There are a number of ways to calculate the 1 in 100 flood, some more complicated than others. This simple way does a great job of explaining the basics (and the shortcomings behind the metric). First we start with historical data, and we need a good chunk of it. Since we're in Boulder I'm going to use the Boulder Creek @ Orodell location because it has over 100 years of data available for download. If you are a local, this location is up the canyon, near the Betasso connector link trail before the first tunnel.
To start with, we're only concerned with the maximum streamflow from each year, so we can trim the data down to ~108 data points (If you skip this step, it'll make things more complicated later).
Once we have this, we sort the floods from lowest to highest, and calculate the probability that the river will exceed that level (Pe).
| Year | Max Flow | Pe |
| 1906 | 20 CFS | 108/108=100% |
| 2002 | 124 CFS | 107/108=99.1% |
| 1966 | 155 CFS | 106/108=98.1% |
| ... | ... | ... |
| 1921 | 1180 CFS | 2/108=1.9% |
| 2013 | 1570 CFS | 1/108=0.9% |
Obviously, out of the data I have, this current flood has a 1% chance of occurring and is the 100-year flood (if this data is representative). It's important to remember that the flooding could be much worse. This flood saw peaks in town close to 7,000 cfs. The last BIG flood in 1894 had flows in town of 11,000 to 13,500 cfs. We don't have long enough records to know if this was an 100 year event, 500 year event, or even maybe a 1000 year event. Also, since then the city has built a lot of infrastructure to mitigate flood risk. So how does this flood compare to the 1894 flood? It's impossible to make a direct comparison.
From the current data we can also get estimates of the 50, 25, and 10 year floods from a graph of this this sorted data:
The problems with the sparseness of our data become obvious. We only have one 1/100 event, one 1/50 event, two 1/25 events and six 1/10 events. 10 total "extreme" events to base our risk analysis off of. Additionally, as I mentioned in my previous post, there's a 34% chance of not having a true "100-year flood" in the 108 year's we're looking at.
About calculating the 100-year flood: Emily Gill, a hydrology instructor at the University of Colorado says:
Unfortunately, it's a hard question to answer and I'm not sure we will ever have firm estimates for 50-year, 100-year, etc floods. There are a couple problems with the term 100-yr flood that make it controversial. Our ability to classify floods based on return periods is extremely limited by the length and accuracy of the records we have. In other words, if we have 100 years of peak streamflow data, and this event is stacked at the top, then yes – technically it's a 100-year event. If we only have 80 years of peak streamflow data, and this one is at the top, then by definition it would be an 80-year flood. If we have more than a 100 years of data and this peak (~ 5000 cfs) is somewhere where the probability of it happening in any given year is 1% then it's a 100-year event by definition.
Our analysis of return periods does not consider a changing climate. If our calculations of return period are based on our existing records, but at the same time we haven't experienced what our atmosphere is entirely capable of (assuming a change in climate variability) then we can't accurately calculate the probability of an event happening.
What Emily is saying is in order to have representative statistics you need more than n=10 events, and we're not even sure if this is a representative data set. What if the past 100 years have been unusually dry? or unusually wet? What if there's a general wetting or drying trend in the data, and the next 100 years (or 10 years) look different than the previous? (Also, see this nice USGS PDF with some additional problems with the "100-year flood" metric)
And according to climate models non-stationarity is exactly what we can expect for the future:
