/[MITgcm]/MITgcm_contrib/articles/ceaice/ceaice_intro.tex
ViewVC logotype

Diff of /MITgcm_contrib/articles/ceaice/ceaice_intro.tex

Parent Directory Parent Directory | Revision Log Revision Log | View Revision Graph Revision Graph | View Patch Patch

revision 1.6 by dimitri, Sat Jun 28 15:44:39 2008 UTC revision 1.9 by dimitri, Thu Aug 14 16:12:41 2008 UTC
# Line 1  Line 1 
1  \section{Introduction}  \section{Introduction}
2  \label{sec:intro}  \label{sec:intro}
3    
4  In recent years, oceanographic state estimation has matured to the  Ocean state estimation has matured to the extent that estimates of the
5  extent that estimates of the evolving circulation of the ocean constrained by  time-evolving ocean circulation, constrained by a multitude of in-situ and
6  in-situ and remotely sensed global observations are now routinely available  remotely sensed global observations, are now routinely available and being
7  and being applied to myriad scientific problems \citep{wun07}.  Ocean state  applied to myriad scientific problems \citep[and references therein]{wun07}.
8  estimation is the process of fitting an ocean General Circulation Model (GCM)  As formulated by the consortium for Estimating the Circulation and Climate of
9  to a multitude of observations.  As formulated by the consortium for Estimating  the Ocean (ECCO), least-squares methods are used to fit the Massachusetts
10  the Circulation and Climate of the Ocean (ECCO), an automatic differentiation  Institute of Technology general circulation model \citep[MITgcm;][]{mar97a} to
11  tool is used to calculate the so-called adjoint code of a GCM.  The method of  the available data.  Much has been achieved but the existing ECCO estimates
12  Lagrange multipliers is then used to render the problem one of unconstrained  lack interactive sea ice.  This limits the ability to utilize satellite data
13  least-squares minimization.  Although much has been achieved, the existing  constraints over sea-ice covered regions.  This also limits the usefulness of
14  ECCO estimates lack interactive sea ice.  This limits the ability to  the derived ocean state estimates for describing and studying polar-subpolar
15  utilize satellite data constraints over sea-ice covered regions.  This also  interactions.  In this paper we describe a dynamic and thermodynamic sea ice
16  limits the usefulness of the derived ocean state estimates for describing and  model that has been coupled to the MITgcm and that has been modified to permit
17  studying polar-subpolar interactions.  This paper is a first step towards  efficient and accurate forward and adjoint integration.  The forward model
18  adding sea-ice capability to the ECCO estimates.  That is, we describe a  borrows many components from current-generation sea ice models but these
19  dynamic and thermodynamic sea ice model that has been coupled to the  components are reformulated on an Arakawa C grid in order to match the MITgcm
20  Massachusetts Institute of Technology general circulation model  oceanic grid and they are modified in many ways to permit efficient and
21  \citep[MITgcm][]{mar97a} and that has been modified to permit efficient and  accurate automatic differentiation.  To illustrate how the use of the forward and
22  accurate automatic differentiation.  adjoint parts together can help give insight into discrete model dynamics, we
23    study the interaction between littoral regions in the Canadian Arctic
24  The availability of an adjoint model as a powerful research tool  Archipelago and sea-ice model dynamics.
25  complementary to an ocean model was a major design requirement early  
26  on in the development of the MITgcm \citep{marotzke99}. It  Because early numerical ocean models were formulated on the Arakawa-B grid and
27  was recognized that the adjoint model permitted computing the  because of the easier treatment of the Coriolis term, most standard sea-ice
28  gradients of various scalar-valued model diagnostics, norms or,  models are discretized on Arakawa-B grids \citep[e.g.,][]{hibler79, harder99,
29  generally, objective functions with respect to external or independent    kreyscher00, zhang98, hunke97}.  As model resolution increases, more and
30  parameters very efficiently. The information associtated with these  more ocean and sea ice models are being formulated on the Arakawa-C grid
31  gradients is useful in at least two major contexts. First, for state  \citep[e.g.,][]{mar97a,ip91,tremblay97,lemieux09}.
32  estimation problems, the objective function is the sum of squared  %\ml{[there is also MI-IM, but I only found this as a reference:
33  differences between observations and model results weighted by the  %  \url{http://retro.met.no/english/r_and_d_activities/method/num_mod/MI-IM-Documentation.pdf}]}
34  inverse error covariances. The gradient of such an objective function  From the perspective of coupling a sea ice-model to a C-grid ocean model, the
35  can be used to reduce this measure of model-data misfit to find the  exchange of fluxes of heat and fresh-water pose no difficulty for a B-grid
36  optimal model solution in a least-squares sense.  Second, the  sea-ice model \citep[e.g.,][]{timmermann02a}.  However, surface stress is
37  objective function can be a key oceanographic quantity such as  defined at velocities points and thus needs to be interpolated between a
38  meridional heat or volume transport, ocean heat content or mean  B-grid sea-ice model and a C-grid ocean model. Smoothing implicitly associated
39  surface temperature index. In this case the gradient provides a  with this interpolation may mask grid scale noise and may contribute to
40  complete set of sensitivities of this quantity to all independent  stabilizing the solution.  On the other hand, by smoothing the stress signals
41  variables simultaneously. These sensitivities can be used to address  are damped which could lead to reduced variability of the system. By choosing
42  the cause of, say, changing net transports accurately.  a C-grid for the sea-ice model, we circumvent this difficulty altogether and
   
 References to existing sea-ice adjoint models, explaining that they are either  
 for simplified configurations, for ice-only studies, or for short-duration  
 studies to motivate the present work.  
   
 Traditionally, probably for historical reasons and the ease of  
 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 72  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.
Legend:
Removed from v.1.6  
changed lines
  Added in v.1.9
  ViewVC Help
Powered by ViewVC 1.1.22