Studying the MaddenJulian oscillation
with
and a model that
doesn’t have one
Brian Mapes
RSMAS, University of Miami
The Oscillation
• Madden and Julian 1972
• Time series analysis
– spectra and cross-spectra
• 40-50 days, eastward moving
MJO vs. convectively coupled waves
Time–longitude CLAUS IR (2.5S–7.5N), Jan–Apr 1987
MJO
(5 m s-1)
Kelvin
waves
(15 m s-1)
WIG
Courtesy
G. Kiladis
Mechanisms
• Convectively coupled Kelvin & WIG waves:
– Density anomalies under gravity (waves)
– Second baroclinic vertical mode of troposphere
• sets speed: 15-20 m/s
– cold @ low levels in T dipole uncaps PBL -> convxn
– dipole comp. of top-heavy heating profile reinforces
• MJO: ??
–
–
–
–
–
No such simple wave theory...
Moisture storage a key process? (a ‘moisture mode’?)
Frictional convergence into 1st baroclinic low p?
Dry dynamics (mom. advection) may suffice? (Pallav)
...
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
there are many simple/toy single-effect
demonstration models, 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
MERRA reanalysis
MERRA = Modern Era (from 1979) Reanalysis for
Research and Applications
Uses GEOS-5 GCM (formerly NSIPP)
½ x 2/3 deg resolution
3D assimilation, with some satellite radiances
~no MJO of its own
OBS
Good news!
precip, u850
GEOS5
MERRA’s
variables
Z [T,u,v,qv]
satisfy:
ΔZ/Δt = Żmodel
+ Żana
ΔZ/Δt = (Żdyn + Żphys) + Żana
free model solution: Żana= 0
(biased, unsynchronized, may lack oscillation altogether)
some analyzed
variable
Z
at some point
use piecewise constant
Żana(t) to make above
equations exactly true
in each 6h time interval*
*through clever predictor-corrector time integration
time
Aside: analyses generated using same model:
already biased toward model’s attractor...
(analyzed MJO a bit weak)
vs.
Observed
Z
time
Poor man’s
ΔZ/Δt
version
ΔZ/Δt
(& interpretive
aid):
= Żmodel
+ Żana
= (Żdyn + Żphys) + Żana
Żana= (Ztarget– Z) /trelax
any analyzed
variable
Z
at 6h intervals
Interpolate among
analyses to have a
continuous (every time
step) target state
time
Poor man’s
ΔZ/Δt
version
ΔZ/Δt
(& interpretive
aid):
= Żmodel
+ Żana
= (Żdyn + Żphys) + Żana
Żana= (Ztarget– Z) /trelax
• Need to choose trelax
• Any small value should
converge to same results
• But can go unstable for q
• (says Ben) - nonlinearities?
• Can avoid (and do science:
discriminate mechanisms) by
using different trelax values for
u,v,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: 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 assimilation
Same lesson (700mb cooling is wrong):
from simple bias errors
• 2 different years, 3 different reference datasets
• DJF zonal means over whole equatorial belt
• All agree: MERRA has a cold bias at 700mb
1990 MERRA
1992 MERRA
-ERA -NCEP2
-JRA
-NCEP2 -ERA
-JRA
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
4 mos OLR 15N-15S (JFMA 1990)
IO
back
WP
OLR min
front
6
5
GIBBS image archive
4
15N-15S
different 4 months DJFM 1992-3
IO
0
WP
5
9
1990
-50
1992-3 COARE
-5
-50
Plotting convention: phase increases right to left
(like longitude, for this E-moving disturbance)
-5
1990 T
1992-3 COARE
250
850
1990
0.5
1992-3 COARE
0.45
1990 OLR: satellite, MERRA
IO
WP
‘back’ (W)
‘front (E)’
MERRA
(MJO weak)
misses
~15W
IO-WP
difference
amplitude a bit weak: analyses biased toward
model’s attractor (which lacks oscillation)
vs.
