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Z error as a function of curvature and slope

Contours on graphs enclose 99%, 95%, 90%, 75%, 50%, 25%, and 10% of data. 95 and 50 percentile contours are red.
Heavy black lines are RMS y for each value of x.

Correlation of relative Z error with local slope

Click on images for close-ups

Correlation of relative Z error with local curvature

Correlation of local slope and local curvature

Curvature values are those reported by
ArcInfo CURVATURE command. From the
ArcInfo documentation:

CURVATURE is the second derivative of the
surface (i.e., the slope of the slope), calculated as

Curvature = -2(D + E) * 100

Coefficients D and E are estimated by fitting the function
Z = Ax²y² + Bx²y + Cxy² + Dx² + Ey² + Fxy + Gx + Hy + I
to the values in a 3x3 window