Quantify the contributions of different drivers to the observed changes using established attribution methods, such as fingerprinting techniques or attribution frameworks.

[ribeiron]

From Bindoff: https://www.ipcc.ch/site/assets/uploads/2018/02/WG1AR5_Chapter10_FINAL.pdf

There are four core elements to any detection and attribution study:

1. Observations of one or more climate variables, such as surface temperature, that are understood, on physical grounds, to be relevant to the process in question

2. An estimate of how external drivers of climate change have evolved before and during the period under investigation, including both the driver whose influence is being investigated (such as rising GHG levels) and potential confounding influences (such as solar activity)

3. A quantitative physically based understanding, normally encapsulated in a model, of how these external drivers are thought to have affected these observed climate variables

4. An estimate, often but not always derived from a physically based model, of the characteristics of variability expected in these observed climate variables due to random, quasi-periodic and chaotic fluctuations generated in the climate system that are not due to externally driven climate change

[ribeiron]

**Correlation Analysis:

Start by conducting correlation analyses between the South Australian upwelling and each of the climatic indices (SAM, ENSO, IOD, Polar vortex). This will provide an initial insight into potential relationships.

**Time Series Analysis:

Use time series analysis techniques to identify patterns, trends, and cyclical behavior in both the upwelling and the climatic indices over the historical period.

**Attribution Framework:

Develop a framework to attribute changes in the South Australian upwelling to the different factors. You might use statistical techniques, such as regression or machine learning, to model the relationship between the upwelling and the climatic indices.

**Modeling:

Build models that simulate the behavior of the South Australian upwelling based on the relationships you've identified. This could involve using multiple regression models or more sophisticated methods like dynamic models that incorporate lagged effects.

**Scenario Analysis:

Run simulations under different scenarios: for instance, simulate periods with strong positive SAM, ENSO, IOD, and Polar vortex weakening, and compare the simulated upwelling behavior with the observed data.

**Quantifying Contributions:

Quantify the contributions of each factor to the observed changes in the upwelling. This might involve calculating the percentage of variability explained by each factor or assessing their relative importance through sensitivity analyses.

**Visualization:

Create visualizations that illustrate the relationships and differences between the upwelling and the climatic indices. Time series plots, correlation matrices, and maps can help communicate your findings effectively.

**Uncertainty Analysis:

Account for uncertainties in your analysis. Sensitivity analysis can help you understand how uncertainties in the climatic indices might impact your results.

[duphrin]

The correlation analysis between the South Australian upwelling and each of the climatic indices (SAM, ENSO, IOD) can be found in the partial_cor.ipynb notebook.