Towards an indirect determination of the mass-balance distribution of glaciers using the kinematic boundary condition

The kinematic boundary condition at the surface is utilized to arrive at an estimate of the mass-balance distribution of the ablation region of Unteraargletscher, Bernese Alps, Switzerland. This is achieved without the use of any ground measurements. The terms of the kinematic boundary condition, involving surface-altitude changes with time, surface slopes, and horizontal surface velocities, are determined using high precision aerial photogrammetry. Estimating the vertical velocity distribution along the surface poses a major problem. Different approaches to solving this problem are discussed, and the potential of one particular approach is evaluated. This approach is, in essence, based on the assumption that the variation of vertical strain rates with depth is simple. The accuracy of the resulting indirect estimate of the mass balance distribution is assessed by a comparison with results from stake measurements made at about 40 different points at the surface. Although calculated values of mass balance are found to be within a reasonable range, they differ, as a function of altitude, in a systematic fashion from stake values. This suggests that the vertical strain-rats variation with depth is too complex to be parameterized in a simple manner.