Publications
95 results found
Bisson KM, Gassó S, Mahowald N, et al., 2023, Observing ocean ecosystem responses to volcanic ash, Remote Sensing of Environment, Vol: 296, ISSN: 0034-4257
Volcanic eruptions can be catastrophic events, particularly when they occur in inhabited coastal environments. They also play important roles in climate and biogeochemical cycles, including through nutrient deposition in the ocean. Volcanic ash studies in the ocean have focused on the phytoplankton response, generally quantifying changes in chlorophyll-a concentration. Many gaps remain in addressing fundamental questions regarding why volcanic ash deposition may enhance or limit both phytoplankton growth and/or drive community composition shifts. Here we outline a wide, multidisciplinary vision for monitoring volcanic eruptions near ocean ecosystems from satellites, including considerations for characteristics of airborne volcanic ash and ash geochemistry in seawater. Ultimately, observations beyond chlorophyll-a are needed to quantify phytoplankton communities (including harmful algal blooms) and possible impacts across higher trophic levels. We synthesize relevant research from volcanic studies as well as atmospheric and ocean sciences to identify the ‘known unknowns’ in ash-ecosystem studies. Our goal is to move toward an improved understanding of how real-time and near-real-time monitoring of volcanic eruptions can help address societally relevant questions.
Kärnä T, Wallwork JG, Kramer SC, 2023, Efficient Optimization of a Regional Water Elevation Model With an Automatically Generated Adjoint, Journal of Advances in Modeling Earth Systems, Vol: 15
Calibration of unknown model parameters is a common task in many ocean model applications. We present an adjoint-based optimization of an unstructured mesh shallow water model for the Baltic Sea. Spatially varying bottom friction parameter is tuned to minimize the misfit with respect to tide gauge sea surface height (SSH) observations. A key benefit of adjoint-based optimization is that computational cost does not depend on the number of unknown variables. Adjoint models are, however, typically very laborious to implement. In this work, we leverage a domain specific language framework in which the discrete adjoint model can be obtained automatically. The adjoint model is both exactly compatible with the discrete forward model and computationally efficient. A gradient-based quasi-Newton method is used to minimize the misfit. Optimizing spatially-variable parameters is typically an under-determined problem and can lead to over-fitting. We employ Hessian-based regularization to penalize the spatial curvature of the friction field to overcome this problem. The SSH dynamics in the Baltic Sea are simulated for a 3-month period. Optimization of the bottom friction parameter results in significant improvement of the model performance. The results are especially encouraging in the complex Danish Straits region, highlighting the benefit of unstructured meshes. Domain specific language frameworks enable automated model analysis and provide easy access to adjoint modeling. Our application shows that this capability can be enabled with few efforts, and the optimization procedure is robust and computationally efficient.
Pilia S, Davies DR, Hall R, et al., 2023, Post-subduction tectonics induced by extension from a lithospheric drip, NATURE GEOSCIENCE, Vol: 16, Pages: 646-+, ISSN: 1752-0894
Pilia S, Davies DR, Hall R, et al., 2023, Post-subduction tectonics induced by extension from a lithospheric drip, NATURE GEOSCIENCE, ISSN: 1752-0894
Scott WI, Kramer SC, Holland PR, et 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
Zhang C, Zhang J, Angeloudis A, et al., 2023, Physical Modelling of Tidal Stream Turbine Wake Structures under Yaw Conditions, ENERGIES, Vol: 16
Zhang C, Angeloudis A, Kramer SC, et al., 2023, Investigating the effect of the sediment transport on tidal turbine array performance, Pages: 189-196
A two-dimensional hydrodynamic model is coupled with a suspended and bedload sediment transport model within the Thetis coastal ocean modelling framework. In investigating the effect of sediment transport on turbine array performance, we consider two artificial scenarios of 16 turbines deployed in aligned and staggered layouts to explore the impact of morphodynamics on power conversion. An optimisation algorithm is then applied to improve the position of turbines to maximize power output. Comparing this optimisation for a case with and without sediment transport we study the effect of morphodynamics on optimal layouts. The results show that sediment transport can significantly influence the performance of the aligned layout turbine array. As for the layout optimisation process, the inclusion of sediment transport makes little difference to the final results, while the computational cost becomes substantial when including the sediment model within the optimisation, even for a steady state case.
