LETTERSPUBLISHED ONLINE: 16 JANUARY 2017 | DOI: 10.1038/NCLIMATE3201

Future increases in extreme precipitation exceedobserved scaling ratesJiawei Bao*, Steven C. Sherwood*, Lisa V. Alexander and Jason P. Evans

Models and physical reasoning predict that extreme precip-itation will increase in a warmer climate due to increasedatmospheric humidity1–3. Observational tests using regressionanalysis have reported a puzzling variety of apparent scalingrates includingstrongrates inmidlatitude locationsbutweakornegative rates in the tropics4,5. Here we analyse daily extremeprecipitation events in several Australian cities to show thattemporary local cooling associated with extreme events andassociated synoptic conditions reduces these apparent scalingrates, especially in warmer climatic conditions. A regionalclimate projection ensemble6 for Australia, which implicitlyincludes these e�ects, accurately and robustly reproducesthe observed apparent scaling throughout the continent fordaily precipitation extremes. Projections from the samemodelshow future daily extremes increasing at rates faster thanthose inferred from observed scaling. The strongest extremes(99.9th percentile events) scale significantly faster thannear-surface water vapour, between 5.7–15% ◦C−1 dependingonmodel details. This scaling rate is highly correlated with thechange in water vapour, implying a trade-o� between a morearid future climate or one with strong increases in extremeprecipitation. These conclusions are likely to generalize toother regions.

Intensification of precipitation extremes is expected to occur in awarmer climate as the saturation water vapour pressure increaseswith temperature at a rate of roughly 6% ◦C−1 at the surface or7–8% ◦C−1 in the column integral, as governed by the Clausius–Clapeyron (C–C) relation1,7. Increase of extreme precipitation hasbeen confirmed in numerous modelling studies2,3,8–11, but the rateof this remains uncertain. Global climate models (GCMs) projectdaily precipitation extremes to increase at below the C–C rate inthe extra-tropics, but there is large model range in the tropics, withsome models predicting super C–C increases2,8 in some regions.GCMs poorly represent the distribution of rain rate and mayunderestimate the sensitivity of precipitation extremes in responseto warming12. Increases of daily and hourly precipitation extremesin convection-permittingmodels have generally shown rates around7% ◦C−1 (refs 3,9,11), but a variety of scaling rates (including superC–C) have also been found depending onmicrophysics scheme andtemperature13. However, most convection-permittingmodel studiesfocusing on precipitation extremes have been conducted only insmall regions that cannot capture synoptic-scale organizations9,13.

It would be desirable to constrain the dependency of extremeprecipitation on temperature using observational records. Recentlya simple ‘binning method’ has been widely used to relate dailyor sub-daily extreme precipitation to local temperature4,5,11,14. Onthe basis of this approach, different scaling behaviour has beenfound in different places. For hourly up to six-hourly extremeprecipitation, increases at or above the C–C rate have been found in

the Netherlands14, Switzerland15, Germany16, the Mediterranean17,the UK18, southern Australia4, North America19 and China20, whilein northern Australia strong negative rates have been observed4. Fordaily extremes, monotonically positive scaling has been found athigh latitudes and monotonically negative scaling in the tropics5.This scaling also shows distinct seasonal characteristics, withpositive rates in winter and negative rates in summer in Europe21.

The decrease in wet-event duration and decline in relativehumidity at high temperatures have been proposed to explain thenegative scaling relations4,5,22. Differences in scaling relations havealso been attributed to seasonal dependencies and changes in thefrequency of large-scale versus convective rain21,23.

In contrast, long-term trends in observed annual maximumdaily precipitation over land suggest higher scaling rates in thetropics than in the midlatitudes, although uncertainties arise fromnatural variability and limited data availability in the tropics7,24,25.Higher scaling rates in the tropics have also been projected bysome GCMs26. Thus, the scaling relations remain debatable, ascontradictory results have been found especially in the tropics. Sinceprecipitation extremes do not necessarily scale with local surface airtemperature7,27 and potential confounding factors discussed belowthat may affect temperature and precipitation are ignored in thebinning method, the question remains: Do conclusions drawn fromthis method accurately represent the influence of warming onextreme precipitation?

