The transition to strong convection

Transcription

1 The transition to strong convection J. David Neelin 1, Ole Peters 1,2, Chris Holloway 1, Katrina Hales 1, 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 Background: precipitation moist convection & its parameterization; Arakawa s 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

2 The transition to strong convection J. David Neelin 1, Ole Peters 1,2, Chris Holloway 1, Katrina Hales 1, 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 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

3 The transition to strong convection J. David Neelin 1, Ole Peters 1,2,*, Chris Holloway 1, Katrina Hales 1, 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 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 * + thanks to Didier Sornette for connecting the authors & Matt Munnich & Joyce Meyerson for terabytes of help

4 Background: Precipitation climatology January Note intense tropical moist convection zones (intertropical convergence zones) July 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) Modified from Arakawa (1997, 2004) 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

7 Background: Convective Quasi-equilibrium cont d Manabe et al 1965; Arakawa & Schubert 1974 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 adjustment time scale τ 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;

8 Xu,, Arakawa and Krueger 1992 Cumulus Ensemble Model (2-D) Precipitation rates (domain avg): Note large variations Imposed large-scale forcing (cooling & moistening) Experiments: Q km domain, no shear Q km domain, shear Q 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 *10 9 ) 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 t A c = -M b F Closure: t A c = -τ - 1 ( A + ξ), (A + ξ > 0) i.e. M b = (A + ξ)(τf) -1 (for M b > 0) Stochastic modification ξ in cloud base mass flux M b modifies decay of CAPE (convective available potential energy) ξ 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-M b 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., avg minus avg. 4 mm/day model climatology black contour for reference mm/day Fourth Assessment Report models: LLNL Prog. on Model Diagnostics & Intercomparison; SRES A2 scenario (heterogeneous world, growing population, ) for greenhouse gases, aerosol forcing 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 mb avg T. CARDS Rawinsondes avgd for 3 trop Western Pacific stations, AIRS monthly (avg for similar Western Pacific box, ) shading < 5% signif. Curve for moist adiabatic vertical structure in red. Holloway & Neelin,, JAS, 2007 (& Chris s s talk March 14 AOS)

28 Vertical Temperature structure AIRS daily T (Daily, as function of spatial scale) (a) Regression of T at each level on mb 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 mb 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 mb avg T. Correlation coeff. CARDS monthly 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 mb T vs. moist adiabat. Model global warming T profile response Regression on of IPCC AR4 20 th C runs, markers signif. at 5%. Pac. Warm pool= 10S-10N, E. Response to SRES A2 for minus (htpps://esg.llnl.gov).

31 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) Vertical structure of moisture *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 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 Transition probability to Precip>0

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 wellknown 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 Background 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 w c ( T))/τ c (if positive) w vertical int. water vapor w c convective threshold, dependent on temperature T τ c time scale of convective adjustment

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 10 4 to 10 7 counts per bin in 5 yrs) 0.25 degree resolution No explicit time averaging Eastern Pacific Western Pacific Peters & Neelin,, 2006

38 Oslo model (stochastic lattice model motivated by rice pile avalanches) Power law fit: OP(ζ)=a(ζ-ζ c ) β 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-w c ) β above transition exponent β 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.

40 Things to expect (cont.) Precip variance σ P(w) should become large at critical point. For susceptibility χ(w,l)= L 2 σ P(w,L), expect χ (w,l) L γ/ν 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 σ 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)

41 log-log Precip. vs (w-w c ) Slope of each line (β) = Eastern Pacific Western Pacific Atlantic ocean Indian ocean shifted for clarity (individual fits to β within ± 0.02)

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

43 How well do the curves collapse when rescaled? Rescale w and P by i i factors f p, f w for each region i Western Pacific Eastern Pacific

44 Collapse of Precip.. & Precip.. variance for different regions Slope of each line (β) = Variance Eastern Pacific Western Pacific Atlantic ocean Indian ocean Precip Western Pacific Eastern Pacific Peters & Neelin,, 2006

45 Precip variance collapse for different averaging scales Rescaled by L 2 Rescaled by L 0.42

46 TMI column water vapor and Precipitation Western Pacific example

47 TMI column water vapor and Precipitation Atlantic example

48 Check pick-up with radar precip data TRMM radar data for precipitation 4 Regions collapse again with w c 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 Cluster size distributions of contiguous cloud pixels in mesoscale meteorology: almost lognormal (Mapes & Houze 1993) since Lopez (1977) Mesoscale convective systems 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 -τ G(s/s ξ )

51 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 w c est from precip power law

52 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 )

53 Preliminary: water vapor Precip.. relation temperature dependence Average Standard deviation July ERA40 reanalysis daily Temperature: Tropospheric vertical average ( mb)

54 Dependence on Tropospheric temperature Averages conditioned on vert. avg. temp. ^ T, as well as w (T mb from ERA40 reanalysis) Power law fits above critical: w c changes, same β [note more data points at 270, 271]

55 Dependence on Tropospheric temperature Find critical water vapor w c 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

56 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 w c 80% of critical critical Water vapor scaled by w c (T) ^

57 Frequency of occurrence.. drops above critical Western Pacific for SST within 1C bin of 30C Frequency of occurrence (all points) Frequency of occurrence Precipitating Precip

58 Extending QE Recall: Critical water vapor w c empirically determined for each vert. avg. ^ temp. T Here use to schematize relationship (& extension of QE) to continuous phase transition/soc properties

59 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

60 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

61 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

62 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

63 Precip pick-up & freqency of occurrence relations on a smaller ensemble Aug. 26 to 29, 2005, over the Gulf of Mexico (100W-80W) Frequency of occurrence Precip Hurricane Katrina

64 TMI Precip.. Rate Aug. 28, 2005 TMI Precipitation Rate: August 28, millimeters/hr land no data

65 Background The transition to strong convection QE and Vertical structures Temperature Moisture Continuous phase transition to strong convection Nature Physics Radar & Clusters Critical moisture as a function of temperature