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In discussions with physically educated among the deniers of the greenhouse effect, it is repeatedly claimed that it is completely pointless to state a quantity such as a global average temperature of the earth, since the temperatures of the earth's surface are very variable in time and space. This objection does not seem to me to be completely absurd. Which physical content has actually this global average temperature?

  • Does its value say anything at all about the total energy stored in the atmosphere?

  • Can this value be used to check the radiation balance according to the Stefan-Boltzmann law? Especialy since the averages $\overline{T^4}$ and ${\overline T}^4$ may be different.

I do not want to discuss here whether the measuring procedures for the production of such a value may be sufficient. My question refers only to the conceptual.

I am also already grateful for references to articles, and I apologize in advance to the moderation if there is already a discussion on this that I have overlooked.


REPLY I

Thanks to all also for the references. Yes I was inaccurate myself, it is of course the global surface temperature that I mean.

My question implies, whether it is possible, in principle at least, to calculate the current warming $\overline T(c)$ ab initio starting from the temperature $\overline T(0)$ of an atmosphere without any greenhouse gas $c_{\mathrm{CO}_2,...}=0$ to additional input of carbon dioxide etc.

The common textbook examples always assume very rough simplifications when determining this $\overline T(0)$ in it: no spherical geometry, no rotation or very fast rotation etc. (Maybe I should formulate another separate question thread to this pure calculation problem?)

Regarding the public discussion: would you agree with my formulation that the common climate models consider temperature changes in contrast to absolute values? The relevant value for calculating would then not be this $\overline T(0)$ but rather the climate sensitivity, which can be determined in other ways?

REPLY II

The mean temperature of the earth is therefore only an indicator. Simplified said, if the average temperature increases, then in any case also the total energy content of the atmosphere increases. In this respect this value is reasonable.

My doubts refer to a calculation often reproduced in textbooks. One compares the temperature, which the earth would have without greenhouse gases (on the basis of a calculation with the law of Stefan-Boltzmann) with the "measured" global average temperature of the earth. One obtains a value around -20°C without greenhouse gases and attributes the difference to the "measured" approximate global temperature of +15°C to the greenhouse effect and from this also obtains an estimate of the climate sensitivity of climate gases. However, this simple calculation alone seems physically disputable in several respects.

So thanks for the clarifying addition.

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    $\begingroup$ There is such a quantity. But measuring it takes thought and care. For example, far more heat is stored in the oceans than the atmosphere. Oceans drive atmospheric weather. This questions should be migrated to earthscience, where you are more likely to get a good answer. $\endgroup$
    – mmesser314
    Sep 15, 2023 at 20:50
  • $\begingroup$ Assuming a constant heat capacity, average temperature is a proxy for the internal energy of earth. This is why it is relatively easy to predict using crude models using the Stefan-Boltzmann law and the albedo effect. $\endgroup$
    – LPZ
    Sep 15, 2023 at 22:13
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    $\begingroup$ Restating the supposed claim of deniers with "measurement" instead of "temperature of the earth": it is completely pointless to state [...] average measurement, since the measurements are very variable in time and space. But isn’t that the point of an average? $\endgroup$ Sep 16, 2023 at 11:13
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    $\begingroup$ Being difficult to measure or having different definitions doesn't prevent us from tracking variations of any magnitude and derive useful knowledge from it. My weight varies a lot even in single a day (it's even changing right now while I'm writing, breathing and sweating but not eating or drinking), but that doesn't prevent me from weighting me regularly and learning that I'm becoming fatter, and even predict that if I follow a diet I'll lose some weight. The way magnitudes are measured just needs to be consistent and appropriate for the problem you need to solve. $\endgroup$
    – Pere
    Sep 16, 2023 at 14:07
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    $\begingroup$ Additionally, the problem of defining a magnitude as it appears in simplified models is the same for nearly all real world magnitudes. If somebody believes that (average) temperature of Earth is meaningless as physical magnitude, I would suggest them to go outdoors if they are in a building, because "strength of concrete" (or steel, or wood) is meaningless because those are highly heterogeneous materials, and we can't predict whether the roof will fall on our heads for the same reason that we can't measure that the Earth is warming. $\endgroup$
    – Pere
    Sep 16, 2023 at 14:13

