# World’s lakes are much shallower than thought, mathematical analysis suggests

**NEW ORLEANS, LOUISIANA—**The world’s lakes are only about two-thirds as deep, on average, as previously thought, researchers reported here this week at a meeting of the American Physical Society. If correct, the finding could help climate scientists more accurately model global climate change, as shallower lakes generate more heat-trapping methane gas.

Satellites show roughly 100 million lakes with areas greater than a hectare dotting Earth. All together, they cover more than 30 billion hectares, roughly 2% of planet’s land surface. But estimating the depths of these bodies of water is a trickier task. Lake depth varies widely: The famed Loch Ness in Scotland is on average 132 meters deep, more than four times as deep as North America’s Lake Erie, even though Erie is 4500 times as large in area. Scientists typically infer a lake’s depth from the local topography—that is, the slopes of the surrounding land—says B. B. Cael, an oceanographer at the Massachusetts Institute of Technology in Cambridge and lead author on the new study. Estimates for the total volume of Earth’s lakes range from 160,000 to 280,000 cubic kilometers, Cael says.

Cael wanted to do better. With Adam Heathcote, an ecologist at the Science Museum of Minnesota in Marine on St. Croix, and David Seekell, an environmental scientist at Umeå University in Sweden, he first developed a model that could explain the observed distribution of lake areas around the world. Using data from multiple surveys, Cael found that the number of lakes in a given area falls as the area increases according to a particular mathematical relationship known as a power law. Put simply, small lakes come in bunches, and big ones are rare: There are only 1/100 as many lakes with an area of 10 hectares as there are with an area of 1 hectare, only 1/100 as many lakes with area of 100 hectares as there are with 10 hectares, and so on. That power law and additional data suggest researchers have underestimated the number of small lakes, so Cael and his colleagues ended up with a slightly higher estimate of the total area of the world’s lakes.

To estimate volumes and depths, Cael then invoked a mathematical model of Earth’s topography. He assumed that Earth’s surface has a fractallike symmetry that makes it approximately “self-affine.” In other words, no matter how much one zooms in or out, the distribution of mountains and valleys will be statistically identical if all the heights are stretched by a particular factor. Specifically, several topographic studies show that if you zoom in on the landscape by a factor of 10, then you need to adjust the heights by a factor of 2.5, Cael says. (Studies also suggest Mars is roughly self-affine, with the same scale factor of five.)

That relationship then enables researchers to infer, statistically, the volumes and depths of lakes from their areas. “We assume that the lake cannot substantially change the underlying topography,” he says. Cael found the total volume of Earth’s lakes to be 199,000 cubic kilometers—on the lower end of previous estimates. Strikingly, the model also suggests the average depth of Earth’s lakes is 42 meters, significantly lower than the previous 62-meter low estimate.

If Earth’s lakes are, on average, significantly shallower than previously thought, that observation could have consequences for understanding climate change, Cael says. Microbes that don’t require oxygen live at the bottom of lakes and produce methane. If lakes are shallower, more of that heat-trapping gas can bubble up to the surface and into the atmosphere. Current methane budgets suggest lakes produce about as much methane as the oceans and roughly half as much methane as the world’s landfills, but that number may have to be revised higher, Cael says.

Although it involves a mathematical model, the study’s strength is that it sticks closely to the data, says Mary Silber, an applied mathematician at the University of Chicago in Illinois. “I liked the care with which he is just trying to collect the data and see if it can be explained with something quite simple.”

**Correction, 20 March, 2:06 p.m.: **This story has been changed to note that Mars is roughly self-affine with a scale factor of five, not 2.5 as originally stated.*