Exploring the Temperature Response of Nighttime Ecosystem Respiration in a Deciduous Broadleaf Forest Using Long-Term Observations and Causal Shapley Value

Robust estimation of the temperature sensitivity of ecosystem respiration (ER) is critical for projecting terrestrial carbon dynamics under climate change.While ER is traditionally modeled as an exponential function of temperature, recent evidence suggests a unimodal response, with respiration peaking at an optimum temperature (T opt ) and declining thereafter.However, confounding variables like soil moisture, vegetation status, and vapor pressure deficit complicate isolating the effect of temperature.In this study, we combined long-term eddy covariance data from the flux tower in Sor, Denmark (DK-Sor) with an explainable machine learning framework to disentangle the direct effects of air temperature (T air ) on nighttime ER.Using an optimized machine learning model and Causal Shapley value, we quantified the marginal contributions of environmental predictors while accounting for known causal dependencies.Then we employed a new concept of Topt, which is a temperature that maximizes the Causal Shapley value of T air (T opt SHAP ).Our results revealed a clear unimodal temperature response (T opt SHAP = 15.99C),suggesting that ER may begin to decline at a cooler temperature than previously assumed (T opt = 18.25C).A binning analysis further revealed that unimodal response could be observed in normalized difference vegetation index ranges where high temperature (15C) occurred, suggesting that unimodal temperature response was not biased by vegetation phenology.These findings underscore the importance of incorporating causal inference and interpretable machine learning in capturing the temperature response of ER.