The rapid increase in the volume and variety of terrestrial biosphere observations (i.e., remote sensing data and in situ measurements) offers a unique opportunity to derive ecological insights, refine process-based models, and improve forecasting for decision support. However, despite their potential, ecological observations have primarily been used to benchmark process-based models, as many past and current models lack the capability to directly integrate observations and their associated uncertainties for parameterization. In contrast, data assimilation frameworks such as the CARbon DAta MOdel fraMework (CARDAMOM) and its suite of process-based models, known as the Data Assimilation Linked Ecosystem Carbon Model (DALEC), are specifically designed for model-data fusion. This review, motivated by a recent CARDAMOM community workshop, examines the development and applications of CARDAMOM, with an emphasis on its role in advancing ecosystem process understanding. CARDAMOM employs a Bayesian approach, using a Markov Chain Monte Carlo algorithm to enable data-driven calibration of DALEC parameters and initial states (i.e., carbon pool sizes) through observation operators. CARDAMOM's unique ability to retrieve localized model process parameters from diverse datasets-ranging from in situ measurements to global satellite observations-makes it a highly flexible tool for analyzing spatially variable ecosystem responses to environmental change. However, assimilating these data also presents challenges, including data quality issues that propagate into model skill, as well as trade-offs between model complexity, parameter equifinality, and predictive performance. We discuss potential solutions to these challenges, such as reducing parameter equifinality by incorporating new observations. This review also offers community recommendations for incorporating emerging datasets, integrating machine learning techniques, strengthening collaboration with remote sensing, field, and modeling communities, and expanding CARDAMOM's relevance for localized ecosystem monitoring and decision-making. CARDAMOM enables a deep, mechanistic understanding of terrestrial ecosystem dynamics that cannot be achieved through empirical analyses of observational datasets or weakly constrained models alone.

Multi-model ensembles are becoming increasingly accepted for the estimation of agricultural carbon-nitrogen fluxes, productivity and sustainability. There is mounting evidence that with some site-specific observations available for model calibration (with vegetation data as a minimum requirement), median outputs assimilated from biogeochemical models (multi-model medians) provide more accurate simulations than individual models. Here, we evaluate potential deficiencies in how model ensembles represent (in relation to climatic factors) the processes underlying biogeochemical outputs in complex agricultural systems such as grassland and crop rotations including fallow periods. We do that by exploring the correlation of model residuals. We restricted the distinction between partial and full calibration to the two most relevant calibration stages, i.e. with plant data only (partial) and with a combination of plant, soil physical and biogeochemical data (full). It introduces and evaluates the trade-off between (1) what is practical to apply for model users and beneficiaries, and (2) what constitutes best modelling practice. The lower correlations obtained overall with fully calibrated models highlight the centrality of the full calibration scenario for identifying areas of model structures that require further development.

