ANTHROPOGENIC EXTREME WEATHER EVENTS OF THE 20 TH CENTURY.

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1 Technical Report No. 28 ANTHROPOGENIC EXTREME WEATHER EVENTS OF THE 20 TH CENTURY. Author names: Pardeep Pall, Tolu Aina, Dáithí A. Stone, Peter A. Stott, Toru Nozawa, Arno G. J. Hilberts, Dag Lohmann, Claudio Piani & Myles R. Allen. Date: 31/05/11 Synoptic structure of Northern Hemisphere autumns

2 Figure (A). Regression pattern (m) of mean autumn 500-hPa geopotential height against total autumn England and Wales precipitation normalized by one standard deviation. a, For all autumns before autumn 2000 in ERA-40 ( ). b, For all simulations in the A2000 climate. Bold contours denote areas significant at 1%, assuming 43-member samples (number of ERA-40 autumns) and normally distributed regression variables. Hemispheric correlation of the two patterns is 0.69, falling within the (5th 95th percentile) range of Monte Carlo bootstrap correlations between the A2000 pattern and patterns constructed using random 43-member sub-samples of A2000 simulations. WATCH is an Integrated Project Funded by the European Commission under the Sixth Framework Programme, Global Change and Ecosystems Thematic Priority Area (contract number: ). The WATCH project started 01/02/2007 and will continue for four years. Title: Authors: Organisations: Quantitative assessment of the contributions to changes in the risk of extreme selected weather events over the 20 th century that are attributable to anthropogenic greenhouse forcing, anthropogenic aerosol forcing and the non-linear interactions between the two. Pardeep Pall 1,2, Tolu Aina 3, Dáithí A. Stone 1,4, Peter A. Stott 5, Toru Nozawa 6, Arno G. J. Hilberts 7, Dag Lohmann 7, Claudio Piani 8 & Myles R. Allen 1,4. 1 Atmospheric, Oceanic and Planetary Physics, Department of Physics, University of Oxford, Oxford OX1 3PU, UK. 2 Institute for Atmospheric and Climate Science, ETH Zurich, CH-8092 Zurich, Switzerland. 3 Oxford e-research Centre, University of Oxford, Oxford OX1 3QG, UK. 4 Tyndall Centre Oxford, Oxford University Centre for the Environment, Oxford OX1 3QY, UK. 5 Met Office Hadley Centre, Fitzroy Road, Exeter EX1 3PB, UK. 6 National Institute for Environmental Studies, Tsukuba, Ibaraki , Japan. 7 Risk Management Solutions Ltd, London EC3R 8NB, UK. 8 International Centre for Theoretical Physics, Trieste, Italy. Submission date: 14/06/11 Function: This report is an output from Work Block 4.1; task Deliverable WATCH deliverable D Table of contents: Abstract. 3 Introduction... 3 Methodology. 3 Results.. 6 Conclusions.. 8 Technical Report No

3 Abstract Interest in attributing the risk of damaging weather-related events to anthropogenic climate change is increasing 1. Yet climate models used to study the attribution problem typically do not resolve the weather systems associated with damaging events 2 such as the UK floods of October and November Occurring during the wettest autumn in England and Wales since records began in ,4, these floods damaged nearly 10,000 properties across that region, disrupted services severely, and caused insured losses estimated at 1.3 billion (refs 5, 6). Although the flooding was deemed a wake-up call to the impacts of climate change at the time 7, such claims are typically supported only by general thermodynamic arguments that suggest increased extreme precipitation under global warming, but fail 8,9 to account fully for the complex hydrometeorology 4,10 associated with flooding. Here we present a multi-step, physically based probabilistic event attribution framework showing that it is very likely that global anthropogenic greenhouse gas emissions substantially increased the risk of flood occurrence in England and Wales in autumn Using publicly volunteered distributed computing 11,12, we generate several thousand seasonal-forecast-resolution climate model simulations of autumn 2000 weather, both under realistic conditions, and under conditions as they might have been had these greenhouse gas emissions and the resulting large-scale warming never occurred. Results are fed into a precipitation-runoff model that is used to simulate severe daily river runoff events in England and Wales (proxy indicators of flood events). The precise magnitude of the anthropogenic contribution remains uncertain, but in nine out of ten cases our model results indicate that twentieth-century anthropogenic greenhouse gas emissions increased the risk of floods occurring in England and Wales in autumn 2000 by more than 20%, and in two out of three cases by more than 90%. Introduction. Recent widespread UK floods such as in spring 1998, autumn 2000, winter 2003 and summer 2007 have prompted debate as to whether these particular events are attributable to anthropogenic climate change 6,7, This is an ill-posed question, given uncertainty in the antecedent conditions; many untraceable factors, anthropogenic or natural, may have contributed to any individual event 13,16. Indeed, observed UK fluvial-flood and high-flow trends for recent decades suggest no clear evidence for any change above that of natural variability 17,18, mirroring the mixed picture in observed precipitation changes 19,20. Technical Report No

