A large amount of carbon is stored in global forests. However, the fraction of carbon stored as plant biomass versus soil organic carbon (SOC) varies among forest types, and potential changes over the 21st century are uncertain. Here, we used extensive data derived from inventories and remote sensing and Coupled Model Intercomparison Project Phase 6 (CMIP6) models to examine the current and 21st century dynamics in the proportion of biomass and SOC across global forests. We found that precipitation, elevation, soil, and wildfire were the primary controls of these differences in carbon pools. Under the SSP5–8.5 climate scenario, CMIP6 models project that the ratio of biomass to ecosystem carbon in global forests will increase across the 21st century, with the largest increases in boreal forests (95 ± 37%) compared to moist tropical forests (16 ± 15%). Changes in forest carbon pools resulting in greater biomass fraction will affect disturbance, and ecosystem carbon and energy balances, all of which interact with the climate system.

Liebig's law of the minimum (LLM) is often used to interpret empirical biological growth data and model multiple substrates co-limited growth. However, its mechanistic foundation is rarely discussed, even though its validity has been questioned since its introduction in the 1820s. Here we first show that LLM is a crude approximation of the law of mass action, the state of art theory of biochemical reactions, and the LLM model is less accurate than two other approximations of the law of mass action: the synthesizing unit model and the additive model. We corroborate this conclusion using empirical data sets of algae and plants grown under two co-limiting substrates. Based on our analysis, we show that when growth is modeled directly as a function of substrate uptake, the LLM model improperly restricts the organism to be of fixed elemental stoichiometry, making it incapable of consistently resolving biological adaptation, ecological evolution, and community assembly. When growth is modeled as a function of the cellular nutrient quota, the LLM model may obtain good results at the risk of incorrect model parameters as compared to those inferred from the more accurate synthesizing unit model. However, biogeochemical models that implement these three formulations are needed to evaluate which formulation is acceptably accurate and their impacts on predicted long-term ecosystem dynamics. In particular, studies are needed that explore the extent to which parameter calibration can rescue model performance when the mechanistic representation of a biogeochemical process is known to be deficient.

Terrestrial carbon (C)-climate feedbacks depend strongly on how soil organic matter (SOM) decomposition responds to temperature. This dependency is often represented in land models by the parameter Q₁₀, which quantifies the relative increase of microbial soil respiration per 10 °C temperature increase. Many studies have conducted paired laboratory soil incubations and inferred “active” and “slow” pool Q₁₀ values by fitting linear two-pool models to measured respiration time series. Using a recently published incubation study (Qin et al. in Sci Adv 5(7):eaau1218, 2019) as an example, here we first show that the very high parametric equifinality of the linear two-pool models may render such incubation-based Q₁₀ estimates unreliable. In particular, we show that, accompanied by the uncertain initial active pool size, the slow pool Q₁₀ can span a very wide range, including values as high as 100, although all parameter combinations are producing almost equally good model fit with respect to the observations. This result is robust whether or not interactions between the active and slow pools are considered (typically these interactions are not considered when interpreting incubation data, but are part of the predictive soil carbon models). This very large parametric equifinality in the context of interpreting incubation data is consistent with the poor temporal extrapolation capability of linear multi-pool models identified in recent studies. Next, using a microbe-explicit SOM model (RESOM), we show that the inferred two pools and their associated parameters (e.g., Q₁₀) could be artificial constructs and are therefore unreliable concepts for integration into predictive models. We finally discuss uncertainties in applying linear two-pool (or more generally multiple-pool) models to estimate SOM decomposition parameters such as temperature sensitivities from laboratory incubations. We also propose new observations and model structures that could enable better process understanding and more robust predictive capabilities of soil carbon dynamics.

