1. J. David Neelin 1,2, Katrina Hales 1, Ole Peters 1,5, Ben Lintner 1,2,7, Baijun Tian 1,4, Chris Holloway 3, Rich Neale 10, Qinbin Li 1, Li Zhang 1, Sam Stechmann 6, Prabir Patra 8, Mous Chahine 9 1 Dept. of Atmospheric Sciences & 2 Inst. of Geophysics and Planetary Physics, UCLA 3 University of Reading 4 Joint Institute for Regional Earth System Science and Engineering, UCLA 5 Imperial College, Grantham Inst. 6 Dept. Of Mathematics, UCLA 7 Dept. of Environmental Sciences, Rutgers 8 Frontier Research Center for Global Change, Japan 9 Jet Propulsion Laboratory 10 National Center for Atmospheric Research Deep convection --- transition and tails Characterizing transition to deep convection Long tails in distributions of column tracers

2. 2. Transition to strong convection ;Convective quasi-equilibrium assumptions: Above onset threshold, convection/precip. increase keeps system close to onset Arakawa & Schubert 1974; Betts & Miller 1986; Moorthi & Suarez 1992; Randall & Pan 1993; Zhang & McFarlane 1995; Emanuel 1993; Emanuel et al 1994; Bretherton et al. 2004; … Pick up a function of buoyancy-related fields – temperature T & moisture (here column integrated moisture w) Elsewhere: Onset of strong convection conforms to list of properties for continuous phase transition with critical phenomena (Peters & Neelin 2006, Nature Physics) ; mesoscale implications (Peters, Neelin & Nesbitt 2009, JAS) Stochastic convective schemes (and old-fashioned schemes too) need to better characterize the transition to deep convection

3. Precip increases with column water vapor at monthly, daily time scales (e.g., Bretherton et al 2004). What happens at shorter time scales needed for stochastic convective parameterization, and for strong precip/mesoscale events? Simple e.g. of convective closure (Betts-Miller 1996) shown for vertical integral: Precip = (w  w c ( T) +  )/  c (if positive, zero otherwise) w vertical integrated column water vapor w c convective threshold, dependent on temperature T  c time scale of convective adjustment  Stochastic modification  ( Lin &Neelin, 2000) Transition to strong, deep convection: Background Transition to strong, deep convection: Background

4. Precip. dependence on tropospheric temperature & column water vapor from TMI* Averages conditioned on vert. avg. temp. T, as well as w (T 200-1000mb from ERA40 reanalysis) Power law fits above critical: P(w)=a(w-w c )  w c changes, same  [note more data points at 270, 271] ^ *TMI: Tropical Rainfall Measuring Mission Microwave Imager (Hilburn and Wentz 2008), 20N-20S Neelin, Peters & Hales, 2009, JAS E. Pacific

5. Collapsed statistics for observed precipitation Precip. mean & variance dependence on w normalized by critical value w c ; occurrence probability for precipitating points (for 4 T values); Event size distribution at Nauru Neelin, Peters, Lin, Holloway & Hales, Phil Trans. Roy. Soc. A, 2008

6. Example from Manna (1991) lattice model (hopping particles—not a model of convection! 20x20 grid shown) Activity (order parameter) & variance dependence on particle density (tuning parameter) [conserving case] Occurrence probability (log scale; very Gaussian) & event size distribution [self organizing case] Neelin, Peters, Lin, Holloway & Hales, Phil Trans. Roy. Soc. A, 2008

7. TMI precipitation and column water vapor spatial correlations

8. TMI-AMSRE precipitation and column water vapor temporal correlations

9. Critical point dependence on temperature Find critical water vapor w c for each vert. avg. temp. T Compare to vert. int. saturation vapor value binned by same T Not e.g., a constant fraction of column saturation lower tropospheric saturation q sat (T) binning gives same results ^ ^ Neelin, Peters & Hales, 2009, JAS

10. Saturation value q sat (T) by level Saturation mixing ratio by level binned by vert. avg. temp. T Compare to critical value & vert. int. saturation value vs. T Appears consistent with substantial control by lower free troposphere proximity to saturation ^ ^

11. 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 roughly same exponent as from TMI microwave rain estimate (2A25 product, averaged to the TMI water vapor grid) (w-w c )/w c Peters, Neelin & Nesbitt, JAS, 2009 Peters, Neelin & Nesbitt, JAS, 2009

12. Entraining convective available potential energy and precipitation binned by column water vapor, w buoyancy & precip. pickup at high w boundary layer and lower free troposph. moisture contribute comparably* consistent with importance of lower free tropospheric moisture (Austin 1948; Yoneyama and Fujitani 1995; Wei et al. 1998; Raymond et al. 1998; Sherwood 1999; Parsons et al. 2000; Raymond 2000; Tompkins 2001; Redelsperger et al. 2002; Derbyshire et al. 2004; Sobel et al. 2004; Tian et al. 2006) *Brown & Zhang 1997 entrainment; scheme and microphysics affect onset value, though not ordering. Neelin, Peters, Lin, Holloway & Hales, Phil Trans. Roy. Soc. A, 2008 Holloway & Neelin, JAS, 2009

