2. Concept of DEM Error Propagation into DoD

Background Theory on Error Propagation

Error Propagation Theory Based on Minimum Level of Detection Logic

Representing Propagated Errors as Probabilities

Further Reading on Error Propagation

Application of Error Propagation in GCD 4.0

A simple spatially uniform DEM Error Example

In this example, we specify spatially uniform estimates of error separately for each input DEM and use the GCD to propagate those errors through to calculating a minimum level of detection from which we threshold the DoD.

A simple spatially uniform DEM Error Example, but with Probabilistic Thresholding

In this example, we again specify spatially uniform estimates of error separately for each input DEM and use the GCD to propagate those errors through to the DoD. However, instead of thresholding that DoD based on treating the propagated error as a minimum level of detection, we instead use that propagated error and compare it to the elevation change estimated in the DoD, and calculate a students t score. From this we can estimate the probability that the elevation changes predicted by the DoD are real. It is worth noting, that even with a spatially uniform error estimate, we get spatial variability in the estimate of the probability that changes are real. For thresholding the DoD, the user then specifies a confidence interval (e.g. 95%) that they wish to impose to threshold the DoD using the probability that the change is real. A high confidence interval is conservative, a low confidence interval is liberal.