Odds of Reaching 100% of Normal Water Year Precipitation

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Drought status is often represented by maps of how much precipitation has fallen in the water year to date (starting October 1), or how that amount differs from normal amounts of precipitation to date. For these products normal is defined as the average precipitation during water years 1981-2010. Up-to-date examples of such maps are presented below:

A somewhat different viewpoint on the development of drought considers how much precipitation has fallen (or not) and how much is likely to fall in coming months, based on climatology. The following are maps of this and previous years’ drought development that explicitly takes both of these aspects into account.

Below uses the same methodology above, but is calculated for various fractions (including 100%) of water year total precipitation.

Below flips the analysis and shows what water year total precipitation percentage has a 50% (and other exceedances) chance of being equaled or exceeded this year.

Odds of Two Water Years Reaching Various Fractions of Normal Precipitation Totals

The above methodology can be applied to time periods spanning multiple water years. The plots below combine the current water year with either the previous or the next water year. The top plots show the probability of reaching 100% (and other exceedances) of normal two year precipitation by the end of the current water year (combining the current and previous water years). The bottom plots show the probability of reaching 100% (and other exceedances) of normal two year precipitation by the end of the next water year (combining the current and next water years).

How the probabilities above were estimated:
At the end of a given month, if we know how much precipitation has fallen to date (in the water year), the amount of precipitation that will be required to close out the water year (on Sept 30) with a water-year total equal to the long-term normal is just that normal amount minus the amount received to date. Thus the odds of reaching normal by the end of the water year are just the odds of precipitation during the remaining of the year equaling or exceeding that remaining amount.

To arrive at the probabilities shown, the precipitation totals for the remaining months of the water year were tabulated in the long-term historical record (WY1948-2017 in these figures) and the number of years in which that precipitation total equaled or exceeded the amount still needed to reach normal were counted. The fraction of years that at least reached that threshold is the probability estimate. The calculation was also made for the probabilities of reaching 75% of normal by end of water year, 125%, etc., for these figures.

[One key simplifying assumption goes into estimating the probabilities this way: The assumption that the amount of precipitation that will fall in the remainder of a water year does not depend on the amount that has already fallen in that water year to date. This assumption was tested (across all climate divisions in California, so far) for each month of the year by correlating historical year-to-date amounts with the remainder-of-the-year amounts, and the resulting correlations were never statistically significantly different from zero.]

Contribution from Dr. M.D. Dettinger, USGS

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