Variational data assimilation

[SCiarella]

Closes #117 by adding a notebook dedicated to Variational data assimilation.

No new features have been added, so the changes are confined to the new notebook (+ docs)

[sonarqubecloud]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

[SarahAlidoost]

@SCiarella the notebook looks awesome 🥇 thanks! The explanations and plots are clear, I was able to run the notebook. There are some comments that should be fixed before the merge. Then we can ask others to have a look and provide feedback.

1. Please add the diffwofost logo at the top, similar to other nbs
2. in cell 1, in section "Variational data assimilation with diffWOFOST", where it says: "Earlier notebooks in this series demonstrated the Kalman-filter route ...", should be changed to "PCSE notebooks demonstrated the Kalman-filter route ...".
3. In section "Background on data assimilation", the equation does not render correctly, please remove space after/before $$.
4. In section "2.2.1 Defining the synthetic observations", the link to test data doesnot work because those test data are only available if someone runs pytest. Similar to other nbs, we should download them as:

import urllib.request

url = "https://raw.githubusercontent.com/ajwdewit/pcse/refs/heads/master/tests/test_data/test_waterlimitedproduction_wofost72_03.yaml"
filename = "test_waterlimitedproduction_wofost72_03.yaml"

urllib.request.urlretrieve(url, filename)
print(f"Downloaded: {filename}")

test_data_path = "test_waterlimitedproduction_wofost72_03.yaml"

5. In section "2.2.1 Defining the synthetic observations", we don't need Truth_external_states as wofost72 does not need external variables.
6. Cells number 39 and 43 are too long. Can you please break them into smaller cells where it is possible and add some inline comments.
7. I like how you defined observations in "2.2.1 Defining the synthetic observations" 👍 This is something to be discussed and get feedback from research group.
8. In cell 33, in class VariationalDiffWofost72, in run_model, where provider = copy.deepcopy(self.base_provider). We don't need this copy anymore right?