--- MITgcm_contrib/articles/ceaice/ceaice.tex 2008/02/26 17:21:48 1.15 +++ MITgcm_contrib/articles/ceaice/ceaice.tex 2008/02/26 19:14:36 1.16 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/MITgcm_contrib/articles/ceaice/ceaice.tex,v 1.15 2008/02/26 17:21:48 mlosch Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/MITgcm_contrib/articles/ceaice/ceaice.tex,v 1.16 2008/02/26 19:14:36 mlosch Exp $ % $Name: $ \documentclass[12pt]{article} @@ -75,26 +75,26 @@ \section{Introduction} \label{sec:intro} -The availability of an adjoint model as a powerful research -tool complementary to an ocean model was a major design -requirement early on in the development of the MIT general -circulation model (MITgcm) [Marshall et al. 1997a, -Marotzke et al. 1999, Adcroft et al. 2002]. It was recognized -that the adjoint permitted very efficient computation -of gradients of various scalar-valued model diagnostics, -norms or, generally, objective functions with respect -to external or independent parameters. Such gradients -arise in at least two major contexts. If the objective function -is the sum of squared model vs. obervation differences -weighted by e.g. the inverse error covariances, the gradient -of the objective function can be used to optimize this measure -of model vs. data misfit in a least-squares sense. One -is then solving a problem of statistical state estimation. -If the objective function is a key oceanographic quantity -such as meridional heat or volume transport, ocean heat -content or mean surface temperature index, the gradient -provides a complete set of sensitivities of this quantity -with respect to all independent variables simultaneously. +The availability of an adjoint model as a powerful research tool +complementary to an ocean model was a major design requirement early +on in the development of the MIT general circulation model (MITgcm) +[Marshall et al. 1997a, Marotzke et al. 1999, Adcroft et al. 2002]. It +was recognized that the adjoint model permitted computing the +gradients of various scalar-valued model diagnostics, norms or, +generally, objective functions with respect to external or independent +parameters very efficiently. The information associtated with these +gradients is useful in at least two major contexts. First, for state +estimation problems, the objective function is the sum of squared +differences between observations and model results weighted by the +inverse error covariances. The gradient of such an objective function +can be used to reduce this measure of model-data misfit to find the +optimal model solution in a least-squares sense. Second, the +objective function can be a key oceanographic quantity such as +meridional heat or volume transport, ocean heat content or mean +surface temperature index. In this case the gradient provides a +complete set of sensitivities of this quantity to all independent +variables simultaneously. These sensitivities can be used to address +the cause of, say, changing net transports accurately. References to existing sea-ice adjoint models, explaining that they are either for simplified configurations, for ice-only studies, or for short-duration @@ -103,24 +103,27 @@ 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}. From the perspective of coupling a + kreyscher00, zhang98, hunke97}. 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. While the smoothing implicitly -associated with this interpolation may mask grid scale noise, it may -in two-way coupling lead to a computational mode as will be shown. By -choosing a C-grid for the sea-ice model, we circumvent this difficulty -altogether and render the stress coupling as consistent as the -buoyancy coupling. +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 render the stress +coupling as consistent as the buoyancy coupling. A further advantage of the C-grid formulation is apparent in narrow straits. In the limit of only one grid cell between coasts there is no flux allowed for a B-grid (with no-slip lateral boundary counditions), -whereas the C-grid formulation allows a flux of sea-ice through this -passage for all types of lateral boundary conditions. We -demonstrate this effect in the Candian archipelago. +and models have used topographies artificially widened straits to +avoid this problem \citep{holloway07}. The C-grid formulation on the +other hand allows a flux of sea-ice through narrow passages if +free-slip along the boundaries is allowed. We demonstrate this effect +in the Candian archipelago. Talk about problems that make the sea-ice-ocean code very sensitive and changes in the code that reduce these sensitivities.