The transition to strong convection

• Background: precipitation moist Background: precipitation moist convection & its parameterization; convection & its parameterization; Arakawa’s Quasi-Equilibrium postulate Arakawa’s Quasi-Equilibrium postulate (QE); + reasons to care(QE); + reasons to care

• QE in vertical structure• The onset of strong convection regime as a continuous phase transition with critical phenomena

J. David NeelinJ. David Neelin11, , Ole PetersOle Peters1,21,2, , Chris HollowayChris Holloway11, , Katrina HalesKatrina Hales11, Steve Nesbitt, Steve Nesbitt33

1Dept. of Atmospheric Sciences & Inst. of Geophysics and Planetary Physics, U.C.L.A.2Santa Fe Institute (& Los Alamos National Lab)

3U of Illinois at Urbana-Champaign

The transition to strong convection The transition to strong convection

• Background: precipitation, moist convection and its parameterization; Arakawa’s Quasi-Equilibrium postulate (QE); + reasons to care

• QE in vertical structureQE in vertical structure• The onset of strong convection regime as a continuous phase transition with critical phenomena

J. David NeelinJ. David Neelin11, , Ole PetersOle Peters1,21,2, , Chris HollowayChris Holloway11, Katrina Hales, Katrina Hales11, Steve Nesbitt, Steve Nesbitt33




• Background: precipitation, moist convection and its parameterization; Arakawa’s Quasi-Equilibrium postulate (QE); + reasons to care

• QE in vertical structure • The onset of strong convection regimeThe onset of strong convection regime as a continuous phase transition as a continuous phase transition with critical phenomenawith critical phenomena


J. David NeelinJ. David Neelin11,, Ole PetersOle Peters1,2,*1,2,*, , Chris HollowayChris Holloway11, Katrina Hales, Katrina Hales11, Steve Nesbitt, Steve Nesbitt33



* + thanks to Didier Sornette for connecting the authors & Matt Munnich & Joyce Meyerson for terabytes of help

JulyJuly

January January

Background: Precipitation climatologyBackground: Precipitation climatology

mm/day4 8 162

Note intense tropical Note intense tropical moist convection zones moist convection zones (intertropical (intertropical convergence zones)convergence zones)

Rainfall at shorter time scalesRainfall at shorter time scales

Weekly accumulation

Rain rate from a 3-hourly period within the week

shown above(mm/hr)

From TRMM-based merged data (3B42RT)From TRMM-based merged data (3B42RT)

Convective quasi-equilibrium (Arakawa & Schubert 1974)Convective quasi-equilibrium (Arakawa & Schubert 1974)

•Convection acts to reduce buoyancy (cloud work function A) on fast time scale, vs. slow drive from large-scale forcing (cooling troposphere, warming & moistening boundary layer, …)

•M65= Manabe et al 1965; BM86=Betts&Miller 1986 parameterizns

Modified from Modified from Arakawa Arakawa (1997, 2004)(1997, 2004)

Background: Convective Quasi-equilibrium cont’dBackground: Convective Quasi-equilibrium cont’d

•Slow driving (moisture convergence & evaporation, radiative cooling, …) by large scales generates conditional instability

•Fast removal of buoyancy by moist convective up/down-drafts

•Above onset threshold, strong convection/precip. increase to keep system close to onset

•Thus tends to establish statistical equilibrium among buoyancy-related fields – temperature T & moisture, including constraining vertical structure

• using a finite adjustment time scale c makes a difference Betts & Miller 1986; Moorthi & Suarez 1992; Randall & Pan 1993; Zhang & McFarlane 1995; Emanuel 1993; Emanuel et al 1994; Yu and Neelin 1994; …

Manabe et al 1965; Arakawa & Schubert 1974Arakawa & Schubert 1974; Moorthi & Suarez 1992; Randall & Pan 1993; Emanuel 1991; Raymond 1997; …

Xu, Arakawa and Krueger 1992Xu, Arakawa and Krueger 1992Cumulus Ensemble Model (2-D)Cumulus Ensemble Model (2-D)

Precipitation rates (domain avg): Note large variationsNote large variations Imposed large-scale forcing (cooling & moistening)

