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.

We have developed an ensemble Kalman Filter (EnKF) to estimate 8-day regional surface fluxes of CO₂ from space-borne CO₂ dry-air mole fraction observations (XCO₂) and evaluate the approach using a series of synthetic experiments, in preparation for data from the NASA Orbiting Carbon Observatory (OCO). The 32-day duty cycle of OCO alternates every 16 days between nadir and glint measurements of backscattered solar radiation at short-wave infrared wavelengths. The EnKF uses an ensemble of states to represent the error covariances to estimate 8-day CO₂ surface fluxes over 144 geographical regions. We use a 12×8-day lag window, recognising that XCO₂ measurements include surface flux information from prior time windows. The observation operator that relates surface CO₂ fluxes to atmospheric distributions of XCO₂ includes: a) the GEOS-Chem transport model that relates surface fluxes to global 3-D distributions of CO₂ concentrations, which are sampled at the time and location of OCO measurements that are cloud-free and have aerosol optical depths <0.3; and b) scene-dependent averaging kernels that relate the CO₂ profiles to XCO₂, accounting for differences between nadir and glint measurements, and the associated scene-dependent observation errors. We show that OCO XCO₂ measurements significantly reduce the uncertainties of surface CO₂ flux estimates. Glint measurements are generally better at constraining ocean CO₂ flux estimates. Nadir XCO₂ measurements over the terrestrial tropics are sparse throughout the year because of either clouds or smoke. Glint measurements provide the most effective constraint for estimating tropical terrestrial CO₂ fluxes by accurately sampling fresh continental outflow over neighbouring oceans. We also present results from sensitivity experiments that investigate how flux estimates change with 1) bias and unbiased errors, 2) alternative duty cycles, 3) measurement density and correlations, 4) the spatial resolution of estimated flux estimates, and 5) reducing the length of the lag window and the size of the ensemble. At the revision stage of this manuscript, the OCO instrument failed to reach its orbit after it was launched on 24 February 2009. The EnKF formulation presented here is also applicable to GOSAT measurements of CO₂ and CH₄.

SummarySatellite-based (e.g., Synthetic Aperture Radar [SAR]) water level observations (WLOs) of the floodplain can be sequentially assimilated into a hydrodynamic model to decrease forecast uncertainty. This has the potential to keep the forecast on track, so providing an Earth Observation (EO) based flood forecast system. However, the operational applicability of such a system for floods developed over river networks requires further testing. One of the promising techniques for assimilation in this field is the family of ensemble Kalman (EnKF) filters. These filters use a limited-size ensemble representation of the forecast error covariance matrix. This representation tends to develop spurious correlations as the forecast-assimilation cycle proceeds, which is a further complication for dealing with floods in either urban areas or river junctions in rural environments. Here we evaluate the assimilation of WLOs obtained from a sequence of real SAR overpasses (the X-band COSMO-Skymed constellation) in a case study. We show that a direct application of a global Ensemble Transform Kalman Filter (ETKF) suffers from filter divergence caused by spurious correlations. However, a spatially-based filter localization provides a substantial moderation in the development of the forecast error covariance matrix, directly improving the forecast and also making it possible to further benefit from a simultaneous online inflow error estimation and correction. Additionally, we propose and evaluate a novel along-network metric for filter localization, which is physically-meaningful for the flood over a network problem. Using this metric, we further evaluate the simultaneous estimation of channel friction and spatially-variable channel bathymetry, for which the filter seems able to converge simultaneously to sensible values. Results also indicate that friction is a second order effect in flood inundation models applied to gradually varied flow in large rivers. The study is not conclusive regarding whether in an operational situation the simultaneous estimation of friction and bathymetry helps the current forecast. Overall, the results indicate the feasibility of stand-alone EO-based operational flood forecasting

River-level estimation is a critical task required for the understanding of flood events and is often complicated by the scarcity of available data. Recent studies have proposed to take advantage of large networks of river-camera images to estimate river levels but, currently, the utility of this approach remains limited as it requires a large amount of manual intervention (ground topographic surveys and water image annotation). We have developed an approach using an automated water semantic segmentation method to ease the process of river-level estimation from river-camera images. Our method is based on the application of a transfer learning methodology to deep semantic neural networks designed for water segmentation. Using datasets of image series extracted from four river cameras and manually annotated for the observation of a flood event on the rivers Severn and Avon, UK (21 November–5 December 2012), we show that this algorithm is able to automate the annotation process with an accuracy greater than 91 %. Then, we apply our approach to year-long image series from the same cameras observing the rivers Severn and Avon (from 1 June 2019 to 31 May 2020) and compare the results with nearby river-gauge measurements. Given the high correlation (Pearson's correlation coefficient >0.94) between these results and the river-gauge measurements, it is clear that our approach to automation of the water segmentation on river-camera images could allow for straightforward, inexpensive observation of flood events, especially at ungauged locations.