Waves and multiscale processes
in the tropics
Brian Mapes
AIM Palo Alto
Dec 5 2010
Simplest full physics realiz: 2D CRM (40000km)
No preferred hor. scale; -5/3 spectrum
5 decades
}
3 decades
Stefan Tulich (Mapes et al. 2009 JMSJ)
Power and information
• Usual 5/3 paradigm based on energetics
– E conserved during local-in-scale interactions
» dimensional analysis from there
• But that’s um not the E budget here?
– convective E source b’w’ active at all scales
– most of energy lives in deepest mode
– but 2nd mode signaling , tracer q’ sculpt b’w’ field
• “Power” spectrum is only half of fft()
• Other half: phase (~ information?)
» back to physical space is only way to make sense of it?
• Are we missing some whole other principle?
Outline
• Dull null hypotheses
– & irreconcilable ambiguities
» the essence of depressingly much of what we see?
• My stuff – it’s what I have
– Quantitative spectral & filtered obs of waves
• Yasunaga and Mapes I & II, submission in next week or so
– Convective events in a 5km mesh global model
• CC waves on 250 km scales
• Small-scale w: just a flux amplifier for large-scale w events?
• Beyond powerpoint?
– further issues on white board
Dull/null hypotheses:
how little might we know?
• “In mathematics you don't understand things.
You just get used to them.” Johann von
Neumann
US (Hungarian-born) computer scientist,
mathematician (1903 - 1957)
1. Self similarity
• Does it imply there is scale interaction? Or
perhaps rather a lack of interactions?
• Dull null: statistical condensation in partly
cloudy skies acts the same for all large scale
waves
– independent of exactly what types of
variability/intermittency/sub-waves make up
“partly cloudy”
2. Modulation
• Convection varies. That’s just what it does.
• Dull null: The active phase of low frequency
convection variations is a locus of enhanced
high frequency variability of all sorts
– no basis for postulating importance of “upscale”
impacts, “interactions” among wave types, etc.
– Yasunaga made a composite of HF filtered wave amplitudes by
MJO phase: DULL; consistent w/ above.
3. Modulation: nonlinear?
• LF modulation of HF
waves: multiplicative
& nonlinear?
• Or is it just additive
beating?
– MATHEMATICALLY =
» as in 0=0
Outline
• Dull null hypotheses
– & irreconcilable ambiguities
» the essence of depressingly much of what we see?
• My stuff – it’s what I have
– New spectral & filtered composite obs
– Yasunaga and Mapes, submission in next week or so
– Convective events in a 5km mesh global model
• CC waves on 250 km scales
• Small scale w: just a flux amplifier for large scale w events?
• Beyond powerpoint
– discussion issues on white board
Differences of wave types
• Yasunaga & Mapes – 2 papers just submitting
• Kazuaki did all the work
• 1. Cross-spectra
– divergence and PW (analyzed fields)
• 2. Composites based on filtered TRMM 3B42
– convective & stratiform rain, cloud system size
» very raw obs, not analyzed via models
Coherence between
rain and divergence
•Coherence at the 1000hPa level
has peaks in all modes.
•Coherence at the 200hPa and
1000 hPa levels shows similar
patterns.
•Coherence at the 500hPa level is
relatively weak in the ER, MRG,
and TD regions, compared to that
in the Kelvin, n=0 EIG, and n=1,2
Weak
WIG wave regions.
Symmetric
Antisymmetric
200 hPa
Strong
500 hPa
1000 hPa
Wave Filtering
Filtered Rain (Pmw)
dPmw/dt
Definition of phase and amplitude
Developing Phase
dPmw/dt
Mature Phase
Suppressed
Phase
decaying Phase
Filtered rain (Pmw)
Procedure to make a composite
•
•
Every obs P(x,t) is repeatedly used for each wave.
Enough samples will emphasize key features, eliminating
incoherent structure.
Unroll the sushi
Convective
Stratiform
Linear fit to envelope  wave signal (P per unit filtered-p amplitude)
Wave modulation
=(Max. Slope)-(min.
slope)
Slope of envelope curve fits comes with error bars
Stratiform and
conv rain
fractions
Stratiform rain is modulated
especially much in fast or
“Divergent” waves, and the
MJO
OK not strongest signal ever
but consistent w/ 
Precipitation Feature Size
Small
Large
XL
Small : ~100 km^2
Medium: 100 km^2 - 1,000 km^2
Large : 1,000 km^2 - 10,000 km^2
XL
: >10,000 km^2
Modulation of the precipitation features # by size category
Rot
Div
Rot
Div
small
Modulation
relative to
total
rainfall:
(num)/(mm/hr)
medium
large
XL
Summary
Waves in the red region
* Rain is highly correlated
with mid-level divergence
* Stratiform rainfall is
modulated more
* Smaller-sized echo
objects modulated less
Waves in the blue region
Westward
Why?
Eastward
* Rain only correlated with
divergence near surface and
upper troposphere
* Modulation difference of
convective and stratiform
rainfall is not distinct.
* Smaller-sized system
number is modulated a lot.
Controlling factor?
Inhibition by T’ (Density)
governs existence of large
systems with a lot of
stratiform rain process?
Time
Moist
Dry
Time
Humidity governs cumulus
cells since they must
entrain their way through
it?
Composite of precipitable water
Symmetric
ER
MJO
Antisymmetric
TD
MRG
•
•
•
•
Data: SSM/I, TMI, AMSRE
JAN 1998 – DEC 2009
Amplitude and phase are based on the
TRMM-3B42 data
Min-to-max modulation: ERn1, TD, MJO, and MRG
Background vapor modulation: Kelvin, WIGn1, EIGn0, and WIGn2
• Fuchs
has
similar
results
? Pers.
comm.
Outline
• Dull null hypotheses
– unexciting & discouraging default expectations
• that can explain depressingly much of what we see
• My stuff – it’s what I have
– New spectral & filtered composite obs
– Yasunaga and Mapes, submission in next week or so
– Convective events in a 5km mesh global model
• CC waves on 250 km scales
• Small scale w: just a flux amplifier for large scale w events?
• Beyond powerpoint
– discussion issues on white board
3D global simulations
• GEOS-5 global AGCM at 5km mesh size
» by Bill Putman, Max Suarez, others at NASA GSFC
• 20-day run analyzed here
• Cubed sphere grid, nonhydrostatic
• GCM physics left on – mostly
• subgridscale plumes hobbled by entrainment
• disabled subgrid orographic gravity wave drag
comparison to satellite imagery
http://earthobservatory.nasa.gov/I
OTD/view.php?id=44246&src=
eoa-iotd
predicted cloud features for
February 6, 2010
2 weeks into simulation
5km GCM: detailed examinations
• 1. Tropical rain events: case studies
– One scale selected in to analysis: 250km events
• Rebin rainrate to 2.5deg, find 10 largest maxima
– in ~20 day simulation period (Jan-Feb 2010)
– in 15N-15S
• Extract space-time cubes around these events
– (+/-18h, +/- 3 degrees)
– 10 wettest cases, plus composite mean case
• 2. Vertical flux [wq], partitioned by scale
» through simple coarse-graining (rebinning)
http://www.rsmas.miami.edu/personal/ssong/research/HR_250kmevents.htm
Tropical cyclone: 1 case in top 10
(in 15N-15S belt, 250km scale)
http://www.rsmas.miami.edu/personal/ssong/research/HR_250kmevents.htm
• m
99% is from
resolved
condensation
process: good
composite basis
HOURS RELATIVE TO MAX 250km RAIN
T’(t,p): 250km area mean
p (hPa)
leading nose
HOURS RELATIVE TO MAX 250km RAIN
250km water vapor mixing ratio (t,p)
W
Low-level “valve” on convection
RH(t,p)
p (hPa)
W
W
HOURS RELATIVE TO MAX 250km RAIN
750
850
trimodal: shallow, medium, deep
similar to obs (a bit off in exact heights)
750
850
Mapes et al. 2006 DAO
Outline
• Dull null hypotheses
– unexciting & discouraging default expectations
• that can explain depressingly much of what we see
• My stuff – it’s what I have
– New spectral & filtered composite obs
– Yasunaga and Mapes, submission in next week or so
– Convective events in a 5km mesh global model
• CC waves on 250 km scales
• Small scale w: just a flux amplifier for large scale w events?
• Beyond powerpoint
– discussion issues on white board
2. Enthalpy flux
• Enthalpy = sensible heat + latent heat
– CpT + Lqv
• Flux thru 500mb level balances ~23 Wm-2
radiative cooling above that level
– sensible heat flux Cp [wT] ~ 7 Wm-2
– latent heat flux
L [wq]: ~ 16 Wm-2
• destined to condense up there
Latent flux
across
500mb
snapshot
by scales
resolved in
80km
rebinning
sub-80km =
total flux
minus the
above
Latent flux
snapshot
by scales
resolved in
250km
rebinning
sub-250km =
total explicit
flux minus
above
Latent flux
snapshot
by scales
resolved in
500 km
rebinning
sub-500km =
total explicit
flux minus
above
sub-80km and super-80km scales
conspire to carry wq flux: convection
occurs in mesoscale clusters
Flux partitoned by scales
• Vapor flux by convective (5-80km) scales is
colocated with flux in >80km scale mesoscale
updrafts.
• Small scales mainly just add a bit (10 - 40%) to
the flux by mesoscale mean updrafts
• Might this be true at still-finer scales?
• Slides from Chin-Hoh Moeng (NCAR)
• Marat
Khairoutdinov
(Stony Brook)
ran “Giga-LES”
• Moeng et al.
2009, 2010
JAMES
Split the LES flow into: “resolvable” grid-scale (GS)
& “unresolved” scale (SGS)
Giga-LES
apply
“smoothing”
CRM resolvable
SGS is the difference.
Moeng et al. 2010 JAMES
Apply “smoothing” with a width of 4 km
SGS(w-var)
GS: CRM-grid scales
SGS: CRM-SGS
GS
SGS(q-var)
GS
GS
large scales
SGS (wq-cov)
most of w-kinetic energy in SGS
~ half of moisture flux in SGS
small scales
Moeng et al. 2010 JAMES
• SGS flux
Moeng et al. 2010- JAMES
• SGS flux is
in clouds
• condensed
water path
(vertical
integral)
Moeng et al. 2009 JAMES
Flux partitoned by scales
• Vapor flux by convective (5-80km) scales is
colocated with flux in >80km scale mesoscale
cloud system updrafts.
• Small scales mainly just add a bit (up to 40%) to
the flux by mesoscale mean updrafts
• Again at LES scale:
• Small scales mainly just add a bit (~40%) to the
flux by convective mean updrafts
Flux summary
• Mesoscale updrafts are moist, fluxing q up
• in GCRM
• Convective updrafts are inside, adding to it
• in GCRM
• Sub-drafts inside the convective drafts: ditto
• in an LES (Moeng)
Outline
• Dull null hypotheses
– unexciting & discouraging default expectations
• that can explain depressingly much of what we see
• My stuff – it’s what I have
– New spectral & filtered composite obs
– Yasunaga and Mapes, submission in next week or so
– Convective events in a 5km mesh global model
• CC waves on 250 km scales
• Small scale w: just a flux amplifier for large scale w events?
• Beyond powerpoint
– discussion issues on white board