4 For this reason, only general explanations are usually offered for any expected increase in flooding 15 ; these typically involve thermodynamic arguments for precipitation extremes increasing with atmospheric water vapour in a warming world. Although oversimplified 8,9, these arguments offer a physically plausible first guess. For example, following this simple thermodynamic framework, one may scale observed daily autumn precipitation extremes in England and Wales around the year 2000 by the reduction in atmospheric water vapour had estimated twentieth-century surface warming attributable to anthropogenic greenhouse gas emissions 21,22 not occurred. That suggests the probability of severe daily precipitation for these autumns is roughly 33% higher than had these emissions and resulting warming not occurred (Figs 1, 2). Thermodynamic change in daily precipitation extremes for England and Wales autumns Figure 1. a-d, Each panel identically shows the distribution of observed daily precipitation extremes from autumns (blue circles, with interpolated curve). Non-blue coloured curves are different for each panel and show the distribution of thermodynamically reduced daily precipitation extremes for this same period, which is deduced by scaling down the 90th percentile and above (delineated by the dotted vertical line) of the observed distribution according to the Clausius-Clapeyron relation and pattern-estimates of attributable twentiethcentury surface warming from, HadCM3 (a; brown), GFDLR30 (b; purple), NCARPCM1 (c; pink), and MIROC3.2 (d; orange). Ten such non-blue curves per panel result from the ten Technical Report No

5 amplitude-scalings per pattern-estimate (see Methods). Bars represent 5-95% confidence intervals estimated using a Monte Carlo bootstrap sampling procedure. Figure 2. A range of changes in risk of daily precipitation extremes for England and Wales autumns. Shown is the range of fraction of attributable risk (FAR) of daily precipitation extremes, estimated using the distributions of observed and thermodynamically reduced autumns precipitation of Supplementary Fig. 1. These FAR estimates are made at the 90th percentile of the observed distribution onwards. Black represents the aggregate FAR. Dashed curves mark the 10-90% confidence intervals estimated using a Monte Carlo bootstrap sampling procedure similar to that for Fig. 5. Solid curves mark the best estimate (median) FAR. Right hand axis shows the equivalent increase in risk. Also marked is the aggregate FAR of autumn 2000 flooding estimated in terms of daily runoff using the PEA framework of the main text; with horizontal bars indicating the 10-90% confidence interval and square indicating the best estimate (median), all located on the solid vertical line that denotes the flooding was a 99.87th percentile event in the A2000 climate. Scaling observed precipitation, however, cannot rigorously quantify the change in probability of a specific type of complex weather-related event. Only by explicitly modelling climates encompassing all possible weather states consistent with antecedent uncertainty for the period of interest, both with and without anthropogenic drivers, can one address a wellposed question: what fraction of the event probability is attributable to the anthropogenic drivers 13,16? If we can assume an unchanging relationship between hazard and resulting damage, then event probability becomes a proxy for risk. Such an attribution framework was used to assess the contribution of anthropogenic drivers to European heatwave risk in summer However, that study used a relatively low-resolution climate model with a limited number of simulations, and assumed unchanging Technical Report No

6 variability about an anthropogenic trend in mean summer temperatures. This is not appropriate for UK flooding, which is a smaller spatio-temporal-scale phenomenon subject to greater variability that may change under anthropogenic drivers 2,15. Here we develop this attribution framework, and assess the contribution of twentiethcentury anthropogenic greenhouse gas emissions to flood risk in England and Wales in autumn (September to November) Experiment outline. We use a seasonal-forecast-resolution climate model, and account for any anthropogenic change in variability by generating time-slice simulations under two driving scenarios constructed for autumn 2000: a realistic scenario representing the actual climatic conditions (A2000), and a hypothetical scenario representing the climatic conditions as they might have been had twentieth-century anthropogenic greenhouse gas emissions not occurred (A2000N). The model is HadAM3-N144, with a global horizontal resolution of 1.25 longitude by 0.83 latitude, and 30 vertical hybrid-pressure levels 24. As atmosphere ocean feedbacks were not believed to play a major role during autumn ,25, we use an atmosphere-only model, with sea surface temperatures (SSTs) and sea ice as bottom boundary conditions. The A2000 scenario attempts to represent realistic autumn 2000 conditions in the model by prescribing greenhouse gas and other atmospheric pollutant (sulphate aerosol, ozone) concentrations for that time, as well as prescribing observed 26 SSTs and sea ice (see Methods). The A2000N scenario attempts to represent hypothetical autumn 2000 conditions in the model by altering the A2000 scenario as follows: greenhouse gas concentrations are reduced to year 1900 levels; SSTs are altered by subtracting estimated twentieth-century warming attributable to greenhouse gas emissions, accounting for uncertainty; and sea ice is altered correspondingly using a simple empirical SST sea ice relationship determined from observed 26 SST and sea ice. The attributable SST warming is derived from estimates 21,22 that used well-established optimal fingerprinting analysis 1,2. Specifically, four spatial patterns of attributable warming were obtained from simulations with four coupled atmosphere ocean climate models (HadCM3, GFDLR30, NCARPCM1 and MIROC3.2), and pattern amplitudes and associated uncertainties were constrained by historical observations (see Methods). Hence the full A2000N scenario actually comprises four scenarios with a range of SST patterns and sea ice, reflecting the uncertainty in large-scale anthropogenic greenhouse gas warming. Technical Report No

