wiki:AvailableOptionsforInitPDAFinPDAF3

Version 2 (modified by lnerger, 8 days ago) ( diff )

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Available options for the different DA methods (PDAF3)

This page documents the options for PDAF 3.
See the page on available options in PDAF 2.31 for the options valid for the ealier releases.

There are different options for each of the filter algorithms that need to be specified in the call to PDAF_init or that canbe set using PDAF_set_iparam and PDAF_set_rparam. 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.

The options are mainly unified over the different DA methods. Here, the nonlinear ensemble methods have somewhaat different options from those for the ensemble Kalman filter variants. Also the 3D-Var methods have a different set of options.

Overview of options

Options for ensemble Kalman filters

Overview of integer options for ensemble Kalman filters. The parameters are explained in the list of options as they are displayed using subtype=-1, which are shown further below.

Parameters shown in italic font have changed in PDAF V3 compared to PDAF V2.3.1. The index position in PDAF V2.3.1 is shown in parenthesis.

iparam SEIK LSEIK EnKF LEnKF ETKF LETKF ESTKF LESTKF ENSRF
1 dim_p dim_p dim_p dim_p dim_p dim_p dim_p dim_p dim_p
2 dim_ens dim_ens dim_ens dim_ens dim_ens dim_ens dim_ens dim_ens dim_ens
3 dim_lag(5) dim_lag dim_lag dim_lag dim_lag
4 rank_ana(3) rank_ana(3)
5 type_forget type_forget type_forget type_forget type_forget type_forget
6 type_trans type_trans type_trans type_trans type_trans type_trans
7 type_sqrt type_sqrt type_sqrt type_sqrt
8 obs_ens obs_ens obs_ens obs_ens obs_ens obs_ens obs_ens obs_ens obs_ens
9 type_obs type_obs type_obs type_obs type_obs type_obs type_obs type_obs type_obs

Overview of real-valued options for ensemble Kalman filters. The parameters are explained in the list of options as they are displayed using subtype=-1, which are shown further below

rparam SEIK LSEIK EnKF LEnKF ETKF LETKF ESTKF LESTKF ENSRF
1 forget forget forget forget forget forget forget forget forget

Options for nonlinear DA methods

Overview of integer options for nonlinear DA methods. The parameters are explained in the list of options as they are displayed using subtype=-1, which are shown further below.

Parameters shown in italic font have changed in PDAF V3 compared to PDAF V2.3.1. The index position in PDAF V2.3.1 is shown in parenthesis.

iparam NETF LNETF LKNETF PF
1 dim_p dim_p dim_p dim_p
2 dim_ens dim_ens dim_ens dim_ens
3 dim_lag dim_lag
4 type_noise type_noise type_hyb(7) type_noise
5 type_forget type_forget type_forget
6 type_trans type_trans type_trans type_resample(3)
7 type_winf type_winf type_winf(6)
8 obs_ens obs_ens obs_ens obs_ens
9 type_obs type_obs type_obs type_obs

Overview of real-valued options:

rparam NETF LNETF LKNETF PF
1 forget forget forget forget(2)
2 limit_winf limit_winf hyb_g limit_winf(3)
3 noise_amp noise_amp hyb_k noise_amp(1)

Options for 3D-Var methods

Overview of integer options for 3D-Var methods. The parameters are explained in the list of options as they are displayed using subtype=-1, which are shown further below.

Parameters shown in italic font have changed in PDAF V3 compared to PDAF V2.3.1. The index position in PDAF V2.3.1 is shown in parenthesis.

iparam 3dvar en3dvar hyb3dvar
1 dim_p dim_p dim_p
2 dim_ens dim_ens dim_ens
3 type_opt type_opt type_opt
4 dim_cvec dim_cvec
5 dim_cvec_ens dim_cvec_ens
6 solver param1 solver param1 solver param1
7 solver param2 solver param2 solver param2
8 obs_ens obs_ens obs_ens
9 type_obs type_obs type_obs
10
11 type_forget type_forget
12 type_trans type_trans
13 type_sqrt type_sqrt

Overview of real-valued options:

rparam 3dvar en3dvar hyb3dvar
1 forget forget forget
2 beta
3 solver param3 solver param3 solver param3
4 solver param4 solver param4 solver param4

Option outputs using subtype=-1 - Local Ensemble Kalman filters

LESTKF (filtertype=PDAF_DA_LESTKF=7)

