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A review of recent research on improvement of physical parameterizations in the GLA GCM

A systematic assessment of the effect of a series of improvements in physical parameterizations of the Goddard Laboratory for Atmospheres (GLA) general circulation model (GCM) are summarized. The implementation of the Simple Biosphere Model (SiB) in the GCM is followed by a comparison of SiB GCM simulations with that of the earlier slab soil hydrology GCM (SSH-GCM) simulations. In the Sahelian context, the biogeophysical component of desertification was analyzed for SiB-GCM simulations. Cumulus parameterization is found to be the primary determinant of the organization of the simulated tropical rainfall of the GLA GCM using Arakawa-Schubert cumulus parameterization. A comparison of model simulations with station data revealed excessive shortwave radiation accompanied by excessive drying and heating to the land. The perpetual July simulations with and without interactive soil moisture shows that 30 to 40 day oscillations may be a natural mode of the simulated earth atmosphere system.

Sud, Y. C.↗

Moderate Resolution Imaging Spectrometer (MODIS) design evolution and associated development and verification of data product efforts

The Moderate Resolution Imaging Spectrometer (MODIS) is a key observing facility to be flown on the Earth Observing System (EOS). The facility is composed of two instruments called MODIS-N (nadir) and MODIS-T (tilt). The MODIS-N is being built under contract to NASA by the Santa Barbara Research Center. The MODIS-T is being fabricated by the Engineering Directorate at the Goddard Space Flight Center. The MODIS Science Team has defined nearly 40 biogeophysical data products for studies of the ocean and land surface and properties of the atmosphere including clouds that can be expected to be produced from the MODIS instruments shortly after the launch of EOS. The ocean, land, atmosphere, and calibration groups of the MODIS Science Team are now proceeding to plan and implement the operations and facilities involving the analysis of data from existing spaceborne, airborne, and in-situ sensors required to develop and validate the algorithms that will produce the geophysical data products. These algorithm development and validation efforts will be accomplished wherever possible within the context of existing or planned national and international experiments or programs such as those in the World Climate Research Program.

Salomonson, Vincent V.↗

Global distribution of photosynthetically active radiation as observed from satellites

In this study the feasibility to derive photosynthetically active radiation (PAR) on a global scale is demonstrated. In the past, information on PAR was obtained from local ground measurements in the 0.4-0.7-micron spectral interval. In the absence of such measurements, PAR was estimated from measured total solar irradiance, using empirical 'conversion factors'. It is demonstrated that this important biogeophysical parameter can now be derived from satellite observations. The inference model is implemented with global satellite data that are available from the International Satellite Cloud Climatology Project to produce for the first time global fields of PAR and corresponding 'conversion factors'.

Pinker, R. T.↗

Geographic information system for fusion and analysis of high-resolution remote sensing and ground truth data

We seek to combine high-resolution remotely sensed data with models and ground truth measurements, in the context of a Geographical Information System, integrated with specialized image processing software. We will use this integrated system to analyze the data from two Case Studies, one at a bore Al forest site, the other a tropical forest site. We will assess the information content of the different components of the data, determine the optimum data combinations to study biogeophysical changes in the forest, assess the best way to visualize the results, and validate the models for the forest response to different radar wavelengths/polarizations. During the 1990's, unprecedented amounts of high-resolution images from space of the Earth's surface will become available to the applications scientist from the LANDSAT/TM series, European and Japanese ERS-1 satellites, RADARSAT and SIR-C missions. When the Earth Observation Systems (EOS) program is operational, the amount of data available for a particular site can only increase. The interdisciplinary scientist, seeking to use data from various sensors to study his site of interest, may be faced with massive difficulties in manipulating such large data sets, assessing their information content, determining the optimum combinations of data to study a particular parameter, visualizing his results and validating his model of the surface. The techniques to deal with these problems are also needed to support the analysis of data from NASA's current program of Multi-sensor Airborne Campaigns, which will also generate large volumes of data. In the Case Studies outlined in this proposal, we will have somewhat unique data sets. For the Bonanza Creek Experimental Forest (Case I) calibrated DC-8 SAR data and extensive ground truth measurement are already at our disposal. The data set shows documented evidence to temporal change. The Belize Forest Experiment (Case II) will produce calibrated DC-8 SAR and AVIRIS data, together with extensive measurements on the tropical rain forest itself. The extreme range of these sites, one an Arctic forest, the other a tropical rain forest, has been deliberately chosen to find common problems which can lead to generalized observations and unique problems with data which raise issues for the EOS System.

