Imperial College London


Faculty of EngineeringDepartment of Earth Science & Engineering

Professor of Computational Geoscience and Engineering



m.d.piggott Website




4.82Royal School of MinesSouth Kensington Campus





Publication Type

197 results found

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

<jats:title>Abstract</jats:title><jats:p>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, <jats:italic>Thetis</jats:italic>. 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.</jats:p>

Journal article

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

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

Anagnostopoulos S, Piggott MD, 2022, Offshore wind farm wake modelling using deep feed forward neural networks for active yaw control and layout optimisation, ISSN: 1742-6588

Offshore wind farm modelling has been an area of rapidly increasing interest over the last two decades, with numerous analytical as well as computational-based approaches developed, in an attempt to produce designs that improve wind farm efficiency in power production. This work presents a Machine Learning (ML) framework for the rapid modelling of wind farm flow fields, using a Deep Neural Network (DNN) neural network architecture, trained here on approximate turbine wake fields, calculated on the state-of-the-art wind farm modelling software FLORIS. The constructed neural model is capable of accurately reproducing single wake deficits at hub-level for a 5MW wind turbine under yaw and a wide range of inlet hub speed and turbulence intensity conditions, at least an order of magnitude faster than the analytical wake-based solution method, yielding results with 1.5% mean absolute error. A superposition algorithm is also developed to construct flow fields over the whole wind farm domain by superimposing individual wakes. A promising advantage of the present approach is that its performance and accuracy are expected to increase even further when trained on high-fidelity CFD or real-world data through transfer learning, while its computational cost remains low.

Conference paper

Warder SC, Angeloudis A, Piggott MD, 2022, Sedimentological data-driven bottom friction parameter estimation in modelling Bristol Channel tidal dynamics, Ocean Dynamics, ISSN: 1616-7341

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.

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

Mackie L, Kramer SC, Piggott MD, Angeloudis Aet al., 2021, Assessing impacts of tidal power lagoons of a consistent design, OCEAN ENGINEERING, Vol: 240, ISSN: 0029-8018

Journal article

Avalos Patino J, Dargaville S, Neethling S, Piggott Met al., 2021, Impact of inhomogeneous unsteady participating media in a coupled convection-radiation system using finite element based methods, International Journal of Heat and Mass Transfer, Vol: 176, Pages: 1-16, ISSN: 0017-9310

Combined convection–radiation is a common phenomenon in many engineering problems. A differentially–heated rectangular enclosure is a widely–used benchmark for testing numerical techniques developed for solving the coupled momentum and energy equations related to combined convection–radiation. Previous studies have tended to describe the phenomenon in cases using simplified characteristics for the participating media including the assumptions of: (i) uniform distribution, (ii) homogeneous cross section, (iii) grey gas radiation and (iv) under steady state conditions. The effects of an inhomogeneous unsteady participating media, e.g. composed of a mixture of gases, are arguably understudied. In this work the effect of an inhomogeneous unsteady participating media on combined convection–radiation inside a rectangular enclosure is considered, under both grey and non-grey gas modelling approaches involving a mixture of gases. A key novelty in this work is the inclusion of the ability to handle inhomogeneous participating media which change in space, time and absorption cross section values as a result of the convection–radiation coupling, allowing us to assess different gas modelling approaches. A global gas radiation model is used and a new non–uniform discretisation method for the absorption distribution function is introduced; this method allows a better handling of those energy groups in which the Planck absorption coefficient is low, improving the performance of the spherical harmonics method and mitigating ray–effects on finite elements in angle discretisation. The momentum and energy equations are solved numerically using finite element based discretisation methods. The radiative transfer equation is solved numerically using both spherical harmonics and finite elements for the angular discretisation, with their relative performance compared. The results highlight the importance that the characteristics of the partic

Journal article

Zhang C, Kramer SC, Angeloudis A, Zhang J, Lin X, Piggott MDet al., 2021, Improving tidal turbine array performance through the optimisation of layout and yaw angles, European Wave and Tidal Energy Conference, Pages: 2205-1-2205-7-2205-1-2205-7, ISSN: 2706-6932

