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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. 

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