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Filling the polar data gap with harmonic functions

Presented by: 
Courtenay Strong University of Utah
Monday 11th September 2017 - 15:30 to 16:00
INI Seminar Room 1
Coauthors: Elena Cherkaev and Kenneth M. Golden

The “polar data gap” is a region around the North Pole where satellite orbits do not provide sufficient coverage for estimating sea ice concentrations. This gap is conventionally made circular and assumed to be ice-covered for the purpose of sea ice extent calculations, but recent conditions around the perimeter of the gap indicate that this assumption may already be invalid. We present partial differential equation-based models for estimating sea ice concentrations within the area of the data gap. In particular, the sea ice concentration field is assumed to satisfy Laplace’s equation with boundary conditions determined by observed sea ice concentrations on the perimeter of the gap region. This type of idealization in the concentration field has already proved to be quite useful in establishing an objective method for measuring the “width” of the marginal ice zone—a highly irregular, annular-shaped region of the ice pack that interacts with the ocean, and typically surrounds the inner core of most densely packed sea ice. Realistic spatial heterogeneity in the idealized concentration field is achieved by adding a spatially autocorrelated stochastic field with temporally varying standard deviation derived from the variability of observations around the gap. Testing in circular regions around the gap yields observation-model correlation exceeding 0.6 to 0.7, and sea ice concentration mean absolute deviations smaller than 0.01. This approach based on solving an elliptic partial differential equation with given boundary conditions has sufficient generality to also provide more sophisticated models which could be more accurate than the Laplace equation version, and such potential generalizations are explored.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons