Understandingtheeffectofglobalwarmingonprecipitationextremes:

progressandchallenges

MartinS.Singh

MonashUniversityARCCentreofExcellenceforClimateExtremes

Workshop2018

Whatareprecipitationextremes?

•Heaviestrainfallevents

•Definedashighpercentileofdistribution• (e.g.,annualmaximumdailyrainfall)

•Rangeoftimeandspatialscalesofinterest 2010Pakistanfloods(photo:UPI)

Areprecipitationextremesstrongerinawarmerworld?

Observationsindicatehigherglobaltemperatureisassociatedwithmoreintenseprecipitationextremes

gauges and partly because of the uneven distribution ofland areas and oceans; this should also be taken intoaccount when interpreting the results.Considering first the fraction of stations exhibiting

significant increases (Fig. 12, middle), it can be seen thatthere are some clear meridional variations, with thelargest proportion of stations that have positive associ-ation with global mean near-surface temperature lo-cated near the equator and a second maxima at about558N. The two locations with the minimum fraction ofsignificant positive associations are at 158S and 68N. It isnoted that the resampling methodology takes the lowersample sizes near the equator into account, with theconfidence interval being much wider in the less wellgauged parts of the domain. The results of our analysisare reasonably consistent with the model-derived resultsunder a future greenhouse gas–enhanced climate (Kharinet al. 2007), except that the latitudes with the minimumfraction of positive associations are closer to the equatorcompared with the modeling studies.Finally, we plot the median estimate of the sensitivity

of annual extreme precipitation per kelvin warming bylatitude (Fig. 12, bottom). The general pattern reflectsthe conclusions of the middle panel, with the largestpositive associations near the equator and a secondmaxima occurring in the higher latitudes of the North-ern Hemisphere. Minima exist at 138S and 118N, andboth these minima are not statistically significantly dif-ferent from the null hypothesis, which is that there is notrend at these latitudes.

4) IMPLICATIONS WHEN USING DIFFERENT DATA

PERIODS

All of the results from the preceding analysis werebased on the set of stations between 1900 and 2009 withat least 30 years of data, with the median number ofyears per station in this dataset being 53 years. As dis-cussed in section 2, the number of stations with rainfalldata increased significantly in the first half of the twen-tieth century, plateauing from about 1960. Therefore,the majority of the dataset is likely to be from the latterpart of the record, although sequences from the earlypart of the twentieth century are also included in theanalysis.To ensure that the results are not substantially influ-

enced by the period of record or the median length ofrecord, we conduct the analysis on different subsets ofdata, summarized in Table 1. The first three analysesconsider the full period from 1900 to 2009 but use dif-ferent thresholds for the minimum record length. Thelast two analyses are for the different periods of record,with the first 60 years of the twentieth century comparedwith the last 40 years of the twentieth century and thefirst 10 years of the twenty-first century.Considering the first three analyses, it can be seen in

Table 1 that by increasing theminimum number of yearsto be analyzed from 30 to 70 years, the number of sta-tions meeting this minimum threshold drops dramati-cally from 8326 stations to 2124 stations. Interestingly,the percentage of stations with positive associations, and

FIG. 11. Global median of estimates of the local sensitivity of annual precipitation extremesto a 1-K increase in global mean near-surface temperature. The histogram represents thedistribution of results from 1000 bootstrap realizations of the global annual maximum rainfalldata, and the red dot represents the value from the observed data.

3914 JOURNAL OF CL IMATE VOLUME 26

Observationalestimateofsensitivityofannualmaximumdailyprecipitationtoglobal-meantemperature(Westra etal.,2013)

observationalestimate

nullhypothesis

-10-50510globalmedian%changeinannualmaximaperKglobaltemperature

Extremeprecipitationeventsovermostofthemid-latitudelandmassesandoverwettropicalregionswillverylikelybecomemoreintenseandmorefrequentbytheendofthiscentury,asglobalmeansurfacetemperatureincreases.

IPCC,AR5,Summaryforpolicymakers

HowmuchwillprecipitationextremeschangeinWollongongby2100?

•Whydoweexpectprecipitationextremestoincreasewithwarming?

•Howcanweconstrainthemagnitudeoffuturechangesinprecipitationextremesatregionalscale

Whatsetstheupperlimitonprecipitationrates?

Whatsetstheupperlimitonprecipitationrates?

•Heaviestrainfallconstrainedbyavailablewatervapour?(Trenberth,1999)

Sat.vapo

ur

pressure

Temperature

~7%/K

“Clausius-Clapeyron relationship”

Whatsetstheupperlimitonprecipitationrates?

•Heaviestrainfallconstrainedbyavailablewatervapour?(Trenberth,1999)

Sat.vapo

ur

pressure

Temperature

~7%/K

What’swrongwiththisargument?

Heavyprecipitationeventsdrawinmoisturefromtheirsurroundings!

