@Sannoso
Clicked just to hear about the Snowball Earth, but I also got a great lesson in the process of modeling. Mathematical modeling always seemed overwhelming but after seeing this example, it makes sense that you would start with the most general properties and then add levels of increasing sophistication.
@jake_gifford
As a water resources economist who builds dynamic network optimization models, I want to thank you for these types of videos. In undergrad, I found your delay differential traffic congestion video and getting to see that modeling process was so insightful. It gave me confidence early on to start modeling systems I had questions about, and helped applied math feel so much more accessible.
@98danielray
Insteas of coupling a system ODEs, it would have been cool to solve the equations for a full PDE and see if there are any relevant differences.
@NevinBR
Once you introduce the latitude bands, then the factor of 4 for surface area is no longer applicable. Bands near the equator have a factor of π, and bands near the poles approach an infinite ratio. At the same time, sunlight striking near the edge of the disk at a glancing angle is far more likely to hit a cloud and reflect away than sunlight striking near the center of the disk.
@bryankrippner7996
Two concepts that perhaps could have been mentioned here: (1) Hysteresis. You described the concept but didn't use the word. (2) Time Lag. There is a LONG time lag between temperatures rising and ice melting, so the feedback effect on temperature is long delayed. It is estimated that if we were to burn every ounce of fossil fuel, including sources we cannot yet access, we would enter ice-free territory, but it would take about 100,000 years for all the ice to melt. This concept, along with the concepts in your video, is not understood by climate changes deniers who keep quoting, correctly but irrelevantly, that "CO2 levels were much higher today in previous ice ages".
@Fikova-db1um
I was solving almost this exact problem last month for a personal project! Super cool to see how we both converged on very similar approaches.
@johnchessant3012
18:17 this graph is really cool
@jessedutton3112
Your model does not include any heat from the nuclear decay of heavy isotopes in the core. This is not an insignificant number.
@purplenanite
oo that's fun - i've wanted to make a climate model for my worldbuilding and this gives me a few ideas!
@arjadre
At 2:39, did you misspeak (quartic vs. quadratic)? Or am I missing something? Anyway, cool video! One of the other commenters mentioned multilayer models... I'd love to see how you'd approach explaining something like radiative-convective equilibrium.
@Gigusx
Very cool! And very scary how the temperature can suddenly drop by a big margin when the conditions change only slightly 👀
@coshy2748
Thank you for presenting an example of mathematical modelling. Good to see you starting with a basic model and then attempt to improve the model.
@parkerbond9400
I would love to see that graph showing the different stable equilibriums for different levels of atmospheric CO2/greenhouse gas levels, especially with more complex atmospheric modeling.
@sonnyRX
Great video! We did some simple modeling of earths climate like this in a climate class I took last year. I was a bit disappointed that you didn't mention n-layer modeling, but for the purpose of the snow ball earth I think it makes sense not to do that. I don't think we actually went and did latitudinal modeling but I do remember it being mentioned in the textbook.
@SiqueScarface
The thawing of Snowball Earth is a very complex process. Volcanoes contribute to CO2, but they also give rise to new minerals, which then are withering and withdrawing the CO2 from the atmosphere again by turning rocks and CO2 into Calcium carbonate. But under Snowball Earth conditions, chemical processes are slowing down, and the ice shield covers new minerals very soon, separating them from atmospheric CO2. Additionally, bacterial life still exists in the ocean and is converting the energy from hot smokers and similar structures into sugar and CO2. This CO2 manages to diffuse through the ice cover and add to the atmospheric CO2. Over million of years, CO2 levels in the atmosphere must have reached up to 13% (350 times of what it is now) to trap enough energy from the Sun to start the melting process. But then, you have that positive feedback loop of a less reflective stripe around the Equator, causing even more Sun light to be trapped, and increasing the speed of thawing. But then, minerals are again exposed to the atmosphere, withering and withdrawing CO2, slowing down the greenhouse effect and the thawing.
@Jochla
Great video! Could you do something similar for other periods in Earth's history, like when the first cyanobacteria emerged?
@kruksog
Really nice application. And I'm not usually into applied stuff. Really nice work Dr. Bazett.
@haldanesghost
Well we’re too far in deep now! We have no choice but to keep adding spice! Next up we incorporate the young Earth’s return to a magma ocean after being whacked by a Mars sized object and thus forming the moon, the dissipative heat from accretion and nuclear decay! They called it the Hadean Earth for a reason! Fourier in 3D spherical coordinates is calling! 🤠
@wjrasmussen666
I can't help but wonder about things like angle of the Sun hitting the Earth, The tilt of the axis, our distance from the Sun, the orbit.
@DrTrefor