Freeman, Anthony↗

Monitoring issues from a modeling perspective

Recognition that earth's climate and biogeophysical conditions are likely changing due to human activities has led to a heightened awareness of the need for improved long-term global monitoring. The present long-term measurement efforts tend to be spotty in space, inadequately calibrated in time, and internally inconsistent with respect to other instruments and measured quantities. In some cases, such as most of the biosphere, most chemicals, and much of the ocean, even a minimal monitoring program is not available. Recently, it has become painfully evident that emerging global change issues demand information and insights that the present global monitoring system simply cannot supply. This is because a monitoring system must provide much more than a statement of change at a given level of statistical confidence. It must describe changes in diverse parts of the entire earth system on regional to global scales. It must be able to provide enough input to allow an integrated physical characterization of the changes that have occurred. Finally, it must allow a separation of the observed changes into their natural and anthropogenic parts. The enormous policy significance of global change virtually guarantees an unprecedented level of scrutiny of the changes in the earth system and why they are happening. These pressures create a number of emerging challenges and opportunities. For example, they will require a growing partnership between the observational programs and the theory/modeling community. Without this partnership, the scientific community will likely fall short in the monitoring effort. The monitoring challenge before us is not to solve the problem now, but rather to set appropriate actions in motion so as to create the required framework for solution. Each individual piece needs to establish its role in the large problem and how the required interactions are to take place. Below, we emphasize some of the needs and opportunities that could and should be addressed through participation by the theoreticians and modelers in the global change monitoring effort.

Mahlman, Jerry D.↗

MODIS. Volume 2: MODIS level 1 geolocation, characterization and calibration algorithm theoretical basis document, version 1

The EOS Moderate Resolution Imaging Spectrometer (MODIS) is being developed by NASA for flight on the Earth Observing System (EOS) series of satellites, the first of which (EOS-AM-1) is scheduled for launch in 1998. This document describes the algorithms and their theoretical basis for the MODIS Level 1B characterization, calibration, and geolocation algorithms which must produce radiometrically, spectrally, and spatially calibrated data with sufficient accuracy so that Global change research programs can detect minute changes in biogeophysical parameters. The document first describes the geolocation algorithm which determines geodetic latitude, longitude, and elevation of each MODIS pixel and the determination of geometric parameters for each observation (satellite zenith angle, satellite azimuth, range to the satellite, solar zenith angle, and solar azimuth). Next, the utilization of the MODIS onboard calibration sources, which consist of the Spectroradiometric Calibration Assembly (SRCA), Solar Diffuser (SD), Solar Diffuser Stability Monitor (SDSM), and the Blackbody (BB), is treated. Characterization of these sources and integration of measurements into the calibration process is described. Finally, the use of external sources, including the Moon, instrumented sites on the Earth (called vicarious calibration), and unsupervised normalization sites having invariant reflectance and emissive properties is treated. Finally, algorithms for generating utility masks needed for scene-based calibration are discussed. Eight appendices are provided, covering instrument design and additional algorithm details.

Barker, John L.↗

Geographic information system for fusion and analysis of high-resolution remote sensing and ground data

We seek to combine high-resolution remotely sensed data with models and ground truth measurements, in the context of a Geographical Information System (GIS), integrated with specialized image processing software. We will use this integrated system to analyze the data from two Case Studies, one at a boreal forest site, the other a tropical forest site. We will assess the information content of the different components of the data, determine the optimum data combinations to study biogeophysical changes in the forest, assess the best way to visualize the results, and validate the models for the forest response to different radar wavelengths/polarizations. During the 1990's, unprecedented amounts of high-resolution images from space of the Earth's surface will become available to the applications scientist from the LANDSAT/TM series, European and Japanese ERS-1 satellites, RADARSAT and SIR-C missions. When the Earth Observation Systems (EOS) program is operational, the amount of data available for a particular site can only increase. The interdisciplinary scientist, seeking to use data from various sensors to study his site of interest, may be faced with massive difficulties in manipulating such large data sets, assessing their information content, determining the optimum combinations of data to study a particular parameter, visualizing his results and validating his model of the surface. The techniques to deal with these problems are also needed to support the analysis of data from NASA's current program of Multi-sensor Airborne Campaigns, which will also generate large volumes of data. In the Case Studies outlined in this proposal, we will have somewhat unique data sets. For the Bonanza Creek Experimental Forest (Case 1) calibrated DC-8 SAR (Synthetic Aperture Radar) data and extensive ground truth measurement are already at our disposal. The data set shows documented evidence to temporal change. The Belize Forest Experiment (Case 2) will produce calibrated DC-8 SAR and AVIRIS data, together with extensive measurements on the tropical rain forest itself. The extreme range of these sites, one an Arctic forest, the other a tropical rain forest, has been deliberately chosen to find common problems which can lead to generalized observations and unique problems with data which raise issues for the EOS System.

