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An optimization approach to sea ice ...

Schaffrin, Helga.

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An optimization approach to sea ice dynamics.

Record Type:	Electronic resources : Monograph/item
Title/Author:	An optimization approach to sea ice dynamics./
Author:	Schaffrin, Helga.
Description:	355 p.
Notes:	Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6015.
Contained By:	Dissertation Abstracts International66-11B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3195483
ISBN:	054240382X

An optimization approach to sea ice dynamics.
Schaffrin, Helga.

An optimization approach to sea ice dynamics. - 355 p.

Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6015.

Thesis (Ph.D.)--New York University, 2005.

A new model for sea ice dynamics is developed, based on a novel mathematical approach treating the equations of motion as constraints in an optimization problem minimizing the pressure field. The scale of interest here is that with grid boxes of a few kilometers, i.e. a scale where individual ice floes cannot be resolved. Following a popular analogy, I treat sea ice as a fluid with the special property that ice on this scale permits divergence, but strongly resists convergence at high concentration. This resistance is limited by the ice strength. My goal is to develop a method for determining the pressure arising from and enforcing this "semi-incompressibility" which is both mathematically elegant and computationally acceptable and whose reliance on empirical parameterizations is kept to a minimum. At the same time, the model should produce realistic results.

ISBN: 054240382XSubjects--Topical Terms:

515831
Mathematics.

An optimization approach to sea ice dynamics.
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020 $a 054240382X
035 $a (UnM)AAI3195483
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100 1 $a Schaffrin, Helga. $3 1905325
245 1 3 $a An optimization approach to sea ice dynamics.
300 $a 355 p.
500 $a Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6015.
500 $a Advisers: David M. Holland; Esteban G. Tabak.
502 $a Thesis (Ph.D.)--New York University, 2005.
520 $a A new model for sea ice dynamics is developed, based on a novel mathematical approach treating the equations of motion as constraints in an optimization problem minimizing the pressure field. The scale of interest here is that with grid boxes of a few kilometers, i.e. a scale where individual ice floes cannot be resolved. Following a popular analogy, I treat sea ice as a fluid with the special property that ice on this scale permits divergence, but strongly resists convergence at high concentration. This resistance is limited by the ice strength. My goal is to develop a method for determining the pressure arising from and enforcing this "semi-incompressibility" which is both mathematically elegant and computationally acceptable and whose reliance on empirical parameterizations is kept to a minimum. At the same time, the model should produce realistic results.
520 $a The pressure p is considered as a Lagrange multiplier in the constrained optimization problem minimizing the deviation from the path without the pressure force, subject to the constraint that ice concentration (fractional area coverage) should not exceed 1. I show that this p can be determined as the solution to the optimization problem minimizing the pressure itself, which permits the use of standard linear optimization techniques.
520 $a To gain insight into the nature and effects of the pressure force, I first consider the simplified problem without any other forces, or freezing or melting. While these components can be added into the model relatively easily, they also contribute significantly to the complexity of the situation, complicating the analysis of the results.
520 $a A series of five increasingly complex models is developed. The first four models treat only one spatial dimension: a Lagrangian model, a Eulerian model with constant thickness, a Eulerian model with varying thickness and a Eulerian model allowing the ice to yield. The last model I introduce is the beginning of a two-dimensional implementation of the theory. For each model, the underlying theory, the numerical set-up and numerical results (as compared to physical intuition, analytical solutions, and/or results from another model) are discussed.
590 $a School code: 0146.
650 4 $a Mathematics. $3 515831
650 4 $a Physical Oceanography. $3 1019163
690 $a 0405
690 $a 0415
710 2 0 $a New York University. $3 515735
773 0 $t Dissertation Abstracts International $g 66-11B.
790 1 0 $a Holland, David M., $e advisor
790 1 0 $a Tabak, Esteban G., $e advisor
790 $a 0146
791 $a Ph.D.
792 $a 2005
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3195483