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

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