Distribution is often used to estimate the flood magnitude. The Gumbel distribution is commonly used in hydrology and other fields to model extreme events.

To estimate the flood magnitude for a return period of 200 years using the Gumbel distribution, you would follow these steps:

1. Sort the flood data in ascending order.
2. Calculate the rank of each flood event by assigning a rank of 1 to the smallest flood, 2 to the second smallest flood, and so on.
3. Calculate the return period (RP) for each flood event using the formula RP = (N + 1) / rank, where N is the number of years in the flood data (100 in this case).
4. Calculate the probability of exceedance (PE) for each flood event using the formula PE = 1 / RP.
5. Fit the Gumbel distribution to the flood data using maximum likelihood estimation (MLE) or another fitting method. This will give you the parameters of the Gumbel distribution, specifically the location parameter (μ) and the scale parameter (β).
6. Use the Gumbel distribution parameters to estimate the flood magnitude for a return period of 200 years. This can be done by calculating the return level (RL) using the formula RL = μ - β * ln(-ln(1 - 1 / RP)).

Note that this estimation assumes that the flood data follows a Gumbel distribution and that the underlying flood process is stationary. It's important to assess the goodness-of-fit of the Gumbel distribution to the data and consider other factors such as climate change or non-stationarity before making predictions or decisions based on the estimated flood magnitude for a 200-year return period.