Instead,considerthedynamicsofprecipitationextremeeventsthemselves

𝑃" = 𝜖×𝜔×𝑞)

extremeprecipitation

rate

large-scaleupwardmotion

(verticalgradientof)

saturationhumidity

efficiency

Humidityisnottheonlyfactorcontrollingprecipitationextremes

e.g.,O’Gorman&Schneider(2009);Muller&O’Gorman(2011);Singh&O’Gorman(2014)

Precipitationextremesunderwarming

𝛿𝑃"𝑃"

≈𝛿𝜖𝜖+𝛿𝜔𝜔+𝛿𝑞)𝑞)

microphysicaldynamical

thermodynamical

Simplethermodynamicscalingforprecipitationextremes

• If𝜖 and𝜔 remainconstant:

𝑃" ∝ 𝑞)

•Precipitationextremesincreaseatroughly4-7%/K

•SimilartoClausius-Clapeyron scaling

Doweexpectprecipitationextremestoscalewithmoisturecontentafterall?

Efficiencypotentiallyimportantforconvective-scaleextremes

• 𝜖 representstheefficiencyofturninglargeratesofcolumnnet-condensationintolargeprecipitationrates

Measureof𝜖 forsimulationsofRCEatdifferentsurfacetemperatures(Singh&O’Gorman.,2014)

0 5 10 15

200

400

600

800

1000

we (m/s)

pres

sure

(hPa

)

aLin−hail

0 5 10 15we (m/s)

bLin−graupel

0 5 10 15we (m/s)

cThompson

Figure S3: Mean vertical velocity profiles for columns in which the instantaneous column net-condensation rate exceeds its 99.99th percentile. (a) Lin-hail simulations with mean temperaturesof the lowest model level (Ts) of 277 (black), 292, 298 and 309 K (orange). (b) Lin-graupel simulationswith Ts equal to 277 (black), 292, 298 and 308 K (orange). (c) Thompson simulations with Ts equalto 277 (black), 292, 298 and 308 K (orange).

280 290 300 310

0.1

1

Ts (K)

Efficiency

εC

εPLin−hailLin−graupelThompson

Figure S4: Condensation e�ciencies [✏C ; defined in (S3)] and precipitation e�ciencies [✏P ; defined in(1)] as a function of the mean temperature of the lowest model level (Ts). Results for simulations usingthe Lin-hail (black), Lin-graupel (gray) and Thompson (dashed) microphysics schemes are shown.

6

Efficiencypotentiallyimportantforconvective-scaleextremes

• 𝜖 representstheefficiencyofturninglargeratesofcolumnnet-condensationintolargeprecipitationrates

Measureof𝜖 forsimulationsofRCEatdifferentsurfacetemperatures(Singh&O’Gorman.,2014)

0 5 10 15

200

400

600

800

1000

we (m/s)

pres

sure

(hPa

)

aLin−hail

0 5 10 15we (m/s)

bLin−graupel

0 5 10 15we (m/s)

cThompson

Figure S3: Mean vertical velocity profiles for columns in which the instantaneous column net-condensation rate exceeds its 99.99th percentile. (a) Lin-hail simulations with mean temperaturesof the lowest model level (Ts) of 277 (black), 292, 298 and 309 K (orange). (b) Lin-graupel simulationswith Ts equal to 277 (black), 292, 298 and 308 K (orange). (c) Thompson simulations with Ts equalto 277 (black), 292, 298 and 308 K (orange).

280 290 300 310

0.1

1

Ts (K)

Efficiency

εC

εPLin−hailLin−graupelThompson

Figure S4: Condensation e�ciencies [✏C ; defined in (S3)] and precipitation e�ciencies [✏P ; defined in(1)] as a function of the mean temperature of the lowest model level (Ts). Results for simulations usingthe Lin-hail (black), Lin-graupel (gray) and Thompson (dashed) microphysics schemes are shown.

6

Atlargetimeandspacescales(e.g.,dailyextremesatGCM-gridbox scale)changesin

efficiencyunimportantforchangesinprecipitationextremes

Butdynamicsareimportant!

Inmodelprojections,thermodynamiccontributiondominatesinthe

extratropics

Climatology Project (GPCP) (19) (Fig. 1). However, there areconsiderable uncertainties in observations of precipitation, andother studies using different datasets or different measures ofprecipitation extremes have found that climate models under-estimate precipitation extremes relative to observations (10–12,†). The simulated precipitation extremes increase at all latitudesas the climate warms, particularly in the tropics where they arelargest (Fig. 1). The water vapor content of the atmosphere alsoincreases at all latitudes, but precipitation extremes do not scalewith the water vapor content (Fig. 2). In the multimodel median,precipitation extremes increase with global-mean surface airtemperature at a smaller rate than the zonal-mean atmosphericwater vapor content (Fig. 2). For example, at 60°N, the 99.9thpercentile of daily precipitation increases at 6% K!1 in themultimodel median, compared with 10% K!1 for the atmo-spheric water vapor content. (Both rates of increase are nor-malized by the change in global-mean surface air temperaturefor each model before taking the median among all models.)There is larger intermodel scatter in the tropics than in theextratropics in both the precipitation extremes and their frac-tional changes with warming (Figs. 1 and 2).

