Mesoscale wind divergence profiles in
convecting regions
Brian Mapes, Jialin Lin, Paquita Zuidema
data thanks to: CSU Radar met group, UW mesoscale group,
TRMM ground validation office
Outline
1. Motivations and methods
2. Results in some easy and hard cases
3. Statistical results
4. A well-measured oddity: JASMINE May 22
5. Summary and future plans
Motivations





Heating in tropical convective clouds drives
larger-scale circulations (LSCs) of many scales
Heating profiles are important to LSC structure,
including feedbacks to convection
Divergence profiles (inflow/outflow) are closely
linked to heating; and affect layer cloudiness
Clear-air (unheated) component of divergence is
smaller, but especially important to feedbacks
Divergent flow is hard to measure accurately, so
better observations may lead to new discovery
Continuing hope: better obs. glimpses of a unique
aspect of deep moist atmospheric convection: it’s
embedded in a stratified environment, where
gravity waves disperse by vertical wavelength
Wind divergence: interpretation
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Rearranging,
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For Q >> dhT/dt (tropical convection scaling), w/the
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= ∂/∂p( Q/s )
Mapes
and
Houze
1995 JAS
Wind divergence : measurement
The divergence theorem for an area A with perimeter P:
Area averaged
divergence =
 V dA



=
Vnormal dP
perim
A
Defining the
perimeter-mean
velocity Vnormal,
For a circular
area, the overbar
is an azimuth mean:
A
 Vnormal
x
P/A
= [Vradial]
x
2pR/pR2
= [Vradial]
x
2/R
Velocity-Azimuth Display (VAD)

At fixed horizontal range (radius) R and altitude,
consider radial velocity Vr vs. azimuth angle
Mean wind =
sine wave
Vr
0
[Vr]
Area-avg divergence
= [Vr] *2/R
(NOTE: no uniformity
wave-2 is
deformation;
real flows
may have
jets, etc. etc.
ws
assumption within circle)
0
azimuth (deg from N)
wd
360
Background: Doppler radar

Precipitation radar
– Radio pulses bounce off hydrometeors
– Z is 6th moment of the DSD, log scale dBZ
– For applications, rainrate R ~some power law in Z

Doppler (coherent) radar
– Pulse pairs sent; Doppler spectrum P(Df) received
– A mean Df gives along-beam velocity:
 Vr = Df/2p * l/Dt
+/- nl/Dt =2nVnyq
– For applications, remove fallspeed Vt(Z)cos(zenith)
Cylindrical data binning for VAD
Dr = 8 km (12 bins, 0-96 km)
Daz = 15° (24 bins)
Dz = 500 m (36 bins)
-->Dp = 50 hPa
Dt = 1 hour
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1 dBZ bins
(for Z-R)
1 m/s bins
4 m/s bins
(only need
nadjust)
Further pool
data, e.g. height
to pressure:
simply sum the
histogram
arrays.
(same for range
or time pooling)
VAD plot for each hour, layer, range (pool)
unfolding
guide for
absolute Vr
(after histogram
compactification)
From GOF, or ind.
ws,wd guess
sampling
error bar
[Vr] <0:
convergence
-2m/s *2/(40km)
= -1e-4 /s
wind: 7 m/s
from 240 deg
used for rel.
weighting in
least-square
3-param fit:
[Vr], ws, wd
Repeat, repeat, repeat…
research radar deployments
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TEPPS: July 1997
 JASMINE: May 1999
 EPIC: September 2001
several 10s of days = many 100s of hours each


