# 10.5.4.7 Probabilistic Projections - Geographical Depictions

Tebaldi et al. (2005) present a Bayesian approach to regional climate prediction, developed from the ideas of Giorgi and Mearns (2002, 2003). Non-informative prior distributions for regional temperature and precipitation are updated using observations and results from AOGCM ensembles to produce probability distributions of future changes. Key assumptions are that each model and the observations differ randomly and independently from the true climate, and that the weight given to a model prediction should depend on the bias in its present-day simulation and its degree of convergence with the weighted ensemble mean of the predicted future change. Lopez et al. (2006) apply the Tebaldi et al. (2005) method to a 15-member multi-model ensemble to predict future changes in global surface temperature under a 1% yr^{–1} increase in atmospheric CO_{2}. They compare it with the method developed by Allen et al. (2000) and Stott and Kettleborough (2002) (ASK), which aims to provide relatively model independent probabilities consistent with observed changes (see Section 10.5.4.5). The Bayesian method predicts a much narrower uncertainty range than ASK. However its results depend on choices made in its design, particularly the convergence criterion for up-weighting models close to the ensemble mean, relaxation of which substantially reduces the discrepancy with ASK.

Another method by Furrer et al. (2007) employs a hierarchical Bayesian model to construct PDFs of temperature change at each grid point from a multi-model ensemble. The main assumptions are that the true climate change signal is a common large-scale structure represented to some degree in each of the model simulations, and that the signal unexplained by climate change is AOGCM-specific in terms of small-scale structure, but can be regarded as noise when averaged over all AOGCMs. In this method, spatial fields of future minus present temperature difference from each ensemble member are regressed upon basis functions. One of the basis functions is a map of differences of observed temperatures from late- minus mid-20th century, and others are spherical harmonics. The statistical model then estimates the regression coefficients and their associated errors, which account for the deviation in each AOGCM from the (assumed) true pattern of change. By recombining the coefficients with the basis functions, an estimate is derived of the true climate change field and its associated uncertainty, thus providing joint probabilities for climate change at all grid points around the globe.

Estimates of uncertainty derived from multi-model ensembles of 10 to 20 members are potentially sensitive to outliers (Räisänen, 2001). Harris et al. (2006) therefore augment a 17-member ensemble of AOGCM transient simulations by scaling the equilibrium response patterns of a large perturbed physics ensemble. Transient responses are emulated by scaling equilibrium response patterns according to global temperature (predicted from an energy balance model tuned to the relevant climate sensitivities). For surface temperature, the scaled equilibrium patterns correspond well to the transient response patterns, while scaling errors for precipitation vary more widely with location. A correction field is added to account for ensemble-mean differences between the equilibrium and transient patterns, and uncertainty is allowed for in the emulated result. The correction field and emulation errors are determined by comparing the responses of model versions for which both transient and equilibrium simulations exist. Results are used to obtain frequency distributions of transient regional changes in surface temperature and precipitation in response to increasing atmospheric CO_{2}, arising from the combined effects of atmospheric parameter perturbations and internal variability in UKMO-HadCM3.

Figure 10.30 shows probabilities of a temperature change larger than 2°C by the end of the 21st century under the A1B scenario, comparing values estimated from the 21-member AR4 multi-model ensemble (Furrer et al., 2007) against values estimated by combining transient and equilibrium perturbed physics ensembles of 17 and 128 members, respectively (Harris et al., 2006). Although the methods use different ensembles and different statistical approaches, the large-scale patterns are similar in many respects. Both methods show larger probabilities (typically 80% or more) over land, and at high latitudes in the winter hemisphere, with relatively low values (typically less than 50%) over the southern oceans. However, the plots also reveal some substantial differences at a regional level, notably over the North Atlantic Ocean, the sub-tropical Atlantic and Pacific Oceans in the SH, and at high northern latitudes during June to August.