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Abstract. The mass conservation equation in the presence of boundary fluxes and chemical reactions from non-equilibrium thermodynamics is used to derive a modified dynamic energy budget (mDEB) model. Compared to the standard dynamic energy budget (sDEB) model (Kooijman, 2009), this modified formulation does not place the dilution effect in the mobilization kinetics of reserve biomass, and it maintains the partition principle for reserve mobilization dynamics for both linear and non-linear kinetics. Overall, the mDEB model shares most features with the sDEB model. However, for biological growth that requires multiple nutrients, the mDEB model is computationally much more efficient by not requiring numerical iterations for obtaining the specific growth rate. In an example of modeling the growth of Thalassiosira weissflogii in a nitrogen-limiting chemostat, the mDEB model was found to have almost the same accuracy as the sDEB model while requiring almost half of the computing time of the sDEB model. Since the sDEB model has been successfully applied in numerous studies, we believe that the mDEB model can help improve the modeling of biological growth and the associated ecosystem processes in various contexts. 

Abstract Understanding factors influencing carbon effluxes from soils to the atmosphere is important in a world experiencing climatic change. Two important uncertainties related to soil organic carbon (SOC) stock responses to a changing climate are (a) whether soil microbial communities acclimate or adapt to changes in soil temperature and (b) how to represent this process in SOC models. To further explore these issues, we included thermal adaptation of enzyme‐mediated processes in a mechanistic SOC model (ReSOM) using the macromolecular rate theory. Thermal adaptation is defined here to encompass all potential responses of soil microbes and microbial communities following a change in temperature. To assess the effects of thermal adaptation of enzyme‐mediated processes on simulated SOC losses, ReSOM was applied to data collected from a 13‐year soil warming experiment. Results show that a model omitting thermal adaptation of enzyme‐mediated processes substantially overestimates observed CO₂effluxes during the initial years of soil warming. The bias against observed CO₂effluxes was lower for models including thermal adaptation of enzyme‐mediated processes. In addition, for a simulated linear 3°C soil warming over 100 years, models including thermal adaptation of enzyme‐mediated processes simulated SOC losses of a factor of three smaller than models omitting this process. As thermal adaptation of microbial community characteristics is generally not included in models simulating feedback between the soil, biosphere and atmosphere, we encourage future studies to assess the potential impact that microbial adaptation has on soil carbon – climate feedback representations in models. 

Abstract The dynamics of methane (CH₄) cycling in high-latitude peatlands through different pathways of methanogenesis and methanotrophy are still poorly understood due to the spatiotemporal complexity of microbial activities and biogeochemical processes. Additionally, long-termin situmeasurements within soil columns are limited and associated with large uncertainties in microbial substrates (e.g. dissolved organic carbon, acetate, hydrogen). To better understand CH₄cycling dynamics, we first applied an advanced biogeochemical model,ecosys, to explicitly simulate methanogenesis, methanotrophy, and CH₄transport in a high-latitude fen (within the Stordalen Mire, northern Sweden). Next, to explore the vertical heterogeneity in CH₄cycling, we applied the PCMCI/PCMCI+ causal detection framework with a bootstrap aggregation method to the modeling results, characterizing causal relationships among regulating factors (e.g. temperature, microbial biomass, soil substrate concentrations) through acetoclastic methanogenesis, hydrogenotrophic methanogenesis, and methanotrophy, across three depth intervals (0–10 cm, 10–20 cm, 20–30 cm). Our results indicate that temperature, microbial biomass, and methanogenesis and methanotrophy substrates exhibit significant vertical variations within the soil column. Soil temperature demonstrates strong causal relationships with both biomass and substrate concentrations at the shallower depth (0–10 cm), while these causal relationships decrease significantly at the deeper depth within the two methanogenesis pathways. In contrast, soil substrate concentrations show significantly greater causal relationships with depth, suggesting the substantial influence of substrates on CH₄cycling. CH₄production is found to peak in August, while CH₄oxidation peaks predominantly in October, showing a lag response between production and oxidation. Overall, this research provides important insights into the causal mechanisms modulating CH₄cycling across different depths, which will improve carbon cycling predictions, and guide the future field measurement strategies. 

Abstract Accurate and cost-effective quantification of the carbon cycle for agroecosystems at decision-relevant scales is critical to mitigating climate change and ensuring sustainable food production. However, conventional process-based or data-driven modeling approaches alone have large prediction uncertainties due to the complex biogeochemical processes to model and the lack of observations to constrain many key state and flux variables. Here we propose a Knowledge-Guided Machine Learning (KGML) framework that addresses the above challenges by integrating knowledge embedded in a process-based model, high-resolution remote sensing observations, and machine learning (ML) techniques. Using the U.S. Corn Belt as a testbed, we demonstrate that KGML can outperform conventional process-based and black-box ML models in quantifying carbon cycle dynamics. Our high-resolution approach quantitatively reveals 86% more spatial detail of soil organic carbon changes than conventional coarse-resolution approaches. Moreover, we outline a protocol for improving KGML via various paths, which can be generalized to develop hybrid models to better predict complex earth system dynamics. 

Abstract Cover crops have long been seen as an effective management practice to increase soil organic carbon (SOC) and reduce nitrogen (N) leaching. However, there are large uncertainties in quantifying these ecosystem services using either observation (e.g. field measurement, remote sensing data) or process-based modeling. In this study, we developed and implemented a model–data fusion (MDF) framework to improve the quantification of cover crop benefits in SOC accrual and N retention in central Illinois by integrating process-based modeling and remotely-sensed observations. Specifically, we first constrained and validated the process-based agroecosystem model,ecosys, using observations of cover crop aboveground biomass derived from satellite-based spectral signals, which is highly consistent with field measurements. Then, we compared the simulated cover crop benefits in SOC accrual and N leaching reduction with and without the constraints of remotely-sensed cover crop aboveground biomass. When benchmarked with remote sensing-based observations, the constrained simulations all show significant improvements in quantifying cover crop aboveground biomass C compared with the unconstrained ones, withR²increasing from 0.60 to 0.87, and root mean square error (RMSE) and absolute bias decreasing by 64% and 97%, respectively. On all study sites, the constrained simulations of aboveground biomass C and N at termination are 29% and 35% lower than the unconstrained ones on average. Correspondingly, the averages of simulated SOC accrual and N retention net benefits are 31% and 23% lower than the unconstrained simulations, respectively. Our results show that the MDF framework with remotely-sensed biomass constraints effectively reduced the uncertainties in cover crop biomass simulations, which further constrained the quantification of cover crop-induced ecosystem services in increasing SOC and reducing N leaching.