The Next-generation Ensemble Data Assimilation System (NEDAS) provides a light-weight Python solution to the ensemble data assimilation (DA) problem for geophysical models. It allows DA researchers to test and develop new DA ideas early-on in real models, before committing resources to full implementation in operational systems. NEDAS is armed with parallel computation (mpi4py) and pre-compiled numerical libraries (numpy, numba.njit) to ensure runtime efficiency. The modular design allows the user to add customized algorithmic components to enhance the DA performance. NEDAS offers a collection of state-of-the-art DA algorithms, including serial assimilation approaches (similar to DART and PSU EnKF systems), and batch assimilation approaches (similar to the LETKF in PDAF, JEDI, etc.), making it easy to benchmark new methods with the classic methods in the literature.

Table of Contents

Quick Start Guide

Code Directories and Components

The DA Problem and Basic Design

Description of Key Variables and Functions

Adding New Models and Observations

Acknowledgements

Quick Start Guide

• Create a python environment for your experiment (optional but recommended)

  Install Python then create environment named <my_python_env>

  python -m venv <my_python_env>

  Enter the environment by

  source <my_python_env>/bin/activiate

• Make a copy of the NEDAS code and place it in your <code_dir>

  cd <code_dir>

  git clone [email protected]:nansencenter/NEDAS.git

• Install the required libraries, as listed in requirements.txt

  Using a package manager such as pip, you can install them by

  pip install -r requirements.txt

• Add NEDAS directory to the Python search path

  To let Python find NEDAS modules, you can add the NEDAS directory to the search paths. In your .bashrc (or other system configuration files), add the following line and then source:

  export PYTHONPATH=$PYTHONPATH:<code_dir>/NEDAS

• Make the yaml configuration file for your experiment

  A full list of configuration variables and their default values are stored in config/default.yml. There are sample configuration files in config/samples/*, you can make a copy to <my_config_file> and make changes.

• Setup runtime environment for the host machine

  In <my_config_file>:

  set host to <my_host_machine>

  set nedas_dir to the directory where NEDAS code is placed

  set work_dir to the working directory for the experiment

  set other directories home_dir, code_dir, etc. accordingly

  In config/env/<my_host_machine>, you can create source files for running model on <my_host_machine>. For example, config/env/betzy/qg.src is sourced when running the 'qg' model on the 'betzy' machine.

• Start the experiment

  In tutorials there are some jupyter notebooks to demonstrate the DA workflow for some supported models.

  On <my_host_machine>, you can start a notebook by

  jupyter-notebook --ip=0.0.0.0 --no-browser --port=<port>

  then create another ssh connection to the machine

  ssh -L <port>:localhost:<port> <my_host_machine>

  once the connection is established, you can access the notebook from your local browser via localhost:<port>/tree?

  In jupyter notebooks you can quickly check the status of model states, observations, and diagnosing the DA performance, you can play with the DA workflow, modify it and create your own approach.

  Once you finished debugging and are happy with the new workflow, you can run the experiments without the jupyter notebooks. In scripts the run_exp.py gives an example of the top-level control workflow to perform cycling DA experiments.

  On betzy, the sbatch submit_job.sh command submits a run to the job queue, so that many experiments can be run simultaneously.

Code Directories and Components

• config/ contains a Config class to handle configuration files, and some sample yaml configuration files are provided.

• scripts/ contains top-level control scripts run_exp.py, and the two main steps ensemble_forecast.py and assimilate.py. Users can take these as an example and create their own workflow in their experiments.

• assim_tools/ contains the functions handling model state variables in state.py, functions handling observations in obs.py, core DA algorithms in analysis.py, and post-processing functions in update.py.

• grid/grid.py provides a Grid class to handle the conversion between 2D fields.

• models/ contains model modules (see details in its documentation), where users provide a set of functions read_var, z_coords etc. to interface with their forecast models.

• dataset/ contains dataset modules (see details in its documentation), where users provide functions such as read_obs to pre-process with their dataset files and form the observation sequence.

• perturb/ contains functions for generating random perturbations.

• diag/ contains functions for computing misc. diagnostics for model forecast verification and filter performance evaluation.

