Angus H. Gibson’s research while affiliated with Australian National University and other places

regional-mom6 is a Python package that provides an easy and versatile way to set up regional configurations of the Modular Ocean Model version 6 (MOM6). code repository: https://github.com/COSIMA/regional-mom6

Reconstructing the thermo-chemical evolution of Earth's mantle and its diverse surface manifestations is a widely recognised grand challenge for the geosciences. It requires the creation of a digital twin: a digital representation of Earth's mantle across space and time that is compatible with available observational constraints on the mantle's structure, dynamics and evolution. This has led geodynamicists to explore adjoint-based approaches that reformulate mantle convection modelling as an inverse problem, in which unknown model parameters can be optimised to fit available observational data. Whilst there has been a notable increase in the use of adjoint-based methods in geodynamics, the theoretical and practical challenges of deriving, implementing and validating adjoint systems for large-scale, non-linear, time-dependent problems, such as global mantle flow, has hindered their broader use. Here, we present the Geoscientific ADjoint Optimisation PlaTform (G-ADOPT), an advanced computational modelling framework that overcomes these challenges for coupled, non-linear, time-dependent systems by integrating three main components: (i) Firedrake, an automated system for the solution of partial differential equations using the finite-element method; (ii) Dolfin-Adjoint, which automatically generates discrete adjoint models in a form compatible with Firedrake; and (iii) the Rapid Optimisation Library, ROL, an efficient large-scale optimisation toolkit; G-ADOPT enables the application of adjoint methods across geophysical continua, showcased herein for geodynamics. Through two sets of synthetic experiments, we demonstrate the application of this framework to the initial condition problem of mantle convection, in both square and annular geometries, for both isoviscous and non-linear rheologies. We confirm the validity of the gradient computations underpinning the adjoint approach, for all cases, through second-order Taylor remainder convergence tests and subsequently demonstrate excellent recovery of the unknown initial conditions. Moreover, we show that the framework achieves theoretical computational efficiency. Taken together, this confirms the suitability of G-ADOPT for reconstructing the evolution of Earth's mantle in space and time. The framework overcomes the significant theoretical and practical challenges of generating adjoint models and will allow the community to move from idealised forward models to data-driven simulations that rigorously account for observational constraints and their uncertainties using an inverse approach.

regional-mom6 is a Python package that provides an easy and versatile way to set up regional configurations of the Modular Ocean Model version 6 (MOM6).

Oceanic internal waves are a major driver for turbulent mixing in the ocean, which controls the global overturning circulation and the oceanic heat and carbon transport. Internal waves are observed to have a continuous energy distribution across all wave frequencies and scales, commonly known as the internal wave continuum, despite being forced at near-inertial and tidal frequencies at large scales. This internal wave continuum is widely thought to be developed primarily through wave-wave interactions. Here we show, using realistic numerical simulations in the subpolar North Atlantic, that oceanic eddies rapidly distribute large-scale wind-forced near-inertial wave energy across spatio-temporal scales, thereby forming an internal wave continuum within three weeks. As a result, wave energy dissipation patterns are controlled by eddies and are substantially enhanced below the mixed layer. The efficiency of this process potentially explains why a phase lag between high-frequency and near-inertial wave energy was observed in eddy-poor regions but not in eddy-rich regions. Our findings highlight the importance of eddies in forming an internal wave continuum and in controlling upper ocean mixing patterns.

