PDAF-OMI Observation Modules

Overview

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 (where 'TYPE' will be replaced by the name of the observation):

• init_dim_obs_OBSTYPE 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_OBSTYPE 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_OBSTYPE 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_OBSTYPE 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_OBSTYPE_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_OBSTYPE as a flag to control whether the observation type should be assimilated.

Note: In contrast to the 'classical' implementation of observation routines for PDAF, the global and local filters use the same routines init_dim_obs and obs_op. PDAF-OMI recognizes whether a global or local filter is used and does the necessary operations by itself.

Data type obs_f

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_OBSTYPE_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 the routine init_dim_obs_l when calling PDAFomi_init_dim_obs_l.

init_dim_obs_OBSTYPE

This is the main routine to initialize observation information.

Please see the template file templates/omi/obs_OBSTYPE_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 variables that the filled in this routine are

1. thisobs%doassim: Specify whether this observation type is assimilated
2. thisobs%disttype: Specify the type of distance computation
3. thisobs%ncoord: Specify the number of dimensions used to compute distances
4. dim_obs_p: Count the number of available observations
5. obs_p: Fill the vector of observations
6. ocoord_p: store the coordinates of the observations
7. ivar_obs_p: store the inverse error variance of each observation
8. 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). For Cartesian distance computation with periodicity one also needs to set thisobs%domainsize.

When parallel model with domain decomposition is used, the variables with suffix _p need to describe the observation information for a particular process domain. The following routine will perform the necessary operations to ensure that the parallelization is taken into account by PDAF.

After these variables are filled, one calls

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

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

The routine PDAFomi_gather_obs returns the number of observations dim_obs which is the return variable for PDAF.

Note: The value is cradius is only used if thisobs%use_global_obs=0.

obs_op_OBSTYPE

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 operators and on how to implement your own observation operator see the documentation of observation operators for OMI.

init_dim_obs_l_OBSTYPE

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, cradius, sradius, 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 and that the unit of coords_l is the same as that used fo rthe observation coordinates.
• Specify the localization variables (These variables are usually set in init_pdaf and included with use mod_assimilation)
  • locweight: Type of localization (see table below)
  • cradius: The localization radius or directional radii (cut-off radius for the observations, weight is always =0 for distances > cradius)
  • sradius: The support radius (or directional redii) of the localization weight function

The setting of locweight influences the weight function for the localization. The choices are standardized as follows

locweight	0	1	2	3	4
function	unit weight	exponential	5-th order polynomial	5-th order polynomial	5-th order polynomial
regulation	-	-	-	regulation using mean variance	regulation using variance of single observation point
cradius	weight=0 if distance > cradius
sradius	no impact	weight = exp(-d / sradius)	weight = 0 if d >= sradius else weight = f(sradius, distance)

Here, 'regulation' refers to the regulated localization introduced in Nerger, L., Janjić, T., Schröter, J., Hiller, W. (2012). A regulated localization scheme for ensemble-based Kalman filters. Quarterly Journal of the Royal Meteorological Society, 138, 802-812. ​​doi:10.1002/qj.945.

Notes:

• isotropic localization: If cradius and sradius are scalar values, the localization is isotropic. Thus, it uses the same cradius in all directions. If different localization scales should be applied e.g. in the vertical compared to the horizonal one needs to scale the vertical coordinates.
• non-isotropic localization: Nonisotropic localization was introduced with PDAF V2.2: cradius and sradius can declared as vectors of length thisobs%ncoords and each element can get a different value. In this case, the values defined a non-isotropic localization according to the values specified in cradius and sradius.

localize_covar_OBSTYPE

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, cradius, sradius, &
         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 table above)
  • cradius: The localization radius (cut-off radius for the observations, weight is always =0 for distances > cradius)
  • sradius: The support radius of the localization weight function

Notes:

• isotropic localization: If cradius and sradius are scalar values, the localization is isotropic. Thus, it uses the same cradius in all directions. If different localization scales should be applied e.g. in the vertical compared to the horizonal one needs to scale the vertical coordinates.
• non-isotropic localization: Nonisotropic localization was introduced with PDAF V2.2: cradius and sradius can declared as vectors of length thisobs%ncoords and each element can get a different value. In this case, the values defined a non-isotropic localization according to the values specified in cradius and sradius.

Additional routines for 3D-Var

For the 3D-Var methods added with PDAF V2.0 two more routines are required in the observation module.

obs_op_lin_OBSTYPE

This routine applies the linearized observation operator to a state vector. It returns the observed state vector to PDAF. The routine is used only by the 3D-Var methods.

Note: A separate routine for obs_op_lin_OBSTYPE is only required if the full observation operator in obs_op_OBSTYPE is nonlinear. If obs_op_OBSTYPE is linear, one can just insert calls to this operator in the routine obs_op_lin_pdafomi in callback_obs_pdafomi.F90.

PDAF-OMI provides several linear 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 operators and on how to implement your own observation operator see the documentation of observation operators for OMI.

obs_op_adj_OBSTYPE

This routine applies the adjoint observation operator to an observation vector. It returns the state vector to PDAF. The routine is used only by the 3D-Var methods.

PDAF-OMI provides consistent pairs of linear observation operators. For example the adjoint observation operator for observations that are grid point values is called as:

    CALL PDAFomi_obs_op_adj_gridpoint(thisobs, ostate, state_p)

Here, ostate is the observation vector and state_p is the state vector.

