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The need to include the effects of year-to-year climate variability has been shown for an ensemble of climate simulations^{11, 12}, but not for a formal set of probabilistic projections that directly affects adaptation planning. For example, the UKCP09 (ref. 6) projections underpinned the UK’s first statutory Climate Change Risk Assessment in 2012. These projections (see Methods) have the added advantage over earlier studies that any conclusions are based on a more comprehensive assessment of key uncertainties. This is because the UKCP09 projections are based on several ensembles (see Supplementary Table 1) of variants of the HadCM3 climate model (about 400 simulations) that explore uncertainties in land, atmosphere and ocean processes, sulphate aerosol chemistry, and the terrestrial carbon cycle, and also use information from an ensemble of international climate models (CMIP3; ref. 13). Observational metrics of model quality are used to constrain the projections by weighting realizations according to their ability to simulate historical mean climate¹⁴ and large-scale temperature trends¹⁵. Unlike UKCIP02, a Bayesian framework¹⁶ is used to transparently synthesize these data into probability density functions (PDFs), which represent the uncertainties explored by the climate simulations but are conditional on the method and its assumptions, as well as the evidence (model output, observational metrics and expert judgement). For a given emissions scenario, spread in these PDFs (ref. 15) comes from three sources: (i) modelling uncertainty, arising from imperfect understanding and the approximate representation by climate models of processes that determine the forcing associated with the emissions, and the climate response to this; (ii) climate variability on multi-decadal timescales; and (iii) errors in statistical estimates of the climate model responses to changes in forcing¹⁵ (see Methods).

By extending the UKCP09 method^{6, 14, 15} to simulated 1-year averages, we effectively add climate variability on timescales of 1–30 years to form projections for individual seasons (grey plumes in Fig. 1). The PDFs across time can be jointly sampled to generate a set of equally probable realizations. A small sample of these realizations (coloured lines in Fig. 1) show a few possible pathways for the future real climate if it was to experience the prescribed emissions. These reflect a range of plausible climate changes that cannot be ruled out by the observational metrics used to constrain the projections, superimposed by natural variability arising within the climate system. For example, some realizations of summer rainfall have strong drying signals (red), whereas some have a lot of very dry summers but can still produce a few very wet summers (blue). Generally, wet summer and cold winter seasons still exist under climate change, despite the tendency towards milder winters and drier summers covered by the UKCIP02/UKCP09 headline messages.

a–e, Data are presented for the five variables (as indicated). Grey shading and lines show percentiles of anomalies in the variables relative to 1961–1990, calculated from 1-year mean PDFs for every year between 1860 and 2100. Coloured lines show three (five for annual global mean temperature) individual realizations of year-to-year variation sampled from the 1-year PDFs so that simulated temporal correlations are captured. Thick black lines show observed annual global and England/Wales temperature and precipitation time series^{27, 28} up to winter 2014/15. The realizations used in each panel are chosen independently, so the same colours in different plots do not correspond to the same realizations.

The method used here to make our probabilistic climate projections^{14, 15} consists of two stages and is based on the six ensembles outlined in Supplementary Table 1. The first stage¹⁴ uses a Bayesian framework¹⁶ to predict, at the resolution of the global climate model, the distribution of equilibrium response to doubled CO₂ levels. The method combines information from: a perturbed parameter ensemble (PPE; ensemble 1 in Supplementary Table 1), where ensemble members are based on a standard version of the HadCM3 climate model but differ in the values of the model parameters that control atmosphere and land-surface processes; multimodel ensembles of other international climate models¹³; and observations. Expert judgement is also included, for example, in specifying prior distributions for uncertain model parameters, and in the choice of observations. The Bayesian method requires a more robust sampling of the set of parameter combinations than provided by the PPE. This is done by building an emulator, a statistical model trained on the emergent properties of the PPE, which can be used to predict the recent mean climate and the equilibrium response to a doubling of CO₂ for any combination of parameter values, not just those sampled by the PPE. The Bayesian framework allows the projections to be constrained by a set of multiannual mean observations by weighting different model variants according to their ability to simulate aspects of historical mean climate. The framework recognizes that climate models are imperfect, and combines information from the emulator and the multimodel ensemble to specify and include structural modelling uncertainty in the land/atmosphere component of the climate model in the predicted probabilities.

The second stage uses a timescaling approach¹⁵ to provide probabilistic projections for regional climate change for different time periods during the twenty-first century by combining information from the probabilistic projections from stage one with GCM ensembles that explore uncertainties in the time-dependent response to historical forcings and projected future emissions (Ensembles 2–6). The time-dependent regional response is emulated by assuming a linear variation with global annual mean temperature change, the latter being predicted by a simple climate model (SCM). The timescaling is done for each sampled parameter combination; the PDFs of equilibrium response to doubled CO₂ concentrations from stage one are sampled jointly to provide the climate feedbacks required to drive the SCM, and the normalized response per unit degree of global temperature change. The SCM is comprised of an energy balance model for prediction of land and ocean temperature change driven by changes in greenhouse gas, aerosol, solar and volcanic forcing, with a one-dimensional diffusion–advection equation for vertical ocean heat transport, and a simple carbon cycle model. By varying SCM parameters, global uncertainties in aerosol forcing, ocean heat uptake and carbon cycle feedbacks are accounted for. Parameters of these Earth System components of the SCM are calibrated to reproduce the response of the transient perturbed physics (Ensembles 3-6) and multimodel ensemble simulations, and then sampled along with the atmospheric parameters during scaling to provide projections for regional change. The sampled projections are then reweighted, based on the likelihood that they correctly replicate observed historical changes in surface temperature, and combined to provide time-dependent PDFs to the end of the twenty-first century for the A1B emissions scenario²⁹. We note that UKCP09 had an additional third stage, not used here, to convert GCM-resolution PDFs produced from the first two stages to PDFs at 25 km.

For each model variant it is also possible to generate a realization by sampling error associated with the timescaling (see Supplementary Information) and adding it to the emulated climate change signal. Furthermore, a set of equally probable realizations is used here. This is generated by sampling with replacement 1,000 model variants 2,000 times according to their likelihood weight, taking the emulated climate change for these 2,000 model variants, and adding sampled ‘noise’ from the timescaling.

In this study we show climate projections for annual global mean temperature and four climate variables over the three grid boxes that represent England and Wales, for two timescales: 30 years and one year. For the 1-year PDFs, we make a minor modification to the second stage described above to account for the short-term signal from volcanic eruptions (see Supplementary Figs 1 and 2 and related discussion).

Corrected online 06 August 2015

In the version of this Letter originally published, the use of UK versus England/Wales was inconsistent. The text has been amended to clarify throughout. These errors have been corrected in all versions of the Letter.

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