100-year Flood - Statistical Assumptions

Statistical Assumptions

There are a number of assumptions which are made to complete the analysis which determines the 100-year flood. First, the extreme events observed in each year must be independent from year-to-year. In other words the maximum river flow rate from 1984 cannot be found to be significantly correlated with the observed flow rate in 1985. 1985 cannot be correlated with 1986, and so forth. The second assumption is that the observed extreme events must come from the same probability distribution function. The third assumption is that the probability distribution relates to the largest storm (rainfall or river flow rate measurement) that occurs in any one year. The fourth assumption is that the probability distribution function is stationary, meaning that the mean (average), standard deviation and max/min values are not increasing or decreasing over time. This concept is referred to as stationarity.

The first assumption has a very low chance of being valid in all places. Studies have shown that extreme events in certain watersheds in the U.S. are not significantly correlated, but this must be determined on a case by case basis. The second assumption is often valid if the extreme events are observed under similar climate conditions. For example, if the extreme events on record all come from late summer thunder storms (as is the case in the southwest U.S.), or from snow pack melting (as is the case in north-central U.S.), then this assumption should be valid. If, however, there are some extreme events taken from thunder storms, others from snow pack melting, and others from hurricanes, then this assumption is most likely not valid. The third assumption is only a problem if you are trying to forecast a low, but maximum flow event (say, you are tying to find the max event for the 1-year storm event). Since this is not typically a goal in extreme analysis, or in civil engineering design, then the situation rarely presents itself. The final assumption about stationarity has come into question in light of the research being done on climate change. In short, the argument being made is that if temperatures are changing and precipitation cycles are being altered, then there is compelling evidence that the probability distribution is also changing. The simplest implication of this is that not all of the historical data are, or can be, considered valid as input into the extreme event analysis.