Convective cloud life cycles Convective cloud life cycles in a wavy stratified environmentin a wavy stratified environment

Brian MapesBrian MapesUniversity of MiamiUniversity of Miami

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

THEY LOOK SO THEY LOOK SO SOLIDSOLID

Where to begin?Where to begin?

Really, more like a Really, more like a voidvoid

BUOYANCY OF LIFTED AIR PARCELSFROM LOW LEVELS

LESSLESS DENSE DENSE THAN ENV.THAN ENV.

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?

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)

= -gw vertical mass flux w, times

gravity

(‘weight flux’)

Vergence of horizontal wind

wind divergence

convergenceor negative divergence

from L. vergere "to bend, turn, tend toward, incline"

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”

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

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

Velocity vs. Azimuth Display (VAD)

Example: 925 mb in deep convection

Vr

(m/s)

SN E W N

Azimuth

[Vr] < 0

convergence

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

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?

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

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, 2Dmass 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 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

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

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?

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?

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

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)

Response to heating

Vertical velocity w

c = N/m ~50 m/s-c

Environment feels mass

source (upper) & sink (lower)

Horizontal velocity u

c -c

Heat radiation

Temperature T

c-cWarm

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

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?

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

“Modes”? Convective and Stratiform

Example: 2 radar echo (rain) maps (w/ VAD circles)

200 km

Convective & stratiform “modes”

Con

Con

Strat

Strat

In pure simplest

theory case

Con: sin(z)

StratStrat: sin(2z)

Houze 1997 BAMS

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

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

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

Melting: forcing is localized in z,

response is

localized in

wavenumber!

Melting mode

Mapes and Houze 1995

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?

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?

Rare, but compelling

(great data

quality)

Jialin Lin

Rare, but compelling

(5h of data, from front to back of storm)

Aboard the R/V BrownJASMINE project

considerable front-back cancellation

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

Re: kookinessnumerical modeling, with advection

Pandya and Durran 1996

u

u later

Re: kookiness

Wavefront 2 stays vertical and coherent despite advection by sheared winds nearly half the wave

speed!Pandya and Durran 1996

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!)

Spectral questions

• Where do the observed modes come from ultimately?

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

?

A fundamental source for c ~ 15 m/s

radiative

cooling

12km

moist adiabat runs

dry 8km

spectrum of square Qrad

forcingobs. strat.

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

Deep convectionheating in GCM

Lee Kang Mapes 2001

20N-20S cooling

Deep convectionheating

obs

Earth

Mapes 2000

Cloud resolving model has it...

Tulich Randall Mapes 2006

shallow cu (SC) & stratiform (ST)

opposed

SC only in lower half of mode

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.)

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

(All the followingwork by Stefan Tulich)

cc3

The life and

death of cc3

a multicellular entity

shallow

deep

strat.

Why die? Why do new cells fail?

1 km w

arm T’

BUOYANCY OF LIFTED AIR PARCELSFROM LOW LEVELS

env warm

(& dried)

cell-killing warm wedge:

a downward displacement in a wave

warm T’ cold pools slide under, but new cu

fail

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

Front edge: wave forces cu clouds

cu heating nestled in low T’, which keeps fallingkeeps falling

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

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

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 large-scale models can miss it via parameterization it via parameterization errorserrors

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 welcomedDiscussion welcomedmapes @ miami.edumapes @ miami.edu

Thank you!Thank you!