Multi-method attribution analysis of extreme precipitation in Boulder, Colorado Eden, JM, Van Oldenborgh, GJ, Hawkins, E & Suckling, EB Published PDF deposited in Coventry University’s Repository Original citation: Eden, JM, Wolter, K, Otto, FEL & Jan Van Oldenborgh, G 2016, 'Multi-method attribution analysis of extreme precipitation in Boulder, Colorado' Environmental Research Letters, vol 11, no. 12, 124009 https://dx.doi.org/10.1088/1748-9326/11/12/124009 DOI 10.1088/1748-9326/11/12/124009 ESSN 1748-9326 Publisher: IOP Publishing Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

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Multi-method attribution analysis of extreme precipitation in Boulder, Colorado

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Environ. Res. Lett. 11 (2016) 124009 doi:10.1088/1748-9326/11/12/124009

LETTER

Multi-method attribution analysis of extreme precipitation inBoulder, Colorado

JonathanMEden1,4, KlausWolter2, Friederike E LOtto3 andGeert Jan vanOldenborgh1

1 RoyalNetherlandsMeteorological Institute (KNMI), De Bilt, Netherlands2 Cooperative Institute for Research in the Environmental Sciences, University of Colorado at Boulder, Boulder, CO,USA3 Environmental Change Institute, University ofOxford, Oxford, UK4 Author towhomany correspondence should be addressed.

E-mail: jonathan.eden@knmi.nl

Keywords: extreme precipitation, extreme value statistics, event attribution

AbstractUnderstanding and attributing the characteristics of extreme events that lead to societal impacts is akey challenge in climate science. Detailed analysis of individual case studies is particularly importantin assessing how anthropogenic climate change is changing the likelihood of extreme events and theirassociated risk at relevant spatial scales. Here, we conduct a comprehensivemulti-method attributionanalysis of the heavy precipitation that led towidespread flooding in Boulder, Colorado in September2013.We provide clarification on the source regions ofmoisture associatedwith this event in order tohighlight the difficulty of separating dynamic and thermodynamic contributions. Using extreme valueanalysis of,first of all, historical observations, we then assess the influence of anthropogenic climatechange on the overall likelihood of one- andfive-day precipitation events across the Boulder area. Thesame analysis is extended to the output of two general circulationmodel ensembles. By combining theresults of differentmethods we deduce an increase in the likelihood of extreme one-day precipitationbut of a smallermagnitude thanwhat would be expected in awarmingworld according to theClausius–Clapeyron relation. For five-day extremes, we are unable to detect a change in likelihood.Our results demonstrate the benefits of amulti-method approach tomaking robust statements aboutthe anthropogenic influence on changes in the overall likelihood of such an event irrespective of itscause.Wenote that, in this example, drawing conclusions solely on the basis of thermodynamicswould have overestimated the increase in risk.

1. Introduction

Episodes of extreme precipitation have recentlyreceived significant attention, both in terms of scien-tific studies and media exposure. Following suchevents, many stakeholders are interested in under-standing whether and to what extent anthropogenicclimate change played a role in the likelihood of suchan event occurring. Given their huge societal cost, theperceived increase in large-scale floods over the courseof the last few decades is of particular interest. On aglobal scale, the atmosphere has become warmer andmoister over the course of the last century andobservations suggest that the extent of this increase inmoisture is largely in linewith the Clausius–Clapeyronrelation of approximately 7% per K [1]. However, the

relationship between atmospheric moisture contentand heavy precipitation is known to exhibit substantialseasonal and regional dependencies, with atmosphericcirculation, vertical stability, and actual moistureavailability regularly playing a more important rolethan the moisture-holding capacity of the atmosphere[2, 3]. Addressing the question of attribution mustthus be placed in a region-specific context that allowsfor results to differ from case-to-case [4]. Previouswork has demonstrated such dependencies, with thelikelihood of heavy precipitation associated withflooding in Thailand [5] andCentral Europe [6] shownto exhibit no detectable change, while heavy rainevents in Southern France [7] and Northern Englandin December 2014 [8] have become more likely. Bycontrast, there are a number of counterexamples: a

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decrease in the likelihood of floods in NorthernEngland in spring [9] and an increase in the likelihoodof pressure patterns associated with low rainfall inSouthernAustralia [10].

