the predictions. This article discusses the sources of uncertainty in biogeochemical models and the potential use of minimal models to inform the selection of the required set of key processes and mathematical formalisms for their explicit description in models of different spatiotemporal scales. This can reduce the structural uncertainty of nonlinear biogeochemical models.