import numpy as np
from issm.averaging import averaging
from issm.thomasparams import thomasparams
[docs]def calcbackstress(md,**kwargs):
'''
Compute ice shelf backstress.
This routine computes backstress based on the analytical formalism of
Thomas (1973) and Borstad et al. (2013, The Cryosphere) based on the
ice rigidity, thickness, the densities of ice and seawater, and
(optionally) damage. Strain rates must also be included, either from
observed or modeled velocities.
Available options:
- 'smoothing' : the amount of smoothing to be applied to the strain rate data.
Type 'help averaging' for more information on its
usage. Defaults to 0.
- 'coordsys' : coordinate system for calculating the strain rate
components. Must be one of:
'longitudinal': x axis aligned along a flowline at every point (default)
'principal': x axis aligned along maximum principal strain rate
at every point
'xy': x and y axes same as in polar stereographic projection
Return values:
'backstress' is the inferred backstress based on the analytical
solution for ice shelf creep
Usage:
backstress=calcbackstress(md,options)
Example:
backstress=calcbackstress(md,'smoothing',2,'coordsys','longitudinal')
'''
# unpack kwargs
smoothing=kwargs.pop('smoothing',0)
if 'smoothing' in kwargs: del kwargs['smoothing']
coordsys=kwargs.pop('coordsys','longitudinal')
if 'coordsys' in kwargs: del kwargs['coordsys']
assert len(kwargs)==0, 'error, unexpected or misspelled kwargs'
# some checks
if not hasattr(md.results,'strainrate'):
raise StandardError('md.results.strainrate not present. Calculate using md=mechanicalproperties(md,vx,vy)')
if not '2d' in md.mesh.__doc__:
raise StandardError('only 2d (planview) model supported currently')
if any(md.flowequation.element_equation!=2):
raise StandardError('Warning: the model has some non-SSA elements. These will be treated like SSA elements')
T=0.5*md.materials.rho_ice*md.constants.g*(1-md.materials.rho_ice/md.materials.rho_water)*md.geometry.thickness
n=averaging(md,md.materials.rheology_n,0)
B=md.materials.rheology_B
if md.damage.isdamage:
D=md.damage.D
else:
D=0.
a0,b0,theta0,ex0=thomasparams(md,eq='Thomas',smoothing=smoothing,coordsys=coordsys)
# analytical backstress solution
backstress=T-(1.-D)*B*np.sign(ex0)*(2+a0)*np.abs(ex0)**(1./n)/((1+a0+a0**2+b0**2)**((n-1.)/2./n))
backstress[np.nonzero(backstress<0)]=0
return backstress