How are +/- error volumes calculated?

[joewheaton]

A GCD user wrote in an email:

Dear Dr Wheaton,

... For my thesis, I am currently doing a study on the morphological evolution of a dune belt in Ravenna (Northern Adriatic Coast, Italy) using UAV topographic surveys. In doing so, I have utilized the GCD software toolbox in ArcMap.

I am already in the process of interpreting the analysis produced in the models. The description on the xml file has been very helpful in interpreting the results. However, I am not sure how the error volumes have been calculated. I am getting relatively high error values, but I cannot quantify it since I am not sure how it was calculated.

I hope that you can put light on this matter. Thank you very much for your time and for providing an open-source toolbox like GCD. It has been very helpful in my current study.

[joewheaton]

This is a good question. The +/- error volumes are very conservatively estimated with error propagation on a cell-by-cell basis. For every change detection that is done based on error surfaces in the inputs, a properror.tif is calculated. This is nothing more than:
√((Error_{DEM New})^2 + (Error_{DEM Old})^2)
This is just error propagation on a cell by cell basis to get an estimate of propagated vertical error. The error volume is estimated just like change detection values are estimated: by multiplying vertical value (in this case propagated DEM error instead of elevation change) by the cell area, which is just the square of cell resolution.

Cell Error Volume = Cell-Resolution^2 * √((Error_{DEM New})^2 + (Error_{DEM Old})^2)

For the summary tabular statistics, these are simply summed up for erosion cells and deposition cells independently the same way that volumetric estimates of change are. In the video I illustrate what is going on: