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Application of adjoints in ocean modeling Patrick Heimbach MIT, Cambridge (MA)

Application of adjoints in ocean modeling Patrick Heimbach MIT, Cambridge (MA). Ocean state estimation - combining data and model The ECCO approach: solving an optimal control problem (The ECCO group) Adjoint sensitivity studies

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Application of adjoints in ocean modeling Patrick Heimbach MIT, Cambridge (MA)

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  1. Application of adjoints in ocean modelingPatrick HeimbachMIT, Cambridge (MA) • Ocean state estimation - combining data and model • The ECCO approach: solving an optimal control problem • (The ECCO group) • Adjoint sensitivity studies • A recent example: coupled ocean-seaice sensitivities in the Arctic • (with D. Menemenlis, M. Losch, J.M. Campin and C. Hill) • Optimal perturbations / singular vectors • Transient growth of equatorial SST • (with L. Zanna, A. Moore and E. Tziperman) • OpenAD - a new tool for automatic differentiation (AD) • Adjoint code generation via AD • (with J. Utke and C. Hill) http://mitgcm.org, http://www.ecco-group.org

  2. Ocean State EstimationAn early vision, ca. 1982: Taken from: C. Wunsch, in "A Celebration in Geophysics and Oceanography 1982. In Honor of Walter Munk on his 65th birthday." C. Garrett and C. Wunsch, Eds., SIO Reference Series 84-5, March 1984

  3. Ocean State Estimation WOCE Argo T/P, Jason GRACE How to synthesize? Estimation/optimal control problem: Use a model (MITgcm) and its adjoint:

  4. Ocean State EstimationECCO products • A dynamical consistent state estimate • Complete set of variables to drive offline calculations • Perform closed property budget calculations • Available via LAS, DODS/OPENDAP, Ingrid servers • Adjusted input / forcing fields • in newer versions: balanced fluxes • Quality controlled observations • A priori uncertainty estimates • An open-source ocean GCM with full adjoint • on the web, downloadable via CVS See also session 036, Wed., 13:30, W204: Scientific Results from Global and Regional Ocean Syntheses

  5. Toward high-resolution ocean state estimationSouthern Ocean State Estimate (SOSE) Matthew Mazloff Ph.D. thesis mmazloff@mit.edu • 780 South to 24.70 South • 1/60 horizontal resolution; • 42 depth levels (partial cells) • ECCO-GODAE like setup • atmos. boundary layer scheme • adjoint generated via TAF • sea-ice model • KPP, GM/Redi param. • optimized for 2005-2006 • 600 processor adjoint on SDSC’s DataStar (IBM SP4) supercomputer Cost ( = squared normalized misfit) between modeled and observed (Reynolds) SST Iter. 0 Iter. 22

  6. Sensitivity studies:A thermodynamic/dynamic sea-ice model • Two-category, zero-layer thermodynamics with snow melting and flooding • Sea-ice loading and dynamic ocean topography • LSR and EVP solvers for sea-ice dynamics • Ported from B-grid to C-grid for use in generalized curvilinear grids @ OS, see also: • A. Nguyen et al. & Schodlok et al., posters 1177 & 1180 (session 036) • D. Menemenlis et al., session 036, Wed. 15:15 (W204) model SSM/I Losch, Menemenlis, Campin, Heimbach, Hill (in preparation)

  7. Sensitivity studyThe coupled Arctic ocean-seaice system Sensitivity of sea-ice export through Fram Strait to temperature perturbations at 200 m depth (Arctic face of ECCO2 cube-sphere, coarsened to 36 km res.)

  8. Generalized stability theory, non-normal growth, singular vectors and optimal perturbations L. Zanna, Ph.D. thesis, zanna@fas.harvard.edu

  9. Optimal initial conditions / SVDsUsing the MITgcm’s ADM, TLM and ARPACK L. Zanna, Ph.D. thesis, zanna@fas.harvard.edu

  10. Optimal initial conditions - preliminay results:Transient growth of equatorial SST L. Zanna, Ph.D. thesis, zanna@fas.harvard.edu

  11. OpenAD: a new open-source automatic differentiation toolhttp://www.mcs.anl.gov/OpenAD @ ANL:J. Utke, B. Norris, M. Strout, P. Hovland @ Rice: N. Tallent, G. Mellor-Crummy, M. Fagan @ MIT: P. Heimbach, C. Hill, D. Ozyurt, C. Wunsch @ RWTH:U. Naumann supported by NSF • Tool design emphases: • modularity • flexibility • use of open-source components • new algorithmic approaches • XML-based language- independent transformation • basic block preaccumulation • other optimal elimination methods • control flow & call graph reversal • taping & hierarchical • checkpointing

  12. Atlantic meridional heat transport:10 year sensitivities at 4o resolution (OpenAD)

  13. Concluding remarks • Adjoint models are useful; they provide complimentary view on the ocean circulation • Number and type of applications steadily increasing • Within MITgcm we’re continuoulsy expanding the adjoint model capabilities, in particular in terms of coupling, e.g. • sea-ice • ocean biogeochemistry • Automatic differentiation is a critical tool to support expansion of adjoint codes and applications

  14. specific humidity surface air temperature zonal wind speed precipitation

  15. Some algebra: How to get the gradient?Forward or finite-difference vs. adjoint methods

  16. Optimal initial conditions - preliminay results:Transient growth of equatorial SST

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