13. Binning q, precip. on vert. int. water vapor Spec. humidity, qPrecip. [Note fewer soundings in high bins] Holloway & Neelin, JAS, 2009 Nauru ARM site observations Binned by: Column water vapor 850- 200 mb Surface- 950mb

14. No mixing Const. mixing (Brown & Zhang 1997) Const. mixing, only q in free tropos. changes Const. mixing, with q in free tropos. constant Lifted parcel buoyancy by column water vapor bins Highest column water vapor bins most buoyant Both boundary layer and lower free troposphere contribute

15. Deep inflow mixing A Deep inflow mixing B Deep inflow mixing B with instant freezing (reversible) Deep inflow mixing A with instant freezing (reversible) Lifted parcel buoyancy by column water vapor bins Highest few column water vapor bins deep convective microphysics between these cases; large potential impact

16. Prec & column water vapor: 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 Neelin, Peters, Lin, Holloway & Hales, 2008, Phil Trans. Roy. Soc. A

17. Precip conditioned on lag/lead column water vapor High water vapor several hours ahead still useful for pickup in precipitation Consistent with high water vapor  favorable environment, but stochastic plume Nauru ARM site upward looking radiometer + optical gauge Holloway& Neelin JAS subm.

18. CAM3.5 * preliminary comparison: Quasi equilibrium mass flux closure: Zhang - McFarlane (1995) scheme modified with entraining plumes, convective momentum transport (Neale et al. 2008) Mass flux M b  entraining CAPE **, A, due to large-scale forcing, F M b = A /(  c F) (for M b > 0) *Community Atmosphere Model 3.5: 0.5 degree short term climate projection experiment (Gent et al. 2009, Clim. Dyn. sub) ** Convective available potential energy

19. Averages conditioned on vert. avg. temp. T, as well as column water vapor w Linear fits above critical (motivated by parameterizn) P(w)=a(w-w c )  as obs. but  =1 : to estimate w c E. Pac. * * Runs, data R. Neale, analysis K. Hales How do models do? CAM3.5 (0.5 degree run) * : Precip. dependence on tropospheric temperature & column water vapor

20. Averages conditioned on vert. avg. temp. T, as well as column water vapor w Linear fits above critical Rain rates can reach high values---0.5 degree res? revisedplumes? W. Pac. * * Runs, data R. Neale, analysis K. Hales

21. Critical point dependence on temperature CAM3.5 preliminary comparison critical water vapor w c for each vert. avg. temp. T Compare to vert. int. saturation vapor value binned by same T Suggests suitable entraining plumes can capture T dependence ^ ^

22. averages conditioned on lower trop. layer q sat (T), &water vapor coarse-grained to 24km grid so far Jan 1997, 1hr av P, each 3hr T dependence ~as expected; small curvature above critical WRF W. Pac (4 km run) preliminary comparison * : Precip. dependence on lower tropospheric temperature ( q sat ) & water vapor * * analysis Hsiao-ming Hsu lower trop. int. water vapor (mm) lower trop. q sat (T) PP

23. Obs. Freq. of occurrence of w/w c (precipitating pts) Gaussian core Critical Eastern Pacific for various tropospheric temperatures But exponential tail above critical pt.  more large events (e.g. Shraiman & Siggia 1994, Pierrehumbert 2000, Bourlioux & Majda 2002) with Gaussian core, akin to forced tracer advection- diffusion problems (e.g. Shraiman & Siggia 1994, Pierrehumbert 2000, Bourlioux & Majda 2002) Exponential tail Peak just below critical pt.  self-organization toward w c

24. Precipitating freq. of occurrence vs. w/w c Gaussian core? Critical Eastern Pacific for various tropospheric temperatures Includes super-Gaussian ~exponential range above critical pt. Exponential range? CAM3.5 preliminary comparison Column saturation

25. coarse-grained to 24km grid so far Jan 1997 (not conditioned on precipitation) exponential range (?) small; faster drop above q sat * * analysis Hsiao-ming Hsu lower trop. int. water vapor (mm) WRF W. Pac (4 km run) preliminary comparison * : frequency of occurrence N of lower tropospheric water vapor by q sat (T) lower trop. q sat (T) N ~Exponential range? q sat =38 w c (38)

