Milankovitch Cycles

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17 Jan 2024

Milankovitch Cycles

28 June 1914, the heir to the Austro-Hungarian Empire, Franz Ferdinand, was assassinated by a Serbian assassin. The already simmering European politics, resembling a boiling pot, completely unraveled with this event, leading to an atmosphere where the strings were entirely severed, and war cries were raised. Meanwhile, another Serbian, whose sole purpose in life was to mathematically model the world's climate system, had recently married and come to his hometown of Dalj for a honeymoon with his wife. However, the town of his birth had been under the rule of the Austro-Hungarian Empire for some time, and the assassination of the heir by a fellow countryman would bring significant trouble upon him. This man, in the happiness of his honeymoon, was in the wrong place at the wrong time.

Following the assassination, as Europe drifted towards what we now know as World War I, he found himself in custody. Among the Serbian citizens arrested by the Austro-Hungarian army, on the first night of his arrest, he would later recount:

"The heavy iron door closed behind me. I sat on the bed, looked around, and began to accept my new social conditions. Among the belongings I brought with me were studies on my cosmic problem. After a brief look at my work, I took my faithful pen and started to calculate. When I lifted my head from my work after midnight, I needed some time to understand where I was. That small room seemed like a place I stayed overnight during my journey in the universe."

The man who, on the first night of his detention, could sit down with astonishing concentration and continue his unfinished scientific work, is today proudly remembered as one of the significant figures contributing to positive science among Serbs, along with names like Nikola Tesla, Mihajlo Pupin, and Pavle Savić. That man is Milutin Milankovitch.

Milankovitch placed himself in a crucial corner of the history of science and made it the main topic of this text with his success in revolutionizing the understanding of climate dynamics mathematically. His studies are not only applicable to Earth but also to other planets in the Solar System. He became the founder of planetary climatology, based on the temperature measurements in the upper atmosphere of the inner planets (Mercury, Venus, Mars) and the atmospheric thicknesses of the outer planets. His most well-known work demonstrated mathematically that the long-term climate changes occurring over millennia on Earth are actually caused by Milankovitch cycles, which also last for thousands of years. These long-term climate changes of Earth are also known as ice ages. These ages, with a certain periodicity, have led to significant periods in which many species on Earth either went extinct or migrated. Thanks to geological data, we can determine when these ages occurred in the past. Milankovitch's explanations have allowed humanity to predict how much time is left until the next ice age.

The new breath that Milankovitch brought to climatology, apart from the daily and yearly movements of Earth, was named 'Milankovitch Cycles' for the very long-period cyclic movements he identified.

Milutin Milankovitch

Milutin Milankovitch was born on May 28, 1879, as the son of a merchant with his twin brother. He took his first steps into the years of childhood with his mother and grandmother after losing his father at the age of eight. He lost three siblings due to tuberculosis. At the age of 17, in 1896, after completing high school, he went to Vienna and started studying Civil Engineering at the Vienna University of Technology. When he graduated from this school in 1902, he would say the following, remembering his mathematics teacher: "Professor Czuber taught us mathematics. Every sentence of his was a masterpiece of solid logic, without any extra words, without any mistakes."

After graduation, he borrowed the money he needed for his Ph.D. from his uncle. Two years later, he completed his Ph.D. with his thesis on 'Pressure Curves Theory,' focusing on concrete and building materials. Now, he was a sought-after engineer. After his Ph.D., he worked for a construction company in Vienna for a while.

His interest in mathematics and basic sciences brought him to the chair of applied mathematics at Belgrade University in 1909. Here, in his applied mathematics lectures, he integrated rational mechanics, celestial mechanics, and theoretical physics, unlike any other European universities had seen. It was this integrative approach that led him to significant achievements in climatology.

