source: issm/oecreview/Archive/17984-18295/ISSM-18010-18011.diff@ 18296

../trunk-jpl/src/m/mech/backstressfrominversion.m

@@ -22 +22 @@
 %                               'xy': x and y axes same as in polar stereographic projection 
 %
 %   Return values:
-%               'backstress' is the inferred backstress necessary to balance the
-%               analytical solution (keeping damage within its appropriate limits, e.g. D
-%               in [0,1]).
+%               'backstress' is the inferred backstress based on the analytical
+%               solution for ice shelf creep
 %
 %   Usage:
 %      backstress=backstressfrominversion(md,options)

../trunk-jpl/src/m/mech/calcbackstress.m

@@ +1 @@
+function backstress=calcbackstress(md,varargin)
+%BACKSTRESSFROMINVERSION - compute ice shelf backstress  
+%
+%        This routine computes backstress based on the analytical formalism of
+%        Thomas (1973) and Borstad et al. (2013) 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=backstressfrominversion(md,'smoothing',2,'coordsys','longitudinal');
+
+% check inputs
+if (nargin<1),
+        help backstressfrominversion
+        error('bad usage');
+end
+if isempty(fieldnames(md.results)),
+        error(['md.results.strainrate is not present.  Calculate using md=mechanicalproperties(md,vx,vy)']);
+end
+if dimension(md.mesh)~=2,
+        error('only 2d model supported currently');
+end
+if any(md.flowequation.element_equation~=2),
+        disp('Warning: the model has some non SSA elements. These will be treated like SSA elements');
+end
+
+% process options
+options = pairoptions(varargin{:});
+smoothing = getfieldvalue(options,'smoothing',0);
+coordsys = getfieldvalue(options,'coordsys','longitudinal');
+tempmask = getfieldvalue(options,'tempmask',false);
+
+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.*sign(ex0).*(2+a0).*abs(ex0).^(1./n)./((1+a0+a0.^2+b0.^2).^((n-1)/2./n));
+backstress(find(backstress<0))=0;

../trunk-jpl/src/m/mech/backstressfrominversion.py

@@ -7 +7 @@
         Compute ice shelf backstress from inversion results.
 
         This routine computes backstress based on the analytical formalism of
-        Thomas (1973) and Borstad et al. (2013, The Cryoshpere).  The model
+        Thomas (1973) and Borstad et al. (2013, The Cryosphere).  The model
         must contain inversion results for ice rigidity.  Strain rates must
         also be included, either from observed or modeled velocities.  Ice
         rigidity B is assumed to be parameterized by the ice temperature in
@@ -28 +28 @@
                                 'xy': x and y axes same as in polar stereographic projection 
 
    Return values:
-                'backstress' is the inferred backstress necessary to balance the
-                analytical solution (keeping damage within its appropriate limits, e.g. D
-                in [0,1]).
+                'backstress' is the inferred backstress based on the analytical
+                solution for ice shelf creep
 
    Usage:
       backstress=backstressfrominversion(md,options)

../trunk-jpl/src/m/mech/calcbackstress.py

@@ +1 @@
+import numpy as npy
+from averaging import averaging
+from thomasparams import thomasparams
+
+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*npy.sign(ex0)*(2+a0)*npy.abs(ex0)**(1./n)/((1+a0+a0**2+b0**2)**((n-1.)/2./n))
+        backstress[npy.nonzero(backstress<0)]=0
+
+        return backstress