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The 4D-Var analysis uses the IFS dynamics and physics to create a sequence of states that fits as closely as possible to the available observations.  These states are consistent with the dynamics and physics of the atmosphere, as expressed by the equations of the IFS model.  4D-Var compares the actual observations with that which would be expected at the time and position of the observation given the model fields - it is in effect a short-range forecast that serves to bring information forward from the previous cycle.  The analysis essentially uses data within a time window, currently 09–21UTC for the 12UTC model run; 21–09UTC for the 00UTC model run.  However in practice for the main forecasts of HRES* and ENS the ensemble the data cut-off used (i.e. the last time) is brought back to 15UTC and 03UTC respectively for the 12UTC and 00UTC runs, in order to be able to deliver forecasts to customers in a timely manner (see the continuing sequence of analyses).  All observational data are processed similarly, including radiances from satellites.   Since the introduction of cycle 45r1 in June 2018 a weakly  A weakly coupled sea-ice atmosphere assimilation has been is used in the surface analyses of the HRES* 4Dthe 4D-Var, and in the ensemble of data assimilations (EDA); previous to this .  Before the introduction of cycle 45r1 in June 2018  a remotely-generated sea ice cover analysis (OSTIA) had been used directly.

4D-Var at ECMWF is based on an incremental and iterative approach to minimising a cost function  - in effect minimizing the departure of the final adjusted analysis from the observed values and the last available short range forecast.  This takes place within a set of nested loops.  The inner loop has low spatial resolution (TL255 L137) and produces preliminary low-resolution analysis increments using full linearised physics (except the first inner loop of the EDA).  By iterating forwards and backwards in time the analyses can be adjusted towards the observations and induce consistent adjustments with other variables.  Subsequent loops are at higher resolution (TL319 L137 and TL399 L137) with the same full linearized physics.  This incremental approach provides considerable flexibility in the use of computer resources.

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