Comparability of Storm Recurrence Intervals of Differing Durations 5

[CEPEJack]

Hi everyone -

Today my boss asked which occurs more frequently - a 10-year 12 hour storm? Or a 10-year 24 hour storm? My understanding of the math is that they have the same frequency. However, my gut says something is wrong about this conclusion because it then means that a more "severe" storm has an equal chance of occurring as a less "severe" storm. I've considered several possible lines of thought on this conclusion, which I'd appreciate your input on:

1. It is nonsensical to compare recurrence intervals for storms of differing durations. Recurrence interval comparison is only possible with storms of the same duration. (If true, why?)
2. I am not fully understanding how rainfall data is collected and assigned a certain duration.
3. This is just the way nature works.
4. I am not seeing / am missing something here...

Thanks in advance!

 

[pinkpig]

10-yr 24hr storm is not more severe than 10-yr 12 hr storm. Longer duration storm has less intensity.

Look at IDF curves you will understand this.

 

[Drew08]

First, I don’t think it’s nonsensical to compare the two. For designing a pump-storage system (or just storage assuming pump failure), volume becomes much more important than peak discharge, and duration has to be very carefully selected. Consideration for this case would be based more on operational conditions (e.g., how fast can an emergency pump be activated) than rainfall probability.

Mathematically speaking, the 12-hour depth has an equal probability of occurring as the 24-hour depth. The confusion comes in when you consider that the occurrences of the 12-hour and 24-hour depths aren't mutually exclusive, they could happen at the same time.

Pinkpig is partially right in saying a 24-hour storm has less intensity than a 12-hour storm, but it can also have the same, or even more. In reality, when the 10-year event occurs, it can happen in any combination: 12-hour alone, 12-hour nested in a 24-hour, or a 24-hour alone.

When you ask, “Which is more “severe?” I’d say the 12-hour nested in the 24-hour event (higher peak intensity, and higher total volume). So it may be beneficial to ask, “What is the annual probability of a nested event?” I suppose you could assume that half the 24-hour events have nested 12-hour events, and half don’t. So for a 10-year event, a 24-hour storm with a nested 12-hour storm might actually have a 20-year return period.

This is of course and an over simplification, but I think it makes the point.

 

[beej67]

Let me break it down for you. They occur with the same frequency by their very definition. That's what "10 year" means.

The 10 year 12 hour storm is the worst slug of rain you can expect over 12 hours in any ten year period. The 10 year 24 hour storm is the worst slug of rain you can expect over 24 hours in any ten year period.

Statistically, the 10 year 12 hour storm will have a higher intensity, but less total rainfall. The 10 year 24 hour storm will have lower intensity, but more total rainfall, spread out over the longer duration.

Which storm is "worse" depends on where you are in the watershed. If you have a house on a river such that the Tc of the basin to your house is 12 hours, then you will experience worse flooding from the 10 year 12 hour storm than the 10 year 24 hour storm. While the 24 hour storm might drop more total rain, only 12 hours worth of it is flowing past your house at any given moment.

If you have a house on a river such that the Tc of the basin to your house is 24 hours, then you will experience worse flooding from the 10 year 24 hour storm than the 10 year 12 hour storm. While that 12 hour storm might have been more intense, it quits raining before it gets to your house, so it's spread about the watershed.

Those explanations are simplified, and not 100% correct, but they're good enough to explain to a layman, or a boss who asks such a question. To get any more technical you really need to take a hydrology class or consult a textbook.



Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[jgailla]

beej67,
That's a great description. I usually explain, even to laymen, that a ten year storm is one that has a 10% probability (100=1%, 500=0.2%, etc.) of happening any given year.
That means a ten year storm has about a two-thirds probability of happening in any ten year period.
Many of my friends are math people, so they understand probabilities. I'm not sure a 10% chance has any more meaning than once every ten years to a non-math layman.

 

[beej67]

I teach hydrology at a university in town, so I have a little experience explaining these things. Honestly, I can totally see how some folks might not get these concepts at first. The whole thing is honestly pretty convoluted.

(let's see if anyone gets that joke)

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[LincolnPE]

To be clear these are "exceedance probabilities". That is for the 10 year, there is a 10% chance that a rainfall event of this magnitude or greater can occur.

Both the 10yr 12hr and 100yr 24hr have the same exceedance probability, just their magnitude of their thresholds for exceedance differ.

 

[LincolnPE]

Typos corrected in previous post:

To be clear these are "exceedance probabilities". That is for the 10 year, there is a 10% chance that a rainfall event of this magnitude or greater can occur in any given year.

Both the 10yr-12hr and 10yr-24hr have the same exceedance probability, just the magnitude of their thresholds for exceedance differ.