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NASA NTRS2016

Spatial and Temporal Uncertainty of Crop Yield Aggregations

The aggregation of simulated gridded crop yields to national or regional scale requires information on temporal and spatial patterns of crop-specific harvested areas. This analysis estimates the uncertainty of simulated gridded yield time series related to the aggregation with four different harvested area data sets. We compare aggregated yield time series from the Global Gridded Crop Model Inter-comparison project for four crop types from 14 models at global, national, and regional scale to determine aggregation-driven differences in mean yields and temporal patterns as measures of uncertainty. The quantity and spatial patterns of harvested areas differ for individual crops among the four datasets applied for the aggregation. Also simulated spatial yield patterns differ among the 14 models. These differences in harvested areas and simulated yield patterns lead to differences in aggregated productivity estimates, both in mean yield and in the temporal dynamics. Among the four investigated crops, wheat yield (17% relative difference) is most affected by the uncertainty introduced by the aggregation at the global scale. The correlation of temporal patterns of global aggregated yield time series can be as low as for soybean (r = 0.28).For the majority of countries, mean relative differences of nationally aggregated yields account for10% or less. The spatial and temporal difference can be substantial higher for individual countries. Of the top-10 crop producers, aggregated national multi-annual mean relative difference of yields can be up to 67% (maize, South Africa), 43% (wheat, Pakistan), 51% (rice, Japan), and 427% (soybean, Bolivia).Correlations of differently aggregated yield time series can be as low as r = 0.56 (maize, India), r = 0.05∗Corresponding (wheat, Russia), r = 0.13 (rice, Vietnam), and r = −0.01 (soybean, Uruguay). The aggregation to sub-national scale in comparison to country scale shows that spatial uncertainties can cancel out in countries with large harvested areas per crop type. We conclude that the aggregation uncertainty can be substantial for crop productivity and production estimations in the context of food security, impact assessment, and model evaluation exercises.

Aggregation uncertainty↗
NASA NTRS2019

A Crop Yield Change Emulator for Use in GCAM and Similar Models: Persephone v1.0

Future changes in Earth system state will impact agricultural yields and, through these changed yields, can have profound impacts on the global economy. Global gridded crop models estimate the influence of these Earth system changes on future crop yields but are often too computationally intensive to dynamically couple into global multisector economic models, such as the Global Change Assessment Model (GCAM) and other similar-in-scale models. Yet, generalizing a faster site-specific crop model’s results to be used globally will introduce inaccuracies, and the question of which model to use is unclear given the wide variation in yield response across crop models. To examine the feedback loop among socioeconomics, Earth system changes, and crop yield changes, rapidly generated yield responses with some quantification of crop response uncertainty are desirable. The Persephone v1.0 response functions presented in this work are based on the Agricultural Model Intercomparison and Improvement Project (AgMIP) Coordinated Climate-Crop Modeling Project (C3MP) sensitivity test data set and are focused on providing GCAM and similar models with a tractable number of rapid to evaluate dynamic yield response functions corresponding to a range of the yield response sensitivities seen in the C3MP data set. With the Persephone response functions, a new variety of agricultural impact experiments will be open to GCAM and other economic models: for example, examining the economic impacts of a multi-year drought in a key agricultural region and how economic changes in response to the drought can, in turn, impact the drought.

Snyder, Abigail↗
NASA NTRS2023

The optimization of model ensemble composition and size can enhance the robustness of crop yield projections

Linked climate and crop simulation models are widely used to assess the impact of climate change on agriculture. However, it is unclear how ensemble configurations (model composition and size) influence crop yield projections and uncertainty. Here, we investigate the influences of ensemble configurations on crop yield projections and modeling uncertainty from Global Gridded Crop Models and Global Climate Models under future climate change. We performed a cluster analysis to identify distinct groups of ensemble members based on their projected outcomes, revealing unique patterns in crop yield projections and corresponding uncertainty levels, particularly for wheat and soybean. Furthermore, our findings suggest that approximately six Global Gridded Crop Models and 10 Global Climate Models are sufficient to capture modeling uncertainty, while a cluster-based selection of 3-4 Global Gridded Crop Models effectively represents the full ensemble. The contribution of individual Global Gridded Crop Models to overall uncertainty varies depending on region and crop type, emphasizing the importance of considering the impact of specific models when selecting models for local-scale applications. Our results emphasize the importance of model composition and ensemble size in identifying the primary sources of uncertainty in crop yield projections, offering valuable guidance for optimizing ensemble configurations in climate-crop modeling studies tailored to specific applications.