Grasslands cover around two-thirds of the agricultural land area of Great Britain (GB) and are important reservoirs of organic carbon (C). Direct assessments of the C balance of grasslands require continuous monitoring of C pools and fluxes, which is only possible at a small number of experimental sites. By relying on our quantitative understanding of ecosystem C biogeochemistry we develop models of grassland C dynamics and use them to estimate grassland C balance at various scales. Model-based estimation of the C budget of individual fields and across large domains is made complex by the spatial and temporal variability in climate and soil conditions, as well as in livestock grazing, grass cutting and other management activities. In this context, earth observations (EOs) provide subfield-resolution proxy data on the state of grassland canopies, allowing us to infer information about vegetation management, to apply observational constraints to the simulated ecosystems and, thus, to mitigate the effects of model input data uncertainty. Here, we show the potential of model–data fusion (MDF) methods to provide robust analyses of C dynamics in managed grasslands across GB. We combine EO data and biogeochemical modelling by implementing a probabilistic MDF algorithm to (1) assimilate leaf area index (LAI) times series (Sentinel-2); (2) infer defoliation instances (grazing, cutting); and (3) simulate livestock grazing, grass cutting, and C allocation and C exchanges with the atmosphere. The algorithm uses the inferred information on grazing and cutting to drive the model's C removals-and-returns module, according to which ≈1/3 of C in grazed biomass returns to the soil as manure (other inputs of manure not considered) and C in cut grass is removed from the system (downstream C emissions not considered). Spatial information on soil C stocks is obtained from the SoilGrids dataset. The MDF algorithm was applied for 2017–2018 to generate probabilistic estimates of C pools and fluxes at 1855 fields sampled from across GB. The algorithm was able to effectively assimilate the Sentinel-2-based LAI time series (overlap = 80 %, RMSE = 1.1 m2 m−2, bias = 0.35 m2 m−2) and predict livestock densities per area that correspond with independent agricultural census-based data (r = 0.68, RMSE = 0.45 LU ha−1, bias = −0.06 LU ha−1). The mean total removed biomass across all simulated fields was 6 (±1.8) t DM ha−1 yr−1. The simulated grassland ecosystems were on average C sinks in 2017 and 2018; the net biome exchange (NBE) was -191±81 (2017) and -49±69 gC m−2 yr−1 (2018). Our results show that the 2018 European summer drought reduced the strength of C sinks in GB grasslands and led to a 9-fold increase in the number fields that were annual C sources (NBE > 0) in 2018 (18 % of fields) compared to 2017 (2 % of fields). The field-scale analysis showed that management in the form of timing, intensity and type of defoliation were key determinants of the C balance of managed grasslands, with cut fields acting as weaker C sinks compared to grazed fields. Nevertheless, extreme weather, such as prolonged droughts, can convert grassland C sinks to sources.

There is a growing realization that the complexity of model ensemble studies depends not only on the models used but also on the experience and approach used by modelers to calibrate and validate results, which remain a source of uncertainty. Here, we applied a multi-criteria decision-making method to investigate the rationale applied by modelers in a model ensemble study where 12 process-based different biogeochemical model types were compared across five successive calibration stages. The modelers shared a common level of agreement about the importance of the variables used to initialize their models for calibration. However, we found inconsistency among modelers when judging the importance of input variables across different calibration stages. The level of subjective weighting attributed by modelers to calibration data decreased sequentially as the extent and number of variables provided increased. In this context, the perceived importance attributed to variables such as the fertilization rate, irrigation regime, soil texture, pH, and initial levels of soil organic carbon and nitrogen stocks was statistically different when classified according to model types. The importance attributed to input variables such as experimental duration, gross primary production, and net ecosystem exchange varied significantly according to the length of the modeler's experience. We argue that the gradual access to input data across the five calibration stages negatively influenced the consistency of the interpretations made by the modelers, with cognitive bias in "trial-and-error" calibration routines. Our study highlights that overlooking human and social attributes is critical in the outcomes of modeling and model intercomparison studies. While complexity of the processes captured in the model algorithms and parameterization is important, we contend that (1) the modeler's assumptions on the extent to which parameters should be altered and (2) modeler perceptions of the importance of model parameters are just as critical in obtaining a quality model calibration as numerical or analytical details.

Climate, nitrogen (N) and leaf area index (LAI) are key determinants of crop yield. N additions can enhance yield but must be managed efficiently to reduce pollution. Complex process models estimate N status by simulating soil-crop N interactions, but such models require extensive inputs that are seldom available. Through model-data fusion (MDF), we combine climate and LAI time-series with an intermediate-complexity model to infer leaf N and yield. The DALEC-Crop model was calibrated for wheat leaf N and yields across field experiments covering N applications ranging from 0 to 200 kg N ha−1 in Scotland, UK. Requiring daily meteorological inputs, this model simulates crop C cycle responses to LAI, N and climate. The model, which includes a leaf N-dilution function, was calibrated across N treatments based on LAI observations, and tested at validation plots. We showed that a single parameterization varying only in leaf N could simulate LAI development and yield across all treatments—the mean normalized root-mean-square-error (NRMSE) for yield was 10%. Leaf N was accurately retrieved by the model (NRMSE = 6%). Yield could also be reasonably estimated (NRMSE = 14%) if LAI data are available for assimilation during periods of typical N application (April and May). Our MDF approach generated robust leaf N content estimates and timely yield predictions that could complement existing agricultural technologies. Moreover, EO-derived LAI products at high spatial and temporal resolutions provides a means to apply our approach regionally. Testing yield predictions from this approach over agricultural fields is a critical next step to determine broader utility.

