Cohort 2024

Project: Differentiable abstractions for coupled geoscientific models

Supervisors: Prof David Ham and Prof Colin Cotter

Project Description:
New numerical models of the Earth system are key to understanding our changing climate. Modelling each component of the system is a complex composition of numerics, solvers, and data assimilation; and this multiplies when coupling ocean, atmosphere, ice and land. However, implementing even a single, simplified, component in low-level code can require years of. Every improvement to the model equations or numerics is painstaking and inefficient.

In contrast, the Firedrake automated simulation system applies a new mathematical programming approach. Model developers write the equations, finite element discretisation, and solver strategies at the level of the mathematics; the resulting implementation code is automatically generated to create a complete simulation. Changes to numerics or solvers are a few lines of code in an afternoon, rather than weeks or months of low-level debugging. The adjoint simulations required to assimilate real-world data are available automatically via the same differentiable programming approach that powers machine learning tools such as PyTorch and TensorFlow. Firedrake is the basis of the Gusto atmospheric toolkit, Thetis ocean model, Icepack glaciology library among others.

However, the Earth system depends on coupling different models of different materials together. In this project, you will extend both the mathematical abstractions that Firedrake users employ, and the underling code generation technology to enable tight coupling of different Earth system model components. You will develop skills as both a mathematician and a creator of professional quality research software, and your work will be employed by scientists and engineers around the world to create coupled models in the field of climate science and beyond.

Project: On the probability of occurrence of breaking waves.

Supervisors: Dr Adrian Callaghan (NOC) and Dr Ioannis Karmpadakis 

Project Description:
Waves are ubiquitous features of our coastal and marine environments. However, our ability to understand and manage ecosystems and human activities in these settings depends upon good characterisation of infrequent or “extreme” wave processes and events. The project is a collaborative and interdisciplinary opportunity to combine leading statistical methods with wave mechanics to advance predictive modelling of these conditions, and thus help to develop measures for societal adaptation and resilience in the face of climate change. 

Project: Estimating the North Atlantic circulation collapse and its climate impacts

Supervisors: Dr Marilena Oltmanns, Dr Chris Wilson, Prof Pavel Berloff, Prof Ted Shepherd & Dr Till Kuhlbrodt  

Project Description:
A shutdown of the Atlantic overturning circulation, triggered by increased surface freshening, is considered as a potential transition into a fundamentally different climate regime. However, the actual risks of crossing this tipping point, the underlying dynamics, and the climate impacts remain elusive.
Thus, this project will test the hypothesis that increased freshwater discharges from Greenland and the Arctic will fundamentally change the North Atlantic Ocean circulation, triggering a transition into a different climate state.
Starting from the two-box model developed by Kuhlbrodt et al. (2001), which consists of a seasonal mixed layer, a deep layer, and a stochastic noise term, the model will be extended to include: the observed trend in surface freshening; observed increases in the seasonal freshwater cycle; improved estimates of lateral eddy fluxes and mixing; negative feedbacks in the atmospheric forcing; as well as newly developed volume estimates of a potential Arctic freshwater release. These new elements are derived from a substantially grown repertoire of observations, new methods to infer the variability of freshwater, and new insights into the ocean-atmosphere feedback to freshwater. Thus, in contrast to more complex models, the idealised models developed in this project will build on realistic parameter ranges and are designed to capture critical feedback mechanisms.
After formulating the model, a dynamical systems approach will be applied on it to test for the existence of critical freshwater thresholds and determine the physical underpinnings. Large-scale climate impacts will be assessed by estimating ocean responses and atmospheric feedbacks using conceptual, reduced-order models.

Project: Statistical space-time models for our climate

Supervisors: Dr Adam Sykulski & Dr Benjamin Marchant (BGS)

Project Description:
Spatio-temporal statistics is concerned with modelling, predicting and forecasting data collected in space and time, taking advantage of information contained in the correlations and dependencies between datapoints in this (up to) four-dimensional space. Classical theory and models exist spanning several decades of research, but many outstanding challenges remain in terms of implementing them on real-world datasets:

•  Modelling large data volumes. Large datasets are challenging to model, where the potential for capturing additional features increases with data size, but become increasingly masked by other features, non-stationarity, and observation noise. Classical methods often miss the predictive potential gained from increasing volumes of data. This project will build new multivariate and non-stationary spatio-temporal models relevant to climate and geological sciences.
• Inference, Forecasting and Prediction. Then, even after finding a great model, there is usually an enormous computational bottleneck specific to spatio-temporal data, where classical inference and prediction methods are often based on matrix inversion which becomes increasingly prohibitive as the dimensions of the data grow. This project will build novel machine learning techniques to solve these issues.
•  Irregular and Missing data. Many existing spatio-temporal methodologies assume data is perfectly observed on a regular grid in space and time, this is not realistic in many applications. This project will build novel models, inference and prediction tools that are robust to irregular and missing data, including techniques for uncertainty quantification that reflect the uncertainty enduced by the irregular nature of the data.

The above-mentioned challenges are ubiquitous in the climate-related datasets and scientific challenges that BGS has. In this project you will work closely with BGS on these datasets to build novel predictions, insights and conclusions.