Tidal stream currents change in magnitude and direction during flood and ebb tides. Setting the most appropriate yaw angles for a tidal turbine is not only important to account for the performance of a single turbine, but can also be significant for the interactions between the turbines within an array. In this paper, a partial differentiation equation (PDE) constrained optimisation approach is established based on the Thetis coastal ocean modelling framework. The PDE constraint takes the form here of the two-dimensional, depth-averaged shallow water equations which are used to simulate tidal elevations and currents in the presence of tidal stream turbine arrays. The Sequential Least Squares Programming (SLSQP) algorithm is applied with a gradient obtained via the adjoint method in order to perform design optimisation. An idealised rectangular channel test case is studied to demonstrate this optimisation framework. Located in the centre of the computational domain, turbine arrays comprised of 12 turbines are tested in aligned and staggered layouts. The setups are initially optimised based on their yaw angles alone; their locations and yaw angles are also optimized simultaneously to improve the array overall performance. Results indicate that for the aligned turbine array case, the energy output can be increased by approximately 80% when considering yaw angle optimisation alone. For the staggered turbine array, the increase is approximately 30%. The yaw optimised staggered array is able to outperform the yaw optimised aligned array by approximately 8%. If both layout and the yaw angles of the turbines are considered within the optimisation then the increase is more significant compared with optimising yaw angle alone.

Conference paper

Goss ZL, Coles DS, Kramer SC, Piggott MDet al., 2021, Efficient economic optimisation of large-scale tidal stream arrays, Applied Energy, Vol: 295, Pages: 1-17, ISSN: 0306-2619

As the tidal energy industry moves from demonstrator arrays comprising just a few turbines to large-scale arrays made up of potentially hundreds of turbines, there is a need to optimise both the number of turbines and their spatial distribution in order to minimise cost of energy. Optimising array design manually may be feasible for small arrays, but becomes an impractically large approach when the number of devices is high, especially if taking into account both the cost effectiveness of each turbine and also the coupled nature of the turbine locations and the local as well as far-field hydrodynamics.Previous work has largely focused on producing computational tools to automatically design the size and layout of large-scale tidal turbine arrays to optimise power. There has been some limited preliminary work to incorporate costs into these models, in order to improve the economic viability of tidal arrays. This paper provides the first in depth implementation and analysis of economic functionals, based upon metrics such as break even power and levelised cost of energy, used for design of explicit array sizing and spatial variation.The addition of these new economic functionals introduces complexity by increasing the number of inputs to the model, each of which are subject to their own uncertainty in value. For this reason, sensitivity analysis becomes both more important as well as more difficult to undertake. This paper presents a novel rapid methodology for deriving the optimal array design (number of turbines and their spatial distribution throughout the farm area) to minimise cost functionals, and its sensitivity to variations in the economic inputs. Importantly, the new aspects of this method introduced here do not rely on repeated model runs and iterative optimisation, two aspects that typically prove to be impractically expensive computationally. This more readily allows for the impact of changes in investor priorities to be investigated. It is also shown tha

Journal article

Rasheed S, Warder SC, Plancherel Y, Piggott MDet al., 2021, An improved gridded bathymetric data set and tidal model for the Maldives Archipelago, Earth and Space Science, Vol: 8, Pages: 1-15, ISSN: 2333-5084

The Maldives faces a unique range of environmental challenges. While the country is almost entirely dependent upon oceanic resources with more than 99% of the area covered by ocean, the absence of a suitable bathymetric map of the seafloor of the Maldives severely limits the adoption and application of modern scientific methods for the prediction of both physical and biological oceanic processes across the country. Here, we present a new bathymetric data set for the country based upon accumulating data from various sources and demonstrate that the synthesis of these provides a far more accurate representation of the shallow water areas of the region than currently available products. We also show that the new bathymetric data set is of sufficiently high resolution to model tidal flows across the archipelago for the first time. The new bathymetric data set provides numerous opportunities to better understand oceanic flow, associated physical and biogeochemical processes, and their correlation to one another across the Maldives archipelago.

