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Terrestrial ecosystems provide multiple services interacting in complex ways. However, most ecosystem services (ESs) models (e.g., InVEST and ARIES) ignored the relationships among ESs. Process‐based models can overcome this limitation, and the integration of ecological models with remote sensing data could greatly facilitate the investigation of the complex ecological processes. Therefore, based on the Carbon and Exchange between Vegetation, Soil, and Atmosphere (CEVSA) models, we developed a process‐based ES model (CEVSA‐ES) integrating remotely sensed leaf area index to evaluate four important ESs (i.e., productivity provision, carbon sequestration, water retention, and soil retention) at annual timescale in China. Compared to the traditional terrestrial biosphere models, the main innovation of CEVSA‐ES model was the consideration of soil erosion processes and its impact on carbon cycling. The new version also improved the carbon‐water cycle algorithms. Then, the Sobol and DEMC methods that integrated the CEVSA‐ES model with nine flux sites comprising 39 site‐years were used to identify and optimize parameters. Finally, the model using the optimized parameters was validated at 26 field sites comprising 135 site‐years. Simulation results showed good fits with ecosystem processes, explaining 95%, 92%, 76%, and 65% interannual variabilities of gross primary productivity, ecosystem respiration, net ecosystem productivity, and evapotranspiration, respectively. The CEVSA‐ES model performed well for productivity provision and carbon sequestration, which explained 96% and 81% of the spatial‐temporal variations of the observed annual productivity provision and carbon sequestration, respectively. The model also captured the interannual trends of water retention and soil erosion for most sites or basins. Plain Language Summary Terrestrial ecosystems simultaneously provide multiple ecosystem services (ESs). The common environmental drivers and internal mechanisms lead to nonlinear and dynamic relationships among ESs. Assessing the spatiotemporal changes of ESs have recently emerged as an element of ecosystem management and environmental policies. However, appropriate methods linking ESs to biogeochemical and biophysical processes are still lacking. In this study, we developed a process‐based model Carbon and Exchange between Vegetation, Soil, and Atmosphere (CEVSA‐ES) that integrates remote sensing data for evaluating ESs. We first described the model framework and detailed algorithms of the processes related to ESs. Then a model‐fusion method was applied to optimize parameters to which the model was sensitive and to improve model performance based on multi‐source observational data. The calibrated CEVSA‐ES model showed good performance for carbon and water fluxes (i.e., gross primary productivity, ecosystem respiration, net ecosystem productivity, and evapotranspiration). The CEVSA‐ES model performed well for productivity provision, and carbon sequestration. It also captured the interannual trends of water retention and soil erosion for most sites or basins in Chinese terrestrial ecosystems. The CEVSA‐ES model not only has the potential to improve the accuracy of simulated ESs, but also can capture the relationships among ESs, which could support the trade‐offs and synergies among ESs. Key Points We developed an ecosystem service model Carbon and Exchange between Vegetation, Soil, and Atmosphere‐ecosystem services (CEVSA‐ES) that integrates ecosystem processes with satellite‐based data Accounting for soil retention/erosion and its impact on carbon cycling was the main difference from other process‐based models The CEVSA‐ES model with optimized parameters explained 47%–96% of the spatial and temporal variations of four ecosystem services in China

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, with R 2 increasing 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.