Zhang C, Kramer SC, Angeloudis A, et al., 2022, Improving tidal turbine array performance through the optimisation of layout and yaw angles, International Marine Energy Journal, Vol: 5, Pages: 273-280
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 array design optimisation. An idealised rectangular channel test case is studied to demonstrate this optimisation framework. Located in the centre of the computational domain, arrays comprised of 12 turbines are tested in aligned and staggered layouts. The setups are initially optimised based on their yaw angles alone. In turn, turbine coordinates and yaw angles are also optimized simultaneously. Results indicate that for an aligned turbine array case under steady state conditions, the energy output can be increased by approximately 80% when considering yaw angle optimisation alone. For the staggered turbine ar-ray, 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.
Clare MCA, Wallwork JG, Kramer SC, et 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.
Chen F, Davies DR, Goes S, et al., 2022, Comparing the Dynamics of Free Subduction in Cartesian and Spherical Domains, GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS, Vol: 23
Chen F, Davies DR, Goes S, et al., 2022, How Slab Age and Width Combine to Dictate the Dynamics and Evolution of Subduction Systems: A 3-D Spherical Study, GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS, Vol: 23
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- Citations: 2
Chen F, Davies DR, Goes S, et al., 2022, Comparing the Dynamics of Free Subduction in Cartesian and Spherical Domains
Halilovic S, Böttcher F, Kramer S, et 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.
Pan W, Kramer SC, Piggott MD, et 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.
Chen F, Davies DR, Goes S, et al., 2022, How slab age and width combine to dictate the dynamics and evolution of subduction systems: a 3-D spherical study
Davies DR, Kramer SC, Ghelichkhan S, et al., 2022, Towards automatic finite-element methods for geodynamics via Firedrake, GEOSCIENTIFIC MODEL DEVELOPMENT, Vol: 15, Pages: 5127-5166, ISSN: 1991-959X
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- Citations: 1
Duvernay T, Davies DR, Mathews CR, et al., 2022, Continental Magmatism: The Surface Manifestation of Dynamic Interactions Between Cratonic Lithosphere, Mantle Plumes and Edge-Driven Convection, GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS, Vol: 23
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- Citations: 4
Clare MCA, Kramer SC, Cotter CJ, et 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.
Zhang J, Zhang C, Angeloudis A, et 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.
Duvernay T, Davies DR, Mathews C, et al., 2022, Continental Magmatism: The Surface Manifestation of Dynamic Interactions Between Cratonic Lithosphere, Mantle Plumes and Edge-Driven Convection
Davies DR, Kramer SC, Ghelichkhan S, et al., 2022, Automating Finite Element Methods for Geodynamics via Firedrake
<jats:p>Abstract. Firedrake is an automated system for solving partial differential equations using the finite element method. By applying sophisticated performance optimisations through automatic code-generation techniques, it provides a means to create accurate, efficient, flexible, easily extensible, scalable, transparent and reproducible research software, that is ideally suited to simulating a wide-range of problems in geophysical fluid dynamics. Here, we demonstrate the applicability of Firedrake for geodynamical simulation, with a focus on mantle dynamics. The accuracy and efficiency of the approach is confirmed via comparisons against a suite of analytical and benchmark cases of systematically increasing complexity, whilst parallel scalability is demonstrated up to 12288 compute cores, where the problem size and the number of processing cores are simultaneously increased. In addition, Firedrake's flexibility is highlighted via straightforward application to different physical (e.g. complex nonlinear rheologies, compressibility) and geometrical (2-D and 3-D Cartesian and spherical domains) scenarios. Finally, a representative simulation of global mantle convection is examined, which incorporates 230 Myr of plate motion history as a kinematic surface boundary condition, confirming its suitability for addressing research problems at the frontiers of global mantle dynamics research. </jats:p>
Piggott MD, Kramer SC, Funke SW, et al., 2022, 8.10 - Optimization of Marine Renewable Energy Systems, Comprehensive Renewable Energy, Second Edition: Volume 1-9, Pages: 176-220, ISBN: 9780128197271
