Math Awareness Month — An Interview with Tapio Schneider

As part of our Math Awareness Month celebrations, we posed our series of questions about mathematics and climate study to Tapio Schneider, a Professor of Environmental Science and Engineering at Caltech. Dr. Schneider conducts research on the dynamics of the Earth’s climate changes, turbulence, and turbulent transport in the atmosphere and oceans. He is also co-editor with Adam H. Sobel of the PUP book The Global Circulation of the Atmosphere.

PUP: What are you currently working on?

Tapio Schneider: I am working on theories of how large-scale (>1000 km) atmospheric turbulence influences the global climate. For example, we study how turbulent transport affects tropical circulations and how it controls the distribution of atmospheric water vapor and rainfall.

PUP: How did you become interested in this field?

TS: I am fascinated by how nature works. I was trained as a physicist and loved how physics helped explain the inanimate world around me, from refrigerators to cell phones to the blue color of the sky and the red color of sunsets. I particularly like the physics of everyday phenomena—phenomena that occur roughly at the energy of sunlight (for example, many quantum phenomena occur at the energy of sunlight, and in part because of that, quantum devices such as the transistor revolutionized our life). When I was looking for a research area for graduate studies, I was looking for a young field with open questions to which young scientists can make lasting and fundamental contributions. Atmospheric dynamics is such a field—and the phenomena certainly occur at the energy of sunlight!

PUP: How do you use mathematics in your work?

TS: Mathematics to me is a means to an end. It gives succinct descriptions of complex relations among natural phenomena. From these relations, we can draw inferences (explanations, predictions) about phenomena through mathematical reasoning. For example, Newton’s laws of mechanics are succinctly expressed in terms of differential equations, and from (numerical) solutions of these equations, we can predict how properties of atmospheric turbulence change with climate. Mathematics is an extraordinary efficient and effective language for expressing the laws of nature, and of climate in particular. In Wigner’s words, “the miracle of the appropriateness of the language of  mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve” (from E. Wigner, “The unreasonable effectiveness of mathematics in the natural sciences,” Communications in Pure and Applied Mathematics, vol. 13, 1960).

PUP: How is mathematics helping us to understand climate change and how the earth works?

TS: Mathematical relations expressing the laws of nature are at the core of everything we do, from building models of climate, to analyzing simulations conducted with such models, to making predictions. Climate models are based on Newton’s laws of mechanics, the laws of thermodynamics, and conservation laws for atmospheric and water mass, expressed in mathematical form for a continuum of microscopic volumes.
Tools of modern applied mathematics, developed in the middle and late 20th century, are used to find numerical solutions of the complex equations with the help of computers. We practice what may be called computational science and what some call experimental mathematics–we use computer simulations the way a laboratory scientist would use experiments, for example, to study how changes in the concentration of atmospheric greenhouse gases affects rainfall patterns. We also use mathematics to analyze data, for example, to condense complex information in high-dimensional datasets into more manageable and more easily interpretable low-dimensional information.

PUP: What are the top 3 biggest problems in climate science that still
need to be solved?  How will mathematics help solve these problems?

TS: How do clouds and their radiative properties respond to climate change? This question is central to understanding how much surface temperatures change for a given change in insolation or in the concentration of greenhouse gases (the “climate sensitivity”). We need coarse-grained (>10-100 km scale) mathematical descriptions of the dynamics and thermodynamics that govern the small scales of rain drops in clouds. We need these coarse-grained descriptions because, with current computers and for the foreseeable future, it is impossible to simulate the small-scale dynamics explicitly in climate models.

How do the large-scale turbulent fluxes of heat, momentum, and water vapor in the atmosphere depend on the mean climate state? This question affects almost all physical questions in climate science, from how the pole-equator surface temperature contrast is controlled, to how the distribution of water vapor, Earth’s most important greenhouse gas, varies with climate. We need macroscopic mathematical descriptions of turbulent fluxes to resolve this question (though we can simulate the microscopic dynamics giving rise to the turbulent fluxes reasonably well on computers).