Precipitation extremes also do not scale with water vaporcontent in individual models. Extratropical precipitation ex-tremes consistently increase less rapidly with surface air tem-perature than does the extratropical water vapor content (Fig.3A). The rate of change in tropical precipitation extremes varieswidely among models; changes in tropical precipitation extremesnormalized by the increase in tropical surface air temperaturerange from 1.3% K!1 to 30% K!1. (Models with small tropicalincreases can be more easily distinguished in Fig. S1, which is thesame as Fig. 3 but with logarithmic axis scales.) In most models,tropical precipitation extremes increase less rapidly than or at asimilar rate as tropical water vapor content; for two outlyingmodels (both from GFDL), the increases in tropical precipita-tion extremes are much greater. The behavior of tropical pre-cipitation extremes in the GFDL models is also sensitive to thepercentile considered, with close to zero ("1% K!1) changes intropical precipitation extremes at the 99th percentile.

Precipitation extremes may occur preferentially in certainseasons or at certain longitudes. Furthermore, one may hypoth-esize that precipitation extremes depend on the saturation watervapor content of the atmosphere when they occur, rather than on

†Models and observations may agree more closely in our study than in some other studiesin part because we use percentiles of precipitation including all days (dry and wet) andbecause we spatially average observations to typical model resolution. The precipitationextremes scaling discussed below implies that if models approximately reproduce thedistribution of vertical velocities but inaccurately simulate the frequency of wet days,inclusion of all days in the percentile analysis will give the most favorable comparison.

Fig. 2. Fractional changes in the 99.9th percentile of daily precipitation(blue), zonally averaged atmospheric water vapor content (green), saturationwater vapor content of the troposphere (black dotted), full precipitationextremes scaling (Eq. 2) (red dashed), and thermodynamic scaling for precip-itation extremes (black dashed). The lines show multimodel medians of thefractional changes relative to 20th-century values, normalized by the global-mean change in surface air temperature for each model. Model scatter isshown for the fractional change in precipitation extremes using the inter-quartile range (shading). The saturation water vapor content is calculatedusing an average of the climatological monthly-mean temperature over alltimes and longitudes at which the extreme precipitation occurs.

A

B

Fig. 3. Fractional changes in the 99.9th percentile of daily precipitation foreach model versus changes in atmospheric water vapor content and scalingsfor precipitation extremes. (A) Atmospheric water vapor content (open sym-bols) and the thermodynamic scaling that neglects changes in upward velocity(solid symbols). (B) Full scaling for precipitation extremes. The fractionalchange are relative to 20th-century values, averaged over the extratropics(Left) or tropics (Right) and normalized by the change in surface air temper-ature averaged over the extratropics or tropics. Solid lines correspond toone-to-one relationships. The extratropics are defined as the regions pole-ward of 30° latitude, and the tropics are defined as the region equatorwardof 30° latitude.

Fig. 1. The 99.9th percentile of daily precipitation (millimeters per day) forthe periods 1981–2000 (blue) and 2081–2100 (red) in the SRES A1B scenario(multimodel median), and based on Global Precipitation Climatology Project(GPCP) data for the period 1997–2006 (black). Model scatter (shading) for theperiod 1981–2000 is shown using the interquartile range (50% of models liewithin the shaded region). The spatial resolution of the GPCP data weredegraded from 1° to 3°, which is comparable with climate model resolutions.A Gaussian smoothing filter of standard deviation 6° latitude was applied toreduce noise in all plots showing variations with latitude.

14774 ! www.pnas.org"cgi"doi"10.1073"pnas.0907610106 O’Gorman and Schneider

Sensitivityof99.9th percentileofprecipitationtosurfacetemperatureinCMIP5models(O’Gorman&Schneider,2009)

Butnoagreementinchangestotropicalprecipitationextremes

Climatology Project (GPCP) (19) (Fig. 1). However, there areconsiderable uncertainties in observations of precipitation, andother studies using different datasets or different measures ofprecipitation extremes have found that climate models under-estimate precipitation extremes relative to observations (10–12,†). The simulated precipitation extremes increase at all latitudesas the climate warms, particularly in the tropics where they arelargest (Fig. 1). The water vapor content of the atmosphere alsoincreases at all latitudes, but precipitation extremes do not scalewith the water vapor content (Fig. 2). In the multimodel median,precipitation extremes increase with global-mean surface airtemperature at a smaller rate than the zonal-mean atmosphericwater vapor content (Fig. 2). For example, at 60°N, the 99.9thpercentile of daily precipitation increases at 6% K!1 in themultimodel median, compared with 10% K!1 for the atmo-spheric water vapor content. (Both rates of increase are nor-malized by the change in global-mean surface air temperaturefor each model before taking the median among all models.)There is larger intermodel scatter in the tropics than in theextratropics in both the precipitation extremes and their frac-tional changes with warming (Figs. 1 and 2).

