MODELING SPATIOTEMPORAL VARIABILITY OF CARBON STOCKS (REVIEW)
Abstract
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.
References
1. Гопп Н.В., Мешалкина Ю.Л., Нарыкова А.Н. и др. Картографирование содержания и запасов органического углерода почв на региональном и локальном уровнях: анализ современных методических подходов // Вопросы лесной науки. 2023. Т. 6, № 1. С. 14–73. 2. Гумусообразование в техногенных ландшафтах. Новосибирск, 1986. 165 с. 3. Романенков В.А., Мешалкина Ю.Л., Горбачева А.Ю. и др. Прогноз динамики запасов углерода в почвах возделываемых земель европейской России в контексте стратегии низкоуглеродного развития // Известия РАН. Серия географическая. 2023. Т. 87, № 4. С. 584–596. https://doi.org/10.31857/S2587556623040106 4. Рыжова И.М. Анализ устойчивости почв на основе теории нелинейных динамических систем // Почвоведение. 2003. № 5. С. 583–590. 5. Рыжова И.М. Обратные связи в системе почва–растительность: сравнение минимальных моделей круговорота углерода // Материалы Пятой конференции «Математическое моделирование в экологии» ЭкоМатМод-2017, Пущино. Россия, 2017. 6. Рыжова И.М., Романенков В.А., Степаненко В.М. Современное развитие моделей динамики органического вещества почв (обзор) // Вестн. Моск. ун-та. 2024. Сер. 17. Почвоведение. № 4. С. 122–129. https://doi.org/10.55959/MSU0137-0944-17-2024-79-4-122-129 7. Рыжова И.М., Романенков В.А., Степаненко В.М. и др. Моделирование насыщения почвы органическим углеродом // Почвоведение. 2026. № 3. С. 454–471. 8. Савин И.Ю., Жоголев А.В., Прудникова Е.Ю. Современные тренды и проблемы почвенной картографии // Почвоведение. 2019. № 5. С. 517–528. https://doi.org/10.1134/S0032180X19050101 9. Семенов В.М., Когут Б.М. Почвенное органическое вещество. М., 2015. 233 с. 10. Сергеев М.В. Динамика процессов почвообразования в техногенном ландшафте // Рекультивация земель, нарушенных горными работами КМА. Воронеж, 1985. С. 51–74. 11. Файкин Г.М., Степаненко В.М., Медведев А.И. и др. Конструктор динамических моделей углеродного цикла почвы // Вычислительные методы и программирование. 2025. Т. 26, № 3. C. 281–303. https://doi.org/10.26089/NumMet.v26r320 12. Флоринский И.В. Гипотеза Докучаева как основа цифрового прогнозного почвенного картографирования (к 125-летию публикации) // Почвоведение. 2012. № 4. C. 19–25. 13. Чертов О.Г., Комаров А.С. Теоретические подходы к моделированию динамики содержания органического вещества почв // Почвоведение. 2013. № 8. https://doi.org/10.7868/S0032180X13080017 14. Чертов О.Г., Надпорожская М.А. Модели динамики органического вещества почв: проблемы и перспективы // Компьютерные исследования и моделирование. 2016. Т. 8, № 2. C. 391–399. 15. Чинилин А.В., Савин И.Ю. Оценка содержания органического углерода в почвах России с помощью ансамблевого машинного обучения // Вестн. Моск. ун-та. Сер. 5. География. 2022. № 6. C. 49–63. https://doi.org/10.55959/MSU0579-9414-5-2022-6-49-63 16. Abramoff R., Xu X., Hartman M. et al. The Millennial model: in search of measurable pools and transformations for modeling soil carbon in the new century // Biogeochemistry. 2018. Vol. 137. https://doi.org/10.1007/s10533-017-0409-7 17. Abramoff R.Z., Guenet B., Zhang H. et al. Improved global-scale predictions of soil carbon stocks with Millennial Version 2 // Soil Biol. Biochem. 