310
Figure 5: typical profile of a valley glacier
where z = ((x , y, t) is the top surface of the ice. Here
8 = d/l
(2.6)
is the aspect ratio and we anticipate 8 « 1. The choice of d and [T] has to be determined
self consistently; we choose l from the given spatial variation of accumulation rate, and we
choose U via 8U = [a], which is a typical accumulation rate. If we choose [T] = pgdsina,
and define
c = 8 cot a ,
then the scaled moment.um equat.ions are
8T12 8T13
- + -
8y
8z
8(
8y
8p
8z
(2.7)
(2.8)
To get some idea of typical magnitudes, use values d rv 100 m, l rv 10 km , tan a rv 0.1;
then 8 rv 10- 2 , C rv 10-\ so that. to leading order ( = ((x , t) and
8T12 8T13
8(
- - + - - = -l+c-;
8y -
8z
8x
(2.9)
we retain the c term for the moment.