Evaluation of GCM convection
schemes via data assimilation:
e.g. to study the Madden-Julian
Oscillation in a model that
doesn’t have one
Brian Mapes
RSMAS, University of Miami
with
Julio Bacmeister
(then NASA, now NCAR)
Why assimilation-based science?
I. MJO is low frequency
= small Eulerian (local) rate of change
–
–
 many small processes (tendency terms),
or small imbalances among bigger terms,
‘could’ cause the observed changes
many simple/toy single-effect demonstration
models exist, but
Why assimilation-based science?
II. Slow speed of motion
even wrt weak tropical flows
–
resting/uniform basic states questionable
III. MJO large scale, yet confined...
zonally, seasonally
Why assimilation-based science?
IV. But GCMs don’t simulate it well...
–
or would be solved long ago
New! MERRA reanalysis
Modern Era (from 1979) Reanalysis
for Research and Applications
incl. analysis tendencies
Uses GEOS-5 GCM (formerly NSIPP)
OBS
no MJO -Good news!
precip, u850
GEOS5
Kim et al. 2009
MERRA’s
variables
Z [T,u,v,qv]
satisfy:
ΔZ/Δt = Żmodel
+ Żana
ΔZ/Δt = (Żdyn + Żphys) + Żana
free model solution: Żana= 0
(biased, weather unsynchronized, lacks MJO)
some analyzed
state variable
Z
at some point
use piecewise constant
Żana(t) to make above
equations exactly true
in each 6h time interval
while visiting analyzed
states exactly
“Replay” analyzed wx
time
ΔZ/Δt = Żmodel
+ Żana
ΔZ/Δt = (Żdyn + Żphys) + Żana
Poor man’s version
(& interpretive aid):
Żana= (Ztarget– Z) /trelax
any analyzed
variable
Z
at 6h intervals
Interpolate analyses to
GCM grid & time
steps: ‘target’ state
time
Misses analysis (in direction toward model attractor)
by a skinch, but analysis is already biased that way
miss analysis by a skinch (a 1/trelax)
(analyzed MJO a bit weak)
vs.
Observed
Z
time
Poor man’s data
assimilation:
nudge to analyses
ΔZ/Δt = Żmodel
+ Żana
ΔZ/Δt = (Żdyn + Żphys) + Żana
Żana= (Ztarget– Z) /trelax
• Need to choose trelax
• Any small value will converge to same results
•Strong forcing (incl. q & div) forces rainfall (M.
Suarez), but can blow up model (B. Kirtman)
• Dodge trouble, and do science: discriminate
mechanisms, by using different trelax values for
different variables (e.g. winds; div vs. rot; T, q)
Learning from analysis tendencies
✔
✔
(ΔZ/Δt)obs = (Żdyn + Żphys) + Żana
• If state is kept accurate (LS flow & gradients),
then (ΔZ/Δt)obs and advective terms Żdyn will be
accurate
• and thus
Żana ≅ -(error in Żphys)
Example 1: mean heating rate errors
dT/dtmoist
dT/dtana
100
500
mb
1000
15-30 December, 1992 (COARE)
(magnitudes much smaller)
Strange “stripe” of moistphysics cooling at 700mb
(melting at 10C, & re-evap)
High wavenumber in model T(p)
profile disagrees w/obs. & so is
fought by data assim = WRONG
Example 2: MJO-related physics errors
just do more sophisticated Żana averaging
(MJO phase composites)
1. Case studies (JFMA90, DJFM92)
of 3D (height-dependent) fields (dT/dtana , dq/dtana , etc)
averaging Indian-Pacific sector longitudes together
1. 27-year composite
of various 2D (single level or vertical integral) datasets
as a function of longitude
• Error lesson:
model convection
scheme acts too
deep (drying
instead of
moistening) in the
leading edge of the
MJO.
When MJO rain is over Indian Ocean,
W. Pac. atmosphere is observed to be
moistening, but GCM doesn’t, so
analysis tendency has to do it
Equatorial section of MJO phase 2
dqdt_ana anomalies
: GEOS-5 moist physics errors
produce -- in addition to sizable MEAN biases -too little moistening & too much conv. rain
here
9
8
7 unbiased-sample
6 5 4 MJO
3 mosaic
2 of
1 CloudSat
0
Objective,
‘back’ (W)
‘front’
(E)echo objects
radar
Riley and Mapes, in prep.
Physics: lack of convective
”organization” ?
(a whole nuther talk)
org = 0.1
New
plume
ensemble
approach
(in prep)
org =0.5
OK, a “better” scheme (candidates)
• For schemes as mission-central as convection,
evaluation has to be comprehensive
• Żana is a powerful guide to errors!
– Mean, MJO... but also diurnal, seasonal, ENSO,...
– simply save d()dt_ana, as well as state vars ()
– send into existing diagnostic plotting codes
– similar to (obs-model) analyses, but automatic
• (all data on same grid, etc.)
How to get Żana datasets?
Nudge GCMs to world’s great analyses
• Full blown raw-data assimilation is expen$$ive,
& really...are we gonna beat EC, JMA, NCEP?
• Multiple GCMs nudged to multiple reanalyses
– Bracket/ estimate/ remove 2-model (anal. model +
eval. GCM) error interactions
• Commonalities teach us about nature, since all
exercises share global obs. & intensive assim.
• Differences play valuable secondary role of
informing individual model improvement efforts
• (Shameless: CPT proposal in community’s hands now...)