# Statisticians’ and Mathematicians’ Critical Contributions to Climate Science and Policy

A version of this article appeared in the March 2023 issue of Amstat News.

Scientists from across the disciplines, including statisticians and mathematicians, have spent decades making the case that our planet is rapidly warming due to anthropogenic emissions of carbon dioxide (CO2) and other greenhouse gasses. The catastrophic consequences of global warming are becoming undeniably obvious. Scientists, economists, and social scientists are now collaborating to improve our understanding and predictions of how Earth’s changing climate will impact humanity and the ecological and social systems upon which life relies.

As a key element of its mission, IMSI, the NSF-funded Institute for Mathematical and Statistical Innovation, held a Long Program on the mathematics and statistics needed for “Confronting Global Climate Change,” Sept. 19-Dec. 9, 2022. IMSI is designed to convene applied mathematicians, statisticians, and scientists who research topics with major societal implications. This long program was divided into six workshops that explored a range of key scientific issues that have direct bearing on humans’ understanding of our warming planet, the regional impacts on annual weather resulting from this evolving dynamical system, and predicting future risk, hazards, and damages due to extreme weather events and the social cost of carbon.

The Earth’s climate is a complex dynamical system whose physics takes place on spatiotemporal scales ranging from nanometers to kilometers, and microseconds to centuries. Modeling such a complex system and making predictions about future outcomes (that is, how climate begets weather), is further complicated by unknowns in, for example, the physics of aerosols and clouds. To improve some of the current shortcomings in climate models, researchers turn to statistical and machine learning strategies that use existing weather & climate data sets to further improve the outputs of these models in predicting future weather and climate.

Much of the discussion throughout the program focused on the verifiability, validity, and uncertainty quantification of climate models, particularly when applying these models to future weather and climate prediction at spatiotemporal scales that are useful for risk planning and adaptation to a warming planet. One key technical challenge lies in “downscaling” the relatively low resolution of the global climate models to the high resolution needed to make local climate impact studies of key variables such as precipitation and temperature. High resolution climate models are particularly important to those responsible for managing the socioeconomic risks and impacts of extreme events. For example, events like flooding and heat waves have major impacts on farmers, emergency management agencies, insurance companies, and just about everyone else thinking long-term about where to live, build, or work. Spatial downscaling introduces uncertainties which are necessary to quantify (i.e., uncertainty quantification), reduce, and communicate, so that the public and policy makers can rely on climate scientists and meteorologists with increasing confidence in their decision making. Linda Mearns (University Corporation for Atmospheric Research) is developing tools to deal with the uncertainties inherent in spatial downscaling from global climate models (ca. 20 km spatial resolution) to regional climate models (ca. 4 km). Her particular focus is on improving the statistical relationships between large scale atmospheric phenomena and local climate (temperature and precipitation) so that policy makers, for example, have more reliable tools for risk planning.

Generally, peoples’ experiences of climate change are two-fold: They experience the slow evolution of annual patterns in local weather, such as droughts becoming a way of life, winters that aren’t as cold, and summers that seem muggier than they used to be. Or they are caught by the seeming onslaught of fearsome extreme events such as freak heat waves in typically cool summer regions, two new seasons of extensive extremes – wildfire and hurricane – and massive flooding on the regional scale of states and nations. Mathematicians and statisticians are working with climate scientists to explore new approaches to understanding how the frequency, intensity, and global distribution of extreme events may be changing as a result of climate change. These mathematical scientists have much to contribute here, particularly in developing tools for quantifying and predicting rare and extreme events within a system that is non-stationary and for which there is a shortage of relevant data.