A framework that introduces the concept of near-activation complexation and differential free energy of activation is presented to extend the capabilities of the classical transition-state theory in enzymatic reactions. In our approach, reaching a near-equilibrium energy level is assumed to be necessary for complexation near the activation point, whereas an additional differential energy level is required for the near-equilibrium complex to activate and release reaction products. Integration of these energy levels within the transition-state theory explains the thermodynamic nature of the Michaelis–Menten (affinity) constant and its relationship with the rate constant under the quasi-steady-state assumption. The concepts of near-activation complexation and differential free energy of activation were tested on 57 independent experiments of NH+4 and NO-3 uptake by various microalgae and bacteria at temperatures ranging between 1 and 45°C. Results showed that near-activation complexation was always favored, whereas the differential energy of activation led to an apparent energy barrier consistent with earlier observations. Temperature affected all energy levels within this framework but did not alter substantially their thermodynamic features. The approach (1) mutually links the thermodynamics and kinetics of Michaelis-Menten and rate constants with a mathematical expression; (2) describes the likelihood of formation of sub-, super-, and activated complexes; and (3) shows direction and thermodynamic likelihood of each reaction branch within the transition state.

Plant root nutrient acquisition, and to a lesser extent foliar nutrient uptake, maintain plant metabolism and strongly regulate terrestrial biogeochemistry and carbon-climate feedbacks. However, terrestrial biogeochemical models differ in their representations of plant root nutrient acquisition, leading to significantly different, and uncertain, carbon cycle and future climate projections. Here we first review biogeochemical principles and observations relevant to three essential plant root nutrient acquisition mechanisms: activity of nutrient acquiring proteins, maintenance of nutrient stoichiometry, and energy expenditure for these processes. We next examine how these mechanisms are considered in three existing modeling paradigms, and conclude by recommending the capacity-based approach, the need for observations, and necessary modeling developments of plant root nutrient acquisition to improve carbon-climate feedback projections.

Dynamic energy budget (DEB) theory has been applied to model a wide range of organisms, including microbes. In the standard DEB model, biomass is partitioned into reserve and structural compartments, where reserve biomass is mobilized in a pseudolinear manner (while the reserve biomass density, defined as the ratio between reserve and structural biomass, decays linearly) to drive maintenance and the growth of structural biomass (and extracellular enzyme production if it is considered). However, the linear dynamics of the reserve biomass density makes the standard DEB model incapable of explaining the slowdown of microbial growth at high reserve density that is caused by macromolecular crowding effect which reduces biochemical reaction rates (a typical situation occurs when microbes are experiencing severe moisture stress) and is inconsistent with the observation that intracellular enzymatic reactions generally follow non-linear kinetics. By partitioning biomass into reserve, kinetic, and structural compartments, we show here that the Equilibrium Chemistry Approximation (ECA) kinetics can be used to represent enzymatically catalyzed reserve biomass mobilization that can then drive the kinetic and structural biomass synthesis. This revised DEB model better represents the tradeoff in ribosome allocation for structural growth and internal enzyme production, is structurally compatible with metabolic models of cell individuals, and includes the standard DEB model and the popular compromise model as special cases for representing population growth. We then applied the revised DEB model to interpret components of bacterial respiration, their dependence on substrate availability, and emergent microbial carbon use efficiency dynamics for an exponentially growing population. We found that the revised DEB model enables a better understanding of bacterial substrates use (carbon in our examples) than that can be derived from a few other models in the literature. In particular, the revised DEB model explains why carbon use efficiency may first increase, then plateau, and finally decrease with growth rate (and substrate uptake rate), as a function of proteomics. Additionally, the revised DEB model explains why the kinetic biomass compartment needs to be divided to reasonably incorporate proteomic control of microbial growth.

