07 Sep 2022
07 Sep 2022
Status: this preprint is currently under review for the journal ESD.

Emergent constraints for the climate system as effective parameters of bulk differential equations

Chris Huntingford1, Peter M. Cox2, Mark S. Williamson2, Joseph J. Clarke2, and Paul D. L. Ritchie2 Chris Huntingford et al.
  • 1U.K. Centre for Ecology and Hydrology, Benson Lane, Wallingford, Oxfordshire, OX10 8BB, U.K.
  • 2College of Engineering and Environmental Science, Laver Building, University of Exeter, North Park Road, Exeter, EX4 4QF, U.K.

Abstract. Planning for the impacts of climate change requires accurate projections by Earth System Models (ESMs). ESMs, as developed by many research centres, estimate changes to weather and climate as atmospheric Greenhouse Gases (GHGs) rise, and they inform the influential Intergovernmental Panel on Climate Change (IPCC) reports. ESMs are advancing the understanding of key climate system attributes. However, there remain substantial inter--ESM differences in their estimates of future meteorological change, even for a common GHG trajectory, and such differences make adaptation planning difficult. Until recently, the primary approach to reducing projection uncertainty has been to place emphasis on simulations that best describe the contemporary climate. Yet a model that performs well for present--day atmospheric GHG levels may not necessarily be accurate for higher GHG levels and vice-versa.

A relatively new approach of Emergent Constraints (ECs) is gaining much attention as a technique to remove uncertainty between climate models. This method involves searching for an inter--ESM link between a quantity that we can measure now and another of major importance for in describing future climate. Combining the contemporary measurement with this relationship refines the future projection. Identified ECs exist for thermal, hydrological and geochemical cycles of the climate system. As ECs grow in influence on climate policy, the method is under intense scrutiny, creating a requirement to understand them better. We hypothesise that as many Earth System components vary in both space and time, their behaviours often satisfy large--scale Partial Differential Equations (PDEs). Such PDEs are valid at coarser scales than the equations coded in ESMs which capture finer high resolution gridbox--scale effects. We suggest that many ECs link to such an effective hidden PDE that is implicit in most or all ESMs. An EC may exist because its two quantities depend similarly on an ESM--specific internal bulk parameter in such a PDE, and with measurements constraining and revealing its (implicit) value. Alternatively, well--established process understanding coded at the ESM gridbox--scale, when aggregated, may generate a bulk parameter with a common ``emergent'' value across all ESMs. This single parameter may link uncertainties in a contemporary climate driver to those of a climate--related property of interest, the EC constraining the latter by measurements of the former. We offer illustrative examples of these concepts with generic differential equations and their solutions, placed in a conceptual EC framework.

Chris Huntingford et al.

Status: open (until 29 Oct 2022)

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Chris Huntingford et al.

Chris Huntingford et al.


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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.