When analyzing extreme rainfall data, why is the Log-Pearson Type III distribution often preferred over the Gumbel distribution for basins in regions experiencing very rare, exceptionally heavy rainfall events?

When analyzing extreme rainfall data, which refers to the largest observed rainfall amounts over specific periods like annual maxima, the Log-Pearson Type III (LP3) distribution is often preferred over the Gumbel distribution for basins in regions experiencing very rare, exceptionally heavy rainfall events due to its superior flexibility in modeling the shape of the data, particularly its skewness. The Gumbel distribution, also known as the Type I extreme value distribution, is a two-parameter probability distribution widely used for modeling extreme events. It assumes a fixed shape for the distribution of extreme values, meaning its coefficient of skewness, a statistical measure of the asymmetry of the data distribution, is inherently constant at approximately 1.139. While the Gumbel distribution is simple to apply and provides a reasonable fit for many datasets, this fixed skewness becomes a significant limitation when dealing with extreme rainfall data that exhibits a different degree of asymmetry. For very rare and exceptionally heavy rainfall events, the observed historical data often show a much higher positive skewness, meaning there is a disproportionately longer or fatter "tail" towards larger values than the Gumbel distribution can represent. The Log-Pearson Type III distribution is a three-parameter probability distribution that is applied to the logarithms of the rainfall data, rather than the raw rainfall values themselves. This transformation helps normalize the data and manage extreme outliers. The three parameters it utilizes are location, scale, and crucially, a shape parameter, which directly controls the skewness of the distribution of the log-transformed data. By having a flexible shape parameter, LP3 can accommodate a wide range of skewness values, both positive and negative, which are directly estimated from the observed data. For basins in regions experiencing very rare, exceptionally heavy rainfall events, such as those influenced by intense meteorological phenomena like tropical cyclones or atmospheric rivers, the annual maximum rainfall amounts typically exhibit a pronounced positive skewness in their distribution. This indicates that the probability of observing extremely large rainfall amounts is higher than what a distribution with a fixed, lower skewness (like Gumbel) would predict. The LP3 distribution's ability to adapt its skewness to match that of the observed extreme rainfall data allows it to more accurately model the upper tail of the distribution. This is critical for estimating the magnitude of events with very long return periods, such as a 100-year or 500-year rainfall event, which refer to rainfall amounts expected to be equaled or exceeded on average once every 100 or 500 years, respectively. By accurately capturing the true skewness inherent in the extreme rainfall data, LP3 provides more reliable and less biased estimates for these high-magnitude, low-frequency events, which are essential for critical infrastructure design and flood risk management.