Agriculture↗
NASA NTRS2019

Parameterization-Induced Uncertainties and Impacts of Crop Management Harmonization in a Global Gridded Crop Model Ensemble

Global gridded crop models (GGCMs) combine agronomic or plant growth models with gridded spatial input data to estimate spatially explicit crop yields and agricultural externalities at the global scale. Differences in GGCM outputs arise from the use of different biophysical models, setups, and input data. GGCM ensembles are frequently employed to bracket uncertainties in impact studies without investigating the causes of divergence in outputs. This study explores differences in maize yield estimates from five GGCMs based on the public domain field-scale model Environmental Policy Integrated Climate (EPIC) that participate in the AgMIP Global Gridded Crop Model Intercomparison initiative. Albeit using the same crop model, the GGCMs differ in model version, input data, management assumptions, parameterization, and selection of subroutines affecting crop yield estimates via cultivar distributions, soil attributes, and hydrology among others. The analyses reveal inter-annual yield variability and absolute yield levels in the EPIC-based GGCMs to be highly sensitive to soil parameterization and crop management. All GGCMs show an intermediate performance in reproducing reported yields with a higher skill if a static soil profile is assumed or sufficient plant nutrients are supplied. An in-depth comparison of setup domains for two EPIC-based GGCMs shows that GGCM performance and plant stress responses depend substantially on soil parameters and soil process parameterization, i.e. hydrology and nutrient turnover, indicating that these often neglected domains deserve more scrutiny. For agricultural impact assessments, employing a GGCM ensemble with its widely varying assumptions in setups appears the best solution for coping with uncertainties from lack of comprehensive global data on crop management, cultivar distributions and coefficients for agro-environmental processes. However, the underlying assumptions require systematic specifications to cover representative agricultural systems and environmental conditions. Furthermore, the interlinkage of parameter sensitivity from various domains such as soil parameters, nutrient turnover coefficients, and cultivar specifications highlights that global sensitivity analyses and calibration need to be performed in an integrated manner to avoid bias resulting from disregarded core model domains. Finally, relating evaluations of the EPIC-based GGCMs to a wider ensemble based on individual core models shows that structural differences outweigh in general differences in configurations of GGCMs based on the same model, and that the ensemble mean gains higher skill from the inclusion of structurally different GGCMs. Although the members of the wider ensemble herein do not consider crop-soil-management interactions, their sensitivity to nutrient supply indicates that findings for the EPIC-based sub-ensemble will likely become relevant for other GGCMs with the progressing inclusion of such processes.

Folberth, Christian↗
NASA NTRS2024

Assessing Effects of Climate and Technology Uncertainties in Large Natural Resource Allocation Problems

The productivity of the world's natural resources is critically dependent on a variety of highly uncertain factors, which obscure individual investors and governments that seek to make long-term, sometimes irreversible, investments in their exploration and utilization. These dynamic considerations are poorly represented in disaggregated resource models, as incorporating uncertainty into large-dimensional problems presents a challenging computational task. In this paper, we apply the SCEQ algorithm (Cai and Judd, 2023) to solve a large-scale dynamic stochastic global land resource use problem with stochastic crop yields due to adverse climate impacts and limits on further technological progress. For the same model parameters and bounded shocks, the range of land conversion is considerably smaller for the dynamic stochastic model than for deterministic scenario analysis.

numerical methods↗
NASA NTRS2021

Climate Impacts on Global Agriculture Emerge Earlier in New Generation of Climate and Crop Models

Potential climate-related impacts on future crop yield are a major societal concern. Previous projections of the Agricultural Model Intercomparison and Improvement Project’s Global Gridded Crop Model Intercomparison based on the Coupled Model Intercomparison Project Phase 5 identified substantial climate impacts on all major crops, but associated uncertainties were substantial. Here we report new twenty-first-century projections using ensembles of latest-generation crop and climate models. Results suggest markedly more pessimistic yield responses for maize, soybean and rice compared to the original ensemble. Mean end-of-century maize productivity is shifted from +5% to −6% (SSP126) and from +1% to −24% (SSP585)—explained by warmer climate projections and improved crop model sensitivities. In contrast, wheat shows stronger gains (+9% shifted to +18%, SSP585), linked to higher CO 2 concentrations and expanded high-latitude gains. The ‘emergence’ of climate impacts consistently occurs earlier in the new projections—before 2040 for several main producing regions. While future yield estimates remain uncertain, these results suggest that major breadbasket regions will face distinct anthropogenic climatic risks sooner than previously anticipated.

