Non-Rayleigh convection is studied in aquifers, where the lateral variations of the temperature field are caused by the ground surface. Analytical solutions for the stream function, the Darcy velocities and the excess water pressure are found for a confined, rectangular and homogeneous aquifer situated at a given depth. The Darcy velocity field and the excess pressure are also found for an unconfined aquifer with a prescribed fluid potential at the top surface of the aquifer. Approximate solutions for excess pressure and Darcy velocities are found for the unconfined aquifer with a free surface. General estimates for the convective Darcy velocities are derived from these solutions. It is also shown that non-Rayleigh flow is unlikely in an unconfined aquifer.