Glacier volume estimation as an ill-posed boundary value problem
D. B. Bahr1,2, W. T. Pfeffer2, and G. Kaser11Institute of Meteorology and Geophysics, University of Innsbruck, Innrain 52, 6020 Innsbruck, Austria 2Institute of Arctic and Alpine Research, UCB 450, University of Colorado at Boulder, Boulder, CO, USA
Received: 23 Nov 2012 – Accepted for review: 08 Dec 2012 – Discussion started: 21 Dec 2012
Abstract. Estimating a glacier's volume by inferring properties at depth from properties observed at the surface creates an instability that grows exponentially with the size of the glacier. Random errors from this instability can overwhelm the volume calculation unless problematic short spatial wavelengths are specifically excluded. Volume-area scaling inherently filters these short wavelengths and automatically eliminates the instability, but typical numerical inversions must filter the correct wavelengths explicitly. The world's total glacier and ice cap (GIC) volume is calculated from the sum of hundreds of thousands of ice masses, dramatically reducing the random error from the "ill-posed" instability. However, the variance of the total GIC volume estimate will be exponentially larger if the instability is not carefully controlled. When all other considerations are equal, greater confidence should be placed in total volume estimates that eliminate the ill-posed instability versus those estimates that do not.
Bahr, D. B., Pfeffer, W. T., and Kaser, G.: Glacier volume estimation as an ill-posed boundary value problem, The Cryosphere Discuss., 6, 5405-5420, doi:10.5194/tcd-6-5405-2012, 2012.