crop model↗
NASA NTRS2016

Regional Disparities in the Beneficial Effects of Rising CO2 Emissions on Crop Water Productivity

Rising atmospheric carbon dioxide concentrations are expected to enhance photosynthesis and reduce crop water use. However, there is high uncertainty about the global implications of these effects for future crop production and agricultural water requirements under climate change. Here we combine results from networks of field experiments and global crop models to present a spatially explicit global perspective on crop water productivity (CWP, the ratio of crop yield to evapotranspiration) for wheat, maize, rice and soybean under elevated carbon dioxide and associated climate change projected for a high-end greenhouse gas emissions scenario. We find carbon dioxide effects increase global CWP by 10[0;47]%-27[7;37]% (median[interquartile range] across the model ensemble) by the 2080s depending on crop types, with particularly large increases in arid regions (by up to 48[25;56]% for rain fed wheat). If realized in the fields, the effects of elevated carbon dioxide could considerably mitigate global yield losses whilst reducing agricultural consumptive water use (4-17%). We identify regional disparities driven by differences in growing conditions across agro-ecosystems that could have implications for increasing food production without compromising water security. Finally, our results demonstrate the need to expand field experiments and encourage greater consistency in modeling the effects of rising carbon dioxide across crop and hydrological modeling communities.

Deryng, Delphine↗
NASA NTRS2022

Impacts of Climate Change on Global Food Trade Networks

Countries' reliance on global food trade networks implies that regionally different climate change impacts on crop yields will be transmitted across borders. This redistribution constitutes a significant challenge for climate adaptation planning and may affect how countries engage in cooperative action. This paper investigates the long-term (2070–2099) potential impacts of climate change on global food trade networks of three key crops: wheat, rice and maize. We propose a simple network model to project how climate change impacts on crop yields may be translated into changes in trade. Combining trade and climate impact data, our analysis proceeds in three steps. First, we use network community detection to analyse how the concentration of global production in present-day trade communities may become disrupted with climate change impacts. Second, we study how countries may change their network position following climate change impacts. Third, we study the total climate-induced change in production plus import within trade communities. Results indicate that the stability of food trade network structures compared to today differs between crops, and that countries' maize trade is least stable under climate change impacts. Results also project that threats to global food security may depend on production change in a few major global producers, and whether trade communities can balance production and import loss in some vulnerable countries. Overall, our model contributes a baseline analysis of cross-border climate impacts on food trade networks.

climate change↗
NASA NTRS1985

Remote Sensing of Earth Terrain

The objective of this research is to develop theoretical models that are useful and practical in the remote sensing of the Earth environment including the Earth terrain, the lower and the upper atmospheres. Various models applicable to the microwave remote sensing of vegetation, snow-ice, and atmospheric precipitation have been developed. Such studies shall be extended to the higher frequency range to unify the optical band and the microwave theoretical foundations. The study, which had an emphasis on vegetation canopy to include all terrain media, and the whole Earth environment will be extended. A data base will be developed to generate scene radiation characteristics which will benefit the studies of global inhabitability, meteorological applications, and crop yield.

Kong, J. A.↗
NASA NTRS2019

Global Crop Production: Adaptation to Temperature Increase Is Possible by Maintaining the Current Growing Periods

Increasing temperature trends are expected to impact yields of major field crops by affecting various plant processes, such as phenology and growth. However, future projections, especially at the global scale, do not consider any agronomic adaptation in farming practices. We use an ensemble of seven Global Gridded Crop Models (GGCMs) contributing to the AgMIP-Gridded project to quantify the impacts and adaptation potential of field crops under increasing temperature. We study how uniform warming scenarios up to 6 K affect the productivity and growing period duration of five major crops. The design of the experiment aims at understanding adaptation measures targeted to temperature-driven impacts and therefore leaves out changes in any other climate variable. We find that, without adaptation the dominant effect of temperature increase is to shorten the growing period and to reduce yields and production, consistently across crops and regions. We then test the potential of two agronomic measures to contrast warming-induced yield reduction, assuming that (i) cultivars with adjusted phenology would be used to regain the reference growing period duration; (ii) rainfed systems would be converted to irrigated. Despite substantial uncertainties in model parametrization and little agreement in spatial patterns, at the global aggregation, model results are robust. We find that up to 3 K of temperature increase, production losses could be fully compensated by maintaining the original crop growing period. Irrigation would also compensate production losses, but would not reduce the temperature impacts. Across regions, the model ensemble estimates larger adaptation potentials from unchanged growing periods in continental and temperate regions, than in tropical and arid regions, where also irrigation has respectively little effects and availability.

Irrigation↗
NASA NTRS2012

The Agricultural Model Intercomparison and Improvement Project (AgMIP): Protocols and Pilot Studies

The Agricultural Model Intercomparison and Improvement Project (AgMIP) is a major international effort linking the climate, crop, and economic modeling communities with cutting-edge information technology to produce improved crop and economic models and the next generation of climate impact projections for the agricultural sector. The goals of AgMIP are to improve substantially the characterization of world food security due to climate change and to enhance adaptation capacity in both developing and developed countries. Analyses of the agricultural impacts of climate variability and change require a transdisciplinary effort to consistently link state-of-the-art climate scenarios to crop and economic models. Crop model outputs are aggregated as inputs to regional and global economic models to determine regional vulnerabilities, changes in comparative advantage, price effects, and potential adaptation strategies in the agricultural sector. Climate, Crop Modeling, Economics, and Information Technology Team Protocols are presented to guide coordinated climate, crop modeling, economics, and information technology research activities around the world, along with AgMIP Cross-Cutting Themes that address uncertainty, aggregation and scaling, and the development of Representative Agricultural Pathways (RAPs) to enable testing of climate change adaptations in the context of other regional and global trends. The organization of research activities by geographic region and specific crops is described, along with project milestones. Pilot results demonstrate AgMIP's role in assessing climate impacts with explicit representation of uncertainties in climate scenarios and simulations using crop and economic models. An intercomparison of wheat model simulations near Obregón, Mexico reveals inter-model differences in yield sensitivity to [CO2] with model uncertainty holding approximately steady as concentrations rise, while uncertainty related to choice of crop model increases with rising temperatures. Wheat model simulations with midcentury climate scenarios project a slight decline in absolute yields that is more sensitive to selection of crop model than to global climate model, emissions scenario, or climate scenario downscaling method. A comparison of regional and national-scale economic simulations finds a large sensitivity of projected yield changes to the simulations' resolved scales. Finally, a global economic model intercomparison example demonstrates that improvements in the understanding of agriculture futures arise from integration of the range of uncertainty in crop, climate, and economic modeling results in multi-model assessments.

Rosenzweig, C.↗
NASA NTRS2014

Uncertainties in Predicting Rice Yield by Current Crop Models Under a Wide Range of Climatic Conditions

Predicting rice (Oryza sativa) productivity under future climates is important for global food security. Ecophysiological crop models in combination with climate model outputs are commonly used in yield prediction, but uncertainties associated with crop models remain largely unquantified. We evaluated 13 rice models against multi-year experimental yield data at four sites with diverse climatic conditions in Asia and examined whether different modeling approaches on major physiological processes attribute to the uncertainties of prediction to field measured yields and to the uncertainties of sensitivity to changes in temperature and CO2 concentration [CO2]. We also examined whether a use of an ensemble of crop models can reduce the uncertainties. Individual models did not consistently reproduce both experimental and regional yields well, and uncertainty was larger at the warmest and coolest sites. The variation in yield projections was larger among crop models than variation resulting from 16 global climate model-based scenarios. However, the mean of predictions of all crop models reproduced experimental data, with an uncertainty of less than 10 percent of measured yields. Using an ensemble of eight models calibrated only for phenology or five models calibrated in detail resulted in the uncertainty equivalent to that of the measured yield in well-controlled agronomic field experiments. Sensitivity analysis indicates the necessity to improve the accuracy in predicting both biomass and harvest index in response to increasing [CO2] and temperature.

crop-model ensembles↗
NASA NTRS2020

Modeling Uncertainty in Large Natural Resource Allocation Problems

The productivity of the world's natural resources is critically dependent on a variety of highly uncertain factors, which obscure individual investors and governments that seek to make long-term, sometimes irreversible investments in their exploration and utilization. These dynamic considerations are poorly represented in disaggregated resource models, as incorporating uncertainty into large-dimensional problems presents a challenging computational task. This study introduces a novel numerical method to solve large-scale dynamic stochastic natural resource allocation problems that cannot be addressed by conventional methods. The method is illustrated with an application focusing on the allocation of global land resource use under stochastic crop yields due to adverse climate impacts and limits on further technological progress. For the same model parameters, the range of land conversion is considerably smaller for the dynamic stochastic model as compared to deterministic scenario analysis. The scenario analysis can thus significantly overstate the magnitude of expected land conversion under uncertain crop yields.