26. Passive tracer advection-diffusion---probability density function from simple flow configuration Bourlioux & Majda 2002 Phys. Fluids “Vertical” flow (across gradient) const in vertical, sinusoidal in horizontal, Gaussian in time; horizontal flow constant in space, sinusoid in time High Peclet number (low diffusivity) PDF 5.10 2 <Pe<10 4 & asymptotic

27. Passive tracer advection-diffusion---probability density function from simple flow configuration S. Stechmann following methods of Bourlioux & Majda 2002 Phys. Fluids “Vertical” flow (across gradient) const in vertical, sinusoidal in horizontal, Gaussian in time; horizontal flow constant in space, sinusoid in time Varying Peclet number Pe=

28. Passive tracer advection-diffusion---probability density function from simple flow configuration Adapted from Bourlioux & Majda 2002 Phys. Fluids “Vertical” flow (across gradient) const in vertical, sinusoidal in horizontal, Gaussian in time; horizontal flow constant in space, sinusoid in time High Peclet number (low diffusivity) Pe=10 4 Varying autocorrelation-time  j of flow ´

29. TMI probability density function for observed column water vapor Analysis: Baijun Tian Anomalies relative to monthly mean, tropical oceans 20S-20N Gaussian core (fit at half power) ~exponential on high side

30. NCEP reanalysis daily column water vapor probability density function Anomalies relative to 30-day running mean Asymmetric exponential tails, assoc. with ascent/descent Low precip.: symmetric exponential tails Analysis: Ben Lintner

31. Column water vapor and Idealized tracer probability density functions from Atm. Chem. Transport Model* Anomalies relative to 30-day running mean, 30S-30N Idealized tracer (no sink, remove slow trend), surface input strip Analysis: Ben Lintner, runs by Prabir Patra *Center for Climate System Research/National Institute for Environmental Studies/ Frontier Research Center for Global Change Chemistry- Transport Model (CCSR/NIES/FRCGC ACTM) 2.8° res ~exponential tails

32. Distribution of Column-int. MOPITT CO obs. & GEOS-Chem simulations 20S-20N & subregions ~exponential tails 2000-2005 2001-2006 Analysis: B. Tian, Q. Li, L. Zhang

33. Idealized tracer probability density functions from Atm. Chem. Transport Model* Anomalies relative to 30-day running mean, 20S-20N Idealized tracer (no sink, remove slow trend), surface input strip 40N Analysis by Ben Lintner, runs by Prabir Patra *Center for Climate System Research/National Institute for Environmental Studies/ Frontier Research Center for Global Change Chemistry- Transport Model (CCSR/NIES/FRCGC ACTM) 2.8° res ~exponential tails

34. Distribution of daily CO 2 anomalies AIRS retrievals (Chahine et al 2005, 2008) GEOS-Chem simulations projected on AIRS weighting functions (Analysis: Ben Lintner) (Analysis: Qinbin Li, Li Zhang)

35. These statistics for precipitation and buoyancy related variables at short time scales provide promising means to quantify the transition to tropical deep convection --- collapse of dependences on temperature and water vapor to simple forms is handy; properties known to appear together in much simpler systems--- it should be possible to capture these in stochastic convection schemes Tracer distributions consistent with simple prototypes; core with stretched exponential tails ubiquitous for various tracers Corroborating evidence that the forced tracer advection problem, with the leading effect due to maintained vertical gradient, creates the long tails above critical in column water vapor--- TBD: implications for extreme events Summary

36. Precip. Collapse for various temperatures For various temp. T, as function of w rescaled by critical value (E. Pacific) Quality of the collapse supports w c fits [note scatter at hi/lowest T assoc with fewer data] Inset: log-log above w c ^ Behavior approaches P(w)= a(w-w c )   above transition

37. 2. Vertical structure of moisture, column water vapor associated with buoyancy, precipitation Deep convection, precip assoc. with high moisture in free troposphere (Austin 1948; Yoneyama and Fujitani 1995; Raymond et al. 1998; Sherwood et al. 1999; Parsons et al 2000; Tompkins 2001; Redelsperger et al. 2002; Sobel et al. 2004; Bretherton et al 2004; Derbyshire et al 2005; Tian et al. 2006; …) Ensemble averages of precip, moisture from rawinsonde, radiometer data at Nauru [Equatorial West Pacific ARM (Atmospheric Radiation Measurement) project site] Relate column water vapor, which is widely available, to onset of convection, buoyancy of entraining plumes  constrain entrainment?

38. Binning q, precip. on vert. int. water vapor Spec. humidity, qPrecip. Preliminary e.g. of model analysis by Yunyan Zhang of multi-scale modeling frame- work CAM 3.0 (PNNL/UW set-up; Roger Marchand, Tom Ackerman : Marchand et al 2008 Zhang et al 2008; Khairoutdinov et al 2005) on cloud resolving model grid at Nauru Binned by: Column water vapor 850- 200 mb Surface- 950mb