2022. Vol. 164. P. 108466. https://doi.org/10.1016/j.soilbio.2021.108466 18. Ahrens B., Braakhekke M.C., Guggenberger G. et al. Contribution of sorption, DOC transport and microbial interactions to the 14C age of a soil organic carbon profile: insights from a calibrated process model // Soil Biol. Biochem. 2015. Vol. 88. P. 390–402. https://doi.org/10.1016/j.soilbio.2015.06.008 19. Blankinship J.C., Berhe A.A., Crow S.E. et al. Improving understanding of soil organic matter dynamics by triangulating theories, measurements, and models // Biogeochemistry. 2018. Vol. 140. P. 1–13. https://doi.org/10.1007/s10533-018-0478-2(0123456789 20. Bernardini L.G., Rosinger C., Bodner G. et al. Learning vs. understanding: When does artificial intelligence outperform process-based modeling in soil organic carbon prediction? // New Biotechnology. 2024. Vol. 81, № 25. 21. Bradford M., Wieder W., Bonan G. et al. Managing uncertainty in soil carbon feedbacks to climate change // Nature Clim Change. 2016. Vol. 6. P. 751–758. 22. Campbell E.E., Paustian K. Current developments in soil organic matter modeling and the expansion of model applications: a review // Environ. Res. Lett. 2015. Vol. 10. P. 123004. https://doi.org/10.1088/1748-9326/10/12/123004 23. Ding Z., Liu K., Zhou M. et al. Advancing Soil Organic Carbon Prediction: A Comprehensive Review of Technologies, AI, Process-Based and Hybrid Modelling Approaches // Advanced Science. 2025. Vol. 12. P. 1–28. 24. Falloon P., Jones C.D., Ades M. et al. Direct soil moisture controls of future global soil carbon changes: An important source of uncertainty // Global Biogeochem. Cycles. 2011. Vol. 25. https://doi.org/10.1029/2010GB003938 25. Friedlingstein P., O'Sullivan M., Jones M.W. et al. Global Carbon Budget 2023 // Earth Syst. Sci. Data. 2023. Vol. 15, № 12. P. 5301–5369. https://doi.org/10.5194/essd-15-5301-2023 26. Ghezzehei T.A., Sulman B., Arnold C.L. et al. On the role of soil water retention characteristic on aerobic microbial respiration // Biogeosciences. 2019. Vol. 16. P. 1187–1209. https://doi.org/10.5194/bg-16-1187-2019 27. Heuvelink G.B., Angelini M.E., Poggio L. et al. Machine learning in space and time for modelling soil organic carbon change // Eur. J. Soil Sci. 2021. Vol. 72. https://doi.org/10.1111/ejss.12998. 28. Kakhani N., Alamdar S., Kebonye N.M. et al. Uncertainty Quantification of Soil Organic Carbon Estimation from Remote Sensing Data with Conformal Prediction // Remote Sens. 2024. Vol. 16. P. 413. https://doi.org/10.3390/rs16030438 29. Khaledian Y., Miller B.A. Selecting appropriate machine learning methods for digital soil mapping // Applied Mathematical Modelling. 2020. Vol. 81. P. 401–418. 30. Le Noë J., Manzoni S., Abramoff R. et al. Soil organic carbon models need independent time-series validation for reliable prediction // Communications Earth & Environment. 2023. Vol. 4. https://doi.org/10.1038/s43247-023-00830–5h 31. Luo Y., Ahlström A., Allison S. et al. Toward more realistic projections of soil carbon dynamics by Earth system models // Global Biogeochem. Cycles. 2016. Vol. 30. P. 40–56. https://doi.org/10.5194/bgd-12-4245-2015 32. Manzoni S., Porporato A. Soil carbon and nitrogen mineralization: Theory and models across scales // Soil Biol. Biochem. 2009. Vol. 41, № 7. 33. McBratney A.B., Santos M.L.M., Minasny B. On digital soil mapping // Geoderma. 2003. Vol. 117, Iss. 1–2. P. 1355–1379. 34. Robertson A.D., Paustian K., Ogle S. et al. Unifying soil organic matter formation and persistence frameworks: the MEMS model // Biogeosciences. 