by Michael Igo, Affil. ASLA, PE, D.WRE, LEED AP, CID
In the age of awareness of climate change, we often hear the terms “100-year storm,” “500-year tides,” or “25-year drought” thrown around. Intuitively, we tend to think that a 100-year storm occurs once every 100 years. However, this is only partly true, as there are key phrases missing from this notion: a 100-year storm will occur once every 100 years on average and based on past data.
The use of an X-Year event derives from what is known in mathematics as the exceedance probability, or the likelihood of an event being greater than a predefined parameter in a given timeframe. Statistics of past data (storms, tides, earthquakes, etc.) are used to create charts based on size and the probability of occurring.
A typical chart (called a probability distribution; see Figure 1 above) shows that the probability of a storm exceeding 7.0 inches (1% chance) is less likely to occur each year than a storm exceeding 4.0 inches (10% chance), which in turn is less likely to occur than a storm exceeding 2.5 inches (50% chance). Since dealing in probabilities tends to drive math-phobic people away, a gentler way to present exceedance probability is to take its inverse, or take 1 and divide it by the probability:
So, while “100-year storm” is more pleasant to say and easier to present than “the storm with 1% exceedance probability,” the reality is that something is lost in translation in the oversimplification. For example, just because a storm is a 100-year event does not mean it will happen at least once in 100 years—or only once.
An interesting calculation is to estimate the probability of a 100-year storm NOT occurring in a 100-year period. If the exceedance probability of having a 100-year storm in a given year is 1%, then the probability of not having the 100-year storm is 99% (1% + 99% = 100% or all possibilities). The probability of not having a 100-year storm in 100 years is:
99% or 0.99 x 0.99 x 0.99 x 0.99 …
100 times for each year = 0.99100 = 0.366 or 36.6%
Therefore, we are not guaranteed to have a 100-year storm within 100 years. There is a slightly greater than 1 out of 3 chance that it never happens within a century. Exceedance probabilities and X-Year events are simply estimates based on historical and current data.
However, we see in climate change news that multiple events are happening in a row. An August 29, 2017 Washington Post headline reads “Hurricane Harvey is the third ‘500-Year’ flood in Houston in 3-Years.” How is this possible? A 500-year storm’s exceedance probability is:
1 ÷ 500 = 0.002 or 0.2% chance
The probability of a 500-year storm occurring three years in a row is:
0.002 x 0.002 x 0.002 = 0.000000008 = 0.0000008% or 1 in 125,000,000
To put it in perspective, the chance of a person getting struck by lightning in any given year is 1 in 700,000. These are slim odds, but if each storm exceeds the 500-year threshold, then it is what it is, right? Not so much.
The problem with the 500-year storm happening three years in a row highlights an axiom in investing and one we should adopt to design for climate change: past performance does not guarantee future results.
We create charts and tables as shown in this article from current and historical data. Often, when we take historical data, we are not putting in any context or weighting it against more recent data points and trends. In other words, some statistical analyses for climate data would assume that the probability of 7.0 inches of rain falling in 1920 is the same as it would be in 2020. Weather data typically shows trends that averages, minimums, and maximums move and vary over time. So based on historical data, Houston may have experienced three years of consecutive 500-year storms but based on data from decades long before the present day. It basically comes down to “garbage in, garbage out.”
Moreover, we do not have 500 years of data in Houston to verify that a 500-year event occurred. Typically, there are 50 – 100 years of data in which none of these events occurred and statisticians extrapolated the observed extreme weather to say these were 500-year or 0.2% probability occurrences. This observation is of little consolation for the devastation these storms caused.
One of the major research areas in climate change is looking to recalibrate mathematical models for design. The implications have both environmental impact by finding ways to predict extreme events more accurately, as well as economic impact. Designers neither want to under-design (leading to damages) nor over-design a site (cost overruns). However, site design and water conservation need to consider the statistics and probability using current and future climate change. Just because we have some notion of what a “100-year storm” or an “extreme event” is, we are not necessarily absolved of designing for events and situations that may occur in the future as amplified by climate change. As a reference, the Conservation Law Foundation (CLF) along with Reed Hilderbrand of Cambridge, MA made a presentation at the 2018 ASLA Conference on Landscape Architecture in Philadelphia (Uncharted Waters: Liability Risks of (In)action in the Face of Climate Change) that highlighted what designers are responsible for in a Standard of Care when dealing with climate change.
An X-Year event is not a mathematical certainty—it is only a guide or compass towards the overarching design principle we should strive towards in resilience. If we design to today’s perfunctory standards, we may quickly find ourselves exposed to failures of our systems in climates that rapidly change. If COVID-19 is considered a 100- or 200-year outbreak event, then it should serve as a reminder of how it has exposed the weaknesses in our economic and social systems.
Michael Igo, Affil. ASLA, PE, D.WRE, LEED AP, CID, is President of Aqueous Consultants, LLC. Michael is a Professional Engineer with 20 years experience, licensed in 12 states, designing and managing water resources projects. As a self-proclaimed “right-brained engineer,” his dual love of science and graphics resonates with architects. Mike fulfilled his lifelong dream by founding Aqueous Consultants in 2014. His unique education with a B.S. in Aerospace Engineering and M.S. in Civil Engineering lends to design of both mechanical (irrigation, pumps, controls) and civil systems (ponds, tanks, drainage). Mike has documented over 100 Water Efficiency credits for LEED and programmed Aqueous’ computer climate model. He has spoken at many national and regional ASLA events, and currently serves as co-chair for ASLA’s Water Conservation Professional Practice Network (PPN).