Tidal power lagoons have the potential to provide a reliable and long-term source of renewable power. The implementation of tidal lagoons will impact the tidal conditions and hydrodynamics of the ...surrounding coastal system. Impact assessments in the academic literature have generally investigated working proposals from industry of various shapes and sizes. As such, differences between the impacts arising from considered power plants in varying sites are in part influenced by the individual scheme characteristics, potentially masking the influence of site-specific factors. In this study, scheme design consistency is maintained, providing a basis to focus solely on the merits of the selected locations with regards to any associated impacts. The simulated tidal power lagoons are located in the Bristol Channel and Irish Sea, two distinct but tidally connected regions on the British coastline with contrasting marine environment characteristics. Results indicate that the more constrained geometry of the Bristol Channel contributes to higher individual and cumulative impacts than potential developments in the Irish Sea. This is in part facilitated by the higher degree of blockage introduced by tidal lagoon developments in the Bristol Channel. Furthermore, far-field impacts are found to be less pronounced compared to predictions reported in tidal barrage modelling studies.
•Consistent tidal lagoon design highlights influence of marine environment on impacts.•Impacts resulting from developments in Bristol Channel and Irish Sea combine linearly.•Cumulative impacts in the Bristol Channel notable in whole region.•Impacts of Irish Sea tidal lagoons more localised than in the Bristol Channel.
Groundwater heat pump systems cause thermal anomalies in the aquifer that can impact upon downstream systems and reduce their efficiency. Therefore, it is important to optimally position the ...extraction and injection wells of such systems to avoid negative interactions and maximize the thermal potential of the aquifer. This paper presents a new method to determine optimal well layouts of groundwater heat pumps using the adjoint approach, which is an efficient way to solve the underlying PDE-constrained optimization problem. An integral part of the method is the numerical groundwater simulation, which here is based on the finite element method. In addition, a multi-start initialization strategy is introduced in an attempt to better reach the global optimum. The method is applied to a real case study with 10 groundwater heat pumps, i.e. 20 wells, and two optimization scenarios with different natural groundwater temperatures. In both scenarios, the optimization method successfully determines a well layout that maximizes groundwater temperatures at all extraction wells. Comparing the results from these scenarios demonstrates that hydro-geological conditions can have a significant impact on the optimal well layout. The proposed method is equally applicable to systems with multiple extraction and injection wells and can be extended to various other shallow geothermal applications, such as combined heating and cooling systems.
•A new optimization method for well layouts of groundwater heat pumps is introduced.•The method is a gradient-based optimization that uses the adjoint approach.•The new method allows for continuous well locations and a large number of wells.•It can be used to find optimal well layouts of several neighboring or single systems.•A real case study with 10 systems is used to demonstrate the method’s applicability.
A new framework for applying anisotropic angular adaptivity in spectral wave modelling is presented. The angular dimension of the action balance equation is discretised with the use of Haar wavelets, ...hierarchical piecewise-constant basis functions with compact support, and an adaptive methodology for anisotropically adjusting the resolution of the angular mesh is proposed. This work allows a reduction of computational effort in spectral wave modelling, through a reduction in the degrees of freedom required for a given accuracy, with an automated procedure and minimal cost.
Wind farm modelling is an area of rapidly increasing interest with numerous analytical and computational-based approaches developed to extend the margins of wind farm efficiency and maximise power ...production. In this work, we present the novel ML framework WakeNet, which reproduces generalised 2D turbine wake velocity fields at hub-height, with a mean accuracy of 99.8% compared to the solution calculated by the state-of-the-art wind farm modelling software FLORIS. As the generation of sufficient high-fidelity data for network training purposes can be cost-prohibitive, the utility of multi-fidelity transfer learning has also been investigated. Specifically, a network pre-trained on the low-fidelity Gaussian wake model is fine-tuned in order to obtain accurate wake results for the mid-fidelity Curl wake model. The overall performance of WakeNet is validated on various wake steering control and layout optimisation scenarios, obtaining at least 90% of the power gained by the FLORIS optimiser. Moreover, the Curl-based WakeNet provides similar power gains to FLORIS, two orders of magnitude faster. These promising results show that generalised wake modelling with ML tools can be accurate enough to contribute towards robust real-time active yaw and layout optimisation under uncertainty, while producing realistic optimised configurations at a fraction of the computational cost.
