Nonlinear Increase of Vegetation Carbon Storage in Aging Forests and Its Implications for Earth System Models

Vegetation carbon stock (C_veg) in global forests, which is important for C cycle-climate feedbacks, commonly increases with forest age. Due to the allometric growth of plants, the nonlinear increase in C_veg with woody fraction (f_w) is expected across space. However, it remains unclear whether such a nonlinear relationship between C_veg and f_w can be constrained by observations and further used to benchmark Earth system models (ESMs). Here, based on the in situ measurements at 1,145 forest sites, we found that the nonlinear relationship between C_veg and f_w followed an exponential equation (i.e., (Formula presented.)). Then, we showed that such an exponential dependence of C_veg on f_w also exists in ESMs of CMIP5 and CMIP6 (all P < 0.01), even though age-dependent processes have not been incorporated in most models. However, the exponential C_veg-f_w relationship varied greatly among the models, and the coefficient b was systematically lower in the ESMs (0.08 ± 0.11; mean ± SD) than the observations (0.28). Based on a compiled forest age data set, we further found that the observed nonlinear increase of C_veg with forest age across the Northern Hemisphere (>30°N) was not captured by ESMs. These findings reveal a high disagreement on the spatially nonlinear relationship between vegetation carbon stock and woody fraction in current ESMs. The exponential relationship based on observations provides one useful benchmark for ESMs when they implement the age-dependent processes in the future.