graphics - Plot a 2D vector path onto a surface

In my calculus 3 course, we're studying gradients and have a project that takes a combination of 3D Gaussian radial surfaces and a basic parametric path $r(t) = \{x(t),y(t)\}$ to see how the gradient changes and so forth with respect to the coordinates of $r(t)$ on the path. I need to figure out a way to plot the surface and path together. I've got both of them figured out, just can't combine them. Any ideas?

So here's what I have so far: 6 Gaussian radials $\lambda e^{-(\epsilon r)^2}$ where $r=||x-x_i||.$ All six are added up to form a "mountain range". A group of hikers are hiking the path

$$r(t)=(2.5 + 1.8 \sin(4t),2 - 1.2 \cos(4 t))$$

which is just a simple ellipse.

I'm trying to figure out a way to "lay" the path on the surface.

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