• utils/ contains some utility functions: fft_lib.py provides an interface to FFTW (faster implementation); netcdf_lib.py is a simple wrapper for netCDF4; parallel.py provides MPI support via mpi4py; and progress.py provides functions to show runtime progress.

• tutorials/ contains some Jupyter notebooks to illustrate how key functions work. Note that all notebooks run in single processor mode.

The DA Problem and Basic Design

DA seeks to optimally combine information from model forecasts and observations to obtain the best estimate of state/parameters of a dynamical system, which is called the analysis. The challenges in solving the analysis for modern geophysical models are: 1) the large-dimensional model state and observations, and 2) the nonlinearity in model dynamics and in state-observation relation.

To address the first challenge, we employ distributed-memory parallel computation strategy, since the entire ensemble state maybe too large to fit in the RAM of a single computer. And for the second challenge, we seek to test and compare new nonlinear DA methods (in the literature, or still in people's head) to try to tackle the problem.

A compromise is made in favor of code flexibility than its runtime efficiency. We aim for more modular design so that components in the DA algorithm can be easily changed/upgraded/compared. A pause-restart strategy is used: the model writes the state to restart files, then DA reads those files and computes the analysis and outputs to the updated files, and the model continues running. This is "offline" assimilation. In operational systems, sometimes we need "online" algorithms where everything is hold in the memory to avoid slow file I/O. NEDAS provides parallel file I/O, not suitable for time-critical applications, but efficient enough for most research and development purposes.

The first challenge on dimensionality demands a careful design of memory layout among processors. The ensemble model state has dimensions: member, variable, time, z, y, x. When preparing the state, it is easier for a processor to obtain all the state variables for one member, since they are typically stored in the same model restart file. Each processor can hold a subset of the ensemble states, this memory layout is called "state-complete". To apply the ensemble DA algorithms, we need to transpose the memory layout to "ensemble-complete", where each processor holds the entire ensemble but only for part of the state variables (Anderson & Collins 2007).

In NEDAS, for each member the model state is further divided into "fields" with dimensions (y,x) and "records" with dimensions (variable, time, z). Because, as the model dimension grows, even the entire state for one member maybe too big for one processor to hold in its memory. The smallest unit is now the 2D field, and each processor holds only a subset along the record dimension. Accordingly, the processors (pid) are divided into "member groups" (with same pid_rec) and "record groups" (with same pid_mem), see Fig. 1 for example. "State-complete" now becomes "field-complete". The record dimension allows parallel processing of different fields by the read_var functions in model modules. And during assimilation, each pid_rec only solves the analysis for its own list of rec_id.

Figure 1: Transpose from field-complete to ensemble-complete, illustrated by a 18-processor memory layout (pid = 1, ..., 18), divided into 2 groups (pid_rec = 0, 1), each with 9 processors (pid_mem = 0, 1, 2). The data has dimensions mem_id = 1:100 members, par_id = 1:9 partitions, and rec_id = 1:4 records. The gray arrows show sending/receiving of data to perform the transpose. The yellow arrows is an additional collection step (only needed by observation data)

For observations, it is easier to process the entire observing network at once, instead of going through the measurements one by one. Therefore, each observing network (record) is assigned a unique obs_rec_id to be handled by one processor. Each pid_rec only needs to process its own list of obs_rec_id. Processors with pid_mem = 0 is responsible for reading and processing the actual observations using read_obs functions from dataset modules, while all pid_mem separately process their own members for the observation priors. When transposing from field-complete to ensemble-complete is done, an additional collection step among different pid_rec is required, which gathers all obs_rec_id for each rec_id to form the final local observation.

When the transpose is complete, on each pid, the local ensemble state_prior[mem_id, rec_id][par_id] is updated to the posterior state_post, using local observations lobs[obs_rec_id][par_id] and observation priors lobs_prior[mem_id, obs_rec_id][par_id].

Figure 2: Memory layout for state variables (square pixels) and observations (circles) using (a) batch and (b) serial assimilation strategies. The colors represent the processor id pid_mem that stores the data.

NEDAS provides two assimilation modes:

In batch mode, the analysis domain is divided into small local partitions (indexed by par_id) and each pid_mem solves the analysis for its own list of par_id. The local observations are those falling inside the localization radius for each [par_id,rec_id]. The "local analysis" for each state variable is computed using the matrix-version ensemble filtering equations (such as LETKF, DEnKF). The batch mode is favorable when the local observation volume is small and the matrix solution allows more flexible error covariance modeling (e.g., to include correlations in observation errors).