Cai, Yongyang↗
NASA NTRS2017

The Uncertainty of Crop Yield Projections Is Reduced by Improved Temperature Response Functions

Increasing the accuracy of crop productivity estimates is a key element in planning adaptation strategies to ensure global food security under climate change. Process-based crop models are effective means to project climate impact on crop yield, but have large uncertainty in yield simulations. Here, we show that variations in the mathematical functions currently used to simulate temperature responses of physiological processes in 29 wheat models account for is greater than 50% of uncertainty in simulated grain yields for mean growing season temperatures from 14 C to 33 C. We derived a set of new temperature response functions that when substituted in four wheat models reduced the error in grain yield simulations across seven global sites with different temperature regimes by 19% to 50% (42% average). We anticipate the improved temperature responses to be a key step to improve modelling of crops under rising temperature and climate change, leading to higher skill of crop yield projections.

Wang, Enli↗
NASA NTRSDate not supplied

The Added Value of SMAP Soil Moisture in Crop Yield Forecasting Over Argentina

Argentina is one of the major producers and exporter of soybeans, corn, and wheat to the world market; therefore, the accurate and timely forecasting of those crops yield is crucial to national crop management and global food security. Previous studies have mainly focused on developing forecasting models for a specific crop type and location using a single source of data (e.g., vegetation indices), thus providing little insight into the forecasting models' performance on different crop types and regions. Besides, these models are based on traditional statistical regression algorithms, while more advanced machine learning approaches have not been explored. This study investigated the estimation of crop yields of three major crops (corn, soybean, and winter wheat) using Multiple Linear Regression (MLR) and Support Vector Machine (SVM), over major growing provinces in Argentina. Our models were trained and evaluated on data from 2015 to 2020, where three remote sensing products (Normalized difference vegetation index (NDVI), SMAP soil moisture, and MODIS evapotranspiration) were used as predictors. Our results indicated that accurate crop yield forecasts using the developed regression models could be made one to two months before harvest. The MLR and SVM model performance varied among different crop types, where soybean and corn exhibited better predictability compare to the wheat. In most cases, the SVM outperformed the multiple linear regression model due to its ability to capture the nonlinear and complex features of the crop-production process. The forecasted model that combines data from multiple sources outperformed single-source satellite data. The highest accuracy was obtained when the three data sources were all considered in the model development. Results also indicated that the inclusion of SMAP soil moisture improved crop yield forecasting in most provinces, and the most significant improvements occurred in the drier region.

Nazmus Shams Sazib↗
NASA NTRS2021

Future Climate Change Significantly Alters Interannual Wheat Yield Variability Over Half of Harvested Areas

Climate change affects the spatial and temporal distribution of crop yields, which can critically impair food security across scales. A number of previous studies have assessed the impact of climate change on mean crop yield and future food availability, but much less is known about potential future changes in interannual yield variability. Here, we evaluate future changes in relative interannual global wheat yield variability (the coefficient of variation (CV)) at 0.25° spatial resolution for two representative concentration pathways (RCP4.5 and RCP8.5). A multi-model ensemble of crop model emulators based on global process-based models is used to evaluate responses to changes in temperature, precipitation, and CO2. The results indicate that over 60% of harvested areas could experience significant changes in interannual yield variability under a high-emission scenario by the end of the 21st century (2066–2095). About 31% and 44% of harvested areas are projected to undergo significant reductions of relative yield variability under RCP4.5 and RCP8.5, respectively. In turn, wheat yield is projected to become more unstable across 23% (RCP4.5) and 18% (RCP8.5) of global harvested areas—mostly in hot or low fertilizer input regions, including some of the major breadbasket countries. The major driver of increasing yield CV change is the increase in yield standard deviation, whereas declining yield CV is mostly caused by stronger increases in mean yield than in the standard deviation. Changes in temperature are the dominant cause of change in wheat yield CVs, having a greater influence than changes in precipitation in 53% and 72% of global harvested areas by the end of the century under RCP4.5 and RCP8.5, respectively. This research highlights the potential challenges posed by increased yield variability and the need for tailored regional adaptation strategies.