And, how do ice sheets and glaciers respond to climate change? This question is central to understanding how sea level may change with climate and to understanding long-term climate changes such as the cycle of ice ages. We need to know more precisely the equations that describe glacier and ice sheet dynamics, and even where we do know the equations, we need better mathematical tools to solve them numerically on a computer (for example, understanding where an ice stream with rapid ice flow forms involves difficult free-boundary problems).

PUP: Why should students who are good in math consider research in climate or earth science?

TS: It is a young field in need of talented mathematicians and physicists to work on some of the most interesting, relevant, and challenging scientific problems!

PUP: What books, Princeton or otherwise, would you recommend to people who want to learn more about how mathematics and physics are helping us to understand how climate works?

TS: Alley’s The Two-Mile Time Machine: Ice Cores, Abrupt Climate Change, and Our Future is an engaging introduction to how ice ages come about, what we know about past climate changes, and what they may imply for the future.

Hartmann’s Global Physical Climatology is a more formal introduction to the laws governing climate on an undergraduate level.

There are many more advanced texts, such as, Peixoto and Oort’s Physics of Climate (a summary of observations and basic laws) and Holton’s An Introduction to Dynamic Meteorology. The book Adam Sobel and I edited, The Global Circulation of the Atmosphere, gives a summary of theories for the atmospheric circulation on the graduate level.

Math Awareness Month — An Interview with Angela and George Shiflet

As part of our Math Awareness Month celebrations, we asked Angela and George Shiflet about their current research and the impact mathematics can have on climate science. The Shiflets first met in a university calculus class, and eventually married. Today, they both are Wofford faculty members. George Shiflet is the Dr. Larry Hearn McCalla professor of biology and chair of the department. Also a department chair, Angela Shiflet is the McCalla professor of computer science and mathematics as well as coordinator of the computational science program. The Shiflets have collaborated to develop computational modules for the Keck Foundation and together they have authored Introduction to Computational Science: Modeling and Simulation for the Sciences.

PUP: What are you currently working on?

Angela and George Shiflet: We are continuing to write computational science educational modules,  discussing applying mathematics and computer science to science problems.  In particular, we are writing about modeling using matrices and graph theory.

PUP: How did you become interested in this field?

AGS: With George being a biologist and Angela being a mathematician and computer scientist, interest in computational science is a natural for us!  Little did we know when we met in calculus class in college and operated on rats together in physiology that we were beginning to lay the foundation of a mutual interest in computational science education.

PUP: How do you use mathematics in your work?

AGS: As college professors, we use mathematics in our teaching as well as in our writing.

PUP: What are three major problems in climate science that need to be solved?

AGS: 1.      Model reduction.   The current models must be simple enough for mathematical analysis.  Once the mathematical ideas are sound, they can be tested on the more complex models.  Additionally, we need to understand the models of climate using stochastic equations, rather than deterministic ones.
2.      Model interpretation.  There are a number of climate models, each having its own strong and weak points.  Mathematicians need to develop tools to evaluate the quality/relevance of the models, including the impact of missing components/processes.  These tools could also help to determine how broad a scale (time/space) we can use in interpreting each model.
3.     Model integration.  Climate models should be integrated with economic models.  How does a carbon tax policy affect production of greenhouse gases?  How would such a policy then affect the climate?

PUP: Why should students who are good in math consider research in climate or earth science?

AGS: There are enormous numbers of interesting problems in this area.  Creating solutions to such problems gives such students grand opportunities to make contributions to improving our understanding of climate, and therefore improving quality of life for future generations.  Besides it is just fun to gain understanding of such a complex system.

PUP: What books, Princeton or otherwise, would you recommend to people who want to learn more about how mathematics and physics are helping us to understand how climate works?

