Features and Requirements

• PDAF is implemented in Fortran90 with some features from Fortran 2003. The standard interface also supports models that are written in other languages like C or C++. Also the combination is Python is possible.
• The parallelization uses the MPI (Message Passing Interface) standard. The localized filters use, in addition, OpenMP-parallelization with features of OpenMP-4.
• The core routines are fully independent of the model code. They can be compiled separately and can be used as a library.

Simplifying the implementation

PDAF simplifies the implementation of data assimilation systems using existing model code by the following:

1. PDAF provides fully implemented, parallelized, and optimized ensemble-based algorithms for data assimilation. Currently, these are ensemble-based Kalman filters like the LETKF, LESTKF, and EnKF methods and nonlinear filters are provided. Starting from PDAF V2.0 also 3D-variational methods are provided.
2. PDAF is attached to the model source code by minimal changes to the code, which we call 'online mode'. These changes only concern the general part of the code, but not the numerics of the model. In addition, a small set of routines is required that are specific to the model or the observations to be assimilated. These routines can be implemented like routines of the model.
3. PDAF is called through a well-defined standard interface. This allows, for example, to switch between the LETKF, LESTKF, and LSEIK methods without additional coding.
4. PDAF provides parallelization support for the data assimilation system. If your numerical model is already parallelized, PDAF enables the data assimilation system to run several model tasks in parallel within a single executable. However, PDAF can also be used without parallelization, for example to test small systems.
5. PDAF does not require that your model can be called as a subroutine. Rather PDAF is added to the model and the formed data assimilation system can be executed pretty much like the model-program would without data assimilation.
6. PDAF also offers an offline mode. This is for the case that you don't want to (or even cannot) modify your model source code at all. In the offline mode, PDAF is compiled separately from the model together with the supporting routines to handle the observations. Then the model and the assimilation step are executed separately. While this strategy is possible, we don't recommend it, because it's computationally less efficient.
7. Starting with PDAF 1.13, the PDAF release also provides bindings to couple PDAF with selected real models. As of PDAF 1.15, modelbindings for the MITgcm ocean circulation model and for the AWI Climate Model (AWI-CM, a coupled model consisting of ECHAM (atmophsere) and FESOM (ocean)) are provided.

Filter algorithms

PDAF provides the following algorithms for data assimilation. All filters are fully implemented, optimized and parallelized. In addition, all filters offer an Ensemble-OI mode in which only a single emseble state needs to be integrated

Local filters:

• LETKF (Hunt et al., 2007)
• LESTKF (Local Error Subspace Transform Kalman Filter, Nerger et al., 2012, see publications)
• LEnKF (classical EnKF with covariance localization)
• LNETF (localized Nonlinear Ensemble Transform Filter by Toedter and Ahrens (2015))
• LSEIK (Nerger et al., 2006)
• LKNETF (Local Kalman-nonlinear Ensemble Transform Filter, Nerger, 2022, see publications, added in PDAF V2.1)

Global filters:

• ESTKF (Error Subspace Transform Kalman Filter, Nerger et al., 2012, see publications)
• ETKF (The implementation follows Hunt et al. (2007) but without localization, which is available in the LETKF implementation)
• EnKF (The classical formulation with perturbed observations by Evensen (1994), Burgers et al. (1998))
• SEEK (The original formulation by Pham et al. (1998))
• SEIK (Pham et al. (1998a, 2001), the implemented variant is described in more detail by Nerger et al. (2005))
• NETF (Nonlinear Ensemble Transform Filter by Toedter and Ahrens (2015))
• PF (Particle filter with resampling)

Smoother algorithms are provided for the following algorithms

• ESTKF & LESTKF
• ETKF & LETKF
• EnKF
• NETF & LNETF

Starting from Version 2.0 of PDAF, 3D variational methods are also provided. The 3D-Var methods are implemented in incremental form using a control vector transformation (following the review by R. Bannister, Q. J. Roy. Meteorol. Soc., 2017) in three different variants:

• 3D-Var - 3D-Var with parameterized covariance matrix
• 3DEnVar - 3D-Var using ensemble covariance matrix. The ensemble perturbations are updated with either the LESTKF and ESTKF filters
• Hyb3DVar - Hybrid 3D-Var using a combination of parameterized and ensemble covariance matrix. The ensemble perturbations are updated with either the LESTKF and ESTKF filters

Requirements

• Compiler
  To compile PDAF a Fortran compiler is required which supports Fortran 2003. PDAF has been tested with a variety of compilers like gfortran, ifort, xlf, pgf90, cce.
• BLAS and LAPACK
  The BLAS and LAPACK libraries are used by PDAF. For Linux there are usually packages with these libraries. With commercial compilers the functions are usually provided by optimized libraries (like MKL, ESSL).
• MPI
  An MPI library is required (e.g. OpenMPI). [For the PDAF versions before V2.0, the assimilation program can also be compiled and run without parallelization. For this, PDAF <2.0 provides functions that mimic MPI operations for a single process.]
• make
  PDAF provides Makefile definitions for different compilers and operating systems.

Test machines

PDAF has been tested on various machines with different compilers and MPI libraries. Current test machines include:

• Linux Desktop machine, Ubuntu, ifort compiler
• Linux Desktop machine, Ubuntu, gfortran, OpenMPI
• Notebook Apple MacBook, Mac OS X, gfortran, OpenMPI
• Atos cluster 'Lise' at HLRN (Intel Cascade Lake processors), ifort, IMPI
• Windows 10 with Cygwin, gfortran, OpenMPI

Past test machines also included

• NEC SX-ACE, sxf90 compiler (rev 530), sxmpi
• Cray CS400, Cray compiler, IMPI
• Cray CS400, ifort, IMPI
• Cray XC30 and XC40, Cray compiler CCE, MPICH
• SGI Altix UltraViolet, SLES 11 operating system, ifort compiler, SGI MPT
• IBM p575 with Power6 processors, AIX6.1, XLF compiler 12.1, ESSL library, POE parallel environment
• IBM BladeCenter with Power6 processors, AIX5.3, XLF compilers 10.1 to 13.1, ESSL library, POE parallel environment

Test cases

The regular tests use a rather small configuration with a simulated model. This model is also included in the test suite of the downloadable PDAF package. In addition, the scalability of PDAF was examined with a real implementation with the finite element ocean model (FEOM, Danilov et al., A finite-element ocean model: Principles and evaluation. Ocean Modeling 6 (2004) 125-150). In these tests up to 4800 processor cores of a supercomputer have been used (see Nerger and Hiller (2013)). In Nerger et al., GMD (2020), the scalability was assessed up to 12144 processor cores for the coupled atmosphere-ocean model AWI-CM (Sidorenko et al., 2015).

To examine PDAF's behavior with large-scale cases, experiments with the simulated model have been performed. By now the biggest case had a state dimension of 8.64^.10¹¹. An observation vector of size 1.73^.10¹⁰ was assimilated. For these experiments, the computations used 57600 processor cores. In this case, the dimensions were limited by the available memory of the compute nodes. Using an ensemble of 25 states, the distributed ensemble array occupied about 2.9 GBytes of memory for each core (about 165 TBytes in total).