PDAF     Available options for LESTKF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: Standard implementation with ensemble integration
PDAF       10: Fixed error space basis
PDAF       11: Fixed state covariance matrix
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): dim_lag
PDAF           Size of smoothing lag (>=0), optional
PDAF            0: no smoothing (default)
PDAF            >0: apply smoother up to specified lag
PDAF       param_int(4): not used
PDAF       param_int(5) type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: fixed forgetting factor (default)
PDAF            1: adaptive forgetting factor for full domain
PDAF            2: locally adaptive forgetting factor
PDAF       param_int(6) type_trans
PDAF           Type of ensemble transformation matrix; optional
PDAF            0: deterministic Omega (default)
PDAF            1: random orthonormal Omega orthogonal to (1,...,1)^T
PDAF            2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
PDAF              (experimental; for random transformations, 1 is recommended)
PDAF       param_int(7) type_sqrt
PDAF           Type of transformation matrix square root; optional
PDAF            0: symmetric square root (default)
PDAF            1: Cholesky decomposition
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF            0: Initialize observations before call to prepoststep_pdaf
PDAF            1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1 for subtype 0; not larger than total number of processors
PDAF           =1 required for subtypes 10 and 11
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the LESTKF ++++++++++

LETKF (filtertype=PDAF_DA_LETKF=5)

PDAF     Available options for LETKF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: full ensemble integration;  apply T-matrix analogously to SEIK
PDAF       1: full ensemble integration; formulation cf. Hunt et al. (2007) without T matrix
PDAF       10: Fixed error space basis; analysis with T-matrix
PDAF       11: Fixed state covariance matrix; analysis with T-matrix
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): dim_lag
PDAF           Size of smoothing lag (>=0), optional
PDAF            0: no smoothing (default)
PDAF            >0: apply smoother up to specified lag
PDAF       param_int(4): not used
PDAF       param_int(5) type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: fixed forgetting factor (default)
PDAF            1: adaptive forgetting factor for full domain
PDAF            2: locally adaptive forgetting factor
PDAF       param_int(6) type_trans
PDAF           Type of ensemble transformation matrix; optional
PDAF            0: deterministic transformation (default)
PDAF            2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF            0: Initialize observations before call to prepoststep_pdaf
PDAF            1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1 for subtypes 0 and 1; not larger than total number of processors
PDAF           =1 required for subtypes 10 and 11
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the LETKF ++++++++++

LEnKF (filtertype=PDAF_DA_LENKF=8)

PDAF     Available options for LEnKF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: Standard EnKF analysis with covariance localization
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): not used
PDAF       param_int(4): rank_ana_enkf
PDAF           maximum rank for inversion of HPH^T, optional, default=0
PDAF            for =0, HPH is inverted by solving the representer equation
PDAF            allowed range is 0 to ensemble size - 1
PDAF       param_int(5): not used
PDAF       param_int(6): not used
PDAF       param_int(7): not used
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF            0: Initialize observations before call to prepoststep_pdaf
PDAF            1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           (>=1; not larger than total number of processors)
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the LEnKF ++++++++++

ENSRF/EAKF (filtertype=PDAF_DA_ENSRF=13)

PDAF     Available options for ENSRF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: ENSRF with serial observation processing (cf. Houtekamer/Mitchell, 2002)
PDAF       1: EAKF/2-step local least squares filter (cf. Anderson, 2003)
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): not used
PDAF       param_int(4): not used
PDAF       param_int(5): not used
PDAF       param_int(6): not used
PDAF       param_int(7): not used
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF            0: Initialize observations before call to prepoststep_pdaf
PDAF            1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           (>=1; not larger than total number of processors)
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the ENSRF ++++++++++

LSEIK (filtertype=PDAF_DA_LSEIK=3)

