15 September 2013

Against the 100-Year Flood

Image above courtesy @The_CUI and @KaiCasey, click on it for link.

Boulder and the Colorado Front Range have experienced devastating floods over the past week. We came out OK, though many friends and neighbors did not. My son's elementary school will be closed for a long while. (Thanks for the many emails of support and concern from friends, colleagues and readers.) If you'd like to help, please see this page with resources.

Boulder has long been recognized as being at risk to major flooding. The local paper, the Daily Camera reported in 2008:
"Boulder is the No. 1 flood-risk community in Colorado," said Cristina Martinez, a city civil engineer. "That's the message we want to get out there."
In 1975 the classic "first assessment " of natural hazards by Gilbert White and colleagues identified Boulder as one of the nation's top major disasters waiting to happen. (White was a long-time University of Colorado geography professor who lived a remarkable life. He died in 2006 aged 94.) The memorial at the top of this post in the Boulder floodplain, demarcating floods of different levels, was raised in White's honor in 2011.

After many decades of relatively frequent flooding in the early parts of the 20th century, Boulder has been on a lucky streak which had, until this week, lasted over forty years:
Serious floods have affected downtown Boulder in 1894, 1896, 1906, 1909, 1916, 1921, 1938, and 1969 with the worst being those of May 31-June 2, 1894 and May 7, 1969. The flood of 1969 was the result of four days of almost continuous rainfall (11.27” measured in Morrison and 9.34” at the Boulder Hydroelectric Plant three miles up Boulder Canyon from town).
This lucky streak led to concerns, such as these expressed in 2008:
Eric Lessard, an engineering project manager with the city's utilities department, said it's hard not to get complacent, because it's been so long since the 1894 flood that inundated the city.

"That's one of the biggest problems we have -- we've been really, really fortunate in Boulder. We haven't had any major floods in many, many years. It starts to give people a false sense of confidence"
Despite the long lucky streak, in recent decades Boulder, and the Colorado Front Range, have devoted considerable resources to flood mitigation efforts. It will be interesting in the months and years to come to assess the effectiveness of those efforts. Many lessons will no doubt be learned about what might have been done better, but I will be surprised if the many years of planning, investment and structural mitigation did not dramatically reduce the possible impacts of the recent floods.

In the aftermath of this week's Boulder flood some observers are already trying to out-do each other by making bigger and bigger claims of the so-called N-year flood. As might be expected the biggest claims (a 1,000-year event has the record so far!) are made by those who seek to link causality of Colorado disaster to human-caused climate change in a simplistic way (those interested in this topic can have a look at the second fallacy covered in the paper below). There has been better reporting too, such as this from NBC.

Below I provide an excerpt from a 1999 paper of mine titled "Nine Fallacies of Floods" (a title suggested by Mickey Glantz) which takes issue with the common usage of the concept of the so-called "100-year flood." The first "fallacy" in that paper is that "flood frequencies are well understood."

Not only is the assumption that flood frequencies are well-understood a fallacy, but the entire notion of the N-year flood is predicated upon a view of stationarity in the statistics of climate that has come into question in the flood research community (which is related to, but also independent of research on human-caused climate change.) See this paper for a discussion of the ongoing debate.

Here is the full citation:
Pielke, Jr. R. A. 1999. Nine fallacies of floods. Climatic Change 42:413-438.
If anything, in the years since I wrote this paper, my views on the utility of the "100-year flood "concept have become stronger -- it is a great example of an oft-repeated scientific-sounding term that is in many important respects utterly wrong or misleading. In fact, it is not even wrong, perhaps wrongheaded is a better descriptor. However, being both wrong and wrongheaded does qualify the term as useful in the ongoing climate wars. So I guess it is here to stay.

Here is the excerpt:

Fallacy #1: Flood Frequencies are Well Understood

Flood experts use the terms ‘stage’ and ‘discharge’ to refer to the size of a flood (Belt, 1975). A flood stage is the depth of a river at some point and is a function of the amount of water, but also the capacity of a river channel and floodplain and other factors. Hence, upstream and downstream levees and different uses of floodplain land can alter a flood’s stage. A flood discharge refers to the volume of water passing a particular point over a period of time. For example, in 1993 St. Louis experienced ‘the highest stage we’ve ever had, but not the biggest volume’.
We’ve had bigger flows, but the stage was different because the water could flow from bluff to bluff. Now we have communities in the floodplain. Every time you do something on a floodplain, you change the flood relationship. Every time a farmer plants a field or a town puts in a levee, it affects upstream flooding. That’s why you can’t really compare flooding at different times in history (G. R. Dryhouse quoted in Corrigan, 1993).
According to the World Meteorological Organization’s International Glossary of Hydrology, ‘flood frequency’ is defined as ‘the number of times a flood above a given discharge or stage is likely to occur over a given number of years’ (WMO, 1993). In the United States, flood frequencies are central to the operations of the National Flood Insurance Program, which uses the term ‘base flood’ to note ‘that in any given year there is a one percent chance that a flood of that magnitude could be equalled or exceeded’ (FIFMTF, 1992, p. 9-7). The ‘base flood’ is more commonly known as ‘the 100-year flood’ and is ‘probably the most misunderstood floodplain management term’ (FIFMTF, 1992, p. 9-7).