Climate change↗
NASA NTRS2020

Feeding Ten Billion People Is Possible Within Four Terrestrial Planetary Boundaries

Global agriculture puts heavy pressure on planetary boundaries, posing the challenge to achieve future food security without compromising Earth system resilience. On the basis of process-detailed, spatially explicit representation of four interlinked planetary boundaries (biosphere integrity, land-system change, freshwater use, nitrogen flows) and agricultural systems in an internally consistent model framework, we here show that almost half of current global food production depends on planetary boundary transgressions. Hotspot regions, mainly in Asia, even face simultaneous transgression of multiple underlying local boundaries. If these boundaries were strictly respected, the present food system could provide a balanced diet (2,355 kcal per capita per day) for 3.4 billion people only. However, as we also demonstrate, transformation towards more sustainable production and consumption patterns could support 10.2 billion people within the planetary boundaries analysed. Key prerequisites are spatially redistributed cropland, improved water–nutrient management, food waste reduction and dietary changes. Adoption of the Sustainable Development Goals by all nations in 2015 is the first ever commitment to a world development path that safeguards the stability of the Earth system as a prerequisite for meeting universal human standards1. The longstanding challenge of achieving food security through sustainable agriculture is particularly acute in this context as world agriculture is a leading cause for the current transgressions of multiple planetary boundaries (PBs) globally and regionally2–5. The PB framework is a comprehensive scientific attempt to synoptically define our planet’s biogeophysical limits to anthropogenic interference. It suggests bounds to nine interacting processes that together delineate a Holocene-like Earth system state. The Holocene is chosen as the reference state as it is the only period known to provide a safe operating space for a world population of several billion people, and according to a precautionary principle, the PBs are set in sufficient distance from processes that may critically undermine Earth system resilience and global sustainability. A challenging question, thus, is whether human development goals such as food security can be met while maintaining multiple PBs along with their subglobal manifestations. Further PB transgressions could jeopardize the chances of providing sufficient food for a world population projected to be wealthier and reach >9 billion by 2050. This conundrum portrays a tradeoff between Earth’s biophysical carrying capacity and humankind’s rising food demand, calling in response for radical rethinking of food production and consumption patterns6–9. Yield gap closures, avoidance of excessive input use, shifts towards less resource-demanding diets, food waste reductions and efficient international trade are crucial options for sustainably increasing the food supply10–15. For example, enhancing water-use efficiency on irrigated and rain-fed farms can triple or quadruple crop yields in low-performing systems, suggesting possible global gains of >20% (ref. 16). Even higher gains appear feasible through globally optimized configurations of the land-use pattern17, and cutting food losses by half could generate food for another billion people18. Thus, collective large-scale implementation of such options could sustain food for a further growing world population19. Yet achieving this within a safe operating space as defined by PBs requires not only a halt to but actually a reversal of existing PB transgressions. Previous studies suggest that such a reconciliation might be possible, but these were based on aggregate representations of PBs (not accounting for the spatial patterns of limits, transgressions and interactions) or considered only one boundary in isolation17,20–23. Here, we systematically quantify to what extent current food production depends on local to global transgressions of the PBs for biosphere integrity, land-system change, freshwater use and nitrogen (N) flows, along with the potential of a range of solutions to avoid these transgressions and still increase food supply (Table 1). To this end, we configured an internally consistent process-based model of the terrestrial biosphere including agriculture (LPJmL) with multiple spatially distributed PBs and their interactions. LPJmL is among the longest-established and best-evaluated biosphere models, showing robust performance regarding simulation of, for example, carbon, water and crop yield dynamics (Supplementary Figs. 1 and 2 and Supplementary Table 1; see ref. 24 for a comprehensive benchmarking and Supplementary Methods for more detail on model evaluations). In principle following established definitions4, we refine the computation of some PBs with respect to their regional patterns and interactions (Methods), providing globally gridded precautionary limits to human interference with the Earth system at a level of great detail. In particular, we account for the evidence that many PBs need to be represented spatially explicitly4 to cover their

Gerten, Dieter↗