The episode of extreme precipitation in andaround Boulder, Colorado that led to widespreadfloods in September 2013 is one such example of ahigh-impact event that established a new record forflooding damages in the state of Colorado. A dailyprecipitation total of 230.6 mm was recorded on 12September 2013 in Boulder, almost double the pre-vious highest annual daily maximum from over a cen-tury of observations, while less than 150 km away, thetown of Fort Carson set a new state record for dailyrainfall with 301.0 mm (http://weather.gov/pub/new24HourRecordColoradoRainfall). Combined withsustained heavy precipitation over a week-long periodand subsequent flooding this resulted in ten fatalitiesand property damages currently estimated at almost$4 billion (http://denverpost.com/2015/09/12/two-years-later-2013-colorado-floods-remain-a-nightmare-for-some/ [3].

In a previous study focusing on a class of eventsclosely resembling that of September 2013, Hoerlinget al [3] found an increase in the intensity of high five-day average precipitable water across the Boulder areato an extent that would be expected from a greateratmospheric moisture capacity in a warming climate.As a result of these thermodynamic consequences, anincrease in the intensity of heavy precipitation over theregion would also be anticipated. However, Hoerlinget al [3] assert that the likelihood of an extreme five-day precipitation event of this nature has likelydecreased as a result of climate change, suggesting acounteracting role of changes in other features of theclimate system including atmospheric circulation.

Recently, Trenberth et al [11] proposed an alter-native framing of the attribution question that seeks toseparate the thermodynamic and dynamic contribu-tions to the likelihood of a given extreme event. Thetwo important differences to previous attribution stu-dies for events similar to the observed case are (1) thefocus on only the thermodynamic component and (2)the consideration of the individual event as observed,not a class of events similar to the observed one. Toillustrate their point, the authors also discuss theBoulder event, strongly suggesting that the attributionquestion should consider the anthropogenic contrib-ution to the role of anomalous Pacific sea surfacetemperature that led to this episode of heavy precipita-tion but excluding any potential influence on atmo-spheric circulation. While Hoerling et al [3] identifiedthe importance of large moisture quantities over theregion, Trenberth et al [11] suggested that a morecomprehensive analysis of the physical mechanisms ofmoisture transport is required in order to fully under-stand the role of climate change in the individualevent.

In order to provide further clarification on some ofthe issues raised in previous work, we conduct a com-prehensive probabilistic event attribution analysis ofthe Boulder heavy precipitation event of September2013. We first of all provide a full diagnosis of thesource and transport of moisture associated with thisevent using back trajectory analysis applied to reana-lysis data. We then apply statistical methods usingextreme value analysis to both historical observationsand the output of two climate model ensembles inorder to assess the influence of anthropogenic climatechange on the likelihood of one- and five-day pre-cipitation events across the Boulder area. In our con-clusions we synthesise the results into attributionstatements.

2.Moisture sources and transport

An extensive report of the heavy rainfall and wide-spread flooding across the Colorado Front Rangeduring September 2013 is given in Gochis et al [12], towhich the reader is directed for a detailed overview ofthe underpinning meteorological mechanisms. Asidentified by the authors, while episodes of precipita-tion leading to flash flooding in this region arerelatively common, it was the persistence and spatialextent of heavy precipitation over the course of a weekthat contributed to the extreme nature of the Septem-ber 2013 event. Gochis et al [12] also describe theprevailing synoptic conditions, characterized by aslow-moving cyclone over the southwestern UnitedStates and a blocking ridge to the north, centred overthe Canadian Rockies. This north–south contrastfostered the development of large-scale atmosphericflow and the drawing of moisture northwards towardColorado. While Hoerling et al [3] acknowledge theabundance of precipitable water across the region,they infer its origin from the southernGreat Plains andthe Gulf of Mexico via 700 hPa flow anomalies (theirfigure 5.1(b)). Trenberth et al [11], in contrast, claimthat the region off the west coast of Mexico was themost important source of moisture associated withthis event based on satellite imagery. Trenberth et al[11] also speculate that anomalous SST in this regionand subsequent record amounts of water vapourwould most likely not have occurred without climatechange. This assertion is key to the argument pre-sented by Trenberth et al [11] that suggests a separa-tion of dynamic and thermodynamic contributions tothe impact of a particular event. Gochis et al [12] alsohighlighted the importance of large-scale tropical SSTin generating anomalous moisture. However, in thiscase, the authors state that such source regions includenot only the eastern tropical Pacific but also theGulf ofMexico.

