README

Test Case for the inverse methods

I)  the control inverse method: Adjoint_Beta.sif  Adjoint_Mu.sif
(cf Morlighem et al., Spatial patterns of basal drag inferred using control methods
	from a full‐Stokes and simpler models for Pine Island Glacier, West Antarctica, Geophys. Res. Lett., 37, 2010
    Petra et al., An inexact Gauss–Newton method for inversion of basal sliding
	and rheology parameters in a nonlinear Stokes ice sheet model, J. Glaciol., 58(211), 2012)

II) the Robin Inverse Method: Robin_Beta.sif
(cf Arthern and Gudmundsson, Initialization of ice-sheet forecasts viewed as an inverse Robin problem, J. Glaciol., 56(197), 2010)


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The setup is based on Mac Ayeal, D.,"A tutorial on the use of control methods in ice-sheet modeling",  J. Glaciol., 39(131), 1993

Synthetic data (for U and V surface velocity, bedrock elevation and surface elevation) used as "perfect" observations are stored under the Data directory and have been generated previously using a slip coefficient defined by
$ function betaSquare(tx) {\
  Lx = 200.0e3;\
  Ly = 50.0e03;\
  yearinsec = 365.25*24*60*60;\
  F1=sin(3.0*pi*tx(0)/Lx)*sin(pi*tx(1)/Ly);\
  F2=sin(pi*tx(0)/(2.0*Lx))*cos(4.0*pi*tx(1)/Ly);\
  beta=5.0e3*F1+5.0e03*F2;\
  _betaSquare=beta*beta/(1.0e06*yearinsec);\
}
and a viscosity defined by
$ function MuSquare(tx) {\
  Lx = 200.0e3;\
  Ly = 50.0e03;\
  yearinsec = 365.25*24*60*60;\
  F1=sin(3.0*pi*tx(0)/Lx)*sin(pi*tx(1)/Ly);\
  F2=sin(pi*tx(0)/(2.0*Lx))*cos(4.0*pi*tx(1)/Ly);\
  mu=sqrt(1.8e08)+1.0e03*(F1+F2);\
  _MuSquare=mu*mu*1.0e-6*(2.0*yearinsec)^(-1.0/3.0);\
}



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TO RUN the TEST:
elmerf90 ./PROG/USF_Init.f90 -o ./USF_Init
ElmerGrid 1 2 mesh2D -metis 4 4
mpirun -n 4 ElmerSolver_mpi

Results established:
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19.03.2015
Laure Tavard,LGGE
Froggy cluster (CIMENT: Grenoble University HPC centre)
Revision 58f71b4
+------------------
05.04.2018
Updated F. Gillet-Chaulet.
- reduce number of iterations from 5 to 2
- test result from more solvers