Articles | Volume 14, issue 2
https://doi.org/10.5194/esd-14-433-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-14-433-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
17 Apr 2023
Research article |
| 17 Apr 2023
| 17 Apr 2023
Emergent constraints for the climate system as effective parameters of bulk differential equations
UK Centre for Ecology and Hydrology, Benson Lane, Wallingford, Oxfordshire, OX10 8BB, UK
Peter M. Cox
Department of Mathematics and Statistics, Faculty of Environment, Science and Economy, University of Exeter, Exeter, EX4 4QF, UK
Global Systems Institute, Faculty of Environment, Science and Economy, University of Exeter, Exeter, EX4 4QE, UK
Mark S. Williamson
Department of Mathematics and Statistics, Faculty of Environment, Science and Economy, University of Exeter, Exeter, EX4 4QF, UK
Global Systems Institute, Faculty of Environment, Science and Economy, University of Exeter, Exeter, EX4 4QE, UK
Joseph J. Clarke
Department of Mathematics and Statistics, Faculty of Environment, Science and Economy, University of Exeter, Exeter, EX4 4QF, UK
Paul D. L. Ritchie
Department of Mathematics and Statistics, Faculty of Environment, Science and Economy, University of Exeter, Exeter, EX4 4QF, UK
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Agriculture and land use are major sources and sinks of greenhouse gases, yet how these emissions feed back through the climate to reshape ecosystems is rarely traced end-to-end. We built a coupled modelling framework that follows this link from land-management decisions to emissions, to the resulting climate change, and back to the land. It reproduces observed emissions, concentrations and climate, and shows that careful land management could slow global warming by a few tenths of a degree.
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Understanding carbon allocation among land-surface components in a changing climate is important, but it remains poorly understood. As a surrogate for missing knowledge and related equations, optimal allocation hypotheses are proposed. Makela et al. (2008) propose foliage nitrogen adjusted to maximise gross primary productivity. We add to that framework models of photosynthesis and respiration, creating an optimal structure that responds to different near-surface meteorological conditions.
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We use artificial intelligence to learn simple equations from historical climate data that describe how North Atlantic ocean temperature, air pressure and rainfall vary and influence each other over decades. Analysing the model's behaviour and equation terms, we find rainfall strongly feeds back on both the ocean and the atmosphere. These interactions are well captured by the models and allow rainfall to be predicted over the ocean, and nearby regions such as Europe over coming decades.
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Agriculture and land use are major sources and sinks of greenhouse gases, yet how these emissions feed back through the climate to reshape ecosystems is rarely traced end-to-end. We built a coupled modelling framework that follows this link from land-management decisions to emissions, to the resulting climate change, and back to the land. It reproduces observed emissions, concentrations and climate, and shows that careful land management could slow global warming by a few tenths of a degree.
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EGUsphere, https://doi.org/10.5194/egusphere-2026-5606, https://doi.org/10.5194/egusphere-2026-5606, 2026
This preprint is open for discussion and under review for Earth System Dynamics (ESD).
Short summary
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Future tipping of key parts of the Earth system, driven by human-induced climate change, poses serious risks to society. These concerns have spurred the development of Early Warning Systems (EWSs) that use data to show how close we are to tipping. However, existing EWSs are often generic statistical forms. We first review current EWS methods, then present a broad set of hypotheses that may help improve them. We argue strongly for process knowledge to guide more refined EWS forms.
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EGUsphere, https://doi.org/10.5194/egusphere-2026-4392, https://doi.org/10.5194/egusphere-2026-4392, 2026
Short summary
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Understanding carbon allocation among land-surface components in a changing climate is important, but it remains poorly understood. As a surrogate for missing knowledge and related equations, optimal allocation hypotheses are proposed. Makela et al. (2008) propose foliage nitrogen adjusted to maximise gross primary productivity. We add to that framework models of photosynthesis and respiration, creating an optimal structure that responds to different near-surface meteorological conditions.
Andrew J. Nicoll, Hannah M. Christensen, Chris Huntingford, and Doug Smith
Earth Syst. Dynam., 17, 1061–1079, https://doi.org/10.5194/esd-17-1061-2026, https://doi.org/10.5194/esd-17-1061-2026, 2026
Short summary
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We use artificial intelligence to learn simple equations from historical climate data that describe how North Atlantic ocean temperature, air pressure and rainfall vary and influence each other over decades. Analysing the model's behaviour and equation terms, we find rainfall strongly feeds back on both the ocean and the atmosphere. These interactions are well captured by the models and allow rainfall to be predicted over the ocean, and nearby regions such as Europe over coming decades.