A determination of the probability of inundation for various elevations within a community is based on analysis of peak flows at a point on a particular river or stream. However, ‘there is no procedure or set of procedures that can be adopted which, when rigidly applied to the available data, will accurately define the flood potential of any given watershed’ (USWRC, 1981, p. 1). For many reasons, including limitations on the data record and potential change in climate, ‘risk and uncertainty are inherent in any flood frequency analysis’ (USWRC, 1981, p. 2). Nevertheless, quantification of risk is a fundamental element of flood insurance as well as many aspects of flood-related decision making.

In order to quantify flood risk, in the early 1970s the National Flood Insurance Program adopted the 100 year-flood standard (FIFMTF, 1992, p. 8-2). The standard was adopted in order to standardize comparison of areas of risk between communities. Since that time the concept of the N-year flood has become a common fixture in policy, media, and public discussions of floods. Unfortunately, ‘the general public almost universally does not properly understand the meaning of the term’ (FIFMTF, 1992, p. 9-7). Misconceptions about the meaning of the term creates obstacles to proper understanding of the flood problem and, consequently, the development of effective responses.

The 100-year standard refers to a flood that has a one percent chance of being exceeded in any given year. It does not refer to a flood that occurs ‘once every 100 years’. In fact, for a home in a 100-year flood zone there is a greater than 26% chance that it will see at least one 100-year flood over a period of 30 years (and, similarly, more than a 74% chance over 100 years). The general formula for the cumulative probability of at least one flood of annual probability P is (1−P )^N >= C where N equals the number of years from now, and C is the cumulative probability over period N (P is assumed to be constant and events are independent from year to year). By choosing values for P and C one can compute the number of years that the cumulative probability (C) covers.

The concept and terminology of the ‘100-year floodplain’ was formally adopted by the federal government as a standard for all public agencies in 1977 under Executive Order 11988. In 1982 FEMA reviewed the policy and found that it was being used in the agencies and, lacking a better alternative, concluded that the policy should be retained (FIFMTF, 1992, p. 8-3). However, despite the FEMA review, use of the concept of the 100-year flood is encumbered by a number of logical and practical difficulties (cf. Lord, 1994).

First, there is general confusion among users of the term about what it means. Some use the term to refer to a flood that occurs every 100 years, as did the Midwestern mayor who stated that ‘after the 1965 flood, they told us this wouldn’t happen again for another 100 years’ (IFMRC, 1994, p. 59). Public confusion is widespread: A farmer suffering through Midwest flooding for the second time in three years complained that ‘Two years ago was supposed to be a 100-year flood, and they’re saying this is a 75-year flood, What kind of sense does that make? You’d think they’d get it right’ (Peterson, 1995).

Second, the ‘100-year flood’ is only one of many possible probabilistic measures of an area’s flood risk. For instance, in the part of the floodplain that is demarcated as the ‘100-year floodplain’ it is only the outer edge of that area that is estimated to have an annual probability of flooding of 0.01, yet confusion exists (Myers, 1994). Areas closer to the river have higher probabilities of flooding, e.g., there are areas of a floodplain with a 2% annual chance of flooding (50-year floodplain), 10% annual chance (10-year floodplain), 50% annual chance (2-year floodplain) etc., and similarly, areas farther from the river have lower probabilities of flooding. The ‘100-year floodplain’ is arbitrarily chosen for regulatory reasons and does not reflect anything fundamentally intrinsic to the floodplain.

Third, the ‘100-year floodplain’ is determined based on past flood records and is thus subject to considerable errors with respect to the probabilities of future floods. According to Burkham (1978) errors in determination of the ‘100-year flood’ may be off by as much as 50% of flood depth. Depending on the slope of the flood plain, this could translate into a significant error in terms of distance from the river channel. A FEMA press release notes that ‘in some cases there is a difference of only inches between the 10- and the 100-year flood levels’ (FEMA, 1996). Further, researchers are beginning to realize an ‘upper limit’ on what can be known about flood frequencies due to the lack of available trend data (Bobée and Rasmussen, 1995).

