Western Kentucky University

Calculus, Caves, and Climate Change

Grade Level at Time of Presentation

Senior

Major

Geology, Mathematics, Biology

Institution 24-25

Western Kentucky University

KY House District #

19

KY Senate District #

9

Department

Department of Earth, Environmental, and Atmospheric Sciences

Abstract

Quickening rates of climate change pose significant global challenges, with increasing levels of atmospheric carbon dioxide (CO2) as a primary driver of rising temperatures and by now well-documented environmental disruptions. The current ability to predict future atmospheric CO2 concentrations requires, similar to a bank account, knowing the current CO2 levels along with ongoing “deposits” and “withdrawals” of CO2 to and from the atmosphere, respectively, but these are incompletely characterized.

Karst landscapes and aquifers developed in limestone bedrock, such as those in southcentral Kentucky where caves and sinkholes are common, influence atmospheric CO2 levels as the geochemical processes associated with limestone dissolution remove CO2 from the atmosphere. Our research team is working within the groundwater flow system of Great Onyx Cave in a remote and relatively pristine forested area of Mammoth Cave National Park to make high-resolution measurements of this CO2 removal rate as part of a broader effort to better measure these processes on a global scale.

The component of the effort described here is focused on the required but relatively difficult measurement of discharge, or flow rate, of Cascade River in Great Onyx Cave, which, when combined with measured geochemical data, allows quantification of the relationship between hydrology and regional atmospheric CO2 removal. A barrel weir equipped to automatically measure water levels was employed below a waterfall along the underground stream to measure water discharge, and mathematical relationships using Torricelli’s law were developed to relate water level in the barrel to discharge under varying flow conditions. Once the theory was established using methods of calculus (both differentiation and integration), Python-based computational modeling enabled efficient processing of large datasets, revealing a strong correlation between rainfall patterns and discharge rates. This research contributes a key element for ongoing studies to better quantify the contribution of limestone dissolution to atmospheric carbon cycling.

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Calculus, Caves, and Climate Change

Quickening rates of climate change pose significant global challenges, with increasing levels of atmospheric carbon dioxide (CO2) as a primary driver of rising temperatures and by now well-documented environmental disruptions. The current ability to predict future atmospheric CO2 concentrations requires, similar to a bank account, knowing the current CO2 levels along with ongoing “deposits” and “withdrawals” of CO2 to and from the atmosphere, respectively, but these are incompletely characterized.

Karst landscapes and aquifers developed in limestone bedrock, such as those in southcentral Kentucky where caves and sinkholes are common, influence atmospheric CO2 levels as the geochemical processes associated with limestone dissolution remove CO2 from the atmosphere. Our research team is working within the groundwater flow system of Great Onyx Cave in a remote and relatively pristine forested area of Mammoth Cave National Park to make high-resolution measurements of this CO2 removal rate as part of a broader effort to better measure these processes on a global scale.

The component of the effort described here is focused on the required but relatively difficult measurement of discharge, or flow rate, of Cascade River in Great Onyx Cave, which, when combined with measured geochemical data, allows quantification of the relationship between hydrology and regional atmospheric CO2 removal. A barrel weir equipped to automatically measure water levels was employed below a waterfall along the underground stream to measure water discharge, and mathematical relationships using Torricelli’s law were developed to relate water level in the barrel to discharge under varying flow conditions. Once the theory was established using methods of calculus (both differentiation and integration), Python-based computational modeling enabled efficient processing of large datasets, revealing a strong correlation between rainfall patterns and discharge rates. This research contributes a key element for ongoing studies to better quantify the contribution of limestone dissolution to atmospheric carbon cycling.