Simple analytical models of glacier-climate interactions - by Prof. J ...

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4. A glacier model with a more complicated geometry Glaciers having a constant width are very rare. Larger valley glaciers often show a pattern of a relatively wide accumulation basin and a narrower snout that flows into the valley. Examples are shown in Fig. 4.1. Fig. 4.1 Nigardsbreen Abramov Glacier N N 1800 400 600 800 1000 1200 1600 1400 1400 2200 1800 1000 800 1800 2000 1952 m 600 2200 2600 400 2400 2987 m 2 km 2901 m 2 km To handle such a situation we use a very schematic geometry in which the glacier consists of two parts having a different width. Again, L is the glacier length and the upper basin has length L ub (Fig. 4.2). Fig. 4.2 L ub L 0 x 14
For L < L ub the solution is given by eq. (3.3): L = 2 (H + b 0 - E) s . (4.1) When the mass budget of the upper basin is positive L will be larger than Lub. The length of the glacier is then determined by L ub L (H + b 0 - s x - E) dx + ξ (H + b 0 - s x - E) dx = 0 0 L ub . (4.2) Here ξ is the width of the glacier tongue divided by the width of the upper basin. Evaluating the integrals yields: - 1 2 ξ s L2 + ξ (H + b 0 - E) L + (1 - ξ) (H + b 0 - E) L ub - 1 2 s (1 - ξ) L ub 2 = 0 (4.3) This is a quadratic equation for L which is easily solved: L = - 1 s E' + E' 2 + 2 s 1-ξ ξ 1/2 E' L ub + 1 2 s L ub 2 (4.4) In this expression E' = E - b 0 - H (note that E' < 0). The solution is illustrated in Fig. 4.3. In this example the upper basin has a length of 5 km. Other parameter values are b 0 =2000 m, s=0.1, H=100 m. L is plotted as a function of E for three different values of ξ. For ξ=0.25, the width of the upper basin is four times that of the glacier tongue. Fig. 4.3 20 L (km) 15 10 ξ =4 ξ=1 ξ =0.25 largest sensitivity 5 0 1400 1500 1600 1700 1800 1900 2000 E (m) 15
Page 1 and 2: SIMPLE ANALYTICAL MODELS OF GLACIER
Page 3 and 4: 1. A mass-balance model The process
Page 5 and 6: (iii) A 0 > A 1 (continuous ablatio
Page 7 and 8: 2. Ice deformation: perfect plastic
Page 9 and 10: = ρ i h ρ i - ρ m = -δ h . (2.7
Page 11 and 12: 3. A simple glacier model We consid
Page 13: d L d T a = ∂ L ∂ E d E d T a =
Page 17 and 18: 5. A volume time scale for valley g
Page 19 and 20: Problem: • The time scale derived
Page 21 and 22: Note that values of L for which N <
Page 23 and 24: 7. Steady state ice-sheet profiles
Page 25 and 26: Fig. 7.2 3500 3000 2500 h (m) 2000
Page 27 and 28: Problem HMB-feedback and response t
Page 29 and 30: Problem ice-sheet profile (P 2) For
Page 31: Problem West Antarcic ice sheet (P

Simple analytical models of glacier-climate interactions - by Prof. J ...

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