convective cloud life cycles in a wavy stratified environment brian mapes university of miami
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Convective cloud life cycles in a wavy stratified environment Brian Mapes University of Miami. Life cycle: resemblances. why? MCS: Zipser 1969 MCS: Zipser et al. 1981 2-day: Takayabu et al. 1996 Kelvin: Straub & Kiladis 2004 MJO: Lin and Johnson 1996. Where to begin?. - PowerPoint PPT PresentationTRANSCRIPT
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Convective cloud life cycles Convective cloud life cycles in a wavy stratified environmentin a wavy stratified environment
Brian MapesBrian MapesUniversity of MiamiUniversity of Miami
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Life cycle: resemblances. why?Life cycle: resemblances. why?a)a) MCS: Zipser 1969MCS: Zipser 1969b)b) MCS: Zipser et al. 1981MCS: Zipser et al. 1981c)c) 2-day: Takayabu et al. 19962-day: Takayabu et al. 1996d)d) Kelvin: Straub & Kiladis 2004Kelvin: Straub & Kiladis 2004e)e) MJO: Lin and Johnson 1996MJO: Lin and Johnson 1996
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THEY LOOK SO THEY LOOK SO SOLIDSOLID
Where to begin?Where to begin?
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Really, more like a Really, more like a voidvoid
BUOYANCY OF LIFTED AIR PARCELSFROM LOW LEVELS
LESSLESS DENSE DENSE THAN ENV.THAN ENV.
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Outline
• The obvious part of convection: white lumpswhite lumps• The invisible embedding flow: a specter. specter. • Spectral laws of stratified flow• “Modes” of convection• The life cycle: why grow just to die?
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Constrained cumuli
• The white part of convection is physically complex
(mixing, microphysics, etc.)
• but bounded by a skin-tight, form-fitting outer surface
”the environment”
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How are white cloud and clear env coupled?
Mass continuity
Even tighter: make sound speed infinite
The shape and size of a cloud can change only as permitted by the massive (but responsive) clear air surrounding it.
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Glimpses of invisible env. flow
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Continutiy in mass coordinates (hydrostatic
pressure)
= -gw vertical mass flux w, times
gravity
(‘weight flux’)
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Vergence of horizontal wind
wind divergence
convergenceor negative divergence
from L. vergere "to bend, turn, tend toward, incline"
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Interpreting a divergence profile
Convection-centric:
“Derivative of the vertical mass flux profile”
Environment-centric:
“Mass source at each pressure level
within the ambient stratification”
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Vn
Measuring divergence: exact area averaging by the divergence theorem
Some area A on Some area A on a pressure a pressure
surface surface
Normal component of
wind along perimeter Vn
Perimeter length increment dl
dl
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Special case: a circular area with a Doppler radar
in the middle
APerimeter =
2RArea = R2
[Vr] = azimuthal mean
of radial velocity
V dA
A=[Vr] x 2/R
Vr
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Velocity vs. Azimuth Display (VAD)
Example: 925 mb in deep convection
Vr
(m/s)
SN E W N
Azimuth
[Vr] < 0
convergence
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low-level con, upper level div
SN E W N
[Vr] < 0at 925 mb
[Vr] > 0at 125 mb
UpwarUpwardd mass mass flux flux in in
betweebetweenn
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Revisiting the outline
• (Intro: white lumps, invisible white lumps, invisible environsenvirons)– will return to observations, I promise
• Spectral laws of stratified flow• “Modes” of convection• The life cycle: why grow just to die?
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Ghosts• specter, from Fr. spectre "image, figure, ghost" (16c.). Spectral from 1815 in the sense of "ghostly".
• spectrum 1611, "apparition, specter, ghost," from L. spectrum.
Online Etymology Dictionarythe other OED
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Ghosts in the laws of motion
•Stratified flow: simplest case–variables:
•w - vertical wind •u - horizontal wind (x-z plane for now)
•b - buoyancy - pressure perturbation
–parameters: •N - buoyancy frequency
(a measure of density stratification)
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Ghosts in the laws of motion
•Stratified flow: simplest case–linearized, Boussinesq, 2Dmass continuity
(rarely put first!)
horiz. momentum (Newton’s 2nd
law)
vertical momentum
1st law of thermodynamics
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Ghosts in the laws of motion
–Familiar game: assume ei(kx+mz-t) form of solution
–diffeq’s yield algebraic dispersion eq. relating ,m,k
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gravity or buoyancy or
internal waves
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Even simpler•Large-scale (hydrostatic) motions–k << m in dispersion relation, or
–discard ∂w/∂t in vertical momentum equation:
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Spectral laws of stratified flow
• phase and group velocities – phase from Gk. ... phantasma "image, phantom".