EPIC 2001:
timepressure
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Ivo Sparse
48h
(Vr data
everywhere, but
sometimes just
noise)
An example
hourly
product
convection
developing
near radar
48 glorious hours: Sept 23-24
RHB-C
RHB-C
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All points on all curves at
all times are from
independent data:
Continuity in range, time,
altitude encouraging
10x sonde div; decent
mass balance ------>
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RH profiles R=44km div
mass flux
(-omega)
ice
sat
dQ/dp >0
‘onion’
dQ/dp >0
RH soundings, sfc rain, mm cloud radar, VAD div: Paquita Zuidema, ETL
Hard case: lots of Doppler folding
Tropical Storm Ivo
Sept. 10, 2001
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TS Ivo, Sept. 10, 2001
cyclone moves westward, N of ship
wind
13Z
15Z
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v<0
u>0
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17
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18
19
a dna ™e mi Tk ciu Q
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convergence 10-4s-1 x 7h = 2.5, ~10-folding of ~100km scale vorticity
21Z
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v>0
u>0
Vr folding problem at
925mb
looks OK
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clutter in S-W
azimuths:
Vr ~0.
Spike hists
dominate fit
N
E
S
W
~OK
N
Mesoscale wind divergence profiles in
convecting regions
Brian Mapes, Jialin Lin, Paquita Zuidema
data thanks to: CSU Radar met group, UW mesoscale group,
TRMM ground validation office
Outline
1. Motivations and methods
2. Results in some easy and hard cases
3. Statistical results (EPIC, cloud model)
4. A well-measured outlier: JASMINE May 22
5. Summary and future plans
EPIC simple-mean divergence
Mapes and Houze 1995
COARE airborne (mid-troposphere)
Doppler radar over W. Pac.
smaller circles’
fluctuations have
larger amplitude;
convergent times
are undersampled
--> divergent bias
(dQ/dp)
mean
s.d.
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ice small circles
liq have fallspeed
overcorrection error
(steep beam tilt)
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noisy - sea clutter
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To isolate latent heat
associated signal,
regress div on R(Z)
overshoot cooling?
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rain
>0.5
all
data
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Regress div(p) to surface rainfall:
reduces scale dependence, biases
scale-dependent fluctuation intensities cancel out
 can pool or average ranges for more robustness

Uses data when available.
Undersampled times
w/upper convergence
& R~0 don’t affect slope
Badness of crude
ice/liq Vt(Z) assumption
is ~uncorrelated w/
surface rainrate, since
that mainly varies with
coverage, not Z.
div per rain (1e-6 s-1 per mm/h)
recalibrated
Moisture
convergence per
unit rainfall:
R(Z) too
great
R(Z) too
small re-calibrated
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should be ~1
Gross variations of
magnitude in rainconvergence regression
slopes between
experiments
e.g. COARE-MIT Z-R rainrate is
about half the linearly
regressed moisture
convergence, 5 dbZ too low?
(Radar has always been low
outlier of rain estimates Weller et al. 2004)
Why is rain weakly associated w/ low-level
convergence? (hourly, simultaneous, ~100km scale)
Convective vs. stratiform
by horiz. echo texture
(thanks QuickTime™
S. Nesbitt,
and a CSU)
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•
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all data
rain
>0.5
°
div>0
div<0


Multiple linear
regression
teases apart
their pure
signatures
C,S rainrates
are correlated
but have
independent
variability too.
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convergence
~525mb
C autocorrelation
C-S cross
correlation
Con-strat evolution
in total precip lag
regression

Rapid rise of
convergence to
middle levels at time
of precip max

Trimodal cloud tops?
(divergence) rising
with time in advance
of precipitation
1 mm per mm/h
precipitable water 0
from microwave
radiometer (ETL)
3D cloud model
Marat Khairoutdinov
KWAJEX case
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
Divergence of cloudy
updraft mass flux

Trimodal cloud tops,
PW rises then falls
3D cloud model’s
KWAJEX forcing
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
Sonde-array div vs.
model rainrate

Triple divergence
levels, sounding PW
rises then falls

Note 55h time axis!
internal variations in
3D cloud model
divergence and rain in
64x64 km subset of
domain (1/16 of area)
 (about VAD size)