2 Answers 2

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There is no unique way to define a global average temperature of the Earth, but that does not mean that calculation of such a quantity is "pointless". If someone tells me that the average surface temperature of Venus is 475°C, I don't need to know the details of how it is determined or if it varies with time or place to know that I don't want to live there. Similarly, scientific understanding of how the Earth's surface is warming does not depend on a particular definition of the Earth's average surface temperature, but being able to state such a number and how it is changing can be very useful in communicating with policy makers and the public.

A single global average temperature cannot be used to check the radiation balance according to the Stefan-Boltzmann law. Instead, the radiation balance can actually be used for a definition of an average temperature better known as the Earth's effective temperature of 255 K. Similarly, another well-known global average temperature is actually the the temperature of the lower troposphere based on satellite measurements of atmospheric oxygen radiance in the microwave band.

Depending on one's definition, the "global average temperature of the Earth" could range from to 255K to 3000 K, where the latter is the temperature averaged over the entire volume of the Earth.

What I believe you are asking about is actually the Earth's global average surface temperature. When people quote this temperature, it is from a model (e.g. GISTEMP v4) based on many measurements from all over the Earth. "Surface" temperatures are usually nominally the temperature of the air about 2 metres above the Earth's surface. Although different models may not agree precisely, their results are strongly correlated.

None of these single global temperature values can be used to simply determine the total energy stored in the atmosphere since the temperature and pressure vary with location and height, but as @mmesser314 notes in their comment, it is the ocean, not the atmosphere, that stores most (~90%) of the excess heat in the Earth's climate system.


Addition in response to "REPLY" edit

Yes, the important point for currently calculating a global average temperature is not to know its absolute value, but that the changes in that value show in a simple way that the Earth is slowly warming. These changes are not monotonic, but the trend is clear and our best scientific models predict that this warming will continue dangerously unless global humanity modifies its activities. If the fabled frog had monitored the average temperature of the water in its pot and extrapolated the trend, it might have jumped and survived.

Simple models are very often useful in physics, but one must be cautious to avoid over-simplified "spherical cows" when trying to understand complex real-world phenomena. One could calculate a surface temperature for a simple model of an ideal uniform albedo featureless planet with an ideal cloudless greenhouse atmosphere illuminated by an ideal constant star, but such a model would be of very limited use in accurately understanding the Earth's climate system. If a galactic super-civilization actually created such a system as an solar-system sized experiment, all the initial simplifications would soon fail:

  • The surface would heat and then warm the atmosphere, starting convection which causes winds that distribute heat over the planet's surface.

  • If the model atmosphere was based on the Earth's, then water vapour would be one of the major greenhouse gases and this would quickly wreck the "uniform featureless" assumption since it may precipitate out forming heat-absorbing oceans or heat-reflecting ice, or clouds that (depending on their details) may also trap or reflect heat and which dynamically form, move, and disappear.

  • Once there is moving water, it will start to erode the formerly featureless surface creating topography that affect the movements of oceans and atmosphere.

  • Depending on how the planet's interior is constructed, water might trigger plate tectonics, causing more topographic changes and volcanic activity modifying the atmosphere's composition and increasing its variability.

You get the idea. Modelling planets and their climate system is complex and tough.

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A global average surface air temperature is not a physical quantity in and of itself but it does provide a reliable indicator of changes to physical properties of global climate. When scientists began looking for indications of global climate change the existing archives of weather records, including (usually) daily maximums and minimums, were found to be useful and they continue to be a principle data source.

These have been augmented by a variety of direct and indirect measurements, including proxy data going back before temperature records. Some are measuring physical properties, eg measurements of ocean, land and atmosphere heat content, or snow cover or ice mass changes or sea levels, but most do not go back as far as weather station data.

Ocean heat content is a real physical quantity -

Ocean Heat Content

The difference between how much energy reaches Earth and how much is radiated back to space is real physical quantity -

Energy Imbalance

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