– group likely from P.Gmc. kruppaz "round mass, lump."
cp = (/k, /m) speed of phantoms
cg = (∂/∂k, ∂/∂m) speed of lumps
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Speed of phantoms AND lumps
• Horizontal phase and group speed samesame:
cp = cg = N/m
• horizontalhorizontal sorting of waves sorting of waves according to their according to their verticalvertical wavelengthwavelength
– hyd. distortion: short waves (small k) go too fast
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Longer verticalvertical wavelengths travel faster horizontallyhorizontally
A complex convective event in a
salt-stratified
tank excites many
vertical wavelengths
in the surrounding
fluid (photo
inverted to resemble a cloud).
Strobe-illuminated dye lines
are displaced horizontall
y, initially in smooth, then more sharply
with time.
Mapes 1993 JAS
earlyearly
latelate
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Revisiting the outline
• (Intro: white lumps, invisible white lumps, invisible environsenvirons)– will return to observations, I promise
• Spectral laws of stratified flow– “Modes” of motion
• “Modes” of convection • The life cycle: why grow just to die?
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Modes: ghosts with boundaries
? ? ?
Upward Upward mass mass fluxflux
divergencedivergence(mass (mass source)source)
solid boundary
how can how can thisthis
really really exist?exist?
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The top
1.The tropopause is a lidlid – Clean discrete modes: show next– Not quite correct, but essence is clear
2.There isn’t one (radiation condition)– Continuum of vertical wavelengths
3.A higher lid (small p where =0)– Vertically prop. waves reflect off the
lid and create an interference pattern– Discretization artificial, bands are
valid
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Tropopause as lid: a pure mode
Response to specified deep convection-like sin(mz) heating, with m =/D
D
Nicholls Pielke Cotton 1991; graphics courtesy S. Tulich
(stratified)
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Response to heating
Vertical velocity w
c = N/m ~50 m/s-c
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Environment feels mass
source (upper) & sink (lower)
Horizontal velocity u
c -c
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Heat radiation
Temperature T
c-cWarm
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Summary of wave/mode background
• The flow of stratified clear air outside convective clouds is dispersive– longer verticalvertical wavelength components expand faster/farther away from source horizontallyhorizontally
• Any vertical profile, e. g. divergence, can be expressed as a spectrum, w/ axis labeled by phase speed. – lid discretizesdiscretizes spectrum; bandsbands robust
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Revisiting the outline
• (Intro: white lumps, invisible white lumps, invisible environsenvirons)
• Spectral laws of stratified flow– “Modes” of motion
• “Modes” of convection • The life cycle: why grow just to die?
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What kinds of vertical structure are observed in
deep convection?
many field obs sources - Houze, Zipser, Johnson,...
Top-Top-heavy heavy heating heating profileprofile
in netin net
deep heating
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“Modes”? Convective and Stratiform
Example: 2 radar echo (rain) maps (w/ VAD circles)
200 km
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Convective & stratiform “modes”
Con
Con
Strat
Strat
In pure simplest
theory case
Con: sin(z)
StratStrat: sin(2z)
Houze 1997 BAMS
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Is all this sin(z) ghost/mode stuff
realistic? realistic? (or kinda (or kinda kookykooky?)?)
• Need: modes of a realistic atmosphere (actual stratification profiles)–Ready: Fulton and Schubert 1985
• Need: realistic heating (divergence) profiles–Ready: many many VAD measurements
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Spectrum of average VAD divergence
from many profiles in tropical rain
different lid different lid pressures -> pressures ->
different different discretizationsdiscretizations
, , bands robustbands robust
Hey -- what’s this?
Mapes 1998
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T response when
observed mean VAD divergence is used as a mass source in observed
mean stratificati
on
Mapes and Houze 1995
Top-heavy CC++SS: spectrum & response
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Melting: forcing is localized in z,
response is
localized in
wavenumber!
Melting mode
Mapes and Houze 1995
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Raw data: Snow melts,
whole troposphere
shivers
(wavelength set by melting layer
thickness?)spectral view spectral view not quite so not quite so
kooky?kooky?
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.m=1
m=3/2
Does this exist?
m=1/2
Re: kookinessAre convective and stratiform really
dynamical modes?
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Rare, but compelling
(great data
quality)
Jialin Lin
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Rare, but compelling
(5h of data, from front to back of storm)
Aboard the R/V BrownJASMINE project
considerable front-back cancellation
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May 22, 1999(figs from U. of Washington webpages on JASMINE)
~15 m/s
Webster et al. 2003, Zuidema 2003
In a storm notable for fast, long-distance
propagation
diurnal
Kousky - Janowiak - Joyce (NOAA CPC)
ship
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Re: kookinessnumerical modeling, with advection
Pandya and Durran 1996
u
u later
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Re: kookiness
Wavefront 2 stays vertical and coherent despite advection by sheared winds nearly half the wave
speed!Pandya and Durran 1996
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Re: kookinessmore numerical modeling
Even convective cells appear to be gravity waves!?
