Mr William Scott

ANU College of Science

Research interests

Polar Science, Glacial Isostatic Adjustment, Sea Level, Oceanography, Glaciology, Numerical Methods, Inversion and Optimisation


I have a broad interest and background in Polar science, numerical modelling, oceanography and geophysics. I develop finite element models for simulating icy processes using Firedrake (

Researcher's projects

Glacial Isostatic Adjustment Modelling

I am currently working as a researcher at ANU, as part of a team developing and validating a finite element model for simulating Antarctic Glacial Isostatic Adjustment (GIA) using Firedrake.

Firedrake is a state-of-the-art framework for solving PDEs with the finite element method using code generation techniques (  GIA is the ongoing response of Earth's surface to changes in ice and water loading as Earth moves into and out of periods of glaciation. Antarctica is today still experiencing uplift in response to the reduction of the Antarctic Ice Sheet thousands of years ago. The present-day uplift rate and associated changes to Earth's gravity field mean that the satellite-based observational techniques used to quantify mass balance change are affected by GIA. Consequently, ice surface changes measured by satellite altimetry need to be corrected for uplift of the Antarctic bedrock, while mass changes derived from space gravity missions need to have the GIA gravity change signal removed. The latter is almost of the same magnitude as the present-day mass loss signal, so the GIA corrections are of immense significance.  


Computational simulations of GIA are fundamental to a quantitative understanding of this process. Such simulations require one to solve for load-induced visco-elastic deformation in a 3-D spherical shell, with further complexities (e.g., rotation) as determined by the nature of the problem under investigation. The accuracy, flexibility, reproducibility, transparency, extensibility, and efficiency of such simulations is becoming more and more important, considering the growing body of observational constraints on melting in Earth's polar regions and the urgent need to quantitatively understand the impact of this melting on global and regional sea level. We are building on the success of an ongoing cross-NCRIS (ARDC, AuScope, NCI) platform grant ( carrying out forward and inverse of mantle convection.  


Although various computational modelling frameworks have been applied to simulating GIA, they suffer from several shortcomings. For example: (i) many assume spherical symmetry in elastic and rheological properties, which is not the case on Earth where, for example, mantle viscosity can vary by several orders of magnitude due to its strong dependence on temperature and other fields; (ii) some are built on commercial software and are difficult to extend, share, and execute across different computational platforms; (iii) they often rely on outdated numerical methods and solution strategies; and (iv) modifications to include different physical approximations or components, which can affect nonlinear coupling and associated solution strategies, often require extensive and time-consuming development and testing, using either separate code forks or increasingly complex options systems. The latter makes reproducibility of a given simulation difficult, resulting in a lack of transparency. This makes scientific studies into the influence of different physical approximations extremely difficult.  


A challenge that remains central to research software development in GIA modelling, therefore, is the need to provide accurate, efficient, flexible, easily extensible, scalable, transparent, and reproducible research software that can be applied to simulating a wide range of scenarios, including problems that incorporate different approximations of the underlying physics. Key to achieving this is to abstract, automate, and compose the various processes involved in numerically solving the governing PDE's underlying the problem, to enable a separation of concerns between developing a technique and using it. As such, software projects involving automatic code generation have become increasingly popular, as these help to separate different aspects of development. Such an approach facilitates collaboration between computational engineers with expertise in hardware and software, computer scientists and applied mathematicians with expertise in numerical algorithms, and domain specific scientists, such as geodynamicists and climatologists.


Ocean modelling under ice shelves


As part of my PhD at Imperial College London, I was developing a new model for ocean flow under ice shelf cavities in Antarctica using Firedrake.

The main motivation was to develop a flexible unstructured mesh model to investigate ocean flow and melting near the grounding zone of glaciers, where the ice starts to float. Glacier flow, and hence ice sheet contribution to sea level rise, is particularly sensitive to how much melting occurs at the grounding line. However, ocean conditions near the grounding zone are highly uncertain owing to the difficulty of making direct observations ( Moreover, traditional ocean models that rely on structured grids struggle to capture the complicated geometry of the ice shelf cavity in these remote regions of the ocean. Alongside the ability to use flexibly unstructured meshes, one of the key advantages of Firedrake is the availability of an automatically generated adjoint model (thanks to the Dolfin Adjoint project ( This enables efficient calculation of model sensitivity to input fields, e.g. to the unknown initial conditions or boundary forcing. Gradient information is essential for scalable optimisation algorithms necessary for Data Assimilation and Parameter estimation studies.

As part of the verification and validation process, I carried out model comparison studies against a community standard finite volume model, MITgcm. Running other scientific codes has helped me to appreciate the philosophy behind Firedrake and I believe that domain specific abstraction is highly desirable for the complex scientific codes that arise in geoscience applications.

One of the key things I have focused on is testing the sensitivity of the melt rate parameterisation to grid resolution and discretisation choice, since spurious mixing can have a significant effect on the melt rate calculation. This was especially true when I compared MITgcm and our Firedrake based model for the ISOMIP+ model intercomparison project. As a result, I set up and developed a Method of Manufactured Solutions test, which includes melt rate, to provide a more rigorous test of the numerical model.  The model development process is documented in this paper:  in Ocean Modelling.  


Through the International Thwaites Glacier Collaboration ( I have had the opportunity to meet and work with a number of scientists based around the world, in particular, at the British Antarctic Survey, Swedish Meteorological and Hydrological Institute, Cornell University, New York University and the University of St Andrews. I am always keen to work with new people on different projects so please get in touch if you are interested in collaborating!


If you are interested our code is available on GitHub here:

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Updated:  23 February 2024 / Responsible Officer:  Director (Research Services Division) / Page Contact:  Researchers