PDAF     Available options for LSEIK:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: full ensemble integration; left-sided application of T
PDAF       1: full ensemble integration; explicit ensemble transformation
PDAF       10: Fixed error space basis
PDAF       11: Fixed state covariance matrix
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): not used
PDAF       param_int(4): not used
PDAF       param_int(5) type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: fixed forgetting factor (default)
PDAF            1: adaptive forgetting factor
PDAF            2: locally adaptive forgetting factor
PDAF       param_int(6) type_trans
PDAF           Type of ensemble transformation matrix; optional
PDAF            0: deterministic Omega (default)
PDAF            1: random orthonormal Omega orthogonal to (1,...,1)^T
PDAF            2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
PDAF              (experimental; for random transformations, 1 is recommended)
PDAF       param_int(7) type_sqrt
PDAF           Type of transformation matrix square root; optional
PDAF            (Only relevant for subtype/=11)
PDAF            0: symmetric square root (default)
PDAF            1: Cholesky decomposition
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF            0: Initialize observations before call to prepoststep_pdaf
PDAF            1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1 for subtypes 0 and 1; not larger than total number of processors
PDAF           =1 required for subtypes 10 and 11
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     --- Internal parameter (defined inside PDAF) ---
PDAF       Nm1vsN: Normalization of covariance matrix; default: 1
PDAF           0: normalization with 1/(Ensemble size)
PDAF              (original SEIK, mainly for compatibility with older studies)
PDAF           1: normalization with 1/(Ensemble size - 1)
PDAF              (sample covariance matrix consistent with other EnKFs)
PDAF     +++++++++ End of option overview for the LSEIK filter ++++++++++

Option outputs using subtype=-1 - Global Ensemble Kalman filters

ESTKF (filtertype=PDAF_DA_ESTKF=6)

PDAF     Available options for ESTKF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: Standard implementation with ensemble integration
PDAF       10: Fixed error space basis
PDAF       11: Fixed state covariance matrix
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): dim_lag
PDAF           Size of smoothing lag (>=0), optional
PDAF            0: no smoothing (default)
PDAF            >0: apply smoother up to specified lag
PDAF       param_int(4): not used
PDAF       param_int(5) type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: fixed forgetting factor (default)
PDAF            1: adaptive forgetting factor (experimental)
PDAF       param_int(6) type_trans
PDAF           Type of ensemble transformation matrix; optional
PDAF            0: deterministic Omega (default)
PDAF            1: random orthonormal Omega orthogonal to (1,...,1)^T
PDAF            2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
PDAF              (experimental; for random transformations, 0 or 1 are recommended)
PDAF       param_int(7) type_sqrt
PDAF           Type of transformation matrix square root; optional
PDAF            0: symmetric square root (default)
PDAF            1: Cholesky decomposition
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF           0: Initialize observations before call to prepoststep_pdaf
PDAF           1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1 for subtype 0; not larger than total number of processors
PDAF           =1 required for subtypes 10 and 11
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the ESTKF  ++++++++++

ETKF (filtertype=PDAF_DA_ETKF=4)

PDAF     Available options for ETKF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: full ensemble integration; apply T-matrix analogously to SEIK
PDAF       1: full ensemble integration; formulation cf. Hunt et al. (2007) without T matrix
PDAF       10: Fixed error space basis; analysis with T-matrix
PDAF       11: Fixed state covariance matrix; analysis with T-matrix
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): dim_lag
PDAF           Size of smoothing lag (>=0), optional
PDAF            0: no smoothing (default)
PDAF            >0: apply smoother up to specified lag
PDAF       param_int(4): not used
PDAF       param_int(5) type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: fixed forgetting factor (default)
PDAF            1: adaptive forgetting factor (experimental)
PDAF       param_int(6) type_trans
PDAF           Type of ensemble transformation matrix; optional
PDAF            0: deterministic transformation (default)
PDAF            2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
PDAF       param_int(7): not used
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF           0: Initialize observations before call to prepoststep_pdaf
PDAF           1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1 for subtypes 0 and 1; not larger than total number of processors
PDAF           =1 required for subtypes 10 and 11
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the ETKF ++++++++++

EnKF (filtertype=PDAF_DA_ENKF=2)

PDAF     Available options for EnKF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: Full ensemble integration; analysis for 2*dim_obs>dim_ens
PDAF       1: Full ensemble integration; analysis for 2*dim_obs<=dim_ens
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): dim_lag
PDAF           Size of smoothing lag (>=0), optional
PDAF           0: no smoothing (default)
PDAF           >0: apply smoother up to specified lag
PDAF       param_int(4): rank_ana_enkf
PDAF           maximum rank for inversion of HPH^T, optional, default=0
PDAF            for =0, HPH is inverted by solving the representer equation
PDAF            allowed range is 0 to ensemble size - 1
PDAF       param_int(5): not used
PDAF       param_int(6): not used
PDAF       param_int(7): not used
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF            0: Initialize observations before call to prepoststep_pdaf
PDAF            1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           (>=1; not larger than total number of processors)
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the EnKF ++++++++++

SEIK (filtertype=PDAF_DA_SEIK=1)