When he started his academic career, he had the idea of choosing an ambitious scientific problem that had not yet been solved and devoting the rest of his life entirely to that subject. Until then, other scientists had avoided the field of meteorology and climatology, where a large amount of data had accumulated because it seemed that progress beyond analyzing and interpreting data in this field was not possible. Nevertheless, Milankovitch conducted research on what could be done in this field. He believed that several previous studies on the amount of sunlight absorbed by the Earth could be advanced and correlated with climatic variables. Moreover, this situation could be explained mathematically. On the other hand, it was also worth investigating what dynamic factors were responsible for the ice ages that had occurred in geological history.

With this perspective, Milankovitch began working on climatology in 1912. Since he knew that the literature created in this field until that day was nothing more than a collection of countless data, he, relying on his background as a mathematician, aimed to put climate changes into a regular and sharp mathematical structure. After studying the effect of sunlight on Earth's temperature and publishing several papers on the subject, he focused on the problem of ice ages, aiming to develop a more universal theory related to the movements of planets. After writing his first article on this topic in 1914, he got married, and the First World War intervened.

While Milankovitch was imprisoned in the Austro-Hungarian Empire during the war, he managed to obtain permission to continue his scientific work in the library of the Hungarian Academy of Sciences in Budapest, thanks to the connections of his former professors from the university. During the war, Milankovitch stayed there for four years. During this time, he conducted studies and publications on the climates of the inner planets of the Solar System (Mercury, Venus, Mars). In the five years, including the war years, he published a total of seven articles on mathematical climate studies.

After the war, he returned to Belgrade, the capital of the newly established Yugoslavia, and continued his academic career at Belgrade University. During his time in Budapest, he collected the studies he conducted on "Mathematical Theory of Heat Phenomena Produced by Solar Radiation" in a book published in 1920. In the book, he calculated annual average temperatures for various latitudes using physical relationships, showing a significant agreement with climatic data from past years. Going further, he included calculations of the amount of sunlight received by the Earth for the past 130,000 years for different latitudes.
The book attracted the attention of scientists, and on September 22, 1922, German climatologist Wladimir Köppen sent him a letter, the first sign that his work was recognized. Köppen, along with his son-in-law Alfred Wegener, was working on past climate data. He noticed that Milankovitch's calculated temperature estimates for the past 130,000 years corresponded remarkably well with the geomorphological evidence of glacial periods in the Alpine region. However, to capture the glacial cycles, it was necessary to go back at least 600,000 years.

In his letter, Köppen explicitly offered Milankovitch to collaborate and asked whether his work could extend to 600,000 years ago. After a series of correspondences, they realized that the beginning of glacial periods was directly related to summer temperatures. This was because whether the snow that fell in winter melted or not depended on the average temperature in summer. If the average summer temperatures decreased, the snow layers would not melt, and the Earth's climate would enter an ice age. They agreed to calculate the amount of sunlight received by the upper atmosphere in different latitudes for the past 600,000 years. Using the mathematical structure he developed to calculate the amount of sunlight absorbed for a given date and latitude, Milankovitch worked continuously for 100 days to complete calculations dating back 600,000 years. When he graphed his work, it revealed a significant decrease in the amount of sunlight absorbed during the four known glacial periods in the last 600,000 years, consistent with other scientific evidence.

Milankovitch's curves clearly showed that the amount of sunlight absorbed during the glacial periods, which took place during the Pleistocene period and were known as the Günz, Mindel, Riss, and Würm glaciations, was significantly reduced. This indicated that Milankovitch's calculations were consistent. The 'physical factors' Milankovitch used in his mathematical approach seemed to align with the data obtained from the field of geology. The theory looks successful, but how could Milankovitch calculate the temperature data from 600,000 years ago while sitting in one place? Isn't the 600,000 years the theory reaches out to a little more than the 100 days of mathematical calculations? At the beginning of the article, I mentioned that Milankovitch's mathematical approach to calculating sunlight amounts was based on physical factors. Well, what are these 'physical factors'?

