Response timetime lag

Advance and retreat of the glacier front normally lag behind the climate forcing because the signal must be transferred from the accumulation area to the snout. This is referred to as the time lag, or preferably the response time, which is longest for long, low-gradient and slowly moving glaciers, and shortest on short, steep and fast-flowing glaciers (e.g. Johannesson et al., 1989; Paterson, 1994). Kinematic wave theory has been applied

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Figure 4.35 The annual (upper panel) and cumulative (lower panel) net balance for Kara-Batkak between 1957 and 1997. (Data from WGMS)

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Figure 4.35 The annual (upper panel) and cumulative (lower panel) net balance for Kara-Batkak between 1957 and 1997. (Data from WGMS)

to calculating response times (Nye, 1960; Paterson, 1994). However, physically based flow models may help to determine the response times more precisely (van de Wal and Oerlemans, 1995).

The advance and retreat of glaciers are commonly the result of glacier mass balance changes. Theoretically, if the mass balance was constant for several years, the glacier would reach a steady state when the glacier size would remain the same, termed the datum state (Paterson, 1994). An increase in mass balance maintained for several years would lead to a new steady state. The altitudi-nal difference between the two glacier surface profiles increases steadily from the upper part and reaches a maximum at the position of the datum terminal position. Consequently, the head of the glacier does not change significantly, while the frontal part does, because the change in ice flux produced by the change in mass balance accumulates down-glacier. The response time is defined as the time a glacier takes to adjust to a change in mass balance (Paterson, 1994). The response time is the time the mass-balance perturbation takes to

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Figure 4.36 The annual (upper panel) and cumulative (lower panel) net mass balance variations for Ts. Tuyuksuyskiy between 1957 and 1997. (Data from WGMS)

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Figure 4.36 The annual (upper panel) and cumulative (lower panel) net mass balance variations for Ts. Tuyuksuyskiy between 1957 and 1997. (Data from WGMS)

remove the difference between the steady-state volumes of the glacier before and after the change in mass balance (Johannesson et ah, 1989). Glaciers in a temperate maritime climate with a thickness of 150-300 m, and an annual ablation at the terminus of 5-10 m, have estimated response times of 15—60 years. On the other hand, ice caps in Arctic Cascade, with a thickness of 500-1000 m and an annual ablation of 1-2 m, have estimated response times of 250-1000 years. The response time of the Greenland ice sheet is estimated to be around

3000 years (Paterson, 1994). It is, however, difficult to test these estimates, because glaciers are constantly adjusting to a complex series of mass-balance changes. Changes in mass balance are propagated down the glacier as kinematic waves, or more accurately a point, moving with a velocity different from the ice velocity (normally 3-4 times faster).

The relationship of glacier response to massbalance changes is of great importance when climate variations are to be understood. McClung and Armstrong (1993) analysed two

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Figure 4.37 The annual (upper panel) and cumulative (lower panel) net mass balance variations for Urumqihe S. No. 1 between 1959 and 1997. (Data from WGMS)

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Figure 4.37 The annual (upper panel) and cumulative (lower panel) net mass balance variations for Urumqihe S. No. 1 between 1959 and 1997. (Data from WGMS)

aspects of this problem: (1) advance/retreat of the glacier front due to mass balance variations, and (2) cross-correlation of mass-balance data from two glaciers in the same climate zone. Their results indicate that the glacier terminus can respond quickly in accordance with expected minimum time-scales and that two adjacent glaciers may experience different annual mass balance and advance/retreat behaviour.

The complex dynamic processes linking glacier mass balance and length variations have only been studied numerically for a few glaciers (e.g. Kruss, 1983; Oerlemans, 1988; Oerlemans and Fortuin, 1992; Greuell, 1992; Raper et al, 1996). After a certain reaction time (fr) following a change in mass balance, the length of a glacier (L0) will start changing and finally reach a new equilibrium (L0 + 6L) after the response time (ia). After full response, continuity requires that:

with bt — (annual) ablation at the glacier terminus. This means that, for a given change in mass balance, the length change is a function

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Figure 4.38 The annual (upper panel) and cumulative (lower panel) net mass balance variations for Hintereisferner in the Tyrol between 1953 and 1997. (Data from WGMS)

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Figure 4.38 The annual (upper panel) and cumulative (lower panel) net mass balance variations for Hintereisferner in the Tyrol between 1953 and 1997. (Data from WGMS)

of the original length of a glacier, and that the change in mass balance of a glacier can be quantitatively inferred from the easily observed length change using estimates of bt as a function of ELA and 6b/6H, where H is altitude of the ice surface. The response time, fa, of a glacier is related to the ratio between its maximum thickness (hmax) and its annual ablation at the terminus (Johannesson et al, 1989)

Corresponding values for valley glaciers are typically some decades. During the response time, the mass balance b will adjust to zero again so that the mean mass balance b is 0.56b for a linear development. Cumulative length variation curves show that the smallest glaciers reflect annual changes in climate and mass balance with only a few years delay. Larger, more dynamic glaciers respond to decadal variations in climate and mass balance with a delay of several years, while the largest valley glaciers give smoothed signals of secular trends with a delayed response of several decades. For the latter two categories, the high-frequency, interannual front variations are filtered out.

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Figure 4.39 The annual (upper panel) and cumulative (lower panel) net mass balance variations for Silvretta from 1960 to 1997. (Data from WGMS)

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Figure 4.39 The annual (upper panel) and cumulative (lower panel) net mass balance variations for Silvretta from 1960 to 1997. (Data from WGMS)

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