2019. Vol. 16. P. 1225–1248. https://doi.org/10.5194/bg-16-1225-2019 35. Shi Z., Crowell S., Luo Y. et al. Model structures amplify uncertainty in predicted soil carbon responses to climate change // Nature Communications. 2018. Vol. 9. 36. Sierra C.A., Trumbore S.E., Davidson E.A. et al. Sensitivity of decomposition rates of soil organic matter with respect to simultaneous changes in temperature and moisture // J. Adv. Model. Earth Syst. 2015. Vol. 7, № 1. P. 335–356. 37. Smagin A., Sadovnikova N., Belyaeva E. et al. Carbon Sequestration as a Driver of Pine Forest Succession on Sandy Alluvium: Quantitative Assessment and Process Modeling // Forests 2025. Vol. 16. https://doi.org/10.3390/f16091482 38. Schmidt M., Torn M., Abiven S. et al. Persistence of soil organic matter as an ecosystem property // Nature. 2011. Vol. 478. P. 1–30. 39. Stewart C.E., Paustian K., Conant R.T. et al. Soil C saturation: concept, evidence, and evaluation // Biogeochemistry. 2007. Vol. 86. P. 19–31. https://doi.org/10.1007/s10533-007-9140–0 40. Stockmann U., Adams M.A., Crawford J.W. et al. The knowns, known unknowns and unknowns of sequestration of soil organic carbon // Agric. Ecosyst. Environ. 2013. Vol. 164. P. 80–99. 41. Sulman B.N., Moore J.A.M., Abramoff R. et al. Multiple models and experiments underscore large uncertainty in soil carbon dynamics // Biogeochemistry. 2018. Vol. 141. P. 109–123. https://doi.org/10.1007/s10533-018-0509-z 42. Technical specifications and country guidelines for Global Soil Organic Carbon Sequestration Potential Map (GSOCseq). Rome: FAO, 2020. 43. Todd-Brown K.E.O., Randerson J.T., Post W.M. et al. Causes of variation in soil carbon simulations from CMIP5 Earth system models and comparison with observations // Biogeosciences. 2013. Vol. 10, № 3. 44. Tuomi M., Vanhala P., Karhu K. et al. Heterotrophic soil respiration – comparison of different models describing its temperature dependence // Ecological Modelling. 2008. Vol. 211. 45. Varney R.M., Chadburn S.E., Burke E.J. et al. Evaluation of soil carbon simulation in CMIP6 Earth system models // Biogeosciences. 2022. Vol. 19. P. 4671–4704. 46. Wieder W.R., Grandy A.S., Kallenbach C.M. et al. Integrating microbial physiology and physio-chemical principles in soils with the Microbial-Mineral Carbon Stabilization (MIMICS) model // Biogeosciences. 2014. Vol. 11. 47. Wutzler T., Reichstein M. Colimitation of decomposition by substrate and decomposers a comparison of model formulations // Biogeosciences. 2008. Vol. 5. P. 749–759. 48. Zhang T., Huang L.M., Yang R.M. Evaluation of digital soil mapping projection in soil organic carbon change modeling // Ecological Informatics. 2024. Vol. 79. https://doi.org/10.1016/j.ecoinf.2023.102394 49. Zhang X., Xie E., Chen J. et al. Modelling the spatiotemporal dynamics of cropland soil organic carbon by integrating process-based models differing in structures with machine learning // Journal of Soils and Sediments. 2023. Vol. 23. P. 2816–2831. https://doi.org/10.1007/s11368-023-03516-9Received: 01/21/2026
Accepted: 03/02/2026
Accepted date: 05/18/2026
Keywords: soil organic carbon; biogeochemical models; minimal nonlinear models; digital soil mapping; soil carbon prediction
DOI: 10.55959/MSU0137-0944-17-2026-81-2-17-26
Available in the on-line version with: 18.05.2026
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