The Effective Transport Difference: A New Concept for Morphodynamic Model Validation

In this study, an improved error metric for morphodynamic models is introduced. Current error metrics, like the classical (Root) Mean Squared Error (RMSE), assume that predictions can be properly validated against observations by regarding the point-wise difference in bed level. This analysis inherently has the problem that phase differences of bottom features are not recognized, such that a misplaced feature is penalised twice, the so called double penalty effect. To reduce the double penalty effect, Bosboom and Reniers (2014) formulated errors metrics based on an optimal smooth displacement field between predictions and observations. Since the employed image warping technique moves pixels rather than sand, sediment continuity is not guaranteed. To overcome this limitation, this study presents an error metric based on the effective (net) sediment transport difference between prediction and observation including a recipe to compute it: the Root Mean Squared Transport Error (RMSTE). This transport difference is minimised by its 2-norm (not 1-norm) for computational efficiency. Intuitively, the RMSTE can be interpreted as a measure for the amount of work to be performed to correct the sediment displacements between prediction and observation. For predictions with equal RMSE, the highest RMSTE is awarded to the one with bed level differences with the largest wave lengths in the sense of Fourier components. This study presents case studies showing a gradual response of the RMSTE to increasing displacement of features. The double penalty effect does not occur if the distance to the boundaries is large in comparison to the feature displacement. Further research should point out if the double penalty effect occurs with real model studies and leads to counter-intuitive behaviour of the RMSTE. The transport difference field and displacement field provide opportunity for a more insightful visual comparison of prediction and observation. Filtering on displacement magnitudes may be useful in subsequent research to asses model skill at smaller scales.Hydraulic Engineering & Water Resources Management (double degree TUD/NUS)Hydraulic EngineeringCivil Engineering and Geoscience