Constraining climate forecasts: The role of prior assumptions

Abstract

[1] Any attempt to estimate climate sensitivity using observations requires a set of models or model-versions that simultaneously predict both climate sensitivity and some observable quantity(-ies) given a range of values of unknown climate system properties, represented by choices of parameters, subsystems or even entire models. The choices researchers make with respect to these unknown properties play a crucial role in conditioning their climate forecasts. We show that any probabilistic estimate of climate sensitivity, and hence of the risk that a given greenhouse gas stabilisation level might result in a ''dangerous'' equilibrium warming, is critically dependent on subjective prior assumptions of the investigators, not simply on constraints provided by actual climate observations. This apparent arbitrariness can be resolved by focussing on the intended purpose of the forecast: while uncertainty in long-term equilibrium warming remains high, an objectively determined 10 -90% (5 -95%) range of uncertainty in climate sensitivity that is relevant to forecasts of 21st century transient warming under nearly all current emission scenarios is 1.4-4.1°C with a median of 2.4°C, in good agreement with the ''traditional'' range. [2] Climate sensitivity, or equilibrium warming due to a doubling of carbon dioxide (CO 2 ), is a key determinant of climate change [Intergovernmental Panel on Climate Change (IPCC), Morgan and Keith, 1995]. Studies [Andronova and Schlesinger, 2000;Forest et al., 2002;Knutti et al., 2002;Gregory et al., 2002;Murphy et al., 2004;Stainforth et al., 2005] attempting to constrain climate sensitivity by comparing models with recent observations report a wide range of distributions. Here we show that much of this variation arises from different prior assumptions regarding climate sensitivity before any physical or observational constraints are applied, suggesting fundamental reasons why a universal consensus on longterm equilibrium warming consistent with any given stabilisation level for greenhouse gases may prove impossible to achieve.[3] We demonstrate our point with a simple global energy balance model (EBM) and diffusive ocean [Hansen et al., 1985], although the reasoning applies to any model in which atmospheric feedbacks scale linearly with surface warming and in which effective oceanic heat capacity is approximately constant under 20th century climate forcing. The diamonds in Figures 1a and 1b show the average warming trend caused by greenhouse gas increase over the 20th century (vertical axis) as a function of effective heat capacity of the troposphere-land-ocean system (horizontal) and the climate sensitivity S (colours) for a range of different settings of model parameters. The black contour encloses the region consistent (at the 5% level) with observations of 20th century greenhouse warming and the effective heat capacity.[4] We isolate the greenhouse warming signal using a pattern-based attribution analysis [Stott and Kettleborough, 2002] allowing for uncertainty in both greenhouse and oth...

Tall tales and fat tails: the science and economics of extreme warming

“…This is visible when we plot transient temperature change for heat capacities of approximately 1.2 GJm −2 K −1 and 0.6 GJm −2 K −1 (see Fig. 4), values closer to the median and lower end of the distribution in Frame et al (2005). 5 The implications for the economic value of the policy are stark.…”

“…1 and 4 shows that ξ 1 = t Cup . The scientific literature does not provide constraints on C up directly, but Frame et al (2005) present uncertainty estimates for effective heat capacity, C eff , giving 95 % confidence intervals of (< 0.2 GJm −2 K −1 , > 1.7 GJm −2 K −1 ) for the latter half of the 20th century. 2 A first approximation of ξ 1 from the observational data would simply be ξ 1 = t Ceff , but this can be refined using values from the first period of the DICE model to give the implied ratio of C up to C eff at the beginning of the 21st century; a value unlikely to be substantially different to that in the latter half of the 20th century and therefore comparable with observations.…”

“…An extension of the above model is therefore to consider that our system includes not the whole ocean but only the upper ocean, which is taken to be a well-mixed layer (and therefore warms uniformly), coupled to a second box which represents the deep ocean and into which heat diffuses. The deep ocean is usually not taken to be well-mixed but rather to have temperatures which decrease with depth (Hansen et al 1985;Frame et al 2005). A simpler form of this extension, though, would assume that the deep ocean too is well-mixed and can be represented by a single temperature, call it T LO .…”

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“…Murphy et al, 2004;Stainforth et al, 2002Stainforth et al, , 2005 have been used to generate probability density function pdfs of global warming -with most studies concentrating on defining 'climate sensitivity' (e.g. Frame et al, 2005) for the prevention of 'dangerous anthropogenic interference with the climate system' (Mastrandrea and Schneider, 2004;Schneider and Mastrandrea, 2005) by providing probabilistic projections for different CO 2 stabilization levels (e.g. Knutti et al, 2005).…”

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“…However, it was noted by Frame et al [10] that the resulting weighted distribution, while dependent on model structure, is also implicitly dependent on arbitrary choices made in the choice of parameter sample. A number of other studies thus attempted to produce probability density functions (PDFs) that were not directly dependent on the prior parameter distribution.…”