Kate Boden, Department of Applied Mathematics, University of Colorado Boulder

Non-Gaussian Data Assimiliation for Sea Ice

The Ensemble Kalman Filter (EnKF) is a powerful tool in the geosciences to integrate real-time observations into dynamical models for an improved estimate of the state. The Gaussian assumptions underlying the EnKF can result in reduced improvements when there are non-Gaussian relationships. Modeled sea ice distributions are highly non-Gaussian due to constraints on the state variables. For example, the CICE/Icepack model divides sea ice within a grid cell into thickness categories and then forecasts the fractional area coverage for each category. The total fractional area, including open water, must sum to one, requiring the forecasted distribution to live on the simplex, a non-Gaussian constraint. There are ways to assimilate sea ice observations using classic EnKF approaches but it requires post-processing, and results may have increased error. This work aims to improve the assimilation of sea ice observations into models by building on a non-Gaussian, two-step framework first put forward by Jeff Anderson in 2002.
 
Given satellite data that provides N total measurements with k of them being open water, the two-step framework works by first applying a scalar Quantile Conserving Ensemble Filter (QCEF)  to update the open water fraction, x_0. The second step uses a transport-based approach to update the remaining variables in the state vector, i.e the fractional area of ice in the other categories. This second step assumes the forecasted distribution (prior) is a mixed Dirichlet and uses the updated open water fraction, x_0, from step one, to transport the remaining state space variables from the prior to the posterior, which is also Dirichlet. This talk will present details on the method and results from synthetic data experiments that compare the EnKF to our new non-Gaussian two-step method.

Passcode for this talk is math-geo