An eddy-permitting, coupled ocean/sea-ice Arctic/subpolar gyre State Estimate (ASTE) P. Heimbach 1, J.M. Campin 1, G. Forget 1, C. Hill 1, D. Menemenlis 2, A. Nguyen 3, P. Rampal 1, C. Wunsch 1 1 MIT, EAPS, Cambridge, MA, USA 2 JPL/Caltech, Pasadena, CA, USA 3 UCLA, Los Angeles, CA, USA Estimating the Circulation and Climate of the Ocean (ECCO)

State Estimation Synthesize diverse/disparate types of observations, … –… taking optimal advantage of sparse observations, –… with best-known dynamics/physics, –… into dynamically consistent, time-evolving estimate, –… obeying known conservation laws, –… to enable time-varying budget calculations, –… and diagnostic of un-observable quantities (e.g., MOC) –… with quantification of posterior uncertainties –ALTERNATIVELY: reject the model as inadequate dynamical interpolator (and detect where/how to improve it)

Combining the knowledge reservoirs: “data assimilation”, “reanalysis” The estimation (interpolation) vs. forecasting (extrapolation) problem Atmosphere –Relatively abundant data sampling of the 3-dim. atmosphere –Most DA applications target the problem of forecasting (NWP)  find initial conditions which produce best possible forecast;  dynamical consistency or property conservation *NOT* required on climate time scales Ocean –Very sparse data sampling of the 3-dim. ocean –Understanding past & present state of the ocean is a major issue all by itself, the forecasting dependent upon it  use observations in an optimal way to extract max. information about the ocean  dynamic consistency & property conservation *ESSENTIAL* over climate time scales “jumps” are unphysical (I. Fukumori)

Lessons from atmospheric reanalysis: Bengtsson et al. (2004) “Can climate trends be calculated from reanalysis data?” Large warming trend in ERA40 an artifact of large changes in observational coverage at the end of the 1970s Large uncertainty in the calculation of trends from present reanalyses Careful evaluation of changes in the global observing system needed Present observing system was set up to support weather forecasting, not directly suitable for climate monitoring Systematic errors in the assimilating models add complications Limited resources currently devoted to address these problems!! Why should the ocean estimation problem be any different? Bengtsson et al. (2004)

First steps at eddy-permitting adjoint-based state estimation in ECCO Gebbie (2004), Gebbie et al. (2006): subduction in the subtropical North Atlantic Hoteit et al. (2006, 2010) tropical Pacific Mazloff (2008), Mazloff et al. (2010) Southern Ocean State Estimate (SOSE) Fenty (2010), Fenty et al. (in prep.) Labrador Sea

Eddy-permitting Southern Ocean State Estimate (SOSE) Mazloff, Ph.D. (2008), Mazloff et al., JPO (2010)  78 0 South to South  1/6 0 Horizontal resolution;  42 depth levels (partial cells)  similar setup to ECCO-GODAE  atmospheric boundary layer scheme  adjoint generated via AD tool TAF  sea-ice model  KPP, GM/Redi parameterizations  currently  800 processor adjoint on SDSC IBM SP4 supercomputer

Eddy-permitting Southern Ocean State Estimate (SOSE) Mazloff, Ph.D. (2008), Mazloff et al., JPO (2010) westward Along streamline spectra vs. wavenumber (left) and frequency (right) streamlines M. Mazloff, Ph.D. thesis (2008) westward | eastward

SOSE supporting regional, high-resolution process studies Vertical structure of anthropogenic carbon transport in the ACC from SOSE (Ito et al., Nature, 2010) Horizontal effective diffusivity at 100m in the DIMES region experiment from SOSE (Abernathey et al., JPO, 2010)