Precipitation extremes also do not scale with water vaporcontent in individual models. Extratropical precipitation ex-tremes consistently increase less rapidly with surface air tem-perature than does the extratropical water vapor content (Fig.3A). The rate of change in tropical precipitation extremes varieswidely among models; changes in tropical precipitation extremesnormalized by the increase in tropical surface air temperaturerange from 1.3% K!1 to 30% K!1. (Models with small tropicalincreases can be more easily distinguished in Fig. S1, which is thesame as Fig. 3 but with logarithmic axis scales.) In most models,tropical precipitation extremes increase less rapidly than or at asimilar rate as tropical water vapor content; for two outlyingmodels (both from GFDL), the increases in tropical precipita-tion extremes are much greater. The behavior of tropical pre-cipitation extremes in the GFDL models is also sensitive to thepercentile considered, with close to zero ("1% K!1) changes intropical precipitation extremes at the 99th percentile.

Precipitation extremes may occur preferentially in certainseasons or at certain longitudes. Furthermore, one may hypoth-esize that precipitation extremes depend on the saturation watervapor content of the atmosphere when they occur, rather than on

†Models and observations may agree more closely in our study than in some other studiesin part because we use percentiles of precipitation including all days (dry and wet) andbecause we spatially average observations to typical model resolution. The precipitationextremes scaling discussed below implies that if models approximately reproduce thedistribution of vertical velocities but inaccurately simulate the frequency of wet days,inclusion of all days in the percentile analysis will give the most favorable comparison.

Fig. 2. Fractional changes in the 99.9th percentile of daily precipitation(blue), zonally averaged atmospheric water vapor content (green), saturationwater vapor content of the troposphere (black dotted), full precipitationextremes scaling (Eq. 2) (red dashed), and thermodynamic scaling for precip-itation extremes (black dashed). The lines show multimodel medians of thefractional changes relative to 20th-century values, normalized by the global-mean change in surface air temperature for each model. Model scatter isshown for the fractional change in precipitation extremes using the inter-quartile range (shading). The saturation water vapor content is calculatedusing an average of the climatological monthly-mean temperature over alltimes and longitudes at which the extreme precipitation occurs.

A

B

Fig. 3. Fractional changes in the 99.9th percentile of daily precipitation foreach model versus changes in atmospheric water vapor content and scalingsfor precipitation extremes. (A) Atmospheric water vapor content (open sym-bols) and the thermodynamic scaling that neglects changes in upward velocity(solid symbols). (B) Full scaling for precipitation extremes. The fractionalchange are relative to 20th-century values, averaged over the extratropics(Left) or tropics (Right) and normalized by the change in surface air temper-ature averaged over the extratropics or tropics. Solid lines correspond toone-to-one relationships. The extratropics are defined as the regions pole-ward of 30° latitude, and the tropics are defined as the region equatorwardof 30° latitude.

Fig. 1. The 99.9th percentile of daily precipitation (millimeters per day) forthe periods 1981–2000 (blue) and 2081–2100 (red) in the SRES A1B scenario(multimodel median), and based on Global Precipitation Climatology Project(GPCP) data for the period 1997–2006 (black). Model scatter (shading) for theperiod 1981–2000 is shown using the interquartile range (50% of models liewithin the shaded region). The spatial resolution of the GPCP data weredegraded from 1° to 3°, which is comparable with climate model resolutions.A Gaussian smoothing filter of standard deviation 6° latitude was applied toreduce noise in all plots showing variations with latitude.

14774 ! www.pnas.org"cgi"doi"10.1073"pnas.0907610106 O’Gorman and Schneider

Sensitivityof99.9th percentileofprecipitationtosurfacetemperatureinCMIP5models(O’Gorman&Schneider,2009)

Whatsetsthespatialpatternofchangestoprecipitationextremeswithwarming?

Multi-modelmeanover22CMIP5models.Stipling where80%ofmodelsagreeonsign.(Pfahl etal.2015)

Whatsetsthespatialpatternofchangestoprecipitationextremeswithwarming?

(Pfahl etal.2015)

Spatialpatterndeterminedbydynamiccomponent

dynamiccomponentthermodynamiccomponent

(Pfahl etal.2015)

Whatcanwesayaboutprecipitationextremes?

• Thermodynamiccomponentgiveslargeandrobustincreaseinprecipitationextremes

• Butdynamiccomponentmayalsobelargeinthetropics,andonregionalscales•magnitudeandspatialpatternofchangesremainuncertain

Understandingchangesinprecipitationextremesrequiresunderstandinghowlarge-scaleupwardmotion

willchangeunderwarming

Howcanweconstrainfuturechangesin(tropical)precipitationextremes?

Howcanweconstrainfuturechangesin(tropical)precipitationextremes?

Problem:Grid-scaleverticalvelocityreliesoninteraction

betweenconvectionandlargescale

•poorlysimulatedinglobalmodels

•Noguaranteethatgoodsimulationofcontrolclimateleadstogoodsimulationofchanges

DirectionI:Observationalconstraints

LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO1568

Model: GFDL¬CM2.0

Implied

Model: ECHAM5/MPI

Observations

P99.9

25% K¬1

¬10

0

10

1992 1996 2000 2004 2008

P99.9

51% K¬1

¬15

0

15

mm

d¬1

1985 1990 1995 2000

Implied

P99.9

11% K¬1

¬3

0

3

mm

d¬1

mm

d¬1

1985 1990 1995 2000

Figure 1 | Time series of precipitation extremes and surface temperatureover the tropical oceans in observations and simulations (GFDL-CM2.0and ECHAM5/MPI). Anomalies in the 99.9th percentile of precipitation(blue) and surface temperature rescaled by the sensitivity (% K�1) forvariability in each case (green) are shown. Also shown (red) for the modelsare surface temperature anomalies rescaled by the sensitivity for variabilityimplied by the sensitivity for climate change (over the whole tropics) andthe regression relationship between sensitivities for variability and climatechange for all the CMIP3 models (Supplementary Table S1). Time series arefiltered with a 6-month running average.

generally analysed over the tropical oceans because this is foundto give the strongest constraint on sensitivities for climate change.Results are also reported using variability over thewhole tropics.

