A minimal model for estimating climate sensitivity
Introduction
Climate sensitivity is a measure of the net temperature response of the Earth to a change in radiative (primarily CO2) forcing. It summarizes the end result of the complex processes of the Earth's dynamic atmosphere and oceans. It can only be calculated from first principles for a theoretical Earth. Many early estimates of sensitivity, defined in terms of response to a doubled forcing, were based on climate models. Sensitivity effectively summarizes what the models say in a single metric and is estimated as 3.0 °C (3.4 °C in AR5) (IPCC, 2007). However, the recent 16+ year halt in global warming, which is not predicted by the models, suggests that the models might have sensitivity set too high. Thus estimates of climate sensitivity that are not based on general circulation models (GCMs) would provide a check on model outputs.
Interestingly, estimates of sensitivity based on energy balance considerations and historical data (Aldrin et al., 2012, Annan and Hargreaves, 2011, Bengtsson and Schwartz, 2013, Hargreaves et al., 2012, Lewis, 2013, Masters, 2013, Michaels et al., 2002, Otto et al., 2013, Ring et al., 2012) consistently estimate equilibrium sensitivity near 2 °C per doubling. That is, they all give much lower sensitivity to a change in forcing than studies based on GCM response. These studies use various methods but generally depend on certain overlapping types of data, including estimates of solar forcing, greenhouse forcing, ocean heat content, historical temperature data, and Earth radiation balance estimates. Unfortunately, the assumption that solar forcing operates only via direct total solar irradiance (TSI) is unproven, and even estimates of TSI are uncertain (Scafetta, 2013). Likewise, the effects of clouds (at multiple levels, e.g., Chen et al., 2013), black carbon, and aerosols, both in terms of strength of forcing and historical data accuracy, are poorly known according to the IPCC (2007) and others (e.g., Scafetta, 2013), as are ocean heat content changes, making estimation of sensitivity uncertain. The net result, as Lindzen and Choi have shown, is that data only weakly constrain estimates of sensitivity. This lack of constraint yields the long upper tails of the sensitivity probability density functions (pdfs) (Lewis, 2013), which are made even longer through use of inappropriate statistical methods, according to Lewis (2013), as well as wide confidence intervals on the best estimate.
One of the factors that complicates attempts to compute climate sensitivity is that there appear to be complex natural fluctuations in Earth's climate (Lüdecke et al., 2013), whether internally or externally forced is unknown. While empirical sensitivity studies attempt to account for known forcings and energy balances, they are unable to fully account for internal climate oscillations or forcings whose mechanisms are not well-understood. An alternate approach is to statistically account for natural climate oscillations even if their cause cannot be determined. After subtracting these oscillations, the remaining signal should be the anthropogenic signal plus noise. This residual can then be used to estimate sensitivity. This is the approach used in this study.
Section snippets
Methods
The approach taken is based on Loehle and Scafetta (2011), who used a signal decomposition method to factor out natural climate fluctuations and estimate the anthropogenic temperature signal. This approach greatly reduces the problem of data uncertainty. Because it has recently become more likely that natural multi-decadal cycles due to solar activity and/or endogenous ocean current patterns have not been properly taken into account in GCMs (de Freitas and McLean, 2013, Fyfe et al., 2013), this
Calculation
The standard metric of climate sensitivity is the warming that results from a linear (over log of concentration) doubling of CO2 (or CO2 equivalent) forcing. In this case, because we have identified a linear warming trend, we can relate this to the rise in the log of CO2 to estimate sensitivity based on comparable time periods. For the period January 1959 to January 2013, CO2 has risen from 315.62 to 395.68 ppm. On a log scale this represents 0.326 of a doubling over the 54 years. The linear 0.66
Discussion
Other studies are based on very uncertain satellite, ocean heat, and forcing data, which leads to wide confidence intervals. In contrast, the model used here is based on the pre-anthropogenic era (pre-1950) for estimating the timing and magnitude of solar and other natural effects, and is able to utilize 100 years worth of data for this purpose. It represents an independent estimate of sensitivity that avoids assumptions about forcing magnitudes and is not subject to errors due to the need to
Conclusions
The model used here is based on the pre-anthropogenic era (pre-1950) for estimating the timing and magnitude of solar and other natural effects, and is able to utilize 100 years of data for this purpose by factoring out natural climatic fluctuations over the past 150 years. It represents an independent estimate of sensitivity that avoids assumptions about forcing magnitudes and is not subject to errors due to the need to estimate difficult to compute or estimate metrics such as ocean heat
Acknowledgments
Thanks to Chip Knappenberger and Nic Lewis for helpful suggestions.
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