Experiments: Q03 512 km domain, no shearQ02 512 km domain, shearQ04 1024 km domain, shear

Departures from QE and stochastic parameterizationDepartures from QE and stochastic parameterization

•In practice, ensemble size of deep convective elements in O(200km)2 grid box x 10minute time increment is not large

•Expect variance in such an avg about ensemble mean

•This can drive large-scale variability – (even more so in presence of mesoscale organization)

•Have to resolve convection?! (costs *109) or– stochastic parameterization? [Buizza et al 1999; Lin and Neelin

2000, 2002; Craig and Cohen 2006; Teixeira et al 2007]

– superparameterization? with embedded cloud model (Grabowski et al 2000; Khairoutdinov & Randall 2001; Randall et al 2002)

Variations about QE: Stochastic convection scheme Variations about QE: Stochastic convection scheme (CCM3(CCM3** & similar in QTCM & similar in QTCM****))

Mass flux closure in Zhang - McFarlane (1995) scheme Evolution of CAPE, A, due to large-scale forcing, F

tA c = -MbF

Closure:tA c = --1( A + ) , (A + > 0)

i.e.Mb = (A + )(F)-1 (for Mb > 0)

Stochastic modification in cloud base mass flux Mb

modifies decay of CAPE (convective available potential energy) Gaussian, specified autocorrelation time, e.g. 1 day

*Community Climate Model 3**Quasi-equilibrium Tropical Circulation Model

Impact of CAPE stochastic convective Impact of CAPE stochastic convective parameterization on tropical intraseasonal parameterization on tropical intraseasonal

variability in QTCMvariability in QTCM

Lin &Neelin 2000

CCM3 variance of daily precipitationCCM3 variance of daily precipitation

Control run

CAPE-Mb scheme(60000 vs 20000)

Observed (MSU)

Lin &Neelin 2002

Background cont’d: Reasons to careBackground cont’d: Reasons to care

•Besides curiosity…

•Model sensitivity of simulated precipitation to differences in model parameterizations

– Interannual teleconnections, e.g. from ENSO

– Global warming simulations*

*models do have some agreement on process & amplitude if you look hard enough (IGPP talk, May 2006; Neelin et al 2006, PNAS)

Precipitation change in global warming simulationsPrecipitation change in global warming simulations

• Fourth Assessment Report models: LLNL Prog. on Model Diagnostics & Intercomparison;

• SRES A2 scenario (heterogeneous world, growing population,…) for greenhouse gases, aerosol forcing

Dec.-Feb., 2070-2099 avg minus 1961-90 avg.

4 mm/daymodel climatologyblack contour for reference

mm/day

Neelin, Munnich, Su, Meyerson and Holloway , 2006, PNAS

GFDL_CM2.0GFDL_CM2.0

DJF Prec. Anom.

CCCMACCCMA

DJF Prec. Anom.

CNRM_CM3CNRM_CM3

DJF Prec. Anom.

CSIRO_MK3CSIRO_MK3

DJF Prec. Anom.

NCAR_CCSM3NCAR_CCSM3

DJF Prec. Anom.

GFDL_CM2.1GFDL_CM2.1

DJF Prec. Anom.

UKMO_HadCM3UKMO_HadCM3

DJF Prec. Anom.

MIROC_3.2MIROC_3.2

DJF Prec. Anom.

MRI_CGCM2MRI_CGCM2

DJF Prec. Anom.

NCAR_PCM1NCAR_PCM1

DJF Prec. Anom.

MPI_ECHAM5MPI_ECHAM5

DJF Prec. Anom.

• QE postulates deep convection constrains vertical structure of temperature through troposphere near convection

• If so, gives vertical str. of baroclinic geopotential variations, baroclinic wind**

• Conflicting indications from prev. studies (e.g., Xu and Emanuel 1989; Brown & Bretherton 1997; Straub and Kiladis 2002)

• On what space/time scales does this hold well? Relationship to atmospheric boundary layer (ABL)?

