PDAF - the Parallel Data Assimilation Framework
Advanced data assimilation algorithms for filtering and smoothing applications with state-of-the-art large-scale geophysical models are of increasing interest. The applied algorithms are typically based on the Kalman filter. Often ensemble-based Kalman filters are used. Their aim is to estimate the state of a geophysical system (atmosphere, ocean, ...) on the basis of a numerical model and measurements by combining both sources of information. In addition, the algorithms provide an estimate of the error in the computed state estimate.
Efficient ensemble-based data assimilation
Data assimilation with these advanced algorithms and large-scale models is computationally extremely demanding. This motivates the parallelization of the assimilation problem and the use of high-performance computers. The implementation of a data assimilation system on the basis of existing numerical models is complicated by the fact that these models are typically not prepared to be used with data assimilation algorithms. The Parallel Data Assimilation Framework - PDAF - has been developed to facilitate the implementation of parallel data assimilation systems. For this task, the model is typically extended by subroutine calls to PDAF such that a single data assimilation program results.
PDAF allows to combine an existing numerical model with data assimilation algorithms, like ensemble-based filters, with minimal changes to the model code. Furthermore, PDAF supports the efficient use of parallel computers by creating a parallel data assimilation system. The most costly part of ensemble-based Kalman filters is the integration of an ensemble of model states. To utilize the fact that each ensemble member can be integrated independently of the others, PDAF supports to extend a model code such that it allows the program to compute multiple concurrent model tasks. Since the model integrations are typically the most time consuming part of the data assimilation problem, their parallelization renders ensemble-based Kalman filters to be highly scalable (by now, PDAF was used with up to 16800 processor cores). For the assimilation step, which combines the observations and the model state estimate, PDAF includes a several filter algorithms. All filters are fully implemented, optimized, and parallelized.
Logical separation of a data assimilation system
PDAF bases on a logical separation of the assimilation system into three components (see figure above):
- On one side, the model provides the initialization and integration of all fields considered in the model.
- On the other side, the measurements provide the observational information. It consists of the information on the variables that are observed as well as the values of the observations and error estimates of them.
- In between the model and observations, the filter algorithm combines the model and observational information. The filter is located in the core of PDAF.
Well defined interfaces serve for the information exchange between the three components. To implement a data assimilation system with PDAF, filter algorithms are attached to the model with minimal changes to the model source code itself. The parts of the filter problem that are model-dependent or refer to the measurements are organized as separate call-back sub-routines. These routines need to be implemented by the user of the framework like routines of the model, while the core routines of PDAF remain unchanged.
The data assimilation system is controlled by the user-supplied routines. This approach leaves the driver functionality remains in the model part of the program. In addition, the user-supplied routines can be implemented in the context of the model code. That is, if the model uses Fortran common blocks or modules they can be also used in the user-supplied routines. These possibilities simplify the implementation of the user-supplied routines as the users typically know about the particularities of their model.
PDAF is implemented in Fortran 90 and parallelized using the MPI standard. For efficiency, BLAS and LAPACK libraries are used. PDAF has been tested on different platforms with various compilers.
Optimized and parallelized filter and smoother algorithms
PDAF includes a selection of commonly used filter algorithms. All filters are optimized and parallelized. The filter algorithms, which are currently included in PDAF are:
- EnKF (Ensemble Kalman Filter)
- SEEK (Singular "Evolutive" Extended Kalman) filter
- SEIK (Singular "Evolutive" Interpolated Kalman) filter
- LSEIK (local SEIK filter)
- ETKF (Ensemble Transform Kalman filter)
- LETKF (Local Ensemble Transform Kalman filter)
- ESTKF (Error Subspace Transform Kalman filter)
- LESTKF (Local Error Subspace Transform Kalman filter)
The first three filters (EnKF, SEEK, SEIK) are described and compared in Nerger et al. (2005a), while the local SEIK filter is described in Nerger et al. (2006). The ETKF and SEIK filters have been examined in Nerger et al. (2012b), where also the new ESTKF was introduced.
Next to the filter algorithms, the following smoothers are available:
- EnKS (Ensemble Kalman Smoother)
- ETKS (Ensemble Transform Kalman Smoother)
- LETKS (Local Ensemble Transform Kalman Smoother)
- ESTKS (Error Subspace Transform Kalman Smoother)
- LESTKS (Local Error Subspace Transform Kalman Smoother)
The smoother extension was described on Nerger et al. (2014) where also the influence of nonlinearity on the smoothing was studied.
PDAF is currently used in several projects inside and outside of AWI. The framework is available as free open-source software. Further information about PDAF as well a possibility to download the source code is available on the project pages of PDAF.