**Summary**

**A hybrid parametrisation for precipitation probability of exceedance
data**

Bureau of Meteorology Research Report

*Precipitation probability of exceedance (PoE) curves are graphs that
represent the odds that rainfall will exceed a given amount on a given day. They
allow users to understand the likelihood of possible rainfall amounts at their
location in a coming period. This is useful for a wide range of users including
agricultural producers and planning authorities. *

*These graphs can be constructed based on historical data or based on
ensemble forecasts. Ensembles are a set of several forecasts that allow for the
odds of different potential outcomes to be investigated, typically the Bureau’s
ensembles are made up of 99 model outputs. Given issues with sampling error,
model uncertainty, measurement error and model error, particularly when sample
size are small, the data is often fit to smooth curves. Fitting these curves
becomes problematic when there are instances of zero precipitation. *

*Researchers
at the Bureau of Meteorology have demonstrated the benefits of using a method
to fit curves even when there are zero values. The method is shown for 556
stations and 23 regions in Australia on timescales from weeks to seasons. The fit
failure rate associated with the PoE curves fitted using this method was 1.51%
for stations and 2.91% for regions. Across locations, the mean error was 0.91%
for forecast data and 1.4% for climate data. This is an accurate method for
most sites, has relatively low computational requirements, and avoids
overfitting while providing an easily interpreted smoothed curve. *