A mass conservation approach for mapping glacier ice thickness

The traditional method for interpolating ice thickness data from airborne radar sounding surveys onto regular grids is to employ geostatistical techniques such as kriging. While this approach provides continuous maps of ice thickness, it generates products that are not consistent with ice flow dynamics and are impractical for high resolution ice flow simulations. Here, we present a novel approach that combines sparse ice thickness data collected by airborne radar sounding profilers with high resolution swath mapping of ice velocity derived from satellite synthetic-aperture interferometry to obtain a high resolution map of ice thickness that conserves mass and minimizes the departure from observations. We apply this approach to the case of Nioghalvfjerdsfjorden (79North) Glacier, a major outlet glacier in northeast Greenland that has been relatively stable in recent decades. The results show that our mass conserving method removes the anomalies in mass flux divergence, yields interpolated data that are within about 5% of the original data, and produces thickness maps that are directly usable in high spatial-resolution, high-order ice flow models. We discuss the application of this method to the broad and detailed radar surveys of ice sheet and glacier thickness.