Combining SAR interferometry and the equation of continuity to estimate the three-dimensional glacier surface-velocity vector

Until now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from syn thetic aperture radar interferometry. We discuss this assumption, which neg lects the influence of the local mass balance and a possible contribution t o the vertical velocity arising if the glacier is not in steady state. We f ind that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreov er, the vertical velocity contribution arising if the ice sheet is not in s teady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizo ntal velocity vector. This equation, valid for both steady-state and non-st eady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between t he surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.