Mathematics and models in an uncertain world
In the run up to COP26, our former Director of Sustainability Dr David Jordan spoke with Dr Chris Dent and Dr Amy Wilson about sustainable energy, data-driven modelling and the many ways mathematics feeds in to sustainability.
David Jordan: First off, I’d like to thank both of you for coming along and agreeing to take part in this interview. I think that through you both we’ll be able to get a good insight into how mathematics feeds in to sustainability as a whole. I’d like to start by asking Amy, when people think about climate change, and research into it, they might think about the environmental sciences, ecology, urban planning, engineering, etc. Why do you feel mathematics is important in that conversation?
Amy Wilson: I think that it’s important because there are many ways mathematicians can contribute to the work on climate change. One particular approach is around statistics and uncertainty. A large part of the problem is, firstly, understanding what the current situation is (in terms of the climate, energy systems, etc) and how we think that might evolve; then, secondly, there are the questions around what to do about it. Mathematics has a lot to contribute to both of these points.
In terms of understanding where we are right now, it’s often based on huge models developed by the sorts of disciplines you mentioned. But they’re just models; they’re not the real world. Part of what Chris and I have worked on, is asking, “how do we link those models to the real world?” That’s a statistical problem.
So, we have these models, and different data sets, telling us things, but we need to take these and form some sort of probabilistic structure to tell us how they relate to the real world. That’s something that statisticians and mathematicians can contribute to, because there’s lots of different uncertainties there. For example: uncertainties around the inputs to the models, the models themselves and the data sets (measurement error, etc).
One problem that we face is linking all these different uncertainties together to try and accurately understand what’s happening around us. I don’t even think it’s clear which uncertainties we fully understand, even at this point in time, let alone how they’re going to evolve as we go forward.
David Jordan: It turns on its head this stereotype of mathematics as abstract, with other sciences grounded in the real world – you’re saying your work is aimed at grounding other sciences to real world data?
Amy Wilson: Yes, it is almost the opposite of how mathematics is thought of!
I worked on a project with the Government’s Department of Business, Energy & Industrial Strategy that was related to climate change. They have a model which they use to investigate different types of energy policy, and see the impact that they will have on things like the percentage of renewable generation, the percentage of emissions, energy prices and so on.
It’s a great economic model, it takes lots of different inputs and it gives you the outputs, but there’s not really any probability in it. We worked with them to try to put some uncertainties on to the inputs (e.g. electricity demand), and understand how that affected the outputs of the model, like the percentage of renewables, so that we could try and make decisions about what to do that were based on the real world, rather than the modelling outputs. We also modelled the uncertainty due to the fact that the model itself is just an approximation.
David Jordan: Chris, this sounds to me a bit like the topic of your webinar for COP26 conference in Glasgow, can you tell us a bit about that?
Chris Dent: The webinar is specifically about the National Digital Twin programme’s Climate Resilience Demonstrator (CReDo) where I’m the technical lead. CReDo is looking at the climate resilience of local area infrastructure systems – water, electric grid, data networks – particularly their exposure to flooding, and brings together important societal implications with the overall goals of the programme. These concern the interoperability of data, and modelling, between organisations.
In understanding how climate model outputs can best be used for decision making, perhaps the most interesting thing for researchers and mathematical decision support people like us, is what the ultimate best practice here might be? In other words, how might the next generation of climate models (such as the UK climate projections) be produced to support better decision making across the huge range of applications for which they are used?
David Jordan: Is this what you mean when you say the “digital twin” project, it’s coming back to Amy’s point about taking a model, and using data science and statistics to reinform and reinvent the model and data is that correct?
Chris Dent: Yes, that’s exactly it. But we hope to take it further, to the design stage.
One of the opportunities that we’ve been thinking about for a long time is to have the chance to work with people in relevant application domains to help design the modelling with the uncertainty treatment baked in from the start. If you design these together then you should get better outputs for real world applications and to support decision making.
