an atmospheric “mesoscale”:
where convection meets waves
(rotation optional)
Brian Mapes
University of Miami
for oceanographers
• In a moist convecting atmosphere, small scale
vertical motions don’t just carry fluxes, they
cause latent heating
• OK, you can view it as a vertical flux of water substance
upward past the condensation level.
• Spectral space: energy injection across scales
• Physical space: feedback  small updrafts
• UV catastrophe of conditional instability (Lilly 1961)
• Smallest updrafts, broadest subsidence (Bjerknes 1938)
mesoscale convection
• “Mesoscale” convection events (meso =
middle, in between L~H “convective” scale and
N/f H “Rossby radius”) are less theoretically
tidy than parcel or exp(ikx) UV catastrophe, but
profound & real
• convectively coupled internal waves
Convectively coupled gravity waves in 2D CRM
No preferred hor. scale
5 decades
}
3 decades
Stefan Tulich (Mapes et al. 2009 JMSJ)
Scale Interactions
cascade...
...pas?
mesoscale convection
• Are these things coherent aspects (the
spectral tail) of the large-scale flow, or an
emergent metaphenomenon bubbling up
from convection?
• Implication: is it better to spend computing
DOFs to resolve the mesoscale? Or rather on
little hi-res but periodic “sample” patches of
convective-scale flow, coupled across an
enforced scale separation?
– (MMF or “super-parameterization”)
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 mesoscale 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, to minimize cyclone dominated cases
• 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
animation
Tropical cyclone: 1 case in top 10
(in 15N-15S belt, 250km scale)
http://www.rsmas.miami.edu/personal/ssong/research/HR_250kmevents.htm
Anim: composite of 10 cases
• m
99% is from
resolved
condensation
process: good
composite basis
HOURS RELATIVE TO MAX 250km RAIN
Tropical radar observations (EPIC 2001)
Time scale is hours even for small space scales
Mesoscale is real (if broadband)
96km radius
cell: <1h
8km radius
MCS: 10h
Mapes and Lin 2006 MWR
• m
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
trimodal: shallow, medium, deep
similar to obs (if a bit off in exact heights)
Mapes et al. 2006 DAO
GCRM detailed examinations
• 1. Tropical mesoscale rain events: case studies
– One scale built in to analysis: 250km
– Rebin rainrate to 2.5deg, find 10 largest maxima
• in ~20 day simulation period (Jan-Feb 2010)
• in 15N-15S, to minimize cyclone dominated cases
– Extract space-time cubes around these
• (+/-18h, +/- 3 degrees)
• 10 cases, and composite mean case
• 2. Vertical enthalpy flux, partitioned by scale
» through simple coarse-graining (rebinning)
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 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?
• Borrowed slides (with permission, and email
discussion last 2 days) 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
• Vapor flux by sub-convective (0.1-4km) scales is
colocated with >4km scale convective cloud
updrafts.
• Small scales mainly just add a bit (~40%) to the
flux by convective mean updrafts
Flux part summary
•
•
•
•
Mesoscale updrafts are moist, fluxing q up
Convective updrafts are inside, adding to it
Sub-drafts inside the convective drafts: ditto
Q: How might poorly-resolved convection be
distorted by having to carry the flux of missing
sub-scales? (and can param’z’n fix it?)
• Q2: Is subgrid param’z’n a flux amplifier? Is
that safe numerically?
Summary
• Deep convection – gravity wave interactions are
common: a “mesoscale”
• Broadband (meso synoptic, in tropics)
– -5/3, but NOT a swirls-advecting-vorticity cascade
– has a velocity scale, not a length scale
– multicellular: hours, not minutes (not just H/w)
• “Mesoscale convection”, convective cells, and
sub-cellular drafts all conspire to carry
geophysically (radiatively) demanded vertical
energy flux
– Do we need to resolve them all? Or might truncation +
parameterization suffice?