Time series are first constructed of precipitation extremes andmean surface temperature over the tropical oceans between 30� Sand 30� N (Methods). The influence of ENSO on precipitationextremes over the tropical oceans is clearly evident in observations,as shown in Fig. 1 for the 99.9th percentile of daily precipitation andconsistent with results from previous studies4–6. Positive anomaliesin surface temperature tend to be associatedwith positive anomaliesin precipitation extremes; the calculated sensitivity to surfacetemperature (Methods) is 25%K�1 with a 90% confidence intervalof 16–36%K�1. A similar behaviour is found in the climate-modelsimulations, but with different time series of surface temperaturebecause coupled models are considered, and with very differentsensitivities depending on the climate model used (Fig. 1 andSupplementary Fig. S1).

Sensitivities for climate change are calculated over the wholetropics in the climate model simulations and are normalizedby changes in mean surface temperature (Methods). For the99.9th percentile of precipitation, the sensitivities for climatechange are strongly correlated across models with the sensitivitiesfor variability (Fig. 2), with a correlation coefficient of 0.866.The relationship between sensitivities is further quantified usingordinary-least-squares regression (Supplementary Table S1). Theregression line passes close to the origin, and the sensitivity forvariability is greater than the sensitivity for climate change byroughly a factor of 2.5.

The relationship between the sensitivities for variability andclimate change, together with the observed sensitivity for variability,yields an inferred sensitivity for climate change. For the 99.9thpercentile of precipitation, the inferred sensitivity for climatechange is 10%K�1, which is higher than what most of the models

Variability (% K¬1)C

limat

e ch

ange

(%

K¬1

)0 20 40 60

Inferred

Observed

IPSL¬CM4INM¬CM3.0

MIROC3.2¬medMIROC3.2¬hiMRI¬CGCM2.32NCAR¬PCM1NCAR¬CCSM3.0

ECHAM4/INGVECHAM5/MPI

BCCR BCM2.0CGCM3.1 T47CGCM3.1 T63CNRM¬CM3CSIRO¬Mk3.0CSIRO¬Mk3.5GFDL¬CM2.0GFDL¬CM2.1FGOALS¬g1.0

0

10

20

Figure 2 | Sensitivities (%K�1) of the 99.9th percentile of precipitationfor variability versus climate change in the CMIP3 simulations. The solidline shows the ordinary-least-squares best fit. Histograms show estimates(with uncertainty) of the observed sensitivity for variability and the inferredsensitivity for climate change. Sensitivities for variability are over thetropical oceans and sensitivities for climate change are over thewhole tropics.

simulate (Fig. 2). Uncertainty is estimated by a bootstrappingprocedure involving resampling of the models used and 12-monthblocks in the observed and simulated time series (Methods). Theresulting 90% confidence interval of 6–14%K�1 is substantiallynarrower than the inter-model scatter of 2–23%K�1, clearlyillustrating the value of the observational constraint.

The inferred sensitivity for climate change increases withpercentile from the 98th to the 99.9th percentile and decreasesslightly to the 99.95th percentile (Fig. 3a); it generally exceedsthe multimodel-median sensitivity (and by as much as 68%),although it maximizes at the 99.9th percentile whereas themultimodel median continues to increase with percentile. Bothintermodel scatter and the strength of the relationship betweensensitivities for variability and climate change increase withpercentile (Supplementary Table S1), such that the observationalconstraint ismore useful for higher percentiles of precipitation.

The inferred sensitivities were also calculated for climate changeover land only, with variability over the ocean as before. A strongrelationship holds between climate change and variability forthe higher percentiles of precipitation considered (SupplementaryFig. S2 and Table S2), and the inferred sensitivities for climatechange over land approach the sensitivities over the whole tropicsat these percentiles (Fig. 3b). This similar response over land andthe whole tropics occurs despite ⇠60% greater surface warmingover land than ocean (all sensitivities for climate change arenormalized by temperature changes over the whole tropics for easeof comparison). Indeed, the percentage changes in precipitationextremes in the simulations of climate change are close to equal overland and ocean across all themodels (Supplementary Fig. S3), whichis likely related to the importance of oceanic water vapour sourcesfor precipitation over land and to decreases in land surface-airrelative humidity under global warming25.