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

Implementing a new observation type

To implement a new observation type, the approach is generally as follows:

1. Create a copy of obs_OBSTYPE_pdafomi_TEMPLATE.F90
2. Rename the module and its subroutines according to the observation (replacing ‘OBSTYPE’ by name of observation).
3. Implement init_dim_obs for the observation type following the instructions in the template
4. Adapt obs_op for the observation type
5. Adapt init_dim_obs_l for the observation type (if using a domain_localized filter)
6. Adapt localize_covar for the observation type (if using a the local EnKF)
7. Add subroutine calls for the new observation type into the routines in callback_obs_pdafomi.F90

Implementation hints for init_dim_obs

thisobs%doassim

Set this variable to 1 to let the filter assimilate this observation. The setting is usually conditional on the value of assim_OBSTYPE which is set in init_pdaf:

   IF (assim_OBSTYPE) thisobs%doassim = 1

thisobs%ncoord

This variable specifies the dimension of the distance computations. Thus thisobs%ncoord=2 will lead to distance computations in 2 dimensions.

thisobs%disttype

This variable specifies the type of distance computation. Possible choices are

• 0: Cartesian distance in ncoord dimension
• 1: Cartesian distance in ncoord dimensions with periodicity (Needs specification of thisobs%domainsize(ncoord))
• 2: Approximate geographic distance in meters with horizontal coordinates in radians (latitude: -pi/2 to +pi/2; longitude -pi/+pi or 0 to 2pi)
• 3: Geographic distance computation in meters using haversine formula with horizontal coordinates in radians (latitude: -pi/2 to +pi/2; longitude -pi/+pi or 0 to 2pi)

For 0 and 1 any distance unit can be used. The computed distance will be in the same unit. For 2 and 3 the input coordinates are in radians and the distance is computed in meters. Essential is that the grid point coordinates and observation coordinates use the same unit.

See /models/lorenz96_omi/ for an example using case 1 with periodicity in one dimension.

dim_obs_p

This is a single integer value giving the number of observations. With a parallel model using domain-decomposition this will be the number of observations for the process sub-domain. For observation files holding all observations one can read these and then check which observation redice within the process sub-domain. dim_obs_p will be used to allocate further arrays and as input argument to PDAFomi_gather_obs.

obs_p

This should be a vector of real values. It will be used as an argument to PDAFomi_gather_obs. The order of the entries has to be consistent in the arrays thisobs%id_obs_p, obs_p, ivar_obs_p, and ocoord_p.

ocoord_p

This should be a rank-2 array of real values with size (thisobs%ncoord, dim_obs_p). It will be used as an argument to PDAFomi_gather_obs. The order of the entries has to be consistent in the arrays thisobs%id_obs_p, obs_p, ivar_obs_p, and ocoord_p.

The coordinates of the observation with index k are given by ocoord_p(:,k).

Note: The observation coordinate values will only be used in case of the local filters or for computing interpolation coefficients. The array has always to be allocated because it is used in the call to PDAFomi_gather_obs.

Note: The unit of ocoord_p and coords_l (in init_dim_obs_l) has to be the same. For geographic coordinate computations (thisobs%disttype=2 or =3) the unit used by PDAF-OMI is radian.

ivar_obs_p

This should be a vector of real values. It will be used as an argument to PDAFomi_gather_obs. The order of the entries has to be consistent in the arrays thisobs%id_obs_p, obs_p, ivar_obs_p, and ocoord_p.

thisobs%id_obs_p

This array is allocated as

   ALLOCATE(thisobs%id_obs_p(NROWS, dim_obs_p))

For a fixed value of the second index the NROWS are the indices of the elements of the state vector that are treated in the observation operator. The value of NROWS depends on the observation operator used for an observation. Examples:

• Using observations that are grid points values:
  • NROWS=1
  • The entry is the index of a single element of the state vector
• Using observations that are determined by bi-linear interpolation of 4 grid points:
  • NROWS=4
  • The entries are the indices of four elements of the state vector

Note: This array is only used in the observation operators provided by PDAF-OMI. If you don't use these observation operators, you might not need this array.

thisobs%domainsize

This array has to be allocated as

   ALLOCATE(thisobs%domainsize(thisobs%ncoord))

Here one has to specify the size of the domain in each of its thisobs%ncoord dimensions. The information is used to compute the Cartesian distance with periodicity.

Setting one dimension to 0 or a negative value indicates that there is no periodicity in this direction.

thisobs%icoeff_p

This array is allocate the in same way as thisobs%id_obs_p:

   ALLOCATE(thisobs%icoeff_p(NROWS, dim_obs_p))

The value of NROWS has to be the same as for thisobs%id_obs_p. For a fixed value of the second index the NROWS of the array hold the interpolation coefficients corresponding to the indices specified in thisobs%id_obs_p.

Please see the documentation of OMI observation operators for information on how to initialize the array thisobs%icoeff_p using functions provided by PDAF-OMI.

thisobs%obs_err_type

The particle filter methods NETF, LNETF and PF can handle observations with non-Gaussian errors. PDAF-OMI supports the following two choices:

• 0: Gaussian errors (default value)
• 1: double-exponential (Laplace) errors

thisobs%use_global_obs

In the domain-localized filters (LESTK, LETKF, LSEIK, LNETF) observations are assimilated that are located within the localization around some grid point. When a model uses parallelization with domain-decomposition some of these observations might belong to a different process-domain. In the default mode (thisobs%use_global_obs=1) PDAF-OMI gathers all globally available observations so that each process has access to all observations. It can be more efficient to limit the observations on a process-domain to those observations that are located inside the domain or within the localization radius around it. Then, in the local analyses less observations have to be checked for their distance. Setting thisobs%use_global_obs=0 activates this feature. However, it needs additional preparations to make PDAF-OMI aware of the limiting coordinates of a process sub-domain.

The use of this feature is described in the documentation on using domain-limited observations.