7 Numerous model simulations are required under both the A2000 and A2000N scenarios to capture what was considered a relatively unpredictable, rare event 3,4,13,16,25. Thus under each scenario we generate an ensemble of several thousand one-year weather simulations covering the autumn 2000 period, with perturbed initial conditions. This is beyond available conventional supercomputing resources, so we used a global, publicly volunteered distributed computing network, using architecture developed under the climateprediction.net project 11,12. The resulting large A2000 and A2000N ensembles of weather simulations respectively constitute our estimates of realistic and hypothetical autumn 2000 climates. Results Autumn 2000 weather was characterized by a general eastwards displacement of the North Atlantic jet stream from its climatological position, bringing intense systems further into western Europe 10. This displacement was associated with a commonplace but anomalously strong Scandinavia atmospheric circulation pattern (a Rossby-wave-like train of tropospheric anomalies in geopotential height, extending from the subtropical Atlantic across Eurasia, with a cyclone over the UK and a strong anticyclone over Scandinavia). This Scandinavia pattern was itself catalysed by anomalous tropical Atlantic and South American upper-tropospheric convergence, and a possible weak secondary northern mid-atlantic SST feedback 10. A regression of mid-tropospheric geopotential height against England and Wales precipitation for all previous autumns ( ) in the observation-based ERA-40 reanalysis 27 certainly yields a structure (Fig. A, left) remarkably similar to the Scandinavia pattern. We use a seasonal-forecast-resolution model that better represents the extra-tropical jets than lower-resolution counterparts typically used for climate simulations 24. Indeed, the ERA-40 pattern is consistent with the analogous synoptic pattern in our A2000 climate (Fig. A, right): it also displays a negative centre over the UK subsumed in a Rossby-wave-like train over the Atlantic-Eurasian region. Although a weak test, because ERA-40 autumns originate from different years with differing conditions whereas A2000 autumns originate from simulations with autumn 2000 conditions alone, this comparison nevertheless provides some confidence in the model s ability to represent the relevant synoptic conditions. Autumn 2000 flood episodes involved sequences of intense weather systems bringing heavy multi-day precipitation pulses to catchments that became saturated 4. Hence we examine Technical Report No

8 daily river runoff, which is a better measure of flooding than total precipitation. We synthesize this runoff using a relatively simple precipitation-runoff model 28, derived from a coupled land-surface and river-routeing scheme with empirically estimated and optimized hydrologic parameters for England and Wales catchments (see Methods). We feed England and Wales total daily precipitation time-series from all our climate model simulations into this model to produce ensembles of synthetic daily river runoff associated with our A2000 and A2000N climates. To test if this runoff adequately represents autumn variability, we compare it with ERA-40 runoff, similarly synthesized using precipitation from all available autumns ( ). Figure 3 demonstrates that England and Wales runoff variability in our A2000 climate is representative of that in ERA-40 autumns over a range of timescales. Power spectra of daily river runoff for England and Wales autumns. Figure 3. Black line shows the spectrum for runoff synthesized from ERA-40 precipitation in all available autumns ( ). Pair of blue lines marks the 5 95% confidence interval of the spectrum for runoff synthesized from all precipitation simulations in the A2000 climate. We compare the runoff ensembles for A2000 and A2000N climates via occurrence frequency (or equivalently, return time ) curves in Fig. 4. A given magnitude of runoff event generally occurs more frequently in the A2000 climate (a decreased return time), and so is more probable in any given autumn, relative to all four estimates of A2000N climate. Technical Report No

9 Change in occurrence frequency of daily river runoff for England and Wales autumn Figure 4. a d, Occurrence frequency curves of runoff (circles) synthesized from all precipitation simulations in A2000 and A2000N climates. Top axis of each panel is equivalent return time. Each panel shows identical A2000 runoff (blue). A2000N runoffs differ, being in climates generated using attributable SST warming estimates from HadCM3 (a; brown), GFDLR30 (b; purple), NCARPCM1 (c; pink) and MIROC3.2 (d; orange), with 10 curves corresponding to equiprobable amplitudes of warming. Bars represent 5 95% confidence intervals (see Methods). Horizontal line marks the highest autumn 2000 runoff synthesized from ERA-40 precipitation (0.41 mm). We thus estimate the fraction of flood risk in England and Wales in autumn 2000 that is attributable to twentieth-century anthropogenic greenhouse gas emissions. This is represented via the change in probability of a severe daily river runoff event, assuming an unchanging relationship between that hazard and resulting damage (this focuses on hydrometeorological contributions to risk: other factors, such as the changing built environment, could also have contributed through changing vulnerability). As the observed floods involved a range of multi-day protracted flows rather than flash events 4, these flows are also reflected in high daily values. Hence we define severe to be anything exceeding the highest observation-based daily runoff for autumn 2000, as synthesized from ERA-40 precipitation (0.41 mm, denoted by the horizontal line in Fig. 4). R and RN are then the Technical Report No

10 fraction of runoff events in the A2000 and A2000N climates respectively that exceed this threshold. It follows that the fraction of attributable risk is FAR = 1 RN/R (refs 13, 16). Uncertainty in this calculation is estimated using a Monte Carlo bootstrap sampling procedure on pairs of A2000 and A2000N runoff ensembles in Fig. 4 (see Appendix A). The resulting distributions of FAR in Fig. 5 (coloured histograms) show significantly (at the 10% level) increased flood risk in the A2000 climate relative to all four A2000N climate estimates. Assuming that these estimates effectively span uncertainty in the true A2000N climate, through the range of attributable SST warming estimates used in generating them, the full increase is given by the aggregate distribution (black histogram). It shows that the increase in risk of occurrence of floods in England and Wales in autumn 2000 that is attributable to twentieth-century anthropogenic greenhouse gas emissions is very likely (nine out of ten cases) to be more than 20%, and likely (two out of three cases) to be more than 90% (all to one significant figure). This assessment assumes that attributable SST warming estimates can simply be subtracted from the SSTs observed in 2000, with seasonal to interannual modes of SST variability otherwise remaining unchanged. Although anthropogenic influence on such modes is indeed very uncertain 1, this assumption of additivity may be inappropriate for events highly dependent on them 29. However, the dependence of UK autumn 2000 precipitation on such modes appears minor 10,25, justifying our approach here. Attributable risk of severe daily river runoff for England and Wales autumn Figure.5 Histograms (smoothed) of the fraction of risk of severe synthetic runoff in the A2000 climate that is attributable to twentieth-century anthropogenic greenhouse gas emissions. Each coloured histogram shows this fraction of attributable risk (FAR) with Technical Report No

