Title: Background (see also David Randall
1Convective quasi-equilibrium (QE) Arakawas
vision upheld and extended
J. David Neelin1, Ole Peters1,2, ( Chris
Holloway1, Katrina Hales1)
1Dept. of Atmospheric Sciences Inst. of
Geophysics and Planetary Physics, U.C.L.A. 2Santa
Fe Institute
- Background (see also David Randalls talk)
- A sample of recent topics with a basis in Akios
work - - QE as seen in vertical T structure
- ( implications for the large
scale flow) - - QE and stochastic parameterization
- - QE and the onset of strong convection
regime as a continuous phase transition with
critical phenomena
2Background Arakawa and Schubert 1974
- When the time scale of the large-scale forcing,
is sufficiently larger than the convective
adjustment time, the cumulus ensemble follows a
sequence of quasi-equilibria with the current
large-scale forcing. We call this the
quasi-equilibrium assumption. - The adjustment will be toward an equilibrium
state characterized by balance of the cloud
and large-scale terms - Convection acts to reduce a measure of buoyancy,
the cloud work function A (for a spectrum of
entraining plumes)
3As summarized in Arakawa 1997, 2004 (modified)
- 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 BM86BettsMiller 1986
4Background Convective Quasi-equilibrium contd
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 q, including constraining vertical
structure - using a finite adjustment time 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
5 1. Tropical vertical Temperature structure
- 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)
6Vertical 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
Holloway Neelin, JAS, 2007 ( Chriss AMS talk
Thursday)
AIRS lev2 v4 daily avg 11/03-11/05
7Vertical 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 lt 5
signif. - Curve for moist adiabatic vertical structure in
red.
Holloway Neelin, JAS, 2007
8QE 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).
9Processes competing in (or with) QE
- Convection wave dynamics constrain T profile
(incl. cold top) - Links tropospheric T to ABL, moisture, surface
fluxes --- although separation of time scales
imperfect - Bretherton and Smolarkiewicz 1989 Yano and
Emanuel 1991 Yu Neelin 1994 Emanuel et al
1994 N97 Raymond 2000 Yano 2000 Zeng et al
2000 Su et al 2001 Chiang et al 2001 Chiang
Sobel 2002 Su Neelin 2002 Fuchs and Raymond
2002
10Departures 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) - Can such variations about QE be represented by
either - a stochastic parameterization? Buizza et al
1999 Lin and Neelin 2000, 2002 Craig and Cohen
2006 Teixeira et al 2007 - or superparameterization? with embedded cloud
model (see talk by D. Randall)
11Xu, 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
12Xu et al (1992) Cumulus Ensemble Model Mesoscale
organization
No shear
With shear
Cloud-top temperatures
13Stochastic convection scheme tested in CCM3 (and
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 -t -1A
ð Mb
A(tF)-1 (for Mb gt 0) Stochastic modification
Mb (A x)(tF)-1 ð tA c -t -1( A
x) , (A x gt 0) i.e., stochastic
effect in cloud base mass flux Mb modifies decay
of CAPE (convective available potential energy) x
Gaussian, specified autocorrelation time, e.g.
1day Quasi-equilibrium Tropical Circulation Model
14Impact of CAPE stochastic convective
parameterization on tropical intraseasonal
variability in QTCM
Lin Neelin 2000
15CCM3 variance of daily precipitation
Control run
CAPE-Mb scheme (60000 vs 20000)
Observed (MSU)
Lin Neelin 2002
16Transition 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 SystemsTRMM
radar 2A25 in progress) - Analysed in tropics 20N-20S
Peters Neelin, Nature Phys. (2006) ongoing
work .
17 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 - wc( T))/tc (if
positive) - w vertical int. water vapor
- wc convective threshold, dependent on
temperature T - tc time scale of convective adjustment
18Western 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
19Oslo 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)
20Things 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)b above
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-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.
21Things to expect (cont.)
- Precip variance sP(w) should become large at
critical point. - For susceptibility c(w,L) L2 sP(w,L),
- expect c (w,L) µ Lg/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
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)
22log-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)
23How well do the curves collapse when rescaled?
24How well do the curves collapse when rescaled?
- Rescale w and P by factors fp, fw for each region
i
i
i
25Collapse 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
26Precip variance collapse for different averaging
scales
Rescaled by L2
Rescaled by L0.42
27TMI column water vapor and PrecipitationWestern
Pacific example
28TMI column water vapor and PrecipitationAtlantic
example
29Dependence 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
30Dependence 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
31How 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 wc
32Frequency of occurrence. drops above critical
Western Pacific for SST within 1C bin of 30C
Frequency of occurrence (all points)
Precip
Frequency of occurrence Precipitating
33Implications
- Transition to strong precipitation in TRMM
observations conforms to a number of properties
of a continuous phase transition evidence
of self-organized criticality - convective 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) - 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 (Mapes
Houze 1993 Nesbitt et al 2006) - Mimic properties in stochastic convection schemes
(Buizza et al 1999, Lin Neelin 2000, Majda and
Khouider 2002)?
34Extending 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
35Extending 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
36Extending 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
37Extending 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
38QE or not QE?
- After 3 decades, QE remains a natural first
approximation - But with new emphasis on the importance of the
adjustment process because - separation of time scales does not hold uniformly
- there are associated critical phenomena
- Although now a little More quasi.
- Arakawas framework of ensembles of convecting
elements acting to constrain moisture and
temperature profiles by reducing the source of
instability remains a pillar of convective
parameterization and a powerful tool in
theoretical exploration of the interaction of
convection with larger scales