For the ‘good-ENSO’ subset of models (Supplementary Infor-mation), the relationship between sensitivities for climate changeand variability is very tight for the 99.9th percentile of precipitation(Supplementary Fig. S4), with a correlation coefficient of 0.997, andthe resulting inferred sensitivities for climate change are similar towhat is obtained using all the models (Supplementary Table S1).This robustness suggests that the inferred response to climatechange is not strongly affected by the relatively poor quality ofsimulated ENSO temperature variability in some of the modelsimulations. Similar results are also obtained using the CMIP5

698 NATURE GEOSCIENCE | VOL 5 | OCTOBER 2012 | www.nature.com/naturegeoscience

Tropical-meanchangesinprecipitationextremesacross18models

(O’Gorman2012)

CombineGCMsandobservationsofvariabilitytoderivean“emergentconstraint”onprecipitationextremes

Couldthisbeappliedonsmallerscales?

Cantheseresultsbeusedtoreasonaboutglobalwarming?

3036 G. Lenderink et al.: Hourly precipitation extremes

1

10

-2 6 14 22 30

inte

nsity

(mm

hou

r-1 )

temperature (oC)

a)

HKO

99.9% 99%90%

1

10

-2 6 14 22 30

inte

nsity

(mm

hou

r-1 )

temperature (oC)

b)

NL

99.9% 99%90%

Fig. 1. Dependency of different percentiles of hourly precipitation extremes on daily mean temperature(left: HKO; right: NL). Stippled lines are estimates from the GPD fitting procedure, whereas solid linesare the percentiles computed from the raw data (in most cases these overlap). The grey shading denotesthe 98% uncertainty range derived from the GPD fit. Red (black) stippled lines denote dependencies of14% (7 %) per degree. For comparison, these lines are identical in all plots; the distance between twolines is a factor 2 in intensity.

19

Fig. 1. Dependency of different percentiles of hourly precipitation extremes on daily mean temperature (left: HKO; right: NL). Stippledlines are estimates from the GPD fitting procedure, whereas solid lines are the percentiles computed from the raw data (in most cases theseoverlap). The grey shading denotes the 98% uncertainty range derived from the GPD fit. Red (black) stippled lines denote dependencies of14% (7%) per degree. For comparison, these lines are identical in all plots; the distance between two lines is a factor 2 in intensity.

are first computed from the GPD fit. Anomalies comparedto the average of all 15-yr periods are then computed, andthen averaged over several months, e.g. June, July and Au-gust (JJA) or the months May until October (MJJASO). Thismeasure is denoted as 1Prh. Error bands are based on the98% confidence interval of the GPD fit procedure, assumingerrors of the separate months to be independent. The choiceof 15 yr is a compromise between being able to determine thedifferent extremes (which are very noisy with less than 10 yrof data) and being able to capture inter-decadal variations(which are more damped with longer aggregation periods).Here, we use the daily mean dew point temperature becausehourly observations are not available for the De Bilt time se-ries before 1950. We note that for the period 1950–2006 sim-ilar results are obtained using hourly dew point temperatures.

3 Scaling of hourly precipitation extremes

Figure 1 shows scaling relations of hourly precipitation ex-tremes derived using the daily mean temperature for datafrom the Hong Kong Observatory (HKO) and the 27 stationsin the Netherlands (NL). For NL, this is the reproduction ofFig. 1d in Lenderink and van Meijgaard (2010), yet with oneyear more data for each station. There is clear hint of a de-crease in precipitation intensity for temperatures above 24 �Cin NL, but the number of observations with rain above thattemperature is very small and consequently the error bandsare large. For instance, above 24 �C there is no observationcorresponding to the 99.9th percentile, and this percentileis computed from the extrapolation by means of the GPD

fit (indicated by the dashed purple line in Fig. 1). There isa very clear fall off in intensity above 24 �C in HKO. Sincethere are many days (about 50% of days in 1971–2000) withdaily mean temperatures above that temperature in HKO, thisfall off in intensity is obviously well sampled. Below 24 �C,both data sources show a super C-C scaling. At the sametemperature, and for the same percentile, intensities in HKOare generally larger than those in NL by 20–30%.Results using the dew point temperature are shown in

Fig. 2, where we used the hourly dew point temperature at thetime of each hourly rainfall observation (h-0), and from two(h-2) and four hours (h-4) before each rainfall observation.Taking the dew point temperature from four hours beforeeach rainfall observation (h-4) the most consistent scaling isobtained. With consistent we mean here the most constantdependency across the largest range in dew point tempera-tures. Taking the dew point temperature at the time of theprecipitation event (h-0) less consistent results are obtained,in particular for the high temperature range. This is becausethe shower affects the dew point temperature by evaporationof precipitation (causing an increase in dew point) and thetransport of dry air by the convective downdrafts associatedwith the shower (causing a decrease in dew point). In par-ticular for the most intense showers often a decrease in dewpoint temperature is observed during the shower. The dewpoint temperature from four hours earlier is therefore a bet-ter measure of the near surface humidity from the air massin which the shower develops. To keep the text concise wewill omit “taken four hours before each hourly precipitationobservation” in the following, and just use “hourly dew pointtemperature”.

Hydrol. Earth Syst. Sci., 15, 3033–3041, 2011 www.hydrol-earth-syst-sci.net/15/3033/2011/

HongKong TheNetherlands

(Lenderink etal.,2011)

Couldthisbeappliedonsmallerscales?

