A

"O

CD O Profile 2

Profile 1

1930

1940

1950

1960

"o

1940

Profile 2 Figure 14.13. (a) Variation in ice surface elevation on three transverse profiles on Nisqually Glacier, 1931-1960. (b) Variations in ice surface elevation, velocity, and surface slope at Profile 2, 1943-1960. ((a) is from Johnson, 1960, Figure 2; (b) is from Meier, 1965, Figure 4; reproduced with permission of the authors.)

Surface elevation

100 O

cd I

1950

1960

1840

1820

1800

Figure 14.13. (a) Variation in ice surface elevation on three transverse profiles on Nisqually Glacier, 1931-1960. (b) Variations in ice surface elevation, velocity, and surface slope at Profile 2, 1943-1960. ((a) is from Johnson, 1960, Figure 2; (b) is from Meier, 1965, Figure 4; reproduced with permission of the authors.)

other mechanisms, such as an increase in sliding speed, were probably involved.

The reader may find it of interest to compare the change in velocity in Figure 14.13b with that predicted by Equation (5.7) with ub = 0:

To do this, take the differential of Equation (14.32) and divide the result by Equation (14.32) to yield:

dus da dh

To make this calculation you need the ice thickness, which is about 80 m at Profile 2. Despite the approximations inherent in Equations (14.32) and (14.33) and in estimating the values of the parameters in Equation (14.33) from the field data, the calculated dus is surprisingly close to that observed. (The numerical computations are left as an exercise for the reader; see Problem 14.2.)

Owing to the availability of an impressive data base, South Cascade Glacier is another that has been analyzed in some detail. We have already mentioned Harrison et al. 's use of these data. In addition, Nye (1963b) used them to test the kinematic wave theory. To do this, he had to take into consideration the three-dimensional character of the glacier. Thus our Equations (14.8) and (14.10) become:

where Q(x) is the ice flux through a cross section of the glacier at position x, and w0(x) is the width of the glacier as a function of x. In addition, c0 and D0 have to be redefined as:

As was the case with Equations (14.8) and (14.10), Equations (14.34) are a pair of simultaneous differential equations that can be solved for the changes in ice flux, Q1(x, t), and thickness, h1(x, t), resulting from a perturbation in mass balance, b1(x, t).

Previously (Equations (14.6) and (14.17)) we found that, in the absence of sliding, c0 and D0 could be related to certain measures of the speed and ice flux. Thus, if the geometry and velocity field of a glacier are known, reasonable estimates of c0(x) andD0(x) can be made. Nye calculated these parameters for South Cascade Glacier (Figure 14.14) and used the results to solve Equations (14.34) for the situation in which perturbations in b1 varied sinusoidally with period, T, inyears, or frequency, m = 2^/T. The solution is expressed in terms of series approximations, and detailed study of it is beyond the scope of this book. Numerical results are shown in Figure 14.15.

Figure 14.14. w0c0 and w0 D0 as functions of x for South Cascade Glacier. (After Nye, 1963b, p. 104, Figure 7. Reproduced with permission of the author and the Royal Society, London.)

10 x104

10 x104 Distance from head of glacier, km

10x10

Distance from head of glacier, km

200-

100-

10,000

Period, a 1,000 100

200-

100-

 iHi/ij ^ - 50 j/w \ / ^^ - - 40 a - 30 20 / \x / \ s / \ s / \ s / \ N - _1_1_1 ■ 1
0 0