Measures of Temporal Precipitation Variability

What sort of information about precipitation would a farmer want in order to determine his/her irrigation needs at the farm for a crop that needs, dependably 23 inches, but with no less than 15 inches of rainfall in any year and no more than around 29 inches?

[Another way of putting this is that the farmer wants climate information regarding the natural precipitation in an area, given that his crop needs around 23 inches of rainfall +/- 7 inches, most of the years (70% of the years or so)].

• Average annual (seasonal) rainfall for sure, but what else?
• Extremes (wettest and driest)?
• Frequency of extremes?
• Number of years that the rainfall was less than 15 inches or greater than 29 inches?

Let's examine this logically by pretending we need to get that sort of information to a farmer who lives in a location near a weather station. Say that station records the following annual precipitation amounts over a 10 year period:

1.        21.92

2.        19.25

3.        28.22

4.        11.10

5.        25.36

6.        31.40

7.        18.77

8.        27.43

9.        20.66

10.      30.39

Average Value

Add up the rainfall and divide by the number of years:  23.40"

Measures of Temporal Variability

Basically, these measures yield a number that can be used as an indication of how reliable the average precipitation is as an estimate of how much precipitation would occur in any given year.

Extreme Values

Gives some information about possible range of values:

31.40" - 11.10" = 20.30"

Drawback? Although the average provides some measure of how much rainfall the farmer can expect, and this measure suggests that the local rainfall would suit the farmer's needs, the extreme values suggest that some of the time the farmer would have problems. 11" would not be enough rainfall, and 31" would be too much. Yet, unless the farmer looked at each year's rainfall, he or she would not know how frequently the local rainfall met his or her needs.

Look at it another way. Often times people will use the average rainfall and the high/low extremes as a complete way of characterizing the rainfall of a region. Look at these two graphs, both of which are for places that have an average rainfall of 27.50", with high of 45.00" and a low of 10.00" during the period of record. You can see that despite an identical mean rainfall, and identical high and low extremes, the rainfall climatology of the two places is quite different. Example 1 and Example 2.

Clearly, we need some additional ways of characterizing the rainfall variability.

Average Variation

Determine the "deviation" of each year's rainfall from the average for the list of years above.

1.        1.98

2.        4.15

3.        4.82

4.        12.30

5.        1.96

6.        8.00

7.        4.63

8.        4.03

9.        2.74

10.      6.99

Add those up and divide by the number of years.

51.60"/10 years = 5.16" per year

Drawback? The same problem is evident as with the high and low extremes used as a way of characterizing the temporal variability of rainfall. Let's say that in one year the rainfall varied 51.60" from the average, and then in all of the other years the rainfall was exactly the average. Then the average deviation would still be 5.16" per year.

# Standard Deviation and Coefficient of Variation

A measure of the spread of values that can occur relative to the mean value and can be used to determine how likely a given deviation will occur in any given year. This measure is computed algebraically (not higher math), and can be calculated easily. It is based on the concept of the standard bell curve. The standard deviation gives an estimate of the range of values around the average that occurs around 67% of the cases (nearly 70% of the time, in other words.)

Another way of viewing the standard deviation is by comparing it to the average annual rainfall. Meteorologists do this by computing the Coefficient of Variation. The Coefficient Variation is simply the standard deviation divided by the average annual rainfall.

For San Francisco's average rainfall of 21.79" for its period of record, the standard deviation is 7.63". Dividing 7.63 by 21.79 gives 0.35. In this case, the Coefficient of Variation provides the following useful information: 67% of the time, at San Francisco, rainfall will vary +/- 35% from its long term average.

By contrast, the Coefficient of Variation for the rainfall at Central Park 0.17 (I got that by dividing the standard deviation of Central Park's annual rainfall (7.78") by its annual average (44.53"). This means that 67% of the time at New York, rainfall will vary only +/-17% from its long term average.

The point of this is that the Mediterranean Climate can also be characterized by its high temporal variability of rainfall.

 Station in California (Climate Zone) Coefficients of Variation Klamath (Marine West Coast) 0.24 Eureka (Marine West Coast) 0.27 Fort Bragg (Marine West Coast) 0.29 Chico (Mediterranean) 0.37 San Francisco (Mediterranean) 0.35 Monterey (Mediterranean) 0.37 Spreckels (Mediterranean) 0.39 Santa Barbara (Mediterranean) 0.41 Los Angeles (Mediterranean) 0.47 San Diego (Mediterranean) 0.46

Click on Map At Left To See Station Locations

and is distinguished from other climates that share some of its other characteristics (such as relatively dry summers, and similar mean annual rainfall).

The conclusion to be made is that Central Park's rainfall is more "dependable" than that at San Francisco. In other words, a farmer in New York can more reliably use the average rainfall as an estimate of what might occur in any given year, than a farmer in San Francisco. Also, the rainfall climate of an area with high Coefficients of Variation tends to be characterized by more extremes (more very dry and very wet years alternating).