Transcript Convective quasi-equilibrium (QE): Arakawa’s vision upheld and extended

Convective quasi-equilibrium (QE):
Arakawa’s 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 Randall’s talk)
• A sample of recent topics with a basis in Akio’s 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
Background: 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 quasiequilibrium 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)
As 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; BM86=Betts&Miller 1986
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 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; …
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)
Vertical Temperature structure
(Daily, as function of spatial scale)
AIRS daily T
(a) 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
(& Chris’s AMS talk Thursday)
[AIRS lev2 v4 daily avg 11/03-11/05]
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
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).
Processes 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
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)
• 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)
Xu, Arakawa and Krueger 1992
Cumulus 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
Xu et al (1992) Cumulus Ensemble Model
Mesoscale organization
No shear
Cloud-top
temperatures
With shear
Stochastic 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
Closure:
tA c = -MbF
tA c = -t -1A
Mb = A(tF)-1 (for Mb > 0)
Stochastic modification
Mb = (A + x)(tF)-1
tA c = -t -1( A + x) ,
(A + x > 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
Impact of CAPE stochastic convective
parameterization on tropical intraseasonal
variability in QTCM
Lin &Neelin 2000
CCM3 variance of daily precipitation
Control run
CAPE-Mb scheme
(60000 vs 20000)
Observed (MSU)
Lin &Neelin 2002
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 ….
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
Western Pacific precip vs column water vapor
• Tropical Rainfall Measuring
Mission Microwave Imager
(TMI) data
Western Pacific
• Wentz & Spencer (1998)
algorithm
• Average precip P(w) in each
Eastern Pacific
4
0.3 mm w bin (typically 10 to
107 counts per bin in 5 yrs)
• 0.25 degree resolution
• No explicit time averaging
Peters & Neelin, 2006
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)
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)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.
Things 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)  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)
log-log Precip. vs (w-wc)
• Slope of each line (b) = 0.215
shifted
for
clarity
(individual fits to b within ± 0.02)
How well do the curves collapse when rescaled?
• Original (seen above)
Western Pacific
Eastern Pacific
How well do the curves collapse when rescaled?
• Rescale w and P by
factors fpi, fwi for each
region i
Western Pacific
Eastern Pacific
Collapse of Precip. & Precip. variance for different
regions
• Slope of each line (b) = 0.215
Variance
Precip
Western Pacific
Eastern Pacific
Peters & Neelin, 2006
Precip variance collapse for
different averaging scales
Rescaled by L2
Rescaled by L0.42
TMI column water vapor and Precipitation
Western Pacific example
Dependence 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 b
• [note more data
points at 270, 271]
Dependence 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
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 wc
80%
of critical
critical
^
Water vapor scaled by wc (T)
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
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 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)?
Extending 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
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
Extending 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 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 …
QE 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”….
• Arakawa’s 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