Group assignment 2.7 Report: Extreme Value Analysis

CEGM1000 MUDE: January 10, 2025.

YOUR GROUP NAME HERE

Before writing your answers, consider this:

• You should include figures in this report.
• Question 5 will have the heaviest weight in the grading (~2-3x that of the other questions).
• Question 1 has the least weight and is mostly used to highlight the nuances discussed in other questions.

Questions

1. Provide a short description of your data set.

Your answer here. Include qualitative and quantitative information; do not duplicate the information from the README or notebook, but rather the observations you make in Task 1, and anything you think is relevant for the EVA. Don't include a figure of the time series, since that is requested in a later question

2. Yearly Maxima. How many extremes do you sample? What distribution do you need to use together with the Block Maxima sampling method? Summarize the parameters of this distribution including the tail type. Comment on the goodness of fit of the distribution.

Your answer here. Summarize the distribution parameters. Include a semi-log plot of exceedance probability that compares the empirical and fitted distribution. Don't include a figure of the time series, since that is requested in a later question.

3. Peak Over Threshold. How many extremes do you sample? What distribution do you need to use together with the POT sampling method? Summarize the parameters of this distribution including the tail type. Comment on the goodness of fit of the distribution. Do you need to add/subtract the threshold when using this method, and if so, at what point in the analysis do you do so?

Your answer here. Summarize the distribution parameters. Include a semi-log plot of exceedance probability that compares the empirical and fitted distribution. Don't include a figure of the time series, since that is requested in a later question.

4. Comparing the methods. Comment on the differences on the sampled extremes. Comment on the differences you see in the goodness of fit of the distributions from the two EVA Methods (just one or two sentences, using the figures included above). In terms of information used to fit each distribution, are there major differences?

Your answer here. Include a figure of the time series that presents sampled block maxima as red dots and POT samples as blue dots, and refer to this in your answer to the first part of the question.

5. Compare return periods of the event of October 2024 produced by the distributions of the two EVA Methods. Reflect on the differences between the two methods and how to tackle them.You may reflect on:

• The source of the differences between both methods.
• Which method would be the most reliable in this situation.
• If possible, how to improve the reliability of the obtained results.
• The meaningfulness of the obtained return periods.

Your answer here. To support your explanation, include the return period figure, as well as a Markdown table that summarizes (quantitatively) the return periods.

6. Which return period would you pick for the event of October 2024? Justify your answer.

Your answer here.

General Comments on the Assignment [optional]

Use this space to let us know if you encountered any issues completing this assignment (but please keep it short!). For example, if you encountered an error that could not be fixed in your Python code, or perhaps there was a problem submitting something via GitLab. You can also let us know if the instructions were unclear. You can delete this section if you don't use it.

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