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?

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: Ż ana = 0 (biased, weather unsynchronized, lacks MJO) initialized free model use piecewise constant Ż ana (t) to make above equations exactly true in each 6h time interval while visiting analyzed states exactly “Replay” analyzed wx ΔZ/Δt = Ż model + Ż ana ΔZ/Δt = (Ż dyn + Ż phys ) + Ż ana MERRA’s variables Z [T,u,v,q v ] satisfy:

time any analyzed variable Z at 6h intervals Ż ana = (Z target – Z) /  relax model drift balanced by nudge ΔZ/Δt = Ż model + Ż ana ΔZ/Δt = (Ż dyn + Ż phys ) + Ż ana Poor man’s version (& interpretive aid): nudged trajectory 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 (analyzed MJO a bit weak) miss analysis by a skinch (  1/  relax 

Ż ana = (Z target – 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 = Ż model + Ż ana ΔZ/Δt = (Ż dyn + Ż phys ) + Ż ana Poor man’s data assimilation: nudge to analyses

Learning from analysis tendencies (ΔZ/Δt) obs = (Ż dyn + Ż phys ) + Ż ana If state is kept accurate (LS flow & gradients), then (ΔZ/Δt) obs and advective terms Ż dyn will be accurate and thus Ż ana ≅ -(error in Ż phys ) ✔ ✔

Example 1: mean heating rate errors dT/dt moist dT/dt ana 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) December, 1992 (COARE)

Example 2: MJO-related physics errors just do more sophisticated Ż ana averaging (MJO phase composites) 1.Case studies (JFMA90, DJFM92) of 3D (height-dependent) fields (dT/dt ana, dq/dt ana, 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

‘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 =0.5 New plume ensemble approach (in prep)

OK, a “better” scheme (candidates) For schemes as mission-central as convection, evaluation has to be comprehensive Ż ana 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 Ż ana 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...)