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?

Why assimilation-based science?

Why assimilation-based science?

New! MERRA reanalysis

OBS precip, u850 GEOS5

no MJO -- Good news!

Kim et al. 2009

some analyzed state variable

Z at some point

time

free model solution: Żana= 0 (biased, weather unsynchronized, lacks MJO)

initialized free model use piecewise constant Żana(t) to make above equations exactly true in each 6h time intervalwhile visiting analyzed states exactly

“Replay” analyzed wx

ΔZ/Δt = Żmodel + Żana

ΔZ/Δt = (Żdyn + Żphys) + Żana

MERRA’s variables Z [T,u,v,qv]satisfy:

time

any analyzed variable

Z at 6h intervals

Żana= (Ztarget– Z) /relax

model drift balanced by

nudge

ΔZ/Δt = Żmodel + Żana

ΔZ/Δt = (Żdyn + Żphys) + ŻanaPoor man’s version (& interpretive aid):

nudged trajectoryInterpolate 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

(analyzed MJO a bit weak)

miss analysis by a skinch ( 1/relax

Żana= (Ztarget– Z) /relax

• Need to choose relax

• 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 relax values for different variables (e.g. winds; div vs. rot; T, q)

ΔZ/Δt = Żmodel + Żana

ΔZ/Δt = (Żdyn + Żphys) + Żana

Poor man’s data assimilation: nudge to analyses

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 errorsdT/dtmoist dT/dtana

100

500

mb

1000

Strange “stripe” of moist-physics 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

(magnitudes much smaller)15-30 December, 1992 (COARE)

Example 2: MJO-related physics errorsjust 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 compositeof various 2D (single level or vertical integral) datasetsas 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

9 8 7 6 5 4 3 2 1 0 ‘back’ (W) ‘front’ (E)

Objective, unbiased-sample MJO mosaic of CloudSat radar echo objects

Riley and Mapes, in prep.

Physics: lack of convective ”organization” ?

(a whole nuther talk)

org = 0.1 org =0.5New plume ensembleapproach(in prep)

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...)