Here, we seek to provide evidence of the sourceand transport of moisture specifically related to thisheavy precipitation episode using back trajectory

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Environ. Res. Lett. 11 (2016) 124009

analysis following a two-dimensional Lagrangianmethod [13, 14]. For each 6 hourly interval for the per-iod 10–16 September 2013 and each grid cell with pre-cipitation within the target region (107°W–103°W;42°N–38°N), the product of the horizontal wind andatmospheric moisture content was vertically inte-grated to construct a series of upstream atmosphericcolumns up to a period of ten days. All meteorologicalfields were taken from the ERA-interim reanalysis[15]. Figure 1(a) shows the cumulative evaporation ateach grid point that is passed by a trajectory as acontribution to the total diagnosed precipitation.Where a grid point is crossed by two or more trajec-tories, evaporation is summed to give a total. For com-parison, the source regions for all Septemberprecipitation between 1979 and 2012 are shown infigure 1(b). There is strong consistency in the spatialspread of the 2013 trajectories and the most promi-nent evaporation sources appear within the Gulf ofMexico. Net moisture gain (evaporation minus pre-cipitation) is greatest further east across the Straits ofFlorida and parts of the western North Atlantic (notshown). These findings contradict the suggestion ofTrenberth et al [11] based on satellite imagery thatanthropogenically-driven SST anomalies in the east-ern tropical Pacific were the major source of moisture,a conclusion that would also have been expected onthe basis of long term diagnosed source regions forSeptember precipitation (figure 1(b)).

The results shown here, in addition to the findingsof previous work, demonstrate one aspect of the diffi-culty in separating the contributions of dynamic andthermodynamic processes to the likelihood of an eventof this nature. Indeed, limiting the analysis to antici-pated thermodynamic consequences might present amisleading impression of the role of anthropogenicclimate change. A robust attribution statementrequires clear communication of the question that isanswered and an experimental set up that does not

prescribe the answer.While conditioning on aspects ofthe circulation will improve the understanding of theevent itself, a thorough assessment of a change in riskdue to external drivers requires more than one sourceof evidence drawn from both observations and modelsimulations [16]. Such an approach is undertaken withregard to the Boulder September 2013 event in the fol-lowing sections.

3. Trends in return times of extremes

Extreme precipitation in the Colorado area is knownto exhibit large seasonal and regional variability, whichwas reported on by Mahoney et al [17] in a recentpaper. The authors showed that the largest dailyprecipitation episodes east of the Continental Divideinvolve the unimpeded movement of moisture fromthe Gulf of Mexico and occur most likely during thesummer months. However, the study concluded thatextreme precipitation has historically occurredthroughout the year in a state with highly variabletopography and that risk assessment should considerpotential impacts during all seasons. It follows thatattribution analysis should also extend to all times ofyear and cover all areas with extreme precipitationrisks.

Trends in precipitation maxima within the obser-vational record and climate model simulations wereinvestigated. In line with themost damaging aspects ofthe Boulder floods [12] and in order to avoid limitingthe analysis to extreme precipitation events over shortperiods that aremost likely caused by convective activ-ity [17], we consider both one- (RX1day) and five-day(RX5day) maxima. The generalized extreme value(GEV) distribution fitted with annual maxima is acommon approach to statistically modelling the dis-tribution of precipitation extremes [19]. When it isanticipated that the distribution of extremes exhibits adegree of dependence on an external environmental

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(a) (b)

Figure 1. (a)Cumulative contribution of evaporation along diagnosed back trajectories to precipitationwithin the Boulder areaduring the period 10–16 September 2013. All trajectories associatedwith occurrences of precipitationwithin each 6 hourly intervaland at each grid cell within the target region are overlain. (b)Climatological cumulative contribution of evaporation to Septemberprecipitation (1979–2012).

