A poor approximation was used for the humidity diffusion which created spurious moisture sources and sinks. This spurious moisture source/sink is positioned by the surface elevation shows a seasonal cycle. More information about the poor approximation are available as either LaTeX or postscript files.
The spurious moisture source/sink can be expected to
Fortunately the approximation is reasonably good whenever the vertical gradient of q is approximately equal to the vertical gradient of the global average of q; i.e.,
dq d(global ave. q) -- = --------------- d(sigma) d(sigma)
Now q is small (large) in the polar (tropics) regions which is the primary reason for dq/d(sigma) to decrease poleward. This is good news as the average value of dq/d(sigma) lies in the mid-latitudes. Thus, the mid-latitudes are expected to have minimal spurious moisture sources/sinks.
One may expect that the magnitude of the moisture sources/sinks are comparable in the tropics and polar regions. However, the relative amplitude is obviously larger when the air is cold and holds less moisture. This is consistent with our results which were that the effects of the spurious moisture were more visually obvious in the winter over the polar and higher mid-latitudes.
The effects of the spurious moisture source/sinks are impossible to undo exactly. Consider a spurious moisture source into a box. The extra moisture should increase both the local precipitation and the advection of moisture out of the box. (See schematic below.) Determining the spurious precipitation requires knowledge of both the moisture source and the advection.
/---------------\ | | spurious moisture ----> | | ---> spurious moisture advection | | | | \---------------/ | | V spurious precipitation
In the previous paragraph, I did not specify the size of the box. Let's consider an extreme case, 1cm x 1cm x 100km in height. Obviously the bulk of the spurious moisture is advected out of the box before precipitating.
At the other extreme, let the box include the whole atmosphere. In this extreme, the advection term vanishes and the spurious precipitation is approximately balanced by the spurious moisture forcing. In addition, the mean spurious moisture forcing is close to zero as the sinks and sources tend to balance.
One possible method to deal with the spurious moisture forcing is to spatially average the precipitation. If the data is spatially averaged over a large enough "box", the net moisture forcing (Kg/m^2/s) tends to be smaller as you've included both sinks and sources. In addition, the spurious moisture advection is less important for larger "boxes".