In serial mode, we go through the observation sequence and assimilation one observation at a time. Each pid stores a subset of state variables and observations with par_id, here locality doesn't matter in storage, the pid owning the observation being assimilated will first compute observation-space increments, then broadcast them to all the pid with state_prior and/or lobs_prior within the observation's localization radius and they will be updated. For the next observation, the updated observation priors will be used for computing increments. The whole process iteratively updates the state variables on each pid. The serial mode is more scalable especially for inhomogeneous network where load balancing is difficult, or when local observation volume is large. The scalar update equations allow more flexible use of nonlinear filtering approaches (such as particle filter, rank regression).

NEDAS allows flexible modifications in the interface between model/dataset modules and the core assimilation algorithms, to achieve more sophisticated functionality:

Multiple time steps can be added in the time dimension for the state and/or observations to achieve ensemble smoothing instead of filtering. Iterative smoothers can also be formulated by running the analysis cycle as an outer-loop iteration (although they can be very costly).

Miscellaneous transform functions can be added for state and/or observations, for example, Gaussian anamorphosis to deal with non-Gaussian variables; spatial bandpass filtering to run assimilation for "scale components" in multiscale DA; neural networks to provide a nonlinear mapping between the state space and observation space, etc.

Description of Key Variables and Functions

Figure 3. Workflow for one assimilation cycle/iteration. For the sake of clarity, only the key variables and functions are shown. Black arrows show the flow of information through functions.

Indices and lists:

• For each processor, its pid is the rank in the communicator comm with size nproc. The comm is split into comm_mem and comm_rec. Processors in comm_mem belongs to the same record group, with pid_mem in [0:nproc_mem]. Processors in comm_rec belongs to the same member group, with pid_rec in [0:nproc_rec]. Note that nproc = nproc_mem * nproc_rec, user should set nproc and nproc_mem in the config file.

• mem_list[pid_mem] is a list of members mem_id for processors with pid_mem to handle.

• rec_list[pid_rec] is a list of field records rec_id for processors with pid_rec to handle.

• obs_rec_list[pid_rec] is a list of observation records obs_rec_id for processors with pid_rec to handle.

• partitions is a list of tuples (istart, iend, di, jstart, jend, dj) defining the partitions of the 2D analysis domain, each partition holds a slice [istart:iend:di, jstart:jend:dj] of the field and is indexed by par_id.

• par_list[pid_mem] is a list of partition id par_id for processor with pid_mem to handle.

• obs_inds[obs_rec_id][par_id] is the indices in the entire observation record obs_rec_id that belong to the local observation sequence for partition par_id.

Data structures:

• fields_prior[mem_id, rec_id] points to the 2D fields fld[...] (np.array).

• z_fields[mem_id, rec_id] points to the z coordinate fields z[...] (np.array).

• state_prior[mem_id, rec_id][par_id] points to the field chunk fld_chk (np.array) in the partition.

• obs_seq[obs_rec_id] points to observation sequence seq that is a dictionary with keys ('obs', 't', 'z', 'y', 'x', 'err_std') each pointing to a list containing the entire record.

• lobs[obs_rec_id][par_id] points to local observation sequence lobs_seq that is a dictionary with same keys as seq but the lists only contain a subset of the record.

• obs_prior_seq[mem_id, obs_rec_id] points to the observation prior sequence (np.array), same length with seq['obs'].

• lobs_prior[mem_id, obs_rec_id][par_id] points to the local observation prior sequence (np.array), same length with lobs_seq.

Functions:

• prepare_state(): For member mem_id in mem_list and field record rec_id in rec_list, load the model module and read_var() gets the variables in model native grid, convert to analysis grid, and apply miscellaneous user-defined transforms. Also, get z coordinates in the same prodcedure using z_coords() functions. Returns fields_prior and z_fields.

• prepare_obs(): For observation record obs_rec_id in obs_rec_list, load the dataset module and read_obs() get the observation sequence. Apply miscellaneous user-defined transforms if necessary. Returns obs_seq.

