Optimal sediment transport for morphodynamic model validation

Optimal sediment transport for morphodynamic model validation

Bosboom, J. (TU Delft Coastal Engineering)
Mol, M. (MIcompany)
Reniers, A.J.H.M. (TU Delft Environmental Fluid Mechanics)
Stive, M.J.F. (TU Delft Coastal Engineering)
de Valk, C. F. (Royal Netherlands Meteorological Institute (KNMI))

2020

Although commonly used for the validation of morphological predictions, point-wise accuracy metrics, such as the root-mean-squared error (RMSE), are not well suited to demonstrate the quality of a high-variability prediction; in the presence of (often inevitable) location errors, the comparison of depth values per grid point tends to favour predictions that underestimate variability. In order to overcome this limitation, this paper presents a novel diagnostic tool that defines the distance between predicted and observed morphological fields in terms of an optimal sediment transport field, which moves the misplaced sediment from the predicted to the observed morphology. This optimal corrective transport field has the “cheapest” quadratic transportation cost and is relatively easily found through a parameter-free and symmetric solution procedure solving an elliptic partial differential equation. Our method, which we named effective transport difference (ETD), is a variation to a partial differential equation approach to the Monge–Kantorovich L² optimal transport problem. As a new error metric, we propose the root-mean-squared transport error (RMSTE) as the root-mean-squared value of the optimal transport field. We illustrate the advantages of the RMSTE for simple 1D and 2D cases as well as for more realistic morphological fields, generated with Delft3D, for an idealized case of a tidal inlet developing from an initially highly schematized geometry. The results show that by accounting for the spatial structure of morphological fields, the RMSTE, as opposed to the RMSE, is able to discriminate between predictions that differ in the misplacement distance of predicted morphological features, and avoids the consistent favouring of the underprediction of morphological variability that the RMSE is prone to.

Effective transport difference
Model accuracy
Model validation
Monge–Kantorovich
Morphodynamic modelling
Optimal transport
Root-mean-squared error
Root-mean-squared transport error

http://resolver.tudelft.nl/uuid:2d312d8b-75c2-4e86-86b0-f7f92ae89471

https://doi.org/10.1016/j.coastaleng.2020.103662

2020-08-06

0378-3839

Coastal Engineering, 158

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2020 J. Bosboom, M. Mol, A.J.H.M. Reniers, M.J.F. Stive, C. F. de Valk