Cantheseresultsbeusedtoreasonaboutglobalwarming?

3036 G. Lenderink et al.: Hourly precipitation extremes

1

10

-2 6 14 22 30

inte

nsity

(mm

hou

r-1 )

temperature (oC)

a)

HKO

99.9% 99%90%

1

10

-2 6 14 22 30

inte

nsity

(mm

hou

r-1 )

temperature (oC)

b)

NL

99.9% 99%90%

Fig. 1. Dependency of different percentiles of hourly precipitation extremes on daily mean temperature(left: HKO; right: NL). Stippled lines are estimates from the GPD fitting procedure, whereas solid linesare the percentiles computed from the raw data (in most cases these overlap). The grey shading denotesthe 98% uncertainty range derived from the GPD fit. Red (black) stippled lines denote dependencies of14% (7 %) per degree. For comparison, these lines are identical in all plots; the distance between twolines is a factor 2 in intensity.

19

Fig. 1. Dependency of different percentiles of hourly precipitation extremes on daily mean temperature (left: HKO; right: NL). Stippledlines are estimates from the GPD fitting procedure, whereas solid lines are the percentiles computed from the raw data (in most cases theseoverlap). The grey shading denotes the 98% uncertainty range derived from the GPD fit. Red (black) stippled lines denote dependencies of14% (7%) per degree. For comparison, these lines are identical in all plots; the distance between two lines is a factor 2 in intensity.

are first computed from the GPD fit. Anomalies comparedto the average of all 15-yr periods are then computed, andthen averaged over several months, e.g. June, July and Au-gust (JJA) or the months May until October (MJJASO). Thismeasure is denoted as 1Prh. Error bands are based on the98% confidence interval of the GPD fit procedure, assumingerrors of the separate months to be independent. The choiceof 15 yr is a compromise between being able to determine thedifferent extremes (which are very noisy with less than 10 yrof data) and being able to capture inter-decadal variations(which are more damped with longer aggregation periods).Here, we use the daily mean dew point temperature becausehourly observations are not available for the De Bilt time se-ries before 1950. We note that for the period 1950–2006 sim-ilar results are obtained using hourly dew point temperatures.

3 Scaling of hourly precipitation extremes

Figure 1 shows scaling relations of hourly precipitation ex-tremes derived using the daily mean temperature for datafrom the Hong Kong Observatory (HKO) and the 27 stationsin the Netherlands (NL). For NL, this is the reproduction ofFig. 1d in Lenderink and van Meijgaard (2010), yet with oneyear more data for each station. There is clear hint of a de-crease in precipitation intensity for temperatures above 24 �Cin NL, but the number of observations with rain above thattemperature is very small and consequently the error bandsare large. For instance, above 24 �C there is no observationcorresponding to the 99.9th percentile, and this percentileis computed from the extrapolation by means of the GPD

fit (indicated by the dashed purple line in Fig. 1). There isa very clear fall off in intensity above 24 �C in HKO. Sincethere are many days (about 50% of days in 1971–2000) withdaily mean temperatures above that temperature in HKO, thisfall off in intensity is obviously well sampled. Below 24 �C,both data sources show a super C-C scaling. At the sametemperature, and for the same percentile, intensities in HKOare generally larger than those in NL by 20–30%.Results using the dew point temperature are shown in

Fig. 2, where we used the hourly dew point temperature at thetime of each hourly rainfall observation (h-0), and from two(h-2) and four hours (h-4) before each rainfall observation.Taking the dew point temperature from four hours beforeeach rainfall observation (h-4) the most consistent scaling isobtained. With consistent we mean here the most constantdependency across the largest range in dew point tempera-tures. Taking the dew point temperature at the time of theprecipitation event (h-0) less consistent results are obtained,in particular for the high temperature range. This is becausethe shower affects the dew point temperature by evaporationof precipitation (causing an increase in dew point) and thetransport of dry air by the convective downdrafts associatedwith the shower (causing a decrease in dew point). In par-ticular for the most intense showers often a decrease in dewpoint temperature is observed during the shower. The dewpoint temperature from four hours earlier is therefore a bet-ter measure of the near surface humidity from the air massin which the shower develops. To keep the text concise wewill omit “taken four hours before each hourly precipitationobservation” in the following, and just use “hourly dew pointtemperature”.

Hydrol. Earth Syst. Sci., 15, 3033–3041, 2011 www.hydrol-earth-syst-sci.net/15/3033/2011/

HongKong TheNetherlands

(Lenderink etal.,2011)

Bao etal.(2017)showed(awardwinningwork!)thatclimateresponsedifferentto

variability

Missing:physicalmodelconnectingvariabilitytoclimatechange

DirectionII:Theoreticalconstraints

•UseQG-omegaequationtoreasonaboutchangestoupwardmotion(e.g.,Tandon etal.,2018)

𝑁/

𝑓/𝛻2/𝜔 + 𝜕44𝜔 = ℱ(𝜁, 𝑇, 𝑄)

•CanuseCRMtocalculatetheconvectiveheating

convectiveheating

Precipitationextremecasestudy– Houstonfloods2015

Precipitationextremecasestudy– Houstonfloods2015

EAR

TH,A

TMO

SPH

ERIC

,A

ND

PLA

NET

AR

YSC

IEN

CES

05/11 05/16 05/21 05/260

10

20

30

40

(mm

/day

)

Prec.obs. mean(12.0)CPC(13.3)GPCP(10.4)ERA(12.2)CRM ctl(12.8)

Prec.

