So unfortunately all I have to work with is a picture. Is there a simple way to make a shadow look like is moving across a surface? Like have a shadow spread across the expanse of a desert, but without masking and all that business?
What do you mean, "Without masking and all of that business"?
How do you propose creating a shadow?
You could create your shadow by casting a shadow by using 3d layers and lights. You'd have to either animate the light or the layer that's casting the shadow. (Or both.)
You can also use a layer (masked or not) as a track matte for an adjustment layer with levels and/or curves applied (or a black solid).