Freeman, Anthony↗

Research support of the WETNET Program

This study examines various aspects of the Microwave Vegetation Index (MVI). MVI is a derived signal created by differencing the spectral response of the 37 GHz horizontally and vertically polarized passive microwave signals. The microwave signal employed to derive this index is thought to be primarily influenced by vegetation structure, vegetation growth, standing water, and precipitation. The state of California is the study site for this research. Imagery from the Special Sensor Microwave/Imager (SSM/I) is used for the creation of MVI datasets analyzed in this research. The object of this research is to determine whether MVI corresponds with some quantifiable vegetation parameter (such as vegetation density) or whether the index is more affected by known biogeophysical parameters such antecedent precipitation. A secondary question associated with the above is whether the vegetation attributes that MVI is employed to determine can be more easily and accurately evaluated by other remote sensing means. An important associated question to be addressed in the study is the effect of different multi-temporal composting techniques on the derived MVI dataset. This work advances our understanding of the fundamental nature of MVI by studying vegetation as a mixture of structural types, such as forest and grassland. The study further advances our understanding by creating multitemporal precipitation datasets to compare the affects of precipitation upon MVI. This work will help to lay the groundwork for the use of passive microwave spectral information either as an adjunct to visible and near infrared imagery in areas where that is feasible or for the use of passive microwave alone in areas of moderate cloud coverage. In this research, an MVI dataset, spanning the period February 15, 1989 through April 25, 1990, has been created using National Aeronautic and Space Administration (NASA) supplied brightness temperature data. Information from the DMSP satellite 37 GHz wavelength SSM/I sensor in both horizontal and vertical polarization has been processed using the MVI algorithm. In conjunction with the MVI algorithm a multitemporal compositing technique was used to create datasets that correspond to 14 day periods. In this technical report, Section Two contains background information on the State of California and the three MVI study sites. Section Three describes the methods used to create the MVI and independent variables datasets. Section Four presents the results of the experiment. Section Five summarizes and concludes the work.

Estes, John E.↗

Predicting Decade-to-Century Climate Change: Prospects for Improving Models

Recent research has led to a greatly increased understanding of the uncertainties in today's climate models. In attempting to predict the climate of the 21st century, we must confront not only computer limitations on the affordable resolution of global models, but also a lack of physical realism in attempting to model key processes. Until we are able to incorporate adequate treatments of critical elements of the entire biogeophysical climate system, our models will remain subject to these uncertainties, and our scenarios of future climate change, both anthropogenic and natural, will not fully meet the requirements of either policymakers or the public. The areas of most-needed model improvements are thought to include air-sea exchanges, land surface processes, ice and snow physics, hydrologic cycle elements, and especially the role of aerosols and cloud-radiation interactions. Of these areas, cloud-radiation interactions are known to be responsible for much of the inter-model differences in sensitivity to greenhouse gases. Recently, we have diagnostically evaluated several current and proposed model cloud-radiation treatments against extensive field observations. Satellite remote sensing provides an indispensable component of the observational resources. Cloud-radiation parameterizations display a strong sensitivity to vertical resolution, and we find that vertical resolutions typically used in global models are far from convergence. We also find that newly developed advanced parameterization schemes with explicit cloud water budgets and interactive cloud radiative properties are potentially capable of matching observational data closely. However, it is difficult to evaluate the realism of model-produced fields of cloud extinction, cloud emittance, cloud liquid water content and effective cloud droplet radius until high-quality measurements of these quantities become more widely available. Thus, further progress will require a combination of theoretical and modeling research, together with intensified emphasis on both in situ and space-based remote sensing observations.