AGS: Climate Change – William J. Burroughs,   Cambridge

Math Awareness Month – An Interview with Richard Alley

As part of our Math Awareness Month celebrations, we posed 7 Questions  to Richard Alley, one of the world’s leading climate researchers, and he obliged us with a very thoughtful interview on the present and future of this important area of study.  Alley, Professor of Geosciences at Pennsylvania State University, studies how glaciers affect climate, sea level, and landscapes. He has won both teaching and research awards for his work, which has included five expeditions to Greenland and three to Antarctica. He is also the author of The Two-Mile Time Machine: Ice Cores, Abrupt Climate Change, and Our Future.

PUP: What are you currently working on?

Richard Alley: Big Picture: will the ice sheets fall in the ocean and flood the coasts; and, what does the history of the Earth’s climate tell us about the near future.  In more detail, we have just submitted or are about to submit several papers, on which I’m coauthor with students or postdocs or colleagues, that address: i) outburst floods rushing from one lake to another beneath an Antarctic ice stream; ii) why we need to know about the deformation of till (unconsolidated sediment) beneath the ice streams, to predict what the ice sheets will do; iii) when, after Europeans reached North America and transmitted diseases to the native peoples that caused huge die-off, what the resulting change in human activity did to the atmosphere; iv) the role of meltwater wedging open crevasses in determining the rate at which ice-sheets grow and shrink during ice ages; v) new ways to use the deposits left by glaciers to learn how large and rapid the climate changes were that caused the glaciers to leave those deposits.

PUP: How did you become interested in this field?

RA: I chose geology because of my interests in caving, hiking, rock collecting, and general out-of-doors-ing.  I focused on ice initially because the glaciologist at Ohio State had a summer job. But, I stayed with ice because it is so important and interesting.

PUP: How do you use mathematics in your work?

RA: Anything we measure turns into a number, and we need to keep track of those numbers and work with them.  Here is one example of many.  Recently, we were interested in the question of  how meltwater gets to the bed of a glacier.  Water in Greenland flows down great holes, called moulins, huge funnels that plunge most of a mile to the bed of the glacier.  But, nature lacks “drills” to make such holes.  So, we worked up a physical model, considering what tools nature does have.  Our result was that first a crack must open.  Where the crack is thin, the cold ice will refreeze the water; where the crack is thicker, water flow will make enough “frictional” heat to keep the flow going, eventually making the hole.  This model is done in equations, and we “ran the numbers”, finding that one needed a big reservoir of water to drive a crack all the way through the ice and along the bed to the ice front, and to make enough heat to keep a “pipe” open.  So, we suggested that the moulins formed by crevasses opening under lakes that form in hollows on the surface of the ice sheet.  A former student, Sarah Das, and a colleague, Ian Joughin, then were able to obtain funding to go look for this and see whether we “got it right”.  They were next to a lake when the crack opened beneath it, causing water to fall into the ice sheet faster than Niagara Falls, raising the ice and causing it to lurch forward.  Our mathematical work with the physics had successfully predicted what they observed.

PUP: How is mathematics helping us to understand climate change and how the earth works?

RA: We use math to track the data.  We put the physics into math in the computers to help interpret the data, and to help predict the future.  The computer models are now showing real skill in predictions—scientists a decade or two made projections based on mathematical representations about the physics of the climate, and on pretty good guesses about what humans would do, and those projections are proving to have been accurate—the specific humidity of the atmosphere is rising, the dry zones of sinking air where the tropical circulation comes down are expanding, and so on.

PUP: What are the top 3 biggest problems in climate science that still need to be solved?  How will mathematics help solve these problems?
What will the ice sheets do?  What will clouds do?  And, what will people do?  Mathematics is surely needed to solve the first two, and I suspect math will prove more important than ever in solving the third one.

