Mathematics and Statistics Contribute to Climate Science and Policy

IMSI - February 2023
Mathematics and Statistics Contribute to Climate Science and Policy Thumbnail Image
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.

IMSI held a Long Program on the mathematics and statistics needed for Confronting Global Climate Change, Sept. 19-Dec. 9, 2022.  This long program included 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.

Much 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 is “downscaling” from the relatively low resolution of the global climate models to the high resolution needed to make locally-relevant predictions of key variables like 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, 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).  One particular focus is on Usable Climate Science (See Fig. 1), which aims to improve the 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. 

Fig. 1 Usable Weather and Climate Data (from: https://ral.ucar.edu/technologies/regional-climate-analysis-and-impact)
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 for understanding how the frequency, intensity, and global distribution of extreme events may be shifting as a result of climate change.  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 statistics 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, are based on historical data whose spatiotemporal statistical distributions may not be adequate for making predictions of 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 considered extreme today may become more frequent.  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 (See Fig. 2). 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. 

Fig. 2 Figure from the McKinnon & Simpson paper on “How Unexpected Was the 2021 Pacific Northwest Heatwave?” showing the statistics of the extreme heat event relative to historically expected probabilities of such occurrences. (Geophysical Research Letters, 49, e2022GL100380).
The partnership of economists, mathematicians, and climate scientists provides a much more complex picture of the dire consequences of the social cost of carbon and the impact of CO2 on weather and climate.  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.  This kind of research is 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.