Milankovitch Cycles

The movements of the Earth are not limited to the well-known rotations around its own axis and the Sun, which everyone is familiar with. In addition to these two fundamental motions that create days and seasons, our planet undergoes other movements over periods spanning thousands of years. If you haven't heard about these movements before, there's no need to worry. It's quite normal not to be aware of these movements, as they have periods that span thousands of years and don't directly impact our daily lives. However, if we had been born in the middle of an ice age, shivering in the cold and lamenting the unfortunate timing of our existence on Earth, understanding and acknowledging the Milankovitch cycles might have provided some warmth to our hearts.

The cycles we refer to as Milankovitch cycles are three in total. These cycles were discovered long before Milankovitch through previous evidence and scientific studies. Milankovitch began calling these Earth movements "Milankovitch Cycles" after mathematically demonstrating how these cycles caused ice ages.

Orbital Eccentricity

As you may know, the Earth's orbit around the Sun is elliptical. Ellipticity, unlike circularity, does not possess perfection and is defined with a measure. This measure is called the degree of ellipticity. A degree of ellipticity of 0 corresponds to a circle, and as it approaches 1, it indicates a highly elliptical orbit.

The ellipticity of the Earth's orbit changes with a period of approximately 100,000 years, ranging from low ellipticity (0.005) to high ellipticity (0.058). This change in ellipticity directly affects the Earth's distance from the Sun. The difference in distance between the perihelion (closest position to the Sun) and aphelion (farthest position from the Sun) points, especially, leads to differences in solar radiation reaching Earth and consequently temperature variations. As ellipticity increases, the perihelion point will get even closer to the Sun, and the aphelion point will move farther away. A 3% difference between perihelion and aphelion (which corresponds to approximately 5 million km) means a 6% difference in solar radiation reaching Earth. When the orbit is at its most elliptical, the radiation received at the perihelion point can vary between 20% and 30%, contributing to more significant temperature variations. Currently, the ellipticity is very close to its minimum value.

The primary factor influencing the change in the Earth's ellipticity is the gravitational force of gas giant planets such as Jupiter and Saturn, which have massive gravitational influences. Due to mutual interactions, the orbital inclination (ellipticity) increases and decreases at certain periods. In reality, these effects have a complex structure depending on the relative positions of the planets. In addition to the 100,000-year cycle, orbital inclination has another periodicity occurring approximately every 400,000 years. Therefore, ellipticity does not uniformly increase and decrease in the mentioned range. There is a periodic change, but it is a complex pattern of increase and decrease.

Axial Tilt

We know that the Earth's axis has an inclination of 23.44°, and this inclination is responsible for the formation of seasons. However, it is essential to add the phrase 'in the present day' to this information because the axial tilt of the Earth varies with a period of 41,000 years, ranging from 22.1° to 24.5°. Currently, the inclination is in a decreasing phase and is projected to reach its minimum value around the year 11,800, according to calculations.

The change in axial inclination can be understood simplistically. An increase in axial inclination means that sunlight can reach higher latitudes at steeper angles during summers, leading to an increase in temperature. For winters, the situation is reversed. Sunlight reaches lower latitudes at shallower angles, resulting in a decrease in temperature. A decrease in axial inclination means cooler summers and milder winters. We previously mentioned the importance of summer temperature averages in ice ages. Cooler summers imply less melting of ice, which, in turn, indicates a trend towards overall coldness and potentially an ice age.
Currently, the axial inclination is decreasing. According to this trend, summers are getting cooler, and winters are becoming milder. Looking solely through the lens of this movement, Earth seems to be heading towards an ice age.

Precession

An everyday example of precession can be seen in the wobbling motion of a spinning top. This movement is a direct result of the conservation of angular momentum. Due to the Earth's rotation around its axis and the inclination of the axis, the Earth precesses like a top with a period of approximately 26,000 years. This movement directly influences the positions of the hemispheres at the solstices and equinoxes, leading to seasonal changes.

About 13,000 years from now, your descendants will probably want to take their vacations in months like January or February. This is because, at that time, our southern coasts will be crowded with those who want to enjoy the sun and the sea. July and August will be considered tough winter months. Cultural remnants associating snowy weather with Christmas will have long been forgotten in the northern hemisphere.