•WakeNet produces generalised wakes 2 orders of magnitude faster than the Curl model.•The local turbulence and generated power can be approximated from 2D flow predictions.•Multi-fidelity transfer learning reduces the mid-fidelity data required for training.•WakeNet performs yaw and layout optimisation 2 orders of magnitude faster than FLORIS.•Deep Learning can produce fast realistic optimised wind farm configurations.
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.
Numerical storm surge models are essential to forecasting coastal flood hazard and informing the design of coastal defences. However, such models rely on a variety of inputs, many of which carry ...uncertainty. An awareness and understanding of the sensitivity of model outputs with respect to those uncertain inputs is therefore essential when interpreting model results. Here, we use an unstructured-mesh numerical coastal ocean model, Thetis, and its adjoint, to perform a sensitivity analysis for a hindcast of the 5th/6th December 2013 North Sea surge event, with respect to the bottom friction coefficient, bathymetry and wind stress forcing. The results reveal spatial and temporal patterns of sensitivity, providing physical insight into the mechanisms of surge generation and propagation. For example, the sensitivity of the skew surge to the bathymetry reveals the protective effect of a sand bank off the UK east coast. The results can also be used to propagate uncertainties through the numerical model; based on estimates of model input uncertainties, we estimate that modelled skew surges carry uncertainties of around 5 cm and 15 cm due to bathymetry and bottom friction, respectively. While these uncertainties are small compared with the typical spread in an ensemble storm surge forecast due to uncertain meteorological inputs, the adjoint-derived model sensitivities can nevertheless be used to inform future model calibration and data acquisition efforts in order to reduce uncertainty. Our results demonstrate the power of adjoint methods to gain insight into a storm surge model, providing information complementary to traditional ensemble uncertainty quantification methods.
•We calibrate an unstructured-mesh finite element storm surge model of the North Sea•We use an adjoint approach to perform sensitivity analysis for modelled skew surges•We compare spatial and temporal patterns of sensitivity with respect to three inputs•We demonstrate the physical insight available through numerical adjoint methods.
•Ocean circulation beneath ice shelves is simulated using an unstructured-mesh.•We represent a smoothly varying ice base in the presence of a vertical ice front.•We implemented ice shelf/ocean ...interaction in the context of finite-element method.
Several different classes of ocean model are capable of representing floating glacial ice shelves. We describe the incorporation of ice shelves into Fluidity-ICOM, a nonhydrostatic finite-element ocean model with the capacity to utilize meshes that are unstructured and adaptive in three dimensions. This geometric flexibility offers several advantages over previous approaches. The model represents melting and freezing on all ice-shelf surfaces including vertical faces, treats the ice shelf topography as continuous rather than stepped, and does not require any smoothing of the ice topography or any of the additional parameterisations of the ocean mixed layer used in isopycnal or z-coordinate models. The model can also represent a water column that decreases to zero thickness at the ‘grounding line’, where the floating ice shelf is joined to its tributary ice streams. The model is applied to idealised ice-shelf geometries in order to demonstrate these capabilities. In these simple experiments, arbitrarily coarsening the mesh outside the ice-shelf cavity has little effect on the ice-shelf melt rate, while the mesh resolution within the cavity is found to be highly influential. Smoothing the vertical ice front results in faster flow along the smoothed ice front, allowing greater exchange with the ocean than in simulations with a realistic ice front. A vanishing water-column thickness at the grounding line has little effect in the simulations studied. We also investigate the response of ice shelf basal melting to variations in deep water temperature in the presence of salt stratification.
Coastal zones are vulnerable to both erosion and flood risk, which can be assessed using coupled hydro-morphodynamic models. However, the use of such models as decision support tools suffers from a ...high degree of uncertainty, due to both incomplete knowledge and natural variability in the system. In this work, we show for the first time how the multilevel Monte Carlo method (MLMC) can be applied in hydro-morphodynamic coastal ocean modelling, here using the popular model XBeach, to quantify uncertainty by computing statistics of key output variables given uncertain input parameters. MLMC accelerates the Monte Carlo approach through the use of a hierarchy of models with different levels of resolution. Several theoretical and real-world coastal zone case studies are considered here, for which output variables that are key to the assessment of flood and erosion risk, such as wave run-up height and total eroded volume, are estimated. We show that MLMC can significantly reduce computational cost, resulting in speed up factors of 40 or greater compared to a standard Monte Carlo approach, whilst keeping the same level of accuracy. Furthermore, a sophisticated ensemble generating technique is used to estimate the cumulative distribution of output variables from the MLMC output. This allows for the probability of a variable exceeding a certain value to be estimated, such as the probability of a wave run-up height exceeding the height of a seawall. This is a valuable capability that can be used to inform decision-making under uncertainty.
