Closest point on surface

[jbw9f]

I have a grid of z points from griddata representing a surface.

For an arbitrary coordinate (x,y,z) in space, how might I find the closest point (x,y,z) on the surface z. I need to do this many times and would rather not minimize the distance formula across all points.

Dsearch,tsearch, etc only work on coordinate arrays, not grids. Any other solution thoughts? Is there a simple function I'm missing?

Thanks!