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.

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.

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.

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.

There's one other thing, the there is a strong correlation between level of CO2 and global temperature, so greenhouse gases definiely need to be mitigate to avoid having to see what would happen if Earth warmed by 4 degrees Celsius. From the ice ages and almost linear. Anyone not understand? Santosh Gupta

Most climate change forecasts predict sea level rise in the range of 3 feet by the end of the century if greenhouse gas emissions are not stopped, but if we think we are in the Ice age, and sea level rise during an ice age cycle tends to be more like 50 - 100 m for the same range of global temperature increase, it should be the same for abut 5 degrees Celsius of global temperature increase. The warming is a lot faster so its difficult to compare, but so far the global temperature increase has only been about 1.6 degrees resulting in only a feet or so of sea level rise, but it seems it getting dangerously high. What do you think? This is the temperature variation during the ice ages, and as you can see the temperature variation is about 5 degrees Celsius. See sea level rise is usually nonlinear The range of temperatures is not the same, and there is less ice around than during an ice age, but it still suggests something. One reason why the sea level rise may not have been that much in the past century is because the warming was very rapid. SO if I warm up a block of ice rapidly rather than slowly the result might not be noticeable immediately. Santosh Gupta

While these reports on wildfires don't seem alarming and it isn't necessarily tied to climate change, one has to keep in mind that the consequences of climate change can accelerate so it is important to keep track of what events are due to climate change and what not. Santosh Gupta

I find it strange since the projected sea level rise by 2050 is 10 inches, which suggests a linear trend, but if it is nonlinear it should be much higher. Is there a mistake here? Santosh Gupta

According to the UN panel, sea level rise was supposed to be about 6 inches per decade, but it seems a linear trend was suggested. However, if you look at past ice ages sea level rise could have been about 100 m, ofcourse it might be less if only a part of the artic and antartic zones are thawed, but could this be nonlinear? In other words, could sea level rise due to global warming be linear for the first degree or two and then accelerate?

I'm not sure of the solution, but reforestation is considered a major approach to carbon capture, so it's definitely important.

The equations you have on the whiteboard represent large scale changes in climate and climate dynamics. If you want equations more relevant to local changes and meteorology you might like to consider the Navier-Stokes equation based on Newton's Laws which describes the motion of a small fluid parcel in a fluid. A simple example of such an equation is the conservation of mass equation describing the balance between mass and the flow of mass, which you can easily look up (look for conservation of mass equation for navier-stokes equations).