Model help:Gc2d
Gc2d
GC2D simulates glacier evolution. The component simulates the formation and evolution of temperate valley glaciers or ice sheets on a two-dimensional topographic surface as driven by a specified meteorological setting. It is presently coupled to TOPOFLOW to investigate glacio-hydrological interactions.
Model introduction
gc2d is a two-dimensional finite difference numerical model that is driven by a calculations of glacier mass balance (snow precipitation - melt rate). The model calculates ice surface elevations above a two-dimensional terrain by solving equations for ice flux and mass conservation using explicit methods.
The present component is a simplified version of the original Gc2d model, it focuses on the interaction with a hydrological model, and thus generates meltwater to a river system.
gc2d integrates glacier and climate simulation components explicitly, and thus has the unique ability to simulate feedbacks between the changing ice surface and the climate forcing.
The efficiency of this model allows simulation of glacial evolution over millennial timescales at spatial scales that resolve valley glaciers. Finally, from a computational standpoint, the simplicity of this model permits the investigation of significant regions of parameter space, allowing us to determine the effect of new processes or altered algorithms for them.
Model parameters
Uses ports
• Meteorology
• Snow
Note: GC2D reads net mass balance from a file and does not use the Meteorology and Snow ports. They were provided by CSDMS in anticipation of future enhancements.
Provides ports
• Ice (can provide variables for valley glaciers and ice sheets)
• Configure (tabbed dialog GUI to change settings)
• Run (only if used as the Driver)
Main equations
Basic Process Relationships
The modeling of a glacier starts with the conservation of mass at each cell in a 2-d grid. Any changes in glacier ice thickness, h, are calculated with the continuity equation: the difference in ice thickness in a grid cell is then a function of bz, the rate of accumulation or ablation, and the ice discharge into neighboring cells, q :
dh/dt = bz-dqx/dx -dqy/dy
Mass Balance
A ‘mass balance’ of a glacier tracks the changes in the mass of a glacier, and the distribution of changes in space and time. A mass balance then is the sum of accumulation and ablation.
Accumulation: all processes by which mass is added. Most input comes through snow, but other accumulation occurs through avalanches, rime and refreezing of rain.
Ablation: all processes that cause mass loss. Melting and runoff of the meltwater, evaporation, snow erosion due to wind.
A glacier has two distinct zones. The upper section of the glacier that receives the most snowfall over a year and experiences no net melt is called the accumulation zone. Rule of thumb is that this makes up 60 – 70% of the total surface area of a stable glacier. The lower end of the glacier is known as the ablation zone where more ice is lost from melt than gained from snow fall. The altitude separating the two zones is called the equilibrium line altitude, ELA. In GC2D, the initial elevation of the ELA is specified at a certain elevation contour (in m), it can subsequently change with changing climate.
The net mass balance, bz, is described as a function of elevation:
bz = min {gradbz(zi-ELA),bzmax}
gradbz = gradient in the mass balance with elevation
zi = ice surface elevation
ELA = elevation of zero net balance
bzmax = prescribed maximum mass balance to mimick the depletion of moisture available for precipitation at high elevations
Meier an Post (1971) showed that the mass balance gradient for typical western North American glaciers flattens out in the accumulation zone; this observation is captured by limiting the mass balance to bzmax.
Ice Flux by deformation and basal sliding
The volumetric ice discharge, q, is transported between grid cells via ice deformation, Ud and basal sliding, Us.
The shallow ice approximation describes ice deformation, U, vertically averaged:
U = 2/5 A * hi * (tau_b)n
A = coefficient of Glen’s Flow Law (Paterson, 1994).
A = 2.1 E-16 Pa-3/yr, this is the Arrhenius constant (MacGregor, 2000).
hi= ice thickness (m)
tau_b = gravitational driving stress (tau_b=rho*g*hi*Zi)
n= 3 assumed for natural glaciers (Paterson, 1994).
Basal sliding velocity, Us (m/yr) is modeled in two possible ways in Gc2d.
One sliding method is originally used by MacGregor (2000). It incorporates a simplified model for glacial hydrology affecting the basal sliding speed.
Us = (C1 *tau_b2)/Ne
C1 = Sliding Coefficient 0.0012 Pa-1/yr, this is a tuning parameter
Ne = effective stresss at the bed, Ne = rho_ice*g*Hi-rho_water*g*Hw
The other method is based on the observation that the basal shear stress often tends to be around 1 bar (or 105 Pa). This is called the attractor state (Kessler, 2006) and modeled as:
Us=Uc e^(1-(tc/tb))
Uc = characteristic sliding velocity (m/yr)
tc = gravitational driving stress (Pa)
Typically in temperate glaciers sliding velocities vary from 0-30m/yr. tb and tc have a narrow range around 0.5-1.5 or 1 bar = 105Pa.
Notes
All variables and their units can be seen by expanding the Nomenclature section above.
Since GC2D is a 2D model it uses an initial topographic surface (a DEM=digital elevation model).
Presently, GC2D has been coupled to TopoFlow, so it needs to work with a similar DEM and flow grids as TOPOFLOW. For TOPOFLOW, these DEM’s and associated files are based on Rivertools-DEM’s (‘rtg-files) and their associated Header files (‘rti-files’). For GC2D in stand-alone mode, the format of the DEM can be just a binary-file.
Similary, an ice thickness grid can be overlayed on top of the DEM if one wants to initialize the simulation with an existing ice topography.
This ice thickness file is also a binary file.
Numerical scheme
Examples
An example run with input parameters, BLD files, as well as a figure / movie of the output
Follow the next steps to include images / movies of simulations:
- Upload file: https://csdms.colorado.edu/wiki/Special:Upload
- Create link to the file on your page: [[Image:<file name>]].
See also: Help:Images or Help:Movies
Developer(s)
Original development was done by Mark Kessler, the component in the CMT as of November 2010, is a simplified Python version (called Gc2dV0) as revised by Scott Peckham.
References
- Paterson, W.S.B., 1994. The Physics of Glaciers. 3rd edition. Elsevier Science, UK.
- MacGregor, K.R., Anderson, R.S., Anderson, S.P., Waddington, E.D., 2000. Numerical Simulations of Glacial-Valley Longitudinal Profile Evolution. Geology, 28, 11,1031-1034, doi:10.1130/0091-7613(2001)029%3C0760:%3E2.0.CO;2.
- Kessler, M.A., R.S. Anderson, and G.S. Stock, 2006. Modeling topographic and climatic control of east-west asymmetry in Sierra Nevada Glacier length during the Last Glacial Maximum, J. Geophys. Res., 111, F2, F02002, doi:10.1029/2005JF000365.
- Kessler, M.A., Anderson, R.S., Briner, J.P. 2008. Fjord insertion into continental margins driven by topographic steering of ice. Nature Geoscience 1, 365-369 (11 May 2008) doi:10.1038/ngeo201 Letter
Links
Link to the model metadata as submitted by the original developer:
Gc2d model metadata
