Multi-level data assimilation for ocean forecasting using the shallow-water equations

This repository contains code, scripts and notebooks related to the work presented in the paper "Multi-level data assimilation for ocean forecasting using the shallow-water equations" by Beiser, Holm, Lye and Eidsvik. The motivation is to setup multi-level Monte Carlo ensembles of simplified ocean models and evaluate the usability of multi-level data assimilating in the presence of sparse observations of ocean currents. We then use the posterior multi-level ensemble to forecast the ocean state and drift trajectories.

All code relies heavily on GPU Ocean v1.3.0.

Result Reproduction

Although the exact figures from the paper will be hard to reproduce due to stochastic processes, the figures can be qualitatively reproduced as follows:

• Figure 0: tikz

• Figure 1: tikz

• Figure 2: scripts/DoubleJetPracticalCost_square.py

• Figure 3: notebooks/DoubleJet-Truth4paper.ipynb (requires running scripts/DoubleJetTruth.py -L 9, but results are stochastic)

• Figure 4: notebooks/DoubleJet-Resoltions4paper.ipynb (results are seeded)

• Figure 5: tikz + requires running scripts/DoubleJetVarianceLevel-DA.py + scripts/DoubleJetVarianceLevel-DA-PP.py (The first script save results in a newly created putput folder. The second script requries to set source_path to the output folder of the first script. Moreover, for different functionals, follow the instructions in the second script to create the a- and b-plot. Also the second script saves results in a newly created output folder.)

• Table 1: notebooks/DoubleJet-SpeedUp.ipynb (requires to set the output folders of the previous cost and variance experiments are manual inputs)

The next figures require running

• scripts/DoubleJetSLDA.py -L 9

Then set the output folder of this script as truth_path in the following scripts

• scripts/DoubleJetSLDA.py -L 9 -Ne 50, and
• e.g. scripts/DoubleJetMLDA.py -ls 6 7 8 9 -Nes 275 134 46 13

Again, output folders are created and those folders paths have to be manually set in the following notebooks!

• Figure 6: notebooks/DoubleJet-DA-PostProcessing-ERR4paper.ipynb (set folder path as explained above)

• Figure 7: notebooks/DoubleJet-DA-PostProcessing-ERRloc4paper.ipynb (set folder path as explained above) + requires running scripts/DoubleJetMLDA.py -ls 6 7 8 9 -Nes 275 134 46 13 (with right truth_path for the output of the truth AND min_localisation_level=1 see comment in the upper part of the script)

• Figure 8: notebooks/DoubleJet-MLDA-PostProcessing-MLscores4paper.ipynb (set folder path as explained above)

• Figure 9: notebooks/DoubleJet-MLRanks-PostProcessing4paper.ipynb (set folder path as explained above) + requires running scripts/DoubleJetMLRanks.py

• Figure 10: notebooks/DoubleJet-DA-PostProcessing-Drifter4paper.ipynb (set folder path as explained above)

• Figure 11: notebooks/DoubleJet-DA-PostProcessing-DrifterERR4paper.ipynb (set folder path as explained above)

• Figure 12: notebooks/DoubleJet-DA-PostProcessing-DrifterKDE4paper.ipynb (set folder path as explained above)

• Table 2: notebooks/DoubleJet-DA-PostProcessing-DrifterKDE4paper.ipynb (set folder path as explained above, see far down in the notebook)

A lot of parameters are collected in utils/DoubleJetParametersReproduction.py.

Funding

This work is funded by the Norwegian Research Council under grant number 310515 (Havvarsel).