We start by estimating the spatial distribution of ‘apparentscaling rate’, or regression slope between 99th percentile wet-day precipitation and daily mean temperature as reported inprevious studies using the binning method. Daily precipitation andnear-surface air temperature data are from the Australian WaterAvailability Project (AWAP)28. Similarly to previous studies4, wefind negative scaling rates of up to −50% ◦C−1 over northernAustralia and positive rates of up to +16% ◦C−1 over southernAustralia (Fig. 1a). In winter there are stronger positive scaling ratesin southern Australia (Fig. 1b). In summer, negative scaling ratesprevail in most regions, even in places where there are positivescaling rates when calculated over the entire year (Fig. 1c).

To find out why there are opposite trends across the Australiancontinent and different seasonal trends, we focus on three specificlocations, Darwin, Sydney andMelbourne. In tropical Darwin, thereis a negative scaling rate (Fig. 1a), whereas in cooler Melbourne, theapparent scaling rate is positive at temperatures up to about 12 ◦C,and flat or slightly declining at higher temperatures (SupplementaryFig. 2c,f). Although not obvious in the Sydney data (SupplementaryFig. 2b,e), a change from positive to negative scaling abovesome threshold temperature has been noted in both daily andhourly precipitation extremes in previous observational studies4,5and in hourly precipitation extremes in a modelling study11.Some studies have attributed the turnaround to relative humidity

Climate Change Research Centre and ARC Centre of Excellence for Climate System Science, University of New South Wales, Sydney,New South Wales 2052, Australia. *e-mail: jiawei.bao@student.unsw.edu.au; s.sherwood@unsw.edu.au

NATURE CLIMATE CHANGE | ADVANCE ONLINE PUBLICATION | www.nature.com/natureclimatechange 1

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

LETTERS NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE3201

Darwin

Sydney

Melbourne

10a b c

20

30

40

120

−21 −14 −7 0 7 14 21 −21 −14 −7 0 7 14 21 −21 −14 −7 0 7 14 21

140Longitude (° E)

120 140Longitude (° E)

120 140Longitude (° E)

Latit

ude

(° S

)

10

20

30

40

Latit

ude

(° S

)

Latit

ude

(° S

)

10

20

30

40

Figure 1 | Spatial distributions of apparent scaling of extreme precipitation with temperature. a–c, Apparent scaling given by regression slopesα1 (% ◦C−1) between 99th percentile daily precipitation and daily mean temperature from all data (a), wintertime (b, June–August) and summertime(c, December–February) in AWAP. The locations of Darwin, Sydney and Melbourne are marked (b). White indicates grids without enough wet days forthe analysis.

−9 −6 −3

Time (d)

Dai

ly m

ean

tem

pera

ture

(°C)

Dai

ly m

ean

tem

pera

ture

(°C)

0 3 6 9 −9 −6 −3

Time (d)

31a b c

30

29

28

27

26

25

Dai

ly m

ean

tem

pera

ture

(°C)

27

24

21

18

15

12

90 3 6 9 −9 −6 −3

Time (d)

0 3 6 9

21

18

15

12

9

6

3

Figure 2 | Evolution of composite extreme events. a–c, Time series of daily mean temperature in AWAP from seven days before to seven days afterextreme events in Darwin (a), Sydney (b) and Melbourne (c). Di�erent colours from darkest blue (coolest) to darkest red (warmest) represent meanevolution of cases in 12 di�erent temperature bins.

decrease4,11, but did not explain why humidity falls in the hightemperature bins.

To gain insight, we examine more closely the extremeprecipitation events in each temperature bin. In Sydney andMelbourne, events in the coolest bin happened mostly in winter,while those in the warmest bin are mainly from summer. Thisimplies that seasonal variations of extreme precipitation dominatethe apparent scaling. However, it is a completely different case inDarwin, where extreme precipitation events are all from Australsummer as there is very little rain in winter. In addition, the entire99th percentile and over half of the 95th percentile precipitationevents in the coolest bin in Darwin are tropical cyclone events.

