I know that in the data assimilation stage in a reanalysis, it will add a moisture increment term to the atmosphere water budget to reconcile with the observations of humidity. 

Is there also a heating increment term in the similar manner in reanalyses (I'm particularly interested in ERA-I and the JRA ones, if this is not a universal feature)? If there is, what kind of observations are used to quantify this term?

Thanks in advance.

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