Adaptive Covariance Inflation in a Multi-Resolution Assimilation Scheme

Abstract:

When forecasts are performed using modern data assimilation methods observation and model error can be scale
dependent. During data assimilation the blending of error across scales can result in model divergence since large
errors at one scale can be propagated across scales during the analysis step. Wavelet based multi-resolution analysis
can be used to separate scales in model and observations during the application of an ensemble Kalman filter. However,
this separation is done at the cost of implementing an ensemble Kalman filter at each scale. This presents problems
when tuning the covariance inflation parameter at each scale. We present a method to adaptively tune a scale dependent
covariance inflation vector based on balancing the covariance of the innovation and the covariance of observations of
the ensemble. Our methods are demonstrated on a one dimensional Kuramoto-Sivashinsky (K-S) model known to
demonstrate non-linear interactions between scales.