By Matthew R. Francis
A series of terrible heat waves struck Europe in the summer of 2022, resulting in more than 20,000 deaths across the continent. In 2021, heat waves led to unprecedented wildfires in both Siberia and the Pacific Northwest, stressing already vulnerable ecosystems. In 2008 and 2010, extreme heat events throughout Asia killed hundreds of thousands of people.
Climate change is increasing both the frequency and severity of deadly heat waves. The most devastating heat events on historical record have all occurred in the past few decades and are unlike anything in the existing paleo-climatological data, which extends back to the dawn of humanity.
“Because of climate change, heat waves that were exceptional [in the past] might become common,” Freddy Bouchet, a climate researcher at the Centre National de la Recherche Scientifique and École Normale Supérieure in Paris, France, said. In other words, the human-driven changes in global climate are causing heat waves to happen more often and reach higher temperatures. However, the rarity of previous extreme heat waves makes it difficult for scientists to predict future occurrences — even as they become more common.
“During the last 20 years, only three events [comprise] nearly all of the total [heat-driven] deaths related to climate disaster,” Bouchet said. But as the number of heat waves grows, a more robust historical record would be useful for predictive purposes. “It’s basically three unprecedented events,” Bouchet continued. “It’s a serious challenge for scientists, to study something without data.”
Figure 1. The grid for the Planet Simulator climate model divides Earth into segments that are roughly 1,000 kilometers wide. The dark purple overlay indicates the North Atlantic region, which was the focus of this particular study. Figure courtesy of [1].
In a paper that recently published in
Physical Review Fluids [1], Bouchet and his colleagues approached this problem with a method from statistical physics called
rare event simulation. They drew on sophisticated climate models that encompass 8,000 years of Earth’s history and utilized neural networks to investigate the likelihood that a recorded heat wave would have transpired in the absence of human-created climate change. Using this information, the group then developed a framework that identifies the signs of future heat waves with the hope of predicting them early enough to enable mitigation strategies.
Isla Simpson, a climate scientist at the U.S. National Center for Atmospheric Research in Boulder, Colo., highlighted the complications of this type of prediction work. “We’re dealing with climate change that’s driven by greenhouse gases and aerosols and other things, but also just the natural variability of the climate system,” she said. “Quantifying how much a heat wave is changing because of greenhouse gases is a big challenge. We need models to help us do that because we have a limited observational record.”
However, Simpson clarified that while specific predictions are tricky, general conclusions are not. “The planet is warming, so any weather that happens on top of that warming is going to lead to more extreme high temperatures,” she said.
Everyone Talks About the Weather
Heat wave prediction faces many of the same problems as local weather forecasting. For instance, the atmosphere is intrinsically chaotic, meaning that small changes in conditions can lead to wildly different outcomes over time. In fact, the Lorenz strange attractor—one of the earliest descriptions of chaos theory—originated from efforts to model the weather. Researchers specifically focus on heat waves that last for more than a few days, since lengthier events can overwhelm a nation’s infrastructure. Bouchet noted that the number of deaths during the 2003 European heat wave grew quadratically with time, meaning that extreme temperatures become increasingly deadly the longer they last. Multiple heat waves over the course of a single season therefore constitute an urgent health crisis.
And to cite the cliché, it’s not just the heat. “It’s a combination of heat and humidity,” Bouchet said. “We reach a level where there is a huge nonlinearity in the body’s ability to respond.” This scenario is particularly salient in humid regions like Southeast Asia and the Indian subcontinent, where wet-bulb temperatures that account for air moisture are progressively exceeding tolerable levels for the human body. In addition, nighttime temperatures do not drop low enough to provide relief.
Arid regions face their own set of issues. “When it gets hot, the evaporation of water can kind of act as a mediator for the temperature,” Simpson said. “If you don’t have water to evaporate, then you’re going to have more extreme heat. Some places are drying out because of climate change, which could alter the nature of land-atmosphere feedbacks and lead to more intense heat waves.”
Simulating the Planet
For obvious reasons, heat waves are defined relative to their location. Temperatures over 90 degrees Fahrenheit (32 degrees Celsius) are not extreme in Death Valley, Calif., but could signal a crisis in parts of Alaska or Siberia that are north of the Arctic Circle. Meanwhile, 115 degrees Fahrenheit (46 degrees Celsius) constitutes extreme heat anywhere on the planet. Climate researchers like Bouchet and Simpson look for temperatures that exceed normal local conditions for an extended period of time.
