A long-standing challenge in studying the global carbon cycle has been understanding the factors controlling inter–annual variation (IAV) of carbon fluxes related to vegetation photosynthesis and respiration, and improving their representations in existing biogeochemical models. Here, we compared an optimality-based mechanistic model and a semi-empirical light use efficiency model to understand how current models can be improved to simulate IAV of gross primary production (GPP). Both models simulated hourly GPP and were parameterized for (1) each site–year, (2) each site with an additional constraint on IAV (CostIAV), (3) each site, (4) each plant–functional type, and (5) globally. This was followed by forward runs using calibrated parameters, and model evaluations at different temporal scales across 198 eddy covariance sites. Both models performed better on hourly scale than annual scale for most sites. Specifically, the mechanistic model substantially improved when drought stress was explicitly included. Most of the variability in model performances was due to model types and parameterization strategies. The semi-empirical model produced statistically better hourly simulations than the mechanistic model, and site–year parameterization yielded better annual performance for both models. Annual model performance did not improve even when parameterized using CostIAV. Furthermore, both models underestimated the peaks of diurnal GPP in each site–year, suggesting that improving predictions of peaks could produce a comparatively better annual model performance. GPP of forests were better simulated than grassland or savanna sites by both models. Our findings reveal current model deficiencies in representing IAV of carbon fluxes and guide improvements in further model development.

Although evapotranspiration (ET) from the land surface is a key variable in Earth systems models, the accurate estimation of ET based on physical principles remains challenging. Parameters used in current ET models are largely empirically based, which could be problematic under rapidly changing climatic conditions. Here, we propose a physically-based ET model that estimates ET based on the surface flux equilibrium (SFE) theory and the maximum entropy production (MEP) principle. We derived an expression for aerodynamic resistance based on the MEP principle, then propose a novel ET model that complementarily depends on the SFE theory and the MEP principle. The proposed model, which is referred to as the SFE-MEP model, becomes equivalent to the MEP state in non-equilibrium conditions when turbulent mixing is weak and the land surface is dry. On the contrary, the SFE-MEP model is similar to ET estimation based on the SFE theory in other conditions meeting land-atmosphere equilibrium. This feature of the SFE-MEP ET model allows accurate ET estimation for most inland regions by incorporating both equilibrium and non-equilibrium characteristics of the atmospheric boundary layer. As a result, the SFE-MEP model significantly improves the performance of SFE ET estimation, particularly for arid regions. The proposed model and its high accuracy in ET estimation enable novel insight into various Earth system models as it does not require any empirical parameters and only uses readily obtainable meteorological variables including reference height air temperature, relative humidity, available energy, and radiometric surface temperature.