A Multiresolution Ensemble Kalman Filter using Wavelet Decomposition

摘要

We present a method of using classical wavelet based multiresolution analysisto separate scales in model and observations during data assimilation with theensemble Kalman filter. In many applications, the underlying physics of aphenomena involve the interaction of features at multiple scales. Blending ofobservational and model error across scales can result in large forecastinaccuracies since large errors at one scale are interpreted as inexact data atall scales. Our method uses a transformation of the observation operator inorder to separate the information from different scales of the observations.This naturally induces a transformation of the observation covariance and weput forward several algorithms to efficiently compute the transformedcovariance. Another advantage of our multiresolution ensemble Kalman filter isthat scales can be weighted independently to adjust each scale's effect on theforecast. To demonstrate feasibility we present applications to a onedimensional Kuramoto-Sivashinsky (K-S) model with scale dependent observationnoise and an application involving the forecasting of solar photospheric flux.The latter example demonstrates the multiresolution ensemble Kalman filter'sability to account for scale dependent model error. Modeling of photosphericmagnetic flux transport is accomplished by the Air Force Data AssimilativePhotospheric Transport (ADAPT) model.