Unfortunately, that’s not the way things are done. What tends to happen is that a model of the system, in the application domain, is produced first; then the statisticians work on this and have the opportunity to perform multiple runs. However, as they work on the model once it’s already been built, what can be done is limited. We want to change that paradigm.
David Jordan: It seems like these kinds of problems, modelling of uncertainty, take on a whole new meaning in an increasingly uncertain world, especially in the context of energy stability and climate change.
Chris Dent: Definitely, I remember one day in back in 2012, I got home at six o’clock – back in the days when I still got home at six o’clock – put the BBC Evening News on, sat down on the sofa and discovered that this project that I’d been involved in was the lead headline. I started thinking this wasn’t normal academic research anymore!
It’s quite easy in academia to end up doing the things that other academics like and getting publications in (whichever are regarded by your fellow academics as being) top journals. Those aren’t necessarily the same points as the ones needed for improving these applied studies.
David Jordan: I can’t help but think right now about some recent seemingly conflicting news reports. On the one hand we, in the UK, are moving towards fully renewable electricity, with carbon neutral electricity a real possibility by 2030, and yet on the other hand we hear about natural gas shortages this winter possibly forcing power outages. How do we reconcile those two predictions?
Chris Dent: So, when you talk about the dichotomy between the good news of the rollout of renewables while also having these energy shortfall issues in the autumn, it’s important to consider the timeline of events. The rollout of renewables will be measured in years, whereas a commodity supply problem (like with the gas supply) can happen suddenly. So in that sense they’re somewhat separate things.
Amy Wilson: Another important point is that, while we get more renewable energy, we’re not in a position to rid ourselves of gas and coal. We still need them to provide power when the wind isn’t blowing and the sun isn’t shining. There are technologies that have been developed that can help us deal with this, like battery storage and demand response, but I don’t think these are at the stage that we need them to be at to help us reduce our dependence on fossil fuels.
On the mathematical modelling side of things, I think the challenge there is that, unlike conventional generators, renewable energy producers are just more uncertain. Conventional generators might break very occasionally, but typically they’re going to be there when you switch them on. This just isn’t true of wind and solar because they’re dependent on weather conditions. In order to make best use of them it’s a case of trying to understand the uncertainty in their output and to use that as best we can.
The more wind farms we have, the less of an issue it will be because we’ll not be so dependent on single geographical locations – interconnection can also help with this. We can reduce the risk using things like storage and demand response to try to spread both the energy use and the energy production across time. This would allow us to better match our rate of use with the rate of production.
We have to think carefully about how we do this, whether that’s through battery storage or changing our behaviour. If we can set a dishwasher so it comes on later, or we charge our car at some point over the next 12 hours without minding when. We need to get used to this way of thinking about energy, instead of demanding it right now we adapt to the uncertainty that wind and solar energy generation brings.
David Jordan: Amy, you mentioned battery storage as an important mitigator for this variability. Of course there are engineering challenges and financial challenges around that. But I wonder, what are the mathematical challenges?
Amy Wilson: One of the interesting things is mathematically understanding the economics of the situation. It’s not all centrally determined by the government, so there are individual players coming in and deciding whether to build batteries or not. One of the things that we’ve worked on, is figuring out how to value the contribution of battery storage to capacity adequacy, and so how to pay people for that service on an open market. This is ultimately a mathematical problem, and with it comes the related problem of how to get these distributed batteries all working together.
Chris Dent: Yes, as Amy says, having cheaper storage gives you a lot of opportunities to shift supply and demand through time to help match what is needed. Equally, it brings new challenges for the mathematical modelling that is associated with operational system planning. This ability to shift through time adds a whole new dimension to the modelling, so it brings greater complexity and new requirements on some of the statistical aspects, like forecasting. If you’re looking to store energy over an extended period, beyond the short timeline which we’re currently using weather forecasts for, then you need an appropriate statistical forecaster’s background to operate this battery or other storage.
David Jordan: That sounds to me like a call to action for our graduating class of mathematicians! Thank you both for sitting down with me, and best of luck with the work ahead.
(Photo by Manny Becerra on Unsplash)