Somerville, Richard C. J.↗

Using Multi-Angle Imaging SpectroRadiometer (MISR) bidirectional reflectances for land surface studies

MISR imagery enables new methods for cloud screening and retrieval of aerosol properties over a wide range of surface types, and these data are used to compensate for atmospheric effects in the surface retrievals. The derived surface angular signatures are governed, at least in part, by macroscopic texture at the subpixel scale. Such information complements spectral data in distinguishing different types of surface cover, retrieving land surface hemispherical reflectance,and determining biogeophysical properties such as leaf area index and fractional absorbed photosynthetically active radiation. Regional and global MISR data products will be presented to illustrate the capabilities of the instrument andassociated retrieval methodologies.

MISR bidirectional surface studies spectr↗

MISR activities at SAFARI 2000

SAFARI 2000 is an international regional science initiative being developed for Southern Africa to explore, study and address linkages between land-atmosphere processes and the relationship of biogenic, pyrogenic or anthropogenic emissions and the consequences of their deposition to the functioning of the biogeophysical and biogeochemical systems of southern Africa.

MISR AIRMISR SAFARI 2000 southern Africa↗

Land Covering Classifications of Boreas Modeling Grid Using AIRSAR Images

Mapping forest types in the boreal ecosystem in an integrated part of any modeling excercise of biogeophysical processes characterizing the interaction of forest with the atmosphere. In this paper, we report the results of the land cover classification of the SAR data acquired during the BOREAS (BOReal Ecosystem Atmospheric Study) intensive field campaigns over the modeling sub-grid of the southern study area in Saskatchewan , Canada. A Bayesian-maximum-a-posteriori classifier has been applied on the NASA/JPL AIRSAR images covering the region during the peak of the growing season in July, 1994.

Atmospheric Study↗

Can MODIS Data Calibrate and Validate Coastal Sediment Transport Models? Rapid Prototyping Using 250 m Data and the ECOMSED Model for Lake Pontchartrain, LA USA

Field measurements from small boats and sparse arrays of instrumented buoys often do not provide sufficient data to capture the dynamic nature of biogeophysical parameters in may coastal aquatic environments. Several investigators have shown the MODIS 250 m images can provide daily synoptic views of suspended sediment concentration in coastal waters to determine sediment transport and fate. However, the use of MODIS for coastal environments can be limited due to a lack of cloud-free images. Sediment transport models are not constrained by sky conditions but often suffer from a lack of in situ observations for model calibration or validation. We demonstrate here the utility of MODIS 250 m to calibrate (set model parameters), validate output, and set or reset initial conditions of a hydrodynamic and sediment transport model (ECOMSED) developed for Lake Pontchartrain, LA USA. We present our approach in the context of how to quickly assess of 'prototype' an application of NASA data to support environmental managers and decision makers. The combination of daily MODIS imagery and model simulations offer a more robust monitoring and prediction system of suspended sediments than available from either system alone.

Miller, Richard L.↗

An EOF Iteration Approach for Obtaining Homogeneous Radiative Fluxes from Satellites Observations

Conventional observations of climate parameters are sparse in space and/or in time and the representativeness of such information needs to be optimized. Observations from satellites provide improved spatial coverage than point observations however they pose new challenges for obtaining homogeneous coverage. Surface radiative fluxes, the forcing functions of the hydrologic cycle and biogeophysical processes, are now becoming available from global scale satellite observations. They are derived from independent satellite platforms and sensors that differ in temporal and spatial resolution and in the size of the footprint from which information is derived. Data gaps, degraded spatial resolution near boundaries of geostationary satellites, and different viewing geometries in areas of satellite overlap, could result in biased estimates of radiative fluxes. In this study, discussed will be issues related to the sources of inhomogeneity in surface radiative fluxes as derived from satellites; development of an approach to obtain homogeneous data sets; and application of the methodology to the widely used International Satellite Cloud Climatology Project (ISCCP) data that currently serve as a source of information for deriving estimates of surface and top of the atmosphere radiative fluxes. Introduced is an Empirical Orthogonal Function (EOF) iteration scheme for homogenizing the fluxes. The scheme is evaluated in several ways including comparison of the inferred radiative fluxes against ground observations, both before and after the EOF approach is applied. On the average, the latter reduces the rms error by about 2-3 W/m2.

