GEOLOGY 445 - GLACIAL GEOLOGY

LAB 2 - Glacier Flow

I) DISCUSS MASS AND ENERGY BALANCE

II) FLOW CALCULATION  A glacial survey team is studying a simple valley glacier of uniform slope. They use a line of measurements equally spaced up the centerline of the glacier to evaluate the glacier's mass balance. Each station is in the center of the area it represents, and the stations are 1 km apart. The data below are the results of their measurements over a balance year. The measurements taken include snow depth and density (end of winter) and change of surface elevation (end of summer). End of summer snow density is 550 kg/m³; assume ablated ice to have a density of 900 kg/m³.  Note:  These data are the same as you used for last week's lab!

Modify the data [mbdata.xls] by:

• deleting columns containing data unnecessary to the calculation of velocity (e.g., seasonal, as opposed to annual, data),
• inserting columns as necessary to add such data,
• inserting rows to reflect cross-sections midway between measurement points, and
• adding columns in which the calculations of mass flux, discharge, slope, thickness, area and velocity will take place.

Calculate the following:

• the net addition/subtraction of mass ["mass flux"] on/from the surface of each increment in the balance year [annual specific change x area],
• the discharge through each cross-section [accumulated from incremental mass flux],
• the approximate slope of the glacier [slope = inv tan (rise/run) - in Excel®, =DEGREES(ATAN((high-low)/run))]
• the approximate center-line thickness of the glacier [from the shear stress equation; thickness (ft) ~ 650/slope (°) at 100 kPa (1 bar) shear strength = stress] and
• the approximate cross-sectional area at each cross-section [the area within a parabola is 2/3 the area of the enclosing rectangle - thickness x width].

Then,

• calculate and graph the average velocity required to transport the mass accumulated above each point through each of those cross-sections [throughput (m³·yr^-1)/area (m²) = velocity (m·yr^-1)].
• Submit your spreadsheet and graph to me by Friday 5 PM.

NOTES:  remember to keep your units consistent!  Also - observe the differences in density between snow, ice, and water, and how that can affect your calculations.

Discuss your results and assumptions.

• In particular: are your results reasonable?  (Did you find what you expected?)   Why aren't seasonal data valuable in this calculation?  Do you think the original assumption of a uniform slope is likely to be valid?  Why (not)?  What would happen to your calculations if measurement points 5 and 6 were 100 m (vertical) apart rather than 50 m?  [You can model this by adding 50 m to all of the elevations above point 5.]  What should the relationship be between basal shear stress and velocity?  Between width and velocity?