I assume that the geometric mineral surface area at the glacier bed is equivalent to the mineral surface area produced by glacier erosion. This implies that there is little storage of fine-grained sediment at the bed of Bench Glacier, an assumption supported by video camera observations of the bed (Harper et al., 2003), year-to-year consistency in sediment yield, and dynamics of the glacier.

The surface area production rate, Sgeo, is given by Sgeo = ngr agr, where agr is the surface area per grain, and ngr is the number of grains produced per unit time, given by ngr = EA/vgr, where E is the erosion rate (length/time), A is the basin area, and vgr is the volume per grain. For a mixture of grains of simple geometry (either spheres or cubes)

geo h D

where Di is the particle size of grain size class i (length) and fi is the fraction of the sediment yield represented by grain size class i. Bench Glacier sediment yield of 1.5 mmyr-1 falls in the middle of the global range for glaciers. I assume a sediment size distribution of 50% coarse material (with insignificant surface area), 25% coarse silt (62|lm) and 25% coarse clay (2|lm). This yields Sgeo = 8100 km2 yr-1 for Bench Glacier.

Natural mineral surfaces are rough compared with Sgeo. The true reactive surface area is approximated with SBET, the surface area determined from gas adsorption isotherms. A roughness parameter l, defined as l = SBET/Sgeo, has values commonly 10 or greater. Surface roughness tends to increase as mineral surfaces age (White & Brantley, 2003), empirically following l = 13.6t0'20 (3)

where t is the exposure age of the mineral surface in years.

Table 16.1 Regressions of r versus time from White & Brantley (2003). The regressions are of the form logr = a + blogt, where t is time in years, and r is the mineral weathering rate

Table 16.1 Regressions of r versus time from White & Brantley (2003). The regressions are of the form logr = a + blogt, where t is time in years, and r is the mineral weathering rate

Mineral |
a |
b |

Plagioclase |
-12.46 |
-0.56 |

K feldspar |
-12.49 |
-0.65 |

Hornblende |
-12.67 |
-0.62 |

Biotite |
-12.32 |
-0.60 |

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