One major challenge in understanding the dynamics of extreme events is that the climate and weather systems under study are changing due to a warming earth. As such, the known geographic distribution of phenomena such as wind, temperature, humidity, and precipitation, that are based on historical data may not follow its current spatiotemporal statistical distributions in the future. By definition, extremes are the events that occur in the tails of these distributions. Yet there is evidence to support the conclusion that as the distributions change with global warming, phenomena thought to be extremes today may be less extreme, in the statistical sense, in the future, that is, more likely to occur in the future than in the past. Karen McKinnon (University of California, Los Angeles) noted that the upper tail of temperature distributions is getting longer than the lower tail; that is, the distribution is skewed toward the hot end. This suggests there will be more heat waves than unusually cold days in the future. In addition, she showed that globally, very humid areas are getting more humid, and dry areas are getting drier. Both of these observations have major implications for human health (impacts of heat waves coupled with high humidity) and so-called “fire weather” – extended hot, dry conditions that amplify the probability of wildfires.

Freddy Bouchet (Ecole Normale Superieure de Lyon) observed that heat waves cause more deaths than all other high temperature weather events combined over the period he examined. Given that these heat waves are relatively rare, he is developing prediction tools that are effective for small data sets. The impact of hot, humid weather on human health is a major area of scientific debate. Jane Baldwin (University of California, Irvine) and Matt Huber (Purdue University) each have research projects underway trying to reconcile differing opinions among physiologists and epidemiologists about how extremes in heat and humidity contribute to heat stroke and death. Physiologists argue that hot, moist conditions (high wet bulb temperature) increase human health risks, while epidemiologists observe that the data don’t back up this conclusion at the population level. Baldwin is using her tools as an atmospheric scientist to reconcile this disconnect. Huber takes as a given that there are thresholds in wet bulb temperature above which mammals’ (including humans) ability to function (dissipate metabolic heat from the core of the body) declines precipitously. These types of weather conditions will become more frequent and extreme in tropical and subtropical regions (that is, in many developing nations), with negative impacts on human health and regional economies due to declines in peoples’ ability to sustain outdoor labor (agriculture and construction, for example).

Kristi Ebi (University of Washington) is working to quantify excess deaths during heatwaves caused by the statistical extremity of the heat wave and anthropogenic climate change. Attributing excess heatwave deaths directly to climate change is difficult because of the complex set of factors that contribute to each death, such as individual vulnerability to heat & humidity, socioeconomic status and access to cooling, local baseline weather, and other factors. Her conclusion, after taking these factors into account, is that there will be statistically significant excess deaths during heat waves that are attributable to climate change.

Angel Hsu (University of North Carolina, Chapel Hill) has similar concerns as Ebi, but she is focusing on the urban heat island effect, recognizing that even within a relatively small geographic region like a city, different neighborhoods will experience extreme heat differently based on local conditions. One of the biggest predictors in urban heat islands is the relative absence of trees and other “greening.” Hsu showed that tree cover in cities correlates with per capita income, and that poor people and people of color are more susceptible to living in urban heat islands. She and her colleagues are developing tools using citizen science, available socioeconomic data, and mapping to measure and predict neighborhood-level urban temperatures. These tools can guide mitigation strategies such as targeted tree planting, thus illustrating that detection and attribution are important for using science to drive policy decisions and resource allocation in regions where potential impacts are large and resources may be limited.

Another major concern among earth scientists is the loss of Arctic sea ice and the ice sheets of Antarctica and Greenland. These climate change-driven phenomena will contribute significantly to catastrophic sea level rise, and in the case of reductions of Arctic sea ice, accelerate ocean warming which will also accelerate the melting of sea ice and the ice sheets. This positive feedback has scientists very concerned, primarily because of the fear of irreversible tipping points leading to coastal inundation faster than threatened regions can adapt.

Scientists’ work to understand the melting of sea ice and the ice sheets, which is complicated by our incomplete understanding of the physics of ice and of ice-air-ocean interactions. Model development and forecasting depend critically on reliable data, which, in the case of phenomena at continental scales in remote areas, like ice sheets, requires remote sensing via a constellation of earth-observing satellites. Fortunately, NASA and other agencies are launching missions that will augment or replace the instruments on the current Earth Observing System such as the NASA Surface Biology & Geology Mission, which will provide 30 meter resolution data at a broad spectrum of wavelengths providing information on, for example, snow, ice, and water cover, photosynthetic activity, and urbanization.