We analyse time series of daily precipitation and temperaturefor individual 95th percentile precipitation events, from seven daysbefore to seven days after the events. The 95th percentile is selectedto increase the sample size (results are similar but noisier for the99th percentile). In Darwin, extreme precipitation reaches 150mmfor the coolest events, and decreases as the event temperatureincreases (Supplementary Fig. 3a). For events in cool bins,temperature starts to decrease up to three days before the extremeprecipitation day and returns to normal shortly afterwards (Fig. 2a).Most of the extreme events in the coolest bin are associated withtropical cyclones and this transient cooling can be as high as 4 ◦C.

Lower temperatures are widely associated with storms and canarise both from local saturated downdraughts and evaporativecooling of the rain itself and from synoptic atmospheric propertiessuch as colder air found generally in low-pressure systems. Theseeffects cause near-surface air to be cooler during, for example,

monsoon periods29 and after storms even over oceans30. Thus,statistics reflect not only how surface air properties affect extremeprecipitation, but how atmospheric conditions correlated withprecipitation affect surface air properties31. This confounding effectis a fundamental problem for use of the binning method to infersensitivity, which assumes one-way causality.

Indeed, results can be profoundly altered by rapid changes insurface air properties during precipitation extremes32. This rapidcooling, and/or earlier cooling associated with precursor synopticconditions shifts many events to lower temperature bins. Therefore,the warmest bins are populated only by events with a weakercooling effect or even warming (Fig. 2a). However, events withless cooling are also those with less rain. The result is a negativeapparent scaling in Darwin, where the weather-related cooling iscomparable to the background temperature variations of only afew degrees.

By contrast, in Sydney and Melbourne the range of backgroundtemperatures is so large, due mostly to the seasonal cycle (Fig. 2b,c),that this bin-shifting has less impact on apparent scaling. Weather-related temperature swings still occur, particularly in Melbournewhere the cooling occurs before rainfall, but is smaller than thebackground temperature range. Thus, temporary cooling cannotshift extreme events all the way to the lowest temperature bins,contributing instead to an intermediate peak in the scalingrelationship. The temperature swings differ from those in Darwin,with a cold anomaly deepening during the peak rain and persistinglonger afterward, reflecting the different character of midlatitudeversus tropical weather. In Sydney, strong rains typically coincide

2

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

NATURE CLIMATE CHANGE | ADVANCE ONLINE PUBLICATION | www.nature.com/natureclimatechange

NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE3201 LETTERS

120

−21 −14 −7 0 7 14 21

140

Longitude (° E)

120 140

Longitude (° E)

120 140

Longitude (° E)

Latit

ude

(° S

)10

20

30

40

Latit

ude

(° S

)

10a b c

20

30

40

Latit

ude

(° S

)

10

20

30

40

0.80.40.0 1.2 1.6 2.0 2.4 −14 −7 0 7 142.8

Figure 3 | Apparent versus climate scaling in simulations. a, Ensemble mean of 99th percentile apparent scaling rates (% ◦C−1) from NARCliM historicalsimulations. b, Changes in simulated mean temperature (◦C) between 2060–2079 and 1990–2009. c, Ensemble mean of 99th percentile climate scalingrates (% ◦C−1).

15a b

12

9

6

3

00 15129

Near-surface water vapour (% °C−1)

Prec

ipita

tion

extr

emes

(% °C

−1)

Prec

ipita

tion

extr

emes

(% °

C−1)

6

ECHAM5 R1

ECHAM5 R2

ECHAM5 R3

MIROC3.2 R1

MIROC3.2 R2

MIROC3.2 R3

CCCMA3.1 R1 CSIRO-Mk3.0 R1

CSIRO-Mk3.0 R2

CSIRO-Mk3.0 R3

ENSEMBLE

CCCMA3.1 R2

CCCMA3.1 R3

3

Column water vapour (% °C−1)

15

12

9

6

3

00 1512963

Figure 4 | Extreme precipitation versus water vapour in simulations. a,b, Fractional changes in the 99.9th percentile precipitation for each model versuschanges in near-surface water vapour (a) and column water vapour (b). Solid lines correspond to identity lines.

with strong advection of humid (but not especially warm) air fromthe Pacific Ocean33, probably reducing the apparent scaling inSydney and other east-coastal regions (Fig. 1c).

