Imperial College London

ProfessorMatthewPiggott

Faculty of EngineeringDepartment of Earth Science & Engineering

Professor of Computational Geoscience and Engineering
 
 
 
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Contact

 

m.d.piggott Website

 
 
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Location

 

4.82Royal School of MinesSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

209 results found

Li S, Robert A, Faisal AA, Piggott MDet al., 2024, Learning to optimise wind farms with graph transformers, Applied Energy, Vol: 359, ISSN: 0306-2619

This work proposes a novel data-driven model capable of providing accurate predictions for the power generation of all wind turbines in wind farms of arbitrary layout, yaw angle configurations and wind conditions. The proposed model functions by encoding a wind farm into a fully connected graph and processing the graph representation through a graph transformer. The resultant graph transformer surrogate demonstrates robust generalisation capabilities and effectively uncovers latent structural patterns embedded within the graph representation of wind farms. The versatility of the proposed approach extends to the optimisation of yaw angle configurations through the application of genetic algorithms. This evolutionary optimisation strategy facilitated by the graph transformer surrogate achieves prediction accuracy levels comparable to industrially standard wind farm simulation tools, with a relative accuracy of more than 99% in identifying optimal yaw angle configurations of previously unseen wind farm layouts. An additional advantage lies in the significant reduction in computational costs, positioning the proposed methodology as a compelling tool for efficient and accurate wind farm optimisation.

Journal article

Wallwork JG, Angeloudis A, Barral N, Mackie L, Kramer SC, Piggott MDet al., 2024, Tidal turbine array modelling using goal-oriented mesh adaptation, Journal of Ocean Engineering and Marine Energy, Vol: 10, Pages: 193-216, ISSN: 2198-6452

To examine the accuracy and sensitivity of tidal array performance assessment by numerical techniques applying goal-oriented mesh adaptation. The goal-oriented framework is designed to give rise to adaptive meshes upon which a given diagnostic quantity of interest (QoI) can be accurately captured, whilst maintaining a low overall computational cost. We seek to improve the accuracy of the discontinuous Galerkin method applied to a depth-averaged shallow water model of a tidal energy farm, where turbines are represented using a drag parametrisation and the energy output is specified as the QoI. Two goal-oriented adaptation strategies are considered, which give rise to meshes with isotropic and anisotropic elements. We present both fixed mesh and goal-oriented adaptive mesh simulations for an established test case involving an idealised tidal turbine array positioned in a channel. With both the fixed meshes and the goal-oriented methodologies, we reproduce results from the literature which demonstrate how a staggered array configuration extracts more energy than an aligned array. We also make detailed qualitative and quantitative comparisons between the fixed mesh and adaptive outputs. The proposed goal-oriented mesh adaptation strategies are validated for the purposes of tidal energy resource assessment. Using only a tenth of the number of degrees of freedom as a high-resolution fixed mesh benchmark and lower overall runtime, they are shown to enable energy output differences smaller than 2% for a tidal array test case with aligned rows of turbines and less than 10% for a staggered array configuration.

Journal article

Li S, Zhang M, Piggott MD, 2023, End-to-end wind turbine wake modelling with deep graph representation learning, APPLIED ENERGY, Vol: 339, ISSN: 0306-2619

Journal article

Shadrick J, Rood D, Hurst M, Piggott M, Wilcken K, Seal Aet al., 2023, Constraints on long-term cliff retreat and intertidal weathering at weak rock coasts using cosmogenic ¹⁰Be, nearshore topography and numerical modelling, Earth Surface Dynamics, Vol: 11, Pages: 429-450, ISSN: 2196-6311

