It seems the level of sea level rise must be nonlinear and we'd be expected sea level rise more in the range of 50 m rather than 2 feet

[thidmir]

On 2/17/2024 at 2:42 PM, J.C.MacSwell said:

Thanks. Hopefully thidmir will clarify and expand on the purpose of that post.

Sorry I kind of messed up showing the plot, what I meant to show was that there is a strong correlation between CO2 and temperature, so that definitely should be a cause for concern given that a lot of Conservatives have been arguing it may not be worth the cost to deal with climate change. Clearly it is worth a lot, because increasing temperatures by a few more degrees would be very risky, and likely would reflect what happened in the ice ages (sea level rise on the order of 50 - 100 meters given 4 degrees Celsius of temperature increases versus a few inches). My suspicion is that the relatively small amount of sea level rise in the past century was random, and something like this happened also at the beginning of the present ice age 20000 years ago (quadratic sea level rise as shown in the first post, and actually I have reasons to thin that it should actually be cubic) so I wouldn't be too surprised if that's what happened recently. The temperature increase and CO2 increase in the past two centuries since the beginning of the Industrial Revolution  is nonlinear and quadratic, probably due to mass production of fossil burning technologies (in contrast in the ice age the rate of CO2 increase and temperature increase is linear, leading to quadratic increase in sea level). I'm actually publishing a popular science book called Climate Science and Engineering soon with these findings as well as other things. 

Edited February 27 by thidmir

[exchemist]

7 minutes ago, thidmir said:

Sorry I kind of messed up showing the plot, what I meant to show was that there is a strong correlation between CO2 and temperature, so that definitely should be a cause for concern given that a lot of Conservatives have been arguing it may not be worth the cost to deal with climate change. Clearly it is worth a lot, because increasing temperatures by a few more degrees would be very risky, and likely would reflect what happened in the ice ages (sea level rise on the order of 50 - 100 meters given 4 degrees Celsius of temperature increases versus a few inches). My suspicion is that the relatively small amount of sea level rise in the past century was random, and something like this happened also at the beginning of the present ice age 20000 years ago (quadratic sea level rise as shown in the first post, and actually I have reasons to thin that it should actually be cubic) so I wouldn't be too surprised if that's what happened recently. The temperature increase and CO2 increase in the past two centuries since the beginning of the Industrial Revolution  is nonlinear and quadratic, probably due to mass production of fossil burning technologies (in contrast in the ice age the rate of CO2 increase and temperature increase is linear, leading to quadratic increase in sea level). I'm actually publishing a popular science book called Climate Science and Engineering soon with these findings as well as other things. 

I would imagine one difficulty relating the present warming to previous interglacials is the rate of CO2 increase and consequent warming has no parallel in the past. We will be farther from equilibrium as regards melting of ice, isostatic rebound etc. than past warming processes. So any effects that take time to manifest themselves can be expected to lag the warming that causes them.

[thidmir]

23 hours ago, exchemist said:

I would imagine one difficulty relating the present warming to previous interglacials is the rate of CO2 increase and consequent warming has no parallel in the past. We will be farther from equilibrium as regards melting of ice, isostatic rebound etc. than past warming processes. So any effects that take time to manifest themselves can be expected to lag the warming that causes them.

That's a good point, , but it seems it would not be consistent with Newton's Law of Cooling and how rate of ice mass melting is proportional to the heat absorbed. I think then the rate of sea level rise should be proportional to the temperature increase. According to Newton's Law of cooling the rate of heat loss is proportional to the difference in temperature between a system and its environment (eg. between ocean and air temperatures and ice mass), and ofcourse the latent heat law says that the latent heat of the ice mass is porportional to the heat transferred, so the rate at which temperature of the ice mass increases is proportional to the difference between temperature of the ice mass and its environment. So if global temperatures are increasing at a quadratic pace, the result for temperature rate of increase of the ice mass should be a cubic, and there should be no rebound. But I'm not sure if Newton's Law of cooling applies in the case where temperature is increasing so rapidly over the course of a century or two. Sort of like applying it to the case of an ice cube melting on a stovetop when the stove is turn to maximum in the course of  20 seconds versus an hour or something like that. 

[TheVat]

Nonlinear.  Melting ice is a phase transition.  

Newton's law of cooling does not apply here since the ice is mostly at a constant temperature.
 

[iNow]

Cows aren’t spherical 

[TheVat]

2 minutes ago, iNow said:

Cows aren’t spherical 

They are if you feed them legumes.  

[iNow]

Har. I’ll go at this another way then:

 

Climate systems can paradoxically become confusing when you oversimplify them. 

[swansont]

On 2/27/2024 at 1:25 PM, thidmir said:

what I meant to show was that there is a strong correlation between CO2 and temperature, so that definitely should be a cause for concern given that a lot of Conservatives have been arguing it may not be worth the cost to deal with climate change.

That’s a political issue, though, and this is in the science section. The basics of global warming are established science. We can start with that as a baseline for discussion.

[thidmir]

7 hours ago, TheVat said:

Nonlinear.  Melting ice is a phase transition.  

Newton's law of cooling does not apply here since the ice is mostly at a constant temperature.
 

Ok you're right newton's law of cooling doesn't apply here, so this is a bit complicated but maybe not too complicated I'm going to try to think about this and what the sea level rise should be. 

11 minutes ago, thidmir said:

Ok you're right newton's law of cooling doesn't apply here, so this is a bit complicated but maybe not too complicated I'm going to try to think about this and what the sea level rise should be. 

Then again, actually I think it would apply to the heat transferred from the ocean and air since they are not undergoing a phase change, it's the ice undergoing the phase change. I need to think about this. 

[thidmir]

Yeah it looks like it should be roughly cubic, because newton's law of cooling says that the rate of heat transfer from a fluid to another substance is proportional to the temperature difference between the fluid and the substance. This should be indepedent of the rate of temperature increase. The system involving ocean, atmosphere, and ice mass may be a little complex but this is also what is observed in the ice age cycles, and I know someone came up with a semi-empirical relationship agreeing with this (Newton's law of cooling is a more "microscopic" law for simple systems, but it agrees with this more macroscopic semi-empirical relationship somehow describing a complex system). The name of the author is Rahmstorf 

S Rahmstorf, A semiempirical approach to projecting future sea-level rise. Science 315, 368–370 (2007).

Rahmstorf found empirically a correlation consistent with this relation between rate of heat transfer and temperature, and since heat transfer is linearly proportional to mass of ice melted (latent heat law) and hence proportional to sea level rise, that means rate of sea level rise is proportional to the temperature difference between ocean and ice mass. 

[sethoflagos]

On 3/28/2024 at 10:39 PM, thidmir said:

Yeah it looks like it should be roughly cubic, because newton's law of cooling says that the rate of heat transfer from a fluid to another substance is proportional to the temperature...

The temperature difference between two adjacent regions aotbe typically decays per a lag function (1 - exp(-t / T_n)) where t is elapsed time and T_n is a characteristic time constant.

Series of multiple connected regions (like Earth's surface) therefore tend towards the product of multiple lags as they move towards a new equilibrium.

A second order lag produces a smooth 'S' shaped function between initial and final states. Higher order lags produce more of an initial delay followed by a more abrupt transition. 

The principal pattern falls straight out of Fourier's Law. I think you might find it a little more useful than a polynomial fit.