Bouchet and his collaborators calculated temperature anomalies for a given time period by averaging the difference between the statistical mean temperature \(\mathbb{E}(\overrightarrow r,t)\) and the temperature \(T_{2m}(\overrightarrow r,t)\), which is measured two meters above the surface at time \(t\) and a point \(\overrightarrow r\) in space:
\[A(t)=\frac{1}{\tau}\int_t^{t+\tau}\frac{1}{|\mathcal{D}|}\int_\mathcal{D}(T_{2m}-\mathbb{E}) \, \textrm{d} \overrightarrow r \textrm{d}t.\]
Depending on the resolution scale and simulator requirements, the heat wave duration \(\tau\) can range from one day to the length of an entire season. The researchers used \(\tau=14\) days and set \(\mathcal{D}\) as a square that is roughly 1,000 kilometers in width — the magnitude of cyclonic atmospheric phenomena (see Figure 1).
Modern climate models are extremely sophisticated but computationally expensive to run. For that reason, Bouchet and his coauthors employed the Planet Simulator (PlaSim): a fluid dynamics model of the atmosphere. PlaSim is compatible with Intergovernmental Panel on Climate Change (IPCC) standards, but its lower resolution and fewer parameters allow it to run roughly 100 times faster than other models (albeit at a cost to accuracy). The simulation couples the atmosphere to the planet’s surface—ice, land, and water—and outputs important physical quantities like air temperature and pressure.
Figure 2. Simultaneous plot of the probability distribution \(P(Y,\mathbf{X})\) from the neural network analysis (green histogram) and the temperature anomaly \(A(t)\) for the 493rd year in the Planet Simulator run. When \(A(t)\) is greater than the threshold (which is depicted as a dotted line), the region in question experiences a heat wave. Figure courtesy of [1].
The group ran the simulator 80 times at 100-year intervals to obtain 8,000 years of data, with a temporal resolution of one day. They simulated the atmosphere at a roughly 2.8-degree scale in latitude and longitude and included 10 vertical slices from the surface to the boundary between the troposphere (the lowest layer of the atmosphere, where weather occurs) and the stratosphere.
With these data in hand, the team specified that an extreme heat wave occurs when the temperature anomaly \(A\) exceeds a threshold of 2.7 degrees Celsius. Accordingly, they defined a binary variable \(Y(t)\) that is equal to \(1\) during a heat wave and \(0\) below that limit; they thus aimed to calculate the probability \(P(Y=1|\mathbf{X}=\mathcal{x})\) of a heat wave when the dynamical parameters \(\mathbf{X} \in \mathbb{R}^d\) of the atmosphere correspond to a particular state \(\pmb{x}\) (see Figure 2). Although this probability function is unknown in principle, the neural network can estimate it via PlaSim’s 8,000 years of training data. “[Our] neural network has some predictive power on a timescale of a week to 10 days, which is the weather prediction range,” Bouchet said. “Because of chaos, we then lose information about the state of the atmosphere.”
But thanks to the slower drivers of atmospheric conditions like ocean properties and soil moisture, the researchers were able to predict heat waves farther out than ordinary weather forecasts. “We have a prediction with a delay of one month for a heat wave that lasted two weeks,” Bouchet said, adding that government weather services use similar probabilistic forecasts to help anticipate stresses on electricity production and agriculture.
When the Past Is No Guide
When predicting events that are historically rare, one must identify important properties in the absence of available data. “There’s the possibility that the [atmospheric] circulation patterns that induce heat waves are becoming more frequent or more intense,” Simpson, who was not involved in Bouchet’s neural network research, said. “That’s a much more difficult question to address because we don’t have a long observational record. Heat waves by definition don’t happen that often, so it’s hard to pick out a trend as to whether these weather systems are changing.”
In other words, disaster preparedness requires more than just the knowledge that heat waves are increasing in frequency, and even more than established correlations between this increase and climate change. Scientists are still trying to determine how large-scale atmospheric behaviors—such as monsoon cycles, for example—are changing as the world heats up. These phenomena could have a terrible feedback effect on regional weather, including heat wave occurrence.
One unfortunate irony is that climate researchers like Bouchet will be able to refine their models in the coming years simply due to the growing frequency of deadly weather events. However, effective heat wave prediction mechanisms could save lives if authorities are willing to take action — it is here that neural network forecasting might have its greatest impact.
References
[1] Miloshevich, G., Cozian, B., Abry, P., Borgnat, P., & Bouchet, F. (2023). Probabilistic forecasts of extreme heatwaves using convolutional neural networks in a regime of lack of data. Phys. Rev. Fluids., 8(4), 040501.
Matthew R. Francis is a physicist, science writer, public speaker, educator, and frequent wearer of jaunty hats. His website is BowlerHatScience.org.