The white chalk cliffs on the south coast of England are one of the most iconic coastlines in the world. Rock coasts located in a weak lithology, such as chalk, are likely to be most vulnerable to climate-change-triggered accelerations in cliff retreat rates. In order to make future forecasts of cliff retreat rates as a response to climate change, we need to look beyond individual erosion events to quantify the long-term trends in cliff retreat rates. Exposure dating of shore platforms using cosmogenic radionuclide analysis and numerical modelling allows us to study past cliff retreat rates across the Late Holocene for these chalk coastlines. Here, we conduct a multi-objective optimisation of a coastal evolution model to both high-precision topographic data and 10Be concentrations at four chalk rock coast sites to reveal a link between cliff retreat rates and the rate of sea-level rise. Furthermore, our results strengthen evidence for a recent acceleration in cliff retreat rates at the chalk cliffs on the south coast of England. Our optimised model results suggest that the relatively rapid historical cliff retreat rates observed at these sites spanning the last 150 years last occurred between 5300 and 6800 years ago when the rate of relative sea-level rise was a factor of 5–9 times more rapid than during the recent observable record. However, results for these chalk sites also indicate that current process-based models of rock coast development are overlooking key processes that were not previously identified at sandstone rock coast sites. Interpretation of results suggest that beaches, cliff debris and heterogenous lithology play an important but poorly understood role in the long-term evolution of these chalk rock coast sites. Despite these limitations, our results reveal significant differences in intertidal weathering rates between sandstone and chalk rock coast sites, which helps to inform the long-standing debate of “wave versus weathering” a

Journal article

Scott WI, Kramer SC, Holland PR, Nicholls KW, Siegert MJ, Piggott MDet al., 2023, Towards a fully unstructured ocean model for ice shelf cavity environments: Model development and verification using the Firedrake finite element framework, OCEAN MODELLING, Vol: 182, ISSN: 1463-5003

Journal article

Zhang C, Zhang J, Angeloudis A, Zhou Y, Kramer SC, Piggott MDet al., 2023, Physical Modelling of Tidal Stream Turbine Wake Structures under Yaw Conditions, ENERGIES, Vol: 16

Journal article

Clare MCA, Piggott MD, 2023, Bayesian neural networks for the probabilistic forecasting of wind direction and speed using ocean data, Trends in Renewable Energies Offshore - Proceedings of the 5th International Conference on Renewable Energies Offshore, RENEW 2022, Pages: 533-540

Neural networks are increasingly used to predict wind direction and speed, two important factors for estimating a wind farm’s potential power output. However classical neural networks lack the ability to express uncertainty and hence here we apply Bayesian Neural Networks (BNNs) to the problem of offshore wind resource prediction. For BNNs, the weights and outputs are distributions leading to well-calibrated probabilistic forecasts which add considerable value to the results. In particular, probabilistic forecasts inform on the network’s ability to make predictions of out-of-sample datapoints. We use this property to conclude that the accuracy and uncertainty of our BNN is unaffected by the construction of a nearby wind farm. For our dataset, we use observations from the FINO1 research platform and ocean data as the predictors. We thus show that at this site, networks trained on pre-farm ocean data can accurately predict wind field information post construction of a wind farm.

Journal article

Clare MCA, Wallwork JG, Kramer SC, Weller H, Cotter CJ, Piggott MDet al., 2022, Multi-scale hydro-morphodynamic modelling using mesh movement methods, GEM: International Journal on Geomathematics, Vol: 13, ISSN: 1869-2672

Hydro-morphodynamic modelling is an important tool that can be used in the protection of coastal zones. The models can be required to resolve spatial scales ranging from sub-metre to hundreds of kilometres and are computationally expensive. In this work, we apply mesh movement methods to a depth-averaged hydro-morphodynamic model for the first time, in order to tackle both these issues. Mesh movement methods are particularly well-suited to coastal problems as they allow the mesh to move in response to evolving flow and morphology structures. This new capability is demonstrated using test cases that exhibit complex evolving bathymetries and have moving wet-dry interfaces. In order to be able to simulate sediment transport in wet-dry domains, a new conservative discretisation approach has been developed as part of this work, as well as a sediment slide mechanism. For all test cases, we demonstrate how mesh movement methods can be used to reduce discretisation error and computational cost. We also show that the optimum parameter choices in the mesh movement monitor functions are fairly predictable based upon the physical characteristics of the test case, facilitating the use of mesh movement methods on further problems.

