Using vertical aerial photography to estimate mass balance at a point

The mass balance distribution over a 0.5 km(2) area of the lower part of So uth Cascade Glacier is obtained from remotely sensed measurements of its ge ometry and velocity field over two periods, 1992-93 and 1993-94. Vertical a erial photography from late summer 1992, 1993, and 1994 is analyzed photogr ammetrically to get surface topography of South Cascade Glacier on a 100-me ter square grid. The known bed topography is subtracted from the surface to pography to get the ice thickness, and the surface topographies are subtrac ted from each other to get the thickness change. Annual displacement vector s, determined at points where natural features could be tracked from one ye ar to the next, are contoured by hand and interpolated to me grid. Assuming that the ice follows Glen's flow law with exponent n = 3, and that 10% of the ice flow is due to sliding at the bed, the surface velocity is scaled b y 0.82 to get the average velocity in the vertical ice column. The average velocities are combined with the thicknesses to calculate the flux divergen ce at each of 46 gridpoints on a 100-m square grid, where it is subtracted from the thickness change to get the mass balance. Use of the same control points from year to year makes any systematic error in photogrammetric coordinates temporally constant, so,such error has no e ffect on the mass balance estimate. Random error in coordinates is assumed to be uncorrelated from coordinate to coordinate, from point to point, from year to year; the standard error is estimated to be 1 m, resulting in a st andard error in coordinate differences of about 1.5 m. A 1 m error in a ver tical coordinate has nearly twice the effect on the estimated balance that one in a horizontal coordinate has and more than ten times the effect that one in ice thickness has. Compared with measurements at a stake, the estima ted balances are about 1 m too negative.