1. Tropical vertical structure (temperature & moisture)1. Tropical vertical structure (temperature & moisture)associated with convectionassociated with convection

**and thus a gross moist stability, simplifications to large-scale dynamics, … (Neelin 1997; N & Zeng 2000)

Vertical Temperature structureVertical Temperature structureMonthly T regression coeff. of each level on 850-200mb avg T.

CARDS Rawinsondes

avgd for 3 trop Western Pacific stations, 1953-99

• shading < 5% signif.• Curve for moist adiabatic vertical structure in red.

AIRS monthly (avg for similar Western Pacific box, 2003-2005)

HollowayHolloway & Neelin, JAS, 2007 (& Chris’s talk March 14 AOS)& Neelin, JAS, 2007 (& Chris’s talk March 14 AOS)

Vertical Temperature structureVertical Temperature structure

AIRS daily T

(a) Regression of T at each level on

850-200mb avg T

For 4 spatial averages,

from all-tropics to 2.5 degree box

Red curve corresp to moist adiabat.

(Daily, as function of spatial scale)

[AIRS lev2 v4 daily avg 11/03-11/05]

(b) Correlation of T(p) to 850-200mb avg T

Vertical Temperature structureVertical Temperature structure

Monthly T regression coeff. of each level on 850-200mb avg T.

(Rawinsondes avgd for 3 trop W Pacific stations)

•CARDS monthly 1953-1999 anomalies, shading < 5% signif.• Curve for moist adiabatic vertical structure in red.

Correlation coeff.

HollowayHolloway & Neelin, JAS, 2007& Neelin, JAS, 2007

QE in climate models QE in climate models (HadCM3, ECHAM5, GFDL CM2.1)(HadCM3, ECHAM5, GFDL CM2.1)

Monthly T anoms regressed on 850-200mb T vs. moist adiabat.

Model global warming T profile response

•Regression on 1970-1994 of IPCC AR4 20thC runs, markers signif. at 5%. Pac. Warm pool= 10S-10N, 140-180E. Response to SRES A2 for 2070-2094 minus 1970-1994 (htpps://esg.llnl.gov).

Vertical structure of moistureVertical structure of moisture

•Ensemble averages of moisture from rawinsonde data at Nauru*, binned by precipitation

•High precip assoc. with high moisture in free troposphere (consistent with Parsons et al 2000; Bretherton et al 2004; Derbyshire 2005)

*Equatorial West Pacific ARM (Atmospheric Radiation Measurement) project site

Autocorrelations in timeAutocorrelations in time

•Long autocorrelation times for vertically integrated moisture (once lofted, it floats around)

•Nauru ARM site upward looking radiometer + optical gauge

Column water vapor

Cloud liquid water

Precipitation

Transition probability to Precip>0Transition probability to Precip>0

•Given column water vapor w at a non-precipitating time, what is probability it will start to rain (here in next hour)

•Nauru ARM site upward looking radiometer + optical gauge

Processes competing in (or with) QEProcesses competing in (or with) QE

• Links tropospheric T to ABL, moisture, surface fluxes --- although separation of time scales imperfect

•Convection + wave dynamics constrain T profile (incl. cold top)

2. Transition to strong convection as a continuous phase 2. Transition to strong convection as a continuous phase transition transition

•Convective quasi-equilibrium closure postulates (Arakawa & Schubert 1974) of slow drive, fast dissipation sound similar to self-organized criticality (SOC) postulates (Bak et al 1987; …), known in some stat. mech. models to be assoc. with continuous phase transitions (Dickman et al 1998; Sornette 1992; Christensen et al 2004)

•Critical phenomena at continuous phase transition well-known in equilibrium case (Privman et al 1991; Yeomans 1992)

•Data here: Tropical Rainfall Measuring Mission (TRMM) microwave imager (TMI) precip and water vapor estimates (from Remote Sensing Systems;TRMM radar 2A25 in progress)

•Analysed in tropics 20N-20S

Peters & Neelin, Nature Phys. (2006) + ongoing work ….