Terrestrial biosphere models offer a comprehensive view of the global carbon cycle by integrating ecological processes across scales, yet they introduce significant uncertainties in climate and biogeochemical projections due to diverse process representations and parameter variations. For instance, different soil water limitation functions lead to wide productivity ranges across models. To address this, we propose the Differentiable Land Model (DifferLand), a novel hybrid machine learning approach replacing unknown water limitation functions in models with neural networks (NNs) to learn from data. Using automatic differentiation, we calibrated the embedded NN and the physical model parameters against daily observations of evapotranspiration, gross primary productivity, ecosystem respiration, and leaf area index across 16 FLUXNET sites. We evaluated six model configurations where NNs simulate increasingly complex soil water and photosynthesis interactions against test data sets to find the optimal structure‐performance tradeoff. Our findings show that a simple hybrid model with a univariate NN effectively captures site‐level water and carbon fluxes on a monthly timescale. Across a global aridity gradient, the magnitude of water stress limitation varies, but its functional form consistently converges to a piecewise linear relationship with saturation at high water levels. While models incorporating more interactions between soil water and meteorological drivers better fit observations at finer time scales, they risk overfitting and equifinality issues. Our study demonstrates that hybrid models have great potential in learning unknown parameterizations and testing ecological hypotheses. Nevertheless, careful structure‐performance tradeoffs are warranted in light of observational constraints to translate the retrieved relationships into robust process understanding. Plain Language Summary Terrestrial carbon cycles simulations commonly focus on either describing the ecological processes with physical yet empirical equations or capturing the statistical relationships between variables using data‐driven techniques. Both approaches have their advantages and disadvantages. Process‐based simulations are grounded in scientific principles but may be inaccurate due to imperfect knowledge of the equations. Machine‐learning techniques can potentially capture the complex relationships between environmental variables but can be hard to extrapolate. In this study, we combine the two approaches into a hybrid model by embedding a set of neural networks within a process‐based model. We tested the model at different locations to study whether it can learn how plants respond to water limitations. The results showed the hybrid modeling approach can successfully retrieve the functional relationships between ecological variables. In addition, the overall performance of the hybrid model improved compared to the baseline model due to increased structural flexibility. We envision such a hybrid approach to help in the presence of imperfect knowledge of the governing equations in terrestrial carbon simulations. Instead of prescribing uncertain governing equations for the unknown ecological relationships, we can let the hybrid model learn these functional relationships from data, while preserving the temporal consistency of the model. Key Points An automatically differentiable hybrid model is developed to learn parameters and functional relationships in land carbon and water cycles Neural network emulators simulate ecological dynamics well but risk equifinality with limited data due to increased degrees of freedom Monthly soil water impacts on GPP and ET are well‐captured by piecewise linear functions, but finer time effects may need more complexity

Constitutive modeling is crucial for engineering design and simulations to accurately describe material behavior. However, traditional phenomenological models often struggle to capture the complexities of real materials under varying stress conditions due to their fixed forms and limited parameters. While recent advances in deep learning have addressed some limitations of classical models, purely data‐driven methods tend to require large data sets, lack interpretability, and struggle to generalize beyond their training data. To tackle these issues, we introduce “Fusion‐based Constitutive model (FuCe): Toward model‐data augmentation in constitutive modeling.” This approach combines established phenomenological models with an Input Convex Neural Network architecture, designed to train on the limited and noisy force‐displacement data typically available in practical applications. The hybrid model inherently adheres to necessary constitutive conditions. During inference, Monte Carlo dropout is employed to generate Bayesian predictions, providing mean values and confidence intervals that quantify uncertainty. We demonstrate the model's effectiveness by learning two isotropic constitutive models and one anisotropic model with a single fiber direction, across six different stress states. The framework's applicability is also showcased in finite element simulations across three geometries of varying complexities. Our results highlight the framework's superior extrapolation capabilities, even when trained on limited and noisy data, delivering accurate and physically meaningful predictions across all numerical examples.

Many parameters in terrestrial biogeochemical models are inherently uncertain, leading to uncertainty in predictions of key carbon cycle variables. At observation sites, this uncertainty can be quantified by applying model‐data fusion techniques to estimate model parameters using eddy covariance observations and associated biometric data sets as constraints. Uncertainty is reduced as data records become longer and different types of observations are added. We estimate parametric and associated predictive uncertainty at the Morgan Monroe State Forest in Indiana, USA. Parameters in the Local Terrestrial Ecosystem Carbon (LoTEC) are estimated using both synthetic and actual constraints. These model parameters and uncertainties are then used to make predictions of carbon flux for up to 20 years. We find a strong dependence of both parametric and prediction uncertainty on the length of the data record used in the model‐data fusion. In this model framework, this dependence is strongly reduced as the data record length increases beyond 5 years. If synthetic initial biomass pool constraints with realistic uncertainties are included in the model‐data fusion, prediction uncertainty is reduced by more than 25% when constraining flux records are less than 3 years. If synthetic annual aboveground woody biomass increment constraints are also included, uncertainty is similarly reduced by an additional 25%. When actual observed eddy covariance data are used as constraints, there is still a strong dependence of parameter and prediction uncertainty on data record length, but the results are harder to interpret because of the inability of LoTEC to reproduce observed interannual variations and the confounding effects of model structural error. Key Points Measurements of carbon pools at flux towers are important model constraints Longer data records reduce model parameter and prediction uncertainty Model parameters associated with carbon pool turnover are poorly constrained