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Short summary
Short summary
The risk of climate change triggering tipping points is a concern. While Earth System Models (ESMs) predict these points, their timing often varies. Equations of nonlinear dynamical systems can model tipping, hysteresis, and inertia, enabling comparison with ESMs. We propose a method to map tipping timing estimates onto a dynamical system that simulates a full hysteresis loop. We focus on solutions to the equation under overshoot forcing in global temperature and different inertia levels.
Patric J. L. Boardman, Joseph Clarke, Peter M. Cox, Chris Huntingford, Chris D. Jones, and Mark S. Williamson
Earth Syst. Dynam., 17, 829–841, https://doi.org/10.5194/esd-17-829-2026, https://doi.org/10.5194/esd-17-829-2026, 2026
Short summary
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Climate sensitivity quantifies how much Earth warms for a given radiative forcing, and is often described by the Transient Climate Response (TCR) value. Although the Intergovernmental Panel on Climate Change (IPCC) estimates the most likely TCR to be 1.8 K, some models predict values >2.4 K. Record warmth in 2023–2024 raises questions as to whether the TCR may be larger than previously suggested. Using up-to-date data, we estimate the TCR to be ~1.8 K. We also show that future warming falls within the low–mid model range, making the 2°C Paris target still feasible.
Isobel M. Parry, Paul D. L. Ritchie, Olivier Boucher, Peter M. Cox, James M. Haywood, Ulrike Niemeier, Roland Séférian, Simone Tilmes, and Daniele Visioni
Earth Syst. Dynam., 17, 387–414, https://doi.org/10.5194/esd-17-387-2026, https://doi.org/10.5194/esd-17-387-2026, 2026
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Contrary to some expectations, results from the latest Earth System Models suggest that Solar Radiation Geoengineering could protect the Amazon rainforest from climate-driven dieback. Under Stratospheric Aerosol Injection, carbon storage in Amazonia was projected to increase by a mean of 10.8 % relative to a high CO2 emissions scenario, and even by 8.6% compared to a more conventional medium CO2 emissions scenario.
Joseph Clarke, Chris Huntingford, Paul D. L. Ritchie, Rebecca Varney, Mark S. Williamson, and Peter Cox
Earth Syst. Dynam., 16, 2087–2100, https://doi.org/10.5194/esd-16-2087-2025, https://doi.org/10.5194/esd-16-2087-2025, 2025
Short summary
Short summary
An increase in CO2 in the atmosphere warms the climate through the greenhouse effect, but also leads to uptake of CO2 by the land and ocean. However, the warming is also expected to suppress carbon uptake. If this suppression were strong enough, it could overwhelm the uptake of carbon, leading to a runaway feedback loop causing severe global warming. We find it is possible that this runaway could be relevant in complex climate models and even at the end of the last ice age.
Hsi-Kai Chou, Anna B. Harper, Arthur P. K. Argles, Maria Carolina Duran Rojas, Emma W. Littleton, Richard A. Betts, and Peter M. Cox
EGUsphere, https://doi.org/10.5194/egusphere-2025-4536, https://doi.org/10.5194/egusphere-2025-4536, 2025
Short summary
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Global warming and climate change caused by greenhouse gas emissions will have multiple impacts on forest ecosystems. A core part of the strategy to mitigating these impacts is to use afforestation and forestry management to implement large-scale Greenhouse Gas Removal. Here we use the JULES-RED model to evaluate the afforestation under a changing environmental condition. We project that Sitka Forest afforestation could meet the target of GGR once the plantation locations been selected properly.
Paul D. L. Ritchie, Chris Huntingford, and Peter M. Cox
Earth Syst. Dynam., 16, 1523–1526, https://doi.org/10.5194/esd-16-1523-2025, https://doi.org/10.5194/esd-16-1523-2025, 2025
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Climate tipping points are not committed upon crossing critical thresholds in global warming, as is often assumed. Instead, it is possible to temporarily overshoot a threshold without causing tipping, provided the duration of the overshoot is short. In this Idea, we demonstrate that restricting the time over 1.5 °C would considerably reduce tipping point risks.
Kerstin Lux-Gottschalk and Paul D. L. Ritchie
Earth Syst. Dynam., 16, 1153–1168, https://doi.org/10.5194/esd-16-1153-2025, https://doi.org/10.5194/esd-16-1153-2025, 2025
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For tipping points at low levels of global warming, overshoots of the threshold are becoming increasingly likely. Importantly, for some systems, tipping can still be avoided provided the forcing is reversed sufficiently quickly. Conditions for a mitigation window, which would avoid tipping, depend on system uncertainties. We highlight the need to account for uncertainty in the threshold location and other system features when designing climate mitigation strategies that avoid tipping.
