onderzoeksvoorstel
Door: Heleen
Blijf op de hoogte en volg Heleen
06 Augustus 2005 | Nederland, Harderwijk
mmmmm ik ben toch niet zo'n internetheld... nou ja, hier dus mijn onderzoeksvoorstel, het is eigenlijk een PDF en dan ziet het er heel mooi uit, nu dus niet meer...
A simple model for Nigardsbreen, Norway
Proposal for a 5-month thesis in Physical Geography
Summary:
The purpose of the project is to develop a model for Nigardsbreen and study the relation between climate change and glacier length. The model will be based on the principal of mass conservation and the ice mechanics will be very simple. Emphasis will be on the parameterisation of the 3-dimensional
topography. An attempt will be made to simulate the observed fluctuations in glacier length during the past 300 years, and to calculate future changes for a set of warming scenarios.
1947 (c. Widerøe, Oslo)
Method - dynamics
Conservation of mass requires
dV
dt
= B + F (1)
Here V is the volume of the glacier and B is the total surface mass budget. F represents the loss of ice due to calving in the proglacial lake (when applicable). To calculate changes in glacier length L from the conservation of mass, the following equation has to be used:
dL
dt
=
!L
!V
dV
dt
= (B + F)
!L
!V
(2)
Therefore the first problem to tackle is to find a relation between volume and length. It is assumed that this relation is unique, i.e. an advancing glacier of a certain length has the same volume as a retreating glacier of the same length. This is a reasonable assumption when changes are not too fast.
Method - geometry
The ice thickness of Nigardsbreen has not been mapped and is basically unknown, except for some place on the glacier tongue. So an approximate method is needed to derive the distribution of the ice thickness.
The first step is to have a digital elevation model (DEM) and a glacier overlay available in a GIS. The glacierised area should be obtained from a Landsat image and compared with an existing glacier map from 1988. The ice thickness can the be estimate by assuming that the product of slope and thickness is
approximately constant:
H !h = C (3)
Here H is the ice thickness, h the surface elevation, and C is a constant (related to the characteristic basal shear stress). Some adjustments are probably needed close to the glacier boundaries. Once H(x,y) is known the ice volume can be calculated and the length is defined along a flowline.
When the length of the glacier changes its mean thickness will change as well. First-order theory of glacier mechanics shows that it is reasonable to assume that
H(x, y,L) = H(x, y,L0) L /L0 (4)
Here L0 is the reference glacier length. It would be simple to calculate
!V / !L from Eq. (4) if the glacier
area would not change. However, when the glacier becomes longer and the thickness larger, the glacier area will increase as well. This is probably a small effect on the plateau, but more important for the lower
part of Nigardsbreen when it flows into the valley. A possible approach is to assume that the glacier surface is level in the cross-flow direction, and then calculate the glacier width from the DEM. By repeating this for different values of the glacier length a relation between volume and length can be
established.
Method - mass balance
For Nigardsbreen the mass balance can be described as a linear function of elevation:
˙ b (h) = !(h " E) (5)
Here
˙ b is the balance gradient and E the equilibrium-line altitude.
The total mass budget is obtained by integrating the specific balance over the entire glacier surface:
B = ˙ b (h) dx dy
area
!! (6)
When the specific balance only depends on elevation h, it is sufficient to know the glacier area A and the (area-weighted!) mean surface elevation h . We then have:
B = !A (h " E) (7)
When the glacier front ends in a lake, the calving of icebergs has to be taken into account. Here the method proposed by Oerlemans and Nick (2005) can be used. The calving rate is proportional to the
water depth, but the constant of proportionality is much smaller than for a tidewater glacier.
Method - time integration
Once the geometry has been parameterised (i.e. V, A and h have been expressed in L; preferably in the form of polynomial fits), the model can be integrated with forward time stepping:
L(t + !t) = L(t) + !t B(t) + F(t) [ ]
"L
"V
t
(8)
A suitable value for the time step would be 1 year.
Useful references
Funk M and H Röthlisberger (1989): Forecasting the effect of a planned reservoir which will partially
flood the tongue of Unteraargletscher in Switzerland. Annals of Glaciology 13, 76-81.
Oerlemans J (1997): A flow-line model for Nigardsbreen: projection of future glacier length based on
dynamic calibration with the historic record. Annals of Glaciology 24, 382-389.
Oerlemans J and F M Nick (2005): A minimal model of a tidewater glacier. Annals of Glaciology 42,
accepted.
Østrem G, O Liestøl and B Wold (1977): Glaciological investigations at Nigardsbreen, Norway. Norsk
Geogr. Tidsskr. 30, 187-209.
Østrem G (1988): Nigardsbreen 1:20000. Issued by the Norges Vassdrags og Energiverk, Oslo, Norway.
A simple model for Nigardsbreen, Norway
Proposal for a 5-month thesis in Physical Geography
Summary:
The purpose of the project is to develop a model for Nigardsbreen and study the relation between climate change and glacier length. The model will be based on the principal of mass conservation and the ice mechanics will be very simple. Emphasis will be on the parameterisation of the 3-dimensional
topography. An attempt will be made to simulate the observed fluctuations in glacier length during the past 300 years, and to calculate future changes for a set of warming scenarios.