• Precip increases with column water vapor at monthly, daily time scales (e.g., Bretherton et al 2004). What happens for strong precip/mesoscale events? (needed for stochastic parameterization)

• E.g. of convective closure (Betts-Miller 1996) shown for vertical integral:

Precip = (w wc( T))/c (if positive)w vertical int. water vapor

wc convective threshold, dependent on temperature T

c time scale of convective adjustment

BackgroundBackground

Western Pacific precip vs column water vaporWestern Pacific precip vs column water vapor

• Tropical Rainfall Measuring Mission Microwave Imager (TMI) data

• Wentz & Spencer (1998)

algorithm

• Average precip P(w) in each 0.3 mm w bin (typically 104 to 107 counts per bin in 5 yrs)

• 0.25 degree resolution

• No explicit time averaging

Western Pacific

Eastern Pacific

Peters & Neelin, 2006Peters & Neelin, 2006

Oslo model Oslo model (stochastic lattice model motivated by rice pile avalanches)(stochastic lattice model motivated by rice pile avalanches)

• Frette et al (Nature, 1996)

• Christensen et al (Phys. Res. Lett., 1996; Phys. Rev. E. 2004)

Power law fit: OP()=a(-c)

Things to expect from continuous phase transition Things to expect from continuous phase transition critical phenomenacritical phenomena

[NB: not suggesting Oslo model applies to moist convection. Just an example of some generic properties common to many systems.]

• Behavior approaches P(w)= a(w-wc)above transition

• exponent should be robust in different regions, conditions. ("universality" for given class of model, variable)

• critical value should depend on other conditions. In this case expect possible impacts from region, tropospheric temperature, boundary layer moist enthalpy (or SST as proxy)

• factor a also non-universal; re-scaling P and w should collapse curves for different regions

• below transition, P(w) depends on finite size effects in models where can increase degrees of freedom (L). Here spatial avg over length L increases # of degrees of freedom included in the average.

Things to expect (cont.)Things to expect (cont.)

• Precip variance P(w) should become large at critical point.

• For susceptibility (w,L)= L2 P(w,L),

expect (w,L) L/ near the critical region

• spatial correlation becomes long (power law) near crit. point

• Here check effects of different spatial averaging. Can one collapse curves for P(w) in critical region?

• correspondence of self-organized criticality in an open (dissipative), slowly driven system, to the absorbing state phase transition of a corresponding (closed, no drive) system.

• residence time (frequency of occurrence) is maximum just below the phase transition

• Refs: e.g., Yeomans (1996; Stat. Mech. of Phase transitions, Oxford UP), Vespignani & Zapperi (Phys. Rev. Lett, 1997), Christensen et al (Phys. Rev. E, 2004)

log-log Precip. vs (w-wlog-log Precip. vs (w-wcc))

• Slope of each line () = 0.215

Eastern Pacific

Western Pacific

Atlantic ocean

Indian ocean

shifted for clarity

(individual fits to within ± 0.02)

How well do the curves collapse when rescaled?How well do the curves collapse when rescaled?

• Original (seen above)

Western PacificEastern Pacific

How well do the curves collapse when rescaled?How well do the curves collapse when rescaled?

• Rescale w and P by factors fp, fw for each region i


i i

Collapse of Precip. & Precip. variance for different Collapse of Precip. & Precip. variance for different regionsregions


Variance

Precip

• Slope of each line () = 0.215

Eastern Pacific

Western Pacific

Atlantic ocean

Indian ocean

Peters & Neelin, 2006Peters & Neelin, 2006

Precip variance collapse for Precip variance collapse for different averaging scalesdifferent averaging scales

Rescaled by L0.42

Rescaled by L2

TMI column water vapor and PrecipitationTMI column water vapor and PrecipitationWestern Pacific exampleWestern Pacific example

TMI column water vapor and PrecipitationTMI column water vapor and PrecipitationAtlantic exampleAtlantic example

Check pick-up with radar precip dataCheck pick-up with radar precip data

•TRMM radar data for precipitation

•4 Regions collapse again with wc scaling

•Power law fit above critical even has approx same exponent as from TMI microwave rain estimate

•(2A25 product, averaged to the TMI water vapor grid)

Mesoscale convective systemsMesoscale convective systems

•Cluster size distributions of contiguous cloud pixels in mesoscale meteorology: “almost lognormal” (Mapes & Houze

