The book "Antenna Theory & Design" by Stutzmand & Thiele says that in patch antenna maximum radiation happens perpendicular to the patch (along z=0) with the patch lying in the x-y.

My dilemma: The reason I fail to see the radiation coming out perpendicular (top of patch) to the patch (+z direction) is because of the ground under it. Based on image theory the effective E-field will be confined to space between the patch and the ground. Thus I can only imagine that the fringing field (which decouples when charge is cancelled) is responsible for the field pattern.
Please see the attachment for my field pattern drawing.
 
If the gnd underneath patch didn't exist then I do see how the max radiation would be perpendicular to the middle of the patch on both sides of the patch as in a dipole.

Please help resolve my mis-understanding (somewhere). I appreciate your reading.