Chris Huntingford, Andrew J. Nicoll, Cornelia Klein, and Jawairia A. Ahmad
Earth Syst. Dynam., 16, 475–495, https://doi.org/10.5194/esd-16-475-2025, https://doi.org/10.5194/esd-16-475-2025, 2025
Short summary
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AI is impacting science, providing key data insights, but most algorithms are statistical requiring cautious "out-of-sample" extrapolation. Yet climate research concerns predicting future climatic states. We consider a new method of AI-led equation discovery. Equations offer process interpretation and more robust predictions. We recommend this method for climate analysis, suggesting illustrative application to atmospheric convection, land–atmosphere CO2 flux, and global ocean circulation models.
Camilla Mathison, Eleanor J. Burke, Gregory Munday, Chris D. Jones, Chris J. Smith, Norman J. Steinert, Andy J. Wiltshire, Chris Huntingford, Eszter Kovacs, Laila K. Gohar, Rebecca M. Varney, and Douglas McNeall
Geosci. Model Dev., 18, 1785–1808, https://doi.org/10.5194/gmd-18-1785-2025, https://doi.org/10.5194/gmd-18-1785-2025, 2025
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We present PRIME (Probabilistic Regional Impacts from Model patterns and Emissions), which is designed to take new emissions scenarios and rapidly provide regional impact information. PRIME allows large ensembles to be run on multi-centennial timescales, including the analysis of many important variables for impact assessments. Our evaluation shows that PRIME reproduces the climate response for known scenarios, providing confidence in using PRIME for novel scenarios.
Mark S. Williamson and Timothy M. Lenton
Earth Syst. Dynam., 15, 1483–1508, https://doi.org/10.5194/esd-15-1483-2024, https://doi.org/10.5194/esd-15-1483-2024, 2024
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Colin G. Jones, Fanny Adloff, Ben B. B. Booth, Peter M. Cox, Veronika Eyring, Pierre Friedlingstein, Katja Frieler, Helene T. Hewitt, Hazel A. Jeffery, Sylvie Joussaume, Torben Koenigk, Bryan N. Lawrence, Eleanor O'Rourke, Malcolm J. Roberts, Benjamin M. Sanderson, Roland Séférian, Samuel Somot, Pier Luigi Vidale, Detlef van Vuuren, Mario Acosta, Mats Bentsen, Raffaele Bernardello, Richard Betts, Ed Blockley, Julien Boé, Tom Bracegirdle, Pascale Braconnot, Victor Brovkin, Carlo Buontempo, Francisco Doblas-Reyes, Markus Donat, Italo Epicoco, Pete Falloon, Sandro Fiore, Thomas Frölicher, Neven S. Fučkar, Matthew J. Gidden, Helge F. Goessling, Rune Grand Graversen, Silvio Gualdi, José M. Gutiérrez, Tatiana Ilyina, Daniela Jacob, Chris D. Jones, Martin Juckes, Elizabeth Kendon, Erik Kjellström, Reto Knutti, Jason Lowe, Matthew Mizielinski, Paola Nassisi, Michael Obersteiner, Pierre Regnier, Romain Roehrig, David Salas y Mélia, Carl-Friedrich Schleussner, Michael Schulz, Enrico Scoccimarro, Laurent Terray, Hannes Thiemann, Richard A. Wood, Shuting Yang, and Sönke Zaehle
Earth Syst. Dynam., 15, 1319–1351, https://doi.org/10.5194/esd-15-1319-2024, https://doi.org/10.5194/esd-15-1319-2024, 2024
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We propose a number of priority areas for the international climate research community to address over the coming decade. Advances in these areas will both increase our understanding of past and future Earth system change, including the societal and environmental impacts of this change, and deliver significantly improved scientific support to international climate policy, such as future IPCC assessments and the UNFCCC Global Stocktake.
Vasilis Dakos, Chris A. Boulton, Joshua E. Buxton, Jesse F. Abrams, Beatriz Arellano-Nava, David I. Armstrong McKay, Sebastian Bathiany, Lana Blaschke, Niklas Boers, Daniel Dylewsky, Carlos López-Martínez, Isobel Parry, Paul Ritchie, Bregje van der Bolt, Larissa van der Laan, Els Weinans, and Sonia Kéfi
Earth Syst. Dynam., 15, 1117–1135, https://doi.org/10.5194/esd-15-1117-2024, https://doi.org/10.5194/esd-15-1117-2024, 2024
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Tipping points are abrupt, rapid, and sometimes irreversible changes, and numerous approaches have been proposed to detect them in advance. Such approaches have been termed early warning signals and represent a set of methods for identifying changes in the underlying behaviour of a system across time or space that might indicate an approaching tipping point. Here, we review the literature to explore where, how, and which early warnings have been used in real-world case studies so far.
