Inferring histories of accumulation rate, ice thickness, and ice flow from internal layers in glaciers and ice sheets

Spatial and temporal variations in past accumulation, ice thickness, and ice flow of polar ice sheets are weakly constrained on Earth, and are fundamental unknowns on Mars. On Earth, the spatial and temporal histories of accumulation and ice-sheet flow are necessary to recreate ice-volume and sea-level histories, and are important to properly interpret ice-core chemistry. On Mars, accumulation and ice-flow histories are necessary to decipher the connection between climate and ice-mass formation, evolution, and observable structure.;Internal layers in ice sheets on Earth and on Mars have been observed with ice-penetrating radar. These layers preserve information about how the ice sheet responded to past spatial and/or temporal changes in accumulation rate and ice flow, and present-day internal-layer shapes observed by radar are the most accessible remaining record of this past information. Deeper layers contain information from further in the past, making them highly valuable, but they are more difficult to decipher.;In this work, an inverse problem is solved to infer transients in accumulation rate, ice-sheet thickness, and ice flow from the shapes of deep internal layers. While some details of these histories can be recovered from ice cores, ice cores represent conditions at only a single point. However, the approach presented here is more robust in combination with ice-core data. If internal layers are dated, for example by an intersecting ice core, then radar-observed internal layers provide both spatial and temporal information. Each layer represents a past surface of a particular age that has been subsequently buried by accumulation and also modified by ice flow.;In this work, the goal of solving this inverse problem is to find a set of model parameters (e.g. accumulation-rate history) that have the minimum variation required to explain the data (e.g. internal-layer shapes). The process of internal-layer formation is described with a 2.5-D thermomechanical ice-flow flowband model. Estimates of the data are matched to measured values within their uncertainties, and to an expected tolerance. We seek an accumulation pattern that is spatially smooth, and a parameter set that is consistent with characteristic values of the parameters. This dissertation presents this inverse approach, and discusses applications to data from Antarctica and from Mars.