===== User Function Budd Sliding Relation =====


==== General Informations ====
  * **USF Fortran File:** ''USF_Sliding.f90''
  * **USF Name:** ''Sliding_Budd''
  * **Required Input Variable(s):** Vertical coord, ''z''


==== General Description ====

This is a summary description.  See comments in the code module for a more complete description.
                                                                                                                                       
Basal shear stress is given by:

<m>  tau_b = C.{u_b}^{m - 1} . u_b . Zab^{q} </m>\\

where Zab is height above bouyancy, C is a friction coefficient, and m and q are exponents.

The parameters to be given (in the bed boundary condition) are:\\
  * ''Budd Friction Coefficient''      -> <m>C</m> 
  * ''Budd Velocity Exponent''         -> <m>m</m>
  * ''Budd Zab Exponent''         -> <m>q</m>
  * ''Budd Linear Velocity'' -> <m>u_{t0}</m>  
  * ''Budd Floatation''

If ''Budd Floatation'' is set to true then the height above buoyancy will be based on the floatation condition instead of inferred from the effective pressure (i.e. depth is used instead of normal stress). Default is false.


===References===

Bill Budd's original work:

Budd, W., Keage, P. L., and Blundy, N. A.: Empirical studies of ice
sliding, J. Glaciol., 23, 157–170, 1979.

Budd,  W.,  Jenssen,  D.,  and  Smith,  I.:  A  3-dimensional  time-
dependent model of the West Antarctic Ice-Sheet, Ann. Glaciol.,
5, 29–36, 1984.

Recent implementation in Elmer/Ice:

Gladstone, R.M., R.C. Warner, B.K. Galton-Fenzi, O. Gagliardini, T. Zwinger and R. Greve, 2017. Marine ice sheet model performance depends on basal sliding physics and sub-shelf melting, The Cryosphere, 11, 319-329, doi:10.5194/tc-11-319-2017 [[https://www.the-cryosphere.net/11/319/2017/|pdf]]