PDAF     Available options for SEIK:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: full ensemble integration; left-sided application of T
PDAF       1: full ensemble integration; right-sided application of T
PDAF       2: full ensemble integration; explicit ensemble transformation
PDAF       10: Fixed error space basis
PDAF       11: Fixed state covariance matrix
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): not used
PDAF       param_int(4): not used
PDAF       param_int(5) type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: fixed forgetting factor (default)
PDAF            1: adaptive forgetting factor (experimental)
PDAF       param_int(6) type_trans
PDAF           Type of ensemble transformation matrix; optional
PDAF            0: deterministic Omega (default)
PDAF            1: random orthonormal Omega orthogonal to (1,...,1)^T
PDAF            2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
PDAF              (experimental; for random transformations, 1 is recommended)
PDAF       param_int(7) type_sqrt
PDAF           Type of transformation matrix square root; optional
PDAF            (Only relevant for subtype/=11)
PDAF            0: symmetric square root (default)
PDAF            1: Cholesky decomposition
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF            0: Initialize observations before call to prepoststep_pdaf
PDAF            1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1 for subtypes 0, 1 and 2; not larger than total number of processors
PDAF           =1 required for subtypes 10 and 11
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     --- Internal parameter (defined inside PDAF) ---
PDAF       Nm1vsN: Normalization of covariance matrix; default: 1
PDAF           0: normalization with 1/(Ensemble size)
PDAF              (original SEIK, mainly for compatibility with older studies)
PDAF           1: normalization with 1/(Ensemble size - 1)
PDAF           (sample covariance matrix consistent with other EnKFs)
PDAF     +++++++++ End of option overview for the SEIK filter ++++++++++

Option outputs using subtype=-1 - Nonlinear DA Methods

NETF (filtertype=PDAF_DA_NETF=9)

PDAF     Available options for NETF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: Standard implementation with ensemble integration
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): dim_lag
PDAF           Size of smoothing lag (>=0), optional
PDAF            0: no smoothing (default)
PDAF            >0: apply smoother up to specified lag
PDAF       param_int(4): type_noise
PDAF           Type of ensemble perturbations, optional
PDAF            0: no perturbations (default)
PDAF            1: constant standard deviation
PDAF            2: relative to ensemble standard deviation
PDAF       param_int(5) type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: forgetting factor on forecast ensemble (default)
PDAF            2: forgetting factor on analysis ensemble
PDAF       param_int(6) type_trans
PDAF           Type of ensemble transformation matrix; optional
PDAF            0: random orthonormal matrix orthogonal to (1,...,1)^T (default)
PDAF            1: deterministic transformation
PDAF       param_int(7): type_winf
PDAF           Type of weights inflation; optional
PDAF            0: no weights inflation (default)
PDAF            1: inflate so that N_eff/N > param_real(2)
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF           Note: This parameter has no influence on the NETF assimilation result
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF           0: Initialize observations before call to prepoststep_pdaf
PDAF           1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF       param_real(2): limit_winf
PDAF           Limit for weigts inflation N_eff/N > param_real(2), optional, default=0.0
PDAF       param_real(3): noise_amp
PDAF           Ensemble perturbation level (>0), required, only used if param_int(4)>0
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1; not larger than total number of processors
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the NETF  ++++++++++

LNETF (filtertype=PDAF_DA_LNETF=10)

PDAF     Available options for LNETF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: Standard implementation with ensemble integration
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): dim_lag
PDAF           Size of smoothing lag (>=0), optional
PDAF            0: no smoothing (default)
PDAF            >0: apply smoother up to specified lag
PDAF       param_int(4): type_noise
PDAF           Type of ensemble perturbations, optional
PDAF            0: no perturbations (default)
PDAF            1: constant standard deviation
PDAF            2: relative to ensemble standard deviation
PDAF       param_int(5) type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: forgetting factor on forecast ensemble (default)
PDAF            1: forgetting factor on forecast ensemble only observed domains
PDAF            2: forgetting factor on analysis ensemble
PDAF            3: forgetting factor on analysis ensemble only observed domains
PDAF       param_int(6) type_trans
PDAF           Type of ensemble transformation matrix; optional
PDAF            0: random orthonormal matrix orthogonal to (1,...,1)^T (default)
PDAF            1: deterministic transformation
PDAF       param_int(7): type_winf
PDAF           Type of weights inflation; optional
PDAF            0: no weights inflation (default)
PDAF            1: inflate so that N_eff/N > param_real(2)
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF           Note: This parameter has no influence on the LNETF assimilation result
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF           0: Initialize observations before call to prepoststep_pdaf
PDAF           1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF       param_real(2): limit_winf
PDAF           Limit for weigts inflation N_eff/N > param_real(2), optional, default=0.0
PDAF       param_real(3): noise_amp
PDAF           Ensemble perturbation level (>0), required, only used if param_int(4)>0
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1; not larger than total number of processors
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the LNETF  ++++++++++