Journal article

Warder SC, Piggott MD, 2022, Optimal experiment design for a bottom friction parameter estimation problem, GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS, Vol: 13, ISSN: 1869-2672

Journal article

Shadrick J, Rood D, Hurst M, Piggott M, Hebditch B, Seal A, Wilcken Ket al., 2022, Sea level rise will likely accelerate rock coast cliff retreat rates, Nature Communications, Vol: 13, ISSN: 2041-1723

Coastal response to anthropogenic climate change is of central importance to the infrastructure and inhabitants in these areas. Despite being globally ubiquitous, the stability of rock coasts has been largely neglected, and the expected acceleration of cliff erosion following sea-level rise has not been tested with empirical data, until now. We have optimised a coastal evolution model to topographic and cosmogenic radionuclide data to quantify cliff retreat rates for the past 8000 years and forecast rates for the next century. Here we show that rates of cliff retreat will increase by up to an order of magnitude by 2100 according to current predictions of sea-level rise: an increase much greater than previously predicted. This study challenges conventional coastal management practices by revealing that even historically stable rock coasts are highly sensitive to sea-level rise and should be included in future planning for global climate change response.

Journal article

Halilovic S, Böttcher F, Kramer S, Piggott M, Zosseder K, Hamacher Tet al., 2022, Well layout optimization for groundwater heat pump systems using the adjoint approach, Energy Conversion and Management, Vol: 268, ISSN: 0196-8904

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 tobetter 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.

Journal article

Clare MCA, Leijnse TWB, McCall RT, Diermanse FLM, Cotter CJ, Piggott MDet al., 2022, Multilevel multifidelity Monte Carlo methods for assessing uncertainty in coastal flooding, Natural Hazards and Earth System Sciences, Vol: 22, Pages: 2491-2515, ISSN: 1561-8633

When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high-fidelity models being more expensive than low-fidelity ones. However, when assessing uncertainty, we can use a multifidelity approach to take advantage of the accuracy of high-fidelity models and the computational efficiency of low-fidelity models. Here, we apply the multilevel multifidelity Monte Carlo method (MLMF) to quantify uncertainty by computing statistical estimators of key output variables with respect to uncertain input data, using the high-fidelity hydrodynamic model XBeach and the lower-fidelity coastal flooding model SFINCS (Super-Fast INundation of CoastS). The multilevel aspect opens up the further advantageous possibility of applying each of these models at multiple resolutions. This work represents the first application of MLMF in the coastal zone and one of its first applications in any field. For both idealised and real-world test cases, MLMF can significantly reduce computational cost for the same accuracy compared to both the standard Monte Carlo method and to a multilevel approach utilising only a single model (the multilevel Monte Carlo method). In particular, here we demonstrate using the case of Myrtle Beach, South Carolina, USA, that this improvement in computational efficiency allows for in-depth uncertainty analysis to be conducted in the case of real-world coastal environments – a task that would previously have been practically unfeasible. Moreover, for the first time, we show how an inverse transform sampling technique can be used to accurately estimate the cumulative distribution function (CDF) of variables from the MLMF outputs. MLMF-based estimates of the expectations and the CDFs of the variables of interest are of significant value to decision makers when assessing uncertainty in predictions.

