On the representation error in data assimilation

TLDR

In data assimilation, terms such as representation error, representativity error, forward interpolation error, forward model error, observation‑operator error, aggregation error, and sampling error collectively describe components of observation error. The article aims to unify the terminology used in earth‑science literature, as proposed at a 2014 ESA workshop. The authors review current practice, present a theoretical framework, and illustrate the terminology with examples from satellite data assimilation, ocean reanalysis, and atmospheric chemistry, while discussing how to diagnose and apply representation‑error statistics in modern data‑assimilation systems.

Abstract

Representation, representativity, representativeness error, forward interpolation error, forward model error, observation‐operator error, aggregation error and sampling error are all terms used to refer to components of observation error in the context of data assimilation. This article is an attempt to consolidate the terminology that has been used in the earth sciences literature and was suggested at a European Space Agency workshop held in Reading in April 2014. We review the state of the art and, through examples, motivate the terminology. In addition to a theoretical framework, examples from application areas of satellite data assimilation, ocean reanalysis and atmospheric chemistry data assimilation are provided. Diagnosing representation‐error statistics as well as their use in state‐of‐the‐art data assimilation systems is discussed within a consistent framework.