The negative apparent scaling rate in Darwin has also beenreported in other tropical regions5. Likewise, the small range ofbackground temperature variations found at Darwin, which allowtemporary cooling to have such a large effect on apparent scaling,is characteristic of the tropics as a whole. Thus, we expect thatthe substantial alteration of apparent scaling in Darwin is typicalthroughout the tropics. This alteration will also affect midlatituderegions such as Sydney and Melbourne especially if calculated onlyfrom summer data (Supplementary Fig. 4).

In general, we conclude that to relate ‘apparent scaling’ to climatesensitivity of extremeprecipitationwill require amodel that includesconfounding atmospheric factors and explicit seasonality.

For this, we turn to regional climate model simulationsfrom the New South Wales-Australian Capital Territory Regional

ClimateModeling (NARCliM)Project6.While these simulations useconvective parameterization schemes similar to those used inGCMsand the resolution is relatively coarse, which could limit the fidelityof extreme precipitation10,15, we employ an ensemble of modelversions that have been shown to simulate extreme precipitationevents at regional scales well across a variety of metrics34. First,we apply the same binning method discussed above to the modelsimulations. The geographic patterns of apparent scaling simulatedin both present-day (Fig. 3a) and future scenarios (SupplementaryFig. 5) are very similar to those in present-day observations (Fig. 1a).

On the basis of this apparent scaling, one might expect futuredaily extreme precipitation to decrease in northern Australia, sincetemperature is projected to increase (Fig. 3b). However, when welook at the ‘climate scaling rate’, we find a consistent increase ofextreme precipitation across the Australian continent (Fig. 3c). Theensemble mean 99th percentile climate scaling over the continent is5.7% ◦C−1, almost equal to the 6.1% ◦C−1 increase in near-surface

NATURE CLIMATE CHANGE | ADVANCE ONLINE PUBLICATION | www.nature.com/natureclimatechange

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

3

LETTERS NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE3201

water vapour. However, higher percentile extremes increase at astronger rate (Supplementary Fig. 6). The ensemble mean 99.5thand 99.9th climate scaling rates are 6.5% ◦C−1 and 9.2% ◦C−1(Supplementary Table 2).

The rate of change in predicted near-surface and column watervapour averaged over the continent varies within the ensemblefrom 2.8% ◦C−1 to 10.5% ◦C−1 for near-surface and 3.7% ◦C−1to 11.8% ◦C−1 for total column (Supplementary Table 2). Thesedifferences are strongly associated with differences in futureAustralian precipitation (correlation coefficient between columnwater vapour change and mean precipitation change r= 0.96) andrelative humidity (Fig. 4).

Daily precipitation extremes have been shown to scale on averagewith near-surface water vapour in Coupled Model IntercomparisonProject phase 3 models35, but in some models scaling can exceedeven that of column water vapour (CWV) for very high percentileevents. In our simulations, 99.9th percentile events scale faster thannear-surface water vapour (Fig. 4a) and usually even faster thanCWV (Fig. 4b), consistently across a range of humidity changes. Theensemble mean 99.9th climate scaling rate is 9.2% ◦C−1, comparedwith 7.4% ◦C−1 for CWV. The ensemblemeanCWVchange over thecontinent is consistent with the global average change, suggestinga typical low- to midlatitude climate scaling over land of around7% ◦C−1 globally.

