Mean versus Maximum

One of my favorite extreme climate indices is the Rx1day.

Figure 1:

Figure 1: The daily precipitation amounts from the Jug Bay CNERR site. You can plot the meteorological data for any NERR site here.

This index measures the biggest rain or snow event every month. As you might imagine, some months we get huge precipitation events while other months go by with nothing memorable.

To understand how the Chesapeake climate has changed, we want to know: have these biggest monthly events gotten bigger, smaller, or have they stayed the same?

Big precipitation events can be just as important to shallow water ecosystems as they are to you! Heavy rainfall can transport nutrients, sediments (which affects the turbidity), and even pollution (for example, those rainbow-sheen oil slicks you see in parking lots contain organic pollutants).

All of these can have adverse effects on aquatic environments and understanding how Rx1day has changed could be helpful in understanding how to help manage ecosystem health.

Same Data, Different Questions

How you plot data can change what information you can get out of it.

Figure 2: The season Rx1day indices using the mean. So this is the mean between the three biggest month events by season.

Figure 2: The seasonal Rx1day index using the mean. So this is the mean of the three biggest monthly events by season. Note that the top plot is the annual maximum event!

Let me explain this concept using our project!

For organizational reasons, I have been analyzing these monthly extreme climate indices by season. This way, we get 4 figures instead of 12 and gain a better understanding of seasonal changes that could affect ecosystems.

When we aggregate the months into a season, I originally had been taking the mean.

(June+July+August)/3 = summer maximum precipitation “event”

This approach makes perfect sense and tells us how the seasonal mean of intense precipitation events has changed (or in some cases didn’t change).

However, we want to know how extreme precipitation is changing and by taking a seasonal mean, we dampen the magnitude of these events.

Figure 3: The biggest precipitation events in the Rx1day are often hurricanes, such as Irene in 2011.

Figure 3: The biggest precipitation events in the Rx1day index are often hurricanes, such as Irene in the summer of 2011.

For example, take the summer of 2011 in the North Chesapeake. The Rx1day for June was 29 mm, July was 31 mm, and August was 120 mm (That’s hurricane Irene!). So, the summer of 2011 mean is 60 mm. So when we take the mean, that biggest event gets smaller and distributed throughout the season.

In a sense, by taking the seasonal mean, the heavy rainfall from Irene was divided over three months. Perhaps a better way to look at this data would be to take the seasonal maximum (now the summer of 2011 is 120 mm).

As I will stress, the seasonal mean still tells us useful information! It can tell us which season is likely to get more intense precipitation events. But if our goal is to investigate extreme events, perhaps taking a maximum would be better for the questions we have!

The Revised Analysis

This revelation came out during a weekly project meeting. Victoria, Raleigh, Dave, Paula, Jacqueline Tay, and myself hold regular meetings to discuss on-going work…because multiple minds are always better than 1!

Figure 4: The season Rx1day indices using the max. So this is the mean between the three biggest month events by season.

Figure 4: The Rx1day index using the seasonal max.

Now that the Rx1day is plotted by seasonal max, we can see some even clearer historical trends that had been dampened by taking a mean! A few really neat patterns can be observed!

1) All seasons, both North and South, had statistically significant increases.

2) Winter had the lowest seasonal rate of change, but take a look at that variability!

3) The greatest change was observed in the Southern region summer season. (always pay attention to the y-axis scale!)

4) In the spring and summer, there is an increase in “big” events after the ~1990’s.

And much more to come!

Final Thoughts

For this project, the seasonal intensity indices (such as Rx1day) will be plotted and analyzed by seasonal maximum whereas monthly frequency indices (such as the percentage of warm days), will remain plotted by mean!

Concluding advise from an early career scientist: School projects that involved working in groups were often terrible! But in the real-world, group work is not only a necessity, but is one of the best parts of being a working scientist!

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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