Fourth, the 100-year floodplain is not a natural feature, but rather is defined by scientists and engineers based on the historical record. Consequently, while the ‘100-year floodplain’ is dynamic and subject to redefinition based on new flood events that add to the historical record, the regulatory definition is much more difficult to change. For instance, following two years of major flooding on the Salt River in Phoenix, Arizona, the previously estimated 100-year flood was reduced to a 50-year flood (FIFMTF, 1992, p. 9-7). What happens to the structures in redefined areas? Any changes in climate patterns, especially precipitation, will also modify the expected probabilities of inundation. For example, some areas of the upper Midwest have documented a trend of increasing precipitation this century (Changnon and Kunkel, 1995; Bhowmik et al., 1994). Furthermore, human changes to the river environment, e.g., levees and land use changes, can also alter the hydraulics of floods. Finally, the extensive use of the term ‘100-year flood’ focuses attention on that aspect of flooding, sometimes to the neglect of the area beyond the 100-year flood plain (Myers, 1994).

What can be done? Given the pervasive use of the concept of the ‘100-year flood’ in flood insurance and regulatory decision-making it seems that adoption of an alternative concept is unlikely. Nevertheless, there are a number of steps that can be taken by those who use the concept when dealing with policy makers and the public. First, we need to be more precise with language. The FIFMTF (1992) recommends the phrase ‘one percent annual chance flood’ as a preferred alternative to ‘100-year flood’, ‘base flood’, or ‘one percent flood’. [NOTE: USGS has since made such a change in terminology.] Another alternative is ‘national base flood standard’ which removes reference to probability (Thomas, 1996, personal communication). Second, when communicating with the public and the media, flood experts could take care to convert annual exceedances into annual probabilities. And third, policy documents could rely less on the ‘100-year flood’ to illustrate examples and propose policies, and at the very least explicitly discuss floods of different magnitudes.


  1. There was a town in Maryland near the confluence of the Potomac and Shenendoah rivers called Point of Rocks. In the early to mid 1990's, they had two 500 year floods...in the same calendar year. They had the good sense not to rebuild the town in the same spot after the second time.

  2. Interesting article - I am so sorry what your community is going through and wish your people - both those affected and those that help - all the strength they require to move forward.

    I have just finished a stint working with a group helping our community after a "200 year flood" (otherwise known as "worst in white man's history"). Therefore, say the councils, we can let everyone build back where they were, because surely it won't happen again... Aaargh, eh?

    Your professor would have been a fantastic person, and what a great approach. Unfortunately "progress" doesn't like such voices assisting in their quest, do they?

  3. Hi Roger,

    I am so sorry to read of the tragic flooding in Colorado. I do hope that the missing 500 people are all OK and that the recovery efforts go well.

    Many metrics have their limitations, and that the 1 in "N" year flood has its limitations has long been known, certainly before you wrote about it in 1999. Unfortunately, just as we are stuck with the misnomer "greenhouse effect", so too we will have to live with the 1 in "N" year flood. That does not mean that we should not endeavour to develop and use better metrics.

    Fortunately, you should know that there are other metrics to consider that speak to the prodigious nature of this event. Not to mention the unusual timing when compared to previous severe flooding events. Don't make the mistake of ignoring those.

    I must admit, when you make comments like "However, being both wrong and wrongheaded does qualify the term as useful in the ongoing climate wars", you come across as belittling the current situation.

    In fact, one comes away after reading your opinion piece with the impression that you are trying to downplay the severity and (for want of a better word) uniqueness of this event. That is likely to annoy many of the people who have been less fortunate than you have been.

  4. -3-Albatross

    "one comes away after reading your opinion piece with the impression that you are trying to downplay the severity"

    Thanks for visiting .. while I see on social media and with your comment that with some fanatics the urge to score points in the climate wars is hard to resist.

    At the same time I expect that if you could walk around my community as I have, listened to the roar of Chinook helicopters a few hundred feet over my house for the past few days and had friends, neighbors and colleagues suffer massive damage, you'd know that there is absolutely nothing in this post or elsewhere remotely seeking to downplay the severity of this event.

    So please take your bullsh*t game playing ad homs elsewhere. It is not welcome here and will be deleted (better -- just resist the urge).

    Do comment all you want on the substance of flood frequency analyses and the utility of the concept of the 100-year flood in flood policy or in the climate debate ... Thanks.

  5. -3-Albatross

    A further thought ... if you would really like to express your concern, rather than worrying publicly about my inner motivations, instead please click on the link at the top of this post and open your wallet.


  6. Hi Roger,

    FWIW, I will be contributing $20 to the Red Cross, and if I were there I would be volunteering.

    My concern was that only that this is probably not the appropriate time to be arguing technicalities. People affected by this flooding event have far, far bigger concerns to deal with right right now than your objections to the 1 in "N" year flood. That is all.