Journal article

Piggott M, 2022, Multilevel multifidelity Monte Carlo methods for assessing coastal flood risk, Natural Hazards and Earth System Sciences, Vol: 22, Pages: 2491-2515, ISSN: 1561-8633

Abstract. When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high fidelity models being more expensive than low fidelity ones. However, when assessing uncertainty, wecan use a multifidelity approach to take advantage of the accuracy of high fidelity models and the computational efficiencyof low fidelity models. Here, we apply the multilevel multifidelity Monte Carlo method (MLMF) to quantify uncertainty by computing statistical estimators of key output variables with respect to uncertain inputs, using the high fidelity hydrodynamicmodel XBeach and the lower fidelity coastal flooding model SFINCS. The multilevel aspect opens up the further advantageouspossibility of applying each of these models at multiple resolutions. This work represents the first application of MLMF in thecoastal zone and one of its first applications in any field. For both idealised and real-world test cases, MLMF can significantlyreduce computational cost for the same accuracy compared to both the standard Monte Carlo method and to a multilevel approach utilising only a single model (the multilevel Monte Carlo method). In particular, here we demonstrate using the case ofMyrtle Beach, USA, that this improvement in computational efficiency allows in-depth uncertainty analysis to be conducted inthe case of real-world coastal environments – a task that would previously have been practically unfeasible. Moreover, for thefirst time, we show how an inverse transform sampling technique can be used to accurately estimate the cumulative distributionfunction (CDF) of variables from the MLMF outputs. MLMF based estimates of the expectations and the CDFs of the variables of interest are of significant value to decision makers when assessing risk.

Journal article

Pan W, Kramer SC, Piggott MD, Yu Xet al., 2022, Modeling landslide generated waves using the discontinuous finite element method, International Journal for Numerical Methods in Fluids, Vol: 94, Pages: 1-33, ISSN: 0271-2091

A new two-layer model for impulsive wave generation by deformable granular landslides is developed based upon a discontinuous Galerkin finite element discretization. Landslide motion is modeled using a depth-averaged formulation for a shallow subaerial debris flow, which considers the bed curvature represented by the local slope angle variable and accounts for inter-granular stresses using Coulomb friction. Wave generation and propagation are simulated with the three-dimensional non-hydrostatic coastal ocean model Thetis to accurately capture key features such as wave dispersion. Two different techniques are used in treating wetting and drying (WD) processes during the landslide displacement and wave generation, respectively. For the lower-layer landslide motion across the dry bed a classical thin-layer explicit WD method is implemented, while for the resulting free-surface waves interacted with the moving landslide an implicit WD scheme is utilized to naturally circumvent the artificial pressure gradient problem which may appear in the dynamic interaction between the landslide and water if using the thin-layer method. The two-layer model is validated using a suite of test cases, with the resulting good agreement demonstrating its capability in describing both the complex behaviors of granular landslides from initiation to deposition, and the consequent wave generation and propagation.

Journal article

Little A, Piggott MD, Buchan AG, 2022, Development of a gamma ray dose rate calculation and mapping tool for Lagrangian marine nuclear emergency response models., Marine Pollution Bulletin, Vol: 181, Pages: 1-12, ISSN: 0025-326X

This paper presents the development and testing of a gamma radiation dose rate calculation model for the marine environment, and evaluates the potential use for such a model in both short term nuclear emergency response management and emergency response planning. This is believed to be the first implementation of a full field gamma radiation mapping model (including air attenuation and buildup) to be incorporated within a Lagrangian marine dispersion model. Calculated surface gamma ray dose rates for nine generic release scenarios are presented and used to undertake an emergency countermeasure optioneering assessment.

Journal article

Christensen AK, Piggott M, van Sebille E, van Reeuwijk M, Pawar Set al., 2022, Investigating microscale patchiness of motile microbes under turbulence in a simulated convective mixed layer, PLOS COMPUTATIONAL BIOLOGY, Vol: 18, ISSN: 1553-734X

Journal article

Song W, Zhang M, Wallwork JG, Gao J, Tian Z, Sun F, Piggott MD, Chen J, Shi Z, Chen X, Wang Jet al., 2022, M2N: mesh movement networks for PDE solvers