Project: Statistical hydrodynamics and geophysical flows

Supervisors: Dr. Michele Coti Zelati & Dr. Matias Delgadino (UT Austin)

Project Description:
In his seminal 1949 article, Onsager presented a groundbreaking theory that delves into the irreversible behaviour of fluids, particularly those operating far from equilibrium. This theory’s profound impact is evident in its influence on various conjectures concerning the long-term dynamics of 2D incompressible Euler solutions. Notably, these conjectures are often grounded in the idea that solutions should maximize vorticity mixing while still adhering to the preservation of conserved quantities. Despite its apparent simplicity in certain scenarios, such as solutions generated by a patch in a disc, the exploration of entropy maximisers at specific energy levels remains vastly uncharted territory. Furthermore, while faint parallels to classical statistical mechanics have been drawn, the full extent of their connection remains elusive. Therefore, the primary objective of this project is to investigate these intriguing aspects of the 2D Euler equations by employing optimization techniques, rearrangement inequalities, and min-max principles. By doing so, we aim to shed new light on these central questions and provide a fresh perspective on this fascinating subject matter.

Project: Hyperparameterization Framework for Mesoscale Oceanic Turbulence

Supervisors: Dr Igor Shevchenko (NOC) and Prof. Pavel Berloff 

Project Description:
This project offers a unique opportunity to work at the interface of idealized ocean models mainly used for development of new methods and process studies, and comprehensive ocean models used in the leading weather forecast institutions (MetOffice, ECMWF, etc.), for providing operational weather forecasts and future climate predictions. The Project assumes going all the way from original ideas, to their conceptual verification and tests in conceptual and low-dimensional dynamical systems, to the ultimate implementation in realistic ocean models.
The Research Program will be gradually unfolding from relatively simple low-resolution models allowing for fast testing and calibration of new HP methods, going through high-resolution realistic models for perfecting the methods, to its final destination – applying the methods within the context of ultra-high-resolution configurations intended for the use on exascale-class computers of the future. The whole Program is tailored with one goal in mind: advancing high-resolution ocean forecast and the use of large ensembles with elevated prediction skills and extended forecast horizons.

The ocean general circulation is the most computationally intensive part of any comprehensive ocean-atmosphere forecasting system and, therefore, its most limiting factor. This is because the model needs to resolve mesoscale eddies, which induce crucial effects on the large-scale circulation. The situation is aggravated by the need to produce ensembles of solutions for the probabilistic ensemble forecast, but the capabilities are severely limited by computational resources. Ocean ensemble forecasts in eddy-resolving regimes are far beyond what supercomputers will be able to compute over the next decades, and here comes in the HP approach which allows to achieve this goal within only a few years. The Project is of high-impact nature for the following reasons:

(i) striking novelty in contrast with the mainstream parameterisation approaches that focus on small-scale physics,

(ii) ambitious scale of research program that goes from development of the methodology applied in conceptual models to working with the most comprehensive oceanic data sets and models.

Project: Analysis and simulations of novel carbon capture processes

Supervisors: Prof Demetrios Papageorgiou

Project Description:
The mass exchanger is configured as a bank of microchannels through which, in the absorption phase, CO2-laden gas flows over liquid-infused trenches containing the immobilized CO2-reactive liquid sorbent (e.g., amine or ionic liquid). Momentum, mass, and heat transfer effects are important in both phases; the sorbent phase adds the complexity of reacting species. The mathematical models involve two-phase advection-diffusion-reaction systems of non-linear PDEs for the fluid flow, temperature and concentration fields for all species. The PDEs are coupled through boundary conditions at the gas-liquid interfaces – velocity and shear stress continuity, temperature and heat flux continuity, and mass flux and a gas law (Henry’s law) for the concentration equations. Longer term, additional boundary conditions will capture evaporation of the compounds in the sorbent solution. The objective is to utilise mathematics to simplify and solve these equations and efficiently generate accurate solutions to use in general models of the impact of this device on global CO2 capture. Direct numerical simulations will inform reduced-order models solved with spectral in-house codes, bridging analysis and CFD. Furthermore, asymptotic methods will be applied to generate analytical or quasi-analytical models of the transport phenomena, providing useful, simple and physically informed expressions to be used in design, optimisation and estimates of large scale techno-economic models on the global impact of the devices. These solutions will also be used in generating data for machine-learning implementations. 

Project: Developing a quasigeostrophic ocean circulation model for irregular domains

Supervisors: Prof Pavel Berloff

Project Description:

The present state-of-art of the ocean general circulation modelling involves a hierarchy of models. On the top level there are climate-type global Earth system models that have heavily parameterised, and, therefore, very badly represented, primitive-equations oceans, because of the necessity to balance all the global complexity involved. On the next level there are so-called “eddy-resolving” ocean models, which are very expensive, both computationally and in terms of the involved output data analyses. The above types of models need specialised research institutions and long-term investments to deal with them. On the next level there are so-called “intermediate-complexity” models, such as multi-layer shallow-water dynamics in simple configurations and its asymptotic quasigeostrophic (QG) incarnation. There are thousands of papers published with the QG approach, proving that it is one of the great theoretical successes, aiming at reproducing realistically physical processes, without capturing many details.

The main problem with QG models is that they are configured to work only in simple rectangular domains, such as double-periodic or closed rectangles, or straight channels, because of the involved direct elliptic-problem solvers that use Fourier transforms. Here, the use of indirect (iterative) elliptic solvers, more adaptable for general domains, is ruled out, because they require too many iterations to converge to an acceptable level of numerical accuracy.

The main objective is to transform the QG modelling landscape and push it to the next level of physical complexity. More specifically, the idea is to upgrade and test in various settings the existing and well-respected QG (oceanic and atmospheric) model code “PEQUOD”. This particular numerical model is algorithmically the most efficient one out of the existing QG models and is widely used (in simple domains). The end goal will be to do realistic coastline for QG-type conceptual and process studies, and develop a QG model of the Mediterranean Sea, with all its complicated coastlines.