Scott Martin (University of Washington) discussed NASA’s upcoming SWOT (Surface Water and Ocean Topography) satellite that will provide data on ocean height, rivers, and surface water such as lakes. These data will improve modeling and prediction of many critical factors, including flooding and available water for agriculture and urban use. Importantly, with regard to sea ice and the ice shelves, SWOT will also help scientists understand the interactions between ocean currents and ice, and the extent to which those dynamics ultimately result in sea level rise. This last area of research is of particular interest to Momme Hall (Brown University) who is developing models to understand how large storms create ocean waves and the impact of those waves on sea ice. Similarly, Monica Martinez Wilhelmus (Brown University) is developing statistical descriptions of sea ice fields to provide a better understanding of the effect of large scale ocean eddies on sea ice. Scientific and policy advancements regarding climate change rely critically on the interconnectedness between NASA’s satellite measurements of the earth; climate scientists improving their physics-based models of sea ice, the ice sheets, and sea level rise; and statisticians who are providing innovative data synthesis and analysis tools for testing models and making predictions about our future climate.

There is also considerable attention being paid to the social cost of carbon, particularly resulting from flooding, changes in agriculture, and attributing economic damages to specific carbon emitters. Ian Bollinger (BlackRock) noted that 15% of the world’s population and 20% of capital assets are in coastal regions (which comprise 2% of global land area). In the absence of adaptation, coastal losses due to sea level rise and tropical cyclones (e.g., hurricanes) could increase by a factor of 100 by the year 2100, whereas there is a 10-fold capacity to reduce risk now via adaptation. BlackRock is developing high resolution (building-level) physical hazard models for coastal regions that also discount future economic value resulting from climate impacts.

Frances Davenport (Colorado State University) noted that floods are among the most common and destructive natural hazards, with an average of 82.7 million people impacted each year and $34 billion in damages. Climate scientists are now able to quantify the attribution of these damages to climate change. For example, they estimate that up to$26 billion of the $90 billion in damages from Hurricane Harvey are due to the influence of climate change in amplifying this extreme weather event. Adding to this body of work, Marshall Burke (Stanford University), is developing models for attributing the negative impacts on national economies to the carbon emissions from a different nation. He has developed a scientific framework for quantifying attribution, economic losses, and damage payments “owed” by emitting nations to those nations that have suffered losses. For example, he estimates that US carbon emissions have caused about$1 trillion in damages to Brazil since 1980.

Andy Hultgren (University of Illinois Urbana Champaign) studies the social cost of carbon by estimating global caloric reductions resulting from climate-induced losses in agricultural productivity. Globally, the highest sources of calories are maize, soy, rice, wheat, cassava, and sorghum. Climate change will cause losses in yield from these crops (except rice) resulting in declines in global caloric availability. Hultgren estimates a daily global caloric loss of 130 kCal per person, per degree C increase in global mean surface temperature. Further, the richest regions in the world – the global breadbaskets – and the poorest regions that rely more on subsistence farming, will have the greatest losses in agricultural productivity and their ability to feed the world.

The partnership of economists, mathematicians, statisticians, social scientists, and climate scientists illuminates a much more complex picture of the dire consequences of the social cost of carbon. They are extending the predictions of future impacts on the earth’s natural systems to the lives of actual people and where they live, while also quantifying the costs of either doing nothing or investing now in mitigation and adaptation. Federal investments in this research, such as the collaborative opportunities provided by IMSI, are critical to advancing our understanding of the complex interconnectedness of Earth and human systems, anthropogenic impacts, and developing strategies for carbon reduction while also mitigating and adapting to the effects of our warming planet.

Note: The author thanks Dorit Hammerling and Bo Li for their editorial input on this article.

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