Grasslands cover around two-thirds of the agricultural land area of Great Britain (GB) and are important reservoirs of organic carbon (C). Direct assessments of the C balance of grasslands require continuous monitoring of C pools and fluxes, which is only possible at a small number of experimental sites. By relying on our quantitative understanding of ecosystem C biogeochemistry we develop models of grassland C dynamics and use them to estimate grassland C balance at various scales. Model-based estimation of the C budget of individual fields and across large domains is made complex by the spatial and temporal variability in climate and soil conditions, as well as in livestock grazing, grass cutting and other management activities. In this context, earth observations (EOs) provide subfield-resolution proxy data on the state of grassland canopies, allowing us to infer information about vegetation management, to apply observational constraints to the simulated ecosystems and, thus, to mitigate the effects of model input data uncertainty. Here, we show the potential of model–data fusion (MDF) methods to provide robust analyses of C dynamics in managed grasslands across GB. We combine EO data and biogeochemical modelling by implementing a probabilistic MDF algorithm to (1) assimilate leaf area index (LAI) times series (Sentinel-2); (2) infer defoliation instances (grazing, cutting); and (3) simulate livestock grazing, grass cutting, and C allocation and C exchanges with the atmosphere. The algorithm uses the inferred information on grazing and cutting to drive the model's C removals-and-returns module, according to which ≈1/3 of C in grazed biomass returns to the soil as manure (other inputs of manure not considered) and C in cut grass is removed from the system (downstream C emissions not considered). Spatial information on soil C stocks is obtained from the SoilGrids dataset. The MDF algorithm was applied for 2017–2018 to generate probabilistic estimates of C pools and fluxes at 1855 fields sampled from across GB. The algorithm was able to effectively assimilate the Sentinel-2-based LAI time series (overlap = 80 %, RMSE = 1.1 m2 m−2, bias = 0.35 m2 m−2) and predict livestock densities per area that correspond with independent agricultural census-based data (r = 0.68, RMSE = 0.45 LU ha−1, bias = −0.06 LU ha−1). The mean total removed biomass across all simulated fields was 6 (±1.8) t DM ha−1 yr−1. The simulated grassland ecosystems were on average C sinks in 2017 and 2018; the net biome exchange (NBE) was -191±81 (2017) and -49±69 gC m−2 yr−1 (2018). Our results show that the 2018 European summer drought reduced the strength of C sinks in GB grasslands and led to a 9-fold increase in the number fields that were annual C sources (NBE > 0) in 2018 (18 % of fields) compared to 2017 (2 % of fields). The field-scale analysis showed that management in the form of timing, intensity and type of defoliation were key determinants of the C balance of managed grasslands, with cut fields acting as weaker C sinks compared to grazed fields. Nevertheless, extreme weather, such as prolonged droughts, can convert grassland C sinks to sources.

