Application of QQ-Plot in Flood Frequency Analysis?

In flood frequency analysis, a QQ-Plot (Quantile-Quantile Plot) can be a valuable tool for assessing the goodness-of-fit of a chosen probability distribution to the observed flood data. Here's how QQ-Plots are applied in flood frequency analysis:

1. Assessment of Distributional Assumptions:

- Flood frequency analysis often involves fitting a probability distribution (such as the Gumbel, Weibull, or Gamma distribution) to historical flood data.

- Before using a particular distribution to model the flood data, it's essential to assess whether the distributional assumptions of the chosen model are met.

- QQ-Plots compare the quantiles (ordered values) of the observed data with the quantiles of the theoretical distribution being tested. If the distributional assumptions hold true, the points on the QQ-Plot will fall approximately along a straight line.

2. Detection of Departures from the Assumed Distribution:

- Deviations from a straight line on the QQ-Plot indicate departures from the assumed distribution. These deviations can suggest potential issues with the fit of the chosen distribution to the data.

- For example, if the points on the QQ-Plot deviate significantly from the straight line in the upper tail of the distribution, it may indicate that the chosen distribution underestimates the frequency of extreme flood events.

- By visually inspecting the QQ-Plot, hydrologists can identify regions of the distribution where the fit is poor and may need to consider alternative distributional models or adjust parameters.

3. Selection of Best-Fitting Distribution:

- QQ-Plots provide a visual comparison of observed and theoretical quantiles, allowing hydrologists to evaluate the goodness-of-fit of different probability distributions.

- Hydrologists can use QQ-Plots to compare multiple distributions and select the one that provides the best fit to the observed flood data.

- By choosing the best-fitting distribution, hydrologists can make more accurate estimates of flood frequencies, return periods, and associated risks.

In summary, QQ-Plots are a valuable diagnostic tool in flood frequency analysis for evaluating the suitability of probability distributions, detecting departures from distributional assumptions, and selecting the best-fitting distribution to model flood data accurately.