Optimal experiment design for a bottom friction parameter estimation problem

Abstract

Calibration with respect to a bottom friction parameter is standard practice within numerical coastal ocean modelling. However, when this parameter is assumed to vary spatially, any calibration approach must address the issue of overfitting. In this work, we derive calibration problems in which the control parameters can be directly constrained by available observations, without overfitting. This is achieved by carefully selecting the ‘experiment design’, which in general encompasses both the observation strategy, and the choice of control parameters (i.e. the spatial variation of the friction field). In this work we focus on the latter, utilising existing observations available within our case study regions. We adapt a technique from the optimal experiment design (OED) literature, utilising model sensitivities computed via an adjoint-capable numerical shallow water model, Thetis. The OED method uses the model sensitivity to estimate the covariance of the estimated parameters corresponding to a given experiment design, without solving the corresponding parameter estimation problem. This facilitates the exploration of a large number of such experiment designs, to find the design producing the tightest parameter constraints. We take the Bristol Channel as a primary case study, using tide gauge data to estimate friction parameters corresponding to a piecewise-constant field. We first demonstrate that the OED framework produces reliable estimates of the parameter covariance, by comparison with results from a Bayesian inference algorithm. We subsequently demonstrate that solving an ‘optimal’ calibration problem leads to good model performance against both calibration and validation data, thus avoiding overfitting.

An empirical formula of bottom friction coefficient with a dependence on the current speed for the tidal models

“…Gad et al (2013) simulated sediment transport near the channel at the entrance of the harbor with different BFCs considered by defining two different Manning's n coefficients for shallow and deep water. Relying on the sedimentological observations, the spatially varying BFC was represented as a segmented constant field based on the distribution of sediment types observed in different locations (Warder and Piggott, 2022). Similarly, Mackie et al (2021) applied Manning's n coefficients obtained from sedimentological observations to the model of Irish Sea.…”