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# PDAF-OMI Observation Modules

#### Contents of this page

The implementation of the observations with OMI is done in observation modules (obs-modules). For each observation type a separate module should be created.

Each obs-module contains four routines:

- init_dim_obs initializes all variables holding the information about one observation type. The information about the observation type is stored in a data structure (Fortran derived type).
- obs_op applies the observation operator to a state vector. One can call an observation operator routine provided by PDAF, or one can to implement a new operator.
- init_dim_obs_l calls a PDAF-OMI routine to initialize the observation information corresponding to a local analysis domain. One can set localization parameters, like the localization radius, for each observation type.
- localize_covar calls a PDAF-OMI routine to apply covariance localization. One can set localization parameters, like the localization radius, for each observation type.

The template file obs_TYPE_pdafomi_TEMPLATE.F90 shows the different steps needed when implementing these routines. The main work is to implement `init_dim_obs`

, while the other routines mainly call a subroutine provided by PDAF-OMI.

In the obs-module the subroutines are named according to the observation type. The template file uses generic names which can be replaced by the user. Having distinct names for each observation type is relevant to include the subroutine from the module in the call-back routine with ‘use’. In the header of each obs-module, the user can declare further variables, e.g. assim_TYPE as a flag to control whether the observation type should be assimilated.

## obs_f data type

To ensure the functionality within each obs-module, we rely on a derived data type called `obs_f`

that contains all information about the observation. One instance of this data type is allocated in each obs-module with the generic variable name `thisobs`

. A few of the elements of `obs_f`

are initialized by the user when the observation information is initialized on `init_dim_obs_f`

. Further variables is set in a call to the routine `PDAFomi_gather_obs`

. This information is then used by all other routines in the obs-module. The template file obs_TYPE_pdafomi_TEMPLATE.F90 shows the different steps needed to initialize thisobs.

The **mandatory variables** in `obs_f`

that need to be set by the user are:

TYPE obs_f ! ---- Mandatory variables to be set in INIT_DIM_OBS ---- INTEGER :: doassim=0 !< Whether to assimilate this observation type INTEGER :: disttype !< Type of distance computation to use for localization ! (0) Cartesian, (1) Cartesian periodic ! (2) simplified geographic, (3) geographic haversine function INTEGER :: ncoord !< Number of coordinates use for distance computation INTEGER, ALLOCATABLE :: id_obs_p(:,:) !< Indices of process-local observed field in state vector ... END TYPE obs_f

In addition there are **optional variables** that the be used:

TYPE obs_f ... ! ---- Optional variables - they can be set in INIT_DIM_OBS ---- REAL, ALLOCATABLE :: icoeff_p(:,:) !< Interpolation coefficients for obs. operator (optional) REAL, ALLOCATABLE :: domainsize(:) !< Size of domain for periodicity (<=0 for no periodicity) (optional) ! ---- Variables with predefined values - they can be changed in INIT_DIM_OBS ---- INTEGER :: obs_err_type=0 !< Type of observation error: (0) Gauss, (1) Laplace INTEGER :: use_global_obs=1 !< Whether to use (1) global full obs. !< or (0) obs. restricted to those relevant for a process domain ... END TYPE obs_f

Apart from these variables, there is a number of variables that are set internally when the routine `PDAFomi_gather_obs`

is called.

Next to the derived data type `obs_f`

, there is a derived type `obs_l`

for localization. This is only used internally. It will be filled in init_dim_obs_l when calling PDAFomi_init_dim_obs_l.

## init_dim_obs_TYPE

This is the main routine to initialize observation information.

Please see the template `templates/omi/obs_TYPE_pdafomi_TEMPLATE.F90`

for a step-by-step description of the implementation steps.

Each observation module uses the generic name **thisobs** for the variable with observation type `obs_f`

. Elements of `thisobs`

are accessed like
`thisobs%doassim`

.

The main steps performed in this routine are

`thisobs%doassim`

: Specify whether this observation type is assimilated`thisobs%disttype`

: Specify the type of distance computation`thisobs%ncoord`

: Specify the number of dimensions used to compute distances`dim_obs_p`

: Count the number of available observations`obs_p`

: Fill the vector of observations`ocoord_p`

: store the coordinates of the observations`ivar_obs_p`

: store the inverse error variance of each observation`thisobs%id_obs_p`

: store the indices of state vector elements that correspond to an observation (A single value for observation at grid points, or multiple values for derived quantities or interpolation)

When the observation operator performs interpolation, one further needs to initialize an array of interpolation coefficients (`thisobs%icoeff_p`

).

After these variables are filled, one calls

CALL PDAFomi_gather_obs(thisobs, dim_obs_p, obs_p, ivar_obs_p, ocoord_p, & thisobs%ncoord, local_range, dim_obs)

This routine will complete all required initializations for OMI. As such it is mandatory to call the routine

## obs_op_TYPE

This routine applies the observation operator to a state vector. It returns the observed state vector to PDAF. The routine is used by all filters.

PDAF-OMI provides several observation operators. For example the observation operator for observations that are grid point values is called as:

CALL PDAFomi_obs_op_gridpoint(thisobs, state_p, ostate)

Here, `state_p`

is the state vector and `ostate`

is the observed state vector.

For more information on the available observation operator and on how to implement your own observation operator see the documentation of observation operators for OMI?.

## init_dim_obs_l_TYPE

This routine initializes local observation information. The routine is only used by the domain-localized filters (LESTKF, LETKF, LSEIK, LNETF).

For the initialization the following routine is called:

CALL PDAFomi_init_dim_obs_l(thisobs_l, thisobs, coords_l, & locweight, local_range, srange, dim_obs_l)

Here, `thisobs`

and `thisobs_l`

are the data-type variables `obs_f`

and `obs_l`

. `dim_obs_l`

, the local size of the observation vector, is the direct output of the routine.

*Implementation steps:*

- Ensure that
`coords_l`

is filled in`init_dim_l_pdaf`

- Specify the localization variables (These variables are usually set in
`init_pdaf`

and included with`use mod_assimilation`

)`locweight`

: Type of localization (see init_pdaf)`local_range`

: The localization weight radius`srange`

: The support radius of the localization

## localize_covar_TYPE

This routine initializes local observation information. The routine is only used by the local EnKF (LEnKF).

For the initialization the following routine is called:

CALL PDAFomi_localize_covar(thisobs, dim_p, locweight, local_range, srange, & coords_p, HP_p, HPH)

Here, `thisobs`

is the data-type variable `obs_f`

. `HP_p`

and `HPH`

are the covariance matrices projected onto the observations. The localization will be applied to these variables.

*Implementation steps:*

- Ensure that
`coords_p`

is filled in`localize_covar_pdafomi`

- Specify the localization variables (These variables are usually set in
`init_pdaf`

and included with`use mod_assimilation`

)`locweight`

: Type of localization (see init_pdaf)`local_range`

: The localization weight radius`srange`

: The support radius of the localization