Convective cloud life cycles
in a wavy stratified environment
Brian Mapes
University of Miami
Life cycle: resemblances. why?
a) MCS: Zipser 1969
b) MCS: Zipser et al. 1981
c) 2-day: Takayabu et al. 1996
d) Kelvin: Straub & Kiladis 2004
e) MJO: Lin and Johnson 1996
Where to begin?
THEY LOOK SO
SOLID
Really, more like a void
BUOYANCY OF
LIFTED AIR PARCELS
FROM LOW LEVELS
LESS DENSE
THAN ENV.
Outline
•
•
•
•
•
The obvious part of convection: white lumps
The invisible embedding flow: a specter.
Spectral laws of stratified flow
“Modes” of convection
The life cycle: why grow just to die?
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”
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.
Glimpses of invisible env. flow
Continutiy in mass coordinates
(hydrostatic pressure)
 = -gw
vertical mass flux w, times gravity
(‘weight flux’)
Vergence of horizontal wind
from L. vergere "to bend, turn, tend toward, incline"
wind
divergence
convergence
or negative
divergence
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”
Measuring divergence: exact area
averaging by the divergence theorem
Some area A on
a pressure
surface
Vn
dl
Normal
component of
wind along
perimeter Vn
Perimeter length
increment dl
Special case: a circular area with a
Doppler radar in the middle
A
Vr
Perimeter = 2R
Area = R2
[Vr] = azimuthal mean
of radial velocity
 V dA

A
= [Vr] x 2/R
Velocity vs. Azimuth Display (VAD)
Example: 925 mb in deep convection
Vr
(m/s)
[Vr] < 0
convergence
N
E
S
Azimuth
W
N
low-level con,
upper level div
[Vr] > 0
at 125 mb
Upward
mass
flux in
between
[Vr] < 0
at 925 mb
N
E
S
W
Revisiting the outline
• (Intro: white lumps, invisible
environs)
– will return to observations, I promise
• Spectral laws of stratified flow
• “Modes” of convection
• The life cycle: why grow just to die?
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 Dictionary
the other OED
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)
Ghosts in the laws of motion
• Stratified flow: simplest case
– linearized, Boussinesq, 2D
mass continuity
(rarely put first!)
horiz. momentum
(Newton’s 2nd law)
vertical momentum
1st law of
thermodynamics
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
gravity or buoyancy
or internal waves
Even simpler
• Large-scale (hydrostatic) motions
– k << m in dispersion relation, or
– discard ∂w/∂t in vertical
momentum equation:
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
Speed of phantoms AND lumps
• Horizontal phase and group speed same:
cp = cg = N/m
• horizontal sorting of waves according
to their vertical wavelength
– hyd. distortion: short waves (small k) go too fast
Longer vertical wavelengths travel
faster horizontally
A complex
convective
event in a saltstratified tank
excites many
vertical
wavelengths in
the surrounding
fluid (photo
inverted to
resemble a
cloud).
early
late
Mapes 1993 JAS
Strobeilluminated dye
lines are
displaced
horizontally,
initially in
smooth, then
more sharply
with time.
Revisiting the outline
• (Intro: white lumps, invisible
environs)
– 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?
Modes: ghosts with boundaries
?
Upwarddivergence
mass
(mass
flux
source)
?
?
how can this
really exist?
solid boundary
The top
1. The tropopause is a lid
– 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
Tropopause as lid: a pure mode
Response to specified deep convection-like sin(mz)
heating, with m =/D
D
(stratified)
Nicholls Pielke Cotton 1991; graphics courtesy S. Tulich
Response to heating
Vertical velocity w
-c
c = N/m ~50 m/s
Environment feels mass
source (upper) & sink (lower)
Horizontal velocity u
-c
c
Heat radiation
Temperature T
-c
Warm
c
Summary of wave/mode
background
• The flow of stratified clear air outside
convective clouds is dispersive
– longer vertical wavelength components
expand faster/farther away from source
horizontally
• Any vertical profile, e. g. divergence,
can be expressed as a spectrum, w/
axis labeled by phase speed.
– lid discretizes spectrum; bands robust
Revisiting the outline
• (Intro: white lumps, invisible
environs)
• Spectral laws of stratified flow
– “Modes” of motion
• “Modes” of convection
• The life cycle: why grow just to die?
What kinds of vertical structure are
observed in deep convection?
deep
heating
Top-heavy
heating
profile
in net
many field obs sources - Houze, Zipser, Johnson,...