RA: Why should students who are good in math consider research in climate or earth science?  Climate and Earth science really matter. In climate science, humans are going to make decisions about our energy future whether to invest close to a trillion dollars per year to avoid future damages of many trillion dollars per year. Dollars are a way of measuring food and medicine and shelter and other things, so we’re talking about people’s lives.  We must get the science right on this; too much depends on it for us to be sloppy.

PUP: What books, Princeton or otherwise, would you recommend to people who want to learn more about how mathematics and physics are helping us to understand how climate works?

RA: David Archer’s The Long Thaw would be a good start, and I’m partial to my Two-Mile Time Machine.

Mathematics and Climate, PUP Celebrates Math Awareness Month – April 2009

April 2009 is Mathematics Awareness Month, and this year’s theme focuses on the importance of mathematics in climate science.  Here, acquiring editors Ingrid Gnerlich (Physical Sciences) and Vickie Kearn (Mathematics) discuss why the theme of climate is so important this April. We plan to post a series of interviews with our authors that specialize in this area of research and hope you’ll return periodically to read those. All of our Math Awareness material will be gathered here, so please feel free to link through from your blog! So without further delay — on to Ingrid and Vickie’s post!

Why climate? Why now?

Math Awareness Month celebrates the many ways math is used by  scientists to study the climate and Ingrid Gnerlich and Vickie Kearn of PUP say that’s a good thing.

One of the biggest challenges of our time is to fully understand the complexity of the global climate system.  Climate science is an interdisciplinary field of research that encompasses atmospheric science, oceanography, geology, biology/ecology, and even space and planetary science.  Climate scientists conduct in-depth research on key components of the climate system— such as the carbon cycle, ocean and atmosphere circulation, the biosphere, and the cryosphere — with the ultimate goal of understanding how each facet works and exactly how every component influences the system as a whole.  By understanding the fundamental physics behind the essential parts of the climate system and how these parts interact, climate scientists can answer exciting questions, like how the ocean circulates heat around the planet and varies weather patterns, how the composition of the atmosphere affects global temperature, how the melting of polar ice caps can lead to feedback effects, and how the climate of our planet thousands of years ago compares to today’s – and they can make predictions about how the Earth’s climate can change if different aspects of the system are perturbed.

As anyone might guess, making predictions about anything is only possible if you start with deep understanding.  Long ago, people were unsure of whether spring would return each year after the cold, barren winter months; they didn’t understand what caused the phenomenon of spring, and so couldn’t make predictions with confidence.  Nowadays, we understand that the warm, long days of spring and summer come about when the hemisphere on which we live is tilted towards the Sun.  Our understanding gives us the freedom to make reliable predictions, and allows us to plan ahead, improve our quality of life, even live longer.  We take this knowledge for granted nowadays, but a predictive understanding of the phenomenon of spring only came as a result of the patient observation and the detailed calculations of dedicated, curious people many centuries ago.  Modern day climate scientists follow in the footsteps of those early scientists by seeking a predictive understanding of the global climate system, in hopes of benefitting humankind and all forms of life on Earth.  And, for their modern day tools, they use mathematics (calculus, differential equations, probability, statistics, and numerical analysis), physics, and computers.

How the Earth’s climate works, how it will change in the future, and how we can best plan for change on a global scale, are questions of enormous importance such as our species has rarely encountered – and math, physics, and computational science are essential to solving these fundamental problems.  This area of research draws upon many of our best minds, yet the field is filled with opportunities for new and important research and discovery, and it is wide open to innovation, as we look for new energy sources and to form new and better approaches to mitigating the potential effects of climate change.

At Princeton University Press, we aim to disseminate the highest quality information on climate science to students, researchers, and an engaged public.  Our authors and their books are meant to encourage intellectually curious readers, especially those who are talented in mathematics, to explore climate science as a remarkably stimulating, diverse, and impactful area of research.  In celebration of Mathematics Awareness Month, we hope that you will enjoy hearing from a few of our authors directly, regarding the fundamental importance of mathematics in their ongoing research on climate.