= Available options for the different filter algorithms =


[[PageOutline(2-3,Contents of this page)]]

There are different operations for each of the filter algorithms that need to be specified in the call to `pdaf_init`. To display the available options in a compiled assimilation program, one can use run with the specification `subtype=-1`. In this case `pdaf_init` wil display the available options for the selected filter algorithm and exit with an error status of -1.

Below we list the options as they are displayed using `subtype=-1`.

== SEEK (filtertype=0) ==

{{{
        Available options:

        Sub-types (Parameter subtype)
          0: Evolve unit modes with finite difference approx. of TLM
          1: like 0 with modes scaled by eigenvalues, unit U
          2: Fixed basis vectors; variable U matrix
          3: Fixed covariance matrix (V and U kept constant)
          5: Offline mode

        Integer parameters (Array param_int)
          param_int(1): Dimension of state vector (>0), required
          param_int(2): Ensemble size (>0), required
          param_int(3): Interval for re-diagonalization of P (>0); optional: default 1
          param_int(4): 1 for incremental updating, 0 else; optional: default 0

        Floating point parameters (Array param_real)
          param_real(1): Forgetting factor (usually >0 and <=1), required
          param_real(2): epsilon for finite-difference approx. of TLM, required

        Further parameters
          n_modeltasks: Number of parallel model integration tasks
              >=1 for subtypes 0 and 1; not larger than total number of processors
              =1 required for subtypes 2 and 3
          screen: Control verbosity of PDAF
              0: no outputs
              1: basic output (default)
              2: 1 plus timing output
              3: 2 plus debug output

        +++++++++ End of option overview for the SEEK filter ++++++++++
}}}


== SEIK (filtertype=1) ==

{{{
        Available options:

        Sub-types (Parameter subtype)
          0: full ensemble integration; left-sided application of T
          1: full ensemble integration; right-sided application of T
          2: Fixed error space basis
          3: Fixed state covariance matrix
          4: Implementation with explicit ensemble transformation
          5: Offline mode

        Integer parameters (Array param_int)
          param_int(1): Dimension of state vector (>0), required
          param_int(2): Ensemble size (>0), required
          param_int(3): not used
          param_int(4): 1 for incremental updating, 0 else; optional, default: 0
          param_int(5): Type of forgetting factor; optional, default: 0
              0: fixed forgetting factor
              1: adaptive forgetting factor (experimental)
          param_int(6): Type of ensemble transformation matrix; optional, default: 0
              0: deterministic omega
              1: random orthonormal omega orthogonal to (1,...,1)^T
              2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
                 (experimental; for random transformations, 1 is recommended)
          param_int(7): Type of transformation matrix square root; optional, default: 0
              (Only relevant for subtype=4)
              0: symmetric square root
              1: Cholesky decomposition

        Floating point parameters (Array param_real)
          param_real(1): Forgetting factor (usually >0 and <=1), required

        Further parameters
          n_modeltasks: Number of parallel model integration tasks
              >=1 for subtypes 0 and 1; not larger than total number of processors
              =1 required for subtypes 2 and 3
          screen: Control verbosity of PDAF
              0: no outputs
              1: basic output (default)
              2: 1 plus timing output
              3: 2 plus debug output

        Internal parameter (defined inside PDAF)
          Nm1vsN: Normalization of covariance matrix; default: 1
              0: normalization with 1/(Ensemble size)
                 (original SEIK, mainly for compatibility with older studies)
              1: normalization with 1/(Ensemble size - 1)
                 (sample covariance matrix consistent with other EnKFs)

        +++++++++ End of option overview for the SEIK filter ++++++++++
}}}


== EnKF (filtertype=2) ==

{{{
        Available options:

        Sub-types (Parameter subtype)
          0: Full ensemble integration; analysis for 2*dim_obs>dim_ens
          1: Full ensemble integration; analysis for 2*dim_obs<=dim_ens
          5: Offline mode

        Integer parameters (Array param_int)
          param_int(1): Dimension of state vector (>0), required
          param_int(2): Ensemble size (>0), required
          param_int(3): maximum rank for inversion of HPH^T, optional, default=0
              (for =0, HPH is inverted by solving the representer equation)
              (if set to >=ensemble size, it is reset to ensemble size - 1)
          param_int(4): not used
          param_int(5): Size of lag for smoothing

