by Judith Curry
An important new paper on this topic has been published in J. Climate, that raises the bar in terms of uncertainty analysis.
Probabilistic Estimates of Transient Climate Sensitivity Subject to Uncertainty in Forcing and Natural Variability
Lauren E. Padilla, Geoffrey K. Vallis, Clarence W. Rowley
Abstract. In this paper we address the impact of uncertainty on estimates of transient climate sensitivity (TCS) of the globally averaged surface temperature, including both uncertainty in past forcing and internal variability in the climate record. We provide a range of probabilistic estimates of the TCS that combine these two sources of uncertainty for various underlying assumptions about the nature of the uncertainty. We also provide estimates of how quickly the uncertainty in the TCS may be expected to diminish in the future as additional observations become available. We make these estimates using a nonlinear Kalman filter coupled to a stochastic, global energy balance model, using the filter and observations to constrain the model parameters. We verify that model and filter are able to emulate the evolution of a comprehensive, state-of-the-art atmosphere-ocean general circulation model and to accurately predict the TCS of the model, and then apply the methodology to observed temperature and forcing records of the 20th century.
For uncertainty assumptions best supported by global surface temperature data up to the present time, we find a most-likely present-day estimate of the transient climate sensitivity to be 1.6 K with 90% confidence the response will fall between 1.3–2.6 K, and we estimate that this interval may be 45% smaller by the year 2030. We calculate that emissions levels equivalent to forcing of less than 475 ppmv CO2 concentration are needed to ensure that the transient temperature response will not exceed 2 K with 95% confidence. This is an assessment for the short-to-medium term and not a recommendation for long-term stabilization forcing; the equilibrium temperature response to this level of CO2 may be much greater. The flat temperature trend of the last decade has a detectable but small influence on TCS. We describe how the results vary if different uncertainty assumptions are made, and we show they are robust to variations in the initial prior probability assumptions.
Padilla, L., Vallis, G. K. and Rowley, C. 2011. Probabilistic estimates of transient climate sensitivity subject to uncertainty in forcing and natural variability. J. Climate , doi: 10.1175/2011JCLI3989.1
Full manuscript is online [link]
Some background information from the Introduction:
The steady-state response of the global-mean, near-surface temperature to an increase in greenhouse gas concentrations (e.g., a doubling of CO2 levels) is given, definitionally, by the equilibrium climate sensitivity (ECS), and this is evidently an unambiguous and convenient measure of the sensitivity of the climate system to external forcing. However, given the long timescales involved in bringing the ocean to equilibrium the ECS may only be realized on a timescale of many centuries or more and so its relevance to policy makers, and indeed to present society, has been debated. Of more relevance to the short and medium term — that is, timescales of a few years to about a century — is the transient climate response (TCR), which is the global and annual mean surface temperature response after about 70 years given a 1% CO2 doubling rate. (Sometimes an average may be taken from 60 to 80 years or similar to ameliorate natural variability.) Although the detailed response of the atmosphere to a doubling in CO2 will likely depend on the rate at which CO2 is added to the atmosphere, recent work with comprehensive models suggests that surface temperatures respond quite quickly to a change in radiative forcing, reaching a quasi-equilibrium on the timescale of a few years (in part determined by the mixed-layer depth) prior to a much slower evolution to the true equilibrium (e.g., Held et al. 2010). In the quasi-equilibrium state, the rate of change of surface temperature is a small fraction of its initial increase, and the response following a doubling of CO2 may be denoted the transient climate sensitivity (TCS). The TCS may be expected to be very similar to the TCR, but it’s definition does not depend so strictly on there being a particular rate of increase of greenhouse gases. As long as the CO2 doubles over a time period short enough for deep ocean temperature to remain far from equilibrium (less than 100 years, for example), the response to that doubling will likely be nearly independent of the emissions path. The ECS, in contrast, will take centuries to be fully realized. Given the timescale separation between the transient and equilibrium responses, the TCS is a useful parameter characterizing the climate system and it is this quantity that is the focus of this paper.
In addition to its relevance, the TCS may be easier to determine from observations than the ECS, in part because there are fewer free parameters to constrain. When estimating the TCS, we sum the atmospheric feedback strength and the rate of ocean heat uptake [also an uncertain quantity (Hegerl et al. 2007; Forest et al. 2002)], rather than constraining each factor separately. The overall response uncertainty, however, may still be dominated more by uncertainty in atmospheric feedbacks than the uptake of heat by the ocean (Knutti and Tomassini 2008; Baker and Roe 2009).
[T]he way that we shall proceed is to construct a simple but physically based model and then to try to constrain the parameters that determine the model’s transient climate sensitivity by a direct comparison with observations. Specifically, we will constrain a simple energy balance model by observations of the 20th century surface temperature record, using a particular nonlinear form of the Kalman filter as a way of estimating parameters. This approach allows us to explicitly examine the way in which probability distributions depend on the underlying assumptions and length of the observed record.
Their methodology is complex and not summarized here in detail, but the key issue IMO is their analysis of the uncertainty of their uncertainty estimate:
For comparison with the results described above, which were obtained with assumptions about uncertainty detailed in section 5a that we consider most plausible, we also consider three limiting cases for past uncertainty: forcing uncertainty 50% larger, forcing uncertainty 50% smaller – both with our plausible estimate of unforced variability, and plausible forcing uncertainty with larger natural variability in the temperature record. These uncertainty scenarios are summarized in table 1 along with the corresponding 90% confidence intervals after assimilation of surface temperature data up to 2008 and 2030. The confidence intervals are also shown in the inset plot of figure 6. The combined range of these intervals is an indication of the effects of uncertainty in our uncertainty estimates. As expected, the larger the forcing uncertainty and natural variability, the broader becomes the spread in the estimated [sensitivity].
From the Conclusions:
Although our estimates are certainly sensitive to these uncertainties and to natural variability, they may be sufficiently narrow as to still be useful. For uncertainties ranging from very large forcing uncertainty to very small forcing uncertainty, our confidence intervals for TCS range from 1.2–2.6 K to 1.4–2.6 K. With a much larger portion of the observed temperature change attributed to natural variability, our TCS interval increases to 1.1–5.5 K. Our probabilistic estimate of the range of TCS that we believe to be best justified by data, namely 1.3–2.6 K with a most probable estimate of 1.6 K, is broadly consistent with the TCR range of IPCC AR4 climate models whose median and mean are 1.6 K and 1.8 K, with 90% confidence interval of 1.2–2.4 K (Randall et al. 2007; Meehl et al. 2007). Figure 15 summarizes our range of probabilistic estimates given data from 1900 to 2008 and 2030. The collection of probability densities and corresponding confidence intervals indicate both the state of TCS uncertainty today and potential for improved understanding 20 years in the future.
JC comments: There are a number of things that I like about this paper:
- observationally based analysis of climate sensitivity
- sophisticated uncertainty analysis
- focus on transient response (rather than equilibrium response), which is more appropriate for an observationally based analysis
- explicitly includes a term for natural (unforced) internal variability
- affiliations of two of the authors (mechanical and aerospace engineering); brings new blood and new ideas to the topic!