11 respect to one of four A2000N climate estimates in Fig. 4 (with corresponding colours). The aggregate histogram (black) represents the FAR relative to the full A2000N climate, with the dot-dashed (solid) pair of vertical lines marking 10th and 90th (33rd and 66th) percentiles. Top axis is equivalent increase in risk. The range of FAR estimated using our explicit-modelling framework (Fig. 5, black histogram) is approximately consistent with the FAR estimated using observations in the simple thermodynamic framework (Fig. 2), and this consistency between approaches of vastly different complexity suggests our results are physically plausible. Allied to this, the range appears independent of any response to rising greenhouse gases of the key atmospheric mode of variability relevant to UK autumnal precipitation (Fig. 6). Hence our results should be relatively insensitive to the choice of modelling tools, but exploring sensitivity to choice of atmospheric and hydrologic model, and SST modes, remains a priority. So does further evaluation of our modelling set-up, although evaluation of extreme event statistics is hampered by limited historical records. We assume that any bias in England and Wales flooding between the A2000 climate and ERA-40 applies identically to the A2000N climate. This assumption is impossible to test explicitly, especially considering that absolute biases can be difficult to assess owing to variation between observation-based values themselves 3,27. Crucially, however, most runoff occurrence frequency curves in Fig. 4 remain approximately linear over a range of extreme values, so our FAR estimate would be consistent over a range of bias-corrected flood thresholds. Conclusions. We have developed a probabilistic event attribution framework that quantifies the anthropogenic contribution to flood risk. We stress that our results relate to autumn 2000-type floods. But other event-types, such as snow-melt floods, might have become less likely under anthropogenic climate change: our framework provides a method for also assessing those likelihoods. Furthermore, just because an event-type becomes more likely does not guarantee it will become even more likely in future but it does highlight a potential impact of climate change. With many purported climate change impacts being reported many related to extreme weather an objective method of distinguishing actual impacts is urgently needed. Our assessment is for the greenhouse gas contribution only: the total anthropogenic contribution would also require consideration of climate drivers such as sulphate aerosols and ozone. Technical Report No

12 Figure 6. As for Fig. 4 but, a, amalgamating the curves (now green) from all four A2000N climate estimates; then grouping all simulations according to the strength of projection (dot product) of their mean autumn 500-hPa geopotential height onto the regression pattern in Fig. A,left over the region bounded 90E, 90N, 90W, 30N, where grouping ranges are defined by the 0-20% (b), 20-40% (c), 40-60% (d), 60-80% (e), and % (f ) pentiles of the distribution of projections of A2000 simulations. However, the recently launched Adaptation Fund, intended to finance climate change adaptation activities in developing nations, operates under the auspices of the United Nations Framework Convention on Climate Change that specifically defines climate change as due to greenhouse gas emissions 30. By demonstrating the contribution of such emissions to the risk of a damaging event, our approach could prove a useful tool for evidence-based climate change adaptation policy. Technical Report No

13 Acknowledgements We thank all members of the public who ran HadAM3-N144 climate model simulations using the BOINC open source computing platform, and the climateprediction.net team for their technical support; M. Collins, N. Rayner, A. Jones and C. Johnson for originally supplying the HadAM3-N144 model, observed SSTs and sea ice, sulphate fields, and ozone fields, respectively; G. Meehl and T. Knutson for permission to use NCARPCM1 and GFDLR30 temperature data, respectively; S. Hay and I. Tracey for assistance with beta tests; C. Lee for technical advice; and W. Ingram and D. Rowlands for scientific advice. P.P. was supported by a NERC CASE studentship with Risk Management Solutions Ltd, by WWF International, and by NCCR climate. D.A.S. and P.P. received partial support from the UK Department for Environment, Food, and Rural Affairs. P.A.S. was supported by the Joint DECC and Defra Integrated Climate Programme DECC/Defra (GA01101). T.N. was supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology. D.A.S. and M.R.A. received additional support from the Climate Change Detection and Attribution Project jointly funded by the US National Oceanic and Atmospheric Administration s Office of Global Programs and the US Department of Energy. This research was also supported by the European Union (FP6) funded Integrated Project WATCH (contract number ) and the Smith School of Enterprise and the Environment. Appendix A. Generating the A2000 climate. All HadAM3-N144 simulations began with a climatological April base state obtained from running the model under average AMIP2 (Atmospheric Model Intercomparison Project number 2) conditions24. For each simulation, this state was initially perturbed via a unique adjustment to its atmospheric potential temperature (but not other variables, owing to distributed computing bandwidth constraints). These perturbations were derived from next-day surface differences in the AMIP2 simulation, and applied to model grid boxes with a vertical taper. Preliminary tests showed almost full divergence between perturbed simulations on all vertical levels within a model fortnight. Each perturbed simulation then ran under the A2000 scenario that prescribed the following conditions in the model for the period April 2000 to March 2001: global-mean time-mean major greenhouse gas and halocarbon concentrations, obtained via the Carbon Dioxide Information Analysis Center 31,32 ; the approximate annual-mean effect of sulphate Technical Report No

