The vertical age profile in sea ice: theory and numerical results
Lietaer, O.; Deleersnijder, E.; Fichefet, T.; Vancoppenolle, M.; Comblen, R.; Bouillon, S.; Legat, V. (2011). The vertical age profile in sea ice: theory and numerical results. Ocean Modelling 40(34): 211226. http://dx.doi.org/10.1016/j.ocemod.2011.09.002
In: Ocean Modelling. Elsevier: Oxford. ISSN 14635003; eISSN 14635011, more
 
Keyword 

Author keywords 
Ice age; Age theory; Thermodynamic sea ice model; Lagrangian; ALE 
Authors   Top 
 Lietaer, O., more
 Deleersnijder, E., more
 Fichefet, T., more
 Vancoppenolle, M., more

 Comblen, R.
 Bouillon, S., more
 Legat, V., more


Abstract 
The sea ice age is an interesting diagnostic tool because it may provide a proxy for the sea ice thickness and is easier to infer from observations than the sea ice thickness. Remote sensing algorithms and modeling approaches proposed in the literature indicate significant methodological uncertainties, leading to different ice age values and physical interpretations. In this work, we focus on the vertical age distribution in sea ice. Based on the age theory developed for marine modeling, we propose a verticallyvariable sea ice age definition which gives a measure of the time elapsed since the accretion of the ice particle under consideration. An analytical solution is derived from Stefan’s law for a horizontally homogeneous ice layer with a periodic ice thickness seasonal cycle. Two numerical methods to solve the age equation are proposed. In the first one, the domain is discretized adaptively in space thanks to Lagrangian particles in order to capture the age profile and its discontinuities. The second one focuses on the mean age of the ice using as few degrees of freedom as possible and is based on an Arbitrary Lagrangian–Eulerian (ALE) spatial discretization and the finite element method. We observe an excellent agreement between the Lagrangian particles and the analytical solution. The mean value and the standard deviation of the finite element solution agree with the analytical solution and a linear approximation is found to represent the age profile the better, the older the ice gets. Both methods are finally applied to a standalone thermodynamic sea ice model of the Arctic. Computing the verticallyaveraged ice age reduces by a factor of about 2 the simulated ice age compared to the oldest particle of the ice columns. A high correlation is found between the ice thickness and the age of the oldest particle. However, whether or not this will remain valid once ice dynamics is included should be investigated. In addition, the present study, based on thermodynamics only, does not support a single agethickness functional relationship. 