Mainstream numerical Partial Differential Equation (PDE) solvers requirediscretizing the physical domain using a mesh. Mesh movement methods aim toimprove the accuracy of the numerical solution by increasing mesh resolutionwhere the solution is not well-resolved, whilst reducing unnecessary resolutionelsewhere. However, mesh movement methods, such as the Monge-Ampere method,require the solution of auxiliary equations, which can be extremely expensiveespecially when the mesh is adapted frequently. In this paper, we propose toour best knowledge the first learning-based end-to-end mesh movement frameworkfor PDE solvers. Key requirements of learning-based mesh movement methods arealleviating mesh tangling, boundary consistency, and generalization to meshwith different resolutions. To achieve these goals, we introduce the neuralspline model and the graph attention network (GAT) into our modelsrespectively. While the Neural-Spline based model provides more flexibility forlarge deformation, the GAT based model can handle domains with more complicatedshapes and is better at performing delicate local deformation. We validate ourmethods on stationary and time-dependent, linear and non-linear equations, aswell as regularly and irregularly shaped domains. Compared to the traditionalMonge-Ampere method, our approach can greatly accelerate the mesh adaptationprocess, whilst achieving comparable numerical error reduction.

Working paper

Clare MCA, Piggott MD, Cotter CJ, 2022, Assessing erosion and flood risk in the coastal zone through the application of multilevel Monte Carlo methods, Coastal Engineering, Vol: 174, ISSN: 0378-3839

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 degreeof uncertainty, due to both incomplete knowledge and natural variability in the system. In this work, we showfor the first time how the multilevel Monte Carlo method (MLMC) can be applied in hydro-morphodynamiccoastal ocean modelling, here using the popular model XBeach, to quantify uncertainty by computing statisticsof key output variables given uncertain input parameters. MLMC accelerates the Monte Carlo approach throughthe use of a hierarchy of models with different levels of resolution. Several theoretical and real-world coastalzone case studies are considered here, for which output variables that are key to the assessment of flood anderosion risk, such as wave run-up height and total eroded volume, are estimated. We show that MLMC cansignificantly reduce computational cost, resulting in speed up factors of 40 or greater compared to a standardMonte Carlo approach, whilst keeping the same level of accuracy. Furthermore, a sophisticated ensemblegenerating 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 probabilityof a wave run-up height exceeding the height of a seawall. This is a valuable capability that can be used toinform decision-making under uncertainty

Journal article

Warder SC, Angeloudis A, Piggott MD, 2022, Sedimentological data-driven bottom friction parameter estimation in modelling Bristol Channel tidal dynamics, OCEAN DYNAMICS, Vol: 72, Pages: 361-382, ISSN: 1616-7341

Journal article

Clare MCA, Kramer SC, Cotter CJ, Piggott MDet al., 2022, Calibration, inversion and sensitivity analysis for hydro-morphodynamic models through the application of adjoint methods, Computers and Geosciences, Vol: 163, Pages: 1-13, ISSN: 0098-3004

The development of reliable, sophisticated hydro-morphodynamic models is essential for protecting the coastal environment against hazards such as flooding and erosion. There exists a high degree of uncertainty associated with the application of these models, in part due to incomplete knowledge of various physical, empirical and numerical closure related parameters in both the hydrodynamic and morphodynamic solvers. This uncertainty can be addressed through the application of adjoint methods. These have the notable advantage that the number and/or dimension of the uncertain parameters has almost no effect on the computational cost associated with calculating the model sensitivities. Here, we develop the first freely available and fully flexible adjoint hydro-morphodynamic model framework. This flexibility is achieved through using the pyadjoint library, which allows us to assess the uncertainty of any parameter with respect to any model functional, without further code implementation. The model is developed within the coastal ocean model Thetis constructed using the finite element code-generation library Firedrake. We present examples of how this framework can perform sensitivity analysis, inversion and calibration for a range of uncertain parameters based on the final bedlevel. These results are verified using so-called dual-twin experiments, where the ‘correct’ parameter value is used in the generation of synthetic model test data, but is unknown to the model in subsequent testing. Moreover, we show that inversion and calibration with experimental data using our framework produces physically sensible optimum parameters and that these parameters always lead to more accurate results. In particular, we demonstrate how our adjoint framework can be applied to a tsunami-like event to invert for the tsunami wave from sediment deposits.