• assign_obs(): According to ('y', 'x') coordinates for par_id and ('variable', 'time', 'z') for rec_id, sort the full observation sequence obs_rec_id to find the indices that belongs to the local observation subset. Returns obs_inds.

• prepare_obs_from_state(): For member mem_id in mem_list and observation record obs_rec_id in obs_rec_list, compute the observation priors from model state. There are three ways to get the observation priors: 1) if the observed variable is one of the state variables, just get the variable with read_field(), or 2) if the observed variable can be provided by model module, then get it through read_var() and convert to analysis grid. These two options obtains observed variables defined on the analysis grid, then we convert them to the observing network and interpolate to the observed z location. Option 3) if the observation is a complex function of the state, the user can provide obs_operator() in the dataset module to compute the observation priors. Finally, the same miscellaneous user-defined transforms can be applied. Returns obs_prior_seq.

• transpose_field_to_state(): Transposes field-complete field_prior to ensemble-complete state_prior (illustrated in Fig.1). After assimilation, the reverse transpose_state_to_field() transposes state_post back to field-complete fields_post.

• transpose_obs_to_lobs(): Transpose the obs_seq and obs_prior_seq to their ensemble-complete counterparts lobs and lobs_prior (illustrated in Fig. 2).

• batch_assim(): Loop through the local state variables in state_prior, for each state variable, the local observation sequence is sorted based on the localization and impact factors. If the local observation sequence is not empty, compute the local_analysis() to update state variables, save to state_post and return.

• serial_assim(): Loop through the observation sequence, for each observation, the processor storing this observation will compute obs_increment() and broadcast. For all processors, if some of its local state/observations are within the localization radius of this observation, compute update_local_ens() to update these state/observations. Do this iteratively for all observations until end of sequence. Returns the updated local state_post.

• update(): Take state_prior and state_post, apply miscellaneous user-defined inverse transforms, compute analysis_incr(), convert the increment back to model native grid and add the increments to the model variables int he restart files. Apart from simply adding the increments, some other post-processing steps can be implemented, for example using the increments to compute optical flows and align the model variables instead.

Adding New Models and Observations

To use NEDAS for your own models/observations, please read the detailed documentation for models and dataset modules, and create a module with functions to interface with the new models and/or dataset files. In the workflow chart the user-provided functions are highlighted in orange.

If you are considering DA experiments for a model, typically some Python diagnostic tools for the model state variables already exist, so the work for implementing the modules shall not be too heavy. Essentially you need to provide functions such as read_var to receive some key word arguments (variable name, time, member, vertical index, etc.) and return a 2D field containing the corresponding model state variable.

For observations, we expect you to already have some preprocessing scripts to read the raw dataset, quality control and screen for valid observations for the analysis domain, etc. These can be implemented in the read_obs function. Some steps in preprocessing are more involved: super-observation, uncertainty estimation, and extraction of information matching the model-resolved scales. We suggest you consult DA experts to implement these steps.

List of currently supported models and observations:

• The TOPAZ system coupled ocean (HYCOM) and sea ice (CICE4) model, with satellite obserations and insitu profiler data.

• The next-generation sea ice model (neXtSIM), with SAR-image-based sea ice drift and deformation observations.

and planned developement for:

• The Weather Research and Forecast (WRF) model (Polar WRF), with satellite observations.

• ECOSMO biogeochemistry model, with ocean color data.

Acknowledgements

NEDAS was initiated by Yue Ying in 2022. Please cite this repository if you used NEDAS to produce results in your research publication/presentation.

The developement of this software was supported by the NERSC internal funding in 2022; and the Scale-Aware Sea Ice Project (SASIP) in 2023.

With contribution from: Anton Korosov, Timothy Williams (pynextsim libraries), NERSC-HYCOM-CICE group led by Annette Samuelsen (pythonlib for abfile, confmap, etc.), Jiping Xie (enkf-topaz), Tsuyoshi Wakamatsu (BIORAN), Francois Counillon, Yiguo Wang, Tarkeshwar Singh (EnOI, EnKF, and offline EnKS in NorCPM).

We provide the software "as is", the user is responsible for their own modification and ultimate interpretation of their research findings using the software. We welcome community feedback and contribution to support new models/observations, please use the "pull request" if you want to be part of the development effort.