The Math Behind Climate Models (in 4 levels of complexity)

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0:00 The Snowball Earth Hypothesis
0:57 Level 1 - Energy Balance Model
3:22 Level 2 - Adding a one layer atmosphere
8:01 Level 3 - Variable Albedo effects
13:21 Level 4 -One Dimensional Model with latitude bands

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[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.

[danielray]

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Once you introduce the latitude bands, then the factor of 4 for surface area is no longer applicable.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.

[mbizmakduplesis]

The more complex this gets, the more it makes sense how these factors play a role and how imperative each of them is to the model.

Also, the way you've presented this is top tier.

[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 👀

[jessedutton]

Your model does not include any heat from the nuclear decay of heavy isotopes in the core. This is not an insignificant number.

[Fikova-dbum]

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.

[bryankrippner]

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".

[coshy]

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.

[parkerbond]

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.

[kruksog]

Really nice application. And I'm not usually into applied stuff. Really nice work Dr. Bazett.

[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.

[blueberry]

Thanks for the video! I recently started working on tipping points, and this video gives the perfect example for that!

[wjrasmussen]

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.

[Petch]

I love mathematical models. 🥰
And this was a fun one that I have not seen before. Thanks for charring it.

This is exactly why I follow this channel. 🤓

[TomFarrell-pz]

Really enjoy applied math, so I hope you do more like this!

[averythau]

Cool video but changes in Milankovich cycles also play a key role in starting and ending ice ages not just changes in CO2 concentrations