Inferred variables in data assimilation: quantifying sensitivity to inaccurate error statistics

The ability of data assimilation systems to infer unobserved variables has brought major benefits to atmospheric and oceanographic sciences. Information is transferred from observations to unobserved variables in two ways: through the temporal evolution of the predictive equations (either a forecast model or its adjoint) or through an error covariance matrix (or a parametrized approximation to the error covariance). Here, it is found that high frequency information tends to flow through the former route, low frequency through the latter. It is also noted that using the Kalman Filter analysis to estimate the correlation between the observed and unobserved variables can lead to a biased result because of an error correlation: this error correlation is absent when the Kalman Smoother is used.