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

The transition to strong convection

- Background: precipitation moist convection & its parameterization; Arakawa’s Quasi-Equilibrium postulate (QE); + reasons to care
- QE in vertical structure
- The onset of strong convection regime

as a continuous phase transition

with critical phenomena

J. David Neelin1, Ole Peters1,2,

Chris Holloway1, Katrina Hales1, Steve Nesbitt3

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

- 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 regime

as a continuous phase transition

with critical phenomena

J. David Neelin1, Ole Peters1,2,

Chris Holloway1, Katrina Hales1, Steve Nesbitt3

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

- 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 regime

as a continuous phase transition

with critical phenomena

J. David Neelin1,Ole Peters1,2,*,

Chris Holloway1, Katrina Hales1, Steve Nesbitt3

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

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

Background: Precipitation climatologyJuly

January

Note intense tropical moist convection zones (intertropical convergence zones)

2

8

16

4

mm/day

Rainfall 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)

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 Arakawa (1997, 2004)

Background: Convective Quasi-equilibrium cont’d

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

- 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 adjustmenttime scale tc 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; …

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

Precipitation rates (domain avg): Note large variations

Imposed large-scale forcing (cooling & moistening)

Experiments: Q03 512 km domain, no shear

Q02 512 km domain, shear

Q04 1024 km domain, shear

Departures 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 (CCM3* & similar in QTCM**)

- Mass flux closure in Zhang - McFarlane (1995) scheme
- Evolution of CAPE, A, due to large-scale forcing, F
- ¶tAc = -MbF
- Closure:¶tAc = -t -1( A + x) , (A + x > 0)
- i.e.Mb = (A + x)(tF)-1(for Mb > 0)
- Stochastic modification x 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 parameterization on tropical intraseasonal variability in QTCM

Lin &Neelin 2000

CCM3 variance of daily precipitation

Control run

CAPE-Mb scheme

(60000 vs 20000)

Observed (MSU)

Lin &Neelin 2002

Background 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 simulations

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

- Fourth Assessment Report models: LLNL Prog. on Model Diagnostics & Intercomparison;
- SRES A2 scenario (heterogeneous world, growing population,…) for greenhouse gases, aerosol forcing

4 mm/day

model

climatology

black contour for reference

mm/day

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

GFDL_CM2.0

DJF Prec. Anom.

CCCMA

DJF Prec. Anom.

CNRM_CM3

DJF Prec. Anom.

CSIRO_MK3

DJF Prec. Anom.

NCAR_CCSM3

DJF Prec. Anom.

GFDL_CM2.1

DJF Prec. Anom.

UKMO_HadCM3

DJF Prec. Anom.

MIROC_3.2

DJF Prec. Anom.

MRI_CGCM2

DJF Prec. Anom.

NCAR_PCM1

DJF Prec. Anom.

MPI_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)?

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

Vertical Temperature structure

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

CARDS Rawinsondes avgd for 3 trop Western Pacific stations, 1953-99

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

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

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

Vertical Temperature structure

(Daily, as function of spatial scale)

AIRS daily T

- 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.

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

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

Vertical Temperature structure

(Rawinsondes avgd for 3 trop W Pacific stations)

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

Correlation coeff.

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

Holloway& Neelin, JAS, 2007

QE in climate models (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 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 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>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) 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 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)### Background

- E.g. of convective closure (Betts-Miller 1996)shown for vertical integral:
- Precip= (w-wc( T))/tc (if positive)
- w vertical int. water vapor
- wcconvective threshold, dependent on temperature T
- tc time scale of convective adjustment

Western 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, 2006

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

Power law fit: OP(z)=a(z-zc)b

- Frette et al (Nature, 1996)
- Christensen et al (Phys. Res. Lett., 1996; Phys. Rev. E. 2004)

Things to expect from continuous phase transition critical 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)babove transition
- exponent b 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-scalingP 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.)

- Precip variancesP(w) should become large at critical point.
- For susceptibility c(w,L)= L2sP(w,L),

expect c (w,L) µLg/n 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 sP(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 maximumjust 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-wc)

- Slope of each line (b) = 0.215

shifted for clarity

Eastern Pacific

Western Pacific

Atlantic ocean

Indian ocean

(individual fits to b within ± 0.02)

How well do the curves collapse when rescaled?

Western Pacific

Eastern Pacific

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

i

i

Collapse of Precip. & Precip. variance for different regions

- Slope of each line (b) = 0.215

Variance

Eastern Pacific

Western Pacific

Precip

Atlantic ocean

Indian ocean

Western Pacific

Eastern Pacific

Peters & Neelin, 2006

Check 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 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 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-tG(s/sx)

Mapping 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 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 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 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?

80%

of critical

critical

^

Water vapor scaled by wc (T)

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

Frequency of occurrence…. drops above critical

Western Pacific for SST within 1C bin of 30C

Frequency of occurrence

(all points)

Precip

Frequency of occurrence

Precipitating

Extending 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

^

Extending QE

- 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

Extending QE

- 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

Extending QE

- “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 …

Implications

- 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 smaller ensemble

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

Precip

Frequency of

occurrence

Hurricane Katrina

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