Optimizing marine renewable energy systems to maximize performance is key to their success. However, a range of physical, environmental, engineering, economic as well as computational challenges means that this is not straightforward. This article considers this topic, focusing on those systems whose performance is coupled to the hydrodynamics providing the resource; tidal power represents a clear example of this. In such cases system design must be optimal in relation to the resource׳s magnitude as well as its spatial and temporal variation, which are all dependent on the system׳s configuration and operation and so cannot be assumed to be known at the design stage. Designing based on the ambient resource could lead to under-performance. Coupling between the design and the resource has implications for the complexity of the optimization problem and potential hydrodynamical and environmental impacts. This coupling distinguishes many marine energy systems from other renewables which do not impact in any significant manner on the resource. The optimal design of marine energy systems thus represents a challenging and somewhat unique problem. However, feedback also opens up a number of possibilities where the resource can be ‘controlled’, to maximize the cumulative power obtained from multiple devices or plants, or to achieve some other complementary goal. Design optimization is thus critical, with many issues to consider. Due to the complexity of the problem a computational based solution is a necessity in all but the simplest scenarios. However, the coupled feedback requires that an iterative solution approach be used, which combined while the vast range of spatial and temporal scales means that methodological compromises need to be made. These compromises need to be understood, with the correct computational tool used at the appropriate point in the design process. This article reviews these challenges as well as the progress that has been made in addressi
Mackie L, Kramer SC, Piggott MD, et al., 2021, Assessing impacts of tidal power lagoons of a consistent design, OCEAN ENGINEERING, Vol: 240, ISSN: 0029-8018
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- Citations: 6
Chen F, Davies DR, Goes S, et al., 2021, How sphericity combines with the age and width of slabs to dictate the dynamics and evolution of subduction systems on Earth
Duvernay T, Davies DR, Mathews CR, et al., 2021, Linking Intraplate Volcanism to Lithospheric Structure and Asthenospheric Flow, GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS, Vol: 22
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- Citations: 13
Duvernay T, Davies DR, Mathews CR, et al., 2021, Linking Intra-Plate Volcanism to Lithospheric Structure and Asthenospheric Flow
Zhang C, Kramer SC, Angeloudis A, et 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.
Goss ZL, Coles DS, Kramer SC, et 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
Kramer S, Davies R, Wilson C, 2021, Analytical solutions for mantle flow in cylindrical and spherical shells, Geoscientific Model Development, Vol: 14, Pages: 1899-1919, ISSN: 1991-959X
Computational models of mantle convection must accurately represent curved boundaries and the associated boundary conditions of a 3-D spherical shell, bounded by Earth's surface and the core–mantle boundary. This is also true for comparable models in a simplified 2-D cylindrical geometry. It is of fundamental importance that the codes underlying these models are carefully verified prior to their application in a geodynamical context, for which comparisons against analytical solutions are an indispensable tool. However, analytical solutions for the Stokes equations in these geometries, based upon simple source terms that adhere to physically realistic boundary conditions, are often complex and difficult to derive. In this paper, we present the analytical solutions for a smooth polynomial source and a delta-function forcing, in combination with free-slip and zero-slip boundary conditions, for both 2-D cylindrical- and 3-D spherical-shell domains. We study the convergence of the Taylor–Hood (P2–P1) discretisation with respect to these solutions, within the finite element computational modelling framework Fluidity, and discuss an issue of suboptimal convergence in the presence of discontinuities. To facilitate the verification of numerical codes across the wider community, we provide a Python package, Assess, that evaluates the analytical solutions at arbitrary points of the domain.
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.
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