Evaluation of GCM convection schemes via data assimilation: e.g. to study the Madden-Julian Oscillation in a model that

1. 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)

2. 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 Physically comprehensive modeling is needed at this stage

3. 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 Geographically realistic modeling is needed at this stage

4. Why assimilation-based science? IV. But GCMs don’t simulate it well... • or would be solved long ago MJO’s well-observed, well-resolved large scale structure needs to be brought into a model’s quantitative framework empirically by assimilation

5. New! MERRA reanalysis Modern Era (from 1979) Reanalysis for Research and Applications Budget datasets incl. analysis tendencies Uses GEOS-5 GCM (formerly NSIPP) OBS precip, u850 GEOS5 • no MJO -- Good news! Kim et al. 2009

6. 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) use piecewise constant Żana(t) to make above equations exactly true in each 6h time interval while visiting analyzed states exactly “Replay” analyzed wx initialized free model some analyzed state variable Z at some point time

7. 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 model drift balanced by nudge nudged trajectory Interpolate analyses to GCM grid & time steps: ‘target’ state time

8. 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) analyzed vs. Observed Z time

9. 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)

10. 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)

11. Example 1: mean heating rate errorsdT/dtmoist dT/dtana 100 500 mb 1000 15-30 December, 1992 (COARE) (magnitudes much smaller) High wavenumber in model T(p) profile disagrees w/obs. & so is fought by data assim = WRONG Strange “stripe” of moist-physics cooling at 700mb (melting at 10C, & re-evap)

12. Example 2: MJO-related physics errorsjust do more sophisticated Żana averaging (MJO phase composites) • Case studies (JFMA90, DJFM92) • of 3D (height-dependent) fields (dT/dtana , dq/dtana , etc) • averaging Indian-Pacific sector longitudes together • 27-year composite • of various 2D (single level or vertical integral) datasets • as a function of longitude

13. Error lesson: model convection scheme acts too deep (drying instead of moistening) in the leading edge of the MJO.

14. 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

15. Equatorial section of MJO phase 2 dqdt_ana anomalies Precip’

16. SUMMARY: GEOS-5 moist physics errors produce -- in addition to sizable MEAN biases -- too little moistening & too much conv. rain here 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.

17. Physics: lack of convective ”organization” ? (a whole nuther talk) org = 0.1 org =0.5 New plume ensemble approach (in prep)

18. 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.)

19. 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...)

20. help wanted (avail. now)