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Temperature, heat, radiation and energy are essential concepts for understanding weather and climate. When you listen to the daily weather forecast or discuss the climate with a stranger, are you sure you know what the temperature is? #temperature #stratosphere #troposphere
In fact, based on my teaching experience in the 1980s, it would take undergraduates several weeks to understand temperature and related ideas in physics.
By definition, the temperature of an object is proportional to the statistical average value of the kinetic energy of randomly moving particles, such as a nitrogen or oxygen molecule in air, at thermal equilibrium. In this 1972 American version of the standard atmosphere, it was loosely called "kinetic temperature".
For gases, such a kinetic temperature can be determined from this simple equation, namely that the average kinetic energy of a molecule is equal to the product of its degree of freedom, f, and half kT, where k is Boltzmann's constant. For a point mass, the degree of freedom is 3.

If we treat near-surface air as an ideal gas, composed of many point particles, then we can calculate the air temperature from the measured atmospheric pressure and the average density of the air, which is very precise and independent of any radiation. By the way, this temperature is about the same as our subjective sensations, such as hot, hot and cold. Why did I say “rude”? Because humans are far from being a simple thermometer.

Speaking of thermometer, I would mention a temperature sensor commonly used by experimental physicists, which is based on an electrical resistance that depends on temperature, like this simple thermal couple. The electric potential difference can be easily measured and converted to temperature in K, using a suitable empirical formula.

In fact, such electrical resistance thermometers have been widely used to measure atmospheric temperature distribution in the atmosphere, as shown in this American Standard Atmospheric Paper.

However, the reading from this type of thermometer becomes unreliable when the air density drops too low to allow frequent molecular collisions, essential for obtaining an average kinetic energy, I mean the population average value, statistically speaking.

Take for example Figure 25 in the American standard atmosphere: the range of systematic variability of atmospheric temperature increases with altitude. This is why stratospheric cooling and warming have been reported from time to time. For Manabe and his supporters, it is a never-ending nightmare, because their theory of global warming relies solely on stratospheric cooling.

You might ask yourself, why don't we use an infrared thermometer, like this one, instead? Good question. In fact, many instrumental observations have been based on the detection of radiation to determine atmospheric temperature distributions, remotely, either on the ground or from satellites.

In this diagram you can see a complete vertical profile of temperature in the atmosphere, from sea level to over 500 km, which is actually space, or the top of the atmosphere. As you can see, the atmospheric temperature can exceed 1000 K in the thermosphere. How come?

Well, to understand why the temperature at TOA seems so high, you need to familiarize yourself with another type of temperature used in physics, called luminosity temperature, or emission temperature, or some people call it "radiation temperature." from a source of radiation. .
Brightness temperature is defined in terms of radiation or electromagnetic wave intensity, based on the Stefan-Boltzmann law. In other words, the brightness temperature is not associated with molecular kinetic energy, but with a phenomenological descriptor of the radiation strength that can be observed there.
To be more precise, we must imagine that the measured radiation is generated by an invisible black body whose surface equilibrium temperature is determined by the intensity of the radiation in W per square meter. If you want to attribute the radiation to a gray body, such as a thin layer in the atmosphere, then the brightness temperature would be higher. For what?
For example, the theoretical overall mean OLR value should be close to 239 Wm-2. If you consider the planet with the atmosphere as a black body, then the luminosity temperature, or emission temperature, would be close to 255K, which happens to be the kinetic temperature of the atmosphere at an altitude of 5 km at above sea level, called "transmission altitude" by many. .

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