        Floating point parameters (Array param_real)
          param_real(1): Forgetting factor (usually >0 and <=1), required

        Further parameters
          n_modeltasks: Number of parallel model integration tasks
              (>=1; not larger than total number of processors)
          screen: Control verbosity of PDAF
              0: no outputs
              1: basic output (default)
              2: 1 plus timing output
              3: 2 plus debug output

        +++++++++ End of option overview for the EnKF ++++++++++
}}}


== LSEIK (filtertype=3) ==

{{{
        Available options:

        Sub-types (Parameter subtype)
          0: full ensemble integration; left-sided application of T
          2: Fixed error space basis
          3: Fixed state covariance matrix
          5: Offline mode

        Integer parameters (Array param_int)
          param_int(1): Dimension of state vector (>0), required
          param_int(2): Ensemble size (>0), required
          param_int(3): not used
          param_int(4): 1 for incremental updating, 0 else; optional, default: 0
          param_int(5): Type of forgetting factor; optional, default: 0
              0: fixed forgetting factor
              1: adaptive forgetting factor for full domain (experimental)
              2: locally adaptive forgetting factor (experimental)
          param_int(6): Type of ensemble transformation matrix; optional, default: 0
              0: deterministic omega
              1: random orthonormal omega orthogonal to (1,...,1)^T
              2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
                 (experimental; for random transformations, 1 is recommended)
          param_int(7): Type of transformation matrix square root; optional, default: 0
              (Only relevant for subtype=4)
              0: symmetric square root
              1: Cholesky decomposition

        Floating point parameters (Array param_real)
          param_real(1): Forgetting factor (usually >0 and <=1), required

        Further parameters
          n_modeltasks: Number of parallel model integration tasks
              >=1 for subtypes 0 and 1; not larger than total number of processors
              =1 required for subtypes 2 and 3
          screen: Control verbosity of PDAF
              0: no outputs
              1: basic output (default)
              2: 1 plus timing output
              3: 2 plus debug output

        Internal parameter (defined inside PDAF)
          Nm1vsN: Normalization of covariance matrix; default: 1
              0: normalization with 1/(Ensemble size)
                 (original SEIK, mainly for compatibility with older studies)
              1: normalization with 1/(Ensemble size - 1)
                 (sample covariance matrix consistent with other EnKFs)

        +++++++++ End of option overview for the LSEIK filter ++++++++++
}}}


== ETKF (filtertype=4) ==

{{{
        Available options:

        Sub-types (Parameter subtype)
          0: full ensemble integration; apply T-matrix analogously to SEIK
          1: full ensemble integration; formulation without T matrix
          2: Fixed error space basis; analysis with T-matrix
          3: Fixed state covariance matrix; analysis with T-matrix
          5: Offline mode; analysis with T-matrix

        Integer parameters (Array param_int)
          param_int(1): Dimension of state vector (>0), required
          param_int(2): Ensemble size (>0), required
          param_int(3): Size of lag for smoothing
          param_int(4): not used
          param_int(5): Type of forgetting factor; optional, default: 0
              0: fixed forgetting factor
              1: adaptive forgetting factor (experimental)
          param_int(6): Type of ensemble transformation matrix; optional, default: 0
              0: deterministic transformation
              2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T

        Floating point parameters (Array param_real)
          param_real(1): Forgetting factor (usually >0 and <=1), required

        Further parameters
          n_modeltasks: Number of parallel model integration tasks
              >=1 for subtypes 0 and 1; not larger than total number of processors
              =1 required for subtypes 2 and 3
          screen: Control verbosity of PDAF
              0: no outputs
              1: basic output (default)
              2: 1 plus timing output
              3: 2 plus debug output

        +++++++++ End of option overview for the ETKF ++++++++++
}}}


== LETKF (filtertype=5) ==

{{{
        Available options:

        Sub-types (Parameter subtype)
          0: full ensemble integration;  apply T-matrix analogously to SEIK
          2: Fixed error space basis; analysis with T-matrix
          3: Fixed state covariance matrix; analysis with T-matrix
          5: Offline mode; analysis with T-matrix

