Why does climate science assume the Earth is a cold rock when its mantle is so hot?

well this is refreshing given the quality of questions we usually get. I don't know much about climate models so I'll frame this in terms of statistics rather than specifics about the flux of heat through the ocean floor.

Others have stated that these influences are considered, but let's assume that they are not. The total atmospheric forcing combined with all other forcing estimates used in the model will explain a given proportion of the variation in the data, with the unexplained proportion being the result of unknown variables. You can used hierarchical models to get a picture on which variables explain most of the variation and which ones appear to operate together, although this kind of modelling is probably too simplistic to be used in the chaotic systems involved in climate science. However if most of the variation is explained by the modelled parameters, any unknowns are going to have minimal impact on the output data. They do reduce uncertainty further, which is always good if you can factor it in; but the amount that they will reduce uncertainty depends on the accuracy and precision of the new data, and of course sample sizes. So there is a trade off between spending resources on getting more information from something like collecting data from nearby a large number of hydrothermal vents and analysing how this affects water temps and currents on local scales, versus using these resources on other parameters which are known to have very large impacts on the model. If the model already has uncertainty of less than 10% then it is extremely good and adding additional parameters doesn't have much influence. But as I said, I don't know much about climate modelling so I don't know if <10% uncertainty is anywhere near what they get.

I suggest that you review (amongst many other studies) Kathy Crane's work on crustal heat flow, both in continental rock and under the oceans, going back to the late 70's. She's the one who figured out that hydrothermal circulation in the seabed was important, and discovered the first seafloor vents. For most oceanic sediments, heat flow is measured using what is essentially a giant rectal thermometer. Thermistors are attached to the side of coring tubes several meters apart, then the temperature differential is measured. That, with the core sample of the sediment to determine heat conductivity, tells what the heat flow is. We've made these measurements all over the world, so we do indeed know quite a bit about these vital details. Total heat flow is about 50 terawatts, compared to the total solar flux of about 175 petawatts. The upward flux from the crust is about .025% of solar input. The two primary effects of heat from the mantle are modification of water chemistry by dissolution of crustal minerals in hot seawater, and the very slight (in total - hotspots can get to 400C or so) warming of bottom water which aids in deep-ocean mixing. The effects are very important over geological time, but hardly vary at all on century to century scales, amounting to a very minor portion of background noise in climate studies.

It rather bothers me when people say " We just don't know anything about any of these vital details." without bothering to check out what we DO know.

I'll start by stating my answer is a guess.

If the amount of heat radiated by the Earth into the oceans and/or atmosphere was relatively constant, then there would be no signal in the variability of the climate. So for it to have some significant effect on the climate, it would not only have to have significant variability, it would also have to have significant (relative) magnitude.

I wouldn't write it off completely but as far as I know, neither of those two parameters have been detected in the climate signal.

One thing I learned in my geology studies is that rock is a pretty good insulator of heat. Imagine that you have a house that has rock walls a foot thick. I am sure you would agree that it would be pretty cool in the summer and warm in the winter. If that rock wall was a yard thick, it would be even better. Imagine if it were thousands of feet thick. In fact, it is nearly a hundred miles to the mantle. This provides a good insulation. That insulating property of rock has preserved much of the original heat of the earth for the last 4.5 billion years. Volcanoes, particularly the ones at mid ocean ridges are probably one of the most productive ways the earth has to move the heat from the core via the mantle to the surface but it isn't much and it is very consistent.

I have never heard this, but if there is any truth in what you are saying, maybe it is relative to other sources of heat in the solar system or even the galaxy.

The same way you could say that hot water out of the tap is 'so hot' but compared to the heat of a barbecue it is nothing, right?

Climate science does not assume the Earth is a "cold rock," and in fact heat and moisture fluxes from the solid Earth are taken into account in most models.

The primary "law" that you should look at is the heat diffusion equation. Ever wonder why when you go into a cave or mine the temperatures are usually constant? Temperature changes at the Earth's surface diminish in size as you go inward, and they take time to propagate down. It will be thousands of years, at least, before any change in the global mean surface temperature makes it down to the mantle, or any change in temperature of the mantle make it up to the surface. Even then, the effect will be so attenuated that it won't matter.

Things are a bit different in the ocean, though, because the ocean is semi-transparent and it also convects, so temperature changes can be communicated faster.

EDIT: Over time periods of hundreds of thousands or millions of years, geothermal heat flux changes could affect the abyssal ocean circulation. In the short term, though, it is another story. One way to look at is to compare the forcings from different terms. Solar radiation averaged over the Earth's surface is a more than 300 watts per square meter; anthropogenic forcing from greenhouse gas changes is between 1 and 2 watts per square meter; geothermal heat flux is about 0.1 watts per square meter. But it's actually a much smaller effect than that, because of thermal diffusion times in the crust we don't get large changes in the heat flux on decadal time scales (it's not just the magnitude that's important, it's the magnitude of the VARIATION). The anthropogenic effects are certainly hundreds of times bigger.

"Well, lets assume the ocean is warmed somewhat by the mantle heat." - You can assume all that you want, but we have direct temperature data from the deepest points of the oceans. It is cold down there, matey. Very cold. Even temperature data taken a few feet from a "black smoker" vent will be cold. There is animal life all along these thermal vents, yet they do not cook. Now take surface temperatures and see what the temperature readings are. What do you assume now?

Jim M

The Earth's core is very hot indeed, but there is too much insulation between the liquid core and the ocean floor. Water requires more heat energy to warm it as opposed to the volume of land or air. Even the near continuous lava flows in Hawaii do not warm the air around them much beyond its immediate area.

CO2 isn't "nutrition for plant life." Did you flunk uncomplicated technology? DO you think of oxygen is nutrition? certainly, we've much less plant life each year, it is not an open ended gadget the place plant life magically seem to eat obtainable carbon. it is not nutrition. the barriers for flowers isn't not adequate CO2. Deforestation enhance each year. each year greater good soil flows into the sea and much less continues to be to enhance plant life.

Earth does generate its own heat from decaying radioactive materials in its interior, but that heat is very small compared with what it gets from the Sun.

You are not up to date on climate science. All this information is included in climate models.