Global warming is happening. The scientific community has reached consensus after years of studying complex computer models taking into account our fossil fuel emissions, wind and ocean currents, carbon uptake in forests, chemical composition of the atmosphere, and many other variables. Despite this scientific confidence, debates about the anthropogenic origins of climate change still carry on in Congress, and a majority of the US population does not see it as a threat.1 Meanwhile, island nations like Tuvalu are already relocating due to rises in sea level that will literally drown the country.2 This schism between belief and fact begs the question: how do we connect global changes like sea level rise, taking place on such long timescales, to personal experience to make the reality of global warming more vivid and the need for solutions more urgent?
This is a massive question whose answer includes a multitude of possible public awareness campaigns. But researchers in Australia have found one creative way to address the issue through education. Using nothing but a scale, flask of water, and glass marble, the research duo has designed an experiment demonstrating the basic physics of climate change that lead to sea level rise.3 The experiment is intended for use in a college physics courses, informing the next generation about global warming, but anyone can follow the same procedure to visualize the effects of climate change in his or her home.
The rising sea
The rise in global ocean levels with anthropogenic climate change occurs for two reasons. First, glaciers and ice that have been landlocked for centuries to thousands of years are melting from increased temperatures. As this melting ice slides from land to water, ocean levels go up (note that melting ice already in the water does not contribute).
The second primary cause of rising sea levels is the thermal expansion of water. As temperature increases, all the atoms inside most objects acquire more energy, causing them to move around more and take up more space, thus decreasing their density in most cases. The same is true of water above about 4 degrees Celsius.
Since 1880, sea levels have risen 200 mm with a 0.85 C temperature increase. This rise is expected to continue at a pace of about 3.2 mm/year.4 Even if global rates stay small, increases in sea level are spatially and temporally dynamic: storm surges create huge rises over short timescales, and rises in the North Atlantic occur about 3-4 times faster than in other regions. Doomsday predictions envision Manhattan skyscrapers peaking out of an ocean that’s suffocated the city. This may be an extreme and unlikely scenario, but the reality that huge populations along coastal cities will have to relocate is completely true.
Archimedes takes a bath
So how can we hit home the idea that this creeping sea level is happening all over the planet? Researchers in Australia have focused on the issue of thermal expansion and designed an experiment showing how this leads to rising sea levels. The apparatus can be used to teach college students about the physics of climate change, but the general public can probably also benefit from seeing the effects directly before their eyes.
Understanding how the experiment works requires a little knowledge about a guy named Archimedes and his famous principle. Archimedes is a legendary Greek polymath – a physicist, engineer, and inventor. He first explored the mathematics of infinitesimal quantities that would blossom into calculus in the hands of Newton. His inventions included a screw pump and even war machines that he built while defending his home city of Syracuse, which unfortunately cost him his life.
Despite all these accomplishments, the Greek is most well known for Archimedes’ Principle, a method to determine the volume of an object based solely on how much water it displaces. As the story goes, King Hiero II wished a crown to be made of pure gold, and asked Archimedes to test whether any silver had been used by the blacksmiths who made it. As Archimedes took a bath, genius struck! He realized that the water level rose as he jumped in, and this same effect could be used to measure the volume of the crown. Since water doesn’t compress easily, the volume of the water displaced must equal the volume of the object placed in it. Since the mass of the object can be found with a scale, dividing the mass by the displaced water volume gives the object’s density. Archimedes compared the density to that expected for gold or silver and found that those devious blacksmiths had indeed mixed in some silver (silver has almost half the density of gold)!
Climate change in a glass
This same idea has inspired researchers to construct an experiment showing how global warming leads to a measurable rise in sea level. The figure below shows the general setup. At the bottom sits a flask filled with water with a glass marble placed inside. A string is fixed to the marble on one end and to a balance or scale at the other end (at the top).
Now we have to remember some facts from introductory physics. The marble in the glass feels two forces: gravity pulling it downward but also a buoyant force in the opposite direction, which arises from the displaced water pressure on the marble. This buoyant force is equal to the product of the water density, the marble volume, and the acceleration due to gravity. Since the scale records the ‘weight’ of the marble as the net force pulling down on the string, this weight will be the sum of the gravitational force on the marble and the opposing buoyant force. Therefore, when the buoyant force is larger, the net force is smaller and thus the scale will read a smaller weight compared to the marble’s weight outside the water. Remember that the buoyant force is proportional to the water density – that’s the key part we’ll use in a second!
Ok, with that information in hand, the experimental goal is to find the weight of the marble, recorded by the scale, as a function of the water temperature. This is done by adding a bunch of ice to the flask of water to start close to freezing. Then, we measure the marble weight and the corresponding water temperature at consistent, precise increments in time. Then we plot the scale readings vs. temperature on a graph.
What do we see? As the temperature increases, the weight reading on the scale begins to go up (over 4 C). What does this mean? If the weight reading goes up, this must mean that the buoyant force is decreasing, since it counteracts the gravitational force less and leads to a higher reading. Remember that the buoyant force is proportional to the density of water and the marble volume. The latter stays constant, so the density of water must be decreasing to make the buoyant force decrease! So the higher temperature decreases the density of water.
The graph to the right shows this behavior, the water density consistently decreasing with temperature beyond a few degrees Celsius. This is the same effect that occurs due to global warming! As we add carbon dioxide to the atmosphere, we trap more heat at the planet’s surface and warm the ocean. As the ocean warms, its density decreases – the exact same effect we see here – which means it must take up more space, raising the sea levels.
Based on the data shown here, a 2 degree change from 17 C to 19 C corresponds to a 0.00037 g/cm3 decrease in water density. This may seem tiny, but this would lead to a 2 m increase in sea levels once the change in temperature spreads to all ocean depths. So small changes go a long way when considering such a large body of water across the entire planet.
Global warming is happening, and the accompanying sea level rise is an inevitable consequence. The same physics guiding the marble and water in the flask on your kitchen counter will guide the oceans to swell as temperatures continue to increase. These types of simple examples, along with understanding the physics behind them, is a great way to bring the impact of climate change into the classroom and your home and get people to pay attention.
- Jones, J.M. “In U.S., most do not see global warming as serious threat.” Gallup. Accessed October 15, 2015.
- Dohert, B. “Climate Change castaways consider move to Australia.” Sydney Morning Herald. Accessed October 15, 2015.
- Hughes S and Pearce D. “Investigating sea level rise due to global warming in the teaching laboratory using Archimedes’ principle.” European Journal of Physics, 36, 065033, 2015.
- Cazenave A et al. “The rate of sea level rise.” Nature Climate Change, 4, 358-61, 2014.
Figures of experimental apparatus and graph courtesy of Reference 3
Hughes, S., & Pearce, D. (2015). Investigating sea level rise due to global warming in the teaching laboratory using Archimedes’ principle European Journal of Physics, 36 (6) DOI: 10.1088/0143-0807/36/6/065033