Mark S. Williamson, Peter M. Cox, Chris Huntingford, and Femke J. M. M. Nijsse
Earth Syst. Dynam., 15, 829–852, https://doi.org/10.5194/esd-15-829-2024, https://doi.org/10.5194/esd-15-829-2024, 2024
Short summary
Short summary
Emergent constraints on equilibrium climate sensitivity (ECS) have generally got statistically weaker in the latest set of state-of-the-art climate models (CMIP6) compared to past sets (CMIP5). We look at why this weakening happened for one particular study (Cox et al, 2018) and attribute it to an assumption made in the theory that when corrected for restores there is a stronger relationship between predictor and ECS.
Rebecca M. Varney, Pierre Friedlingstein, Sarah E. Chadburn, Eleanor J. Burke, and Peter M. Cox
Biogeosciences, 21, 2759–2776, https://doi.org/10.5194/bg-21-2759-2024, https://doi.org/10.5194/bg-21-2759-2024, 2024
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Soil carbon is the largest store of carbon on the land surface of Earth and is known to be particularly sensitive to climate change. Understanding this future response is vital to successfully meeting Paris Agreement targets, which rely heavily on carbon uptake by the land surface. In this study, the individual responses of soil carbon are quantified and compared amongst CMIP6 Earth system models used within the most recent IPCC report, and the role of soils in the land response is highlighted.
Emma L. Robinson, Chris Huntingford, Valyaveetil Shamsudheen Semeena, and James M. Bullock
Earth Syst. Sci. Data, 15, 5371–5401, https://doi.org/10.5194/essd-15-5371-2023, https://doi.org/10.5194/essd-15-5371-2023, 2023
Short summary
Short summary
CHESS-SCAPE is a suite of high-resolution climate projections for the UK to 2080, derived from United Kingdom Climate Projections 2018 (UKCP18), designed to support climate impact modelling. It contains four realisations of four scenarios of future greenhouse gas levels (RCP2.6, 4.5, 6.0 and 8.5), with and without bias correction to historical data. The variables are available at 1 km resolution and a daily time step, with monthly, seasonal and annual means and 20-year mean-monthly time slices.
Rebecca M. Varney, Sarah E. Chadburn, Eleanor J. Burke, Simon Jones, Andy J. Wiltshire, and Peter M. Cox
Biogeosciences, 20, 3767–3790, https://doi.org/10.5194/bg-20-3767-2023, https://doi.org/10.5194/bg-20-3767-2023, 2023
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This study evaluates soil carbon projections during the 21st century in CMIP6 Earth system models. In general, we find a reduced spread of changes in global soil carbon in CMIP6 compared to the previous CMIP5 generation. The reduced CMIP6 spread arises from an emergent relationship between soil carbon changes due to change in plant productivity and soil carbon changes due to changes in turnover time. We show that this relationship is consistent with false priming under transient climate change.
Nina Raoult, Tim Jupp, Ben Booth, and Peter Cox
Earth Syst. Dynam., 14, 723–731, https://doi.org/10.5194/esd-14-723-2023, https://doi.org/10.5194/esd-14-723-2023, 2023
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Climate models are used to predict the impact of climate change. However, poorly constrained parameters used in the physics of the models mean that we simulate a large spread of possible future outcomes. We can use real-world observations to reduce the uncertainty of parameter values, but we do not have observations to reduce the spread of possible future outcomes directly. We present a method for translating the reduction in parameter uncertainty into a reduction in possible model projections.
Paul D. L. Ritchie, Hassan Alkhayuon, Peter M. Cox, and Sebastian Wieczorek
Earth Syst. Dynam., 14, 669–683, https://doi.org/10.5194/esd-14-669-2023, https://doi.org/10.5194/esd-14-669-2023, 2023
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Complex systems can undergo abrupt changes or tipping points when external forcing crosses a critical level and are of increasing concern because of their severe impacts. However, tipping points can also occur when the external forcing changes too quickly without crossing any critical levels, which is very relevant for Earth’s systems and contemporary climate. We give an intuitive explanation of such rate-induced tipping and provide illustrative examples from natural and human systems.