Observed
time
Second interpretation of Żana
(ΔZ/Δt)obs = (Żdyn + Żphys) + Żana
• If analyzed oscillation in omega is too weak
• then vertical advection terms in Żdyn too weak:
MJO Żana oscillations will have a
component in phase with (strengthening)
the Żdyn term
1990 Rain rate
too rainy
here
MERRA
10-4
x
mm/s
SSMI
0
Total rain:
convective:
anvil:
large-scale cloud:
1992-3
deep
Mc
dq/dtana
1990
1992-3
[qv] DJF 1990 minus JRA ... typical of MERRA minus all others: it’s MERRA’s bias
Bias stripes mimic Moist Phys tendencies
1992-3
1990
+
+
-
Żana ≅ -(error in Żphys)
-
+
-
MJO phase dependent dq/dtana
1990
1992-3
• Interpretation:
model convection
scheme acts too
deep, too soon in
the early stages of
the MJO.
MJO-related physics errors:
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
Vertical integral of dq/dtana
1990
case
Long-term (1979-2005) composite of
MJO defined by RMM1-RMM2
Amplitude is distance
from origin
Phase angle is
longitude of
convection
Wheeler and Hendon
2004
27 years (1979-2005) MJO composite
Red: pos. anomalies, Blue: neg.
Analysis is moistening
extra(since physics fails to)
esp. in W. Pac ahead of rainy part
ANA term smaller: color scale is about 1/3 to emphasize it
Vertical section of dqdt_ana:
RMM phase 2
Vertical section of dqdt_ana:
Where too
mean
much rain,
Rainfall bias wrt GPCP
too much
physical q
sink. Ana
source
compensates
(with its
distinctive
vertical str.)
mean q
bias
Interpretations of dqdt_ana
1. Żana ≅ -(error in Żphys)
2. If analyzed MJO anomalies are too weak, then
MJO Żana oscillations will have a component in
phase with (strengthening) the Żdyn term
: GEOS-5 moist physics errors
produce -- in addition to sizable MEAN biases -too little moistening & too much conv. rain
here
9
8
7
6
‘back’ (W)
5
4
3 2
1
‘front’ (E)
0
MJO mosaic of CloudSat radar echo objects
by Emily Riley
An objective basis for these hypotheses:
1.(about a model): GEOS-5’s poor MJO simulation is caused by
moist physics shortcomings on the front side
2.(about nature): Front-side moisture storage and the shallow-deep
convection transition are key processes in the MJO
Problematic
area
Art: Benedict & Randall 2007
Testing hypotheses
• Alter (“improve”) hypothesized-bad GCM physics.
1.Does MJO phase dependence of Żana’s decrease?
– in re-assimilation (expen$$ive, NASA)
– in “replay” (nudge to MERRA, EC, JRA, NCEP)
»
stimulus money: green jobs right here at home
2.FINAL TEST: does the resulting model produce a
better MJO in free running simulations?
Is simple subtraction of mean Żana to get “MJO” Żana valid?
Verify:
ΔZ/Δt = Żbias_corrected_model
+ Żana2(t)
ΔZ/Δt = (Żdyn + Żphys + [Żana]) + Żana2(t)
Żana2(t) = (Ztarget– Z) /trelax
Will MJO composites of [Żana] + Żana2(t) look just like
the above composites of the original Żana(t) ?
some analyzed
variable
Z
nudged
at some point
Bias corrected model w/ Żana2 = 0
(still unsynchronized - still lacks MJO?)
time
Conclusions
• Analysis tendencies informative about GEOS-5
• Model hypothesis: shallow vs. deep convection
on the front is a key MJO-related shortcoming
– model convection does too little moistening there
»
too much q sink & rain & T source & deep mass flux
• Nature hypothesis: front-side moisture storage is
a key mechanism in the MJO
Larger strategy
• Multiple GCMs nudged to multiple reanalyses
» Study 4D fields of Żana
• Commonalities among results will increasingly
comprise scientific evidence about nature, since
what all exercises share is the totality of global
obs (Vast!) entering assimilations (Serious!)
• Differences will be relegated to the secondary
(but valuable) role of informing individual model
improvement efforts