By Andy May
In my last post, “Defining Temperature,” we saw that temperature is a simple measurement that has little meaning without context. If one is referring to the equilibrium system state variable or “thermodynamic equilibrium temperature,” they should state that to provide clarity because there are many types of temperature measurements and they mean different things. Thermodynamic equilibrium temperature is defined in the previous post. There are many definitions of temperature, I will discuss the most common ones used in physics and everyday life in this post and perhaps in subsequent posts. The fundamental meaning of thermodynamic equilibrium temperature and the temperature measured with a thermometer are very different and they should not be confused.
Measuring Kinetic Temperature
Whereas the thermodynamic temperature state variable of a system in equilibrium is proportional to the total internal energy of the system, kinetic temperature is the temperature proportional to the average translational kinetic energy in the system. It can be measured using thermal expansion (liquid in glass thermometers), electrical resistance (thermistors, etc.), or infrared emissions (pyrometers). Normal thermometers respond to total internal energy, not just translational kinetic energy. They correlate with kinetic temperature in gases, but in solids and liquids they respond to vibrational energy, which is not purely kinetic. Common thermometers do not measure translational kinetic energy directly (except in gases); they measure a bulk property that correlates with it under certain conditions (Reif, 2009).
Kinetic temperature in gases
Kinetic temperature can be measured in gases, liquids, and solids. However, in liquids and solids, the relationship between kinetic energy and temperature becomes more complicated because molecular motion is constrained by bonds and intermolecular forces. In gases the direct connection between kinetic energy and temperature is cleaner, so we will start there.
The ideal gas law: [Eq. 1] PV = N·kB·T
In the ideal gas law, P is pressure, V is volume, N is the number of molecules in the volume considered, kB is Boltzmann’s constant, and T is temperature. Now, divide both sides by volume (V) and we get:
The kinetic theory version of the ideal gas law: [Eq. 2] P = n·kB·T
Now “n” is the number density, or the number of molecules per unit volume. Writing the ideal gas law as in Eq. 2 shows that pressure depends only on number density (n) and kinetic temperature. This relation holds for gases in local thermodynamic equilibrium. In non-equilibrium gases, temperature must instead be inferred from the particle velocity distribution, not from pressure.
In solids, vibrational modes dominate. In most solids, atoms sit in a repeating lattice and behave like they are connected by tiny springs. When they vibrate collectively, they create waves that travel through the material. The movement increases when the solid warms. In quantum mechanics, these vibrational waves come in discrete packets of energy called a phonon. A phonon is a quantized unit of sound-like mechanical energy in a solid.
In both solids and liquids, the kinetic part of thermal energy is often less than half the total thermal energy. Most of the energy is stored in intermolecular potential wells. Intermolecular wells are an energy valley created by attractive forces between molecules. The valley gets deeper or shallower depending upon the energy added to the system. The molecules of liquids and solids are trapped in these wells. Most thermal energy is stored as vibrational potential energy, not just kinetic energy. The temperature of the solid or liquid reflects how vigorously molecules oscillate inside the well. This is why the simple “temperature – average kinetic energy” idea works well for gases but fails for condensed phases.
The depth of the intermolecular potential well determines the boiling point and the melting point of the substance. It also defines the surface tension and viscosity of the material. This concept is not theoretical; it explains everyday physical properties.
So, if you tried to define temperature purely from kinetic energy in condensed phases, sometimes you’d get the wrong value. Temperature is proportional to average kinetic energy only for ideal gases. In even more complicated situations, like plasmas or in astrophysics, kinetic temperature is inferred from Doppler broadening of spectral lines and time-of-flight measurements.
Doppler Broadening
Atoms moving toward you emit light that is Doppler‑shifted slightly higher in frequency. Atoms moving away emit light slightly lower in frequency.
Here we need to define the Maxwell–Boltzmann velocity distribution (“Maxwellian distribution”). It gives the probability that a gas molecule has a particular speed. At any temperature, some molecules move slowly, some extremely fast, and most cluster around a characteristic speed. The distribution’s shape depends only on temperature and molecular mass. Thus, if the mass is known, the temperature can be determined from the distribution but only if the atoms or molecules have this characteristic Maxwellian distribution. Maxwellian distributions are shown in figure 1 for -100°C, 20°C and 600°C.
