Rain events, the sand pile effect and climate change

Houghton flooding

Flash floods at Lake Linden (near Houghton), Michigan, June 2018 (Detroit Free Press)

I spent a lot of grandmother-visiting time in my youth, and went to university for a time, in the far-northern Michigan town of Houghton, located on the Keweenaw Peninsula protruding like a thumb into Lake Superior. This place regularly gets over 200 inches of “lake effect” snowfall each winter, but it has rarely been hit with up to seven inches of rain in a single day until June 17, 2018. [1]

Was this “rain event” cause by anthropogenic (human-caused) climate change? Or is it “God playing dice”? In this post I want to present a mathematical analogy and familiar example that might help get us to a better understanding of this question and its possible answers.

Since we were children playing in a kindergarten sandbox we have intuitively known something unique about the behavior of sand piles. If you are careful in sprinkling sand down from above, you can create a near-perfect cone of sand up to a certain height, but then at some point the cone will suddenly collapse. If you keep playing at this game, you will learn that you can make that collapse happen faster or slower, but you can never quite guess exactly when any given sand pile will collapse.

There is a technical name for this sand pile phenomenon, called self-organized criticality. Depending on the characteristics of the sand grains you are playing with and the force of gravity on the falling grains, this conical sand pile will “self-form.” But at some point, again depending on the characteristics of the sand grains and the rate of sand coming down onto the pile, that pile will reach a critical point (or critical state) where each additional grain of sand has an increasing probability of causing the next collapse.

In other words, you can never exactly predict the next collapse, but with enough data gathering, you can begin to express the probabilistic odds of collapse in any particular interval. This is a complex version of a Poisson distribution (pronounced pwa-sahn), which I have discussed in earlier posts. Poisson events happen all the time around us, from the replication of skin cells to the arrival of phone calls into a telephone call center. In these events, we can predict the probability of one or more events occurring in a particular time interval, but as the time interval gets smaller, the effect gets harder and harder to predict. For instance, with some data in hand, I can likely predict quite accurately how many customers will come into my restaurant on any particular day, but still have a hard time predicting how many will come in between 10:00 and 10:01.

So it is with the sand pile. Given enough trials, I can get a good handle on predicting that the pile will collapse at some point within a specified long interval, but it gets tougher to predict the shorter the interval. Interestingly, our “brain chemistry” appears to exhibit the sand pile effect, as chemicals build up to a certain point in a group of cells until they “collapse” and “fire” as a group. [2] You can see this model of brain neuron activity and mathematical probability in functions like swinging a baseball bat, which I discussed in a recent post.

Rain events and sand piles

A “rain event” is a loose definition for an “out of the ordinary” quantity of rain within a specified period. For instance, we commonly talk about a “100-year flood,” but even that designation is usually somewhere between a data-based prediction and a “best guess.” It doesn’t say that we can expect one “event” every 100 years, rather, each year has a 1% chance of seeing an event. And even that number gets squishy during times of climate change. Regardless of the difficulties of definition, we can safely call the Michigan flash flood noted above a significant “rain event,” and the consequences for many residents were very frightening and costly.

The lack of repeatable data is the problem here because of the infrequency. We have not been keeping detailed statistics for long enough to get super-confident about our assessment on most rain events. However, we do know how heat causes water on the ground to vaporize and form clouds. Given enough vapor and the right surrounding weather conditions, that “building sand pile” of water vapor in the atmosphere will reach that “critical point” and suddenly collapse, quickly dumping the water onto the ground as rain in a fairly-confined area.

In a sense, this is “normal.” We have always had rain. The “climate change” question is whether environmental changes to carbon levels in the atmosphere, increased evaporation in the Gulf of Mexico, and far-away melting of arctic icecaps are changing the “nature of the sand going into the sand pile,” so that, first, some areas get less rainfall because the warmer atmosphere can hold more water vapor, and then followed by more frequent and higher volume rain events as those water vapor “sand piles” reach their point of criticality and “collapse,” dumping the water in one localized spot. The scientific consensus has long said “Yes,” and even more conservative observers are reluctantly coming on board. [3]

Several scientific studies have looked at the mathematics of “sand pile effect” in relation to climate change, and the math appears to apply well. [4] I am not a climate scientist, but I do understand the math of “self-organized criticality.” As it is with most weather events that appear to be occurring more frequently, one can rarely say that “this event” was caused by climate change. However, it would be correct to say that the “odds have clearly changed,” and that, in the language of this blog, “God’s dice” are loaded.

Even the most conservative business owner will purchase insurance for low-risk catastrophic events like fires. The risks of climate change have long surpassed that “reasonable need for insurance” threshold, so it is safe to say that the remaining opposition here is neither conservative nor reasonable. It is instead blindly ideological. It’s time to go back and think about our kindergarten sand pile-making days. We knew the correct answer even back then.


  1. Paige, DeAsia. “What We Know about Flooding in Houghton, Michigan.” Detroit Free Press, 19 June 2018.
  2. “Functioning Brain Follows Famous Sand Pile Model.” EpilepsyU, 23 June 2015. See also Ouellette, Jennifer. “Sand Pile Model of the Mind Grows in Popularity.” Scientific American, 7 Apr. 2014.
  3. Eller, Donnelle. “Iowa Is Getting Hotter, Bringing More Frequent and Intense Storms.” Des Moines Register, 9 Aug. 2018.
  4. For instance, Liu, Zuhan, et al. “Self-Organized Criticality of Climate Change.” Springer Dordrecht, 25 May 2013.

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