Maths today is at the frontier of almost any scientific problem you can envision. Though still relatively unknown to the wider public, mathematicians are acutely aware of this and take great pride in it. Having said that, polar bears, rifles and immersive theatre shows are three things I would still have told you mathematicians have absolutely nothing to do with. Well, I would have been completely wrong, as I learned from my conversation with mathematician-turned-polar scientist Sammie Buzzard.
Countering collapse with calculus
Sammie, as she tells me, is a glaciologist and climate scientist. “Glaciologists study all different kinds of ice. That can range from the frozen ocean in the Arctic, to my focus of Antarctica, which is mostly ice on top of land.” In particular, she is studying Antarctica’s ice shelves, which are floating bodies of ice that form at the edge of a land mass. They have found recent fame because of their unfortunate habit of collapsing, most recently in March of this year, with the loss of the Conger ice shelf making top headlines.
This sudden disintegration is precisely what Sammie hopes to learn more about with her research. “They are areas that are particularly vulnerable to changes in climate because they’re affected by changes in the ocean below and the atmosphere above. I look at the above part, so I create numerical simulations or models of the melting of this ice on the surface of these ice shelves and then work out where that water is going and where that is moving around on the surface of the ice. We think water is key in the sudden collapse of ice shelves.” Losing our ice shelves could be disastrous for mankind because of the sea level rise it causes—however, not for the reasons one might naively expect. The ice is already in the sea so, according to Archimedes’ principle, it melting does not cause any rise. “But all the ice that’s behind them is held back by ice shelves. We call that a buttressing effect, where it’s holding back the ice on the land, so you take the ice shelf away, then all the ice on the land is free to accelerate and get into ocean, and that does contribute to sea level rise.”
Perhaps the most famous example of ice shelf collapse was Larsen B, an ice shelf twice the size of Greater London which rapidly disintegrated over the first few months of 2002. The polar science community scrambled to understand why this had happened and how it could be prevented in future. A crucial clue lying on the surface of the ice would eventually become the focus of Sammie’s research. “What we’ve noticed about Larsen B is that it was covered in lakes before it collapsed, from melting on the surface of the ice. Essentially it’s all about water kind of getting into crevasses, and the pressure of that water freezing and unfreezing and adding load to the ice each year caused that collapse. So I am trying to work out if that could happen anywhere else.”
Very interesting—but, of course, as Chalkdust readers, we need the gory mathematical details. “The model is coded in Python. It’s based on a one-dimensional column model, so there are lots of vertical columns looking through the ice and we calculate the surface energy balance at the top and then solve the heat equation moving down through the ice using a finite difference method.” The heat equation is a partial differential equation (a type of differential equation with more than one independent variable) which governs the flow of heat through a space as time passes. “Each column is solved independently, but then we can move water laterally between all these different columns both on the surface and within the snow at the top of the ice shelf. Thinking about water moving laterally is also really important, because you do get these lakes and rivers that we need to simulate.”
Of particular concern is the George VI ice shelf on the Antarctic peninsula. “There are some satellite images from the start of 2020 that show the ice shelf is covered in bright blue water because it was melting so much. That’s a really interesting case study, even though the structure of the ice shelf maybe means it’s not the most concerning one in terms of preventing sea level rise. Just the sheer amount of processes that are going on there mean that’s one that I wanted to focus on, especially because there are people working on the field site, so you can get the validation and calibration from that.”Speaking of the field, don’t go thinking Sammie only ever gets to sit around on her computer all day—she has been to the Arctic herself. “I went on a field work training course while I was doing my PhD. We went up to Ny-Ålesund [the northernmost civilian settlement in the world], which is essentially just a big research town, so each country that works up there has different base that you can stay in while you do your field work. We went up to the glaciers and took some measurements and put all that training into practice, which was a great experience. You don’t expect a mathematician to end up in the Arctic.”
Her trip was not without excitement; anyone doing fieldwork in the Arctic must undergo some pretty unique training: “I never thought as a mathematician I would be learning to shoot a rifle to potentially defend myself from polar bear attack.” She is keen to emphasise that she would never use the rifle unless absolutely forced—if even then. “I feel bad for the polar bears. I remember on the training course I said maybe if a polar bear came for me I would just let it eat me because I just really don’t want to shoot it, and they said ‘OK, tomorrow you’re not carrying the rifle!'” If what you’ve read so far wasn’t surprising enough, try this: it wasn’t cold. “It was really nice! We got given so much gear but I ended up just lugging around this massive coat. I got sunburn!” What is it called when you get a tan in the Arctic? An arctan!