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Environ. Res. Lett. 11 (2016) 124009

process, it is necessary for the distribution parametersto reflect such a dependency. Here, the GEV fit isassumed to scale with a measure of anthropogenic cli-mate change, in this case taken as the global meantemperature smoothed with a 4 year running mean todampen the influence of interannual variability of theclimate system, particularly the El Niño SouthernOscillation. The adjusted location μ′ and scale σ′ para-meters are determined such that the ratio between thetwo remains constant, with an exponential depend-ence on temperature inspired by the Clausius–Cla-peyron relation:

m mam

¢ = ⋅T

exp ,

s sam

¢ = ⋅T

exp ,

where μ and σ are the location and scale parameters ofthe original distribution and α is the linear trend inprecipitation maxima as a function of global meantemperature T. The remaining GEV parameter, ξ, wasassumed to be stationary. Such an approach has beenapplied in previous work in the context of eventattribution (e.g. [6, 8]).

For the observational analysis, all stations withinthe spatial domain 42°–37°N and 105.5°–103°Wwithat least 30 years of data were chosen from the GHCN-D v2 dataset [18]. The north–south dimension waschosen in order to include notable Front Range heavyprecipitation events earlier in the historical record,such as in June 1965 south of Denver. The westernborder more or less follows the Rocky Mountain foot-hills as the mountain stations further to the west havedifferent characteristics [17]. We thus do not studyextremes in the Rocky Mountain area, as these are toodiverse in the observations and depend on orographythat is not resolved in the models. The eastern borderis not too far away as annual maximum rainfall increa-ses to the east. Our definition allows the maximumprecipitation to be considered similarly distributed. AGEV was fitted separately to RX1day and RX5dayaggregated over the set of 116 stations, providing 7452station years for analysis. In each case, we compare theGEV fit when scaled with the globalmean temperatureof 1915 and 2013. The exceptional events of 2013 arenot included in the GEV fit. The uncertainty marginswere estimated using bootstrapping with a sample sizeof 1000. Spatial dependencies between the stationswere taken into consideration using a moving blocktechnique in which, for a given sample station, allremaining stations with RX1day and RX5day pre-cipitation exhibiting a correlation greater than 1/ewith the station in question were included in the sam-ple alongside the original bootstrap. This gives about21 degrees of freedom in the 116 stations for RX1day.For RX5day there are approximately 12 degrees offreedom. This does not affect the central value, butincreases the uncertainty margins to more realistic

values compared to the wrong assumption that all sta-tions are independent.

As a crosscheck, figure 2(a) shows spatial maximaof RX1day and RX5day between 1879 and 2015, high-lighting the exceptional magnitude of the September2013 event with RX1day and RX5day totals of266.7 mm and 391.0 mm respectively in our set of sta-tions. The number of stations in this set is roughlyconstant from 1945 to now, with a slight decline overthe last twenty years. The changes in number of sta-tions imply that we cannot use a fit to establish howrare the event was and whether the probability haschanged.

Figures 2(b), (c) use all data to show differences inthe return levels associated with 1915 and 2013 fitsindicated by the solid blue and red lines respectively.The upper and lower lines indicate the range of the95% confidence interval associated with a given returnperiod. The likelihood of a one-day precipitationannual maximum of the magnitude of the 2013 event,indicated by the horizontal line in figure 2(b), hasincreased by a factor of 1.4 between 1915 and 2013,within a 95% confidence interval range of 1.0–2.0(p<0.05). For the 2013 five-day precipitation max-imum, a larger increase in likelihood is found: 1.9within a range of 1.1–4.1 (figure 2(c)) (p<0.01).These results correspond to an estimated increase inextreme one- and five-day precipitation of 3.8%(within a confidence interval range of −0.6% to10.5%) and 4.8% (within a range of 1.0%–13.7%)respectively. This suggests only a small increase in thelikelihood of extreme precipitation events in thisregion. However, the uncertainty bands make thefindings compatible with both the null result found byHoerling et al [3] and an increase in accordance withthe Clausius–Clapeyron relation as suggested by Tren-berth et al [11].

The same analysis was applied to ensemble outputfrom two general circulation models (GCMs): EC-Earth2.3 and HadGEM3-A. As noted by van Old-enborgh et al [8], extending the analysis to model dataallows us to partially remove the statistical uncertaintyassociated with observations at the expense of greateruncertainty associated with systematic model bias.The spatial resolution of eachmodel is too low to suffi-ciently resolve complex topography and its influenceon daily (and sub-daily) precipitation characteristics.However, it may give an indication of the probabilitieson the plains, even though the grid-box averages of aclimate model have different characteristics than thepoint observations of the station data. Indeed, theGEV fit parameters show that the coarser-resolutionEC-Earth model has a smaller scale parameter σ rela-tive to the location parameter μ compared to theobservations, with the higher-resolutionHadGEM3-Amodel in between these (table 1). The shape para-meters do not differ significantly. In the following, weassume that trends in grid box averages and pointvalues are the same.

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Environ. Res. Lett. 11 (2016) 124009

Figure 2. (a)Annual precipitationmaxima in the analysis domain (1879–2015); (b) return level plot for GEVfitted on observed one-day and (c)five-day precipitationmaxima (1879–2015); (d) return level plot forGEVfitted onEC-EARTH2.3 one-day and (e)five-dayprecipitationmaxima (1860–2015); (f) return level plot for GEVfitted onHadGEM3-A (ANT) one-day and (g)five-day precipitationmaxima (1960–2013) (h) return level plot for GEVfitted onHadGEM3-A (NAT) one-day and (i)five-day precipitationmaxima(1960–2013).

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Analysis of EC-Earth2.3 [20] was applied to a 16-member ensemble at a T159L62 (approximately1.125°×1.125°) resolution for the period1860–2015, following the CMIP5 framework [22]withhistorical conditions for 1860–2005 and RCP8.5 for2006–2015. Figures 2(d), (e) shows the return levels forGEV distributions fitted to simulated precipitationmaxima and scaled with 4 year smoothed global meantemperature from the same ensemble. We find no sig-nificant change in the likelihood of extreme one- orfive-day precipitation episodes between 1915 and2013. The likelihood of a one-day precipitation total ofcomparable magnitude to the 2013 event, indicated bythe horizontal line in figures 2(d), (e), has changed by afactor of between 0.92 and 1.94. Likewise, the like-lihood of a 2013-type five-day precipitation event haschanged within a very similar range (0.87–1.92). Theseresults correspond to a change of between−1.0% and6.4% (−1.2% to 5.9%) in one-day (five-day) extremeprecipitation.

The analysis was repeated for two 15-memberensembles of HadGEM3-A at a N216 (approximately0.833°×0.555°) resolution for the period 1960–2013[21]. The first was driven with observed forcings(including anthropogenic forcings) and sea-surfacetemperatures (hereafter ‘historical’ or ANT). The sec-ond was a ‘counterfactual’ ensemble driven with pre-industrial forcings and sea-surface temperatures(‘historicalNat’ or NAT), and thus representative ofthe evolution of a climate system in a world withoutanthropogenic climate drivers. Again, comparison ismade between the GEV fit scaled to the climates of1915 and 2013. For the historical HadGEM3-Aensemble we find a trend in the likelihood of a 2013-type one-day precipitation event (p<0.1), which isestimated to have changed by a factor of between 0.88and 2.34 (figure 2(f)). This is equivalent to a change inthe magnitude of such events of between −2.6% and16.2%. The five-day precipitation maximum is foundto be between 0.62 and 2.23 times more likely in 2013than 1915 (figure 2(g), although the runs start only in1960 we can set the global mean temperature to thevalue of 1915). This trend is not significantly differentfrom zero, even at p<0.1. This corresponds to achange in the expectedmagnitude of−6.9% to 12.8%.No trends are found in the historicalNat ensemble

either, allowing us to conclude that the natural for-cings have not significant changed the likelihood ofeither one- or five-day precipitation extremes(figures 2(h), (i)).

