A General Ensemble Filtering Framework Using Quantiles

• Activity Number: 131 - Methods for Spatial, Temporal, and Spatio-Temporal Data
• Type: Contributed
• Date/Time: Monday, August 9, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Jeffrey Anderson*
• Companies: National Center for Atmospheric Research
• Keywords: Filtering; Ensemble; Data Assimiation; NonGaussian

Abstract

Ensemble Kalman filters are commonly used for data assimilation (data fusion) in earth science applications like numerical weather prediction. These methods fit a normal distribution to the prior ensemble (sample) estimate and use Bayes’ rule with a normal likelihood to generate a sample from a normal posterior. A novel efficient algorithm that allows use of arbitrary continuous priors and likelihoods is presented. The key innovation is to select posterior ensemble members with the same quantiles with respect to the continuous posterior distribution as the prior ensemble had with respect to the prior continuous distribution. This is a generalization of previously documented square root ensemble Kalman filters for normal distributions. It also generalizes non-parametric ensemble filters such as the rank histogram filter. Examples using continuous priors that are gamma, inverse gamma, beta and a sum of normal kernels are presented. These examples are useful for physical variables that are bounded on one or both sides such as the concentration of a pollutant, relative humidity, or fractional sea ice coverage.