•First use of MLMC (multilevel Monte Carlo) with a coupled hydro-morphodynamic model.•Large drop in computational cost for same accuracy using MLMC instead of Monte Carlo.•Determine the distribution of variables of interest in coastal zone cases using MLMC.
•A multi-layer non-hydrostatic coastal ocean model is developed using the discontinuous Galerkin finite element method.•The model is shown to predict nearshore dispersive wave processes accurately ...using only a small number of vertical layers.•Use of arbitrary unstructured meshes allows for non-uniform resolution and accurate representation of complex geometries.•Automated code generation techniques are employed promoting code efficiency, readability, extensibility and maintainability.
A multi-layer non-hydrostatic version of the unstructured mesh, discontinuous Galerkin finite element based coastal ocean model, Thetis, is developed. This is accomplished using the PDE solver framework, Firedrake, which is used to automatically produce the code for the discretised model equations in a rapid and efficient manner. The motivation for this work is a need to accurately simulate dispersive nearshore free surface processes.
In order to resolve both frequency dispersion and non-linear effects accurately, additional non-hydrostatic terms are included in the layer-integrated hydrostatic equations, producing a form similar to the layered non-linear shallow water equations, but with extra vertical velocities at the layer interfaces. An implementation process is adopted to easily handle the inter-layer connection, i.e. the governing equations are transformed into a depth-integrated system through the introduction of depth-averaged variables.
The model is verified and validated through comparisons against several idealised and experimentally-based test cases. All the comparisons demonstrate good agreement, showing that the developed non-hydrostatic model has excellent capabilities in representing coastal wave phenomena including shoaling, refraction and diffraction of dispersive short waves, as well as propagation, run-up and inundation of non-linear tsunami waves.
With increased nutrient inputs to estuaries in recent decades exacerbating their susceptibility to eutrophication, assessment of the response of individual estuaries to nutrient enrichment is ...attracting considerable attention. Nonetheless, the impact of tidal energy extraction on estuarine nutrient dynamics and the risk of eutrophication has been largely overlooked despite the detrimental consequences of eutrophication on ecosystem functioning. It is understood that tidal energy schemes such as the tidal lagoon previously proposed in Swansea Bay would alter tidal flow characteristics, potentially having knock-on impacts on physical estuarine characteristics and ecological processes in the impounded area. This study examined the existing physical estuarine characteristics in Swansea Bay and evaluated the risk of eutrophication following tidal power plant operation under ebb-only and two-way strategies using a simple risk assessment model. Two surveys were conducted to measure in-situ temperature, salinity, dissolved oxygen, chlorophyll-a, dissolved inorganic nitrogen and turbidity in the water column at 12 sampling stations selected to cover the location in the tidal energy scheme proposal. The water column was found to be nutrient enriched and essentially vertically homogenous with no strong evidence of stratification. High dissolved oxygen, low turbidity and high phytoplankton biomass indicated by the chlorophyll-a concentrations were observed. The bay did not show any signs of eutrophication as the phytoplankton biomass did not reach the level typical of harmful algal blooms and oxygen depletion was not observed indicating that eutrophication is not currently present in the bay. Based on numerical model predictions, the bay was found to exhibit a moderate response to nutrient enrichment with no risk of eutrophication and no net change in its status following the operation of the lagoon under both ebb-only and two-way operational modes. These findings suggest that the management strategies for protecting water quality in heavily modified estuaries such as Swansea Bay may not need to be altered following the operation of a tidal lagoon. But given the conditions for phytoplankton growth are likely to be more favourable under ebb-only operational mode compared to two-way operational mode, measures that control nutrient inputs to the impounded water column within the lagoon should be considered under the ebb-only operational mode as a prudent precautionary step.
•We applied a risk assessment model and field data to estimate the eutrophication risk of a tidal lagoon.•We demonstrated that the study area is mesotrophic and exhibits a moderate response to nutrient enrichment.•Model predictions showed no risk of eutrophication under two tidal lagoon operational scenarios.•Conditions were least favourable for phytoplankton growth under two-way operational scenario.
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