Igor Appel
Air Stress
Despite obvious achievements in theoretical study of interaction between ice cover and adjoining media, the parameterization of several processes should be based upon empirical observations. Primary of these processes concerns the relationship between the wind above the atmospheric boundary layer and surface wind determining tangential air stress.
Appended is a copy of a proposal to study "Relationship in the System Geostrophic Wind - Surface Wind - Ice Drift in the Arctic Ocean" using ARGOS buoy data and information from "North Pole" stations. The results of the study will immediately help to improve PIPS calculations.
Studying the relationships between surface wind, geostrophic wind, and ice drift is oriented toward the development of parameterization of dynamic interaction between the atmosphere and ice cover. But the results of investigation will also give valuable information on the influence of internal stress in ice cover.
Ice Dynamics
First priority - dynamical model of anisotropic ice. Until the present
time, as far as is known, the only working anisotropic ice model has been
developed by the author. Direct measurements of stress and deformation
corresponding to specific phenomena of ice dynamics (SIMI and other
experiments)along with analysis of Radarsat data has allowed significant
improvement in the anisotropic model. The new model now directly brings in
small scale ice mechanics and reflects all revealed features of ice cover
behavior, some of which recently seemed mutually exclusive.
Attached is a copy of a proposal "Anisotropic Behavior of Ice Cover and its Modelling". The recommended approach allows one to calculate the following parameters of leads: relative area, orientation, spacing between leads, and their width.
We propose the simplest possible formulation of oriented constitutive law,
keeping the main features of anisotropic ice behavior and dropping
secondary ones. As a result, in a certain sense, the proposed anisotropic
approach turns out even simpler than some isotropic models.
Allowing for Floe Size
The degree of ice anisotropy depends upon an aggregated state that
determines the possibility of elements composing ice cover to be
redistributed under influence of acting forces, especially in the event when
signs of principal strains are different.
When ice floe size is included in the mathematical description, the model will successfully work for all range of ice conditions from multiyear pack ice to marginal sea ice zone.
An approach to determine the characteristic size of ice floes is also briefly described in the proposal "Anisotropic Behavior of Ice Cover and Its Modelling". Allowing for ice strength is proposed to be realized on the basis of modeling vertical profile of ice temperature.
Including ice floe dimensions as an internal parameter of the model will
also help to improve mathematical description of lateral melting.
Ice Thermodynamics
I believe that the first priority in improving the mathematical model of
thermal processes is to specify calculations of ice thickness changes on the
basis of parameterizing vertical profile of ice temperature and taking into
account the relationship between heat capacity and heat of fusion.
Suppression of Numerical Viscosity
One of main limitations of the present PIPS model is connected with
"computational viscosity" that excessively smooths spatial distribution of
calculated parameters and does not allow reliable simulation of the ice edge
position.
The application of finite difference schemes and other methods to determine
kinematic changes in ice cover parameters is connected with computational
errors, comparable with calculated changes of the parameters. We propose to
increase accuracy of computation by taking into account information on
subgrid changes of the parameters: not only mean value of parameter, but
also the first moments of its spatial distribution.
Simulation of Ice Edge Configuration
The pronounced features of mathematical modeling ice cover and a number of
specific calculating problems are related to the varying configuration of
the ice-covered zone.
We propose to consider an original approach to simulate varying configuration of the ice-covered zone. Eiler-Lagrangian representation of the ice edge is based on approximation of the edge by the segments of line. The location of the segment is defined by prescribing the coordinates of the point at the segment and the direction of the segment. This approach allows us to simulate motion of ice edge and take into account features of thermal processes in its vicinity.