Dynamics of Climate Change: Explaining Glacier Retreat Mathematically

• Main Author: Guillette, Robert
• Format: Text
• Language: unknown
• Published: Virtual Commons - Bridgewater State University 2015
• Subjects: Mathematics; Norway; glacier; glaciers; Alaska
• Online Access: https://vc.bridgew.edu/undergrad_rev/vol11/iss1/14; https://vc.bridgew.edu/cgi/viewcontent.cgi?article=1314&context=undergrad_rev

Climate change is an important topic that has become extremely relevant this day and age. The world’s climate is undergoing monumental shifts with over two-thirds of the estimated 150 glaciers existing in 1850 disappearing by 1980. The melting of glaciers offers tangible evidence of broader environmental changes as they respond directly to long-term trends in temperature, precipitation, and solar radiation. Since the study of glacier retreat provides a barometer of climate change, it is important to better understand the effects of climatic factors on glaciers. In my project I created a mathematical model for the melting of glaciers and used the software Mathematica to create a program that simulates the evolution of glaciers over time. In particular, we used multiple regression to analyze the effects of climatic factors such as summer temperature and winter precipitation on glacier retreat. Moreover, we performed a time series regression and computed 95% prediction intervals to forecast how the ice mass of glaciers will change over the course of the next century. To test our model we used data from two glaciers, the Midtfonna glacier in Norway and the Gulkana glacier in Alaska. Our model showed that in the case of Midtfonna there is a statistically significant linear relationship over the course of the last 50 years between glacier area and the two predictor variables, average summer temperature (inducing melting) and average winter precipitation (inducing snow accumulation). In the case of Gulkana, we noted that glacier area measurements were only available for 3 out of the last 50 years, and so we could not apply the same instrument to analyze this glacier. Instead, we used glacier mass balance (the yearly recorded ice budget caused by the amount of snow that accumulated in the winter minus the amount lost in the summer) and showed that summer temperatures and winter precipitations explain 65% of the total variation in the mass balance data. Finally, our analysis showed that by the year 2100 the Midtfonna glacier will reach between 0% and 24% of its current area, while for the Gulkana glacier we did not have data to make such predictions.