Sea change

What do you need to study the impact of climate change on the oceans? Flow cytometer? Sediment trap? Large ship? Well yes… and no.

At Imperial, Professor Darryl Holm, Chair in Applied Mathematics, and Professor Dan Crisan, Professor of Mathematics, reckon what you really need is… a supercomputer.

The team are working on a mathematical model to help understand the major issue in oceanography – principally how our oceans are changing. It matters because the world’s oceans cover 71 per cent of its surface and they have quietly absorbed 93 per cent of the heat trapped by greenhouse gas emissions from human activity. The problem is that absorbing all this heat has caused the oceans to change in dramatic ways and we may no longer be able to rely on them to keep the Earth from overheating.

The Stochastic Transport in Upper Ocean Dynamics (STUOD) project brings together mathematicians, physicists, computational scientists and oceanographers. The results are set to provide decision-makers with a means of quantifying the effects of sea level rise, heat uptake, carbon storage and change of oxygen content and the acidity of the ocean. It should also support better understanding of the transport of marine debris, including the accumulation of plastic in the sea and the tracking of oil spills.

“Five years ago, we decided to put our heads together to try to collaborate on the major problem in oceanography, trying to predict the evolution of the top 200 or so metres of the planet’s oceans where most human activity happens and which regulates the climate,” says Crisan. “We then applied to the European Research Council along with our partners and were granted €10 million in 2019. Partnerships with the French National Institutes for Research in Digital Science and Technology, and for Ocean Science (Inria and Ifremer) place us in a strong position to engage with global challenges.”

The dynamics of this upper ocean layer are influenced by many external factors, including atmosphere fluxes, rain, ice, river runoff and the action of waves, as well as biological processes. Rather than simulating each of these complex processes individually, the project looks at their combined effect. Stochastic processes – those with a random probability distribution – involve noise and uncertainty, such as the flow of currents in an ocean. While the movement of currents cannot be predicted, their average can be worked out statistically. And that’s where the modelling comes in.

“It’s a bit like the static white noise you get on a television with bad reception, where the television signal is hidden by the noise,” says Crisan. “Previous attempts to model the upper ocean have tried to create a mathematical model of the signal itself. They came up with more and more sophisticated models that characterised the evolution of the signal. We have shifted our attention onto the noise itself, creating models that satisfy the physical constraints.”

“The noise models what we don’t know,” adds Holm. There is so much we can’t resolve, so we have to admit there is a part of this that we don’t know. What we do know is that there are spatial correlations of the fluctuations – that is, there will be interdependence between the fluctuations at neighbouring locations in the ocean and sometimes even distant ones.

The scale of this challenge is daunting. “You can’t just do these things on pen and paper,” says Holm. The sheer number of data points – gathered by satellite, floats and ocean drifters, free-floating buoys that can measure currents – means that even supercomputers struggle to crunch the data in any reasonable amount of time.

“People say I need to have a better and better approximation of model and therefore I need bigger and bigger supercomputers to approximate it at a smaller and smaller scale. But it is never going to be enough,” says Crisan. “We do it the other way: we work on a very coarse scale and accept it is not going to be perfect with the additional influence from the parts that are not taken into account added to the noise.”

The mathematical model of the ocean used in the project is based on complementary theories of turbulence created by Holm, Crisan and former PhD student Valentin Resseguier, whose thesis focuses on stochastic fluid dynamics. The outputs are combined with a wave model and details of the impact of the atmosphere on the ocean, then compared to the real observations from the network of satellites and drifters. This is then fed back into the model for the next round of calculations.

The continually tweaked outputs from the team’s mathematical model are then included in ocean-modelling software called NEMO, used by many meteorological offices around the world. The model may also be of use in the shipping trade, providing high resolution information for use in route optimisation systems to reduce fuel consumption and greenhouse gas emissions of ships.

All this cannot come a moment too soon. The heating of the ocean by global warming is making the ocean far more energetic than it was, meaning the currents flow differently than they did previously. “The ocean has thermal fronts, with a warm part sliding over a colder part, just like in the atmosphere. It means the ocean is developing its own kind of fast ‘weather’ and it is occurring at smaller and smaller scales that cannot be studied numerically by computational simulations,” says Holm.

Meanwhile, continuing to understand exactly what is happening is becoming ever more vital. “The ocean is the key to predicting the climate, because ocean timescales are very long compared to the atmosphere,” says Holm. “The melting of the polar ice caps is changing the flows of the ocean and that is going to change the climate. We cannot rely on the ocean to keep absorbing more and more heat indefinitely.”