Journal article

Jordan C, Dundovic D, Fragkou AK, Deskos G, Coles DS, Piggott MD, Angeloudis Aet al., 2022, Combining shallow-water and analytical wake models for tidal-array micro-siting, Journal of Ocean Engineering and Marine Energy, Vol: 8, Pages: 193-215, ISSN: 2198-6444

For tidal-stream energy to become a competitive renewable energy source, clustering multiple turbines into arrays is paramount. Array optimisation is thus critical for achieving maximum power performance and reducing cost of energy. However, ascertaining an optimal array layout is a complex problem, subject to specific site hydrodynamics and multiple inter-disciplinary constraints. In this work, we present a novel optimisation approach that combines an analytical-based wake model, FLORIS, with an ocean model, Thetis. The approach is demonstrated through applications of increasing complexity. By utilising the method of analytical wake superposition, the addition or alteration of turbine position does not require re-calculation of the entire flow field, thus allowing the use of simple heuristic techniques to perform optimisation at a fraction of the computational cost of more sophisticated methods. Using a custom condition-based placement algorithm, this methodology is applied to the Pentland Firth for arrays with turbines of 3.05m/s rated speed, demonstrating practical implications whilst considering the temporal variability of the tide. For a 24-turbine array case, micro-siting using this technique delivered an array 15.8% more productive on average than a staggered layout, despite flow speeds regularly exceeding the rated value. Performance was evaluated through assessment of the optimised layout within the ocean model that treats turbines through a discrete turbine representation. Used iteratively, this methodology could deliver improved array configurations in a manner that accounts for local hydrodynamic effects.

Journal article

Wallwork JG, Barral N, Ham DA, Piggott MDet al., 2022, Goal-oriented error estimation and mesh adaptation for tracer transport modelling, Computer-Aided Design, Vol: 145, Pages: 1-21, ISSN: 0010-4485

This paper applies metric-based mesh adaptation methods to advection-dominated tracer transport modelling problems in two and three dimensions, using the finite element package Firedrake. In particular, the mesh adaptation methods considered are built upon goal-oriented estimates for the error incurred in evaluating a diagnostic quantity of interest (QoI). In the motivating example of modelling to support desalination plant outfall design, such a QoI could be the salinity at the plant inlet, which could be negatively impacted by the transport of brine from the plant’s outfall. Four approaches are considered, one of which yields isotropic meshes. The focus on advection-dominated problems means that flows are often anisotropic; thus, three anisotropic approaches are also considered. Meshes resulting from each of the four approaches yield solutions to the tracer transport problem which give better approximations to QoI values than uniform meshing, for a given mesh size. The methodology is validated using an existing 2D tracer transport test case with a known analytical solution. Goal-oriented meshes for an idealised time-dependent desalination outfall scenario are also presented.

Journal article

Zhang J, Zhang C, Angeloudis A, Kramer SC, He R, Piggott MDet al., 2022, Interactions between tidal stream turbine arrays and their hydrodynamic impact around Zhoushan Island, China, Ocean Engineering, Vol: 246, Pages: 1-13, ISSN: 0029-8018

Tidal currents represent an attractive renewable energy source particularly because of their predictability. Prospective tidal stream development sites are often co-located in close proximity. Under such circumstances, in order to maximise the exploitation of the resource, multiple tidal stream turbine arrays working in tandem would be needed. In this paper, a continuous array optimisation approach based on the open source coastal ocean modelling framework Thetis is applied to derive optimal configurations for four turbine arrays around Zhoushan Islands, Zhejiang Province, China. Alternative optimisation scenarios are tested to investigate interactions between the turbine arrays and their hydrodynamic footprint. Results show that there are no obvious competition effects between these four arrays around Hulu and Taohua Island. However, significant interactions could arise among the three turbine arrays situated around Hulu Island, with a maximum decrease in average power of 42.2%. By optimising all turbine arrays simultaneously, the competition effects can be minimised and the cost of energy reduced as less turbines are required to deliver an equivalent energy output. As for the potential environmental impact, it is found that the turbine array around Taohua Island would affect a larger area than turbine arrays around Hulu Island.

