Sep 17 2007
US Composite Spring Precipitation Data
Unlike many geophysical data, precipitation is not normally distributed about a mean value. A gamma distribution fits the data much better than a Gaussian distribution.
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α is called the shape parameter and β is the inverse of the scale parameter. The larger α is, the more the distribution resembles the Gaussian distribution. The closer β is to zero, the more spread out the distribution is. That means that a gamma distribution with a small β is highly skewed. Below is a map of the inverse scale parameter (β) plotted for the US and Mexico during the years 1950-2000 for only the spring months: March, April, and May.
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Notice that β varies widely across the US and Mexico. In the case of precipitation, a small β means that there are many years when the area gets little to no precipitation, but once in a while they receive a large amount during the spring. Areas such as central California have a large β and thus have a fairly normal distribution of rainfall from year to year.
But this plot doesn’t actually tell us that much. We can’t compare one area of the country to another because the means for these areas are so different. A drought in Chicago wouldn’t necessarily be a drought in Phoenix. In order to compare areas with widely differing rainfall amounts, the standardized precipitation index was developed.
The nice thing about the SPI is that it can be computed on different time scales. Here’s a 12-month SPI compared to a 9-month SPI. In this case, the 12- and 9-month SPI maps are extremely similar. There has been a drought in the West and the Southeast, while the Central and Northeast portions of the country have had a wet year.
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2 Responses to “US Composite Spring Precipitation Data”
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Oh lordy. “A gamma distribution fits the data much better than a Gaussian distribution.” …
Well there goes your popular audience (ie me).
A Gaussian distribution is the “bell curve”. It is symmetric about its mean. Several specific gamma distributions can be seen here. Notice the peak is not in the middle (especially for the green, red, and blue curves). If there is a dataset that is skewed, meaning that the mean is not the median (the middle value), then a distribution other than the Gaussian must be used. For rainfall, the gamma distribution works nicely.