The determination of the sensitivity of the climate system to increasing greenhouse gas concentrations, usually stated in terms of the surface temperature change in response to a doubling of pre-industrial levels of atmospheric CO2 (2XCO2), has remained elusive. In the forcing-feedback paradigm of climate change departures from global energy balance, the top-of-atmosphere (TOA) radiative energy imbalance N is the sum of an imposed radiative forcing F and a feedback response -λΔT,
where the net feedback factor λ determines the climate sensitivity and ΔT is the global average surface temperature departure from the normal equilibrium state (Charney et al. 1979). For example, the radiative forcing from a doubling of atmospheric CO2 is generally accepted to be 3.7 W m− 2 (Forster et al. 2021) and as the system warms over many centuries the TOA energy imbalance N is removed, and a final equilibrium climate sensitivity change in temperature ΔT is achieved at F/λ.
For over 30 years the range of equilibrium climate sensitivities (ECS) diagnosed either from theory (3D Earth System Models, ESMs) or from observations has persisted over a broad range between 1.5 and 4.5 deg. C, with a few outlier estimates (Meehl et al. 2020, and references therein). The most recent estimates from ESMs participating in the sixth Coupled Model Intercomparison Project (CMIP6, Eyring et al. 2016) cover the widest range yet (1.8 to 5.7 deg. C) although the CMIP6 expert evaluation of the most likely range has narrowed to 2.5 to 4.0 deg. C, with a best estimate of 3.0 deg. C (IPCC 2021a). Due to the long time scale (centuries) required for the deep ocean to reach a new equilibrium state, the possibility that feedbacks can change on multi-century time scales, and the differences in efficacy of various forcing agents (e.g. aerosols vs. CO2), a shorter-term “effective” climate sensitivity (EffCS, e.g. Gregory et al. 2020) is usually preferred over ECS as a more practical measure for energy policy decisions and mitigation planning.
The EffCS uncertainty on a theoretical level arises from the complexity of the feedback responses of the climate system to a radiative imbalance, such as how clouds change to either amplify or dampen warming. On an observational basis, EffCS uncertainty comes from a lack of accurate knowledge of both the radiative forcing and the temperature response of the system to that forcing over the last 50 to 100 years or more. Gregory et al. (2020) addressed reasons why such estimates can produce biased results, for example due to the influence of major volcanic eruptions.
Alternatively, one can instead examine shorter-term interannual co-variations in TOA radiative flux and temperature to estimate λ, but non-feedback variations in TOA radiative flux de-correlate those variations leading to underestimates of λ made through standard least-squares linear regression (e.g. Spencer and Braswell 2011).
Further complicating observational diagnosis of sensitivity is the large heat capacity of the ocean, causing a delay in surface warming compared to if there was no sub-surface energy storage, which necessitates accurate measurements of ocean heat content over most of the global oceans’ volume. While heat storage by the landmass is usually ignored in such evaluations, here we include an estimate of its impact on diagnosed climate sensitivity.
Finally, uncertainty in diagnosing ECS from observations arises from multi-decadal time scale internal fluctuations in the climate system which can cause 10–20 year periods with either strong warming or no warming unrelated to the system’s long-term response to anthropogenic forcing (e.g. Meehl et al. 2013).
The complexity of the wide range of processes which determine climate sensitivity, combined with the rather wide range of sensitivities exhibited by climate models, leads to a need for simple alternative methods for examining what range of sensitivities are implied by the observed rates of global warming. Here we use a 1D time-dependent model of temperature departures from energy equilibrium, over land and ocean separately, to diagnose EffCS for a range of observed temperature trends over land and ocean, utilizing two significantly different radiative forcing datasets. The model could be considered the simplest approximation of ESMs where time-dependent equations are used to compute temperature tendencies in response to sources and sinks of energy. The simplicity of the model allows rapid computation of the sensitivity of EffCS to choices of assumed TOA radiative forcing and temperature datasets. Here we include deep-ocean (below 2,000 m) storage of heat as well as deep-land storage to 200 m depth, based upon borehole temperature measurements. The storage of heat in the global landmass is still not well handled by ESMs, which contain Land Surface Models (LSMs) with bottom boundary condition placement (BBCP) at only 2 to 10 m in depth (Cuesta-Valero et al. 2016; Burke et al. 2020), despite borehole evidence of warming to 200 m depth over recent centuries (National Research Council 2006; Harris and Chapman 2001).
The energy budget approach to estimating EffCS is similar to that of Lewis and Curry (2018, hereafter LC18), which obtained EffCS values ranging from 1.5 to 1.8 deg. C by examining 100 + year time scale changes in temperature and assumed forcing. In contrast to LC18, we use a time dependent model, which allows us to examine features such as the acceleration of deep-ocean (0-2000m) warming in recent decades (Cheng et al. 2019). The other difference is that we focus on the most recent 50 years (1970–2021) during which radiative forcing from greenhouse gas increases has been the largest and when observed deep-ocean temperature changes have the least measurement error. This hopefully maximizes the signal-to-noise of the ECS estimation, keeping in mind that the time period cannot be too short otherwise natural interannual climate variations can corrupt the diagnoses. While the largest volcanic eruption in modern history occurred during this period (Pinatubo in 1991), it was positioned near the middle of the period, hopefully reducing its impact on the computed temperature trends and associated uncertainties in volcanic radiative forcing (Gregory et al. 2020).
While the simplicity of the model allows simulations to be carried out quickly, it is at the expense of not knowing what specific feedback processes determine EffCS. Only their net effect on the TOA radiative flux and temperature are determined. To include the effect of uncertainty in the history of radiative forcing over that period (which is quite large, due mostly to sulfate aerosol forcing uncertainty, Smith and Forster 2021) two substantially different radiative forcing histories are included. Thousands of simulations are carried out spanning the full range of observed temperature trends and potential range of model free parameters to produce frequency distributions of diagnosed EffCS for all model fits to the observational data.