Forecasts of tropical ecosystem C cycling diverge among models due to differences in simulation of internal processes such as turnover, or transit times, of carbon pools. Estimates of these processes for the recent past are needed to test model representations, and so build confidence in model forecasts within and across biomes. Here, we evaluate carbon cycle process representation in two land surface models [Joint UK Land Environment Simulator (JULES) and Integrated Model of Land Surface Processes (INLAND)] for the period 2001–10 across Brazilian biomes. Model outputs are evaluated using the ILAMB system. Probabilistic benchmarking data were created using the carbon data model framework that assimilates observational times series of leaf area index and maps of woody biomass and soil C. New custom uncertainty metrics assess if models are within benchmark uncertainties. Simulations are better in homogeneous areas of vegetation type, and are less robust at ecotones between biomes, likely due to disturbance effects and parameter errors. Gross biosphere‐atmosphere fluxes are robustly modelled across Brazil. However, benchmark uncertainty is too high on net ecosystem exchange to provide an accurate evaluation of the models. The LSMs have significant differences in internal carbon allocation and the dynamics of the different C pools. JULES models dead C stocks more accurately while living C stocks are best resolved for INLAND. JULES' over‐estimate of the C wood pool results from over‐estimation of both inputs to wood and the transit time of wood. INLAND's under‐estimate of dead C stocks arises from an under‐estimate of the transit time of dead organic matter. The models are better at simulating annual averages than seasonal variation of fluxes. Analyses of monthly net C exchanges show that INLAND correctly simulates seasonality, but over‐estimates amplitudes, whereas JULES correctly simulates the annual amplitudes, but is out of phase with the benchmark. Forecasts of tropical C cycling diverge among models due to differences in ecosystem representation. Using regional carbon cycle data linked in an analytical framework, we evaluate process representation in two land surface models across Brazilian biomes. We found that the models broadly reproduced the benchmark C fluxes between biosphere and atmosphere, but the processes underpinning these fluxes differed between models and often were at odds with the benchmark data. We provide recommendations for how to improve the models for better forecasts. Legend: The mean annual cycle of GPP (gross primary production) across the Cerrado biome of Brazil. The red line how the predictions for the INLAND model; the green line for the JULES model. The black line shows the benchmark estimate with 95% confidence intervals (dashed grey).