14 aerosols, via modification of cloud droplet effective radius using cloud albedo responses to sulphate emissions pre-estimated from versions of the Hadley Centre atmospheric model with an interactive sulphur cycle and predicted cloud droplet number concentration 33 ; zonal-mean monthly-mean ozone, extrapolated from 1990 estimates using a Hadley Centre chemical transport model and chlorine estimates for the troposphere and stratosphere respectively (C. Johnson, personal communication); weekly-mean observed 26 SSTs and sea ice, interpolated to suit the 360-day HadAM3-N144 year. All other conditions (for example, solar forcing, land surface properties) were kept at the base state or at model default settings. All simulations ran under Windows and Linux operating systems, in a global network of publicly-volunteered computers using climateprediction.net 11,12 client-server distributed computing architecture. We fed each completed simulation s England and Wales total daily precipitation timeseries from April 2000 onwards into our precipitation-runoff model 28, to synthesize September 2000 to November 2000 daily river runoff. Thereby we fed both the model s baseflow storage term accounting for preceding long-term processes and the model s convolution filter accounting for preceding short-term processes, in synthesizing the runoff for 1 September onwards. (We also note that for ERA-40, precipitation in non-30-day months is first scaled to accommodate for the 30-day HadAM3-N144 months.) Generating the A2000N climate. All HadAM3-N144 simulations began with initially perturbed April base states similar to those for the A2000 climate. Each perturbed simulation then ran under the A2000N scenario constructed by altering A2000 scenario gases, SSTs, and sea ice, as described below (all other conditions left as in the A2000 scenario). To construct A2000N gases, A2000 greenhouse gas and halocarbon concentrations were reduced to year 1900 annual-mean global-mean estimates taken from historical forcing data sets 34. To construct corresponding A2000N SSTs, A2000 SSTs were altered by subtracting estimated twentieth-century warming attributable to greenhouse gas emissions (Figs 5 7). To construct corresponding A2000N sea ice, A2000 sea ice was altered using the A2000N SSTs, and a simple empirical SST sea ice relationship determined from observed gridded weekly-mean SST and sea ice data 26. Aggregating these observed data over years 2000 to 2001 and all grid boxes, we constructed a scatter plot of sea ice fractional grid box Technical Report No

15 coverage versus SST, for Northern and Southern Hemispheres separately. In each hemisphere we applied a linear fit to the scatter, with one end anchored at the freezing point of sea water corresponding to 100% sea ice coverage. This linear SST sea ice relationship was then applied to the change from A2000 to A2000N SSTs at each HadAM3-N144 grid box, to determine corresponding change in sea ice fractional coverage there. Finally, this sea ice change was subtracted from the A2000 sea ice to produce corresponding A2000N sea ice, and in this way we preserved the scatter characteristics of sea ice coverage. Similarly to the A2000 simulations, all A2000N simulations were generated using distributed computing, and fed into the precipitation-runoff model. Calibrating the precipitation-runoff model. The coupled hydrologic hydraulic scheme operates on a 10-m-resolution digital terrain model, with the hydrologic component strongly based on TOPMODEL35 and the hydraulic component implementing a Muskingum-Cunge scheme. The hydrologic component runs in 3-h time steps (to capture the intra-day evaporation cycle) and was calibrated against observed 36 daily mean river runoff time-series available for The hydraulic component runs in 5-min time steps (mainly for stability) and was calibrated against return period statistics of the observed daily maxima at gauging stations available from as far back as 1883 to Parameters were optimized by minimizing the root-mean-squared error (RMSE) so that mismatches of high deviations (runoff peaks) were more heavily penalized; thus the scheme is expected to perform well for wet periods. The scheme is evaluated in Table 1, via RMSE and correlation against the observed daily mean river runoff for each of the 11 England and Wales catchments. RMSE varies between catchments, with higher values typically reflecting higher mean runoff. Importantly, correlation is good for all catchments and is perhaps a more insightful indicator of performance given the issues with assessing change in absolute biases and extremes noted in the main text. For computational efficiency, we fitted a linear transfer function precipitation-runoff model 28 to 1,000 years of continuous daily river runoff time-series generated with the calibrated scheme, for the largest (area-wise) gauges in each catchment. This transfer function has a fast and slow component, accounting for direct surface runoff and base-flow processes respectively, with the latter incorporating a linear reservoir storage term active from the first day of input precipitation. Technical Report No

16 Evaluation of the coupled hydrologic-hydraulic scheme. Catchment RMSE Correlation Anglian Dee Northumbria North West Severn Solway Tweed South East South West Thames Trent Wales Table 1. Shown are the root-mean-squared error (RMSE) in mm and coefficient of correlation for daily river runoff from the coupled hydrologic-hydraulic scheme against observations 36, for 11 England and Wales catchments. Evaluation is for Area-weighted mean RMSE and correlation across catchments is 0.61 and 0.85 respectively (see Methods). Briefly, after computing each day s storage, fast and slow components are both passed through a convolution filter accounting for their lumped travel times to and within the catchment s river channel. Thus while this filter only has a 12-day memory, longer-term memory is accounted for via the storage term. This approach is reasonable, given that the ground saturated quickly at the beginning of autumn 2000 and remained that way 4, so that while preceding wet spring conditions may have had some importance, shorter-term precipitation dominated flooding. Indeed, changes in 10-day and less rainfall events over recent decades have been implied 37 as being relevant to UK autumnal flooding. The model is evaluated in Table 2, in terms of England and Wales totals across catchments as considered in the main text. We only show correlations, both for the reasons above and because here we are more interested in how accurately precipitation is translated to runoff (that is, high/low runoff following high/low precipitation). The performance is reasonable and, though poorer for extremes reflecting the limitations of a relatively simple transfer function, is comparable to the coupled scheme s performance and is better for autumnal than annual runoff. Technical Report No

