Non-deterministic effects in modelling the tidal currents in a high-energy coastal site

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Simon Charles Warder , Stephan C Kramer, Matthew D Piggott


Numerical models are commonly employed for predicting tidal stream resource, since harmonic analysis is typically insufficient for representing tidal currents. This is particularly true in regions of high-energy flow and complex bathymetric and coastline features, resulting in highly nonlinear dynamics. Within this work, we demonstrate that non-deterministic effects pose a further barrier to resource predictability in such regions. We take the Inner Sound of the Pentland Firth as a case study region, situated between mainland Scotland and the island of Stroma, where non-deterministic effects are introduced by eddy shedding off islands and headlands in the region. We set up a numerical model of the region using the Thetis finite element coastal ocean model. We first demonstrate the presence of non-deterministic effects, by forcing the model with a single tidal constituent and observing the departure from purely periodic behaviour within the Inner Sound, and also by comparing an ensemble of fully-forced model runs generated with perturbed initial conditions. We then take steps towards model calibration with respect to the model bottom friction and viscosity parameters, comparing a variety of choices of model-observation error metrics for this purpose. The non-deterministic component not only places a limit on the predictability of the flow (and hence the tidal stream resource), but also on the calibration process. Focusing on calibration with respect to the bottom friction parameter, we quantify the identifiability limit which the non-deterministic behaviour places on the parameter. We explore the sensitivity of this identifiability limit with respect to the viscosity parameter and the choice of error metric. We find that calibration based on matching the modelled and observed mean kinetic power density is a good choice, and is relatively robust with respect to the non-deterministic behaviour. Based on these results, and on the sensitivity of the error metrics to each model parameter and the mesh resolution, we make recommendations for how to proceed with model calibration in the presence of non-deterministic flow. Since the non-deterministic effect is due to complex, high-energy flow leading to highly nonlinear dynamics, we expect these results to generalise to other regions of high tidal stream resource.



Environmental Sciences, Oceanography


Predictability, Non-deterministic behaviour, Tidal stream, Pentland Firth


Published: 2021-05-27 13:14

Last Updated: 2021-05-27 20:14


CC BY Attribution 4.0 International

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