Beyond a deterministic representation of the temperature dependence of soil respiration

Soil CO₂ efflux represents a complex interplay of biological and physical processes that result in the production and transfer of CO₂ from soils to the atmosphere. Temperature has been widely recognized as a critical factor regulating soil CO₂ 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 CO₂ efflux relationship. The BCC accounts for the joint probability distribution and temporal dependence of soil CO₂ efflux, which are often overlooked in deterministic models. The BCC was implemented as a proof of concept using two years of data on soil CO₂ efflux conditioned by soil temperature in a temperate forest. The BBC accurately reproduced the original probability distribution, temporal dependency, and temperature-soil CO₂ efflux relationship. Our findings show that a deterministic method, such as the commonly employed exponential relationship between soil CO₂ efflux and temperature, is limited for comprehensively capturing the intricate nature of the temperature-soil CO₂ 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 CO₂ efflux is not constant, which raises the concern that deterministic approaches introduce incorrect assumptions for estimating temperature-soil CO₂ relationship. In conclusion, we propose that probabilistic approaches hold promise for effectively depicting dependency relationships for soil CO₂ efflux modeling, and for improving predictions of the effects of weather variability and climate change.