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 article reviews developments towards assimilating cloud‐ and precipitation‐ affected satellite radiances at operational forecasting centres. Satellite data assimilation is moving beyond the “clear‐sky” approach that discards any observations affected by cloud. Some centres already assimilate cloud‐ and precipitation‐affected radiances operationally and the most popular approach is known as “all‐sky,” which assimilates all observations directly as radiances, whether they are clear, cloudy or precipitating, using models (for both radiative transfer and forecasting) that are capable of simulating cloud and precipitation with sufficient accuracy. Other frameworks are being tried, including the assimilation of humidity retrieved from cloudy observations using Bayesian techniques. Although the all‐sky technique is now proven for assimilation of microwave radiances, it has yet to be demonstrated operationally for infrared radiances, though several centres are getting close. Assimilating frequently available all‐sky infrared observations from geostationary satellites could give particular benefit for short‐range forecasting. More generally, assimilating cloud‐ and precipitation‐affected satellite observations improves forecasts in the medium range globally and can also improve the analysis and shorter‐range forecasting of otherwise poorly observed weather phenomena as diverse as tropical cyclones and wintertime low cloud.

Until January 2013, data from the high‐resolution sounder IASI were assimilated with a diagonal observation‐error covariance matrix within the Met Office 4D‐Var assimilation scheme, assuming no correlation between channels. The errors were inflated to account indirectly for known inter‐channel error correlations. This is sub‐optimal as it artificially down‐weights observations from these instruments. The true nature of these correlations for IASI are estimated here using data from the Met Office 4D‐Var assimilation scheme and a posteriori diagnostics based on analysis and background departures. The diagnosed matrices are symmetrised and reconditioned, to make them suitable for use in the operational assimilation scheme. These matrices have been tested in full assimilation experiments. The results of these experiments show that using the new matrices improves forecast accuracy due to more weight in the assimilation being given to the IASI observations, particularly those from water‐vapour‐sensitive channels.

This article presents coupled data assimilation (DA) activities at the European Centre for Medium‐Range Weather Forecasts (ECMWF). Coupled DA is an essential component of the ECMWF Earth‐system strategy. It aims at providing consistent initial conditions to the coupled atmosphere, land, and ocean forecast model. The article introduces the different DA systems and observing systems for each Earth‐system component. It discusses challenges related to observation consistency, availability, and sustainability across the components. It gives a review of coupling methodologies and presents coupling methods in development at the ECMWF. The current ECMWF system relies on weakly coupled DA approaches between land and atmosphere, between wave and atmosphere, and between ocean and atmosphere. Research on coupled DA has been centred on outer loop coupling developments and evaluation, focused on ocean–atmosphere coupling for reanalysis and for numerical weather prediction. The latest configuration of the ocean–atmosphere outer loop coupling combines weak and outer loop coupling methods. The article discusses the challenges in assimilating surface‐sensitive observations and it presents opportunities that coupled DA offers to enhance the exploitation of interface observations. It presents recent developments on land–atmosphere forward operator coupling and multilayer snow‐emission modelling and shows the potential for coupled radiative transfer modelling at low‐frequency passive microwave. The article discusses ongoing developments of in‐house sea‐surface temperature analysis based on coupled skin temperature assimilation. It presents preliminary results that demonstrate meaningful upper ocean temperature increments when assimilating skin temperature information from four‐dimensional variational assimilation. Coupled assimilation results are illustrated and discussed in the context of several applications related to reanalysis, scatterometer impact on coupled ocean–atmosphere, tropical cyclone, impact of weakly coupled sea‐ice–atmosphere data assimilation as well as land surface coupled DA case studies. These examples illustrate benefits and challenges of coupled DA developments. The article discusses future plans of coupled DA developments in support of ECMWF's Earth‐system 2021–2030 strategy.

Ground‐based GNSS Zenith Total Delay (ZTD) observations have been assimilated into the Met Office numerical weather prediction (NWP) models since 2007, and into the Met Office UKV model since its introduction in 2009. The UKV model is a 1.5 km resolution convective‐scale model and uses a 3D‐Var assimilation system. There is a plan to upgrade the UKV assimilation system from 3D‐Var to 4D‐Var in the near future, giving the opportunity to increase the temporal resolution of ZTDs assimilated. The ZTD observation‐error covariances used operationally are assumed to be uncorrelated in both space and time despite the expectation that ZTDs have temporally and spatially correlated observation errors due to the production method (e.g. batch processing using a sliding window and (time) relative constraints). To assess whether these error correlations should be accounted for in order to use ZTDs at higher temporal resolution, a posteriori diagnostics to estimate the extent of temporal and spatial error correlations in ZTD observations over the UK, BENELUX and Northern France are used. Over two separate month‐long periods, we find that ZTD observations within the same processing batch are correlated, and that correlations persist between different batches to at least 1 h. Spatially, ZTD observations are found to be correlated to a minimum of 62.5 km. We find that the extent of the diagnosed correlation between observations separated in space and time is affected by the value of the relative constraints parameter chosen by the processing centre in the GNSS processing software. The impact of the relative constraints parameter on the diagnosed error variances is greater than that revealed by innovation statistics alone.

Weather centres use a variety of data assimilation schemes to analyze different land variables in their operational forecast systems. Current activities at the European Centre for Medium‐Range Weather Forecasts (ECMWF) are working towards a unified and more consistent land data assimilation system to provide more accurate initial conditions for the atmospheric forecasts. The first step is to replace the current 1D optimal interpolation (1D‐OI) used for first‐layer soil and snow temperature analyses, and integrate multi‐layer soil and first‐layer snow temperature into the ensemble‐based simplified extended Kalman filter (SEKF) currently used for multi‐layer soil moisture. This work focuses on the technical developments and the evaluation of the atmospheric forecast skill of a series of numerical weather prediction experiments to compare different SEKF configurations with the former 1D‐OI over a three‐month summer and winter period. Using the SEKF leads to seasonally varying significant improvements in the 2‐m temperature forecast in the verification against own analyses and to slightly improved results in the validation using independent synoptic observations. This work lays the foundation for integrating additional land variables into the SEKF and investigating stronger land–atmosphere coupling.