Rationale for ASTE “Mirror” Southern Ocean effort in the subpolar gyre and Arctic Combine subpolar and Arctic effort! A coupled state estimate that can incorporate both ocean and sea-ice observations Provide a framework –into which to incorporate the diverse observations –to support field programs (observing system design) Initial science questions: Target the climate problem: account for property changes through closed budgets over decade (and beyond) Connection between deep water formation processes Atlantic (meridional overturning) circulation Freshwater input at high latitudes and its pathways Interaction between Atlantic Water, Arctic halocline formation and sea-ice Heat delivery to the Greenland margins

Sea-ice state estimation in a limited-area setup of the Labrador Sea (Ian Fenty, Ph.D. thesis, MIT) MITgcm with curvilinear grid: 30 km x 30 km  30 km x 16 km resolved Labrador and Greenland shelves –critical for sea ice production and advection –important for boundary currents

Sea-ice state estimation in a limited-area setup of the Labrador Sea (Ian Fenty, Ph.D. thesis, MIT)

In the making: Arctic/subpolar gyre State Estimate (ASTE) (analogue for the Southern Ocean, see Mazloff et al., JPO, 2010) Project leads: Heimbach (MIT), Ponte (AER), Nguyen (JPL/UCLA) horizontal resolution: km (each plotted “tile” contains 36 x 36 grid points). vertical resolution: 50 levels Target periods: present (beginning of TOPEX) present (GRACE & Argo) Will provide a framework for: data synthesis assessment through OSE/OSSE base config. For 2-way nested very-high resolution domains re-connect to global ECCO2

Grid on a “distorted cubed-sphere” Generated from 1/48 o super-grid - collapsable to coarse-res. setups Much effort went into initial grid definition Development from a single super- grid should facilitate 2-way nested setups down the road to zoom into critical regions Zoom from global into Arctic domain Zoom from Arctic domain into key process areas

Close ties to ECCO2 & An Nguyen’s work Model development jointly; source codes kept in sync Observations, formats and quality controls shared ECCO-GODAE learning from ECCO2 how to run high-res. forward model ECCO2 learning from ECCO-GODAE how to do large adjoints ECCO2 will remain computationally challenging, therefore experimental ASTE will build on –adjusted boundary conditions from ECCO2 as first guess –Green’s function adjustments from A. Nguyen’s Arctic calculations –but extend into subtropics

Initial observations (partial list)

Challenges & Outlook Cope with improved, yet imperfect atmospheric re-analyses, especially property conservation (precip., runoff, radiation,…) Computational challenge of running adjoint at eddy-permitting scales A well-chosen control space (internal model parameters) Entraining observationalists! –correct treatment of obs. –access to “all” available obs. –proper prior errors (incl. representation errors) and covariances –inhomogeneous sampling in space and time –data inconsistencies Modeling: –required model improvements (sea-ice, mixing, numerics, …) in the context of adjoint are crucial part of the process –options for 2-way nesting down the road –avoid SSS relaxation? –biases, drift…

Discussion - challenges in state estimation Cope with improved, yet imperfect atmospheric re-analyses, especially property conservation (precip., runoff, radiation,…) Lack of atmospheric feedbacks (would require the fully coupled problem) A well-chosen control space (internal model parameters) Entraining observationalists! –correct treatment of obs. –access to “all” available obs. –proper prior errors (incl. representation errors) and covariances, e.g. use of point measurements –inhomogeneous sampling in space and time –data inconsistencies –relative weighting of data types Modeling: –required model improvements (sea-ice, mixing, numerics, …) in the context of adjoint are crucial part of the process –options for 2-way nesting down the road –avoid SSS relaxation? –biases, drift… –entrain AOMIP (+ WGOMD) knowledge on model comparisons Data assimilation methods: pro’s & con’s –twin experiments –sensitivity to resolution –sequential vs. variational –covariance estimates –posterior error estimates Observing system experiments –are results “robust”, I.e. applicable to real world (e.g. sharply confined boundary currents) –observing system sensitivities model-dependent? –need to be peformed w.r.t. optimized model trajectory Can DA help in refuting certain model formulations, e.g. sea ice rheology laws?