pyDARTdiags example DA notebook for MOM6/CICE DA

## DA Diagnostics

**Summary:**
[pyDARTdiags](https://ncar.github.io/pyDARTdiags/) is a Python package for **observation-space diagnostics** within the **Data Assimilation Research Testbed (DART)** framework. It provides tools for analyzing, visualizing, and interpreting the performance of data assimilation (DA) systems by comparing model predictions with observational data.
The package includes an **example gallery** showcasing typical diagnostic workflows:
[https://ncar.github.io/pyDARTdiags/examples/index.html](https://ncar.github.io/pyDARTdiags/examples/index.html)

**Motivation:**
Understanding where and why data assimilation performs poorly is crucial for improving forecast skill and model accuracy.
In particular, identifying **spatial and vertical regions** of high analysis error or innovation bias can reveal issues with model physics, observation quality, or sampling.
This project focuses on making these diagnostics more **interactive and intuitive** through visualization.

**Goals:**

Develop a Jupyter notebook that enables users to:
- Display the **MOM6 model grid** on a geographic map.
- Overlay **observation-space diagnostics** (e.g., innovations, observation-minus-forecast, observation-minus-analysis).
- Interactively explore **regional**, **temporal**, and **depth-dependent** patterns in assimilation performance.

Optional extensions could include:
- Interactive filtering by variable, depth, or observation type.
- Statistical summaries (e.g., RMS innovation by region).
- Support for additional DART model interfaces beyond MOM6.

**Approach:**
The project will combine **pyDARTdiags** capabilities with **Python visualization libraries** such as `matplotlib`, `cartopy`, and `xarray` to display diagnostics on curvilinear ocean grids.

Steps:
1. Plotting MOM6 output on geographical grids
2. Overlaying DART observation space data
3. Building an interactive Jupyter notebook for visualization and exploratory analysis.

**Key Questions to Explore:**
- Which fields, regions and depth levels are most relevant to ocean modelers and observationalists?
- Which visualization approaches (e.g., contour maps, scatter overlays, heatmaps) best highlight regions of poor DA performance?
- How can pyDARTdiags outputs be linked with existing tools such as CUPiD or CESM diagnostics?

**Skills Needed:**
- Python programming
- Data analysis with `xarray`, `numpy`, and `pandas`
- Visualization with `matplotlib`, `cartopy`, or `plotly`
- Basic understanding of **data assimilation concepts** and **ocean model grids (MOM6)**

**Possible Challenges:**
- Managing large diagnostic datasets efficiently.
- Designing intuitive visualizations that convey complex spatio-temporal patterns.
- Ensuring compatibility with various DART output formats and model configurations.

**References:**
- [pyDARTdiags documentation](https://ncar.github.io/pyDARTdiags/)
- [CESM Unified Postprocessing and Diagnostics (CUPiD)](https://ncar.github.io/CUPiD)
- [Data Assimilation Research Testbed (DART)](https://docs.dart.ucar.edu)