  7. -6-Albatross

    "I will be contributing $20 to the Red Cross"

    The Boulder community appreciates it, thanks!

  8. Hi Roger,

    You are welcome, I wish I could afford to donate more.

    You said above "....while I see on social media and with your comment that with some fanatics the urge to score points in the climate wars is hard to resist."

    Such rhetoric is really not helpful. I am truly sorry that you feel that way, but you are misreading the situation. I assure you that I am no "fanatic", nor am I interested in using this as an opportunity for scoring points.

    Hopefully we can leave it at that.

    All the best.

  9. First, good luck to you and everyone who has been affected by this natural disaster. It speaks well of your community's efforts that the loss of property and lives has not been greater.

    Second, perhaps describing this process, and similar (e.g. climate), as chaotic, would enable a better understanding of the limitations inherent to forecasting their development. It wouldn't be as comfortable as employing statistical methods, but it would permit the proper characterization of these phenomena, and respond to them accordingly. This would not preclude the use of statistical methods, but they would constrained to limited time frames, where they are capable of providing detailed guidance for short-term planning.

  10. All ... no piling on Albatross, such comments will be deleted.

    Reminder: The topic is floods, their estimation, frequency and the communication and utility of such concepts in policy and politics. Thanks!

  11. Neither climate or weather are unconstrained. That being said the amounts in the current storms are without precedent, the single day record was 4.80 inches and on Sept 12, 9.08 inches fell. Taking into account that the average rainfall in September is 1.63 inches this has indeed been an unprecedented event.

    The extraordinary amount of precipitation should not be downplayed. So there are two questions. First, is this a move towards a new normal, and second, if so what adaptations are needed in flood control and what will they cost. If n.n. is right and weather and climate are chaotic, then there is no point of doing anything. Flood control projects are long term serious commitments of money and resources, 30-50 years. Third, should policy makers have done more before the storm.

    Best to all in Colorado as they work through the flooding.

  12. 1 in N years also suggests events independent of each other. How likely is it that flooding events tend to cluster? ie: After a series of non-flooding years, the chances are 1 in 100, but after a flooding year the chances of flooding for the following year are much higher?

    Also, doesn't the flood itself tend to change the hydrology of a region?

  13. EliRabett:

    A chaotic process is also bounded, unless there is something to cause a runaway reaction or a sudden change in its direction. The concern should be to properly characterize the processes, and fairly attribute the different modeling techniques we have at our disposal.

    In the long term, the process is chaotic, and our ability to predict its development is severely limited. This is for two reasons: improper or insufficient characterization and an unwieldy system. While in the short term, the processes can be reasonable modeled as probabilistic, and we can use statistical methods to forecast their path.

    So, there is reason to pursue reasonable mitigation activities. There is a reason to develop our understanding, which may forever remain imperfect, of the underlying processes, and the resulting phenomenon. The classification of a process as chaotic does not preclude its utility for planning; but, it does constrain our knowledge to a limited frame. It's the same general limitation under which science operates.

    Human life is itself chaotic, throughout its evolution from conception to death; but, that does not prevent us from pursing reasonable (e.g. justifiable) measures to mitigate risk. Life is an exercise in risk management.

  14. Roger,

    These events seem overly common in practice and not well described using the tables that NOAA uses at http://hdsc.nws.noaa.gov/hdsc/pfds/pfds_map_cont.html?bkmrk=co . For example, if you use the 1976 Big Thompson event (14" in 4 hours), and extrapolate the tables (after transforming), you'll find that such a flood is around a 32,000 year event. You can get similar results for 1997 Spring Creek event in Fort Collins (10" inches in four hours). And of course there is the 1921 Pueblo event which affected the entire front range. And Boulder would also be described as a very low frequency event by these charts (on the order of 0.001/yr). But we know it floods much more frequently, it just hasn't lately. So these large and costly events obviously occur at much higher probabilities than the distribution would indicate.

    Do you have any suggestions on a better probability distribution to use that can capture the effects of these fairly common front range, very large events, yet still give reasonable estimates of more mundane stream flow? Something that can capture the wild tail of this phenomenon?

  15. I just went through the 100 year flood this spring in Calgary along with most of southern Alberta. A small town south of here called "High River" was hit particularly hard. There was billions in damage, but thankfully, not much loss of life. I think three deaths were attributed to the flooding. The best quote I heard was from an old cowboy from High River who said "If this is the 100 year flood, I must be 400 years old!".

  16. First of all, good luck to you and your community in rebuilding after this disaster.

    Thank you for this article. It provides a perspective on the issue, and for me it provides insight into an area I know too little about. It also spurs my interest to find out more. I really appreciate these articles of yours that bring different perspectives to light. In my eyes you do well in providing balanced views, and I thank you for that.