Journal article

Warder SC, Horsburgh KJ, Piggott MD, 2021, Adjoint-based sensitivity analysis for a numerical storm surge model, Ocean Modelling, Vol: 160, Pages: 1-13, ISSN: 1463-5003

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.

Journal article

Mackie L, Evans PS, Harrold MJ, ODoherty T, Piggott MD, Angeloudis Aet al., 2021, Modelling an energetic tidal strait: investigating implications of common numerical configuration choices, Applied Ocean Research, Vol: 108, Pages: 1-15, ISSN: 0141-1187

Representation of the marine environment is key for reliable coastal hydrodynamic models. This study investigates the implications of common depth-averaged model configuration choices in sufficiently characterising seabed geometry and roughness. In particular, applications requiring a high level of accuracy and/or exhibiting complex flow conditions may call for greater detail in marine environment representation than typically adopted in coastal models. Ramsey Sound, a macrotidal strait in Pembrokeshire, Wales, UK is considered as a case study. The site contains various steeply inclined bathymetric features, including a submerged pinnacle named Horse Rock and a rocky reef called “The Bitches”. The available energy in Ramsey Sound’s tidal currents has attracted attention from tidal energy developers. There is interest in accurately modelling the energetic hydrodynamics surrounding its pronounced bathymetry. The coastal flow solver Thetis is applied to simulate the flow conditions in Ramsey Sound. It is shown that notable prominent bathymetric features in the strait influence localised and, most importantly, regional hydrodynamic characteristics. “The Bitches” consistently accelerate flow in the strait while Horse Rock induces a notable wake structure and flow reversals. The model is calibrated against bed- and vessel-mounted Acoustic Doppler Current Profiler (ADCP) observations, by altering seabed roughness parameterisations. A spatially variable and locally scaled Manning coefficient based on diverse seabed classification observations is found to improve model performance in comparison to uniformly applied constants, the latter a more common approach. The local impact of altering the Manning coefficient configuration is found to be greatest during spring flood periods of high velocity currents. Meanwhile, the effect of coarsening the computational mesh around bathymetric features towards values more typically applied in coastal models i

Journal article

Rasheed S, Warder SC, Plancherel Y, Piggott MDet al., 2021, Response of tidal flow regime and sediment transport in North Male' Atoll, Maldives to coastal modification and sea level rise, Ocean Science, Vol: 17, Pages: 319-334, ISSN: 1812-0784

Changes to coastlines and bathymetry alter tidal dynamics and associated sediment transport processes, impacting upon a number of threats facing coastal regions, including flood risk and erosion. Especially vulnerable are coral atolls such as those that make up the Maldives archipelago, which has undergone significant land reclamation in recent years and decades and is also particularly exposed to sea level rise. Here we develop a tidal model of Malé Atoll, Maldives, the first atoll-scale and multi-atoll-scale high-resolution numerical model of the atolls of the Maldives and use it to assess potential changes to sediment grain size distributions in the deeper atoll basin, under sea level rise and coastline alteration scenarios. The results indicate that the impact of coastline modification over the last two decades at the island scale is not limited to the immediate vicinity of the modified island but can also significantly impact the sediment grain size distribution across the wider atoll basin. Additionally, the degree of change in sediment distribution which can be associated with sea level rise that is projected to occur over relatively long time periods is predicted to occur over far shorter time periods with coastline changes, highlighting the need to better understand, predict and mitigate the impact of land reclamation and other coastal modifications before conducting such activities.

