Elevation profiles approximation with polynomials/splines

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enter image description hereI am to approximate natural ground elevation profiles with a mathematical function. Let say the elevation profiles can be approximated with n^2 degree of polynomials. In my case 5th or 6th degree would work quite ok. Then an approximate embankment should be fund which is a good representation of the terrain. My question is, how to mathematically define/find the appropriate embankment function? The same should work for valleys as well.

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