“Modes”? Convective and Stratiform
Example: 2 radar echo (rain) maps (w/ VAD circles)
200 km
Convective & stratiform “modes”
Con
Strat
In pure simplest
theory case
Con: sin(z)
Strat: sin(2z)
Con
Strat
Houze 1997 BAMS
Is all this sin(z) ghost/mode stuff
realistic? (or kinda kooky?)
• Need: modes of a realistic atmosphere (actual
 stratification profiles)
– Ready: Fulton and Schubert 1985
• Need: realistic heating (divergence) profiles
– Ready: many many VAD measurements
Spectrum of average VAD divergence
from many profiles in tropical rain
different lid
pressures ->
Hey -what’s
this?
Mapes 1998
different
discretizations,
bands robust
Top-heavy C+S: spectrum & response
T response
when observed
mean VAD
divergence is
used as a mass
source in
observed mean
stratification
Mapes and Houze 1995
Melting mode
Melting:
forcing is
localized in z,
response is
localized in
wavenumber!
Mapes and Houze 1995
Raw data:
Snow melts,
whole
troposphere
shivers
(wavelength set
by melting layer
thickness?)
spectral view not
quite so kooky?
Re: kookiness
Are convective and stratiform really dynamical modes?
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
m=1/2
m=3/2
m=1
Does this exist?
Rare, but compelling
(great data
quality)
Jialin Lin
Rare, but compelling
Aboard the R/V Brown
JASMINE project
considerable
front-back
cancellation
(5h of data, from
front to back of
storm)
In a storm notable
for fast, longdistance
propagation
May 22, 1999
(figs from U. of
Washington web
pages on JASMINE)
diurnal
~15 m/s
ship
Webster et al. 2003, Zuidema 2003
Kousky - Janowiak - Joyce (NOAA CPC)
Re: kookiness
numerical modeling, with advection
u
u later
Pandya and Durran 1996
Re: kookiness
Wavefront 2 stays vertical and coherent despite advection by
sheared winds nearly half the wave speed!
Pandya and Durran 1996
Re: kookiness
more numerical modeling
Yang and
Houze 1995
Even convective cells appear to be gravity waves!?
This stuff hasn't totally sunk in to the
convection community (myself included!)
Spectral questions
• Where do the observed modes come from
ultimately?
Modal (band)
responses seen away
from convection
Fast ghosts zipping
everywhere - only
statistics are available
reliably
• Yes, Convective and
stratiform “modes” seen
in T fluctuations, but
• ~15 m/s also prominent
?
A fundamental source for c ~ 15 m/s
radiative
cooling
12km
moist
adiabat
runs dry
8km
obs.
strat.
spectrum of square
Qrad forcing
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
No fundamental source -> GCMs fail
Lack of stratiform processes, or of cumulus showers?
GCM
Earth
20N-20S
cooling
Deep convection
heating
obs
Mapes 2000
Deep convection
heating in GCM
Lee Kang Mapes 2001
Cloud resolving model has it...
SC only in lower
half of mode
shallow cu (SC) &
stratiform (ST)
opposed
Tulich Randall Mapes 2006
Revisiting the outline
• (Intro: white lumps, invisible
environs)
• 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.)
Bigger things have longer lives
suggests a key velocity scale (not x or t)
Mapes Tulich Lin Zuidema 2006
Clean: 4000 km rain waves in a 2D model
cc3
(All the following
work by Stefan Tulich)
shallow
The life
and death
of cc3
a
multicellular
entity
deep
strat.
Why die? Why do new cells fail?
BUOYANCY OF
LIFTED AIR PARCELS
FROM LOW LEVELS
(& dried)
env warm
cell-killing warm wedge:
a downward displacement in a wave
cold pools slide under,
but new cu fail
What does the
LS wave look
like?
a larger
version of
cc3, of
course!
Note T’ no bigger in
heated areas equilibrated wave
cu in
front
LS wave motion to right
deep
strat.
Front edge: wave forces cu clouds
cu heating nestled in low T’, which keeps falling
But why does the large scale wave exist?
Must go back to origins
(different model run - main wave went R->L)
widening river
of wave amplitude
as events trigger
next events
Key mechanism: short vertical wavelength
changed
mode
wavelength
spectrum
change it via
radiative
cooling depth
and/or lapse
rate
actual wave
speed
changes
accordingly
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
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?
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 it
via parameterization errors
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...
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
Is the MCS just
another convectively
coupled wave type?
• small scale, large amp.,
but qualitatatively...
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?
Discussion welcomed
mapes @ miami.edu
Thank you!