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
- See pages 250-256 of:
- Lane, S.N., Westaway, R.M. and
Hicks, D.M., 2003. Estimation of erosion and deposition volumes in a
large, gravel-bed, braided river using synoptic remote sensing. Earth
Surface Processes and Landforms, 28(3): 249-271. DOI: 10.1002/esp.483.
- See pages 306-314 of:
J., Langham, J. and Rumsby, B., 2003. Methodological sensitivity of
morphometric estimates of coarse fluvial sediment transport.
Geomorphology, 53(3-4): 299-316. DOI: 10.1016/S0169-555X(02)00320-3
- See pages 78-90 of:
- See page 140 of:
Application of Error Propagation in GCD 4.0
A simple spatially uniform DEM Error Example
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
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.