The differing setups used permit additional analy-sis in which we calculated inter-scenario differencesand deduce any change in probability as a result ofanthropogenic climate change. By comparing the 2013return times in the historical and historicalNat Had-GEM3-A ensembles, we find no change in the like-lihood of a one-day precipitation event similar inmagnitude to that observed in 2013 due to anthro-pogenic emissions. For the five-day precipitationevent, the risk ratio is 0.72 (within a range of0.25–1.22). The large uncertainties do not permit us toconclude that this trend is statistically significant.Unlike in the comparison of the GEV fit scaled to dif-ferent climate in single scenario analysis, the percent-age change in precipitation magnitude is notindependent of the return time for which it is eval-uated. In order to produce uncertainty quantities thatare comparable with the previous observation- andmodel-based analyses, we evaluate the ANT-NAT dif-ferences in themagnitude of precipitation events asso-ciated with a 100 year return time. For one-dayprecipitation, the degree of change is almost zero(−0.2%) with a large uncertainty range (−10.7% to11.1%) but the magnitude of five-day precipitationtotals appears to have decreased (−9.0% within arange of −18.8% to 1.0%). The suggestion in thismodel that the magnitude of five-day precipitationextremes has decreased in response to climate changeis broadly consistent with previous work [3].

4. Summary and conclusion

A multi-method approach in attribution analysis hasthe potential to increase confidence in results but theinterpretation of findings that are either contradictoryin nature or associated with large uncertainties isproblematic. Here, both observation- and model-based methods were used to conduct a probabilisticattribution analysis of the extreme precipitation eventthat led to widespread flooding in the Boulder regionof Colorado in September 2013. Trends in one- and

Table 1. Summary of theGEV fits for observation- andmodel-based data: the location μ, the scale σ and the shape ξparameters of theGEV fit for 2013. Confidence intervals (95%) shown in brackets.

RX1day μ σ σ/μ ξ

Observations 33.6 (32.8K 34.1) 12.4 (12.0K12.8) 0.370 (0.358K0.385) 0.070 (0.067K0.121)EC-Earth2.3 21.7 (21.3K21.9) 5.9 (5.7K6.2) 0.274 (0.263K0.285) 0.071 (0.034K0.102

HadGEM3-A 33.3 (32.5K34.2) 10.6 (9.9K11.3) 0.319 (0.295K0.341) 0.164 (0.103K0.228)

RX5day μ σ σ/μ ξ

Observations 10.3 (10.1K10.5) 3.8 (3.7K3.9) 0.372 (0.357K0.385) 0.034 (0.016K0.071)EC-Earth2.3 8.5 (8.4K8.6) 2.1 (2.0K2.2) 0.247 (0.235K0.255) 0.041 (0.019K0.08)HadGEM3-A 11.5 (11.3K11.9) 3.4 (3.3K3.7) 0.296 (0.281K0.325) 0.094 (0.044K0.165)

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Environ. Res. Lett. 11 (2016) 124009

five-day precipitation events of similar magnitude tothe September 2013 event have been investigated bycomparing the climate of 2013 with that of either 1915or a counterfactual world absent of anthropogenicforcings.

A summary of the risk ratios calculated for eachmethod is given in figure 3. Figure 4 summarizes theequivalent change in the magnitude of extremes inpercentage terms, allowing a direct comparison withthe change that would be expected in a warming worldin line with the Clausius–Clapeyron increase of themoisture-holding capacity of the atmosphere (6%–

7%/K) for a warming since the pre-industrial era of1 K, which is roughly what is observed world-wide.Regional Jun–Sep trends differ from 0.8 times the glo-bal mean in the source region of this event, the Gulf of