Reconstructing the thermo-chemical evolution of Earth's mantle and its diverse surface manifestations is a widely-recognised grand challenge for the geosciences. It requires the creation of a digital twin: a digital representation of Earth's mantle across space and time that is compatible with available observational constraints on the mantle's structure, dynamics and evolution. This has led geodynamicists to explore adjoint-based approaches that reformulate mantle convection modelling as an inverse problem, in which unknown model parameters can be optimised to fit available observational data. Whilst recent years have seen a notable increase in the use of adjoint-based methods in geodynamics, the theoretical and practical challenges of deriving, implementing and validating adjoint systems for large-scale, non-linear, time-dependent problems, such as global mantle flow, has hindered their broader use. Here, we present the Geoscientific Adjoint Optimisation Platform (G-ADOPT), an advanced computational modelling framework that overcomes these challenges for coupled, non-linear, time-dependent systems. By integrating three main components: (i) Firedrake, an automated system for the solution of partial differential equations using the finite element method; (ii) Dolfin-Adjoint, which automatically generates discrete adjoint models in a form compatible with Firedrake; and (iii) the Rapid Optimisation Library, ROL, an efficient large-scale optimisation toolkit; G-ADOPT enables the application of adjoint methods across geophysical continua, showcased herein for geodynamics. Through two sets of synthetic experiments, we demonstrate application of this framework to the initial condition problem of mantle convection, in both square and annular geometries, for both isoviscous and non-linear rheologies. We confirm the validity of the gradient computations underpinning the adjoint approach, for all cases, through second-order Taylor remainder convergence tests, and subsequently demonstrate excellent recovery of the unknown initial conditions. Moreover, we show that the framework achieves theoretical computational efficiency. Taken together, this confirms the suitability of G-ADOPT for reconstructing the evolution of Earth's mantle in space and time. The framework overcomes the significant theoretical and practical challenges of generating adjoint models, and will allow the community to move from idealised forward models to data-driven simulations that rigorously account for observational constraints and their uncertainties using an inverse approach.

Oceanic internal waves are a major driver for turbulent mixing in the ocean, which controls the global overturning circulation and the oceanic heat and carbon transport. Internal waves are observed to have a continuous energy distribution across all wave frequencies and scales, commonly known as the internal wave continuum, despite being forced at near-inertial and tidal frequencies at large scales. This internal wave continuum is widely thought to be developed primarily through wave-wave interactions. However, the development through wave-wave interactions occurs on yearly timescales and is insufficient to maintain the observed continuum given the large episodic wind energy input. Here we show, using realistic numerical simulations in the subpolar North Atlantic, that oceanic eddies rapidly distribute large-scale wind-forced near-inertial wave energy across spatio-temporal scales, thereby forming an internal wave continuum within three weeks. As a result, wave energy dissipation patterns are controlled by eddies and are significantly enhanced below the mixed layer. The efficiency of this process potentially explains why a phase lag between high-frequency and near-inertial wave energy was observed in eddy-poor regions but not in eddy-rich regions. Our findings highlight the importance of eddies in forming an internal wave continuum and in controlling upper ocean mixing patterns.

Several of Earth’s intra-plate volcanic provinces lie on or adjacent to continental lithosphere. Although many are believed to mark the surface expression of mantle plumes, our limited understanding of how buoyant plumes interact with heterogeneous continental lithosphere prevents further progress in identifying mechanisms at the root of continental volcanism. In this study, using a suite of 3-D geodynamical models, we demonstrate that the magmatic expression of plumes in continental settings is complex and strongly sensitive to the location of plume impingement, differing substantially from that expected beneath more homogeneous oceanic lithosphere. Within Earth’s continents, thick cratonic roots locally limit decompression melting. However, they deflect plume conduits during their ascent, with plume material channelled along gradients in lithospheric thickness, activating magmatism away from the plume conduit, sometimes simultaneously at locations more than a thousand kilometres apart. This magmatism regularly concentrates at lithospheric steps, where it may be difficult to distinguish from that arising through edge-driven convection. At times, the flow field associated with the plume enhances melting at these steps long before plume material enters the melting zone, implying that differentiating geochemical signatures will be absent. Beneath regions of thinner lithosphere, plume-related flow can force material downwards at lithospheric steps, shutting off pre-existing edge-related magmatism. Additionally, variations in lithospheric structure can induce internal destabilisation of ponding plume material, driving intricate magmatic patterns at the surface. Our analysis highlights the challenges associated with linking continental magmatism to underlying mantle dynamics, motivating an inter-disciplinary approach in future studies.

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 of creating 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 are confirmed via comparisons against a suite of analytical and benchmark cases of systematically increasing complexity, whilst parallel scalability is demonstrated up to 12 288 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 non-linear 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 Firedrake's suitability for addressing research problems at the frontiers of global mantle dynamics research.

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.