Precipitation Concentration Index

Fig 1. Precipitation Concentration Index (PCI) of the U.S. (using 1991-2020 normals) and Canada (using 1991-2020 monthly averages).

The PCI

How do we quantify the seasonality of precipitation? The short answer is that there is no one satisfactory method. Nevertheless, it is worth trying to get a handle on how precipitation varies throughout the year. A method that I prefer is the use the Precipitation Concentration Index (PCI) (Oliver 1980). The PCI looks at monthly average precipitation over a specified time period (although you can computed it for an individual year) and assesses how uniform the precipitation is. If a station had the exact same average precipitation every month, we would say it is perfectly uniform. If the received all their annual precipitation in a single month, we would say is it the opposite of uniform. 

The PCI was developed to characterize areas with pronounced wet/dry seasons – particularly equatorial monsoon regions. Still, we can apply the calculation to any location with monthly precipitation. The calculation is as follows, take a month's precipitation and square it. Do this for each of the 12 months and add up the total. This is the numerator of the equation. Then, take annual precipitation and square that. This is the denominator of the equation. Now divide the numerator into the denominator and multiply by 100. This gives you the PCI. Fig. 2 shows the formula.

Fig 2. PCI formula.

If a station averaged exactly 5.0" every month of the year, we compute the PCI by squaring 5.0 (5.0^2 = 25.0) and doing this 12 times. When you add all those up you get 300. When you square the 60.0" annual precipitation, you get 3,600. To get the PCI, you solve: 300/3600*100 = 8.333. This is the lowest possible PCI score and indicates a perfectly uniform precipitation distribution.

According to Oliver, a PCI value < 10.0 represents mostly uniform precipitation distribution. A value between 11 and 15 represents moderate precipitation concentration. A value above between 16 and 20 denotes irregular distribution. Values above 20 represent strong irregularity. I sliced and diced these ranges a little to make the map in Fig. 1. Specifically, I used the following categories from most to least uniform: 8.33 to 8.5, 8.5 to 9.0, 9 to 10, 10 to 11, 11 to 15, 15 to 16.7, and 16.7 to 21.8.

As the map shows, the lowest values are from east Texas through Maine. The interpretation of this is that there is not much difference between average monthly precipitation totals. Of course a lot can happen in any given year, but when we aggregate the numbers, there's a lot of similarity between the monthly values. Conversely, areas in southern California have a pronounced wet  season and a pronounced dry season. Several summer months have almost no precipitation at all. Fig. 3 shows the monthly precipitation distribution for the U.S. stations with the lowest and highest PCI values. The PCI computation does not care about the total annual precipitation. It only cares about the distribution across the 12 months compared to it's own annual total.

Fig 3. Highest and lowest PCI values in the U.S. Brewerton Lock 23, NY, has a PCI of 8.37 and Morongo Valley North, CA, has a PCI of 21.76.

Looking at "major" stations only (see Fig. 4), we see that the lowest PCI values are all in the eastern Lower 48 with a primary concentration in the Northeast. For large cities, Charlotte, NC and Boston, MA, have the most uniform precipitation distribution. On the other side of the ledger, nearly all the stations with the highest PCI values are in southern California. A few Alaska stations are also on this list. For large cities, Los Angeles has the least uniform distribution .

Fig 4. Lowest and highest 25 PCI values in the U.S. for major stations. I took some liberty in deciding what was a major station.
References: 

Oliver, J.E. 1980. Monthly Precipitation Distribution: A Comparative Index. Professional Geographer. 32, 300-9.