We attempted to minimize the cooling artefacts on the binningmethod by sampling the temperature one or two days priorto the extreme precipitation. This produced a weaker negativeapparent scaling relation in Darwin (Supplementary Fig. 7b), butdid not bring the result close to the model’s climate scaling.This is probably due to the influence of atmospheric variations(for example, monsoons and El Niño cycles) on timescaleslonger than a few days29. Excluding tropical cyclones does notsignificantly affect results (Supplementary Fig. 7c). We alsoexamined near-surface dew point temperature and found that,while less obviously affected by storms than temperature, this airproperty also produces inconsistent apparent versus climate scalings(Supplementary Fig. 8).

In summary, we find that regional climate models cansuccessfully explain the puzzling observation-based estimatesof the temperature scaling of daily extreme precipitation, andindicate that climate scaling is strong, geographically consistent,and comparable to changes in precipitable water36. Inconsistenciesin the observational estimates arise because of seasonal effects andthe impact of local atmospheric processes on local near-surfaceair properties. Future daily precipitation extremes are projected toincrease faster than has been inferred by such observation-basedstudies or most model studies, exceeding the surface C–C scalingfor the very strong events. We find that 2 ◦C warming wouldproduce 11.3–30% (11.3–25% if excluding MIROC3.2 R3) increase,while 4 ◦C would produce 22.6–60% (22.6–50% if excludingMIROC3.2 R3) increase in 99.9th percentile (once per three years)rainfalls on average across Australia.

Less severe scaling rates are associated with reduced relativehumidity and mean rainfall, which implies increased aridity37, suchthat our projections imply a trade-off between amore arid climate orone with strong increases in extreme precipitation. In other words,while important uncertainties remain, our simulations suggest thatrainfall characteristics cannot avoid significant change of one kindor another. The Australian continent spans tropical andmidlatituderegimes and we expect our conclusions to hold more broadly acrossother continental regions.

MethodsMethods, including statements of data availability and anyassociated accession codes and references, are available in theonline version of this paper.

Received 18 August 2016; accepted 7 December 2016;published online 16 January 2017

References1. Trenberth, K. E., Dai, A., Rasmussen, R. M. & Parsons, D. B. The changing

character of precipitation. Bull. Am. Meteorol. Soc. 84, 1205–1217 (2003).2. O’Gorman, P. A. & Schneider, T. The physical basis for increases in

precipitation extremes in simulations of 21st-century climate change.Proc. Natl Acad. Sci. USA 106, 14773–14777 (2009).

3. Ban, N., Schmidli, J. & Schär, C. Heavy precipitation in a changing climate:Does short-term summer precipitation increase faster? Geophys. Res. Lett. 42,1165–1172 (2015).

4. Hardwick Jones, R., Westra, S. & Sharma, A. Observed relationships betweenextreme sub-daily precipitation, surface temperature, and relative humidity.Geophys. Res. Lett. 37, L22805 (2010).

5. Utsumi, N., Seto, S., Kanae, S., Maeda, E. E. & Oki, T. Does higher surfacetemperature intensify extreme precipitation? Geophy. Res. Lett. 38,L16708 (2011).

6. Evans, J. P. et al . Design of a regional climate modelling projection ensembleexperiment–NARCliM. Geosci. Model Dev. 7, 621–629 (2014).

7. O’Gorman, P. A. Precipitation extremes under climate change. Curr. Clim.Change Rep. 1, 49–59 (2015).

8. Kharin, V. V., Zwiers, F. W., Zhang, X. & Wehner, M. Changes in temperatureand precipitation extremes in the CMIP5 ensemble. Climatic Change 119,345–357 (2013).

9. Muller, C. J., O’Gorman, P. A. & Back, L. E. Intensification of precipitationextremes with warming in a cloud-resolving model. J. Clim. 24,2784–2800 (2011).

10. Kendon, E. J. et al . Heavier summer downpours with climate change revealedby weather forecast resolution model. Nat. Clim. Change 4, 570–576 (2014).

11. Chan, S. C., Kendon, E. J., Roberts, N. M., Fowler, H. J. & Blenkinsop, S.Downturn in scaling of UK extreme rainfall with temperature for future hottestdays. Nat. Geosci. 9, 24–28 (2016).

