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I have calculated curvature using ArcGIS (curvature) and SAGA (Slope, Aspect, Curvature; based on 9 parameter 2nd order polynom (Zevenbergen & Thorne 1987) method), however, the output rasters are not the same.

I've done some research and now I understand how curvature works in ArcGIS: http://pro.arcgis.com/en/pro-app/tool-reference/spatial-analyst/how-curvature-works.htm

But it's still a mystery to me how SAGA calculates curvature.

Which formula is used?

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I've come across similar questions here and here but none have provide responses to what you are looking for.

However, I did find this question here that yielded a link which provides a module library containing the formula and additional details. Plus this academic peer-reviewed paper that delves into SAGA and a use case study.

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