Parameter Estimation to Improve Coastal Accuracy in a Global Tide Model

Global tide and surge models play a major role in forecasting coastal flooding due to extreme events or climate change. The model performance is strongly affected by parameters such as bathymetry and bottom friction. In this study, we propose a method that estimates bathymetry globally and the bottom friction coefficient in the shallow waters for a Global Tide and Surge Model (GTSMv4.1). However, the estimation effect is limited by the scarcity of available tide gauges. We propose to complement sparse tide gauges with tide time-series generated using FES2014. The FES2014 dataset outperforms GTSM in most areas and is used as observations for the deep ocean and some coastal areas, such as Hudson Bay/Labrador, where tide gauges are scarce but energy dissipation is large. The experiment is performed with a computation and memory efficient iterative parameter estimation scheme applied to Global Tide and Surge Model (GTSMv4.1). Estimation results show that model performance is significantly improved for deep ocean and shallow waters, especially in the European Shelf directly using the CMEMS tide gauge data in the estimation. GTSM is also validated by comparing to tide gauges from UHSLC, CMEMS, and some Arctic stations in the year 2014.

Boundary layer dynamics and bottom friction in combined wave–current flows over large roughness elements

In the coastal ocean, interactions of waves and currents with large roughness elements, similar in size to wave orbital excursions, generate drag and dissipate energy. These boundary layer dynamics differ significantly from well-studied small-scale roughness. To address this problem, we derived spatially and phase-averaged momentum equations for combined wave–current flows over rough bottoms, including the canopy layer containing obstacles. These equations were decomposed into steady and oscillatory parts to investigate the effects of waves on currents, and currents on waves. We applied this framework to analyse large-eddy simulations of combined oscillatory and steady flows over hemisphere arrays (diameter $D$ ), in which current ( $U_c$ ), wave velocity ( $U_w$ ) and period ( $T$ ) were varied. In the steady momentum budget, waves increase drag on the current, and this is balanced by the total stress at the canopy top. Dispersive stresses from oscillatory flow around obstacles are increasingly important as $U_w/U_c$ increases. In the oscillatory momentum budget, acceleration in the canopy is balanced by pressure gradient, added-mass and form drag forces; stress gradients are small compared to other terms. Form drag is increasingly important as the Keulegan–Carpenter number $KC=U_wT/D$ and $U_c/U_w$ increase. Decomposing the drag term illustrates that a quadratic relationship predicts the observed dependences of steady and oscillatory drag on $U_c/U_w$ and $KC$ . For large roughness elements, bottom friction is well represented by a friction factor ( $f_w$ ) defined using combined wave and current velocities in the canopy layer, which is proportional to drag coefficient and frontal area per unit plan area, and increases with $KC$ and $U_c/U_w$ .

Equilibration of baroclinic instability in westward flows

We explore the dynamics of baroclinic instability in westward flows using an asymptotic weakly nonlinear model. The proposed theory is based on the multilayer quasi-geostrophic framework, which is reduced to a system governed by a single nonlinear prognostic equation for the upper layer. The dynamics of deeper layers are represented by linear diagnostic relations. A major role in the statistical equilibration of baroclinic instability is played by the latent zonally elongated modes. These structures form spontaneously in baroclinically unstable systems and effectively suppress the amplification of primary unstable modes. Special attention is given to the effects of bottom friction, which is shown to control both linear and nonlinear properties of baroclinic instability. The reduced-dynamics model is validated by a series of numerical simulations.

Sedimentological data-driven bottom friction parameter estimation in modelling Bristol Channel tidal dynamics

Accurately representing the bottom friction effect is a significant challenge in numerical tidal models. Bottom friction effects are commonly defined via parameter estimation techniques. However, the bottom friction coefficient (BFC) can be related to the roughness of the sea bed. Therefore, sedimentological data can be beneficial in estimating BFCs. Taking the Bristol Channel and Severn Estuary as a case study, we perform a number of BFC parameter estimation experiments, utilising sedimentological data in a variety of ways. Model performance is explored through the results of each parameter estimation experiment, including applications to tidal range and tidal stream resource assessment. We find that theoretically derived sediment-based BFCs are in most cases detrimental to model performance. However, good performance is obtained by retaining the spatial information provided by the sedimentological data in the formulation of the parameter estimation experiment; the spatially varying BFC can be represented as a piecewise-constant field following the spatial distribution of the observed sediment types. By solving the resulting low-dimensional parameter estimation problem, we obtain good model performance as measured against tide gauge data. This approach appears well suited to modelling tidal range energy resource, which is of particular interest in the case study region. However, the applicability of this approach for tidal stream resource assessment is limited, since modelled tidal currents exhibit a strong localised response to the BFC; the use of piecewise-constant (and therefore discontinuous) BFCs is found to be detrimental to model performance for tidal currents.

Does Topographic Form Stress Impede Prograde Ocean Currents?

Topographic form stress (TFS) plays a central role in constraining the transport of the Antarctic Circumpolar Current (ACC), and thus the rate of exchange between the major ocean basins. Topographic form stress generation in the ACC has been linked to the formation of standing Rossby waves, which occur because the current is retrograde (opposing the direction of Rossby wave propagation). However, it is unclear whether TFS similarly retards current systems that are prograde (in the direction of Rossby wave propagation), which cannot arrest Rossby waves. An isopycnal model is used to investigate the momentum balance of wind-driven prograde and retrograde flows in a zonal channel, with bathymetry consisting of either a single ridge or a continental shelf and slope with a meridional excursion. Consistent with previous studies, retrograde flows are almost entirely impeded by TFS, except in the limit of flat bathymetry, whereas prograde flows are typically impeded by a combination of TFS and bottom friction. A barotropic theory for standing waves shows that bottom friction serves to shift the phase of the standing wave’s pressure field from that of the bathymetry, which is necessary to produce TFS. The mechanism is the same in prograde and retrograde flows, but is most efficient when the mean flow arrests a Rossby wave with a wavelength comparable to that of the bathymetry. The asymmetry between prograde and retrograde momentum balances implies that prograde current systems may be more sensitive to changes in wind forcing, for example associated with climate shifts.

On the Role of Bottom Pressure Torques in Wind-Driven Gyres

Previous studies have concluded that the wind-input vorticity in ocean gyres is balanced by bottom pressure torques (BPT), when integrated over latitude bands. However, the BPT must vanish when integrated over any area enclosed by an isobath. This constraint raises ambiguities regarding the regions over which BPT should close the vorticity budget, and implies that BPT generated to balance a local wind stress curl necessitates the generation of a compensating, nonlocal BPT and thus nonlocal circulation. This study aims to clarify the role of BPT in wind-driven gyres using an idealized isopycnal model. Experiments performed with a single-signed wind stress curl in an enclosed, sloped basin reveal that BPT balances the winds only when integrated over latitude bands. Integrating over other, dynamically motivated definitions of the gyre, such as barotropic streamlines, yields a balance between wind stress curl and bottom frictional torques. This implies that bottom friction plays a nonnegligible role in structuring the gyre circulation. Nonlocal bottom pressure torques manifest in the form of along-slope pressure gradients associated with a weak basin-scale circulation, and are associated with a transition to a balance between wind stress and bottom friction around the coasts. Finally, a suite of perturbation experiments is used to investigate the dynamics of BPT. To predict the BPT, the authors extend a previous theory that describes propagation of surface pressure signals from the gyre interior toward the coast along planetary potential vorticity contours. This theory is shown to agree closely with the diagnosed contributions to the vorticity budget across the suite of model experiments.