  Artificial ensemble inflation is a common technique in ensemble data
assimilation, whereby the ensemble covariance is periodically increased in
order to prevent deviation of the ensemble from the observations and possible
ensemble collapse. This manuscript introduces a new form of covariance
inflation for ensemble data assimilation based upon shadowing ideas from
dynamical systems theory. We present results from a low order nonlinear chaotic
system that supports using shadowing inflation, demonstrating that shadowing
inflation is more robust to parameter tuning than standard multiplicative
covariance inflation, outperforming in observation-sparse scenarios and often
leading to longer forecast shadowing times.
