Signs of rust in Engine any Ideas
The moisture comes out of the ground and gets trapped under the car and/or tarp.
Ever see farmers that cover the cultivated rows with plastic to keep the plants in moisture? Place some plastic on the ground overnight and in the morning turn it over and see how wet it is.
Never park for more than a week on grass or dirt without putting down at least a tarp.
And as moparhead stated, get a breathable car cover.