Clark, Curtis. 1993. How dry is a drought? Crossosoma 19(2):37-48.

How Dry is a Drought?

Curtis Clark

Biological Sciences
California State Polytechnic University
Pomona CA 91768

Since 1985, the National Oceanic and Atmospheric Administration (NOAA) has included in each yearly climatic summary of California a "departure map". This map of California shows climatic reporting stations as circles. The size of each circle is roughly proportional to the difference (or departure) between the precipitation of that year and the average precipitation for that station over its history. The circles are black when the yearly total exceeds the average, and white when it is less than the average. Looking at these maps for the drought years 1986–1990, one sees fewer and fewer black circles, and more and more large white ones. Initially, it would seem that these maps provide a good visual characterization of the drought.

However, the maps are misleading, for three reasons. First, they, like the records they summarize, are based on a calendar year, which includes portions of two rainy seasons. Second, the departures are absolute, not relative to the average, so that the circle for a dry desert station with no precipitation in a given year might be smaller than the circle for a rainy mountain locality with a moderate decrease. Third, the figures do not account for the variability of precipitation.

It is well known that precipitation in some regions varies greatly from year to year, and in other regions is more constant. Consider two hypothetical locations, both of which have an average annual precipitation of 500 mm. Location A has 500 mm every year, and location B varies from year to year, with a low of 50 mm and a high of 950 mm. If both locations have 400 mm of rain in a given year, they have the same departure, whether that departure is measured in absolute or relative terms. However, the vegetation at location B is likely to be very different from that of location A, since the plants at location B must be adapted to 50 mm of rain, while those at location A can always expect 500 mm. A year with 400 mm would be ordinary for location B, but it would represent a drought of historic proportions for location A.

A useful way to express variability is the coefficient of variation, which is the standard deviation of a population divided by its mean. In this study, I calculated the coefficient of variation of 22 reporting stations (Table 1) over the period from 1955 to 1990. For convenience, calculations were based on calendar year figures; rainfall season figures must be calculated from monthly totals, and the resulting coefficients do not differ significantly from those calculated by calendar year.


Table 1. Climatic reporting stations used for study of the coefficient of variation.

Alturas

Los Angeles

San Diego

Bakersfield

Mount Wilson

San Francisco

Barstow

Needles

Santa Ana

Bishop

Palm Springs

Santa Barbara

Crescent City

Redding

Santa Monica

Cuyamaca

Riverside

Yosemite

Fresno

Sacramento

 

Indio

Salinas

 

The coefficient of variation correlates with other climatic and geographic measures (Fig. 1). It increases with decreasing precipitation (dry stations are more variable than wet stations), decreasing latitude (stations in the south are more variable than stations in the north); decreasing longitude (stations in the east are more variable than stations in the west), and increasing mean annual temperature (warm stations are more variable than cool stations). This reflects well-known geographic trends in California (Fig. 2).

Comparison of the coefficients of variation shows that there are differences in variability among California climatic reporting stations, but the coefficient of variation itself does not provide a measure of departure from the average. A related measure that does is the standard score or z-score, the absolute departure divided by the standard deviation. A departure expressed as a standard score shows how the precipitation of a given year differs from the mean in terms of the inherent variability of that station.


Fig. 1. Correlation of the coefficient of variation of annual precipitation for 22 California stations with average annual precipitation (mm), latitude (degrees), longitude (degrees), and mean annual temperature (C).


Fig. 2. Coefficient of variation of the sample stations.


Four stations were selected for the calculation of yearly standard scores: Barstow, Crescent City, Mount Wilson, and Santa Monica. Precipitation was determined for years beginning on July 1; this corresponds well with the dry season and is a commonly used starting date for "rainfall years". On the graphs, the first year of a season is labeled, so that "1985" refers to the 1985–1986 rainfall year. The graphs cover the years 1955–1956 through 1989–1990.

The absolute precipitation for Crescent City (Fig. 3, top; gaps in the line indicate gaps in the data) varied from 30 to over 90 inches per year. The year 1976–1977 showed a departure of two and a half standard deviations below the average (Fig. 3, bottom). Beginning in the fall of 1981, there were three years of above-average precipitation, and all but one of the years following were below average. Notice that no above-average year had a standard score of 2.0 or above.


Fig. 3. Crescent City. Yearly precipitation (top), yearly departure measured as standard score (bottom).


