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The four basic types of assimilation are depicted schematically in Fig2.5.-1.  Compromises between these approaches are possible.  The aim is to assimilate data in a manner which does not produce sudden jumps in analysed values and some sort of continuous assimilation seems preferable.  It is expensive in computing time and a compromise has been adopted with 4D-Var assimilating data observed at various times over several hours. This avoids sudden jumps at in analyses for the forecasts (e.g. 00UTC, 12UTC).  Continuous Assimilation is used during 4D-Var analysis process for the early cut-off analysis. 

Fig2.5.-1: Representation of four basic strategies for data assimilation as a function of time.   Observations are made at different times and arrive at irregular times.  Intermittent assimilation of observations induces step changes in the model analysis (red line) while continuous assimilation of observations gives smoother changes in the model analyses. 

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The analysis process seeks to realistically represent in the model the actual state of the atmosphere.  However, inconsistencies in time and space of the observations mean that this aim will never be actually attained and the best that can be done is to approximate (hopefully closely) the actual state of the atmosphere while maintaining the stability (in the numerical sense) of the model atmosphere both horizontally and vertically.  The assimilation process is carried out by 4D-Var (see below).  In simple terms the previous analysis step has used model processes (e.g. dynamics, radiation, etc) to reach a forecast first guess value at a given location.  This will usually differ from an observation at that location and time. The difference between them is the "departure".  The analysis scheme now adjusts the value at the location towards the observed value while retaining stability in the model atmosphere. This adjustment is the "Analysis Increment".  The magnitude, if large, suggests the model is not capturing the state of the atmosphere well (e.g. a jet is displaced, a trough is sharper, large scale active convection has not been completely captured).  However, a large Analysis Increment may also suggest poor data.  Analysis Increment charts are a powerful tool for identifying areas of uncertainty which might propagate downstream. 

Fig2.5.-2: Schematic of the data assimilation process (from a diagnostic perspective).  All the model forecast parameters (dynamics, radiation, etc.) are used in the model forecast to deliver the first guess forecast (red).  The observations (grey) however will normally differ to a greater or lesser extent from the first guess forecast (red) and the analysis increment (yellow) is evaluated to bring the the evolution more into line with the observations while maintaining model stability.  The resultant value (blue) becomes the first guess for the next analysis.

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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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Fig25.A(left)Fig2.5-3: The ECMWF 4-dimensional data assimilation system determines a correction to the background initial condition (blue line) that leads to an analysis that is somewhere "midway" between background and observations. In simplest terms the analysis is a weighted mean of the background and observations.

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Fig25.B(right)Fig2.5-4: 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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