LKNETF (filtertype=PDAF_DA_LKNETF=11)

PDAF     Available options for LKNETF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: HNK: 2-step LKNETF with NETF before LETKF
PDAF       1: HKN: 2-step LKNETF with LETKF before NETF
PDAF       2: HSync: LKNETF synchronous
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): not used
PDAF       param_int(4): type_hyb
PDAF           Type of hybrid weight; optional
PDAF            0: fixed value
PDAF            1: gamma_lin: (1 - N_eff/N_e)*param_real(2) (default)
PDAF            2: gamma_alpha: hybrid weight from N_eff/N>=param_real(2)
PDAF            3: gamma_ska: 1 - min(s,k)/sqrt(param_real(3)) with N_eff/N>=param_real(2)
PDAF            4: gamma_sklin: 1 - min(s,k)/sqrt(param_real(3)) >= 1-N_eff/N>=param_real(2)
PDAF       param_int(5): type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: inflate forecast ensemble by 1/forget (default)
PDAF            1: inflate forecast ensemble by 1/forget only observed domains
PDAF            2: inflate analysis ensemble by 1/forget
PDAF            3: inflate analysis ensemble by 1/forget only observed domains
PDAF            5: adaptive forgetting factor for full domain in LETKF part
PDAF            6: locally adaptive forgetting factor in LETKF part
PDAF       param_int(6): type_trans
PDAF           Type of ensemble transformation matrix; optional
PDAF            0: random orthonormal matrix orthogonal to (1,...,1)^T (default)
PDAF            1: deterministic transformation
PDAF       param_int(7): not used
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF       param_real(2): hyb_g
PDAF           prescribed hybrid weight gamma (usually >0 and <=1), optional, default=0.95
PDAF       param_real(3): hyb_k
PDAF           hybrid norm kappa (>0), optional, default=dim_ens
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1; not larger than total number of processors
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the LKNETF  ++++++++++

PF (filtertype=PDAF_DA_PF=12)

PDAF     Available options for PF:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: Standard implementation with ensemble integration
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): type_resample
PDAF           Resampling type, optional
PDAF            1: probabilistic resamping (default)
PDAF            2: stochastic universal resampling
PDAF            3: residual resampling
PDAF       param_int(4): type_noise
PDAF           Type of ensemble perturbations, optional
PDAF            0: no perturbations (default)
PDAF            1: constant standard deviation
PDAF            2: relative to ensemble standard deviation
PDAF       param_int(5) type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: forgetting factor on forecast ensemble (default)
PDAF            2: forgetting factor on analysis ensemble
PDAF       param_int(6): not used
PDAF       param_int(7): type_winf
PDAF           Type of weights inflation; optional
PDAF            0: no weights inflation (default)
PDAF            1: inflate so that N_eff/N > param_real(2)
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF           Note: This parameter has no influence on the PF assimilation result
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF           0: Initialize observations before call to prepoststep_pdaf
PDAF           1: Initialize observations after call to prepoststep_pdaf (default)
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): forget
PDAF           Forgetting factor (usually >0 and <=1), required
PDAF       param_real(2): limit_winf
PDAF           Limit for weigts inflation N_eff/N > param_real(2), optional, default=0.0
PDAF       param_real(3): noise_amp
PDAF           Ensemble perturbation level (>0), required, only used if param_int(4)>0
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1; not larger than total number of processors
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for the PF  ++++++++++

Option outputs using subtype=-1 - Observation Geneeration

GENOBS (filtertype=PDAF_DA_GENOBS=100)

PDAF     Available options for GENOBS:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: Standard implementation with ensemble integration
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): seedset
PDAF           seed set index for random number generator, optional
PDAF           valid are values between 1 and 20; default=1
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): Forgetting factor (usually >0 and <=1), required, but not used
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           =1 for GENOBS; not larger than total number of processors
PDAF           =1 required for subtypes 10 and 11
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for GENOBS  ++++++++++

Option outputs using subtype=-1 - 3D-Var Methods

3D-Var (filtertype=PDAF_DA_3DVAR=200)