Journal article

Wallwork J, Barral N, Ham D, Piggott Met al., 2022, Goal-Oriented Error Estimation and Mesh Adaptation for Tracer Transport Modelling

<jats:p>This paper applies metric-based mesh adaptation methods to advection-dominated tracer transport modelling problems in two and three dimensions, using the finite element package Firedrake. In particular, the mesh adaptation methods considered are built upon goal-oriented estimates for the error incurred in evaluating a diagnostic quantity of interest (QoI). In the motivating example of modelling to support desalination plant outfall design, such a QoI could be the salinity at the plant inlet, which could be negatively impacted by the transport of brine from the plant's outfall. Four approaches are considered, one of which yields isotropic meshes. The focus on advection-dominated problems means that flows are often anisotropic; thus, three anisotropic approaches are also considered. Meshes resulting from each of the four approaches yield solutions to the tracer transport problem which give better approximations to QoI values than uniform meshing, for a given mesh size. The methodology is validated using an existing 2D tracer transport test case with a known analytical solution. Goal-oriented meshes for an idealised time-dependent desalination outfall scenario are also presented.</jats:p>

Working paper

Anagnostopoulos S, Piggott M, 2022, Offshore wind farm wake modelling using deep feed forward neural networks for active yaw control and layout optimisation, WindEurope Electric City Conference, Publisher: IOP PUBLISHING LTD, ISSN: 1742-6588

Conference paper

Zhang M, Wang J, Tlhomole J, Piggott MDet al., 2022, Learning to Estimate and Refine Fluid Motion with Physical Dynamics, INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 162, ISSN: 2640-3498

Journal article

Shadrick JR, Hurst MD, Piggott MD, Hebditch BG, Seal AJ, Wilcken KM, Rood DHet al., 2021, Multi-objective optimisation of a rock coast evolution model with cosmogenic Be-10 analysis for the quantification of long-term cliff retreat rates, Earth Surface Dynamics, Vol: 9, Pages: 1505-1529, ISSN: 2196-6311

This paper presents a methodology that uses site-specific topographic and cosmogenic 10Be data to perform multi-objective model optimisation of a coupled coastal evolution and cosmogenic radionuclide production model. Optimal parameter estimation of the coupled model minimises discrepancies between model simulations and measured data to reveal the most likely history of rock coast development. This new capability allows a time series of cliff retreat rates to be quantified for rock coast sites over millennial timescales. Without such methods, long-term cliff retreat cannot be understood well, as historical records only cover the past ∼150 years. This is the first study that has (1) applied a process-based coastal evolution model to quantify long-term cliff retreat rates for real rock coast sites and (2) coupled cosmogenic radionuclide analysis with a process-based model. The Dakota optimisation software toolkit is used as an interface between the coupled coastal evolution and cosmogenic radionuclide production model and optimisation libraries. This framework enables future applications of datasets associated with a range of rock coast settings to be explored. Process-based coastal evolution models simplify erosional processes and, as a result, often have equifinality properties, for example that similar topography develops via different evolutionary trajectories. Our results show that coupling modelled topography with modelled 10Be concentrations can reduce equifinality in model outputs. Furthermore, our results reveal that multi-objective optimisation is essential in limiting model equifinality caused by parameter correlation to constrain best-fit model results for real-world sites. Results from two UK sites indicate that the rates of cliff retreat over millennial timescales are primarily driven by the rates of relative sea level rise. These findings provide strong motivation for further studies that investigate the effect of past and future relative sea level

