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Improved representation of ocean heat content in energy balance models


Anomaly-diffusing energy balance models (AD-EBMs) are routinely employed to analyze and emulate the warming response of both observed and simulated Earth systems. We demonstrate a deficiency in common multi-layer as well as continuous-diffusion AD-EBM variants: They are unable to, simultaneously, properly represent surface warming and the vertical distribution of heat uptake. We show that this inability is due to the diffusion approximation. On the other hand, it is well understood that transport of water from the surface mixed layer into the ocean interior is achieved, in large part, by the process of ventilation—a process associated with outcropping isopycnals. We, therefore, start from a configuration of outcropping isopycnals and demonstrate how an AD-EBM can be modified to include the effect of ventilation on ocean uptake of anomalous radiative forcing. The resulting EBM is able to successfully represent both surface warming and the vertical distribution of heat uptake, and indeed, a simple four-layer model suffices. The simplicity of the models notwithstanding, the analysis presented and the necessity of the modification highlight the role played by processes related to the down-welling branch of global ocean circulation in shaping the vertical distribution of ocean heat uptake.

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  1. 1.

    e.g., because of their computational intensity, ESMs themselves are never run long enough to directly assess climate sensitivity.

  2. 2.

    In order to exclude the possibility that our results are due to poor parameter tuning in the EBMs we consider, we apply a Bayesian statistical framework and Monte Carlo sampling to widely explore the space of parameter uncertainties.

  3. 3.

    We note that the intention of the CMIP abrupt 4×CO2 forcing experiment is one of calibration and diagnosis of equilibrium climate sensitivity since post-industrial surface warming itself is compatible with a wide range of climate sensitivities.

  4. 4.

    All experiments are run with each of the three forcings under consideration (abrupt4x, 1%, and historical), and the quantities of interest (QoI) are the SAT with each forcing and the 0–700-m and 700–2000-m OHC with historical forcing. While we also considered radiative non-equilibrium (RN), those results are left out for brevity.

  5. 5.

    In the two-layer EBM, warming of the ocean extends only to the depth of the two layers. That is, there is no warming below the depth of the second layer. Furthermore, the depth of the top layer should be thought of as roughly equivalent to the globally averaged mixed-layer depth (O (100 m); ≪ 700 m) The 0–700-m and 700–2000-m warming is obtained using linear interpolation.

  6. 6.

    When a number of the variations mentioned are considered in combination, and with a large number of layers, calibration of the resulting model can sometimes lead to, e.g., the top-layer depth being different from the a priori estimate of around 70 m. In such cases, we performed a companion experiment in which the top-layer depth is fixed at 70 m, and so on.


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BTN would like to thank W. Riley Casper for the help in identifying the zero entries of \(\widetilde {A}\) in Eq. 10. All of the data used in this article has been previously archived and may be obtained as follows: The Levitus ocean heat content data may be obtained from the the National Oceanographic Data Center at CMIP5 data may be obtained from one of the Earth System Grid Federation nodes, e.g., The SAT data may be obtained from The historical radiative forcing and the RCP8.5 scenario forcing may be obtained from (Meinshausen et al. 2011b). We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups for producing and making available their model output. For CMIP, the US Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals.

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Correspondence to Balasubramanya T. Nadiga.

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Nadiga, B.T., Urban, N.M. Improved representation of ocean heat content in energy balance models. Climatic Change 152, 503–516 (2019).

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  • Surface warming
  • Ocean heat uptake
  • Ocean heat content
  • Energy balance model
  • Climate sensitivity
  • Bayesian analysis
  • Simple climate model
  • Radiative nonequilibrium