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The transition to strong 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.

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The transition to strong convection

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  1. 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

  2. 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

  3. 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

  4. Background: Precipitation climatology July January Note intense tropical moist convection zones (intertropical convergence zones) 2 8 16 4 mm/day

  5. 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)

  6. 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)

  7. 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; …

  8. 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

  9. 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)

  10. 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

  11. Impact of CAPE stochastic convective parameterization on tropical intraseasonal variability in QTCM Lin &Neelin 2000

  12. CCM3 variance of daily precipitation Control run CAPE-Mb scheme (60000 vs 20000) Observed (MSU) Lin &Neelin 2002

  13. 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)

  14. 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

  15. GFDL_CM2.0 DJF Prec. Anom.

  16. CCCMA DJF Prec. Anom.

  17. CNRM_CM3 DJF Prec. Anom.

  18. CSIRO_MK3 DJF Prec. Anom.

  19. NCAR_CCSM3 DJF Prec. Anom.

  20. GFDL_CM2.1 DJF Prec. Anom.

  21. UKMO_HadCM3 DJF Prec. Anom.

  22. MIROC_3.2 DJF Prec. Anom.

  23. MRI_CGCM2 DJF Prec. Anom.

  24. NCAR_PCM1 DJF Prec. Anom.

  25. MPI_ECHAM5 DJF Prec. Anom.

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

  27. 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)

  28. 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]

  29. 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

  30. 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).

  31. 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

  32. 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

  33. 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

  34. 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)

  35. 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 ….

  36. 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))/tc (if positive) • w vertical int. water vapor • wcconvective threshold, dependent on temperature T • tc time scale of convective adjustment Background

  37. 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

  38. 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)

  39. 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.

  40. 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)

  41. 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)

  42. How well do the curves collapse when rescaled? Western Pacific Eastern Pacific • Original (seen above)

  43. 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

  44. 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

  45. Precip variance collapse for different averaging scales Rescaled by L2 Rescaled by L0.42

  46. TMI column water vapor and PrecipitationWestern Pacific example

  47. TMI column water vapor and PrecipitationAtlantic example

  48. 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)

  49. 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)

  50. 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)

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