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Dynamics of the Global Energy Budget: the Time Dependence of the Climate Feedback Parameter and Climate Sensitivity.
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  • Robin Guillaume-Castel,
  • Benoit Meyssignac,
  • Jonathan Chenal,
  • Remy ROCA
Robin Guillaume-Castel
LEGOS, Université de Toulouse

Corresponding Author:[email protected]

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Benoit Meyssignac
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Jonathan Chenal
Ecole Nationale des Ponts et Chaussées
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The most simple representation of the dynamics of the global energy budget is the 0-dimensional energy balance model (EBM) introduced by Budyko (1965). Budyko’s EBM assumes a linear relationship between the Earth’s radiative response and the global surface temperature such that the dynamics of the global energy budget reads CdTs/dt = N = F - λ Ts, where Ts is the global surface temperature, N is the Earth Energy Imbalance, C is the ocean heat capacity and λ is the constant climate feedback parameter. Such simple conceptual model depicts reasonably well the centennial time scale response of the steady state preindustrial global energy budget under an anomalous forcing such as the increase of atmospheric greenhouse gases concentrations. For this reason it has served as the basis for the definition of the effective climate sensitivity to atmospheric CO2 concentrations. However recent studies identified limitations to Budyko’s EBM. Indeed climate model simulations show that the radiative response of the Earth not only depends on the global surface temperature but also on its geographical pattern: the so-called “pattern effect”. It arises from changes in the mix of radiative forcings, lag-dependent responses to forcings, or unforced variability and it leads to an apparent time variation in λ. This time variation must be accounted for in Budyko’s EBM to represent the longer term response of the global energy budget under increased CO2 concentrations. Here, a simple theory is developed to account for the time dependency of λ in the global energy budget. The resulting differential equation accurately reproduces the long term response (i.e. >200 years) of climate under abrupt changes in CO2 concentrations as simulated in the longrunmip experiment. Analysis of the asymptotic form of the differential equation yields a new expression of the climate sensitivity which not only depends on the climate feedback parameter but also on its temporal change. We evaluate this new climate sensitivity for all runs of the longrunmip experiment and show how it relates with the classical effective climate sensitivity from Gregory et al. (2004). We find that the spread in climate sensitivity among climate models of the longrunmip experiment is essentially due to different temporal changes in λ (and thus different pattern effect) among models.