A 9‐km coupled ice‐ocean model (CIOM) was implemented in the entire Bering Sea to investigate seasonal cycles of sea ice and ocean circulation under atmospheric forcing. Sea ice cover with a maximum of 0.6 × 106 km2 in February to late March was reasonably reproduced by the Bering‐CIOM and validated by Special Sensor Microwave/Imager (SSM/I) measurements. The model also captures some important spatial variability and downscaling processes such as polynyas and ridging, which the SSM/I measurements cannot reproduce because of their coarse (25 km) resolution. There are two distinct surface ocean circulation patterns in winter and summer on the Bering shelves because of the dominant winds, which are northeasterly in winter and southwesterly in summer. Summer low‐temperature, high‐salinity water mass (<3°C) on the Bering shelf is formed locally during winter because of strong vertical convection caused by salt injection when ice forms, wind, and wind‐wave mixing on the shelf. The northward volume transport across the 62.5°N line, with an annual mean of 0.8 ± 0.33 Sv (1 Sv = 106 m3 s−1) that is consistent with the measurements in the Bering Strait, has barotropic structure, which transports heat flux (with an annual mean of 7.74 TW; 1 TW = 1012 W) northward. The Anadyr Current advects warmer, saltier water northward during summer; nevertheless, it reverses its direction to southward during winter because of predominant northeasterly and northerly wind forcing. Therefore, the Anadyr Current advects cold, salty water southward. The volume transport on the broad midshelf is northward year round, advecting heat (3.3 ± 2.4 TW) and freshwater (−8 ± 10 × 104 practical salinity unit (psu) m3 s−1) northward. One important finding is that the Anadyr Current and the midshelf current are out of phase in volume and heat transports. The Alaskan Coastal Current also transports heat and freshwater northward on an annual basis. The Bering‐CIOM also captures the winter dense water formation along the Siberian coast, which is promoted by the downwelling favorable northeasterly wind, and the summer upwelling due to the basin‐scale upwelling favorable southwesterly wind, which brings up the cold, salty, and nutrient‐rich water from the subsurface to the surface within a narrow strip along the west coast. This upwelling found in the model was also confirmed by satellite measurements in this study.

We present an approach for dealing with coarse‐resolution Earth observations (EO) in terrestrial ecosystem data assimilation schemes. The use of coarse‐scale observations in ecological data assimilation schemes is complicated by spatial heterogeneity and nonlinear processes in natural ecosystems. If these complications are not appropriately dealt with, then the data assimilation will produce biased results. The “disaggregation” approach that we describe in this paper combines frequent coarse‐resolution observations with temporally sparse fine‐resolution measurements. We demonstrate the approach using a demonstration data set based on measurements of an Arctic ecosystem. In this example, normalized difference vegetation index observations are assimilated into a “zero‐order” model of leaf area index and carbon uptake. The disaggregation approach conserves key ecosystem characteristics regardless of the observation resolution and estimates the carbon uptake to within 1% of the demonstration data set “truth.” Assimilating the same data in the normal manner, but without the disaggregation approach, results in carbon uptake being underestimated by 58% at an observation resolution of 250 m. The disaggregation method allows the combination of multiresolution EO and improves in spatial resolution if observations are located on a grid that shifts from one observation time to the next. Additionally, the approach is not tied to a particular data assimilation scheme, model, or EO product and can cope with complex observation distributions, as it makes no implicit assumptions of normality. Key Points Scaling issues must be considered when assimilating satellite observations Standard data assimilation methods will produce biased results We present a method for avoiding these biases

What is the uncertainty of climate–carbon cycle projections in response to anthropogenic greenhouse gas emissions, and how can we reduce this uncertainty? We address this question by quantifying the ability of available ocean tracer observations to constrain the values of diapycnal diffusivity in the pelagic ocean (Kv), a key uncertain parameter representing sub‐grid‐scale diapycnal (vertical) mixing in physical circulation models. We show that model versions with weak mixing (i.e., low Kv) lead to higher projections of atmospheric CO2 and larger global warming than do models with vigorous mixing. Slower heat uptake and slower carbon uptake by the oceans contribute about equally to the accelerated warming in the low‐mixing models. A Bayesian data‐model fusion method is developed to quantify the likelihood of different structural and parametric model choices given an array of observed 20th century ocean tracer distributions. These spatially resolved observations provide strong limits on the upper value of Kv, whereas global metrics used in previous studies, such as the historical evolution of global average surface air temperature, global ocean heat uptake, or atmospheric CO2 concentration, provide only poor constraints. We compare different methods to quantify the probability of a particular diffusivity value given the observational constraints. One‐dimensional, globally horizontally averaged data result in sharper probability density functions compared with the full 3‐D fields. This perhaps unexpected result opens up an avenue to objectively determine the optimal degree of aggregation at which model predictions have skill, and at which observations are most helpful in constraining model parameters. Our best estimate for Kv in the pelagic pycnocline is around 0.05–0.2 cm2/s, in agreement with earlier independent estimates based on tracer dispersion experiments and turbulence microstructure measurements.