Odds of Reaching 100% of Normal Precipitation for Water Year 2018 (January Update)
January 8, 2018
Contribution from Dr. M.D. Dettinger, USGS
The odds shown here are the odds of precipitation in the rest of the water year (after December 2017) totaling a large enough amount to bring the water-year total to equal or exceed the percentage of normal listed. “All Yrs” odds based on monthly divisional precipitation totals from water year 1896-2015. Numbers in parenthesis are the corresponding odds if precipitation through December had been precisely normal (1981-2010 baseline).
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How these probabilities 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 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. This simple calculation was performed for a full range of possible starting months (from November thru September) and for a wide range of initial (year-to-date) precipitation conditions. The calculation was also made for the probabilities of reaching 75% of normal by end of water year, 125%, and 150%, to ensure that the resulting tables of probabilities cover almost the full range of situations that will come up in the future.
[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 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, except possibly when the beginning month is March, for which there is a small positive correlation between Oct-Mar and Apr-Sept precipitation historically.]
Contact: Michael Dettinger (USGS)