Alec Knutsen
October 23, 2014
HNRS 190: Th: 10:00 a.m.-10:50 a.m.
Dr. Van Vleck
I.Abstract:
Bifurcations or “tipping points” represent the idea that a small change can have a big impact. In terms of climate modeling, the idea of a tipping point or bifurcation gives the notion that a change in a parameter such as temperature can change some aspect of our climate.
Specifically, the tipping point is some critical value that the parameter can take which changes the whole system being analyzed. Probably three of the most important climate systems that involve tipping points are the Atlantic thermohaline circulation, the Arctic ice sheet, and the
Greenland ice sheet. Various current models try to find tipping points for these three climate models. Similarly, my goal is to analyze various models and tipping points for these three climate systems and draw conclusions on how our climate can be altered by various tipping points within these three systems.
II.Background and Introduction:
Thermohaline circulation is guided by the principle that warm water heated near the equator travels to the higher latitudes where it gets colder. Colder water is denser, so the cold water sinks and travels deep in the ocean. One model that is currently used to model thermohaline circulation is the Stommel Box Model. The Stommel Box Model consists of two boxes representing the low latitudes and high latitudes, and it shows that the flow strength or the circulation of the ocean is dependent on temperature and salinity. Some of today’s climate changes such as rising temperature could result in a bifurcation or tipping point which could upset the delicate balance of the thermohaline circulation. It has been observed that the
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Alec Knutsen
October 23, 2014
HNRS 190: Th: 10:00 a.m.-10:50 a.m.
Dr. Van Vleck
Greenland ice sheet (GIS) is nearing a tipping point or bifurcation in which its melting may be irreversible. Likewise, it has been shown that the Arctic ice has been reduced in area. If enough ice is lost, there would be a tipping point or bifurcation which would alter the thermohaline circulation. As ice melts, more freshwater sinks into the ocean which makes the water more dilute. With lower salinity levels, freshwater is less dense and less likely to sink, reducing the formation of North Atlantic deep water. Also, the rising temperature of the earth could alter the thermohaline circulation. With increasing temperature, water becomes less dense which would also prevent sinking of water, slowing the North Atlantic deep water formation. Thus, in the case of the thermohaline circulation, a bifurcation or tipping point could be reached in which water becomes less dense because of either increasing temperatures or more dilute waters, disrupting the formation of the North Atlantic deep water and slowing the thermohaline circulation.
It has been shown in studies, first by Stommel, that the North Atlantic deep water flow slows when freshwater less than 0.06 Sverdrups (0.06 x 10 6 m 3 /s) is introduced into the North
Atlantic. In the two figures on page seven, one can see that when the introduction of freshwater is between 0.05 and 0.07 Sverdrups of freshwater, the flow rate of the North
Atlantic deep water is reduced from around twelve Sverdrups to around two Sverdrups; thus, a bifurcation occurs around 0.06 which drastically disrupts the North Atlantic deep water formation and the thermohaline circulation. Disrupting the thermohaline circulation would have far-reaching impacts for our climate. The circulation carries about 12 x 10 15 Watts of heat northward, and it carries around seventeen Sverdrups of cold North Atlantic deep water. If the circulation is disrupted, the warm surface water would not be brought to the North Atlantic,
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Alec Knutsen
October 23, 2014
HNRS 190: Th: 10:00 a.m.-10:50 a.m.
Dr. Van Vleck making the North Atlantic region much colder. In research, my goal is to first study various models for thermohaline circulation, specifically the Stommel Box Model. Then, I will analyze different bifurcations within these models and analyze the impact of these bifurcations on our climate.
Other important climate systems that involve bifurcations and tipping points are ice sheets, specifically the Arctic ice sheet and the Greenland ice sheet. In the past, tipping points have been reached in which the Arctic ice sheet and Greenland ice sheet melted and our climate was abruptly altered. Around 125,000 years ago, the climate was warmed by 11-13% in the summer, causing Arctic ice loss and almost the total collapse of the Greenland ice sheet.
Today, a number of factors such as increased absorption of solar radiation, increased ocean heat from the Pacific and Atlantic, and less cloud cover have reduced the summer and winter area cover of Arctic sea ice. Similarly, the Greenland ice sheet is losing mass at a rate that has been accelerating. With the Arctic, many model estimates are predicting an ice-free ocean by
2050; however, an ice free Arctic does not involve an irreversible bifurcation because sea ice could reform with cooling. In contrast, the Greenland ice sheet could undergo an irreversible bifurcation. If the surface mass balance (the difference between ice accumulation and melting) goes negative, the surface height of the ice declines and the ice gets warmer, making the ice loss irreversible. Recent studies show that an irreversible tipping point could occur at increases in temperature from as low as 0.7-1.7 degrees Celsius to as high as six degrees Celsius.