Currently, we experience the perihelion around January 3rd and the aphelion around July 4th. The fact that the northern hemisphere experiences winter during the perihelion, the closest point to the Sun, indicates that axial inclination is the dominant factor for seasonal changes. Nevertheless, the northern hemisphere still experiences winter during the perihelion, which increases the average temperature. In the future, approximately 13,000 years from now, assuming that axial inclination and orbital inclination do not change significantly, the northern hemisphere will experience summer during the perihelion and winter during the aphelion. This situation will make summers hotter and winters colder.

Milankovitch, using a mathematical framework that focused on these cycles as physical factors, calculated the amount of sunlight at a given latitude and time proposed by Köppen. Finally, visualizing these cyclic movements on a graph can be helpful.

Milankovitch Cycles' Overall Impact on Earth's Climate

Even when each Milankovitch cycle is considered in isolation, it can independently cause significant changes in Earth's climate. While trying to understand these cycles individually, we assumed that the others did not exist. However, to obtain results close to reality, we must abandon this assumption. Our planet is under the combined influence of these three cyclic movements. Therefore, to calculate the total effect created by the three cycles on the sunlight amount, we need to consider the superposition of their graphs. Milankovitch, following Köppen's suggestion, made calculations for sunlight at 65° north latitude, taking into account the total effect created by these three cycles.

Although Milankovitch cycles were known before Milankovitch, they were not yet correlated with climatic data. Milankovitch's revolutionary success in climatology lies in his ability to create a mathematical structure using his mathematical skills to calculate the total effect on sunlight caused by these three movements. Despite receiving the necessary attention and appreciation from a few respectable names in the field, Milankovitch's work was largely ignored by the scientific community for about 50 years. The reason for this could be the lack of confidence in the evidence of ice ages in the geological history of the Earth by some scientific circles. However, by 1976, a paper titled 'Variations in the Earth’s Orbit: Pacemaker of the Ice Ages' by Nicholas Shackleton and his team presented high-precision findings in deep-sea sediments that matched the periodicity of ice ages with the changes in Milankovitch cycles.

The Future of Ice Ages

Our Earth enters glacial periods periodically based on the amount of sunlight it receives, primarily due to Milankovitch cycles. While Milankovitch cycles may appear to be the dominant character of ice ages for now, human-induced destruction on a global scale has the potential to disrupt all these balances in the future. Analyzing and making predictions about past and future ice ages based solely on Milankovitch cycles, even though scientifically accurate to a large extent, may still contain a certain amount of error.

The last glacial period, known as the Würm, reached its upper limit about 18,000 years ago and completely ended approximately 10,000 years ago. Currently, our Earth is in a general warming phase. However, as in the past, ice ages will occur again in the future. If the Milankovitch theory can provide consistent data corroborated by other scientific fields for the past, it would be wise to pay attention to the predictions it makes about our future. It is essential to note that these predictions are made solely based on Milankovitch cycles. For instance, the warming trend on a global scale due to greenhouse gases released into the atmosphere in recent times is entirely beyond the scope of the theory.

Looking at the graph above and turning our heads from the '0' point symbolizing today towards the findings for future years, we see that there will be no significant decrease in sunlight due to Milankovitch cycles for about 50,000 years. The decrease that will occur approximately 50,000 years from now does not seem to be a herald of an ice age by itself. About 130,000 years from now, another decrease, followed by a significant decrease around 180,000 years later, could mark the beginning of an ice age.

While Milankovitch cycles currently seem to be the dominant character of ice ages, the potential for human-induced disruptions in the future may alter this scenario. Predictions for 200,000 years from now made in an era where more and more mechanisms of destruction and a mentality of nature exploitation emerge every day may be misleading. Nevertheless, according to scientific findings, if humanity, as part of nature rather than its master, understands this truth on a societal scale 180,000 years from now, given that everything else has gone well, we will find ourselves in an ice age. Undoubtedly, the youth of that day will eagerly learn about Milankovitch and his contributions to climatology, appreciating the universality and durability of science.

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