1993) since Lopez (1977)

Mesoscale cluster size frequency (log-normal = straight line).From Mapes & Houze (MWR 1993)

Mesoscale cluster sizes from TRMM radarMesoscale cluster sizes from TRMM radar

•clusters of contiguous pixels with radar signal > threshold (Nesbitt et al 2006)

•Ranked by size

•Cluster size distribution alters near critical: increased probability of large clusters

Note: spanning clusters not eliminated here; finite size effects in s-G(s/s)

Mapping water vapor to occupation probabilityMapping water vapor to occupation probability

•For geometric questions, consider probability p of site precipating

•2D percolation is simplest prototype process (site filled with probability p, stats on clusters of contiguous points); view as null model

•p incr near critical water vapor wc est from precip power law

Mean cluster size increase below criticalMean cluster size increase below critical

•Check how mean cluster size changes with probability p of precipitating

•Try against exponent and critical p for site percolation

•~ consistent with this ‘null model’ in a small range below critical; but differs above (to be continued…)

Dependence on Tropospheric temperatureDependence on Tropospheric temperature

•Averages conditioned on vert. avg. temp. T, as well as w (T 200-1000mb from ERA40 reanalysis)

•Power law fits above critical: wc changes, same

•[note more data points at 270, 271]

^

Dependence on Tropospheric temperatureDependence on Tropospheric temperature

•Find critical water vapor wc for each vert. avg. temp. T (western Pacific)

•Compare to vert. int. saturation vapor value binned by same T

•Not a constant fraction of column saturation

^

^

How much precip occurs near critical point?How much precip occurs near critical point?

Contributions to Precip from each T

^

•90% of precip in the region occurs above 80% of critical (16% above critical)---even for imperfect estimate of wc

80%of critical

^

critical

Water vapor scaled by wc (T)

Frequency of occurrence…. drops above criticalFrequency of occurrence…. drops above critical

Frequency of occurrence(all points)

Frequency of occurrencePrecipitating

Precip

Western Pacific for SST within 1C bin of 30CWestern Pacific for SST within 1C bin of 30C

Extending QEExtending QE

•Recall: Critical water vapor wc empirically determined for each vert. avg. temp. T

•Here use to schematize relationship (& extension of QE) to continuous phase transition/SOC properties

^


•Above critical, large Precip yields moisture sink, (& presumably buoyancy sink)

•Tends to return system to below critical

•So frequency of occurrence decreases rapidly above critical


•Frequency of occurrence max just below critical, contribution to total precip max around & just below critical

• Strict QE would assume sharp max just above critical, moisture & T pinned to QE, precip det. by forcing


•“Slow” forcing eventually moves system above critical

•Adjustment: relatively fast but with a spectrum of event sizes, power law spatial correlations, (mesoscale) critical clusters, no single adjustment time …

ImplicationsImplications• Transition to strong precipitation in TRMM observations

conforms to a number of properties of a continuous phase transition; + evidence of self-organized criticality

• convective quasi-equilibrium (QE) assoc with the critical point (& most rain occurs near or above critical)

• but different properties of pathway to critical point than used in convective parameterizations (e.g. not exponential decay; distribution of precip events, high variance at critical,…)

• probing critical point dependence on water vapor, temperature: suggests nontrivial relationship (e.g. not saturation curve)

• spatial scale-free range in the mesoscale assoc with QE •Suggests mesoscale convective systems like critical clusters in other systems; importance of excitatory short-range interactions; connection to mesocale cluster size distribution

• TBD: steps from the new observed properties to better representations in climate models

• + the temptation of even more severe regimes …

Precip pick-up & freqency of occurrence relations on a Precip pick-up & freqency of occurrence relations on a smaller ensemblesmaller ensemble

Frequency of occurrence

Precip

Hurricane Katrina

Aug. 26 to 29, 2005, over the Gulf of Mexico (100W-80W)

TMI Precip. Rate Aug. 28, 2005TMI Precip. Rate Aug. 28, 2005

TMI Precipitation Rate: August 28, 2005

0 105millimeters/hr

land no data

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The transition to strong convection