Deriving a Quantitative Relationship between Model QPF and Probability of Precipitation (PoP)

Given a set of m models, the most definite forecast of probability of precipitation (PoP) is when the most models forecast the most QPF. But which is more definite—a case when eight models out of ten forecast at least .01”, or a case when five models out of the same ten forecast at least .05”?

Each situation of n models (out of m total models) that forecasts at least q QPF has associated with it a history that can be retrieved from the NWS grid database BOIVerify (Barker, 2006).

When only one model forecasts at least .01” and the others forecast zero, BOIVerify might find 50 such cases. Those cases form that situation’s history, and if observations show that measurable rain fell on 6 of those cases the PoP would be 12%.

Other situations may have more “productive” histories. If, as before, eight models out of ten forecast at least .01”, BOIVerify may find 40 such past cases, and if it rained on 24 of them the PoP would be 60%. But if five of those same models also forecast at least .05”, BOIVerify may find a more select history of only 20 cases, and if it rained on 15 of them the PoP would be 75%.

Even though both forecasts came from the same ten models the more definite forecast was the one when five models forecast at least .05”, and that is the one from which the final PoP is chosen, provided there are enough historical cases to be statistically significant. Finding enough cases for a given history can be a serious practical limitation

To apply the ideas systematically in a GFE tool, the tool must first determine how many models actually forecast at least .01” QPF in a given period. The number of models may vary throughout the grid.

Next, the tool searches BOIVerify for all cases when at least that many models forecast at least .01”. The number of occurrences (the history) also may vary throughout the grid.

Wherever at least 20 occurrences are found the tool notes how often measurable rain actually fell (i.e., QPE). This results in a PoP.

The process is then repeated for at least .02” QPF. Wherever the PoP for at least .02” is higher than for at least .01” the higher PoP is used, provided the history for at least .02” has enough members. Then we move up to .03”, and .04”, etc, up to .10”, and use the highest PoP whenever the history has enough members. The finished product is a grid that shows the PoP corresponding to the most definite QPF forecast made by the most models at every grid point, and calibrated to the BOIVerify database.

The article traces the process for an actual forecast in more detail. General verification for many cases is also provided.