If the atoms have a Maxwellian distribution, they are likely in local thermodynamic equilibrium or “LTE”, but this is not guaranteed. If a gas is in LTE, collisions enforce a Maxwellian distribution. The line‑of‑sight component of that distribution is Gaussian, even though the full 3‑D distribution is not. Because Doppler shifts depend linearly on velocity, the resulting spectral line profile is also Gaussian. This is the origin of thermal Doppler broadening. The width of the Gaussian is proportional to kinetic temperature, and in anisotropic systems the width depends on viewing angle, allowing direction‑dependent temperatures to be measured.
Time-of-flight
Time-of-flight is kinetic temperature in its purest form. Let the particles fly freely and see how long they take to get to the detector. Faster ones arrive first. The spread in arrival times tells the spread in velocities. The spread in velocities tells you the temperature.
Time-of-flight measurements measure the time it takes for molecules escaping from a plasma, a small aperture in a gas container, or desorbed from a surface, to reach a detector. Molecules or particles arrive at different times and form a distribution which can be converted into a time-of-flight velocity spectrum. Fit this velocity distribution to a Maxwellian distribution and the kinetic temperature can be computed. Time-of-flight gives the full velocity distribution, not just an average. In anisotropic systems, it can measure the various temperatures in all directions. It is also effective at determining species specific temperatures, for example electron, ion, and neutral temperatures in plasmas and gases.
Discussion
Almost daily we discuss the outdoor and indoor temperature, and our body temperature. All are intended to be kinetic temperatures as discussed in this post and all can have problems, especially if they assume LTE. The indoor temperature is not in LTE most of the time since most houses are either heated or air conditioned. The outdoor temperature certainly isn’t, since it varies locally depending upon the location and which side of the Stevenson screen the Sun is on and which way the wind is blowing. Our body temperature is usually taken by placing a thermometer in our mouth, where the saliva and the flesh have different temperatures. The examples are endless.
The kinetic temperature of a system is convenient since there are many, relatively easy, ways of determining it and full system equilibrium is not required. Unfortunately, as a measure of temperature, it does not always work (Bormashenko, 2020). The thermodynamic equilibrium temperature as defined in the previous post, is not related to the average kinetic motion of the particles in the system. Thus, the very common kinetic temperature is unrelated in concept and meaning to the thermodynamic definition (Bormashenko, 2020).
What is temperature?
As Bormashenko admits in his essay on “What is Temperature?” in Entropy:
“The operational definition of temperature is shaped as follows: Temperature is what we measure with a thermometer.” (Schroeder, 2000)
This is an acceptable and quite logical everyday definition; it certainly defines how the word “temperature” is normally used. Common thermometers respond to bulk properties (expansion, resistance, radiation) that correlate with internal energy. In gases this correlates directly with translational kinetic energy, but in solids and liquids the signal comes primarily from vibrational energy. I recommend that in technical writing the author should be more specific and say “kinetic temperature” if that is what he or she means.
Bormashenko goes on to show that the kinetic temperature is a very narrow definition of temperature, and it does not always work. This is true and I list some problems with it in this post. However, this does not mean that the “thermodynamic equilibrium temperature” definition discussed in my previous post is an appropriate definition of “temperature” or that the two are somehow synonymous. They are not, and to do so is disingenuous, since the reader will assume the kinetic temperature, aka the thermometer temperature.
In the twitter (or X) discussion referred to in my previous post (see the link at the bottom of this post) many commentors wanted to change the common definition of “temperature” to mean the very uncommon thermodynamic equilibrium temperature, but that is nonsense. That temperature can only be used in a laboratory where it is possible to accurately determine the internal energy and entropy of a system that must be in equilibrium. This is clearly not the thermometer temperature, and it is an awkward definition to use. No one would know what you are talking about, the thermodynamic temperature means something completely different to the everyday definition.
Future
The requirement for thermodynamic equilibrium temperature discussed in my previous post is lessened for the kinetic temperature which does not require equilibrium, although we often assume LTE when using thermometers. To eliminate the equilibrium requirement completely we need to recognize that the particle velocity distribution may not be Maxwellian and the system may not be isotropic. It is also possible for different system components to have different temperatures, for example a porous rock can have a different temperature than the fluid flowing through it. In some systems, the pressure may not be isotropic. In these circumstances you often cannot use the kinetic equation described above and you certainly cannot use the thermodynamic equilibrium temperature. Non-equilibrium temperature will be discussed in the next post.
