Observation impact in data assimilation: the effect of non-Gaussian observation error

Abstract

A B S T R A C T Data assimilation methods which avoid the assumption of Gaussian error statistics are being developed for geoscience applications. We investigate how the relaxation of the Gaussian assumption affects the impact observations have within the assimilation process. The effect of non-Gaussian observation error (described by the likelihood) is compared to previously published work studying the effect of a non-Gaussian prior. The observation impact is measured in three ways: the sensitivity of the analysis to the observations, the mutual information, and the relative entropy. These three measures have all been studied in the case of Gaussian data assimilation and, in this case, have a known analytical form. It is shown that the analysis sensitivity can also be derived analytically when at least one of the prior or likelihood is Gaussian. This derivation shows an interesting asymmetry in the relationship between analysis sensitivity and analysis error covariance when the two different sources of non-Gaussian structure are considered (likelihood vs. prior). This is illustrated for a simple scalar case and used to infer the effect of the non-Gaussian structure on mutual information and relative entropy, which are more natural choices of metric in non-Gaussian data assimilation. It is concluded that approximating non-Gaussian error distributions as Gaussian can give significantly erroneous estimates of observation impact. The degree of the error depends not only on the nature of the non-Gaussian structure, but also on the metric used to measure the observation impact and the source of the non-Gaussian structure.

Model Error, Information Barriers, State Estimation and Prediction in Complex Multiscale Systems

“…which depends on the true state u m+1 through (55). In (57), p(v m+1 |u m+1 ) is known as the likelihood of estimating u m+1 given observation v m+1 .…”

“…Another important application of the information-theoretic framework is that it provides a novel and unbiased approach to assess the online data assimilation/filtering and prediction skill in complex multiscale dynamical systems [31,[53][54][55][56][57][58]. The traditional path-wise measurements such as the root-mean-square error and pattern correlation [59,60] are misleading in assessing the model error in both filtering and prediction [31,61].…”

A local particle filter for high-dimensional geophysical systems

“…For the LPF, it is straightforward to generalize to arbitrary non-Gaussian likelihood functions. As an example, we also apply a multivariate Gaussian mixture model (GM 2 ) following Fowler and van Leeuwen (2013) with probability density function (pdf):…”

ERA-Interim/Land: a global land water resources dataset

“…This is expected to provide a fast land surface reanalysis as envisaged within the EU-funded ERA-CLIM project, moreover it can open up new possibilities of considering more advanced data assimilation schemes (e.g. Fowler and van Leeuwen, 2012), especially designed for non-linear systems. The skill of an ERA-Interim/Land variant (with no precipitation readjustment) together with other model-based and remote-sensing datasets for the detection of soil moisture climate trends in the past 30 yr is evaluated in Albergel et al (2013).…”