No 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.

This paper is a continuation of earlier research in which a simple inversion scheme was given for inverse scattering problems in the resonance region which is easy to implement and is relatively independent of the geometry and physical properties of the scatterer. The purpose of the paper is to give new and improved theorems establishing the mathematical basis of this method and to show how noisy data can be treated using Morozov's discrepancy principle where the regularization parameter is a function of an auxiliary parameter appearing in the inversion scheme.

An ensemble Kalman filter for convective-scale data assimilation (KENDA) has been developed for the COnsortium for Small-scale MOdelling (COSMO) model. The KENDA system comprises a local ensemble transform Kalman filter (LETKF) and a deterministic analysis based on the Kalman gain for the analysis ensemble mean. The KENDA software suite includes tools for adaptive localization, multiplicative covariance inflation, relaxation to prior perturbations and adaptive observation errors. In the version introduced here, conventional data (radiosonde, aircraft, wind profiler, surface station data) are assimilated. Latent heat nudging of radar precipitation has also been added to the KENDA system to be applied to the deterministic analysis only or additionally to all ensemble members. The performance of different system components is investigated in a quasi-operational setting using a basic cycling environment (BACY) for a period of six days with 24 h forecasts. For this period and an additional 28 day period, deterministic KENDA forecasts are compared with forecasts based on the observation nudging data assimilation scheme, which is currently operational at the German Weather Service (Deutscher Wetterdienst, DWD). For our experiments, lateral boundary conditions for the regional model are given by a global ensemble Kalman filter for the ICOsahedral Nonhydrostatic (ICON) model. The performance of the KENDA system proves overall to be superior to the forecast quality of the operational nudging scheme, in particular with regard to precipitation. Latent heat nudging improves precipitation forecasts in both systems and has slightly more benefit in combination with the LETKF than with observation nudging.