Some additional non-equilibrium temperature references are cited and discussed here.
The original X thread that started all this can be seen here.
Works Cited
Bormashenko, E. (2020). What Is Temperature? Modern Outlook on the Concept of Temperature. Entropy, 22(12). https://doi.org/10.3390/e22121366
Reif, F. (2009). Fundamentals of Statistical and Thermal Physics. Waveland Press, Inc.
Schroeder, D. V. (2000). Thermal Physics. San Francisco: Addison Wesley Longman.
Handwavium obfuscation.
From the article it is clear that temperatures in different local thermodynamic equilibria cannot be averaged.
It is also clear that one cannot establish a global temperature merely by averaging averages.
Tru dat!
What’s also risible is those weather apps that offer a temp forecast accompanied by a “FEELS LIKE” advisory number.
I’m always tempted to ask them –
“Is that with or without clothes & hats on? If with clothes, what materials? If not with clothes, please accompany your advisory with a pic of a saucy female model demonstrating her reaction to the “feels like temp forecast”
On the other hand, the target audience is ordinary people going about their ordinary business in their usual attire and are indeed very interested because they are experiencing the environmental conditions subjectively – comfortable, too cold, too hot, sticky from perspiration etc.
Neither reporter or audience is trying to save the world, just to decide on the appropriate attire, optimal comfort and socially demanded uniform taking into consideration the weather.
There is an ASHRAE std that covers this
Not correct
So by the same token, we could strike a number for the “average” number of grapes per bunch in vineyards all around the world?
You Couldn’t calculate it if you had the data?
It’s not that it couldn’t be calculated. It’s that it would be meaningless.
You nailed it! The big issue is that though you can average extensive properties, they need to be weighted in some cases to account for external influences, e.g. soil conditions, diurnal range, etc.
That also means that the average wouldn’t mean anything unless you know your local external influences and how they were weighted for the average.
Being able to perform a math operation doesn’t mean the result has any physical meaning.
The average human has one boob and one ball.
In gases the direct connection between kinetic energy and temperature is cleaner, so we will start there.
The ideal gas law: [Eq. 1] PV = N·kB·T
_________________________________________________________________________________________________________
Uh Huh, So why did Sir John Houghton choose to calculate his Global Warming Potential numbers for greenhouse gas based on mass?
I think you are pointing out that temperature is based on molecular activity and the IPCC (and Houghton) chose to use a mass-based GWP (global warming potential) policy metric. Temperature is a per-molecule property, but GWP is mass based, and assumes an unproven connection between CO2 and temperature. Not logical.
Ants can lift between 10 and 50 times their own body weight. An Olympic
weightlifter can lift about 2 to 3 times his own body weight*. So an ant is
~40+ times stronger than an Olympian and you should consider using one
to move your grand piano. (*source: google AI)
If you look at the absorption spectrum of greenhouse gases, methane is
clearly not 82.5 times more powerful at “trapping heat” than CO2
Without regard to feedbacks, doubling CO2 will get ~1.2°C and CH4 ~0.3°C
of global warming which makes CO2 four times stronger at trapping heat than
methane.
Thanks for your reply
I do not believe anybody in the IPCC ever gave a rat’s arse about the precise definitions – the entire aim was one of pushing a point of view through directed propaganda.
I suspect you are correct.
It’s well proven. In 1896
Carbonic acid? 😉
To quote your response above, “not correct.”
CO2 has a mole weight of 44 while Houghton was quite concerned about the IR absorption of high molecular weight gases such as the chloro-fluorocarbons with MW in the hundreds and thousands. Houghton was fearful of the effects of global warming caused by big man-made gaseous molecules in the atmosphere, which humanity was copiously producing industrially. He felt that comparing the heat absorption effect of a tonne addition of any one of these chemicals to the atmosphere compared to adding one tonne of CO2 to the atmosphere…was a number that could be relatively easily calculable by lay-people…who mostly only knew how many tonnes of Air conditioning gas, dry-cleaning fluid, or foaming agents they had bought. Also, the method had his desired effect of amplifying the “number”, which was named “Global Warming Potential”, for low concentrations of high IR absorbing chemicals. Depending on your viewpoint, his methodology is either conniving or brilliant…
Mean kinetic temperature is a simplified way of expressing the overall effect of temperature fluctuations during storage or transit of perishable goods. The MKT is widely used in the pharmaceutical industry. [Wikipedia]
Temperature reflects the average energy across all available molecular degrees of freedom, which can include rotation and vibration in complex molecules, not just linear translation.
