• Background: precipitation Background: precipitation moist convection & its moist convection & its parameterization; Arakawa’s parameterization; Arakawa’s Quasi-Equilibrium postulate 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 Neelin J. David Neelin 1 , , Ole Peters Ole Peters 1,2 1,2 , , Chris Holloway Chris Holloway 1 , , Katrina Hales Katrina Hales 1 , Steve Nesbitt , Steve Nesbitt 3 1 Dept. of Atmospheric Sciences & Inst. of Geophysics and Planetary Physics, U.C.L.A. 2 Santa Fe Institute (& Los Alamos National Lab) 3 U of Illinois at Urbana-Champaign The transition to strong convection The transition to strong convection
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Background: precipitation moist convection & its parameterization; Arakawa’s Quasi-Equilibrium postulate (QE); + reasons to careBackground: precipitation.
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• 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
The transition to strong convection The transition to strong convection
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
• 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
The transition to strong convection The transition to strong convection
J. David NeelinJ. David Neelin11,, Ole PetersOle Peters1,2,*1,2,*, , Chris HollowayChris Holloway11, Katrina Hales, Katrina 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
* + thanks to Didier Sornette for connecting the authors & Matt Munnich & Joyce Meyerson for terabytes of help
•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)
•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;
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.]
• 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
Western PacificEastern Pacific
i i
Collapse of Precip. & Precip. variance for different Collapse of Precip. & Precip. variance for different regionsregions
Western PacificEastern Pacific
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
•So frequency of occurrence decreases rapidly above critical
Extending QEExtending 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 QEExtending 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 …
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