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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 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.  A weakly coupled sea-ice atmosphere assimilation is used in the surface analyses of the 4D-Var, and in the ensemble of data assimilations (EDA).  Before the introduction of cycle 45r1 in June 2018  a remotely-generated sea ice cover analysis (OSTIA) had been used directly.

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To estimate the flow-dependent uncertainty, a set of 3-hour forecasts, valid at the start of the 4D-Var time-window, is computed from 25 perturbed, equally likely analyses. Small variations are imposed on the observations and the sea surface temperature to reflect uncertainties, and also within the error parameterisation to cope with uncertainties in the forecast evolution.  The perturbations produced using this Ensemble of Data Assimilations(EDA) are also used for the construction of the perturbations in the forecast ensemble.

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Fig2.5.1B(right): Each observation has an error (instrumental, representativeness, etc) and error within the IFS forecast models is also taken into account.  A way to simulate both these effects is to run an Ensemble of Data Assimilation (EDA). These are shown in green.

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Suppose a forecaster wants to create a sequence of manually analysed hourly synoptic charts for their region, which evolve smoothly, continuously and realistically from one time to the next, throughout.  To achieve this one approach would be to draw up one chart, using all available data, surface observations, imagery etc, then another for a subsequent time in the same way. Then the forecaster might go back to the first chart, rub something out and re-draw it in a rather different fashion, that still fits the available observations reasonably well, but  that allows the next chart to follow on better.  Then they might draw up other charts for other times, and repeat this process many times, rubbing out and re-drawing, probably all of the charts in some way or other, to achieve the final goal of sensible continuity.  Each time a chart is readjusted the changes needed will become smaller and smaller, until finally the forecaster is happy that they have a full and consistent sequence.  This is the forecaster's equivalent of 4D-Var.  Of course in 4D-Var there is the additional constraint of full vertical consistency also, though in the forecaster world soundings and imagery may indeed be contributing in an analogous way.

Meanwhile the Ensemble of Data Assimilation (EDA) could be thought of as being equivalent to the above process, but activated several times producing slightly different smooth and continuous but equally probable sequences.  Where there are lots of observations the several sequences might end up almost the same, but where data is sparse one could end up with much more variability between sequences.  And where there is large dynamic instability (e.g. a developing frontal wave rather than the centre of an anticyclone) this 'spread' might be even greater.  In the real EDA this is essentially also what happens; more spread is found amongst members in data sparse areas and when there is larger innate uncertainty in actual atmospheric developments.

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• Read more on 4D-Var.
• Read more on the use of EDA in 4D-Var.
• Read more on data assimilation and interpolation of data.
• Watch a webinar on Data assimilation and 4D-Var (30sec delay).

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