Using the Precipitation Attribution Distance for localized verification and in a global domain

Precipitation is one of the most important meteorological parameters and is notoriously difficult to measure, predict, and also to verify. Distance measures are one of the five classes of spatial verification metrics that try to address the problems of traditionally used non-spatial methods (which only compare values at collocated grid points). Distance measures provide the results in terms of distance or displacement between the precipitation in the forecast and observation fields. Recently we developed a new distance measure, called the Precipitation Attribution Distance (PAD), that is based on a random nearest-neighbor attribution concept - it works by sequentially attributing randomly selected precipitation in one field to the closest precipitation in the other. Here we tried to adapt the PAD to provide localized verification information and take into account the spherical geometry of the Earth. Namely, most distance measures only provide a single estimate of the distance/displacement of precipitation in the forecasts, representing the whole domain. In the real world, in a large domain encompassing multiple geographical regions with different climatological characteristics, the typical displacement errors will likely differ in each individual region, so identifying localized estimates of errors would be more meaningful. Many spatial verification methods also have a hard time dealing with global domains. It is either hard to use them in such a way to properly account for the spherical geometry of a global domain, or the computation time in spherical geometry increases so much that it makes them difficult to be used. Luckily PAD can be adapted to provide localized verification information and can also be modified for use in a global domain without a significant increase in computation time. We analyzed the behavior of the adapted metric on various idealized and real-world examples, which show that it provides meaningful localized verification results and properly accounts for the spherical geometry of the Earth in a global domain.