Climate change mitigation targets are often described in terms of annually averaged global mean temperature increases. However local interpretation of impacts resulting from these targets are required if the public is to have a sound appreciation of their consequences. Some of the largest impacts are likely to arise from changes in extreme events, for example heatwaves and floods. This article estimates future regional heat extreme changes consistent with specific global warming targets, using a new and presently unique ensemble of physically plausible climate simulations. We find that a subset of ensemble members giving globally averaged temperature increases of 2.0 ± 0.5°C shows a wide range of changes in regional temperature extremes. For example, changes in extreme single-day hot events range between 2 and 6 °C for large parts of Europe, North America and Asia for this target. Plausible variations in the model representation of forest roughness length, vegetation root depth and boundary layer cloud make the largest individual contributions to the spread of changes found in different parts of the world. However, a wide range of processes contribute to the uncertainties in the regional changes, particularly through their direct or indirect influences on the simulation of soil moisture.
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 Recent discussions between governments on determining a response to anthropogenic climate change have centred on limiting the increase in global average temperature. The European Union reiterated its longstanding commitment to a 2°C target in January 2009 (European Commission, Communication from the Commission to the European Parliament, the Council, the European Economic and Social Committee and the Committee of the Regions—Towards a comprehensive climate change agreement in Copenhagen, 2009, available at http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri =COM:2009:0039:FIN:EN:HTML).
 However, such targets do not convey the associated risk of enhanced local changes, particularly from extremes, and thus may hinder the acceptance of CO2 reduction targets by the public. It is well known, for example, that climate model projections show land warming faster than oceans [Sutton et al., 2007]. Further regional contrasts are dependent on spatial variations in the effects of climate change feedback processes and changes in atmospheric and oceanic circulation [Intergovernmental Panel on Climate Change (IPCC), 2007]. Furthermore, targets are typically expressed as multi-year averages of annual means, hiding the seasonality of changes and future year to year variability. Translating such targets into seasonally and regionally based metrics is important to inform debate, and help achieve public consent. To address this, we describe the projected regional changes in extreme hot events, consistent with a 2°C globally averaged target being approximately met. We choose to examine extreme hot events since their societal and economic impacts are already large [Trigo et al., 2005].
2. Model Runs and Methodology
 Different climate models with the same climate forcing give different projections of future changes, due to uncertainties inherent in the modelling process. Modelling uncertainties arise both from alternative structural choices (such as spatial resolution, or the fundamental assumptions made in parameterisations of sub-grid scale processes), and from the values of poorly-constrained parameters within specific parameterisation schemes. Multi-model ensembles partially quantify the effects of structural uncertainties [IPCC, 2007], but are too small to support analysis of the spread of regional changes consistent with a given global mean temperature change. However, larger ensembles addressing the effects of parameter uncertainties are now available, which can be used for this purpose. These ensembles neglect structural uncertainties, but produce a spread of projected changes comparable to those found in multi-model ensembles [Collins et al., 2010].
 We use an ensemble of 224 simulations of the equilibrium response to doubled CO2, using perturbed variants of HadSM3, a coupled atmosphere/mixed-layer ocean configuration of the HadCM3 climate model.
 The ensemble members explore perturbations to 31 parameters controlling key processes in the model parameterizations of large-scale cloud, convection, radiative transfer, sea ice, surface and boundary layer process and dynamical transports.
 Originally fifty three members considered perturbations to individual parameters, relative to the settings used in the standard version of the atmospheric component, exploring ranges of plausible values estimated by experts [Murphy et al., 2004; Barnett et al., 2006; Rougier et al., 2009]. Clark et al.  found that members of this ensemble gave levels of internal variability in JJA daily maximum temperature similar to or greater than observations. More recently, a new set of 128 members explored a set of multiple parameter perturbations designed to sample a wide range of climate sensitivity values, provide skilful simulations of present climate and sample a wide range of possible parameter values [Webb et al., 2006]. The 224 members used in this study consists of this new ensemble plus 96 additional model variants subsequently produced to improve further the sampling of interactions between the effects of different parameters [Rougier et al., 2009]. Webb et al.  and Collins et al.  find that ranges of global and regional climate changes derived from perturbed physics ensembles are comparable to the spread of changes found in corresponding multi-model ensemble simulations [e.g., IPCC, 2007].
 The atmosphere/mixed layer ocean configuration used in this study allows a much larger ensemble to be produced than would be possible using a three-dimensional dynamical ocean component, at the cost of neglecting changes in ocean transport. While such changes can potentially influence regional climate changes [Boer and Yu, 2003], Harris et al.  show that patterns of equilibrium land surface temperature change generally resemble those found in corresponding simulations of time-dependent changes using a dynamical ocean component, especially over land. Each of the 224 variants was run for 20 years beyond equilibrium under present-day and doubled CO2 conditions.
