## 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:
- Brasington,
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:
- Chapter 4 of Wheaton JM. 2008. Uncertainty in Morphological Sediment Budgeting of Rivers. Unpublished PhD Thesis, University of Southampton, Southampton, 412 pp.
- See page 140 of:
- Wheaton JM, Brasington J, Darby SE and Sear D. 2010. Accounting for Uncertainty in DEMs from Repeat Topographic Surveys: Improved Sediment Budgets. Earth Surface Processes and Landforms. 35 (2): 136-156. DOI: 10.1002/esp.1886.
## Application of Error Propagation in GCD 4.0## A simple spatially uniform DEM Error ExampleIn 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 ThresholdingIn 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. |

Downloads > Older Versions > GCD 4.0 > GCD 4 Help > 2. Video Tutorials > D. Types of DoD Analyses >