17 Evaluation of the precipitation-runoff model. Correlation Correlation Correlation Against scheme Against obs. (all quantiles) ( 75 th quantile) ( 90 th quantile) Annual Autumnal Annual Autumnal Table 1. Shown is the coefficient of correlation for England and Wales total daily river runoff from the precipitation-runoff model, against both the coupled hydrologic-hydraulic scheme and observations 36. This is shown annually and autumnally both for all runoff quantiles, and for all quantiles at or above the 75 th and 90 th quantiles. Evaluation is for (see Methods). Estimating fraction of attributable England and Wales flood risk in autumn 2000 using a simple thermodynamic framework A popular simple thermodynamic argument assumes precipitation extremes are constrained to change with the water vapour capacity of the atmosphere that can be determined, under conditions of constant relative humidity, using change in mean surface temperature alone according to the Clausius-Clapeyron relation 38. This argument is typically invoked in the aftermath of floods as an explanation for possible increases in such severe wet events under an anthropogenically warming climate. While this is an oversimplified treatment 8,9 not fully accounting for the complex hydrometeorology typically associated with UK flooding 4,10,15, it may nevertheless provide a physically plausible first guess of increases in mid-latitude precipitation extremes under warming 39,40,41. Indeed, a recently updated analysis of observed atmospheric column water vapour for past decades finds increasing trends over the UK and western Europe, and a significant autumnal increase more generally over Europe and the Northern Hemisphere 42 ; and this appears in agreement with a similar analysis finding increases in observed atmospheric humidity under warming for these regions that are within expected moistening rates for near-constant relative humidity 43.This latter analysis in particular appears broadly consistent with observations of Clausius-Clapeyron scale increases in surface specific humidity (the principle source for the free-troposphere) under warming over past decades, again with near-constant relative humidity including for an European region incorporating the UK 44,45. Since these surface specific humidity increases have been attributed to mainly Technical Report No

18 anthropogenic drivers 46, this lends support to a thermodynamic mechanism for increasing UK precipitation, and hence flooding, under anthropogenic warming. Here we use this thermodynamic argument to deduce the reduction in observed 3 England and Wales total daily precipitation extremes for an autumn 2000 climate, had estimated 21,22 twentieth-century surface warming attributable to anthropogenic greenhouse gas emissions not occurred. Then regarding this reduction in precipitation extremes as a direct measure of reduction in flooding, we calculate the fraction of attributable risk (FAR) 13,16 of these extremes, and compare it to the FAR of autumn 2000 flooding explicitly modelled in terms of severe daily river runoff using our more rigorous multi-step probabilistic event attribution (PEA) framework of the main text. One limitation of this simple thermodynamic framework is that only the single observed state of precipitation in autumn 2000 is available for sampling extremes in that climate (cf. the PEA framework where many possible states are generated). To try to overcome this we assume observed precipitation from autumns is representative of precipitation under the conditions that obtained in autumn 2000, and hence representative of the climate for that time. Alternative nearby autumns could have been chosen, but we specifically choose these years because the attributable twentieth-century surface warming, according to which the precipitation is to be reduced, is for the 1990s relative to the 1900s (see Methods). The blue curve in Fig. 1 shows the distribution of observed precipitation extremes from autumns Applying the Clausius-Clapeyron relation (which at mid-latitudes typically dictates a change in daily precipitation extremes of approximately 6.5% per degree temperature change 39 ), we scale down the distribution of observed precipitation according to the mean England and Wales portion of the attributable twentieth-century surface warming. Since the relation only applies to precipitation extremes 38 we only scale down precipitation above the 90 th percentile. The resulting distributions of thermodynamically reduced precipitation extremes, had the warming not occurred, are shown by non blue-coloured curves in Fig. 1. Given this reduction in precipitation extremes, we now estimate the FAR of a severe precipitation event in the observed climate and so directly, in this simple framework, of flooding. However, because the precipitation distributions exhibit noise due to limited sampling of extremes in the relatively short observation period, because the Clausius-Clapeyron relation can reasonably apply to a range of extreme percentiles, and because severe is generally not well defined, we consider a range of percentiles above the 90 th percentile of the observed distribution as defining severe precipitation event thresholds, Technical Report No