Yang and Houze 1995
This stuff hasn't totally sunk in This stuff hasn't totally sunk in to the convection community to the convection community
(myself included!)(myself included!)
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Spectral questions
• Where do the observed modes come from ultimately?
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Modal (band) responses seen
away from convection
• Yes, Convective and stratiform “modes” seen in T fluctuations, but
• ~15 m/s also prominent
Fast ghosts zipping everywhere - only statistics are
available reliably
?
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A fundamental source for c ~ 15 m/s
radiative
cooling
12km
moist adiabat runs
dry 8km
spectrum of square Qrad
forcingobs. strat.
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NO fundamental source for c ~ 25 m/s ("stratiform
mode")• Apparently excited by processes internal to convective cloudiness
– half-troposphere depth cumulus congestus rainclouds
– precipitating stratiform anvil clouds
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No fundamental source -> GCMs fail
Lack of stratiform processes, or of cumulus showers?
GCM
Deep convectionheating in GCM
Lee Kang Mapes 2001
20N-20S cooling
Deep convectionheating
obs
Earth
Mapes 2000
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Cloud resolving model has it...
Tulich Randall Mapes 2006
shallow cu (SC) & stratiform (ST)
opposed
SC only in lower half of mode
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Revisiting the outline• (Intro: white lumps, invisible white lumps, invisible environsenvirons)
• Spectral laws of stratified flow• “Modes” of convection • The life cycle: why grow just to die?
– A question of coupling between the 2 halves of convective circulations
»(white part + spectral env.)
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Bigger things have longer lives
suggests a key velocity scale (not x or t)
Mapes Tulich Lin Zuidema 2006
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Clean: 4000 km rain waves in a 2D model
(All the followingwork by Stefan Tulich)
cc3
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The life and
death of cc3
a multicellular entity
shallow
deep
strat.
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Why die? Why do new cells fail?
1 km w
arm T’
BUOYANCY OF LIFTED AIR PARCELSFROM LOW LEVELS
env warm
(& dried)
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cell-killing warm wedge:
a downward displacement in a wave
warm T’ cold pools slide under, but new cu
fail
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What does the LS
wave look like?
a larger version of cc3,
of course!
cu in front
deep
strat.
LS wave motion to right
Note T’ no bigger in heated areas - equilibrated wave
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Front edge: wave forces cu clouds
cu heating nestled in low T’, which keeps fallingkeeps falling
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But why does the large scale wave exist?
Must go back to origins(different model run - main wave went R->L)
widening riverwidening riverof wave of wave
amplitudeamplitudeas events as events
trigger next trigger next eventsevents
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Key mechanism: short vertical wavelength mode
change it via
radiative cooling depth and/or
lapse rate
changed wavelengt
h spectrum
actual wave speed changes
accordingly
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Conclusions•Illusion of clouds as substantial is visually compelling–Must be resisted with rationality
•Motions of embedding environment are inseparable, and spectral–Longer vert. waves travel faster –chromatography of outgoing signals–sloped destabilizing by incoming signals
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Not kooky, but a little spooky
•Artifice of upper lid not too bad–believe bands not modes •(but mode is a convenient word)
•Neglect of advection not too bad–wavefronts remain upright & coherent even in shear•how ??
–secondary circs?
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Where does wave-1 of troposphere activity
come from?• Precipitating stratiform anvils force it
• Cumulus congestus showers force it»lower half only
•These cancel on average - there is no physically fundamental source
»large-scale models can miss large-scale models can miss it via parameterization it via parameterization errorserrors
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Convective & stratiform
–Inevitable microphysical outcomes of bubble ascent (rain, ice, etc)? –Or dynamical modes of motion?•What governs downdraft depth for example?
»rain could just saturate air & stop evaporating if descent didn’t agree with the ambient airflow...
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Leading edge of the life cycle
• Is this 2000 km / 20 hour wedge scale governed by the cumulus dynamics of moisture buildup?
• Or does wave cooling invite (by buoyancy) or demand (for balance) a certain heating?
»Sensitivity to precipitation efficiency of cu?
shallow cu heating
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Is the MCS just another
convectively coupled wave
type?
• small scale, large amp., but qualitatatively...
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What’s up with this?
Substantial, very repeatable
deviation from a moist adiabat.
CRMs don’t get it.
microphys (e.g. ice?)
small cu effects?
LS (trades) crucial?
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Discussion welcomedDiscussion welcomedmapes @ miami.edumapes @ miami.edu
Thank you!Thank you!