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Model Data Assimilation, 4D-Var

The four-dimensional variational analysis (4D-Var) system uses an optimisation procedure whereby the initial condition is adjusted to obtain an optimal fit through all the observations in the assimilation time window and at the same time tries to stay as close as possible to the first guess.  4D-Var uses the concept of a continuous feedback between observations and IFS model data analysis.  The impact of the observations is determined by three considerations:

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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.

Analogies to 4D-Var and the EDA

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.

Additional Sources of Information

(Note: In older material there may be references to issues that have subsequently been addressed)

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