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

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d V' d t = w f H m,0 d L' d t = amount of mass added . (5.4) In a perturbation analysis we have two contributions to the mass added to or removed from the glacier: change of volume = A 0 B' + w f B f L' . (5.5) B' is the perturbation of the balance rate (constant over the glacier), and B f the characteristic balance rate at the glacier front. The first term is simply the amount of ice added or removed by the balance perturbation on the reference glacier area. The second term is the amount of ice lost or gained because the length of the glacier deviates from that of the reference state. Combining eqs. (5.4)-(5.6) yields d L' d t = A 0 w f H m,0 B' + B f H m,0 L' . (5.7) The equilibrium state is obtained by setting the time derivative to zero. This gives: L' = - A 0 w f B f B' . (5.8) The response time for glacier length according to this model is apparently t L = - H m,0 B f . (5.9) Some examples on response times are given in the table below. The quantities marked with • are the input data. Eq. (6.1) has been used to calculate H o . The response time is then obtained from eq. (5.9). •Ao •Lo •s •β Ho •W f •B f t L (km 2 ) (km) (m 2 yr -1 ) (m) (m) (m yr -1 ) (yr) Nigardsbreen 48.8 10.4 0.13 0.0078 125 500 -10 13 Abramov Glac. 25.9 9.1 0.09 0.0055 136 700 -4 34 Rhonegletscher 18.5 9.8 0.13 0.0066 122 900 -5 24 Franz-Josef Gl. 36 11.4 0.21 0.0125 107 600 -22 5 Aletschgletscher 86.8 24.7 0.1 0.0066 215 1200 -8 27 Ob. Grindelw.gl. 10.1 5.0 0.25 0.0066 65 500 -7 9 18
Problem: • The time scale derived above is not very accurate, because it ignores the HMBfeedback. Repeat the analysis and include the HMB-feedback by assuming that H m ' = η L'. Find η by linearising eq. (6.1). Calculate the newly derived time scale for the glaciers in the table. Conclusion? 19
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 and 14: d L d T a = ∂ L ∂ E d E d T a =
Page 15 and 16: For L < L ub the solution is given
Page 17: 5. A volume time scale for valley g
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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