Mexico, to 1.5 times the global mean in the coastalPacific that corresponds to the climatological sourceand in Colorado itself. In both figures 3 and 4, weinclude the multi-method average weighted againstthe degree of uncertainty associatedwith eachmethod.Note that this only includes the uncertainty due to nat-ural variability and not the model uncertainty, so thetrue uncertainty range is larger. However, it was notpossible to estimate the model uncertainty with thedata available. A chi-squared goodness of fit test wasused to assess consistency among methods. As themodel spread is comparable to the natural variabilityin RX1day (χ2=1.07) and notmuch larger in RX5day(χ2=1.38) the model uncertainty is estimated not tobe larger than the uncertainty due to natural varia-bility. This also validates the assumption that the

Figure 3. Summary of risk ratios for ((a); top) one- and ((b); bottom)five-day precipitation derived from the four differentmethodsdescribed in section 3 and themulti-methodweighted average. Each bar is representative of the 95%confidence intervals. The centralvalues, indicated by the solid black lines, represent the risk ratiowhen applied to all data prior to resampling.

Figure 4. Summary of percentage change in themagnitude of ((a); top) one- and ((b); bottom)five-day precipitation derived from thefour differentmethods described in section 3 and themulti-methodweighted average. Each bar is representative of the 95%confidence intervals. The central values, indicated by the solid black lines, represent the percentage changewhen applied to all dataprior to resampling. The red dashed lines indicate the expected range of change in linewith an increase globalmean temperaturebetween 1915 and 2013 according to the Clausius–Clapeyron relation (6%–7%).

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Environ. Res. Lett. 11 (2016) 124009

trends in grid box averages are similar to the trends instation data, at least to the level discernible in the nat-ural variability.

For one-day precipitation, all results are compa-tible with a modest increase in the likelihood ofextremes (figure 3(a)). Themagnitude is less thanwhatwe would expect due to thermodynamics alone. Onthe low side, the 95% uncertainty range among meth-ods includes no change in extremes (figure 4(a)). Forfive-day precipitation, while a significant trend isfound in the observed record, no trend is apparent inany of themodel-basedmethods.We conclude that wecannot detect a change in the likelihood of five-dayprecipitation extremes as a result of anthropogenic cli-mate change (figure 3(b)) and that it is less than expec-ted by the Clausius–Clapeyron relation alone(figure 4(b)).

Clearly, while there is considerable uncertainty inthe results shown, their collation suggests thatdynamic effects and/or local forcings may exert acounteracting influence on the changing likelihood ofextremes in a warming world beyond simple thermo-dynamics. It should not be unexpected that anthro-pogenic climate change has altered relationshipsbetween large-scale drivers and local events. A so-called conditional approach to attribution may seek toaddress this issue specifically and remains an impor-tant means by which to understand the mechanismsinvolved. However, the diagnosis of moisture sourcesand transport detailed in section 2 illustrates theBoulder event as an example where there are incon-sistencies in the conclusions of different approachesseeking to understand the large- and local-scale lin-kages. In the meantime, most stakeholders are ulti-mately interested in defining an event in terms of thedamage caused and attribution analysis aiming toanswer questions of most relevance to stakeholdersshould instead follow a holistic approach in order toprioritise an understanding of the changes of overallrisk rather than the contribution of different fac-tors [16].

While increases in the frequency andmagnitude ofprecipitation extremes as a result of a warming worldare anticipated on a global scale, the understanding ofregion- and case-specific changes remains a key chal-lenge in climate science. The extent to which the eva-luation of the risk of such changes should beconditional on different contributory factors has beenthe topic of recent debate (e.g. [11, 16, 23]). In the caseof the extreme precipitation event in Boulder, it waspossible to draw reasonably robust conclusions aboutthe influence of anthropogenic climate change on theoverall likelihood of an event of such amagnitude irre-spective of its cause, showing that thermodynamicsalone would have overestimated the increase in risk.Ultimately, to be of maximum benefit to the stake-holder, attribution studies should clearly state theassumptions made at their outset, particularly ifthe attribution is conditional upon rather than

independent of a prescribed set of meteorologicalcircumstances.

Acknowledgments

This research was funded by the European Union’sSeventh Framework Programme for research, techno-logical development and demonstration under theEUCLEIA project (grant agreement no. 607085).

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