PDAF     Available options for 3D-Var:
PDAF     --- Sub-types (Parameter subtype) ---
PDAF       0: incremental 3D-Var with parameterized covariance matrix
PDAF       1: 3D ensemble Var using LESTKF for ensemble transformation
PDAF       2: 3D ensemble Var using ESTKF for ensemble transformation
PDAF       3: hybrid 3D-Var using LESTKF for ensemble transformation
PDAF       4: hybrid 3D-Var using ESTKF for ensemble transformation
PDAF     --- Integer parameters (Array param_int) ---
PDAF       param_int(1): Dimension of state vector (>0), required
PDAF       param_int(2): Ensemble size (>0), required
PDAF       param_int(3): type_opt
PDAF           Select optimization method (solver), required
PDAF            1: LBFGS (default)
PDAF            2: CG+
PDAF            3: direct implementation of CG
PDAF            12: CG+ with decomposed control vector
PDAF            13: direct implementation of CG with decomposed control vector
PDAF       param_int(4): size of parameterized control vector (for 3D-Var and hybrid 3D-Var), required
PDAF       param_int(5): size of ensemble control vector (required for ensemble and hybrid 3D-Var), 
PDAF       param_int(6): Solver-specific parameter, optional
PDAF           LBFGS: parameter m (default=5)
PDAF                Number of corrections used in limited memory matrix; 3<=m<=20
PDAF           CG+: parameter method (default=2)
PDAF                (1) Fletcher-Reeves, (2) Polak-Ribiere, (3) positive Polak-Ribiere
PDAF           CG: maximum number of iterations (default=200)
PDAF       param_int(7): Solver-specific parameter, optional
PDAF           CG+: parameter irest (default=1)
PDAF                (0) no restarts; (n>0) restart every n steps
PDAF       param_int(8): observe_ens
PDAF           Application of observation operator H, optional
PDAF            0: Apply H to ensemble mean to compute innovation
PDAF            1: Apply H to ensemble states; then compute innovation from their mean (default)
PDAF               param_int(8)=1 is the recomended choice for nonlinear H
PDAF       param_int(9): type_obs_init
PDAF           Initialize observations before or after call to prepoststep_pdaf
PDAF           0: Initialize observations before call to prepoststep_pdaf
PDAF           1: Initialize observations after call to prepoststep_pdaf (default)
PDAF       param_int(10): not used
PDAF       ___Options for ESTKF/LESTKF for En3DVar/hyb3DVar___
PDAF       param_int(11) type_forget
PDAF           Type of forgetting factor; optional
PDAF            0: fixed forgetting factor (default)
PDAF            1: adaptive forgetting factor (experimental)
PDAF            2: locally adaptive forgetting factor (experimental)
PDAF       param_int(12) type_trans
PDAF           Type of ensemble transformation matrix; optional
PDAF            0: deterministic Omega (default)
PDAF            1: random orthonormal Omega orthogonal to (1,...,1)^T
PDAF            2: use product of 0 with random orthonomal matrix with eigenvector (1,...,1)^T
PDAF              (experimental; for random transformations, 0 or 1 are recommended)
PDAF       param_int(13) type_sqrt
PDAF           Type of transformation matrix square root; optional
PDAF            0: symmetric square root (default)
PDAF            1: Cholesky decomposition
PDAF     --- Floating point parameters (Array param_real) ---
PDAF       param_real(1): Forgetting factor (usually >0 and <=1), required;
PDAF           (only used for ensemble and hybrid 3D-Var)
PDAF       param_real(2): hybrid weight beta, optional (only for hybrid 3D-Var)
PDAF           range >=0.0 and <=1.0, =1.0 for pure ensemble 3D-var  (default=0.5)
PDAF       param_real(3): Solver-specific parameter, optional
PDAF           LBFGS: Limit for stopping iterations (pgtol, default=1.0e-5)
PDAF           CG+: convergence parameter eps (default=1.0e-5)
PDAF           CG: convergence parameter eps (default=1.0e-6)
PDAF       param_real(4): Solver-specific parameter, optional
PDAF           LBFGS: Tolerance in termination test (factr, default=1.0e+7)
PDAF     --- Further parameters ---
PDAF       n_modeltasks: Number of parallel model integration tasks
PDAF           >=1 for subtypes >0; not larger than total number of processors
PDAF           =1 required for subtype 0
PDAF       screen: Control verbosity of PDAF
PDAF           0: no outputs
PDAF           1: basic output (default)
PDAF           2: 1 plus timing output
PDAF           3: 2 plus debug output
PDAF     +++++++++ End of option overview for 3DVAR ++++++++++
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