Parameterization of bed roughness in the SIA

Schoof [91] describes how to alter the SIA stress balance to model ice flow over bumpy bedrock topgraphy. One computes the amount by which bumpy topography lowers the SIA diffusivity. An internal quantity used in this method is a smoothed version of the bedrock topography. As a practical matter for PISM, this theory improves the SIA’s ability to handle bed roughness because it parameterizes the effects of “higher-order” stresses which act on the ice as it flows over bumps. For additional technical description of PISM’s implementation, see Using Schoof’s parameterized bed roughness technique in PISM.

There is only one associated option: -bed_smoother_range gives the half-width of the square smoothing domain in meters. If zero is given, -bed_smoother_range 0 then the mechanism is turned off. The mechanism is on by default using executable pismr, with the half-width set to 5 km (-bed_smoother_range 5.0e3), giving Schoof’s recommended smoothing size of 10 km [91].

This mechanism is turned off by default in executables pisms and pismv.

Under the default setting -o_size medium, PISM writes fields topgsmooth and schoofs_theta from this mechanism. The thickness relative to the smoothed bedrock elevation, namely topgsmooth, is the difference between the unsmoothed surface elevation and the smoothed bedrock elevation. It is only used internally by this mechanism, to compute a modified value of the diffusivity; the rest of PISM does not use this or any other smoothed bed. The field schoofs_theta is a number \(\theta\) between \(0\) and \(1\), with values significantly below zero indicating a reduction in diffusivity, essentially a drag coefficient, from bumpy bed.

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