Journal article

Kadiri M, Zhang H, Angeloudis A, Piggott MDet al., 2021, Evaluating the eutrophication risk of an artificial tidal lagoon, OCEAN & COASTAL MANAGEMENT, Vol: 203, ISSN: 0964-5691

Journal article

Clare M, Piggott M, Cotter C, 2021, Assessing erosion and flood risk in the coastal zone through the application of the multilevel Monte Carlo method, Publisher: California Digital Library (CDL)

The risk from erosion and flooding in the coastal zone has the potential to increase in a changing climate. The development and use of coupled hydro-morphodynamic models is therefore becoming an ever higher priority. However, their use as decision support tools suffers from the high degree of uncertainty associated with them, due to incomplete knowledge as well as natural variability in the system. Here we show for the first time how the multilevel Monte Carlo method (MLMC) can be applied to hydro-morphodynamic models, in this case XBeach, to quantify uncertainty by computing statistics of 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. A variety of theoretical and real-world coastal zone case studies are considered, for which output variables that are important to the assessment of flood and erosion risk are estimated, such as wave run-up height and total eroded volume. We show that MLMC can significantly reduce computational cost, resulting in speed up factors of 40 or greater compared to a simple Monte Carlo approach, whilst still maintaining the same level of accuracy. Furthermore, MLMC is used to estimate the cumulative distribution of these output variables for given uncertain parameters. This allows the risk of a variable exceeding a certain value to be calculated, for example the risk of the wave run-up height exceeding the height of a physical structure such as a seawall; this is a useful capability to inform decision-making processes.

Working paper

Pan W, Kramer SC, Piggott MD, 2021, A sigma-coordinate non-hydrostatic discontinuous finite element coastal ocean model, Ocean Modelling, Vol: 157, Pages: 1-21, ISSN: 1463-5003

A𝜎-coordinate non-hydrostatic coastal ocean model is developed using the discontinuous Galerkin fi-nite element method. With the selection of the low-order piecewise-constant PDG0and piecewise-linearPDG1discretisations in the vertical for the velocity and pressure fields, respectively, the proposed𝜎-coordinatemodel can naturally retain the wave dispersion characteristics of the widely-adopted multi-layer approach ofZijlema and Stelling (2005), which is demonstrated through both mathematical derivation and numerical tests.Under the finite element approach, higher-order vertical discretisation choices can also be readily made whichcan reduce the number of vertical layers required for the accurate representation of wave dispersion. Themodel is verified and validated through comparisons against a series of test cases with analytical solutions orexperimental measurements. All the comparisons demonstrate good agreement, indicating that the proposedmodel can accurately represent dispersive barotropic surface waves with as few as one vertical layer, and cansimulate baroclinic internal waves with reasonable accuracy using relatively coarse mesh resolution. It is alsodemonstrated that consistency in the coupling of barotropic and baroclinic flows can be properly ensured.

Journal article

Clare MCA, Percival JR, Angeloudis A, Cotter CJ, Piggott MDet al., 2021, Hydro-morphodynamics 2D modelling using a discontinuous Galerkin discretisation, Computers and Geosciences, Vol: 146, Pages: 1-13, ISSN: 0098-3004

The development of morphodynamic models to simulate sediment transport accurately is a challenging process that is becoming ever more important because of our increasing exploitation of the coastal zone, as well as sea-level rise and the potential increase in strength and frequency of storms due to a changing climate. Morphodynamic models are highly complex given the non-linear and coupled nature of the sediment transport problem. Here we implement a new depth-averaged coupled hydrodynamic and sediment transport model within the coastal ocean model Thetis, built using the code generating framework Firedrake which facilitates code flexibility and optimisation benefits. To the best of our knowledge, this represents the first full morphodynamic model including both bedload and suspended sediment transport which uses a discontinuous Galerkin based finite element discretisation. We implement new functionalities within Thetis extending its existing capacity to model scalar transport to modelling suspended sediment transport, incorporating within Thetis options to model bedload transport and bedlevel changes. We apply our model to problems with non-cohesive sediment and account for effects of gravity and helical flow by adding slope gradient terms and parametrising secondary currents. For validation purposes and in demonstrating model capability, we present results from test cases of a migrating trench and a meandering channel comparing against experimental data and the widely-used model Telemac-Mascaret.