Shrinkage of the Arctic ice sheet and Greenland ice sheet are extremely important to analyze; reaching a tipping point in which melting is irreversible will increase the freshwater input in the oceans and upset the thermohaline circulation. Again, in my research, I will study many
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Alec Knutsen
October 23, 2014
HNRS 190: Th: 10:00 a.m.-10:50 a.m.
Dr. Van Vleck different models that analyze the rate of sea ice loss. After looking at various tipping points, I will analyze how the ice loss will impact our climate, especially the thermohaline circulation.
III.Significance to the applicant:
Conducting mathematical research in terms of climate will enhance my university experience in many ways. Mathematical research will help me understand what research entails, and how I can apply my mathematical skills in a real-world setting rather than the classroom. In addition, doing research in a pivotal area such as climate bifurcations would be extremely interesting and exciting; understanding tipping points in our climate is crucial for understanding the future climate of our earth. As a member of the University Honors Program, a research experience would satisfy one of my requirements to graduate with honors. Most importantly, a research experience would enhance my interest and ability to achieve my goal of going to graduate school to study mathematics and becoming a professional mathematician.
IV.Applicant’s qualifications:
Although I am only a freshman, my qualifications include being an honors student and having a very strong mathematical background up through differential equations in high school.
I am currently taking upper level mathematical courses including Intermediate Analysis (Math
500). Having taken differential equations in high school, I am familiar with certain types of differential equations and bifurcations such as saddle-node bifurcations and pitch-fork bifurcations; thus, when analyzing climate data, I will have some familiarity with the different types of bifurcations. Also, I am majoring in computer science and have familiarity with Matlab which could be useful in analyzing specific types of climate data. Besides familiarity with
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Alec Knutsen
October 23, 2014
HNRS 190: Th: 10:00 a.m.-10:50 a.m.
Dr. Van Vleck bifurcations and familiarity with some computing programs, I am also a dedicated, hardworking student who would be honored to do research in such an important field such as climate modeling.
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Alec Knutsen
October 23, 2014
HNRS 190: Th: 10:00 a.m.-10:50 a.m.
Dr. Van Vleck
Rahmstorf, Stefan. "Bifurcations of the Atlantic Thermohaline Circulation in Response to Changes in the
Hydrological Cycle." Nature 378.6553 (1995): 145-49. Web. 19 Oct. 2014
Lenton, Timothy M. "Arctic Climate Tipping Points." Ambio 41.1 (2012): 10-22. Web. 19 Oct. 2014.
Lenton, Timothy M. "Earth System Tipping Points." Accessed October 14, 2014. http://yosemite.epa.gov/ee/epa/eerm.nsf/vwAN/EE-0564-112.pdf/$file/EE-0564-112.pdf
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Willeit, Matteo. "Klimageschichte Ubung 9 Thermohaline Circulation - the Stommel Box Model." https://www.pik-potsdam.de/members/willeit/. Accessed October 14, 2014. https://www.pikpotsdam.de/members/willeit/klimageschichte-ubungen/stommel-model/tutorial.pdf
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Bergman, Jennifer. "Thermohaline Circulation: The Global Ocean Conveyor." - Windows to the Universe.
January 26, 2011. Accessed October 14, 2014. http://www.windows2universe.org/earth/Water/circulation1.html
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"OCEANS & SEA LEVEL RISE Consequences of Climate Change on the Oceans RISE." Climate Change and
Sea Level Rise. Accessed October 14, 2014. http://www.climate.org/topics/sea-level/ .
Kloeppel, James. "News Bureau | University of Illinois." Global Warming Could Halt Ocean Circulation, with Harmful Results. Accessed December 6, 2005. http://www.news.illinois.edu/news/05/1206climate.html
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Alec Knutsen
October 23, 2014
HNRS 190: Th: 10:00 a.m.-10:50 a.m.
Dr. Van Vleck
Reference: Rahmstorf, Stefan. "Bifurcations of the Atlantic Thermohaline Circulation in Response to
Changes in the Hydrological Cycle." Nature 378.6553 (1995): 146. Web. 19 Oct. 2014
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