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Why does the change in precipitable water not exactly match the sum of moisture convergence and evaporation, minus precipitation?

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Why does the change in precipitable water not exactly match the sum of moisture convergence and evaporation, minus precipitation?

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There are a number of reasons why this does not happen, why the “water budget” cannot be “closed” using the terms mentioned above, and even using all of the NARR fields available. The most obvious reason is the “analysis increment”, change in the total water of the atmospheric column (precipitable water, PWAT) resulting form the 3D-Var analysis step. Note that the analysis increment has been monitored and is obtainable from NARR files, since both PWAT entering the 3D-Var at the end of the 3 hr forecast, and PWAT out of the 3D-Var are available, within fields of the merged files B and A, respectively. Yet other budget terms that have been monitored and are available are water vapor and water condensate increments (WVINC, WCINC) that are made within the precipitation assimilation during the 3-h forecasts in between the consecutive 3D-Var steps. Note that, for example, if the precipitation analysis being assimilated at a grid point shows precipitation, and the model at that location does

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