Optimal experiment design for bottom friction parameter estimation

It is common practice within numerical coastal ocean modelling to perform model calibration with respect to a bottom friction parameter. While many modelling studies employ a spatially uniform coefficient, within the parameter estimation literature the coefficient is typically taken to be spatially (or even temporally) varying. A parameter estimation experiment requires an appropriate set of observations, and also the selection of an appropriate parameter space which captures the spatial variability of the bottom friction parameter. In regions such as the Bristol Channel, which is used as a case study within this work, observation data is relatively abundant; here we use observations of M2 and S2 harmonic amplitudes and phases at 20 locations within the Channel. However, as is typical within friction parameter estimation problems, there is no obvious constraint on the spatial variation of the friction coefficient. Here, we define the parameter estimation ‘experiment design’ as the mapping from a small number of friction parameters onto the model domain. We propose a robust method for the appropriate selection of a low-dimensional experiment design, utilising an optimal experiment design (OED) technique via construction of the Fisher Information Matrix. The objective is to identify the experiment design resulting in the tightest possible constraints on the unknown parameters, given the available observation data. We construct the Fisher Information Matrix via the use of an adjoint shallow water numerical model, Thetis, and perform a variant of D-optimal design to find the optimal experiment design from within two a priori choices of design space. These are based on splitting the model domain either by simple slices across the channel, or by the type of sediment found on the sea bed. We first validate the OED framework by utilising a Bayesian inference algorithm to perform parameter estimation using a selection of experiment designs, which confirms that the OED framework offers a good estimate of the true parameter uncertainty resulting from the use of a given experiment design. An exploration of the full space of experiment designs shows that up to three Manning’s n coefficient values can be estimated from the observation data to within an uncertainty of approximately 0.001 s m−1/3, but that the experiment design is highly influential in achieving this threshold, thus demonstrating the value of our approach as a preliminary step in a parameter estimation study. We also investigate the sensitivity of the achievable parameter uncertainty to the availability of observation data and its measurement uncertainty, providing insights useful to the design of future observation surveys. Finally, we further demonstrate our OED framework with an application to a model of the northwest European continental shelf.