Density assumptions for converting geodetic glacier volume change to mass change

The geodetic method is widely used for assessing changes in the mass balance of mountain glaciers. However, comparison of repeated digital elevation models only provides a glacier volume change that must be converted to a change in mass using a density assumption or model. This study investigates the use of a constant factor for the volume-to-mass conversion based on a firn compaction model applied to simplified glacier geometries with idealized climate forcing, and two glaciers with long-term mass balance series. It is shown that the 'density' of geodetic volume change is not a constant factor and is systematically smaller than ice density in most cases. This is explained by the accretion/removal of low-density firn layers, and changes in the firn density profile with positive/negative mass balance. Assuming a value of 850 +/- 60 kg m(-3) to convert volume change to mass change is appropriate for a wide range of conditions. For short time intervals (3 yr), periods with limited volume change, and/or changing mass balance gradients, the conversion factor can however vary from 0-2000 kg m(-3) and beyond, which requires caution when interpreting glacier mass changes based on geodetic surveys.