Beyond a deterministic representation of the temperature dependence of soil respiration.

Soil CO ₂ efflux represents a complex interplay of biological and physical processes that result in the production and transfer of CO ₂ from soils to the atmosphere. Temperature has been widely recognized as a critical factor regulating soil CO ₂ efflux and is commonly utilized in deterministic empirical models to predict this important flux for the carbon cycle. This study introduces the Bernstein copula-based cosimulation (BCC) as a data-driven probabilistic approach to model the temperature-soil CO ₂ efflux relationship. The BCC accounts for the joint probability distribution and temporal dependence of soil CO ₂ efflux, which are often overlooked in deterministic models. The BCC was implemented as a proof of concept using two years of data on soil CO ₂ efflux conditioned by soil temperature in a temperate forest. The BBC accurately reproduced the original probability distribution, temporal dependency, and temperature-soil CO ₂ efflux relationship. Our findings show that a deterministic method, such as the commonly employed exponential relationship between soil CO ₂ efflux and temperature, is limited for comprehensively capturing the intricate nature of the temperature-soil CO ₂ efflux relationship. This is due to the confounding and interacting effects of environmental drivers beyond temperature, which are not fully accounted for in such a deterministic approach. Furthermore, the BCC revealed that the probability density between the joint cumulative probability of temperature and soil CO ₂ efflux is not constant, which raises the concern that deterministic approaches introduce incorrect assumptions for estimating temperature-soil CO ₂ relationship. In conclusion, we propose that probabilistic approaches hold promise for effectively depicting dependency relationships for soil CO ₂ efflux modeling, and for improving predictions of the effects of weather variability and climate change.
Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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