Modern studies of the behaviors of glaciers, ice-sheets, and ice-streams rely heavily on both observations and physically based models. Data acquired via remote-sensing provide critical information on geometry and movement of ice over large sections of the Antarctic and Greenland. Though these datasets represent significant advances in terms of spatial coverage and the range of processes we can observe, the physical systems to be modeled are nevertheless incompletely observed. Uncertainties associated with measurement errors are also present. In addition, physical models are also subject to uncertainties. Hence, there is a need for combining observations and models in a fashion that incorporates uncertainty and quantifies its impact on conclusions.