 Changes are shown for two indicative types of northern hemisphere JJA summer heat events, both using daily maximum temperature data. These are the 99th percentile of temperature (hereafter TX99) and the intensity of 7-day heatwaves with a 20 year return period (see auxiliary material for full descriptions).
 The changes in TX99 and heatwave intensity are categorised according to the globally averaged warming responses 2, 3 and 4 °C ± 0.5, produced by 44, 110 and 49 members respectively. The remaining members have responses greater than 4.5°C.
 For a given category of global mean changes, lower and upper estimates of the regional changes are defined by ranking the changes and identifying values which encapsulate the central 80% of simulated changes.
 Maps of these lower and upper estimates are shown in Figure 1, corresponding to the 2 ± 0.5°C global target. Over many land regions, even the lower estimate exceeds the globally averaged target, particularly for TX99. Perhaps even more striking are the upper estimates. The tabulated summary in Figure 1 show these to be several degrees greater than the corresponding global average response. The lower to upper estimate ranges are consequently much wider than the 1.0°C global response range. Spatial variations in the lower end changes are due mainly to spatial variations in the mean warming, whereas regional changes in the shape of daily temperature distributions also affect the upper end changes, increasing uncertainties in changes in regional extremes compared to those in mean temperatures (see auxiliary material). Corresponding analysis for global increase categories of 3°C and 4°C (see summary table in Figure 1) gives similar results.
 The wide range in regional estimates suggests that a high sensitivity of extreme heat events to climate change cannot be ruled out, even if the global average warming could be restricted to 2°C. Over Eastern North America and Northern Europe for example, the range in heatwave change estimates (2.1 to 9.8°C and −1.1 to 9.2°C) is over six times greater than the corresponding range in the global response (1.5–2.5°C). Using a subset of equilibrium simulations with a limited range of global responses may underestimate uncertainties in the regional changes in extremes. However, re-scaling the estimates of all 224 members based on their respective global responses (see auxiliary material) suggests that considering a wider range of climate sensitivities does not widen the uncertainty estimates significantly. The ranges are considerably larger than the equivalent ranges of 3.1 and 2.4°C respectively expected from unforced internal variability, estimated by splitting 600 year control and double CO2 simulations of the HadSM3 model variant with standard parameter settings [Murphy et al., 2004] into 30 pairs of 20 years.
 We now investigate possible reasons for the large ranges, focusing on changes in TX99 for the subset of ensemble members giving a global mean warming between 1.5°C and 2.5°C.
 Changes in soil moisture are known to be associated with heatwaves and surface energy balance [e.g., Brabson et al., 2005]. In our simulations, moisture is characterised in terms of soil moisture available to vegetation (Θ). We use the normalised moisture defined by (Θ − Θw)/(Θc − Θw) where Θw is the wilting point and Θc is the soil critical point, dependent on porosity, above which evapotranspiration is not constrained by the soil. In the model, transpiration tends to zero as the normalised moisture tends to zero.
 To address the effects of changes in soil moisture on heat extremes in a given ensemble member, each of the 1800 summer days in the control and doubled CO2 simulations were categorised as being either “dry” or “damp”, corresponding to normalised available soil moisture below or above 0.5 respectively. Percentiles of the 1800 normalised daily values were then calculated for each simulation, and a soil moisture percentile was identified as making the transition from damp in the control simulation to dry in the doubled CO2 simulation if its normalised value changed from being >0.5 to <0.5 whilst reducing by more than 0.1. The average daily maximum temperature on days corresponding to each soil moisture percentile was also calculated for the control and 2 × CO2 simulations, allowing changes to be calculated as a function of soil moisture.
Figure 2a shows the ensemble average of the additional temperature increase for all soil moisture percentiles which change from damp to dry, relative to the increase for percentiles which remain damp (i.e., above 0.5). The results show an average additional warming in the range 2–6°C over Europe, Canada and North–east Asia associated with drying (noting that there is significant uncertainty in the degree of enhancement across different ensemble members – not shown). However the relevance of this result to extreme hot days is subtle. Analysis of the control simulations indicates that extreme hot days are often already associated with dry soil moisture conditions. Figures 2b–2d (see auxiliary material for further guidance) show how soil drying is associated with temperature change over Northern Italy for example, in three ensemble members. All three members give their greatest temperature increases where soil moisture reduces significantly, but in differing parts of the soil moisture spectrum. Where TX99 coincides with parts of the spectrum which are dry in the control simulation (e.g., blue diamond in Figure 2b), soil moisture reductions and temperature increases on doubling CO2 are small. Conversely, when TX99 days are originally moist, but become dry with CO2 doubling, temperature increases are large (Figure 2d). This spread in behaviour across the ensemble is typical of results found at other locations, and suggests that part of the substantial uncertainty in extreme hot day changes in Figure 1 is associated with inter-member variability in the control simulations of hot days and soil moisture. Similar results (not shown) were found for 7-day heatwaves.