Fig. 4. Mount Wilson. Yearly precipitation (top), yearly departure measured as standard score (bottom).


Fig. 5. Santa Monica. Yearly precipitation (top), yearly departure measured as standard score (bottom).


Fig. 6. Barstow. Yearly precipitation (top), yearly departure measured as standard score (bottom).


The absolute precipitation at Mount Wilson ranged from ten inches to over 90 inches during the period (Fig. 4, top). Only four dry years had a standard score of -1.0 or less (Fig 4, bottom), even during the drought of the late 1980s (but note the missing data). Two very wet years exceed a standard score of 2.0, however.

The absolute precipitation at Santa Monica varied between four and 37 inches (Fig. 5, top). Only a single drought year had a standard score less than -1.0, but two wet years exceeded 2.0 (Fig 5, bottom).

Precipitation at Barstow ranged from one inch to just over ten inches (Fig. 6, top). Three drought years had standard scores of less than -1.0, and four wet years reached or exceeded 2.0 (Fig 6, bottom).

It should be apparent that standard scores better reflect wet and dry spells: the absolute departure of a moderately dry year in Crescent City would exceed the total range of precipitation in Barstow. Likewise, 30 inches of precipitation in Crescent City can be seen to be a severe drought. But why is it that of the four stations, only Crescent City had a drought with a standard score less than -2.0?

This is the result of a fundamental property of precipitation: it can never be less than zero. For the southern stations, even no precipitation at all would yield a standard score less than -2.0.

Assuming the data fit a normal distribution (the "bell-shaped curve" of statisticians), one can calculate the probability that a year with a given standard score will occur. For example, a standard score of -2.0 would be expected in about 2% of all years. If we assume a normal distribution (note that this is not always the case), we can calculate the standard score for a year with no precipitation, and then calculate its probability. This tells us for any given station the likelihood of having a year with no precipitation.

When we examine the probability of a totally dry year for the 22 stations examined earlier (Table 2), we see that for some stations the possibility is remote (less than one chance in ten thousand at Crescent City, for example), but for others it is almost routine (seven chances in 100, or 7%, in Indio). This suggests that even years without rain are not unexpected in many southern California locations.

As I mentioned, calculating probabilities only works when the data are normally distributed. Of the four stations examined on a rainfall year basis, Crescent City and Indio have a normal distribution. Santa Monica and Mount Wilson have a lognormal distribution, in which lower yearly totals are more common than higher ones. Lognormal distributions can be adjusted mathematically to yield probabilities just a normal distributions do. That would result in a somewhat different probability of a totally dry year, but it does not change the basic observation that dry years are not always rare.

Table 2. Probability of a year with no precipitation, based on the climatic data from 1955–1990, and assuming normally distributed yearly totals.

Station

Standard score (z)

Probability

Crescent City

-4.98

< 0.0001

Alturas

-3.93

< 0.0001

Redding

-3.30

0.0005

Yosemite

-2.97

0.0015

Sacramento

-2.90

0.0019

Bakersfield

-2.82

0.0024

San Francisco

-2.78

0.0027

Salinas

-2.74

0.0031

Fresno

-2.70

0.0035

San Diego

-2.40

0.0082

Cuyamaca

-2.30

0.0107

Santa Barbara

-2.15

0.0158

Riverside

-2.07

0.0192

Needles

-2.03

0.0212

Santa Ana

-1.96

0.0250

Los Angeles

-1.92

0.0274

Barstow

-1.87

0.0307

Santa Monica

-1.82

0.0344

Bishop

-1.78

0.0375

Mount Wilson

-1.75

0.0401

Palm Springs

-1.57

0.0582

Indio

-1.45

0.0735

Conclusions

Any attempt to characterize the ecological effects of precipitation differences in California should use a rainfall year beginning on July 1. Showing precipitation departures as standard scores would be more informative than showing them as absolute differences. Standard scores are useful in this role even when yearly totals are not normally distributed.

Precipitation is more variable in southern California than in northern California. This undoubtedly affects the vegetation of these regions. It will be worthwhile to compare the vegetation of areas that differ primarily in the variability of their precipitation.

In much of southern California, years with near-zero precipitation are not unlikely. This means that from the plants’ standpoint, a single dry year does not make a drought. Thus, future studies should focus on drought as a multi-year phenomenon. It’s not how dry the drought is, it’s how long it lasts.


This page Copyright © 1993, 1999 by Curtis Clark.