1947 (c. Widerøe, Oslo)
Method - dynamics
Conservation of mass requires
dV
dt
= B + F (1)
Here V is the volume of the glacier and B is the total surface mass budget. F represents the loss of ice due to calving in the proglacial lake (when applicable). To calculate changes in glacier length L from the conservation of mass, the following equation has to be used:
dL
dt
=
!L
!V
dV
dt
= (B + F)
!L
!V
(2)
Therefore the first problem to tackle is to find a relation between volume and length. It is assumed that this relation is unique, i.e. an advancing glacier of a certain length has the same volume as a retreating glacier of the same length. This is a reasonable assumption when changes are not too fast.
Method - geometry
The ice thickness of Nigardsbreen has not been mapped and is basically unknown, except for some place on the glacier tongue. So an approximate method is needed to derive the distribution of the ice thickness.
The first step is to have a digital elevation model (DEM) and a glacier overlay available in a GIS. The glacierised area should be obtained from a Landsat image and compared with an existing glacier map from 1988. The ice thickness can the be estimate by assuming that the product of slope and thickness is
approximately constant:
H !h = C (3)
Here H is the ice thickness, h the surface elevation, and C is a constant (related to the characteristic basal shear stress). Some adjustments are probably needed close to the glacier boundaries. Once H(x,y) is known the ice volume can be calculated and the length is defined along a flowline.
When the length of the glacier changes its mean thickness will change as well. First-order theory of glacier mechanics shows that it is reasonable to assume that
H(x, y,L) = H(x, y,L0) L /L0 (4)
Here L0 is the reference glacier length. It would be simple to calculate
!V / !L from Eq. (4) if the glacier
area would not change. However, when the glacier becomes longer and the thickness larger, the glacier area will increase as well. This is probably a small effect on the plateau, but more important for the lower
part of Nigardsbreen when it flows into the valley. A possible approach is to assume that the glacier surface is level in the cross-flow direction, and then calculate the glacier width from the DEM. By repeating this for different values of the glacier length a relation between volume and length can be
established.
Method - mass balance
For Nigardsbreen the mass balance can be described as a linear function of elevation:
˙ b (h) = !(h " E) (5)
Here
˙ b is the balance gradient and E the equilibrium-line altitude.
The total mass budget is obtained by integrating the specific balance over the entire glacier surface:
B = ˙ b (h) dx dy
area
!! (6)
When the specific balance only depends on elevation h, it is sufficient to know the glacier area A and the (area-weighted!) mean surface elevation h . We then have:
B = !A (h " E) (7)
When the glacier front ends in a lake, the calving of icebergs has to be taken into account. Here the method proposed by Oerlemans and Nick (2005) can be used. The calving rate is proportional to the
water depth, but the constant of proportionality is much smaller than for a tidewater glacier.
Method - time integration
Once the geometry has been parameterised (i.e. V, A and h have been expressed in L; preferably in the form of polynomial fits), the model can be integrated with forward time stepping:
L(t + !t) = L(t) + !t B(t) + F(t) [ ]
"L
"V
t
(8)
A suitable value for the time step would be 1 year.
Useful references
Funk M and H Röthlisberger (1989): Forecasting the effect of a planned reservoir which will partially
flood the tongue of Unteraargletscher in Switzerland. Annals of Glaciology 13, 76-81.
Oerlemans J (1997): A flow-line model for Nigardsbreen: projection of future glacier length based on
dynamic calibration with the historic record. Annals of Glaciology 24, 382-389.
Oerlemans J and F M Nick (2005): A minimal model of a tidewater glacier. Annals of Glaciology 42,
accepted.
Østrem G, O Liestøl and B Wold (1977): Glaciological investigations at Nigardsbreen, Norway. Norsk
Geogr. Tidsskr. 30, 187-209.
Østrem G (1988): Nigardsbreen 1:20000. Issued by the Norges Vassdrags og Energiverk, Oslo, Norway.
-
07 Augustus 2005 - 07:41
Japke:
Jeetje, ik ben halverwege het verhaal een beetje afgehaakt, sorry! Ik ben niet zo van de modellen! Maar ik wens je heel veel pelzier en een toffe stage!
Dikke kus! -
09 Augustus 2005 - 03:20
Niekolaas:
Haha, ik ben ook een beetje afgehaakt..uhm om eerlijk te zijn heb ik zelfs stukken overgeslagen aangezien ik ook niet echt van de modellen ben. Leuk, ook een site!!!
Hier gaat het iets minder met het onderzoek. Een machine is net kapot gegaan G(&%^%#D!! Afijn, it's all part of the game!! Alvast veel succes met je onderzoek!!
liefs Niek -
10 Augustus 2005 - 16:39
Roel:
Nou ik heb niet eens zin om het te lezen! haha, sorry heleen,ik kan gewoon niet liegen. Bel je me nog een keertje deze week?
Knuffel -
13 Augustus 2005 - 12:41
Mieke:
Moeten wij hier iets van leren, of begrijp jij het nog niet helemaal.
liefs Mieke -
16 Augustus 2005 - 10:17
Dineke:
Hallo!
Nou ik begin niet eens met lezen maar wanneer ga je nu weg?
Nou groetjes van de camping.. -
16 Augustus 2005 - 14:04
Marloes:
Heleen, check je mail snel!
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