The terms “100-year flood” or “500-year flood”, are very commonly used, but are not very well understood. So here is the scoop on what flood recurrence intervals truly mean, and how they are estimated.
Too often, people assume they are safe from a 100-year flood scenario since the 100-year flood just occurred a couple years ago. That just isn’t the case. No one thinks it’s impossible for a coin to land on tails after it has already landed on tails twice in a row, and people should think of floods in the same way. It’s all a matter of chance, and the previous outcome does not influence the next outcome. The term 100-year flood simple means that there is a 1% chance of that level of flooding occurring in any one year. Similarly, 50-year flood flows have a 2% chance of occurring in any one year, and 10-year flood flows have a 10% chance of occurring in any one year. Simply divide 100 by the flood recurrence interval to estimate the percentage chance that specific flood flows will be exceeded in any one year, this is called “annual exceedance probability.”
Hydrologists have largely stopped using the flood recurrence interval in favor of using the annual exceedance probability to try and better communicate flood risks to the public. This is especially important considering that, in most years, flooding causes more damage to property in the US than any other type of natural disaster. (Source: https://www.pewtrusts.org/en/research-and-analysis/articles/2017/02/01/flooding-disasters-cost-billions-in-2016)
Now that we have the terminology sorted out, how is an annual exceedance probability estimated? And how could you possibly know what the “100-year flood” is if you only have 20 years’ worth of streamflow data? The answer is: statistics. Remember back in math class when you learned about normal distribution, and this bell curve?
Flows in rivers, and many other patterns in nature, are normally distributed. That means, if I plot just 20 years maximum annual streamflows, those data, arranged from smallest to largest, will look like the normal distribution curve from math class. Once we know the flows are normally distributed, all we need to know to estimate the annual exceedance probability is the average and standard deviation of the dataset. Those two numbers dictate the shape of any normally-distributed curve. In a normally-distributed system, we know that 68% of all values fall within one standard deviation of the average, 95% are within two standard deviations, and 99.7% are within 3 standard deviations of the average. Obviously, our estimates will be more accurate with more data, but we do not need one hundred years to estimate the size of the “100-year flood”.
Now, even though our maximum annual flows are normally distributed and fit well on a bell curve, when it comes to flows, we don’t want to know the probability that the annual maximum flow will be exactly 5 cubic feet per second (“cfs”), we want to know the probability that the maximum annual flow will exceed 5 cfs. The math behind this curve is still normal distributions and standard deviations, but instead of starting at zero, rising to the average and falling back to zero, we want to start at 100% probability there will be greater than zero flow, and then drop down to 0% probability of high flow. I made the following Annual Exceedance Probability Curve for a fictitious stream called Lytle Creek as an example of this type of curve.
Notice at the lowest flow, the curve estimate is a near 100% chance the annual maximum flow will exceed 10 cfs. As the flow rate rises, the probability of that flow rate being exceeded drops. At our average flow of 50 cfs, the probability that the maximum flow will be greater than 50 cfs is 50%. This makes sense, as we know half of the values should be above the average, and half should be below. Then, as we approach the higher flows, the probability of that flow rate being exceeded in any one year drops to nearly 0%.
Estimating the flood flows with a 1% annual exceedance probability is rather simple. Determining how much land will be flooding based on that flow is much harder. But luckily, you don’t have to figure that out yourself. FEMA has done this work and mapped most of the floodplains in the United States, all you have to do is enter an address to see the annual probability your home will experience flooding. Here is the link to the database: https://msc.fema.gov/portal/search
If you need any information about a stream system with very little, or even zero, available data, don’t get discouraged, just give Lytle Water Solutions a call. Our team is highly experienced in flow estimation where data points are few and far between.