The adiabatic lapse rate for dry air is something of a theoretical value … to use it in this Grand Canyon scenario we have to assume calm winds everywhere and the ground in thermal equilibrium with the atmosphere … then it’s just a simple matter of lowering pressure, holding mass constant; then by the basic gas law we either increase volume, decrease temperature or some of both… and this is empirically determined … if we’re heating the air from the ground or precipitating water out, all adiabatic characteristics are lost …
Again theoretically, lowering an air parcel 3.5 km will increase pressure, thus decreasing volume and increasing temperature … but the walls of the mine provide heat energy to the air parcel and as such the air parcel loses it’s adiabatic characteristics in the mine …
Not really. An adiabatic process is one where a parcel of air moves rapidly up or down, and to a first approximation does not move toward temperature equilibrium with its surroundings through mixing. This can occur if a strong horizontal wind were forced up quickly over a mountain range.
The environmental lapse rate is a function of heat being added, principally from below, then convective mixing. Convective mixing still means that we expect lower temperatures with the lower pressure at higher altitudes, but when the mixing that leads toward the equilibrium of the ELR it is not an adiabatic process.
Terrain heating at various elevations in the GC means that we do not necessarily expect the lapse rate from the top to bottom of the GC to be quite the same as the lapse rate in “open air” away from terrain, but we still expect a temperature gradient due the pressure difference with elevation.
But in the GC we would only expect the temperature gradient to be equal to the adiabatic lapse rate if there were a constant lateral strong wind, that would presumably have to blow constantly down one side of the canyon and up the other. There is no such prevailing wind.
But I don’t think you’re correctly expressing where this theoretical value is applicable. In fact, for the adiabatic lapse rate to be relevant, we require the *opposite *of calm air. The adiabatic lapse rate is relevant with rapid vertical airflow, where air expands and contracts but does not have time to exchange heat and equilibrate with the surroundings. In calm (windless) air, convective mixing (along with any heat addition/loss) leads to a lapse rate that differs from the adiabatic lapse rate.
The dry adiabatic lapse rate is used as a reference … if our column of air has an actual lapse rate equal to the dry adiabatic lapse rate, then every layer of the air column is at the correct temperature for the pressure … an equilibrium state … there is no vertical motion …
If our actual rate is less than the dry adiabat … then our air above is too warm … buoyancy forces are inhibited … a “stable” atmosphere …
If the rate is more than the dry adiabat … the air below will be warmer and buoyancy will cause it to rise in the air column … an “unstable” atmosphere …
Here’s a radiosonde chart … heavy black lines are actual measurements, green lines are the dry adiabats … looks like a cloud deck at 800 mb, another at 600 mb and a nasty inversion at 550 mb … the rest looks stable and the one line shows the stratosphere clearly at 175 mb …
That’s a real handy way to use the dry adiabatic lapse rate !!!
… and there’s no reason why we couldn’t continue the data downward from 1,000 mb …
No, you have this completely backwards. “Adiabatic” and “at equilibrium” are opposite in meaning.
The Environmental Lapse Rate (ELR) is the (average) lapse rate that prevails in the atmosphere when it reaches equilibrium, taking into account all heat input and output and reaching vertical equilibrium principally through convective mixing (also radiation & absorption, conduction). Reaching this equilibrium is not, by definition, an adiabatic process.
An Adiabatic process is one which does not reach equilibrium with its surroundings. The adiabatic lapse rate (ALR) applies to a parcel of air that moves up or down rapidly and does not reach equilibrium because it does not exchange heat energy with its surroundings.
Yes, the stability of the atmosphere depends upon the relationship between the ELR and the ALR. But it is the ELR that is the equilibrium “background” state of the bulk of the atmosphere, and the ALR determines how a rapidly rising parcel of air (one that moves too quickly to equilibriate with the surroundings) will change in temperature.
