## University of Louisville

# Ice Stream Basal Friction Fields Using Control Methods and Inversion Techniques

## Institution

University of Louisville

## Faculty Advisor/ Mentor

Gerard Williger; Todd Dupont

## Abstract

Ice stream movement cannot be modeled using inland ice algorithms. There are additional stresses that work on these faster moving flows, and consequently they require a different approach. Given thickness, surface elevation, and basal friction, the MacAyeal-Morland equations calculate an ice stream’s velocity. Unfortunately, basal friction is difficult to measure directly. Conversely, velocity data are more readily obtained. It follows that in order to gain useful data concerning fast moving ice flow, we must use inverse methods to solve for the basal friction field. In this project we adopt a control method approach to minimizing the data-to-model mismatch. This approach allows for an optimal solution given potential incompatibilities between the data and forward-model assumptions. Additionally, the control method provides a direct form of the cost (or objective) function's gradient, greatly reducing the computational load required in the minimization process. Using this reduced problem helps us establish a more complete body of code which incorporates the control method technique. With this algorithm, we develop a basal friction field for the Thwaites Glacier, located in the Amundsen Sea sector of West Antarctica.

Ice Stream Basal Friction Fields Using Control Methods and Inversion Techniques

Ice stream movement cannot be modeled using inland ice algorithms. There are additional stresses that work on these faster moving flows, and consequently they require a different approach. Given thickness, surface elevation, and basal friction, the MacAyeal-Morland equations calculate an ice stream’s velocity. Unfortunately, basal friction is difficult to measure directly. Conversely, velocity data are more readily obtained. It follows that in order to gain useful data concerning fast moving ice flow, we must use inverse methods to solve for the basal friction field. In this project we adopt a control method approach to minimizing the data-to-model mismatch. This approach allows for an optimal solution given potential incompatibilities between the data and forward-model assumptions. Additionally, the control method provides a direct form of the cost (or objective) function's gradient, greatly reducing the computational load required in the minimization process. Using this reduced problem helps us establish a more complete body of code which incorporates the control method technique. With this algorithm, we develop a basal friction field for the Thwaites Glacier, located in the Amundsen Sea sector of West Antarctica.