Grasslands, natural and managed, cover a large part of the Earth's surface and play an important role in the global carbon (C) cycle. Human management strongly affects grassland C budgets through grass cutting and removal, varied grazing intensities, and organic matter additions. Thus managed grassland C cycles are highly heterogeneous and challenging to quantify. In this study, we combine a process-based model of the grassland C cycle, validated against field data on C fluxes and pools, with satellite-derived data (Proba-V and Sentinel-2) on leaf area index (LAI) in order to quantify field-scale grassland productivity and C dynamics under climatic and management conditions typical of northwest Europe. Input data on the weekly vegetation canopy anomaly (estimated from Proba-V LAI) and meteorology are used to drive the grassland C model (DALEC-Grass) that is integrated into a Bayesian model-data fusion (MDF) framework. The novelty of the MDF algorithm is that it infers weekly livestock grazing and grass cutting events based on expected canopy growth estimated by the model, and constrained by LAI observations (estimated from Sentinel-2). The MDF approach also resolves observational, parametric, and input uncertainties on C cycling estimates. We analysed four years (2015-2018) of C dynamics at three variably-managed fields of the Rothamsted Research North Wyke Farm Platform (UK). Compared against independent field data, the MDF was able to (i) identify 87.5% of the harvest events that occurred, (ii) accurately predict the annual yields in 83% of the identified harvest years and (iii) reproduce the observed grazing intensity in each field (r = 0.8, overlap = 90%). We demonstrate that the fusion of process modelling with earth observations is an effective method for monitoring biomass removals and quantifying management impacts on field-scale C balance, without the need for frequent and laborious ground measurements. This approach can support the delivery of more robust national greenhouse gas (GHG) accounting that takes account of grassland vegetation management.

Grasslands are an important component of the global carbon (C) cycle, with a strong potential for C sequestration. However, an improved capacity to quantify grassland C stocks and monitor their variation in space and time, particularly in response to management, is needed in order to conserve and enhance grassland C reservoirs. To meet this challenge we outline and test here an approach to combine C cycle modelling with observational data. We implemented an intermediate complexity model, DALEC-Grass, within a probabilistic model-data fusion (MDF) framework, CARDAMOM, at two managed grassland sites (Easter Bush and Crichton) in the UK. We used 3 years (Easter Bush, 2002-2004) of management data and observations of leaf area index (LAI) and Net Ecosystem Exchange (NEE) from eddy covariance to calibrate the distributions of model parameters. Using these refined distributions, we then assimilated the remaining 7 years (Easter Bush, 2005-2010 and Crichton, 2015) of LAI observations and evaluated the simulated NEE, above and below-ground biomass and other C fluxes against independent data from the two grasslands. Our results show that fusing model predictions with LAI observations allowed the CARDAMOM MDF system to diagnose the effects of grazing and cutting realistically. The overlap of MDF-predicted and measured NEE (both sites) and ecosystem respiration (Easter Bush) was 92% and 83% respectively while the correlation coefficient (r) was 0.79 for both variables. This study lays the foundation for using MDF with satellite data on LAI to produce the spatially and temporally-resolved estimates of C cycling needed in shaping and monitoring the implementation of relevant policies and farm-management decisions.

Croplands and grasslands are agricultural systems that contribute to land-atmosphere exchanges of carbon (C). We evaluated and compared gross primary production (GPP), ecosystem respiration (RECO), net ecosystem exchange (NEE) of CO2, and two derived outputs - C use efficiency (CUE = -NEE/GPP) and C emission intensity (Int(C) = -NEE/Offtake [grazed or harvested biomass]). The outputs came from 23 models (11 crop-specific, eight grassland-specific, and four models covering both systems) at three cropping sites over several rotations with spring and winter cereals, soybean and rapeseed in Canada, France and India, and two temperate permanent grasslands in France and the United Kingdom. The models were run independently over multi-year simulation periods in five stages (S), either blind with no calibration and initialization data (S1), using historical management and climate for initialization (S2), calibrated against plant data (S3), plant and soil data together (S4), or with the addition of C and N fluxes (S5). Here, we provide a framework to address methodological uncertainties and contextualize results. Most of the models overestimated or underestimated the C fluxes observed during the growing seasons (or the whole years for grasslands), with substantial differences between models. For each simulated variable, changes in the multi-model median (MMM) from S1 to S5 was used as a descriptor of the ensemble performance. Overall, the greatest improvements (MMM approaching the mean of observations) were achieved at S3 or higher calibration stages. For instance, grassland GPP MMM was equal to 1632 g C m(-2) yr(-1) (S5) while the observed mean was equal to 1763 m(-2) yr(-1) (average for two sites). Nash-Sutcliffe modelling efficiency coefficients indicated that MMM outperformed individual models in 92.3 % of cases. Our study suggests a cautious use of large-scale, multi-model ensembles to estimate C fluxes in agricultural sites if some site-specific plant and soil observations are available for model calibration. The further development of crop/grassland ensemble modelling will hinge upon the interpretation of results in light of the way models represent the processes underlying C fluxes in complex agricultural systems (grassland and crop rotations including fallow periods).

Managed grasslands are extensive terrestrial ecosystems that provide a range of services. In addition to supporting the world’s various livestock production systems they contain climatically significant amounts of carbon (C). Understanding and quantifying the C dynamics of managed grasslands is complicated yet crucial.This presentation describes a process-model of C dynamics in managed grasslands (DALEC-Grass). DALEC-Grass is a model of intermediate complexity, which calculates primary productivity, dynamicallyallocates C to biomass tissues and describes the impacts of grazing/harvesting activities. The model is integrated into a Bayesian model-data fusion framework (CARDAMOM). CARDAMOM uses observations of ecosystem functioning (e.g. leaf area, biomass, C fluxes) to optimise the model’s parameters while respecting a set of biogeochemical and physiological rules. The model evaluation results presented demonstrate the model’s skill in predicting primary productivity and C allocation patterns in UK grasslands using both ground and satellite based leaf area index (LAI) time series as observational constraints.

The application of nitrogenous fertilisers to agricultural soils is a major source of anthropogenic N2O emissions. Reducing the nitrogen (N) footprint of agriculture is a global challenge that depends, among other things, on our ability to quantify the N2O emission intensity of the world's most widespread and productive agricultural systems. In this context, biogeochemistry (BGC) models are widely used to estimate soil N2O emissions in agroecosystems. The choice of spatial scale is crucial because larger-scale studies are limited by low input data precision, while smaller-scale studies lack wider relevance. The robustness of large-scale model predictions depends on preliminary and data-demanding model calibration/validation, while relevant studies often omit the performance of output uncertainty analysis and underreport model outputs that would allow a critical assessment of results. This study takes a novel approach to these aspects. The study focuses on arable eastern Scotland – a data-rich region typical of northwest Europe in terms of edaphoclimatic conditions, cropping patterns and productivity levels. We used a calibrated and locally validated BGC model to simulate direct soil N2O emissions along with NO3 leaching and crop N uptake in fields of barley, wheat and oilseed rape. We found that 0.59 % (±0.36) of the applied N is emitted as N2O while 37 % (±6) is taken up by crops and 14 % (±7) is leached as NO3. We show that crop type is a key determinant of N2O emission factors (EFs) with cereals having a low (mean EF<0.6 %), and oilseed rape a high (mean EF=2.48 %), N2O emission intensity. Fertiliser addition was the most important N2O emissions driver suggesting that appropriate actions can reduce crop N2O intensity. Finally, we estimated a 74 % relative uncertainty around N2O predictions attributable to soil data variability. However, we argue that higher-resolution soil data alone might not suffice to reduce this uncertainty.

