Surge tanks vs. rain barrels III - storm intensity

In order to answer questions that I have about how large a surge tank is needed to accommodate a certain number of local storms, we need to know about rainfall intensity.  Intensity tells us how much rain we get in a unit of time.

Intensity has a simple answer when considering the duration of a storm as your time interval.  If a storm lasts T hours and it drops 1" of rain, then 1"/ T is the average rate of rainfall.  However, real storms of consequence don't behave like that.  Typically they start out slowly, have a peak rate of rainfall, and then taper off.  From what I've been able to tell, there are two main ways to estimate storm intensity: Using a model hyetograph or using Intensity Duration Frequency (IDF) graphs.


Fair warning: Once again, I'm in slightly-edited stream-of-consciousness mode as I write.

Hyetograph method
Los Angeles County has a hydrology guide that shows how they model storms for purposes of storm water analysis.  The prototypical storm is presented below in a "unit hyetograph" taken from the 2006 Hydrology Manual and lasts 24 hours (1440 minutes).  "Unit", since the cumulative rainfall (green triangles, left axis) is just 1 (inch, but it could be cm or another unit in our preferred measurement system). "Hyetograph" from the Greek word hyeto meaning rain.  The rainfall in a given increment of time is shown with blue diamonds and read out on the right hand axis in units of per hour* (I'll use inches and inches per hour for the rest of this discussion).  There's an 80-80 rule in play here: 80% of the precipitation has dropped by 80% of the time through the storm.  There's a large amount of statistical data that support this as a reasonable model for the larger storms that come through our area.** 

Here's how I think one uses the unit hyetograph:Take the maximum rainfall of your storm. This number scales the left hand axis. The peak at 80% of elapsed time is right on 0.6, so the maximum rainfall rate in inches per hour is 0.6*the total rainfall in the storm. Elapsed time for the heaviest period of rainfall (between an incremental depth of 0.3, through the peak at 0.6 and back down to 0.3) is about 15 minutes, indicating the timing of cloudburst activity.  Using some estimation, I determined that within this time period about 11% of the total rainfall in the storm occurs.

So for the 24 hour storm of D total depth, 0.6D / hour is the maximum rate of rainfall, and in the 15 minutes of most intense rainfall, we accumulate 0.11D.

There's one more factor that's not captured in the unit hyetograph, and that is a geographic factor that scales your local rainfall against the rest of your region. Where I live it's slightly less than 1, but I'll ignore it going forward.  I just wanted to acknowledge that it exists. 

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* After some labor, I determined that the right hand axis units are given in "per hour".  I wish all graphs came with a requirement to show their units.  If you are using inches to measure total rainfall, then it would be inches/hour.  If you are using centimeters, then cm/hour, and so forth. 

** "An analysis of the hourly distribution of large historical 24-hour events showed rainfall intensities increasing during the first 70 to 90 percent of the period and decreasing for the remaining time. Approximately 80 percent of the total 24-hour rainfall occurs within the same 70 to 90 percent of the period."


Intensity, Duration, Frequency (IDF) graph
An IDF graph for the LA area is presented below.

Here's an example of how I think the graph is interpreted: A storm containing within it a 60 minute interval with a sustained rainfall rate of 0.6" per hour can be expected to occur every 2 years.  Every 100 years a sustained intensity of 1.5" per hour during a storm event is expected.  As indicated in the caption, the analysis period for this table is 1903 to 1950, so these values might change in the face of climate change, but they offer a good starting point.

The shortest duration, lowest intensity rainfall for which data are presented is 5 minutes at about 2" per hour, which recurs every two years.

Let's see if we can use this information to assess how good a surge tank of size X really is.