05/11 05/16 05/21 05/260

10

20

30

40

50

(mm

/day

)

297 K(10.1)299 K(12.8)301 K(17.7)

A

B

Fig. 2. (A) Daily precipitation from the Climate Prediction Center (CPC)data, the Global Precipitation Climatology Project (GPCP) precipitation data(38), ERA reanalysis (12-h reforecast), and CRM simulation of the controlcase. The blue line is the mean of the three observations and reanalysisdataset. (B) Daily precipitation of the control case and two perturbed cases.Error bars indicate the SD among six ensemble members, which are differentrealizations with small random noise in the initial conditions (SI Appendix).Numbers in brackets are the mean precipitation between May 22 and 26(marked by the black vertical dash lines).

simulation also matches the reanalysis reasonably well (SIAppendix, Fig. S3). The precipitation comparisons between thecontrol and perturbed cases show the sensitivity of the pre-cipitation to the background climate. As an example, Fig. 2Bshows daily precipitation from the control case (Ts =299 K), theTs =297 K case, and the Ts =301 K case. Each case includessix ensemble members with different realizations of small ran-dom noise in the initial conditions (SI Appendix). Precipitationincreases with warming strongly and far above the variabilitywithin the ensemble. We focus on the 5-d mean precipitationbetween May 22 and May 26, 2015 (denoted P) hereafter. Pre-cipitation totals on this timescale are relevant to impacts onlarger scales (e.g., flooding in large river basins) and also rele-vant to interpretations of GCM results often used in the contextof climate change studies. Many previous studies have usedhigh-resolution regional simulations to examine changes withwarming of convective-scale precipitation and updrafts (13, 15–19), which are of great societal relevance to local areas (39).Analyses of convective-scale responses to the surface warmingare presented in SI Appendix as a complement to our primaryfocus on the larger space and timescale.

As Ts increases from 293 K to 305 K, P increases expo-nentially from 7.4 to 36.3 mm/d (Fig. 3A). We calculate theexponential growth rate locally at each Ts ( �lnP

�Tsusing centered

differences, except for the first and last values, in which forwardand backward differences are used) (Fig. 3B). The precipita-tion sensitivity to surface temperature, �lnP

�Ts, is not constant but

increases from 7% K�1 at Ts =293 K to 17% K�1 at Ts =301 K;then, it remains roughly constant as Ts further increases. Over-all, the extreme precipitation sensitivity substantially exceeds CCscaling, implying an important role for dynamic feedbacks. Theresults here are qualitatively consistent with the super-CC scalingof extreme precipitation found in observations on the interan-nual timescale (12) and in some numerical modeling studies (10,14, 16).

We apply the conventional decomposition (10) to quantifythe thermodynamic and dynamic components of the extremeprecipitation sensitivity. This decomposition is based on the

-12 -10 -8 -6 -4 -2 0hPa/hr

200

400

600

800

1000

hPa

293 295 297 299 301 303 305Ts (K)

0

10

20

30

40

mm

/day

P

293 295 297 299 301 303 305Ts (K)

-5

0

5

10

15

20

25

30

% p

er K

lnP/ Ts

293 295 297 299 301 303 305Ts (K)

-10

0

10

20

30

% p

er K

lnP/ Ts

lnD

lnD

lnHln

Q

lnQ

lnH

-12 -10 -8 -6 -4 -2 0hPa/hr

200

400

600

800

1000

hPa

D, Q

dashed line: D

solid line: Q

A

B

C

D

E

Fig. 3. (A) P, P̂, P̂D, and P̂Q as functions of Ts. B and C are the decomposi-tions of �lnP

�Tsbased on Eqs. 3 and 5, respectively. The black solid lines show

the sum of the color lines. D and E show !, !D, and !Q. The changing ofthe line colors from blue to red corresponds to cases in which Ts increasesfrom 293 to 305 K. Note that the dashed lines in E almost all collapse to thesame line.

Nie et al. PNAS | September 18, 2018 | vol. 115 | no. 38 | 9469

warmerclimate

large-scaleupwardmotion Nie etal.(2018)

DirectionIII:Regional-scalesimulationswithcloudpermittingmodels

•Somestudiesfindsuper-CCscalinginconvectiveprecipitationextremes(Kendon etal.,2014)whileothersdonot(Banetal.,2015)

•Maydependonregion,modelorboundaryconditions

•Muchworktobedone…

Climatechangewillverylikelycauseincreasesinprecipitationextremesacrosstheglobe

•Tounderstandmagnitudeandspatialpatternneedtopredictchangestothedynamics(woo!)

•Needtocombineobservations,theory,andhigh-resolutionmodels(alongwithGCMs)toachievethis