As I recall from introductory physics, we were taught the kinetic temperature definition with no reference to any other way of doing it.
The controversial concept of a global average temperature has now become much more controversial.
I Agree.
or far more clearly as being an absurd idea with no grounding in utility or reality.
How so?
For the simple reason that temperature is an intensive property (an intensity) independent of the quantity of matter, and therefore averaging it is a physical absurdity.
Temperatures of individual stations are first converted to temperature anomalies (changes from the reference value); then the Raw numbers are not just averaged; scientists weight grid cells or station locations to prevent overrepresented areas (like dense city networks) from skewing results.
the result is not a precise measurement of global avg temperature, but rather an average anomaly or an average temperature rise.
Which bakes in UHI growth. Dense city networks occur when cities grow from the time of the reference period. More people, more concrete, more air conditioning, etc.
the effect of the uhi has been examined many times. It’s quite small, and doesn’t change the overall upward trend
Anomalies don’t help.
1.The variance of the base temperatures are different for cold seasons, warm seasons, and hot seasons. The anomalies inherit the same variances. Spatial weighting won’t fix this. Without weighting for this issue, the “average” won’t fix this.
2.If climate science uses (Tmax+Tmin)/2 as their base data they are using a RANGE-dependent value, not a statistical average. The data then takes on the variance of the diurnal range and so does any anomaly. Since the diurnal range has several factors, e.g. latitude, these must also be weighted appropriately or the base data and the anomalies become useless.
The excuse “but anomalies fix all problems” is just plain climate science garbage. It derives from the climate science meme that “numbers is just numbers” and no physical meaning has to be assigned to them. If “numbers is just numbers” then *anything* can be “averaged”.
1) you assume that the goal is a statistically valid average global temperature over time. It isn’t.
2) the purpose is to yield a temperature rise from one year to the next. Seasonal variations are immaterial.
3) Same with diurnal variation.
the result is that anomalies track temp rise from one period in time to a different point in time. The variations you worry about are immaterial. All we care about is temp rise , not absolute temperature.
If you wish to obtain a “global anomaly”, you should use a common global temperature, i.e., 15°C. Averaging local anomalies from all the globe is joke.
Anomalies are tracked, not absolute temperature. it’s the way it’s done. Sorry you don’t understand.
Anomalies inherit the variances of the parent variables. Those parent variables have variances that are significantly different – trying to average them is a waste of time unless they are weighted to equalize the variances. E.g. coastal temperatures have vastly different variances than inland temperatures. Colder temperatures have different variances than warmer temperatures.
Throwing the anomalies in a common pot along with their significantly variances, hoping to be able to track changes is a fool’s errand – which is common in climate science.
In addition, the parent temperatures are *NOT* averages, they are mid-range temperatures that are based on diurnal ranges and not on an average of the actual temperature profile. Different diurnal ranges can give the same mid-range temperature – meaning identifying changes is impossible. In addition, the diurnal range is latitude dependent, meaning the mid-range temperatures, AND THEIR ANOMLIES, should be weighted by latitude before calculating a “global average”.
Spatial weighting won’t fix these issues. And that seems to be all climate science ever does, spatial weighting.
You need to understand before saying other need to.
Back to school, Gorman:
Temperature anomalies reduce error in climate data by measuring a local change or departure from a long-term average rather than an absolute temperature. This method cancels out large spatial variations, geographic biases, and missing station data, making regional and global comparisons far more accurate. Global trends rely on these localized deviations because absolute values fluctuate wildly over short distances. NOAA National Centers for Environmental Information (NCEI) (.gov)
Why Absolute Temperatures Fail
How Anomalies Fix the Problem
“Temperature anomalies reduce error in climate data by measuring a local change or departure from a long-term average rather than an absolute temperature”
Nope. This just shows the typical lack of knowledge of climate science when it comes to metrology.
That long term average will have measurment uncertainty. The local absolute temperature will have measurement uncertainty.
Subtracting the two values CAUSES THE MEASUREMENT UNCERTAINTIES TO ADD!
The measurement uncertainty of the anomalies is LARGER than the measurement uncertainty of the parent data.
Another load of garbage from climate science.
