Return Periods for Annual Precipitation

Introduction to Return Periods

Flooding of Crabtree Creek, Raleigh, North Carolina photo by Gary Allen of the News & Observer Publishing Co. in Raleigh

A rescue after the flooding of Crabtree Creek in Raleigh, North Carolina after Hurricane Fran in 1996.
Photo by Gary Allen of the News & Observer Publishing Co. in Raleigh

Return period, also called a recurrence interval, is likely a term you’ve come across, even if it’s currently drawing a blank. A return period is the same as saying “this is a 100-year flood.” By definition, a return period is the likelihood that an event will occur. Thus, a 100-year flood can also be described as a 1 out of 100 event (1/100)….or that there is a 1% chance that this flood will occur each year.

However, a 100-year event does not mean it will only happen every 100 years. (I’m sure many climate scientists wish it was that easy to predict!) It is perfectly, statistically possible to get two 100 year events in back-to-back years.

But, in a changing world, we have to add one more complication to return periods. Most calculated return periods have a stationary mean. As a note, these analysis are done with incredible science practice and rigor and are set using the best available science! However, a stationary mean cannot take into account factors which may be increasing that mean baseline, such as climate change.

Total Annual Precipitation Climate Index

Our historical climate analysis of the near-shore Chesapeake Bay region suggests that the total annual precipitation has been increasing over the last century (Figure 1). The 21-year rolling mean for the HadEX2 from 1901-2010 predicts an increase of 6.75 mm per decade. Additionally, the mean difference from 1981-2010 compared to 1951-1980 is +40 mm (~1.6 inches of precipitation).

Figure 1: The total annual precipitation index

Figure 1: The total annual precipitation index of the near-shore Chesapeake Bay region using the HadEX2 data set.

Return levels for the total annual precipitation can be easily calculated using the extRemes package in R. A return level is how much annual precipitation corresponds to your desired X-year event. For our purposes, I selected a 2-, 5-, 10-, 25-, and 50-year event. I purposely did not include a 100-year event due to the length of our time series (110 years).

Figure 2: Calculated return periods from 1901-2010 for the near-shore Chesapeake Bay.

Figure 2: Calculated return periods from 1901-2010 for the near-shore Chesapeake Bay.

For Chesapeake Bay from 1901-2010 (Figure 2), the 2-year return level for total annual precipitation is 1102.5 mm (43.4 inches), 10-year is 1280.2 mm (50.4 inches), and 50-year is 1384.6 (54.5 inches). The return level for the 50-year total annual precipitation tells us the amount of precipitation which would qualify as a really wet year.

So, which years exceeded the 50-year return period for total annual precipitation? There were 4 years over this 110 year record: 1972, 1975, 1996, and 2002. Note that all 4 events occurred after 1970, thus were all in the more recent past!

Are Return Levels changing?

If we want to investigate if (and how) return periods have changed, a really simple approach is to re-calculate the return levels for 1901-1955 and compare them to the return levels from 1956-2010.

This type of information could be incredible important to the ecosystems within the Chesapeake Bay watershed, such as the marshes. Of course, it is also important since extreme events can cause property damage, asset damage (such as a farmer’s crops), and loss of life. Thus, it is important to understand the probability that a really wet year may occur in order to allow us to better prepare for a changing climate.

Figure 3 shows the difference between a 25-year annual precipitation event in the early 20th century compared to the more recent past. Interestingly, there was not much of a difference in the 2-year return level (only a +0.02 inches). However, for the 10-year return level, there was an increase by +3.09 inches and even greater, an increase of +6.13 inches for the 50-year return level. This analysis suggests that the amount of annual precipitation for many return periods has increased in the last 55 years.

Figure 3: The return levels from 1901-1955 compared to 1956-2010.

Figure 3: The return levels from 1901-1955 compared to 1956-2010.

It also means that the earlier return periods are being exceeded more frequently. For example, the 10-year return period from 1901-1955 is now a 4.743-year event in 1956-2010. Even more extreme, the 50-year event in the earlier time span is now a 7.374 year event. (I was critical of this value, and after some rigorous data checks, it is my current best estimate).

The adjusted 50-year return level would now suggest that 1996 was the only year which exceeded this threshold. As a side note, 1996 was an ‘eventful’ year with major storms hitting the Chesapeake region such as the North American Blizzard (January 6-8) and Hurricane Fran (early September).Picture1

While this is an early work, and over a regional spatial area, it appears that the return levels are increasing, suggesting that annual precipitation is getting more extreme. Of course, my next step would be to assess the confidence intervals of these estimates!


Kari Pohl

About Kari Pohl

I am a post-doctoral researcher at NOAA and the University of Maryland (Center for Environmental Science at Horn Point Laboratory). My work investigates how climate variability and extremes affect the diverse ecosystems in Chesapeake Bay. I received a Ph.D. in oceanography from the University of Rhode Island (2014) and received a B.S. in Environmental Science and a B.A. in Chemistry from Roger Williams University (2009). When I am not busy being a scientist, my hobbies include running, watching (and often yelling at) the Boston Bruins, and taking photos of my cat.
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2 Responses to Return Periods for Annual Precipitation

  1. Kari,
    Thank you for the nice work you have posted on this site. Recently my country was declared a state of disaster due to heavy rains whcih casued severe flooding. When i compared rainfall hstorically, it was the second highest record figure in some areas and the first in some. I am there interested in reproduce the graph of return periods just as you have displayed. Can you please share your R scripts used in your work.
    Thank you

    • Kari Pohl Kari Pohl says:

      Hi Charles,

      Thank you very much!

      I used the extRemes package in R (https://cran.r-project.org/web/packages/extRemes/extRemes.pdf). I used the return.level function to estimate a 2,5,10, 25, and 50 year return period on my annual precipitation time series. This is an extremely helpful package!

      I plan on drafting a post in the future that will investigate this topic further, as well as provide the code for the aesthetics of my plots!

      Thank you, and I hope that helps! Let me know if you come across any issues.

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