Journal article

Zhang M, Piggott MD, 2020, Unsupervised learning of particle image velocimetry, ISC High Performance 2020, Publisher: Springer International Publishing, Pages: 102-115, ISSN: 0302-9743

Particle Image Velocimetry (PIV) is a classical flow estimation problem which is widely considered and utilised, especially as a diagnostic tool in experimental fluid dynamics and the remote sensing of environmental flows. Recently, the development of deep learning based methods has inspired new approaches to tackle the PIV problem. These supervised learning based methods are driven by large volumes of data with ground truth training information. However, it is difficult to collect reliable ground truth data in large-scale, real-world scenarios. Although synthetic datasets can be used as alternatives, the gap between the training set-ups and real-world scenarios limits applicability. We present here what we believe to be the first work which takes an unsupervised learning based approach to tackle PIV problems. The proposed approach is inspired by classic optical flow methods. Instead of using ground truth data, we make use of photometric loss between two consecutive image frames, consistency loss in bidirectional flow estimates and spatial smoothness loss to construct the total unsupervised loss function. The approach shows significant potential and advantages for fluid flow estimation. Results presented here demonstrate that our method outputs competitive results compared with classical PIV methods as well as supervised learning based methods for a broad PIV dataset, and even outperforms these existing approaches in some difficult flow cases. Codes and trained models are available at

Conference paper

Mackie L, Coles D, Piggott M, Angeloudis Aet al., 2020, The potential for tidal range energy systems to provide continuous power: a UK case study, Journal of Marine Science and Engineering, Vol: 8, Pages: 1-23, ISSN: 2077-1312

The extraction of tidal energy from head differences represents a predictable and flexible option for generating electricity. Here, we investigate the generation potential of prospective tidal power plants in the UK. Originally conceived as separate projects, operating these schemes as a cooperative system could prove beneficial. Combined with the inherent operational flexibility of tidal range-based schemes, a notable tidal phase difference in selected sites allows for the system to spread power generation over a larger proportion of the day. Using depth-averaged modelling and gradient-based optimisation techniques, we explore how a flexible cumulative operation schedule could be applied to provide a degree of continuous supply if desirable. While fully continuous operation is not achieved, a number of different optimisation schedules deliver cumulative continuous supply for over half of the year. The average minimum cumulative power output on these days is consistently over 500 MW out of a total installed capacity of 6195.3 MW. Furthermore, by introducing financial incentives associated with reliable, baseload supply, we provide an economic assessment of the tidal power plant system. The daily minimum cumulative power output determines income in the modelled idealised baseload market, while excess supply is traded in an hourly variable wholesale energy market. Results indicate that subsidies would be required in order to make a pursuit of continuous generation financially advantageous over energy maximisation strategies.

Journal article

Smith RC, Hill J, Mouradian SL, Piggott MD, Collins GSet al., 2020, A new methodology for performing large scale simulations of tsunami generated by deformable submarine slides, Ocean Modelling, Vol: 153, Pages: 1-56, ISSN: 1463-5003

Large tsunamis can be generated by submarine slides, but these events are rare on human timescales and challenging to observe. Experiments and numerical modelling offer methods to understand the mechanisms by which they generate waves and what the potential hazard might be. However, to fully capture the complex waveform generated by a submarine slide, the slide dynamics must also be accurately modelled. It is computationally difficult to model both a three-dimensional submarine slide whilst simultaneously simulating oceanic-scale tsunamis. Past studies have either coupled localised models of the slide generation to oceanic-scale tsunami simulations or simplified the slide dynamics. Here, we present a new methodology of model coupling that generates the wave in the ocean-scale model via boundary-condition coupling of a two-dimensional dynamic slide simulation. We verify our coupling methodology by comparing model results to a previous simulation of a tsunamigenic slide in the Gulf of Mexico. We then examine the effect of slide deformation on the risk posed by hypothetical submarine slides around the UK. We show the deformable submarine slide simulations produce larger waves than the solid slide simulations due to the details of acceleration and velocity of the slide, although lateral spreading is not modelled. This work offers a new methodology for simulating oceanic-scale tsunamis caused by submarine slides using the output of a two–dimensional, multi-material simulation as input into a three–dimensional ocean model. This facilitates future exploration of the tsunami risk posed by tsunamigenic submarine slides that affect coastlines not normally prone to tsunamis.