Zhang, Banglin↗

Comparison Between NPP-VIIRS Aerosol Data Products and the MODIS AQUA Deep Blue Collection 6 Dataset Over Land

Aerosols are small particles suspended in the atmosphere and have a variety of natural and man-made sources. Knowledge of aerosol optical depth (AOD), which is a measure of the amount of aerosol in the atmosphere, and its change over time, is important for multiple reasons. These include climate change, air quality (pollution) monitoring, monitoring hazards such as dust storms and volcanic ash, monitoring smoke from biomass burning, determining potential energy yields from solar plants, determining visibility at sea, estimating fertilization of oceans and rainforests by transported mineral dust, understanding changes in weather brought upon by the interaction of aerosols and clouds, and more. The Suomi-NPP satellite was launched late in 2011. The Visible Infrared Imaging Radiometer Suite (VIIRS) aboard Suomi-NPP is being used, among other things, to determine AOD. This study compares the VIIRS dataset to ground-based measurements of AOD, along with a state-of-the-art satellite AOD dataset (the new version of the Moderate Resolution Imaging Spectrometer Deep Blue algorithm) to assess its reliability. The Suomi-NPP satellite was launched late in 2011, carrying several instruments designed to continue the biogeophysical data records of current and previous satellite sensors. The Visible Infrared Imaging Radiometer Suite (VIIRS) aboard Suomi-NPP is being used, among other things, to determine aerosol optical depth (AOD), and related activities since launch have been focused towards validating and understanding this new dataset through comparisons with other satellite and ground-based products. The operational VIIRS AOD product is compared over land with AOD derived from Moderate Resolution Imaging Spectrometer (MODIS) observations using the Deep Blue (DB) algorithm from the forthcoming Collection 6 of MODIS data

Sayer, Andrew M.↗

Modeling the Distribution and Type of High-Latitude Natural Wetlands for Methane Studies

High latitude (>50N) natural wetlands emit a substantial amount of methane to the atmosphere, and are located in a region of amplified warming. Northern hemisphere high latitudes are characterized by cold climates, extensive permafrost, poor drainage, short growing seasons, and slow decay rates. Under these conditions, organic carbon accumulates in the soil, sequestering CO2 from the atmosphere. Methanogens produce methane from this carbon reservoir, converting stored carbon into a powerful greenhouse gas. Methane emission from wetland ecosystems depends on vegetation type, climate characteristics (e.g, precipitation amount and seasonality, temperature, snow cover, etc.), and geophysical variables (e.g., permafrost, soil type, and landscape slope). To understand how wetland methane dynamics in this critical region will respond to climate change, we have to first understand how wetlands themselves will change and therefore, what the primary controllers of wetland distribution and type are. Understanding these relationships permits data-anchored, physically-based modeling of wetland distribution and type in other climate scenarios, such as paleoclimates or future climates, a necessary first step toward modeling wetland methane emissions in these scenarios. We investigate techniques and datasets for predicting the distribution and type of high latitude (>50N) natural wetlands from a suite of geophysical and climate predictors. Hierarchical clustering is used to derive an empirical methane-centric wetland model. The model is applied in a multistep process first to predict the distribution of wetlands from relevant geophysical parameters, and then, given the predicted wetland distribution, to classify the wetlands into methane-relevant types using an expanded suite of climate and biogeophysical variables. As the optimum set of predictor variables is not known a priori, the model is applied iteratively, and each simulation is evaluated with respect to observed high-latitude wetlands.

Romanski, Joy↗

Thirty-Six Combined Years of MODIS Geolocation Trending

Two Moderate Resolution Imaging Spectroradiometer (MODIS) sensors have been in operations for more than 19 and 17 years (thus 36 combined years) as part of NASA's Earth Observing System (EOS) on the Terra platform that was launched in December 1999 and on the Aqua platform that was launched in May 2002, respectively. Accurate geolocation is a critical element needed for accurate retrieval of global biogeophysical parameters. In this paper, we describe the latest trends in the continuously improved MODIS geolocation accuracy in Collection-5 (C5), C6 and C6.1 re-processing and forward-processing data streams. We improved geolocation accuracy in the re-processed data and corrected for geolocation biases found in forward-processed data, including those caused by operations such as the stop-go-stop status of the Advanced Microwave Scanning Radiometer for EOS (AMSR-E) instrument on the Aqua platform. We discuss scan-toscan underlaps near nadir over the equator regions that was discovered in checking the non-underlapping requirement in the Visible Infrared Imaging Radiometer Suite (VIIRS) based on trending parameters from the actual Suomi National Polar-orbiting Partnership (S-NPP) satellite orbit. The underlaps are closely tied to instrument effective focal length that is measured from on-orbit data using a technique we recently developed. We also discuss potential improvements for the upcoming C7 re-processing.

ground control point↗

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↗