Satellite-observed microwave radiances provide information on both surface and atmosphere. For operational weather forecasting, information on atmospheric temperature, humidity, cloud and precipitation is directly inferred using all-sky radiance data assimilation. In contrast, information on the surface state, such as sea surface temperature (SST) and sea ice fraction, is typically provided through third-party retrieval products. Scientifically, this is a sub-optimal use of the observations, and practically it has disadvantages such as time delays of more than 48 hours. A better solution is to jointly estimate the surface and atmospheric state from the radiance observations. This has not been possible until now due to incomplete knowledge of the surface state and the radiative transfer that links this to the observed radiances. A new approach based on an empirical state and empirical sea ice surface emissivity model is used here to add sea ice state estimation, including sea ice concentration (SIC), to the European Centre for Medium-range Weather Forecasts atmospheric data assimilation system. The sea ice state is estimated using augmented control variables at the observation locations. The resulting SIC estimates are of good quality and they highlight apparent defects in the existing OCEAN5 sea ice analysis. The SIC estimates can also be used to track giant icebergs, which may provide a novel maritime application for passive microwave radiances. Further, the SIC estimates should be suitable for onward use in coupled ocean-atmosphere data assimilation. There is also increased coverage of microwave observations in the proximity of sea ice, leading to improved atmospheric forecasts out to day 4 in the Southern Ocean.

Satellite microwave radiance observations are strongly sensitive to sea ice, but physical descriptions of the radiative transfer of sea ice and snow are incomplete. Further, the radiative transfer is controlled by poorly-known microstructural properties that vary strongly in time and space. A consequence is that surface-sensitive microwave observations are not assimilated over sea ice areas, and sea ice retrievals use heuristic rather than physical methods. An empirical model for sea ice radiative transfer would be helpful but it cannot be trained using standard machine learning techniques because the inputs are mostly unknown. The solution is to simultaneously train the empirical model and a set of empirical inputs: an “empirical state” method, which draws on both generative machine learning and physical data assimilation methodology. A hybrid physical-empirical network describes the known and unknown physics of sea ice and atmospheric radiative transfer. The network is then trained to fit a year of radiance observations from Advanced Microwave Scanning Radiometer 2 (AMSR2), using the atmospheric profiles, skin temperature and ocean water emissivity taken from a weather forecasting system. This process estimates maps of the daily sea ice concentration while also learning an empirical model for the sea ice emissivity. The model learns to define its own empirical input space along with daily maps of these empirical inputs. These maps represent the otherwise unknown microstructural properties of the sea ice and snow that affect the radiative transfer. This “empirical state” approach could be used to solve many other problems of earth system data assimilation.

We assess the ability of neural network emulators of physical parametrization schemes in numerical weather prediction models to aid in the construction of linearised models required by 4D-Var data assimilation. Neural networks can be differentiated trivially, and so if a physical parametrization scheme can be accurately emulated by a neural network then its tangent-linear and adjoint versions can be obtained with minimal effort, compared with the standard paradigms of manual or automatic differentiation of the model code. Here we demonstrate this idea by emulating the non-orographic gravity wave drag parametrization scheme in an atmospheric model with a neural network, and deriving its tangent-linear and adjoint models. We demonstrate that these neural network-derived tangent-linear and adjoint models not only pass the standard consistency tests but also can be used successfully to do 4D-Var data assimilation. This technique holds the promise of significantly easing maintenance of tangent-linear and adjoint codes in weather forecasting centres, if accurate neural network emulators can be constructed.