12. Allan, R. P. & Soden, B. J. Atmospheric warming and the amplification ofprecipitation extremes. Science 321, 1481–1484 (2008).

13. Singh, M. S. & O’Gorman, P. A. Influence of microphysics on the scaling ofprecipitation extremes with temperature. Geophys. Res. Lett. 41,6037–6044 (2014).

14. Lenderink, G. & Van Meijgaard, E. Increase in hourly precipitation extremesbeyond expectations from temperature changes.Nat. Geosci. 1, 511–514 (2008).

15. Ban, N., Schmidli, J. & Schär, C. Evaluation of the convection-resolvingregional climate modeling approach in decade-simulations. J. Geophys. Res.Atmos. 119, 7889–7907 (2014).

16. Berg, P., Moseley, C. & Haerter, J. O. Strong increase in convective precipitationin response to higher temperatures. Nat. Geosci. 6, 181–185 (2013).

17. Drobinski, P. et al . Scaling precipitation extremes with temperature in theMediterranean: past climate assessment and projection in anthropogenicscenarios. Clim. Dynam. https://dx.doi.org/10.1007/s00382-016-3083-x (2016).

18. Blenkinsop, S., Chan, S. C., Kendon, E. J., Roberts, N. M. & Fowler, H. J.Temperature influences on intense UK hourly precipitation and dependency onlarge-scale circulation. Environ. Res. Lett. 10, 054021 (2015).

19. Shaw, S. B., Royem, A. A. & Riha, S. J. The relationship between extreme hourlyprecipitation and surface temperature in different hydroclimatic regions of theUnited States. J. Hydrometeorol. 12, 319–325 (2011).

20. Miao, C., Sun, Q., Borthwick, A. G. & Duan, Q. Linkage between hourlyprecipitation events and atmospheric temperature changes over China duringthe warm season. Sci. Rep. 6, 22543 (2016).

21. Berg, P. et al . Seasonal characteristics of the relationship between dailyprecipitation intensity and surface temperature. J. Geophys. Res. 114,D18102 (2009).

22. Lepore, C., Veneziano, D. & Molini, A. Temperature and CAPE dependence ofrainfall extremes in the eastern United States. Geophys. Res. Lett. 42,74–83 (2015).

23. Berg, P. & Haerter, J. O. Unexpected increase in precipitation intensity withtemperature—A result of mixing of precipitation types? Atmos. Res. 119,56–61 (2013).

24. Westra, S. et al . Future changes to the intensity and frequency of short-durationextreme rainfall. Rev. Geophys. 52, 522–555 (2014).

25. Westra, S., Alexander, L. V. & Zwiers, F. W. Global increasing trends in annualmaximum daily precipitation. J. Clim. 26, 3904–3918 (2013).

26. O’Gorman, P. A. Sensitivity of tropical precipitation extremes to climatechange. Nat. Geosci. 5, 697–700 (2012).

27. Dettinger, M. Climate change, atmospheric rivers, and floods in California–amultimodel analysis of storm frequency and magnitude changes. J. Am. WaterResour. Assoc. 47, 514–523 (2011).

28. Jones, D. A., Wang, W. & Fawcett, R. High-quality spatial climate data-sets forAustralia. Aust. Meteorol. Oceanogr. J. 58, 233–248 (2009).

4

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

NATURE CLIMATE CHANGE | ADVANCE ONLINE PUBLICATION | www.nature.com/natureclimatechange

NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE3201 LETTERS29. Kullgren, K. & Kim, K. Y. Physical mechanisms of the Australian summer

monsoon: 1. Seasonal cycle. J. Geophys. Res. 111, D204104 (2006).30. Sherwood, S. C. & Wahrlich, R. Observed evolution of tropical deep convective

events and their environment.Mon. Weath. Rev. 127, 1777–1795 (1999).31. Waliser, D. E. & Graham, N. E. Convective cloud systems and warm-pool sea

surface temperatures: coupled interactions and self-regulation. J. Geophys. Res.98, 12881–12893 (1993).