Access for all in the Arctic
Luckily, I didn’t make the arctan joke in person so the interview continued. We discussed Sammie’s outreach work, which includes giving talks at events such as Maths Inspiration, and giving interviews to magazines such as Chalkdust.She says there are two reasons why she believes outreach is very important for her field. “First of all, because we’re studying areas that are so affected by climate change, it’s important to talk to people about that and let them know what’s going on, because it’s so disconnected from what people do every day and what they see. The majority of people are never going to go to the Arctic or the Antarctic but what’s happening there is going to affect all of us.”
The second reason is to improve diversity in polar science. “The British Antarctic Survey had their first women go to Antarctica in the 1983, which is insane. When I was born, women weren’t allowed to go to Antarctica from the UK. I went to a fairly standard state school and the idea of being a researcher or scientist never crossed my mind, so I wanted to let people know those opportunities are out there.” She says this can be even worse for racial minorities or minority genders. But how can we improve the situation? “We are running a workshop on race and systemic bias within Arctic science, to essentially work out what we should be doing because it feels to me that there’s a lot more awareness now but we don’t really talk very much about solutions.”
One of her outreach projects particularly piqued my interest: New Atlantis. “That was kind of crazy actually. It was an immersive theatre show. The organisation New Atlantis was like a United Nations for water so it was set in the future. We were in a water crisis and the audience had to decide how we would deal with it. So were we going to rely on science, would we share the water out nicely, or were we going to have military control? And as part of that there were lots of actual scientists playing the role of future scientists. We would talk a bit about our current work but put it in the context of how things might look in 100 years or so in the future. And the audience did generally vote to leave Antarctica alone.” I wonder why that was. “I think people generally recognise that Antarctica is one of our last pristine, untouched wildernesses. Everyone loves David Attenborough, watching Frozen Planet. You look at it and think, ‘Maybe we shouldn’t touch this, and we should just let the penguins carry on as they are.'”
From cats and dogs to stats and logs
Many people assume that in order to have a career as a mathematician, you must have been incredibly gifted from a young age. Maths is something you either get or don’t, and that reflects something immutable about you that can’t be changed. Sammie is here to tell you that this is not true, and in fact hard work and determination can be far more important than ‘natural gift’ (whatever that is). “I think I was quite good at school, but I wasn’t the best. My best friend in secondary school would get maths much more quickly than me: she would just scribble it down and be like ‘OK, I’m done!’ Meanwhile, I would take five pages to make mistakes and work out where I was going, but… I persevered.”
It was her maths teacher who told her that even though her friend seemed to have the more natural talent, her perseverance meant Sammie was more likely to get to the answer. “She would get it straight away or she would give up, whereas I would think, ‘No, I am going to get to these answers and I’ll take those five pages I need.'” But even with determination like Sammie’s, it was a while before she came to consider maths as a viable career option for her, and initially she went to university to study to become a vet. “I didn’t really know what the careers were in maths, which didn’t help. You could either become a maths teacher or an accountant and I didn’t really want to do either of those things. So I never really considered it until I actually went to vet school and realised it was not the right place for me. Then I looked more into applications like the maths of climate, cryptography and mathematical biology. I restarted my degree, and didn’t look back.”I think probably a lot of readers can relate to that—personally, I always found maths fun at school, but even so I struggled to envision what it would be used for in the real world. Because financial careers didn’t appeal to me, I was turned off from it until I was older and learned you could do all kinds of things with it. Applications of maths are generally not taught in school and for a lot of children, that obscures what makes it so cool. It was something Sammie had to go digging for to find out. “I did a lot of internet searches for maths careers and read a few popular maths books. I think generally universities have got a bit better at promoting where their graduates end up, so looking through prospectuses I saw people in cool jobs.” Perhaps including more about these applications that are largely unknown to the public in school curricula could go some way to encourage more children to take up maths—and maybe non-mathematicians wouldn’t keep asking us ‘What do you actually do?!’ (Just kidding. Obviously mathematicians never speak with non-mathematicians: it’s too scary!)
After choosing to study maths at the University of Exeter, Sammie then sought a PhD at the University of Reading. “I met with the person who turned out to be my supervisor, and I was actually quite concerned at the time because I didn’t know anything about ice, and he said it didn’t matter—as long as I had the maths, he would teach me the rest of it.” If any mathematicians are now feeling tempted by a career in climate science (I certainly am), that news should be reassuring. “Obviously it took a bit of work to fill in the gaps, but there was the support there because so many people come into it: it’s not like most people have a degree in glaciology.”
If there is one thing she emphasises throughout this interview, it is that climate science is for everyone. “I feel like what I do is really cool, so I want everyone to be able to do it if they want to!”
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