Ensemble transform Kalman filter (ETKF) extensions for near-bound variables: Results from simple aerosol data assimilation experiments

Traditional data assimilation (DA) methods approximate the error distributions using Gaussian probability density functions (PDFs). However, the error distributions of some variables, such as clouds, precipitation, and aerosols, could be better approximated by gamma and inverse-gamma PDFs. For such bounded variables, the error standard deviation will likely increase with the distance of the unknown true value from its bound. To properly include these error distributions, a previous study by C. Bishop invented a method called the GIG filter, which is based on gamma and inverse-gamma distributions. We compared the performance of this new method and the traditional DA method with cycled DA experiments using a new tracer model based on the Lorenz-96 model. The GIG filter's performance is better for assimilating near-bound variables in our experiments.