A quantile-conserving ensemble filter framework. Part III: Data assimilation for mixed distributions with application to a low-order tracer advection model

The quantile-conserving ensemble filter framework is extended to explicitly deal with discrete or mixed distributions. An example is given using bounded normal rank histogram probability distributions applied to observing system simulation experiments in a low-order tracer advection model. Analyses of tracer concentration and tracer source are shown to be improved when using the extended methods.

A key feature of the resulting ensembles is that there can be ensemble members with duplicate values. An extension of the rank histogram diagnostic method to deal with potential duplicates shows that the ensemble distributions from the extended assimilation methods are more consistent with the truth.