Ice in Action: Sea ice at the North Pole has something to say about climate change

Talk of climate change in the news is ubiquitous. Everywhere we look, headlines are popping up, from deadly record-breaking heat waves in Pakistan and India to the notoriously cold and rainy London reaching a record high of 98 degrees Fahrenheit this past July. Earth’s climate cycle is becoming increasingly erratic, which has two conflicting effects — mapping these patterns is simultaneously more important than ever, and more difficult than ever.

In many ways, climate change is a complicated beast. In a single season, we might see intense spikes in temperature in one area of the world and colder than normal weather elsewhere. It is a problem fueled largely by human activity, and so motivating environmentally friendly behavior is important. But change takes time: The climate concerns we are experiencing now are the result of hundreds, if not thousands, of years of change. Similarly, the positive lifestyle choices we might implement in service of our planet will not fix climate disruption overnight. These positive changes in human activity are crucial, but the sobering truth is that the earth does not respond immediately to change.

These complex issues are exacerbated by the fact that measuring climate change is equally complicated. Reliable, hard and fast data on climate change patterns would perhaps be universally convincing and motivating, but is extremely hard to come by. Scientists use diverse parameters in quantifying climate change: They might measure sea surface temperatures or precipitation. Maybe they track volcanic eruptions. Of course one method stands out as particularly effective, and that is measuring the thickness of Arctic sea ice.

The existing tactic to understand the distribution of sea ice thickness up by the North Pole is centered on a formula called the partial differential equation. This formula depends on three variables, one of which is particularly problematic. A Yale duo has found a way to circumvent this problem, updating the partial differential equation so that it can more accurately convey information about Arctic sea ice, and about global climate change.

The team consists of John Wettlaufer, a professor of geophysics, mathematics, and physics at Yale, and Srikanth Toppaladoddi, a graduate student. Their new model for calculating Arctic sea ice thickness could make a big splash in the field of climate science.

All eyes on the Arctic

Wettlaufer and Toppaladoddi’s model is significant not only because it is a more accurate measure of sea ice thickness, but because Arctic sea ice thickness is a highly sensitive indicator of the Arctic climate as a whole. And changes in Arctic climate have long been understood as a harbinger for what is to come farther south.

An important reflection of Earth’s climate regulation is the hydrologic cycle, more commonly known as the water cycle — a staple of elementary school education. At lower latitudes, this cycle is regulated by the flux between evaporation and precipitation. But in the polar regions, the processes of freezing and melting are extremely important, as they create density differences that drive global water circulation. Earth’s cryosphere — its frozen water — has a global impact on climate, and disruptions can cause temperatures to plunge in some regions and skyrocket in others.

Not all Arctic ice is created equally. The Greenland ice sheet sits three kilometers thick upon a landmass and influences global sea levels. This is one way to facilitate the effects of global warming, namely a rise in sea level. In contrast to Greenland, sea ice is only a few meters thick and does not alter sea level at all. Instead, sea ice affects global climate because it rejects salt when it forms, making it uniquely responsible for patterns in global ocean circulation. Large ocean currents, in turn, move warm and cold water around the globe, and thus impact weather events.

In addition, small changes in climate at lower latitudes are amplified up in the Arctic, a phenomenon known as polar amplification. Thus, sea ice thickness up North is a strong signal for the global climate condition.

In 1969, Russian climatologist Mikhail Budyko developed a simple energy-balance theory of climate that captured a key feature of polar amplification. We know from common experience that the bright light reflected from a snow-covered field in the winter is far more glaring than that reflected from grass in the summer. The reflectivity of a material, called albedo, underlies Budyko’s theory of ice-albedo feedback: Floating white ice has a much higher albedo, or greater reflectivity, than the adjacent blue ocean. Since the latter absorbs more of the sun’s radiant energy than does ice, the ocean warms and melts the ice. This in turn exposes more ocean, which absorbs more energy, which again melts more ice. The cycle causes a runaway effect, and the Arctic shoulders much of the burden.

Budyko’s theory only emphasizes the need for a reliable means of tracking Arctic sea ice, which is likely to be in flux as the planet warms. Prior methods were insufficient. Enter Wettlaufer and Toppaladoddi — and a new, tractable equation.

The microscopic and the macroscopic

Geophysicists in 1975 developed a partial differential equation that would in principle allow for the calculation of the distribution of Arctic ice thickness. The equation has three terms that describe the dynamics of sea ice. The terms that characterize how wind and heat affect ice thickness have a firm grounding. But the term that describes the mechanical redistribution of ice floes, or floating ice sheets, is difficult to characterize mathematically. Without a sound mathematical model, there is no way to test the partial differential equation observationally. Until recently, this intransigent term has been a roadblock, getting in the way of our complete understanding of Arctic sea ice and global climate change patterns.

Yale’s Wettlaufer and Toppaladoddi have devised a different approach to the problem of Arctic ice thickness. The duo brought a new piece of information to the table, and in doing so, made a fascinating connection between the physics of the microscopic and macroscopic worlds.

The concept the team evoked is known as Brownian motion, first observed in 1827 by Scottish botanist Robert Brown as he was watching the random motions of pollen grains in water. When Brown made his observations, atoms and molecules were only abstract concepts. It was not until 1905 that Brown’s observations were quantified by Albert Einstein. A synthesis of Brown’s and Einstein’s ideas has led to a crucial conclusion: It was the thermally induced motion of water molecules colliding with Brown’s pollen grains that produced an overall motion in the fluid.

Wettlaufer and Toppaladoddi used the analogy of Brownian motion to deal with the partial differential equation’s 40 year-old uncompromising term. They recognized that mechanical events such as ice rafting, or the movement of objects via ice rafts, occur in seconds or less, whereas a system of many rafts changes ice thickness distribution only slowly. By drawing from Einstein and Brown’s theory of microscopic change and applying it to a macroscopic environmental problem, they were able to separate these two time scales and convert the unsolvable partial differential equation into a tractable one.

To test their modified equation, the researchers used it to back predict ice thickness between the years 2003 and 2010. They compared their theoretical results to real Arctic data collected by NASA’s Ice, Cloud, and Land Elevation Satellite. Wettlaufer and Toppaladoddi found that their solution curve accurately predicted the observed distribution of Arctic sea ice. With this verifying result in hand, the two hope to soon extend their equation to the task of predicting future changes in ice thickness distribution.

The updated technique has huge implications for understanding climate dynamics, both in historical hindsight and in preparation for the future. Eventually, we may be able to track our own impact on Earth’s climate using this revamped equation. Such control over the future is encouraging as we continue to change our behaviors in small, positive ways while recognizing that our planet’s response to these changes will not be immediate. Over time, the sum total of our positive actions could amount to noticeable change for the better. Wettlaufer and Toppaladoddi’s method for studying Arctic sea ice and climate dynamics may provide just the tool for us to notice that change.

Their recent research was published in the October edition of Physical Review Letters. It quickly sparked conversation among climate scientists everywhere, as people search for better ways to predict and understand our climate. Arguably, this goal is now more important than ever, as climate change becomes ever more pressing.

Film’s like the 2004 hit The Day After Tomorrow shock viewers with a spine chilling — albeit unrealistic — dramatization of extreme weather events spurred by frightening climate change. With any luck, researchers like Wettlaufer and Toppaladoddi will prevent us from reaching this point, by elucidating the intricacies of climate and how it is changing around the globe.