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

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

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

revision 1.15 by mlosch, Tue Feb 26 17:21:48 2008 UTC revision 1.16 by mlosch, Tue Feb 26 19:14:36 2008 UTC
# Line 75  example results from coupled ocean and s Line 75  example results from coupled ocean and s
75  \section{Introduction}  \section{Introduction}
76  \label{sec:intro}  \label{sec:intro}
77    
78  The availability of an adjoint model as a powerful research  The availability of an adjoint model as a powerful research tool
79  tool complementary to an ocean model was a major design  complementary to an ocean model was a major design requirement early
80  requirement early on in the development of the MIT general  on in the development of the MIT general circulation model (MITgcm)
81  circulation model (MITgcm) [Marshall et al. 1997a,  [Marshall et al. 1997a, Marotzke et al. 1999, Adcroft et al. 2002]. It
82  Marotzke et al. 1999, Adcroft et al. 2002]. It was recognized  was recognized that the adjoint model permitted computing the
83  that the adjoint permitted very efficient computation  gradients of various scalar-valued model diagnostics, norms or,
84  of gradients of various scalar-valued model diagnostics,  generally, objective functions with respect to external or independent
85  norms or, generally, objective functions with respect  parameters very efficiently. The information associtated with these
86  to external or independent parameters. Such gradients  gradients is useful in at least two major contexts. First, for state
87  arise in at least two major contexts. If the objective function  estimation problems, the objective function is the sum of squared
88  is the sum of squared model vs. obervation differences  differences between observations and model results weighted by the
89  weighted by e.g. the inverse error covariances, the gradient  inverse error covariances. The gradient of such an objective function
90  of the objective function can be used to optimize this measure  can be used to reduce this measure of model-data misfit to find the
91  of model vs. data misfit in a least-squares sense. One  optimal model solution in a least-squares sense.  Second, the
92  is then solving a problem of statistical state estimation.  objective function can be a key oceanographic quantity such as
93  If the objective function is a key oceanographic quantity  meridional heat or volume transport, ocean heat content or mean
94  such as meridional heat or volume transport, ocean heat  surface temperature index. In this case the gradient provides a
95  content or mean surface temperature index, the gradient  complete set of sensitivities of this quantity to all independent
96  provides a complete set of sensitivities of this quantity  variables simultaneously. These sensitivities can be used to address
97  with respect to all independent variables simultaneously.  the cause of, say, changing net transports accurately.
98    
99  References to existing sea-ice adjoint models, explaining that they are either  References to existing sea-ice adjoint models, explaining that they are either
100  for simplified configurations, for ice-only studies, or for short-duration  for simplified configurations, for ice-only studies, or for short-duration
# Line 103  studies to motivate the present work. Line 103  studies to motivate the present work.
103  Traditionally, probably for historical reasons and the ease of  Traditionally, probably for historical reasons and the ease of
104  treating the Coriolis term, most standard sea-ice models are  treating the Coriolis term, most standard sea-ice models are
105  discretized on Arakawa-B-grids \citep[e.g.,][]{hibler79, harder99,  discretized on Arakawa-B-grids \citep[e.g.,][]{hibler79, harder99,
106  kreyscher00, zhang98, hunke97}. From the perspective of coupling a    kreyscher00, zhang98, hunke97}. From the perspective of coupling a
107  sea ice-model to a C-grid ocean model, the exchange of fluxes of heat  sea ice-model to a C-grid ocean model, the exchange of fluxes of heat
108  and fresh-water pose no difficulty for a B-grid sea-ice model  and fresh-water pose no difficulty for a B-grid sea-ice model
109  \citep[e.g.,][]{timmermann02a}. However, surface stress is defined at  \citep[e.g.,][]{timmermann02a}. However, surface stress is defined at
110  velocities points and thus needs to be interpolated between a B-grid  velocities points and thus needs to be interpolated between a B-grid
111  sea-ice model and a C-grid ocean model. While the smoothing implicitly  sea-ice model and a C-grid ocean model. Smoothing implicitly
112  associated with this interpolation may mask grid scale noise, it may  associated with this interpolation may mask grid scale noise and may
113  in two-way coupling lead to a computational mode as will be shown. By  contribute to stabilizing the solution. On the other hand, by
114  choosing a C-grid for the sea-ice model, we circumvent this difficulty  smoothing the stress signals are damped which could lead to reduced
115  altogether and render the stress coupling as consistent as the  variability of the system. By choosing a C-grid for the sea-ice model,
116  buoyancy coupling.  we circumvent this difficulty altogether and render the stress
117    coupling as consistent as the buoyancy coupling.
118    
119  A further advantage of the C-grid formulation is apparent in narrow  A further advantage of the C-grid formulation is apparent in narrow
120  straits. In the limit of only one grid cell between coasts there is no  straits. In the limit of only one grid cell between coasts there is no
121  flux allowed for a B-grid (with no-slip lateral boundary counditions),  flux allowed for a B-grid (with no-slip lateral boundary counditions),
122  whereas the C-grid formulation allows a flux of sea-ice through this  and models have used topographies artificially widened straits to
123  passage for all types of lateral boundary conditions. We  avoid this problem \citep{holloway07}. The C-grid formulation on the
124  demonstrate this effect in the Candian archipelago.  other hand allows a flux of sea-ice through narrow passages if
125    free-slip along the boundaries is allowed. We demonstrate this effect
126    in the Candian archipelago.
127    
128  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
129  changes in the code that reduce these sensitivities.  changes in the code that reduce these sensitivities.
Legend:
Removed from v.1.15  
changed lines
  Added in v.1.16
  ViewVC Help
Powered by ViewVC 1.1.22