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.

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 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.

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.

Land surfaces are characterised by strong heterogeneities of soil texture, orography, land cover, soil moisture, snow, and other variables. The complexity of the surface properties is very challenging to represent accurately in radiative transfer models, which have a limited reliability over land, especially for observations such as given. This has resulted in difficulties in assimilating land-surface related satellite observations in numerical weather prediction models. Simple statistical relationships between satellite observations and surface variables have therefore been considered in the last 20 years. In this study, we propose to compare two such approaches: cumulative distribution function (CDF)-matching (used as a normalisation and an inversion technique) and neural network (NN) methods. CDF-matching finds a simple monovariate relationship at the local scale and is very dependent on the land-surface model (LSM) on which it is calibrated. NNs are global multivariate models able to exploit auxiliary information and the synergy of multiple instruments, but the solution is global and no local characteristics constrain the solution. One of these two methods will be better suited, depending on the application-in particular the simplicity of the satellite/variable relationship. We illustrate these concepts here using Advanced SCATerometer (ASCAT) observations for soil moisture (SM) retrieval in an assimilation context. The two approaches are compared and combined. We also compare the more traditional inversion scheme and forward modelling, which could be attractive for assimilation purposes. We show that, in the context of ASCAT, the inversion approach seems better suited than the forward modelling.We also show that it is possible to combine the global model obtained using the NN and the localised information of the LSM offered by CDF-matching.