These variances DO NOT CANCEL. Therefore the weighting for the anomalies *should* be exactly the same as for the absolute temperatures.
Hubbard and Lin found clear back in 2002 that you cannot even use regional adjustment factors as a calibration crutch across multiple measurement station because of microclimate differences. Each station requires its own adjustment factor based on a calibration against a known standard and only applies to future measurements, not to past measurements.
But that change for one station will have a different variance than for another stations. You can’t just simply add the two in order to create an average change.
More climate science garbage. The issue isn’t “error”, the issue is measurement uncertainty. Climate science assumes all measurement uncertainty is random, Gaussian, and cancels leaving only the sampling uncertainty for the mean value. And that sampling uncertainty can be made arbitrarily small by increasing the sample size.
IT IS GARBAGE. The measurement uncertainty does *NOT* cancel, in fact it grows with each uncertain measurement added into the data set!
“A 2 °C anomaly means the same warming impact whether it happens in a hot desert or a cold polar region.”
More climate science garbage! A 2 °C anomaly in Miami has a big difference over the same change in Phoenix because of the difference in enthalpy at the two locations. Because of the higher humidities in Miami a 2 °C change in temperature requires far more heat energy input than the same change in Phoenix.
Since the humidity in a hot desert is likely to be low because of the lack of water vapor it will be very similar to the humidity in a polar region due to a lack of water vapor due to freezing. So the comparison provided is between similar regions.
This just doesn’t apply globally. It’s a garbage assumption!
Climate science is so full of these garbage assumptions that it is literally incredible that scientists profering these assumptions are not drummed out of science!
You continue to miss the point, Gorman.
Using temperature anomalies (differences from a standard baseline) rather than absolute temperatures does not reduce physical measurement errors, but it minimizes the impact of geographic and systemic variations when calculating long-term climate trends.
Why Climate Scientists Use Anomalies
NO, it doesn’t. And I have explained twice why it doesn’t. This is a garbage assumption by climate science.
For the third time, coastal temperatures will produce anomalies with a different variance than inland temperatures will produce.
You simply cannot say that this impact somehow disappears by using anomalies so you can just do a straight average on the anomalies. It’s garbage.
The exact same thing applies to two stations where one is in a river valley and the other is on the surrounding plateau. The variances of the absolute temperatures are inherited by the anomalies meaning a WEIGHTED average should be used to equalize them.
But climate science doesn’t do this. It’s too hard. So they just assume it away. Just like they do with ALL measurement uncertainty.
NO, it does *NOT*. Again, cold temperatures have a different variance than warmer temperatures. You cannot assume the deviations from the local average will be comparable.
This is just assuming the variances out of existence just like assuming measurement uncertainty doesn’t exist!
Again, climate science is so full of these garbage assumptions that no self-respecting scientist I know would want to be associated with the entire discipline!
The final lesson:
Mean temperature
The mean daily temperature can be determined in multiple ways. Nowadays, it is easy to measure the temperature frequently, store it in a digital memory and compute the daily average. Also in the past something similar was possible using a thermograph. However, such an instrument was expensive and fragile.
Thus normally other ways were used for standard measurements, using minimum and maximum thermometers and by computing a weighted average over observations at 3 or 4 fixed times. Another good approximation for many climate regions is to average over the minimum and maximum temperature. Special minimum and maximum thermometers were invented in 1782 for this task.
Not in every climate region the minimum and maximum temperature are well suited. For example in Iceland, the diurnal temperature range is small compared to the natural day to day (synoptic) variability. In such a case, fixed hour measurements are preferred. Fixed hour measurements are also performed for meteorological purposes. Four times a day, meteorologists all over the world make measurements, at the same time: 0, 6, 12 and 18 hour universal time (UTC).
Measuring four times a day is no fun, you have to get up at night, every night. Thus often the so-called Mannheimer hours (German Wikipedia) are used: 7, 14 and 21 hour local time; to compute the daily mean temperature, the measurement at 21 hours get a double weight.
In general, minimum and maximum temperature measurements are performed at voluntary climatological stations, whereas professional meteorological stations also perform fixed hour observations. Nowadays more and more stations are converted in automatic weather stations to save labour costs, which is an important change in the statistical properties of daily temperature records.
Time of observation bias
Naturally you can get a time of observation bias with the fixed hour measurements and changing these hours could thus produce a jump in a climatic temperature record. How large this jump would be could be determined by performing hourly measurements.