 The effects of individual perturbed model parameters on the range of TX99 changes were investigated using members with 1.5 to 2.5°C globally averaged increases. For the eighteen continuously variable parameters [see Rougier et al., 2009], this was done by differencing the average changes found in simulations containing values of the relevant parameter in the upper and lower terciles of its expert-specified range. For parameters consisting of switches (of 2, 3 and 4 values), average differences of the most extreme settings were calculated.
 The ranges of temperature change are shown in Figure 3a–3e, expressed as percentages of the total range shown in the upper panels of Figure 1. Due to space constraints, only the perturbations with the five largest impacts, based on land area averages, are shown. Figure 3f also shows the equivalent range that occurs in the simulations purely as a result of internal variability, estimated from 600 year control and 2×CO2 simulations of changes in maximum temperature from the model variant with standard parameter settings. Each 600 year time series was divided into thirty 20 year periods. A range of changes attributable to internal variability was then derived by differencing ten randomly picked pairs of control and 2×CO2 periods, repeating this process 10000 times. The mean value of the range is plotted in the Figure 3f.
 The effects of the model parameters show a strong regional dependence. Perturbations to the forest roughness and vegetation root depth produce the largest spread in hot day temperature changes over North America and Russia (Figures 3a and 3b). Here, the spread due to these perturbations is up to three times larger than that due to internal variability alone. The root depth parameter also contributes substantially to the uncertainties (cf. Figure 1) found over western Europe and the US. Figure 3g shows the relative effects of all of the perturbed parameters in terms of the fraction of land for which grid point temperature changes are greater than those expected from internal variability at the 95% level. An analysis on 7-day heatwaves (not shown) yielded similar results although fractions of land values were generally 0.1 to 0.2 smaller.
 Several parameters directly controlling aspects of surface moisture or radiation balance appear among the leading influences, however Figure 3g suggests that perturbations in all parameters contribute to the spread of responses beyond the level attributable to internal variability, often through indirect influences on summer temperatures. This is also true for 7-day heatwaves (not shown). For example, uncertainties in sea-ice albedo (Figure 3g) significantly affect the spread of changes in the intensity of TX99 over north–eastern Russia, possibly through effects on the seasonal cycle of soil moisture driven by the impact of variations in winter and spring temperatures on the timing of snowmelt. The large regional ranges therefore reflect uncertainties arising from an array of feedback processes, some of which operate directly at a regional level, while others operate indirectly via effects remote in space and/or season. This general conclusion supports previous studies [e.g., Kharin and Zwiers, 2005; Soden and Held, 2006], however the systematic design of the perturbed physics ensemble used here allows the influence of individual physical processes to be isolated more precisely.
 The results of Figure 3 illustrate the challenges associated with reducing uncertainties in projections of extreme events through the development of improved models, given the complex array of model processes which potentially needs to be addressed. Nevertheless, Figure 2 suggests that progress can be made by focusing on the simulation of certain critical variables (in this case soil moisture), since the present day climatology and future changes in this variable play a significant role in determining the simulated changes in hot summer days. Uncertainties can potentially be reduced either by improving the simulation of soil moisture in models, or by including soil moisture observations in metrics used to weight alternative projections according to observations. However these are substantial challenges which depend on the ability to refine multiple processes which affect the simulation of soil moisture [e.g., Wood et al., 1998], and on the development of more comprehensive and suitable observational datasets [e.g., Kerr et al., 2001].
 To assess the credibility of the upper estimates, the average simulation skill of the 10% of members giving increases in TX99 greater than the upper estimates of Figure 1 was compared to the average skill of the remaining simulations. This was done for present-day simulations of the ensemble against climatological average observations of a set of key climate variables (see auxiliary material). Skill levels between the two subsets were found to be similar and comparable to the sixteen models used by IPCC . As a result, there is currently no basis for the ruling out of the upper ends of our extreme event estimates.
 Our results indicate the need for further research to reduce uncertainties in these regional high impact events, through a combination of model improvements allied to better use of observations to discriminate between alternative projections.
 This work was supported by the Defra and MoD Integrated Climate Programme - (Defra) GA01101, (MoD) CBC/2B/0417_Annex C5.