Journal article

Goss ZL, Coles DS, Piggott MD, 2020, Identifying economically viable tidal sites within the Alderney Race through optimization of levelized cost of energy, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 378, Pages: 1-20, ISSN: 1364-503X

Costs of tidal stream energy generation are anticipated to fall considerably with array expansion and time. This is due to both economies of volume, where arrays comprising of large numbers of turbines can split fixed costs over a greater number of devices, and learning rates, where the industry matures and so arrays of the same size become cheaper due to lessons learned from previous installations. This paper investigates how tidal energy arrays can be designed to minimize the levelized cost of energy (LCOE), by optimizing not only the location but also the number of devices, to find a suitable balance between decreased costs due to economies of volume and diminishing returns due to global blockage effects. It focuses on the Alderney Race as a case study site due to the high velocities found there, making it a highly suitable site for large-scale arrays. It is demonstrated that between 1 and 2 GW could be feasibly extracted as costs in the tidal industry fall, with the LCOE depending greatly on the assumed costs. A Monte–Carlo analysis is undertaken to account for variability in capital and operational cost data used as inputs to the array optimization. Once optimized, the estimated P50 LCOE of an 80 MW array is £110/MWh. This estimate aligns closely with the level of subsidy considered for tidal stream projects in the Alderney Race in the past.

Journal article

Kramer S, Wilson C, Davies R, Funke SW, Greaves T, Avdis A, Lange M, Candy A, Cotter CJ, Pain C, Percival J, Mouradian S, Bhutani G, Gorman G, Gibson A, Duvernay T, Guo X, Maddison JR, Rathgeber F, Farrell P, Weiland M, Robinson D, Ham DA, Goffin M, Piggott M, Gomes J, Dargaville S, Everett A, Jacobs CT, Cavendish ABet al., 2020, FluidityProject/fluidity: New test cases "Analytical solutions for mantle flow in cylindrical and spherical shells"

This release adds new test cases described in the GMD paper "Analytical solutions for mantle flow in cylindrical and spherical shells"


Baker AL, Craighead RM, Jarvis EJ, Stenton HC, Angeloudis A, Mackie L, Avdis A, Piggott MD, Hill Jet al., 2020, Modelling the impact of tidal energy on species communities, Ocean and Coastal Management, Vol: 193, ISSN: 0964-5691

Tidal energy has the potential to form a key component of the energy production in a number of countries, including the UK. Nonetheless, the deployment of tidal energy systems is associated with potential environmental impacts as prime resource sites often coincide with unique ecosystems inhabited by sensitive organisms. Previous studies have generally focused on the hydrodynamic impact of tidal energy schemes, i.e. how schemes alter the flow dynamics and sedimentary transport processes. Whilst these efforts are key in understanding environmental impacts, there is no straightforward step for translating sediment to faunal changes. Species distribution models offer methods to quantitatively predict certain possible impacts of tidal energy extraction. The River Severn is a distinguished candidate region for tidal energy in the UK featuring sites under stringent ecological protection regulations. We examine the impact of a proposed Severn tidal barrage on 14 species via the linking of hydrodynamic modelling to species distribution models. Through a selection of species that are linked via a simple food web system we extrapolate changes in prey species to the respective predator species. We show that species at lower trophic levels would be adversely affected by the barrage, but higher trophic level organisms increase in possible habitable area. Once food web relationships are acknowledged this increase in habitat area decreases, but is still net positive. Overall, all 14 species were affected, with most gaining in distribution area, and only four losing distribution area within the Severn Estuary. We conclude that a large-scale tidal barrage may have detrimental and complex impacts on species distribution, altering food web dynamics and altering food availability in the Severn Estuary. The methodology outlined herein can be transferred to the assessment and optimisation of prospective projects globally to aide in the sustainable introduction of the technology.

Journal article

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