Gang Liu, Shushi Peng, Chris Huntingford, and Yi Xi
Geosci. Model Dev., 16, 1277–1296, https://doi.org/10.5194/gmd-16-1277-2023, https://doi.org/10.5194/gmd-16-1277-2023, 2023
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Due to computational limits, lower-complexity models (LCMs) were developed as a complementary tool for accelerating comprehensive Earth system models (ESMs) but still lack a good precipitation emulator for LCMs. Here, we developed a data-calibrated precipitation emulator (PREMU), a computationally effective way to better estimate historical and simulated precipitation by current ESMs. PREMU has potential applications related to land surface processes and their interactions with climate change.
Morgan Sparey, Peter Cox, and Mark S. Williamson
Biogeosciences, 20, 451–488, https://doi.org/10.5194/bg-20-451-2023, https://doi.org/10.5194/bg-20-451-2023, 2023
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Accurate climate models are vital for mitigating climate change; however, projections often disagree. Using Köppen–Geiger bioclimate classifications we show that CMIP6 climate models agree well on the fraction of global land surface that will change classification per degree of global warming. We find that 13 % of land will change climate per degree of warming from 1 to 3 K; thus, stabilising warming at 1.5 rather than 2 K would save over 7.5 million square kilometres from bioclimatic change.
Isobel M. Parry, Paul D. L. Ritchie, and Peter M. Cox
Earth Syst. Dynam., 13, 1667–1675, https://doi.org/10.5194/esd-13-1667-2022, https://doi.org/10.5194/esd-13-1667-2022, 2022
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Despite little evidence of regional Amazon rainforest dieback, many localised abrupt dieback events are observed in the latest state-of-the-art global climate models under anthropogenic climate change. The detected dieback events would still cause severe consequences for local communities and ecosystems. This study suggests that 7 ± 5 % of the northern South America region would experience abrupt downward shifts in vegetation carbon for every degree of global warming past 1.5 °C.
Rebecca M. Varney, Sarah E. Chadburn, Eleanor J. Burke, and Peter M. Cox
Biogeosciences, 19, 4671–4704, https://doi.org/10.5194/bg-19-4671-2022, https://doi.org/10.5194/bg-19-4671-2022, 2022
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Soil carbon is the Earth’s largest terrestrial carbon store, and the response to climate change represents one of the key uncertainties in obtaining accurate global carbon budgets required to successfully militate against climate change. The ability of climate models to simulate present-day soil carbon is therefore vital. This study assesses soil carbon simulation in the latest ensemble of models which allows key areas for future model development to be identified.
Louise J. Slater, Chris Huntingford, Richard F. Pywell, John W. Redhead, and Elizabeth J. Kendon
Earth Syst. Dynam., 13, 1377–1396, https://doi.org/10.5194/esd-13-1377-2022, https://doi.org/10.5194/esd-13-1377-2022, 2022
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This work considers how wheat yields are affected by weather conditions during the three main wheat growth stages in the UK. Impacts are strongest in years with compound weather extremes across multiple growth stages. Future climate projections are beneficial for wheat yields, on average, but indicate a high risk of unseen weather conditions which farmers may struggle to adapt to and mitigate against.
Rebecca J. Oliver, Lina M. Mercado, Doug B. Clark, Chris Huntingford, Christopher M. Taylor, Pier Luigi Vidale, Patrick C. McGuire, Markus Todt, Sonja Folwell, Valiyaveetil Shamsudheen Semeena, and Belinda E. Medlyn
Geosci. Model Dev., 15, 5567–5592, https://doi.org/10.5194/gmd-15-5567-2022, https://doi.org/10.5194/gmd-15-5567-2022, 2022
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We introduce new representations of plant physiological processes into a land surface model. Including new biological understanding improves modelled carbon and water fluxes for the present in tropical and northern-latitude forests. Future climate simulations demonstrate the sensitivity of photosynthesis to temperature is important for modelling carbon cycle dynamics in a warming world. Accurate representation of these processes in models is necessary for robust predictions of climate change.
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Short summary
Emergent constraints (ECs) reduce the spread of projections between climate models. ECs estimate changes to climate features impacting adaptation policy, and with this high profile, the method is under scrutiny. Asking
What is an EC?, we suggest they are often the discovery of parameters that characterise hidden large-scale equations that climate models solve implicitly. We present this conceptually via two examples. Our analysis implies possible new paths to link ECs and physical processes.
Emergent constraints (ECs) reduce the spread of projections between climate models. ECs estimate...
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