Abstract 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 L 2 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.

中文翻译：

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用于形态动力学模型验证的最佳沉积物输送

摘要 虽然通常用于验证形态学预测，但逐点精度指标，例如均方根误差 (RMSE)，并不适合证明高变异性预测的质量；在存在（通常不可避免的）位置错误的情况下，每个网格点的深度值的比较倾向于支持低估可变性的预测。为了克服这一限制，本文提出了一种新的诊断工具，它根据最佳沉积物输送场来定义预测和观察到的形态场之间的距离，将错位的沉积物从预测的形态移动到观察到的形态。这种最优的校正输运场具有“最便宜”的二次输运成本，并且通过求解椭圆偏微分方程的无参数对称求解程序相对容易找到。我们的方法，我们命名为有效传输差异 (ETD)，是对 Monge-Kantorovich L 2 最优传输问题的偏微分方程方法的一种变体。作为一种新的误差度量，我们提出均方根传输误差（RMSTE）作为最优传输域的均方根值。我们展示了 RMSTE 在简单的 1D 和 2D 情况下的优势，以及使用 Delft3D 生成的更逼真的形态学场的优势，用于潮汐入口的理想化情况，从最初高度图解的几何形状发展而来。