19 and calculate the FAR each time. Similarly to the main text, we estimate uncertainty in these FAR calculations using a Monte Carlo bootstrap sampling procedure on precipitation in pairs of observed and thermodynamically reduced distributions. Figure 2 shows the variation of FAR with percentile of the observed precipitation distribution. Clearly there is noise due to limited sampling, but the best estimate (median) aggregate FAR is roughly stable at 0.25 (corresponding to a 33% increase in flood risk) which is within range of the aggregate FAR of autumn 2000 flooding estimated using our PEA framework (10-90% confidence interval of the black histogram in Fig. 5 is (1 s.f), as indicated by the horizontal bars in Fig. 2). This consistency of increased flood risk between the simple thermodynamic framework and more rigorous PEA framework supports the physical plausibility of our model-based PEA result. However an exact comparison of attributable autumn 2000 flood risk between frameworks is difficult because the PEA framework s estimate uses a severe event threshold corresponding to approximately a 99.9 th percentile event (horizontal line in Fig. 4 intersects A2000 curve at approximately an one-in-nine-autumn occurrence frequency, as indicated by the solid vertical line in Fig. 2), whereas limited sampling in the simple framework prevents reliable estimates for approximately 99 th percentile events and above. In particular, the simple framework s best estimate aggregate FAR of roughly 0.25 for lower percentile events falls appreciably short of the PEA framework s best estimate FAR of 0.6 (median of the black histogram in Fig. 5 to 1 s.f., as indicated by the square in Fig. 2), and it is difficult to assess whether there would be better agreement were simple framework estimates closer to the 99.9 th percentile possible, and thus whether a thermodynamic change in precipitation extremes is a reasonable determinant of change in flood risk there or if other factors such as dynamics and hydrology become more important. This is an inherent limitation in the simple framework of having only a few observed realisations of precipitation extremes available from which to estimate attributable flood risk and demonstrates why the PEA framework, with many realisations all of which account for thermodynamics, dynamics, and hydrology, can better quantify this risk. Robustness of modelled response to greenhouse gas emissions: thermodynamic versus dynamic contributions The analysis of the last section showed that the response of England and Wales total daily autumn river runoff to twentieth-century anthropogenic greenhouse emissions in an explicit-modelling framework is approximately consistent with a simple thermodynamic response. However, the response in the explicit-modelling framework was generally higher, Technical Report No

20 suggesting that dynamics were tending to reinforce the simple thermodynamic response. This could happen on many scales: from feedback in local moisture convergence to changes in continental-scale circulation regimes. But simulation of the statistics of circulation regimes with climate models, even at a seasonal-forecast resolution such as used here, is strongly model-dependent 47. Here we assess, therefore, to what extent our key results in the main text might have arisen from increasing greenhouse gas emissions inducing a regime-shift in our climate model which would make those results acutely model-dependent. Figure 6a shows the runoff response in going from the A2000N to the A2000 climate, via the change in occurrence frequency curves (identical to those in Fig. 4, but with the curves from all four A2000N climate estimates amalgamated onto a single panel for simplicity). For each climate model simulation contributing to these curves, the prevalence of the weather regime relevant to UK autumn 2000 weather may be represented by the projection of the simulated mean autumn 500-hPa geopotential height onto the observed synoptic structure in Fig. A that is closely related to the Scandinavia circulation pattern 10. So to estimate the impact of any changes in the strength of the Scandinavia pattern on our results, we attempt to first eliminate this impact from the runoff response by extracting and comparing only subensembles of A2000N and A2000 simulations in Fig. 6a having similar autumn-mean projections onto the Scandinavia pattern. Thereby, we isolate changes due only to smaller scale dynamics and thermodynamics. We define similar here as being within the same pentiles of the distribution of projections of A2000 simulations. Figures 6b-f show the runoff response in going from the A2000N to the A2000 climate, with simulations now grouped in sub-ensembles according to the pentile projection ranges (from weakest to strongest projection range respectively). We see that runoff in all A2000 and A2000N sub-ensembles generally increases with projection strength, as would be expected for wetter UK conditions under a stronger Scandinavia pattern 10. Moreover, we see that for A2000 and A2000N sub-ensembles corresponding to the different near-fixed strengths of this weather regime, runoff response is generally similar to that for the full ensemble (Fig. 6a) in which changes in this weather regime were free to also influence that response. This suggests the flood risk response in the full ensemble is dominated by smallscale dynamics and thermodynamics, not by a shift in the occupation-frequency of the key atmospheric mode of variability for UK autumnal precipitation. This gives some assurance that our results regarding FAR would be robust to use of a different (for example, higher resolution) atmospheric climate model: because while thermodynamic responses are generally consistent across models of varying resolution, at Technical Report No

21 least at mid-latitudes 39,40,41, the response of weather regimes to external driving is not even consistent in sign. Hence, although another model might simulate a different response of the Scandinavia pattern to anthropogenic greenhouse gas emissions, our results do not appear to depend on it. Indeed, to reverse our key results, such a hypothetical model would have to simulate a substantial weakening of the Scandinavia pattern in response the emissions, which is the opposite of what is seen in our ensemble. It remains important that we used a climate model capable of simulating the synoptic conditions observed in autumn 2000, including the magnitude of the Scandinavia pattern, but our results do not depend on the simulated response of that pattern to anthropogenic greenhouse gas emissions. While we would strongly welcome efforts by other modelling groups to test our results using other atmospheric models, the above sensitivity studies provide some assurance that our key results are likely to be robust across models. Subtracting twentieth-century SST warming attributable to greenhouse gas emissions To construct A2000N SSTs we subtracted, from the observed 26 A2000 SSTs, estimated twentieth-century warming attributable to greenhouse gas emissions. We did this for all weeks in the April 2000 to March 2001 simulation period, but illustrate the procedure here using autumn (September to November) mean values. Figure 7 shows the autumn mean for the observed A2000 SSTs, as well as sea ice. These gridded weekly-mean observations are supplied with SSTs in the marginal ice zone generated from sea ice coverage using a quadratic relationship and set to -1.8 o C where coverage in a grid box is at least 90% 26. We then spatio-temporally interpolate these observations to suit the HadAM3-N144 model. The attributable twentieth-century greenhouse gas warming in these SSTs cannot be found directly from observations, because observations also contain the signal of both natural (e.g. solar and volcanic) and other anthropogenic (e.g. sulphate aerosol) drivers, and internal variability. Instead we derived this warming from estimates in prior studies 21,22 that used established optimal fingerprinting analysis 1,2. This uses multiple linear regression to compare observed surface temperature change, Y, against that simulated, X, by a climate model under m external drivers (greenhouse gas, sulphate aerosol, solar, volcanic, etc.). Thus Y is considered a linear superposition of separately simulated spatio-temporal responses, X i, to m external drivers, giving m i i( X 1 i νi) ν0 Y (1) Technical Report No