Mostly, the term time of observation bias (TOB), however, refers to minimum and maximum temperature measurements. At first glance, one might not expect any problem here. However, there are two reasons. If a thermometer is read before 24 hour, this means that partially the previous day is involved. And in case of monthly averages that a few hours of the previous month are included in this mean. This small temporal drift can make a difference, especially in spring and autumn.
A second bias may occur if the maximum temperature is read close to the typical maximum of the day or if the minimum temperature is read close to the time of the minimum temperature. If, for example, one night is exceptionally cold and the thermometer is read in the morning and then reset for the next day, the minimum temperature of that next day may be the same cold night. Such events may thus be counted double. The same can happen in reverse to the maximum temperature readings around noon.
Correction of the TOB
The corrections for the TOB are here explained using the method of the NOAA as example (Vose et al., 2003). In the cooperative Network the observations are taken at an hour that is convenient for the volunteer observer (DeGaetano, 2000). It can change when the observer changes or when the observer preference changes.
The correction for the slightly different period can be corrected using a simple linear function including the observation time and the temperature difference between the current and the previous month (Karl et al. 1986).
The bias due to double counting of exceptionally cold or warm days depends on the local weather (diurnal cycle and synoptic variability). To derive this correction, hourly measurements are needed. (Subhourly measurements are only a little more precise.) This is only available for some stations, in the USA for about 500 stations. For these stations the correction can be computed for every possible “reading hour”. To be able to correct the stations, which only have daily observations, a simple equation is derived (multiple linear regression) in which the monthly TOB bias correction is a function of the station coordinates (time zone, latitude and longitude), observation hour, average diurnal temperature rangeand average day-to-day temperature difference (Karl et al. 1986).
The performance of this correction can be tested on the 500 stations for which hourly measurements are available. (For the statisticians: The correction function was derived using data from 1957 to 1964)
This is just a load of shite!
The daytime temperature is primarily a sinusoid. The nighttime temperature is primarily a exponential decay. Three temperature measurements per day will *NOT* provide an accurate *average* for those two curves.
TOB corrections are hooey as well. It doesn’t matter WHEN you make your two observations, you will not get an AVERAGE defined by a sinusoid and an exponential decay.
And you didn’t address the obvious problems with anomalies at all! I can only assume that you either don’t understand how variance propagates when combining variables or that you don’t care any more than climate science about what ignoring variances does to the statistical analyses.
Other disciplines have move beyond using mid-range degree-day calculations to do integrative degree-day calculations – but not climate science. Hell, climate science refuses to even use degree-days, an extensive property, instead of temperature, an intensive property, let alone use integrative techniques!
When you can explain how coastal temperatures with smaller variance can produce anomalies equal to those from inland temperatures with higher variance then come back and explain it to all of us.
I’m not going to hold my breath waiting.
Boobies that can’t understand basic science just pound their keyboards in frustration.
You are a great practitioner of unadulterated ad hominem attacks. Too bad they are worthless scientifically.
The discussion of Doppler broadening brings back memories of learning about how the thermally induced motion of atoms affect neutron capture cross sections for neutron energies close to a resonance absorption peak. This is -um- critical for reactor operation as increasing temperature will broaden the absorption lines and thus reduce reactivity.
“In the twitter (or X) discussion “
there is no Twitter. Why is this difficult?
My windows 11 app is still labeled Twitter.
A label doesn’t mean there’s a Twitter. What happens when you open it?
I open X.
I rest my case.
Really, Nick?
So men wearing dresses ain’t women
Let’s stop pretending they can identify as women and kick them out of women-only spaces
Ummm, what?
This discussion needs to continue it is important. I’m sure that there are many people at WUWT that understand what you just wrote, I understood a little of it. I look forward to your next post. All of the scientific terms and calculations are very important to the people that use them and to insure that you know what you are talking about. It is pretty much meaningless to the rest of us. The kind of thing I am talking about is should I wear a coat today or is it warm enough to swim in the river? In the case of swimming in the river I would have to know the air temperature and the river temperature. Having said that is that what the other side is talking about when explaining the dangers of a 1.5 to 2.0 Celsius increase in average global temperature? That would be a 2.7 to 3.6 Fahrenheit increase. They are speaking of this increase over more than 100 years. If we are talking about the same thing I fail to see the emergency.
