On Google Maps and various other mapping programs, one can see contour lines that correspond to elevation. Sometimes these contour lines are concentric corresponding to a mountain.
My question is what would be the most suitable function to represent such data? I thought the simplest choice would be multiple Gaussian "bumps" placed additively on a map; whose composition would define a certain map? Are there any other functional representation methods that could give this output?
My next goal would be fitting such function to a set of elevation data collected on a grid.
This is a huge question...
It depends on the precision you'd like and on the kind of input data you have.
For discrete methods, you can use Delaunay triangulation. See for example Delaunay Triangulation Algorithm and Application to Terrain Generation. You have commercial packages like https://www.geo-media.com/solutions/logiciel-covadis/modele-numerique-de-terrain.
You also have continuous methods that can be based on spline surfaces.