        Integer parameters (Array param_int)
          param_int(1): Dimension of state vector (>0), required
          param_int(2): Ensemble size (>0), required
          param_int(3): Size of lag for smoothing
          param_int(4): not used
          param_int(5): Type of forgetting factor; optional, default: 0
              0: fixed forgetting factor
              1: adaptive forgetting factor for full domain (experimental)
              2: locally adaptive forgetting factor (experimental)
          param_int(6): Type of ensemble transformation matrix; optional, default: 0
              0: deterministic transformation
              2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T

        Floating point parameters (Array param_real)
          param_real(1): Forgetting factor (usually >0 and <=1), required

        Further parameters
          n_modeltasks: Number of parallel model integration tasks
              >=1 for subtypes 0 and 1; not larger than total number of processors
              =1 required for subtypes 2 and 3
          screen: Control verbosity of PDAF
              0: no outputs
              1: basic output (default)
              2: 1 plus timing output
              3: 2 plus debug output

        +++++++++ End of option overview for the LETKF ++++++++++
}}}


== ESTKF (filtertype=6) ==

{{{
        Available options:

        Sub-types (Parameter subtype)
          0: Standard implementation with ensemble integration
          2: Fixed error space basis
          3: Fixed state covariance matrix
          5: Offline mode

        Integer parameters (Array param_int)
          param_int(1): Dimension of state vector (>0), required
          param_int(2): Ensemble size (>0), required
          param_int(3): Size of lag for smoothing
          param_int(4): not used
          param_int(5): Type of forgetting factor; optional, default: 0
              0: fixed forgetting factor
              1: adaptive forgetting factor (experimental)
          param_int(6): Type of ensemble transformation matrix; optional, default: 0
              0: deterministic omega
              1: random orthonormal omega orthogonal to (1,...,1)^T
              2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
                 (experimental; for random transformations, 0 or 1 are recommended)
          param_int(7): Type of transformation matrix square root; optional, default: 0
              0: symmetric square root
              1: Cholesky decomposition

        Floating point parameters (Array param_real)
          param_real(1): Forgetting factor (usually >0 and <=1), required

        Further parameters
          n_modeltasks: Number of parallel model integration tasks
              >=1 for subtypes 0 and 1; not larger than total number of processors
              =1 required for subtypes 2 and 3
          screen: Control verbosity of PDAF
              0: no outputs
              1: basic output (default)
              2: 1 plus timing output
              3: 2 plus debug output

        +++++++++ End of option overview for the ESTKF  ++++++++++
}}}


== LESTKF (filtertype=7) ==

{{{
        Available options:

        Sub-types (Parameter subtype)
          0: Standard implementation with ensemble integration
          2: Fixed error space basis
          3: Fixed state covariance matrix
          5: Offline mode

        Integer parameters (Array param_int)
          param_int(1): Dimension of state vector (>0), required
          param_int(2): Ensemble size (>0), required
          param_int(3): Size of lag for smoothing
          param_int(4): not used
          param_int(5): Type of forgetting factor; optional, default: 0
              0: fixed forgetting factor
              1: adaptive forgetting factor for full domain (experimental)
              2: locally adaptive forgetting factor (experimental)
          param_int(6): Type of ensemble transformation matrix; optional, default: 0
              0: deterministic omega
              1: random orthonormal omega orthogonal to (1,...,1)^T
              2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
                 (experimental; for random transformations, 1 is recommended)
          param_int(7): Type of transformation matrix square root; optional, default: 0
              0: symmetric square root
              1: Cholesky decomposition

        Floating point parameters (Array param_real)
          param_real(1): Forgetting factor (usually >0 and <=1), required

        Further parameters
          n_modeltasks: Number of parallel model integration tasks
              >=1 for subtypes 0 and 1; not larger than total number of processors
              =1 required for subtypes 2 and 3
          screen: Control verbosity of PDAF
              0: no outputs
              1: basic output (default)
              2: 1 plus timing output
              3: 2 plus debug output

        +++++++++ End of option overview for the LESTKF ++++++++++
}}}