Chaos in the rain

Ian Popple | Listen to the rhythm of the falling rain and you might just detect a pattern — a chaotic pattern. A team of McGill scientists have refuted an age-old assumption about the randomness of rainfall. The research, which may one day improve our ability to predict weather, demonstrates that rain falls in complicated patterns closely resembling that of wind turbulence.

Physics professor Shaun Lovejoy
Linda Dawn Hammond

For the purposes of weather forecasting, rainfall has always been considered uniform — if it rains in Montreal, the rain's the same no matter where you are in the city. It's easy to see the inaccuracy of this assumption. "During a storm you can actually see alternations between light and heavy rainfall," said physics professor Shaun Lovejoy.

The difficulty in measuring rain has been the lack of a decent technique. The rain gauge (which in its simplest form is a bucket in a downpour) has remained unchanged for centuries, and it "records the total amount of rain in that bucket, at that location, over that period of time," explained Lovejoy. "We've never had an accurate way of measuring rainfall over areas larger than this." Consequently, scientists have had to assume that the rainfall around the point being directly measured was homogeneous.

The assumption was not regarded as a problem, however, and scientists used the oddly oxymoronic term "uniformly random" to describe rainfall. Mathematically, random rain can be considered uniform at large sample sizes.

In order to explain this phenomenon, imagine a bathtub full of marbles. If two identical cups are filled with marbles, cup A might contain ten marbles and cup B might contain a couple more or less than this value — a difference of 20 percent. Standard mathematical theory predicts that identical samples should fluctuate by no more than the square root. If we increase the sample size, the relative difference between two identical samples should decrease. For example by filling two large buckets, instead of the smaller cups, we may find that bucket A contains 10,000 marbles, but bucket B now contains a difference of 100 marbles more or less — a relative difference of only one percent.

On the roof of the Rutherford Physics building, Lovejoy and his team of graduate students tested the uniformly random assumption of rainfall. The team used a technique called stereo photography to capture multiple images of rainfall from different angles. The raindrops were hard to see during the day, so two powerful lamps were positioned to illuminate the particles for night photography.

Despite the logistics of standing next to a 10,000 volt transformer in the pouring rain with only an umbrella for company, PhD student Nicolas Desaulniers-Soucy managed to collect numerous images of both rain and snow over a three-year period.

Three-dimensional models of rainfall were then created from the stills. "The images contained up to 100,000 drops of rain," said Lovejoy. "Each spherical drop had to be unambiguously identified in order to create the model." This task was relatively simple for the infrequent, large raindrops; the difficulty came in identifying the thousands of smaller drops, many of which were less than half a millimetre in diameter.

Refusing to blame it on the rain, Desaulniers-Soucy developed approximately 50,000 lines of specialized computer code to identify and catalogue the raindrops. After a further four years and a bucketful of patience, he succeeded in transcribing 90 percent of the raindrops into the 3-D model.

After seven years of work the team was finally able to refute the uniformly random raindrop theory. "Our results indicate that smooth, constant rain does not exist at any observed scale," explained Lovejoy. "Instead, the raindrops are hierarchically bunched — a pattern commonly referred to as a fractal."

These patterns are used in chaos theory to describe countless unpredictable phenomena from minute cracks in metallic alloys to wind turbulence. "The patterns are a hierarchy of eddies and whirlpools," explained Lovejoy. "The images contain aspects that are the same irrespective of the scale at which they are studied."

Lovejoy's rain fractals are consistent with those already discovered for wind turbulence. This research, published in the journal Physical Review, represents the first definitive demonstration that rain is hierarchically coupled to the wind — a new understanding that could one day improve our hourly weather forecasts.

For Lovejoy, the demonstration of chaos in rain is a reminder of the erratic aspect of nature. The conventional mindset, that nature is smooth and uniform with occasional periods of unpredictable, erratic behaviour is wrong. Nature is chaotic with occasional periods of relative uniformity. "When rain comes and goes unexpectedly, or a downpour seems to come from nowhere, I don't think that this is strange or bizarre anymore," mused Lovejoy. "Rather that it is the norm."