Implementation of Observation Generation with PDAF

Overview

Twin data assimilation experiments are a common approach to assess data assimilation methods. In twin experiments one uses the model to generate a true model state. Further one generates synthetic observations by adding random perturbations to the true state. The, in the actual twin experiment one starts the data assimilation with a state estimate that is different from the true state and assimilates the synthetic observations. One can analyze the assimilation result by comparing the state estimate from the twin experiment with the previously generated true state.

Starting with version 1.14, PDAF provides functionality to generate synthetic observations. The functionality bases on the normal implementation of the assimilation used with PDAF. However, one can run the observation generation with an ensemble of just one member, which should be initialized with the initial true state. PDAF provides the routines PDAF_generate_obs and PDAF_put_state_generate_obs to perform the observation generation. These routines use the observation operator routines which the user implements e.g. for assimilating real observations.

Here we describes the steps need to generate synthetic obsrvations.

Initialization

The implementation of the initialization of PDAF is explained on the [wikiInitPdaf page on init_pdaf and PDAF_init].

For the observation generation one just has to set filtertype = 11.

There are no particular options for the observation generation functionality. So for filter_param_i one just has to specify the mandatory values of the state dimension and the ensemble size. For filter_param_r one has to specify the mandatory values of the forgetting factor (even though, this value is ignored for the observation generation)

Observation Generation Step

This step replaces the analysis step. However, the implementation is analogous to implementing the analysis step as described on the page on implementing the analysis step.

PDAF_generate_obs

This routine is used in the same way as the filter specific routines PDAF_assimilate_*. Thus the general aspect have been described on the page Modification of the model code for the ensemble integration and its sub-page on inserting the analysis step. The routine PDAF_generate_obs is used in the fully-parallel implementation variant of the data assimilation system. When the 'flexible' implementation variant is used, the routines PDAF_put_state_generate_obs' is used as described further below. Here, we list once more the full interface. Subsequently, the full set of user-supplied routines specified in the call to PDAF_generate_obs` is explained.

  SUBROUTINE PDAF_generate_obs(U_collect_state, U_distribute_state, &
                                  U_init_dim_obs_f, U_obs_op_f, U_get_obs_f, U_init_obserr_f, &
                                  U_prepoststep, U_next_observation, status_pdaf)

with the following arguments:

• U_collect_state: The name of the user-supplied routine that initializes a state vector from the array holding the ensemble of model states from the model fields. This is basically the inverse operation to U_distribute_state used in PDAF_get_state
• U_distribute_state: The name of a user supplied routine that initializes the model fields from the array holding the ensemble of model state vectors.
• U_init_dim_obs_f: The name of the user-supplied routine that provides the size of the full observation vector
• U_obs_op_f: The name of the user-supplied routine that acts as the full observation operator on some state vector
• U_get_obs_f: The name of the user-supplied routine that receives the full vector of generated synthetic observations from PDAF
• U_init_obserr_f: The name of the user-supplied routine that initializes the vector of observations error standard deviations for for full observation vector
• U_prepoststep: The name of the pre/poststep routine as in PDAF_get_state
• U_next_observation: The name of a user supplied routine that initializes the variables nsteps, timenow, and doexit. The same routine is also used in PDAF_get_state.
• status_pdaf: The integer status flag. It is zero, if PDAF_assimilate_lestkf is exited without errors.

PDAF_put_state_generate_obs

When the 'flexible' implementation variant is chosen for the assimilation system, the routine PDAF_put_state_generate_obs has to be used instead of PDAF_generate_obs. The general aspects of the filter specific routines PDAF_put_state_* have been described on the page Modification of the model code for the ensemble integration. The interface of the routine is identical with that of PDAF_generate_obs with the exception the specification of the user-supplied routines U_distribute_state and U_next_observation are missing.

The interface is the following:

  SUBROUTINE PDAF_put_state_generate_obs(U_collect_state, U_init_dim_obs_f, U_obs_op_f, U_get_obs_f, &
                                  U_init_obserr_f, U_prepoststep, status_pdaf)