Numerical methods for Data Assimilation

We simulate a simple 1D homogene heat equation given by :

• We perturb the initial condition with

• The approximative solution is obtened by the -schema

• Routine for the integration of the dynamical model l_next_iteration.m

• Tangent linear model d_next_iterate.m

• Choise configuration

  • Overdetermined case, no noise'

  • Underdetermined case, no noise

  • Overdetermined, noisy case

  • Underdetermined, noisy case

  • Undertetermined no Noise - regularization

  • Overdetermined noise - regularization

  • Underdetermined, noisy case

• Operators

  • Apply Binv.m

  • Apply Rinv.m

  • Apply observation operator hh.m

  • Apply generalized observation operator h.m

  • Apply generalized adjoint observation operator ht.m

  • For preconditionning B.m

• Generate observation from truth observation.m

• Perform minimization by choising method : fomos.m rpcg.m cg.