32. Lenderink, G., Mok, H. Y., Lee, T. C. & Van Oldenborgh, G. J. Scaling andtrends of hourly precipitation extremes in two different climate zones–HongKong and the Netherlands. Hydrol. Earth Syst. Sci. 15, 3033–3041 (2011).

33. Pepler, A., Coutts-Smith, A. & Timbal, B. The role of East Coast Lows onrainfall patterns and inter-annual variability across the East Coast of Australia.Int. J. Climatol. 34, 1011–1021 (2014).

34. Cortés-Hernández, V. E. et al . Evaluating regional climate models forsimulating sub-daily rainfall extremes. Clim. Dynam. 47, 1613–1628 (2016).

35. O’Gorman, P. A. & Schneider, T. The physical basis for increases inprecipitation extremes in simulations of 21st-century climate change.Proc. Natl Acad. Sci. USA 106, 14773–14777 (2009).

36. Kunkel, K. E. et al . Probable maximum precipitation and climate change.Geophys. Res. Lett. 40, 1402–1408 (2013).

37. Sherwood, S. & Fu, Q. A drier future? Science 343, 737–739 (2014).

AcknowledgementsWe thank the Bureau of Meteorology, the Bureau of Rural Sciences, and CSIRO forproviding AWAP data and Met Office Hadley Center for providing HadISD data. Modeldata used here came from the NSW Office of Environment and Heritage-backedNSW/ACT Regional Climate Modelling Project (NARCliM). This work was funded byARC grants FL150100035, LE150100089, FT110100576 and DP160103439.

Author contributionsJ.B. conducted all analyses and led the writing of the manuscript. S.C.S. assisted in studydesign and interpretation, L.V.A. assisted in choice and interpretation of observationaldata, and J.P.E. performed the NARCliM simulations. All authors assisted in writing themanuscript.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints.Correspondence and requests for materials should be addressed to J.B. or S.C.S.

Competing financial interestsThe authors declare no competing financial interests.

NATURE CLIMATE CHANGE | ADVANCE ONLINE PUBLICATION | www.nature.com/natureclimatechange

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

5

LETTERS NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE3201

MethodsDaily precipitation and near-surface air temperature data for the period 1979–2013are obtained from the 0.05◦×0.05◦ resolution Australian Water Availability Project(AWAP) data set28, covering the Australian continent. Daily mean temperature iscalculated from the average of daily maximum and minimum temperature. Datafrom the grid boxes of the regridded 0.5◦×0.5◦ AWAP data set encompassingSydney, Melbourne and Darwin are extracted. Sub-daily station data for the period1973–2011 from HadISD38 confirm the scaling results from AWAP at stationlocations (Supplementary Fig. 1). We calculate the daily mean temperature andprecipitation from HadISD using sub-daily observations.

The regional climate simulation data are from NARCliM (NSW/ACT RegionalClimate Modeling project)6. In NARCliM, 12 sets of simulations were performedwith three versions of a regional climate model (RCM) each driven by four separateglobal climate models (GCMs). GCM-driven RCM simulations were conductedfrom 1990–2010 for historical runs and from 2020–2040 and 2060–2080 for futureprojections under the SRES A2 emission scenarios39. The four GCMs areECHAM5, MIROC3.2 (medres), CCCM3.1 and CSIRO-Mk3.0. The RCM used isthe Weather Research and Forecasting model40. On the basis of the modelperformance41,42 and independence43, simulations with three different sets ofphysics parameterization schemes (R1, R2, R3) were chosen (SupplementaryTable 1). To examine the precipitation and temperature change over the Australiancontinent, we focus on the outer domain at a horizontal resolution of 50 km. Giventhat a few precipitation values (mostly in the cores of tropical cyclones) from rawprecipitation output in NARCliM simulations are unrealistically high, we use theavailable ‘filtered’ data set wherein rain rates (above 1,200mmd−1) have beenreplaced by the maximum precipitation from the eight surrounding grid cells.