Journal article

Collins DS, Avdis A, Wells MR, Dean CD, Mitchell AJ, Allison PA, Johnson HD, Hampson GJ, Hill J, Piggott MDet al., 2021, Prediction of shoreline–shelf depositional process regime guided by palaeotidal modelling, Earth-Science Reviews, Vol: 223, ISSN: 0012-8252

Ancient shoreline–shelf depositional systems are influenced by an unusually wide array of geological, biological and hydrodynamic processes, with sediment transport and deposition primarily determined by the interaction of river, wave (including storm) and tidal processes, and changes in relative sea level. Understanding the impact of these processes on shoreline–shelf morphodynamics and stratigraphic preservation remains challenging. Numerical modelling integrated with traditional facies analysis provides an increasingly viable approach, with the potential to quantify, and thereby improve understanding of, the impact of these complex coastal sedimentary processes. An integrated approach is presented here that focuses on palaeotidal modelling to investigate the controls on ancient tides and their influence on sedimentary deposition and preservation – one of the three cornerstones of the ternary process classification scheme of shoreline-shelf systems. Numerical tidal modelling methodology is reviewed and illustrated in three palaeotidal model case studies of different scales and focus. The results are synthesised in the context of shoreline–shelf processes, including a critique and modification of the process-based classification scheme.The emphasis on tidal processes reflects their global importance throughout Earth’s history. Ancient palaeotidal models are able to highlight and quantify the following four controls on tidal processes: (1) the physiography (shape and depth) of oceans (1000s km scale) determines the degree of tidal resonance; (2) the physiography of ocean connections to partly enclosed water bodies (100–1000s km scale) determines the regional-scale flux of tidal energy (inflow versus outflow); (3) the physiography of continental shelves influences shelf tidal resonance potential; and (4) tides in relatively local-scale embayments (typically 1–10s km scale) are influenced by the balance of tidal amplification

Journal article

Coles D, Angeloudis A, Greaves D, Hastie G, Lewis M, Mackie L, McNaughton J, Miles J, Neill S, Piggott M, Risch D, Scott B, Sparling C, Stallard T, Thies P, Walker S, White D, Willden R, Williamson Bet al., 2021, A review of the UK and British Channel Islands practical tidal stream energy resource, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 477, Pages: 1-33, ISSN: 1364-5021

This review provides a critical, multi-faceted assessment of the practical contribution tidal stream energy can make to the UK and British Channel Islands future energy mix. Evidence is presented that broadly supports the latest national-scale practical resource estimate, of 34 TWh/year, equivalent to 11% of the UK’s current annual electricity demand. The size of the practical resource depends in part on the economic competitiveness of projects. In the UK, 124 MW of prospective tidal stream capacity is currently eligible to bid for subsidy support (MeyGen 1C, 80 MW; PTEC, 30 MW; and Morlais, 14 MW). It is estimated that the installation of this 124 MW would serve to drive down the levelized cost of energy (LCoE), through learning, from its current level of around 240 £/MWh to below 150 £/MWh, based on a mid-range technology learning rate of 17%. Doing so would make tidal stream cost competitive with technologies such as combined cycle gas turbines, biomass and anaerobic digestion. Installing this 124 MW by 2031 would put tidal stream on a trajectory to install the estimated 11.5 GW needed to generate 34 TWh/year by 2050. The cyclic, predictable nature of tidal stream power shows potential to provide additional, whole-system cost benefits. These include reductions in balancing expenditure that are not considered in conventional LCoE estimates. The practical resource is also dependent on environmental constraints. To date, no collisions between animals and turbines have been detected, and only small changes in habitat have been measured. The impacts of large arrays on stratification and predator–prey interaction are projected to be an order of magnitude less than those from climate change, highlighting opportunities for risk retirement. Ongoing field measurements will be important as arrays scale up, given the uncertainty in some environmental and ecological impact models. Ba

Journal article

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