Hi Bob,
This post and my previous one are about defining the word “temperature.” It was clear to me (as a former petrophysicist that worked with temperature measurements every day) that many very educated people had no clue what temperature meant. Temperature is just a measurement, it has no deeper meaning until the type of temperature measurement is explained. It could be a thermodynamic temperature at equilibrium or a kinetic temperature. In everyday usage, the latter is assumed, the temperature measurement with a thermometer. Some in the X or twitter discussion wanted it to be the former. Needless to say, I was a little startled by that, but many would not back off, thus these posts.
Temperature is a simple thing, but more complex under the surface. Sorry about the complexity, I tried to keep it to a minimum as much as possible.
Ah, “complexity”.
Can ruin one’s day if allowed to enter any of one’s mind spaces.
Best way to avoid it is to just accept without question everything / anything put out by the UN, IPCC, WEF, BBC, Guardian, Met, CNN, ABC, CBC, etc.
In short – embrace their ‘ideology’.
No room for contemplation, consideration, logical thinking, reasoning or rationality when ideology fills the mind space.
Sounds like a global conspiracy. Are Martians involved?
Well, you’re involved, so maybe.
and, as you pointed out, temperature is the reading shown of a thermometer
No thank you Andy. Everything was so much simpler before I read a definition of temperature and heat. Eventually we will come up with the elevator definitions. Half the time I don’t know if I’m talking about temperature, heat or something else.
I always try to keep it simple for myself. I just picture a metal rod being heated by a torch. If that rod is laying on an asbestos sheet I have to add “x” amount of heat to make it glow cherry red, i.e. a certain temperature. If that metal rod is laying on a metal table I have to use a larger torch and add more heat to the rod to get it to glow cherry red, i.e. the same temperature.
In both cases you have temperature equilibrium, at least eventually, but the “heat” involved can be very different!
Temperature reflects the average energy across all available molecular degrees of freedom, which can include rotation and vibration in complex molecules, not just linear translation.
When people talk about absorption line broadening as a mechanism for increased absorption with increased density of greenhouse gases, is this Doppler broadening?
IIRC, the broadening due to increase gas density (increased collision rate) is related to the shorter emission lifetime. A short tone burst has a wider frequency range than a long burst – think amplitude modulation. There’s also a broadening due to molecular rotation which produces another type of modulation.
Pat, I don’t know but I sure hope someone answers because been wondering about the line (or band or shoulder) broadening also. Can’t remember where and don’t know if it’s correct, but I think I remember reading that the line broadening is what’s responsible for the logarithmic decrease in absorption rather than complete CO2 saturation.
Whatever you call it, the spread of exchanged radiation can appropriately be thought of as black-body radiation; in contrast, so much of the published discussions here confine the emission/absorption calculations to the unique spectra of different molecules.
No. The broadening that increases IR absorption with increasing greenhouse density is not Doppler broadening. It is pressure (collisional) broadening and the physics is different.
If you increase the CO2 concentration, the Doppler broadening does not change. What does change is the number of molecular collisions, this causes the Lorentzian wings to get wider. It slightly increases the size of the CO2 15 micrometer divot.
“Lorentzian wings” – Great, now I have something else I need to look up and read about. 🙂
Line broadening in the atmosphere is mostly dependent on two factors: collisional and Doppler broadening. In the lower atmosphere collisional dominates and is an approximately exponentially decreasing function of height, Doppler broadening is dependent on temperature and thus is only weakly dependent on height and dominates at higher altitudes.
I’m quite okay with thermometer temperatures being averaged, either locally, regionally or even globally. It’s just math. But the single “global climate” construct usually attached to it, I am not.
Climate is local and regional. Australia alone has about 8 “climates”. Imagine someone quoting climate based on averaging all its capital cities. pointless.
“Whereas the thermodynamic temperature state variable of a system in equilibrium is proportional to the total internal energy of the system, kinetic temperature is the temperature proportional to the average translational kinetic energy in the system. “
Strictly speaking one needs to subtract off the centre of mass motion before talking about the average translational kinetic energy. If you throw a cold brick it does not change its temperature no matter how fast it is moving.
Are you saying that spacecraft don’t need heat shields on re-entry?
I doubt even the best pitchers in MLB could throw a brick at 400-800 m/s.
A related piece I wrote three years ago describes how conflating temperature definitions complicated discussions of equilibrium lapse rate.