The above data sets are analysed by applying the same method used in earlierstudies4 referred to here as the binning method. Only data on wet days are used.The wet days are defined as having precipitation of over 1mmd−1. At each stationor grid box, the wet events are ranked on the basis of the temperature for each day.Then all events are divided into 12 bins by temperature with roughly an equalnumber of events in each bin. The median temperature in each bin is used torepresent the temperature for that bin. Then the 99th percentile daily precipitationintensity in each bin is determined by ranking the precipitation amounts. Onlystations or grid boxes with more than 100 events in each bin are used. However,given the limited available wet events in summer and winter, we require at least50 events in each bin when analysing the scaling rates in either season. Finally, anexponential regression is used to relate the extreme precipitation (P1, P2) withtemperature change (1T ):

P2=P1(1+0.01α1)1T

where α1 is the rate at which extreme precipitation changes with temperature,which we refer to as the ‘apparent scaling rate’.

A similar equation is applied in investigating the future extreme precipitationwith temperature:

Pfut=Phis(1+0.01α2)1T

where Pfut and Phis are the averages of daily precipitation amounts above the99th, 99.5th or 99.9th percentile including all days for the period 2060–2079 and1990–2009 respectively, and1T here represents the local mean temperaturechanges of 2060–2079 relative to 1990–2009. Unlike apparent scaling rates, climatescaling rates are computed using all days44. Here α2 is the ‘climate scaling rate’.Fractional changes of mean near-surface water vapour and column water vapourare also calculated with this equation. The model ensemble climate scaling rates areobtained by averaging the climate scaling rates computed separately from12 members. Changes in near-surface and column water vapour are highlycorrelated across the model ensemble (r=0.98). Scaling of near-surface watervapour is about 6.1% ◦C−1 at constant relative humidity, so values below thisindicate that relative humidity is decreasing as climate warms.

In an attempt to minimize the temporary cooling effect, we also considered therelationship between daily extreme precipitation and prior dry-day temperature inDarwin with the AWAP data. The dry-day temperature is that of the most recentday with no precipitation up to two days before the precipitation day. If neither daywas dry, this event was not included in our calculation. We also repeated resultsexcluding tropical cyclones found in the Australian Tropical Database from Bureauof Meteorology (http://www.bom.gov.au/cyclone/history) to have passed withinroughly 500 km of Darwin, but this only modestly affected results.

Data availability. AWAP data sets are available from the Australian Bureau ofMeteorology website (http://www.bom.gov.au/climate). NARCliM data sets areavailable from NSW Climate Data Portal (https://climatedata.environment.nsw.gov.au). HadISD data sets are available from the Met Office website(http://www.metoffice.gov.uk/hadobs/hadisd).

References38. Dunn, R. J. et al . HadISD: a quality-controlled global synoptic report database

for selected variables at long-term stations from 1973–2011. Clim. Past. 8,1649–1679 (2012).

39. IPCC, Special Report on Emissions Scenarios (eds Nakićenović, N.& Swart, R.) (Cambridge Univ. Press, 2000).

40. Skamarock, W. C. et al . A Description of the Advanced Research WRF Version 3NCAR Technical Note (NCAR, 2008).

41. Evans, J., Ekström, M. & Ji, F. Evaluating the performance of a WRFphysics ensemble over South-East Australia. Clim. Dynam. 39,1241–1258 (2012).

42. Ji, F., Ekström, M., Evans, J. P. & Teng, J. Evaluating rainfall patterns usingphysics scheme ensembles from a regional atmospheric model. Theor. Appl.Climatol. 115, 297–304 (2014).

43. Evans, J. P., Ji, F., Abramowitz, G. & Ekström, M. Optimally choosing smallensemble members to produce robust climate simulations. Environ. Res. Lett. 8,044050 (2013).

44. Schär, C. et al . Percentile indices for assessing changes in heavy precipitationevents. Climatic Change 137, 201–216 (2016).

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

NATURE CLIMATE CHANGE | www.nature.com/natureclimatechange