Affinity parameters are essential for substrate kinetics-based modeling of soil biogeochemistry. These parameters were originally defined for well-mixed aqueous solutions to represent enzyme substrate binding. For variably saturated soils, they are often calibrated and highly uncertain. Here we develop a predictive theory of effective substrate affinity parameters to account for other processes that affect microbial substrate acquisition, so that the substrate kinetics for well-mixed aqueous solutions can be similarly applied to variably saturated soils. The theory is based on an analytical approximation of how diffusive substrates are intercepted by soil microbial cells and integrates microbial characteristics, microsite structure, and soil physical properties. The predicted effective substrate affinity thus closely integrates the physical substrate limitation in soils with the intrinsic substrate affinity parameter. The theory predicts that, as moisture changes, the effective diffusive substrate delivery rates vary by orders of magnitude, resulting in highly variable effective affinity parameters for substrates like oxygen, methane, and nonvolatile solutes. As an example, we apply the theory with three substrate kinetics to aerobic soil incubations. Our models accurately reproduced observations of 32 soil incubations in four soil classes, demonstrating that the soil moisture versus respiration relationship varies with maximum respiration rate, soil texture, soil carbon content, and microbial biomass. This example suggests that the traditional use of a single static multiplicative function to parameterize how soil respiration depends on moisture is inappropriate. Because of its capability to integrate microbial traits and soil physical properties, our theory will help develop more robust soil biogeochemistry models.

Current generation Land Surface Models (LSMs) routinely simulate many nonlinear multiphysics processes. The complexity of future generation LSMs is expected to increase as critical new biophysical and biogeochemical processes are incorporated. Current generation LSMs have several shortcomings including the lack of robust numerical methods to solve discretized equations, monolithic software design that hinders testing of a process representation in isolation from other components, and absence of a flexible coupling framework to solve tightly coupled multiphysics problems. While the LSMs community vigorously evaluates the accuracy of the conceptual model to represent reality (validation), the accuracy of the numerical implementation of the conceptual model (verification) is seldom examined. Method of Manufactured Solutions is a technique for verifying complex codes when analytical solutions are unavailable. In this work, we present a stand-alone, open source numerical library for solving global terrestrial multiphysics processes that includes a flexible coupling framework. Robust numerical solution for linear and nonlinear equations is provided via the Portable, Extensible Toolkit for Scientific Computation library. We verify the numerical library using Method of Manufactured Solutions for a range of problems comprising single and multiphysics steady state problems that are applied in one or multiple physical domains. This work provides an example of incorporating code verification as an integral part of Land Surface Model development activities.

While coupling carbon and nitrogen processes is critical for Earth system models to accurately predict future climate and land biogeochemistry feedbacks, it has not yet been analyzed how numerical methods that land biogeochemical models apply to couple soil mineral nitrogen mobilizing and immobilizing processes affect predicted ecosystem carbon and nitrogen cycling. These effects were investigated here by using the E3SM land model and an evaluation of three plausible and widely used numerical couplings: 1) the mineral nitrogen-based limitation scheme, 2) the net uptake–based limitation scheme, and 3) the proportional nitrogen flux–based limitation scheme. It was found that these three schemes resulted in large differences (with a range of 316 PgC) in predicted cumulative land–atmosphere carbon exchanges under the RCP4.5 atmospheric CO2 simulations. This large uncertainty is without accounting for the different representations of the many land biogeochemical processes, but is about 73% of the range (434 PgC) reported for CMIP5 RCP4.5 simulations. These results help explain the large uncertainty found in various model intercomparison experiments and suggest that more robust numerical implementations are needed to improve carbon–nutrient cycle coupling in terrestrial ecosystem models.

Terrestrial plants assimilate anthropogenic CO₂ through photosynthesis and synthesizing new tissues. However, sustaining these processes requires plants to compete with microbes for soil nutrients, which therefore calls for an appropriate understanding and modeling of nutrient competition mechanisms in Earth System Models (ESMs). Here, we survey existing plant-microbe competition theories and their implementations in ESMs. We found no consensus regarding the representation of nutrient competition and that observational and theoretical support for current implementations are weak. To reconcile this situation, we applied the Equilibrium Chemistry Approximation (ECA) theory to plant-microbe nitrogen competition in a detailed grassland ¹⁵ N tracer study and found that competition theories in current ESMs fail to capture observed patterns and the ECA prediction simplifies the complex nature of nutrient competition and quantitatively matches the ¹⁵ N observations. Since plant carbon dynamics are strongly modulated by soil nutrient acquisition, we conclude that (1) predicted nutrient limitation effects on terrestrial carbon accumulation by existing ESMs may be biased and (2) our ECA-based approach may improve predictions by mechanistically representing plant-microbe nutrient competition.