22 where the regression co-efficient i is a scaling factor on the amplitude of each response, i represents noise in each response due to its estimation from a finite sample of simulations, and 0 represents noise in the observations due to natural internal variability of the climate system. Accordingly, the regression is performed in the ( optimal ) direction of maximum signal-to-noise of a response ( fingerprint ) rather than the direction of maximum signal 50. It returns an uncertainty distribution on, and if the hypothesis = 0 can be confidently rejected then the response is detected and the observed change can be attributed in some part to the corresponding driver. Mean autumn A2000 SSTs and sea ice. Figure 7. Observed 27 SSTs are interpolated from the supplied 1 o gridded weekly-mean values to 6-day weekly -mean values suited to the HadAM3-N144 grid and 360-day year, using methods 48,49 attempting to preserve those observed means. The autumn 2000 mean of these regridded 6-day weekly-mean values is shown in a; likewise for sea ice coverage in b. Figure 8 shows uncertainty distributions on for the twentieth-century surface temperature response to greenhouse gas driving, estimated in the prior studies using four coupled atmosphere-ocean climate models (HadCM3, GFDLR30, NCARPCM1, and MIROC3.2). All four distributions demonstrate a response is detected in observed change, with differences reflecting the relative strength of response (for example, the NCARPCM1 is overall highest because the response is weakest in that model). To what extent responses from other differently formulated coupled models are also detectable it is to date undetermined; even though more advanced optimal fingerprinting methods exist 51 to account for such inter-model variance. Likewise it is difficult to assess how this would affect the robustness of our main result (Fig. 5), without repeating our whole study. Here we assumed the four available detected responses, scaled by their respective Technical Report No

23 distribution, effectively span uncertainty in the true twentieth-century surface warming attributable to greenhouse gas emissions. Scaling factors for modelled twentieth-century surface temperature response to greenhouse gas driving. Figure 8. Curves show the uncertainty distribution on the amplitude-scaling factor,, for the twentieth-century surface temperature response to greenhouse gas driving; estimated 21,22 using optimal fingerprinting analysis of HadCM3 (brown), GFDLR30 (purple), NCARPCM1 (pink), and MIROC3.2 (orange) simulations. Solid vertical lines mark deciles of a distribution, ranging from the 5 th to the 95 th percentile. =0 implies a response is not detected in observed change; =1 implies the response is identical to that change. The distributions were estimated for annual responses, but given the timescale of England and Wales autumn 2000 flooding we required seasonal resolution at the very least. In the absence of clear evidence of a trend in the magnitude of the seasonal cycle, we further assumed these scaling factors apply equally to seasonal response patterns. These seasonal patterns were constructed for each coupled model by subtracting surface temperature averaged over a lengthy pre-industrial control simulation having constant external drivers (assumed equivalent to decadal-mean climatology), from the decadal-mean surface temperature averaged over the small ensembles of simulations used in the prior optimal fingerprinting analyses having historical greenhouse gas driving up to the end of that decade. Figure 9 shows our constructed response patterns for autumn. They are generally similar across coupled models due to domination of the land-sea contrast, with differences mainly reflecting different formulations of sea ice. We scale these patterns by deciles of the respective distributions (5 th, 15 th,, 95 th percentiles; solid vertical lines in Supplementary Fig. 8) yielding 10 equiprobable estimates of attributable warming, per coupled model, that are subtracted from the A2000 SSTs. Technical Report No

24 Modelled twentieth-century surface temperature response to greenhouse gas driving. Figure 9. Maps show 1990s decadal-mean autumn surface temperature anomalies, constructed from the average of a small ensemble of historical greenhouse gas driven simulations relative to the average of a lengthy pre-industrial control simulation, using HadCM3 (a), GFDLR30 (b), NCARPCM1 (c), and MIROC3.2 (d). Ideally one would repeat this procedure to construct A2000N sea ice. However, optimal fingerprinting analysis is limited in its ability to detect changes in variables having relatively small spatial coverage and sharp gradients, and both coupled model simulations and early twentieth-century observations of sea ice are unreliable. Instead we used a simple empirical SST-sea ice relationship, determined from observations, to construct sea ice consistent with our constructed A2000N SSTs and ensure it was consistent with the characteristics of sea ice coverage. References 1. Hegerl, G. C. et al. in Climate Change 2007: The Physical Science Basis (eds Solomon, S. et al.) Ch. 9, (Cambridge Univ. Press, 2007). 2. Stott, P. A. et al. Detection and attribution of climate change: a regional perspective. Wiley Interdiscip. Rev. Clim. Change 1, (2010). 3. Alexander, L. V. & Jones, P. D. Updated precipitation series for the U.K. and discussion of recent extremes. Atmos. Sci. Lett. 1, (2000). 4. Marsh, T. J. & Dale, M. The UK floods of : a hydrometeorological appraisal. J. Chart. Inst. Wat. Environ. Mgmt 16, (2002). Technical Report No