Additional Math Pages & Resources

Monday, January 18, 2010

Dry as a bone isn't quite good enough

Do you ever wonder where all our trillions of dollars in taxes go?

The National Oceanic and Atmosphere Administration is a division of the US Department of Commerce. They watch and forecast the weather for the rest of us. They monitor the atmosphere, the oceans and fish, and do lots of research in the water and air. They have some satellites. And they teach us about what they do. In the process the 10 thousand employees of NOAA spend about 4 billion dollars a year.

Keeping track of the weather costs about a billion dollars a year. We get lots of useful data from NOAA. Today as San Diego is facing a severe set of storms, so I'd like to talk about the Palmer Drought Severity Index (PDSI), a tool developed by Wayne Palmer in 1965.


The PDSI describes relative dryness or wetness in the USA - that is, long-term moisture shortfalls or excess. It's not just variations in rain. The index is calculated for hundreds of climatic regions in the United States (see above map). They consider the weekly precipitation total, average temperatures, water capacity of the soil, etc. plus previously-recorded history for the past 78 years.

The PDSI is a primary tool for predicting the scope, severity, and frequency of abnormally dry or wet weather. It can help forecast disasters. It is considered by people concerned with irrigation, reservoir levels and potential forest fires.

The equation for the index was originally derived from studying the monthly temperature and precipitation in 13 instances of extreme drought in western Kansas and central Iowa. Palmer gave a value of -4 for these droughts. He assigned a +4 to extremely wet conditions. The result is 7 categories of wet and dry conditions (as well as decimals in between the whole numbers).

The index is a combination of the current moisture conditions, combined with a fractional value from the most-recently-calculated index. This means the scale includes the effect of duration of the drought or wet spell as well as the intensity. The moisture sum is the product of climate weighting and moisture departure. The weighting factor means that the index can be comparable across various regions - for example, Kansas and Florida.

The moisture departure factor means the difference between water supply and demand. Supply is (1) precipitation plus (2) stored soil moisture. Demand is (1) evaporation, (2) water needed to recharge the soil, and (3) runoff which keeps rivers, lakes, and reservoirs at a normal level.

The duration adjustment to the drought (or wet spell) is determined by calculations based on different historical wet and dry spells. A week of normal or better rainfall is welcome in an area having a long drought but may be only a brief respite and not the end of the drought. We can predict based on decades of experience with weather in that region.

One thing the PDSI doesn't do too well is account for water held in what we Westerners call the snowpack, so other factors need to be used along with the Palmer scale if you are talking about weather in the Sierra Nevada or Rocky Mountains.

Here's the January 2010 rainfall forecast for the continental US. It looks like San Diego will have more than normal rainfall in the next month.

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