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.