Temperature reflects the average energy across all available molecular degrees of freedom, which can include rotation and vibration in complex molecules, not just linear translation.
For such an everyday concept, temperature is difficult. One would think that temperature and energy are exactly related, but the relation is complicated because energy in a molecular compound (like water) exists in more than one degree of freedom.
I think the best definition of temperature is simply “thermodynamic potential.” What I mean by that is: temperature determines the direction of the flow of heat energy between two parcels. The mass with the higher temperature transfers energy toward the mass with lower temperature.
If two parcels A and B are the same temperature, then the flow of heat from A to B is identical to the flow of heat from B to A. Having the same temperature does not mean that there is no exchange of heat. It means the average of the exchanges of heat is zero; energy out and energy in are equal.
As long as a substance exists in one state, then adding heat will raise the temperature. But, as soon as the state changes (evaporation, melting, sublimation) then heat and temperature are no longer linearly related.
The quantity that describes this is enthalpy, which is the sum of the internal energy and the pressure times volume of a substance. At constant pressure, adding heat to a solid will increase temperature until the melting point is reached, where adding heat results in a state change from solid (lower enthalpy) to liquid (higher enthalpy) at constant temperature. Then adding more heat will increase the temperature (and enthalpy) of the liquid until the boiling point is reached. At the boiling point adding more heat results in a state change from liquid (lower enthalpy) to vapor (higher enthalpy), again at constant temperature. Once the substance is fully vaporized, adding heat raises the temperature.
Standard atmospheric profiles for various substances are given in USAF Geophysics Laboratory report AFGL-TR-86-0110 (copy of here). An interesting thing about this is the standard water vapor curve for the stratosphere at 50% RH; the standard atmospheric pressure/temperature profile follows the water vapor saturation/sublimation curve exactly up to about 12 KM altitude. This is not an accident. It shows that the atmosphere which contains water vapor does not exhibit pure adiabatic expansion with increasing altitude; rather, it shows that significant heat is dumped into the atmosphere as water vapor condenses, where the temperature is determined by the partial pressure of the water vapor in the atmospheric mix. The 50% RH profile is given as a standard, but that average is driven by the fact that WV does not exceed 100% RH anywhere without condensation along the saturation curve. Yes, condensation nuclei must be present, and usually it is. Where the dearth of condensation nuclei is apparent is in the upper stratosphere where contrails readily form behind jet exhaust. Those contrails would not form if there were no water there beyond that created from burning jet fuel.
So, temperature does NOT equal energy. It changes with energy, as long as phase change is not involved. Phase change of water in the atmosphere is evident wherever clouds exist.
-BillR
Troposphere… not stratosphere. Sigh…
I like that, thanks. At a fundamental level, temperature really does direct the direction of heat transfer.
Whatever temperature data you record from whatever instrument, inevitably comes down to how fast atoms are vibrating from what atoms you are measuring. By removing the seasonal baseline at each stationary measuring point and dealing with anomalies, you are comparing your locale with others which comes down to how fast are the atoms at each location vibrating relative to the baseline. If those differences at each location (globally) are summed by month, you have a global metric of anomalies, average departures from normal throughout the dataset. Attempting to do the same thing with absolutes gives you an average temperature of all the instruments in the dataset, and that is pretty much close to worthless if you expect to find correlations, that is why we use anomalies and it works well.
Not disagreeing, this is way over my head, just question for clarification. When removing a seasonal baseline, are you removing a global seasonal baseline from each station or a local, station-specific seasonal baseline from each station?
I’m sorry, anomalies do not work either. Anomalies inherit all of the variances of the base data. Cold temperatures have different variances from warm temperatures. Those carry over to the anomalies. You can’t average variables with different variances unless you somehow weight them. And it’s not just seasonal weighting. It’s weighting for elevation, geography (e.g. coastal vs inland), terrain, humidity, etc.
In essence you need to convert the temperatures and surrounding environments into an extensive variable that can be averaged.
And this doesn’t even begin to address the issue of (Tmax+Tmin)/2 not being an average”. It is a range-dependent variable and not an average. As such it’s not even useful for distinguishing different climates since vastly different climates with differences in diurnal temperature ranges can result in the same mid-range temperature value. How do you “weight” that away? Latitude?
Are we saying that Joule was wrong? The internal energy is at best a function of temperstute.
Along with several other variables as well.