specific humidity in
same area
Tracing back to cases
(fold)
day 270
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a dn a ™ emiTk ci uQ
ro ss e rpm oc ed ) WZ L ( FFIT
.e r ut ci p sih t e es ot d ed ee n e r a
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note
JASMINE
oddity
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Similar picture
from other radar
deployments
(convergence rises
up over several
hours as
convective clouds
turn stratiform)
Convective, stratiform,…?
Are these archetypal components of convective
rainfall rooted in physical processes…?
detrainment
ice physics
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m=1/2
entrainment
(…and is there a
physical process
behind it)?
m=3/2
m=1
water physics
…or in dynamical modes?
(strictly, spectral bands)
One clue:
Does this exist?
(A: Yes, and
Maybe)
A nice touch: interleaved tilts,
for buttery-smooth vert. res.
when pooled over an hour
(2+ volumes)
Mesoscale wind divergence profiles in
convecting regions
Brian Mapes, Jialin Lin, Paquita Zuidema
data thanks to: CSU Radar met group, UW mesoscale group,
TRMM ground validation office
Outline
1. Motivations and methods
2. Results in some easy and hard cases
3. Statistical results
4. A well-measured outlier: JASMINE May 22
5. Summary and future plans
40N
Eastern
Ghats
JASMINE
Bay of
Bengal
May 1999
equator
Dave Lawrence
Mean diurnal cycle of 210K
Meteosat-5 Infrared Imagery
figs by Paquita Zuidema
Mean diurnal cycle of 210K
Meteosat-5 Infrared Imagery
figs by Paquita Zuidema
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JASMINE
May 1999,
spanning
monsoon
onset in the
Bay of
Bengal
JASMINE
squall
(wave?)
May 22, 1999
(figs from U. of
Washington web
pages on JASMINE)
~15 m/s
Webster et al. 2003, Zuidema 2003
17-18Z
JASMINE div(p)
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1604 Z
mass
flux
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JASMINE wavy div(p):
Double-decker convection?
from UW JASMINE web pages
20-21Z
JASMINE div(p)
bad
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bad
JASMINE May22 time-height section
Or is it moist (dry air) processes?
Is it dynamical wave# 3/2?
x - old/
folded
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note very low drying
mm cloud radar data and overlay presentation
by Paquita Zuidema, ETL
Recalling the EPIC case…
dry intrusion: a
physical process,
not simply related
to a dynamical
mode…
but note
deeper layer of
descent drying
in this case,
onion RH min
~3km (725 mb)
JASMINE case IS significantly unusual….
SUMMARY & CONCLUSIONS:
Hourly VAD gives simple, automatic, good divergence measurements
Sensibly consistent w/ surface rain & zenith cloud radar obs.
(full EPIC and JASMINE overlay sections at http://www.etl.noaa.gov/~pzuidema)
We see good ol’ convective & stratiform profiles (ho-hum), but also
•Anvils snowing into dry layers, moistening and cooling their tops
(cooling flattens the dry layer by diabatic divergence dQ/dp>0)
•Steady convergence below 700mb in TS Ivo, to ~10-fold z in 7h
•m=3/2 divergence profile in JASMINE propagating squall/wave:
double-decker convection, and deviations from that pillar of tropical
meso-meteorology, middle level convergence in stratiform rain
•Wavy profiles of div regressed on shallow convective rainfall - are
high and low tropospheric clouds/heating dynamically coupled on
the mesoscale? If so, is random overlap a good assumption?
Mapes and Houze 1992 airborne Doppler, EMEX
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sd
1km res
(subjectively categorized samples)
•Better top!
•Whole troposphere
shorter in EPIC thanQuickTime™
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and a
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(LZW)
decompressor
Australian monsoon
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•More complete life cycle:
MH92 obs were in mature
MCSs and rarely saw
fresh development
convective rain
from 0-5km top
cells
>10km tops
(like MH92
“intermediary”?)
5-10km tops
stratiform
EPIC MLR for 4
categories of
precipitation:
shallow, deep,
very deep
convection;
stratiform
~~Vertical waviness?~~
~~~~
convective rain
from 0-5km top
cells
>10km tops
5-10km tops
stratiform
Corresponding
omega
EPIC MLR for 4
categories of
precipitation:
shallow, deep,
very deep
convection;
stratiform
Difficulty of measuring
divergence: sounding arrays
Erroneous
barotropic part
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divergence is
comparable
to signals
sought in
baroclinic
component…
low bar for our work!
Hard case: a
sparse time
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N
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E
(sea clutter?)
S
W
N