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revision 1.7 by dimitri, Fri Jul 18 19:09:20 2008 UTC revision 1.9 by dimitri, Thu Aug 14 16:12:41 2008 UTC
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1  \section{Introduction}  \section{Introduction}
2  \label{sec:intro}  \label{sec:intro}
3    
4  In recent years, ocean state estimation has matured to the extent that  Ocean state estimation has matured to the extent that estimates of the
5  estimates of the time-evolving ocean circulation, constrained by a multitude  time-evolving ocean circulation, constrained by a multitude of in-situ and
6  of in-situ and remotely sensed global observations, are now routinely  remotely sensed global observations, are now routinely available and being
7  available and being applied to myriad scientific problems \citep[and  applied to myriad scientific problems \citep[and references therein]{wun07}.
8  references therein]{wun07}.  As formulated by the consortium for Estimating  As formulated by the consortium for Estimating the Circulation and Climate of
9  the Circulation and Climate of the Ocean (ECCO), least-squares methods, i.e.,  the Ocean (ECCO), least-squares methods are used to fit the Massachusetts
10  filter/smoother \citep{fuk02}, Green's functions \citep{men05}, and adjoint  Institute of Technology general circulation model \citep[MITgcm;][]{mar97a} to
11  \citep{sta02a}, are used to fit the Massachusetts Institute of Technology  the available data.  Much has been achieved but the existing ECCO estimates
12  general circulation model  lack interactive sea ice.  This limits the ability to utilize satellite data
 \citep[MITgcm;][]{marshall97:_finit_volum_incom_navier_stokes} to the  
 available data.  Much has been achieved but the existing ECCO estimates lack  
 interactive sea ice.  This limits the ability to utilize satellite data  
13  constraints over sea-ice covered regions.  This also limits the usefulness of  constraints over sea-ice covered regions.  This also limits the usefulness of
14  the derived ocean state estimates for describing and studying polar-subpolar  the derived ocean state estimates for describing and studying polar-subpolar
15  interactions.  This paper is a first step towards adding sea-ice capability to  interactions.  In this paper we describe a dynamic and thermodynamic sea ice
 the ECCO estimates.  That is, we describe a dynamic and thermodynamic sea ice  
16  model that has been coupled to the MITgcm and that has been modified to permit  model that has been coupled to the MITgcm and that has been modified to permit
17  efficient and accurate forward integration and automatic differentiation.  efficient and accurate forward and adjoint integration.  The forward model
18    borrows many components from current-generation sea ice models but these
19  Although the ECCO2 optimization problem can be expressed succinctly in  components are reformulated on an Arakawa C grid in order to match the MITgcm
20  algebra, its numerical implementation for planetary scale problems is  oceanic grid and they are modified in many ways to permit efficient and
21  enormously demanding.  First, multiple forward integrations are required to  accurate automatic differentiation.  To illustrate how the use of the forward and
22  derive approximate filter/smoothers and to compute model Green's functions.  adjoint parts together can help give insight into discrete model dynamics, we
23  Second, the derivation of the adjoint model, even with the availability of  study the interaction between littoral regions in the Canadian Arctic
24  automatic differentiation tools, is a challenging technical task, which  Archipelago and sea-ice model dynamics.
25  requires reformulation of some of the model physics to insure  
26  differentiability and the addition of numerous adjoint compiler directives to  Because early numerical ocean models were formulated on the Arakawa-B grid and
27  improve efficiency \citep{marotzke99}.  The MITgcm adjoint typically requires  because of the easier treatment of the Coriolis term, most standard sea-ice
28  5--10 times more computations and 10--100 times more storage than the forward  models are discretized on Arakawa-B grids \citep[e.g.,][]{hibler79, harder99,
29  model.  Third, every evaluation of the cost function entails a full forward    kreyscher00, zhang98, hunke97}.  As model resolution increases, more and
30  integration of the assimilation model and multiple forwards (and adjoint for  more ocean and sea ice models are being formulated on the Arakawa-C grid
31  the adjoint method) iterations are required to achieve satisfactorily  \citep[e.g.,][]{mar97a,ip91,tremblay97,lemieux09}.
32  converged solutions.  Finally, evaluating the cost function also requires  %\ml{[there is also MI-IM, but I only found this as a reference:
33  estimating the error statistics associated with unresolved physics in the  %  \url{http://retro.met.no/english/r_and_d_activities/method/num_mod/MI-IM-Documentation.pdf}]}
34  model and with incompatibilities between observed quantities and numerical  From the perspective of coupling a sea ice-model to a C-grid ocean model, the
35  model variables.  These statistics are obtained from simulations at even  exchange of fluxes of heat and fresh-water pose no difficulty for a B-grid
36  higher resolutions than the assimilation model.  For all the above reasons, it  sea-ice model \citep[e.g.,][]{timmermann02a}.  However, surface stress is
37  was decided early on that the MITgcm sea ice model would be tightly coupled  defined at velocities points and thus needs to be interpolated between a
38  with the ocean component as opposed to loosely coupled via a flux coupler.  B-grid sea-ice model and a C-grid ocean model. Smoothing implicitly associated
39    with this interpolation may mask grid scale noise and may contribute to
40    stabilizing the solution.  On the other hand, by smoothing the stress signals
41    are damped which could lead to reduced variability of the system. By choosing
42  Traditionally, probably for historical reasons and the ease of  a C-grid for the sea-ice model, we circumvent this difficulty altogether and
 treating the Coriolis term, most standard sea-ice models are  
 discretized on Arakawa-B-grids \citep[e.g.,][]{hibler79, harder99,  
   kreyscher00, zhang98, hunke97}, although there are sea ice models  
 diretized on a C-grid \citep[e.g.,][]{ip91, tremblay97,  
   lemieux09}. %  
 \ml{[there is also MI-IM, but I only found this as a reference:  
   \url{http://retro.met.no/english/r_and_d_activities/method/num_mod/MI-IM-Documentation.pdf}]}  
 From the perspective of coupling a sea ice-model to a C-grid ocean  
 model, the exchange of fluxes of heat and fresh-water pose no  
 difficulty for a B-grid sea-ice model \citep[e.g.,][]{timmermann02a}.  
 However, surface stress is defined at velocities points and thus needs  
 to be interpolated between a B-grid sea-ice model and a C-grid ocean  
 model. Smoothing implicitly associated with this interpolation may  
 mask grid scale noise and may contribute to stabilizing the solution.  
 On the other hand, by smoothing the stress signals are damped which  
 could lead to reduced variability of the system. By choosing a C-grid  
 for the sea-ice model, we circumvent this difficulty altogether and  
43  render the stress coupling as consistent as the buoyancy coupling.  render the stress coupling as consistent as the buoyancy coupling.
44    
45  A further advantage of the C-grid formulation is apparent in narrow  A further advantage of the C-grid formulation is apparent in narrow
# Line 70  and models have used topographies with a Line 49  and models have used topographies with a
49  avoid this problem \citep{holloway07}. The C-grid formulation on the  avoid this problem \citep{holloway07}. The C-grid formulation on the
50  other hand allows a flux of sea-ice through narrow passages if  other hand allows a flux of sea-ice through narrow passages if
51  free-slip along the boundaries is allowed. We demonstrate this effect  free-slip along the boundaries is allowed. We demonstrate this effect
52  in the Candian archipelago.  in the Candian Arctic Archipelago (CAA).
53    
54  Talk about problems that make the sea-ice-ocean code very sensitive and  Talk about problems that make the sea-ice-ocean code very sensitive and
55  changes in the code that reduce these sensitivities.  changes in the code that reduce these sensitivities.
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