Simulation models are extensively used to predict agricultural productivity and greenhouse gas emissions. However, the uncertainties of (reduced) model ensemble simulations have not been assessed systematically for variables affecting food security and climate change mitigation, within multi‐species agricultural contexts. We report an international model comparison and benchmarking exercise, showing the potential of multi‐model ensembles to predict productivity and nitrous oxide (N 2 O) emissions for wheat, maize, rice and temperate grasslands. Using a multi‐stage modelling protocol, from blind simulations (stage 1) to partial (stages 2–4) and full calibration (stage 5), 24 process‐based biogeochemical models were assessed individually or as an ensemble against long‐term experimental data from four temperate grassland and five arable crop rotation sites spanning four continents. Comparisons were performed by reference to the experimental uncertainties of observed yields and N 2 O emissions. Results showed that across sites and crop/grassland types, 23%–40% of the uncalibrated individual models were within two standard deviations ( SD ) of observed yields, while 42 (rice) to 96% (grasslands) of the models were within 1 SD of observed N 2 O emissions. At stage 1, ensembles formed by the three lowest prediction model errors predicted both yields and N 2 O emissions within experimental uncertainties for 44% and 33% of the crop and grassland growth cycles, respectively. Partial model calibration (stages 2–4) markedly reduced prediction errors of the full model ensemble E‐median for crop grain yields (from 36% at stage 1 down to 4% on average) and grassland productivity (from 44% to 27%) and to a lesser and more variable extent for N 2 O emissions. Yield‐scaled N 2 O emissions (N 2 O emissions divided by crop yields) were ranked accurately by three‐model ensembles across crop species and field sites. The potential of using process‐based model ensembles to predict jointly productivity and N 2 O emissions at field scale is discussed.

Process-based agroecosystem biogeochemistry models are widely used to quantify the flow of water and nutrients in agricultural ecosystems and they have become important tools in the effort to address the twin challenges of reducing greenhouse gas emissions and improving agricultural sustainability. Model parameters require careful calibration, as they affect the simulated processes and outputs. Sensitivity analysis (SA) is commonly used to quantify the impacts of parameters on outputs, and guide the calibration process. Here we demonstrate a systematic approach for SA, which assures that (1) the role of time-dependency in the sensitivity indices is considered and (2) the SA is not biased by the edapho-climatic conditions at individual sites. Demonstrating this approach, we examine the parametric sensitivity of an advanced agroecosystem model (Landscape-DNDC) using a framework that is based on (1) the Sobol SA method, (2) model simulations at three UK arable sites and (3) the grouping of the model's parameters according to the processes they affect. The findings of this research identify the parameters and processes that should be carefully examined in order to minimise the impact of parametric uncertainty on model outputs. We show that a limited number of parameters are responsible for a large part of the sensitivity of model outputs. The description of soil microbial dynamics is identified as a key source of output sensitivity. Also, we show that individual management activities can significantly affect the time-dependency of the parametric sensitivity indices for certain model outputs. (C) 2017 Elsevier B.V. All rights reserved.

The biogeochemical processes that lead to the production of N2O in arable soils are controlled by temporally and spatially varying drivers. The need for prediction of soil N2O emissions across scales means that agroecosystem biogeochemistry models are widely used to simulate N2O emissions. Due to the parameter-dense nature of agroecosystem models their parameters have to be calibrated according to the soil and climatic conditions of the intended area of application. Bayesian calibration is considered one of the most advanced ways to complete this task. In this study, we calibrate nine parameters of the Landscape-DNDC process-based agroecosystem model, which are key to its N2O prediction. The Metropolis-Hastings algorithm is used at four separate implementations in order to estimate parameter posterior distributions at four arable sites in the UK. The results of this process are visualised, summarised and assessed against measured N2O data from ten independent arable sites. The study shows that, in many cases, soil N2O emission peaks that were not predicted with the default model parameters were predicted after calibration. Overall, the prediction of soil N2O fluxes across all the sites that were considered was improved by 33% when using the calibrated parameters.

The loss of nitrogen from fertilised soils in the form of nitrous oxide (N2O) is a side effect of modern agriculture and the focus of many model-based studies. Due to the spatial and temporal heterogeneity of soil N2O emissions, the measured data can introduce limitations to the use of those statistical methods that are most commonly employed in the evaluation of model performance. In this paper, we describe these limitations and present an algorithm developed to address them. We implement the algorithm using simulated and measured N2O data from two UK arable sites. We show that possible time lags between the measured and simulated data can affect model evaluation and that their consideration in the evaluation process can reduce measures such as the Mean Squared Error (MSE) by 30%. We also analyse the algorithm's results to identify patterns in the estimated lags and to narrow down their possible causes.