“Adiabatic” mean without the exchange of energy or matter … “equilibrium” is a condition where energy and matter are not being exchanged … hardly opposite …
Your citation specifically states the ELR is for a stationary atmosphere … as though the large-scale convective flow is stopped … as long as that energy conveyor belt is rolling there’s not going to be any equilibrium in the atmosphere … I’m sure the ELR is a fantastic reference to compare with actual conditions … just as the dry ALR is … but we still have to send up weather balloons regularly to find out what’s really going on the atmosphere …
The standard example of a “column of air” precludes the effects of the surroundings … there is no mass or energy exchange … you’ll need to solve the stress tensor to find out what the surrounding air is doing, or use N-S … in the simplified example, we just have a column of air and not considering the effects of the rest of the fluid …
So the challenge is to describe how a buoyancy force can develop in this column of air if the entire column carries the dry ALR … otherwise, if there are no forces involved then the Second Law of Thermodynamics is satisfied … [smile] … equilibrium …
The stability of the atmosphere depends upon the relationship between the actual lapse rate and the dry ALR … if the atmosphere just happen to be stationary, then we can compare the ELR with the dry ALR …
… and all this assumes clear blue skies … if we have clouds then we need to reference the pseudo-adiabatic lapse rate as well …
An packet of air that is expanding and cooling adiabatically is assumed not to be exchanging heat energy with the surrounding air, so it is not moving toward equilibrium with the surrounding air. This assumption of is reasonable because air conducts poorly, and the convective mixing that eventually redistributes heat toward equilibrium is slow.
The definition of the ELR is the actual conditions, the readings that you get from a weather ballon. (Perhaps you are confusing observed ELR with the theoretical ISA ELR, the latter is an idealized global average ELR.)
When that article states “in stationary air”, the point is that balloon measurements of the ELR temperatures should ideally be taken away from areas of active convection, i.e. away from packets of quickly-rising air that are behaving adiabatically and are in the short term out of equilibrium with the general surrounding temperature.
Of course, the ELR is constantly fluctuating, perfect equilibrium is never achieved. But the point is that the ELR is the result of slower radiative and convective mixing processes by which heat energy is exchanged and redistributed around the atmosphore, i.e. that tend toward equilibrium. Again, this longer term heat redistribution process that yields the ELR is the opposite of the assumption inherent in a short-term adiabatic processes which assumes no heat transfer.
Fair enough. IIRC, what you’re describing is a polytropic process, i.e. one in which part of the temperature change is driven by heat transfer due to local mixing and ground heating, and part of it is driven by compression/expansion of the air as it changes altitude.
I won’t call it ‘adiabatic’ anymore, but In the case of the Grand Canyon or other situations where ground level exists at disparate altitudes, compression/expansion of the air sure looks like the only plausible mechanism for explaining why high ground would be cooler than low ground. To the extent that such a difference is less than the adiabatic lapse rate, yes, ground heating and atmospheric mixing are the other drivers.
I think the troposphere is best described as a condition of radiative-convective equilibrium. If the atmosphere were in purely radiative equilibrium, that would lead to an unstable environmental lapse rate (ELR) that exceeds the dry adiabatic lapse rate (ALR). Therefore, convective packets of air constantly rise and mix to redistribute heat energy from below to above.
The adiabatic behavior of packets of air is certainly relevant to understanding the altitude-pressure-temperature relationship, but (by definition) the adiabatic behavior is the initial short-term convective movement that ignores subsequent mixing. In the short term, any packet of air that rises through either convection or wind being pushed up over terrain can be assumed to behave adiabatically and follow the ALR, because mixing and equilibration take time to occur. Thus, short-term weather patterns (and notably thunderstorms) are sensitive to the relationship between ALR and background ELR.
Medium term, of course, the packets or air that rise convectively are part of the mixing heat-redistribution process that eventually averages out to the radiative-convective equilibrium of the ELR.
My assumption is that the air is not interacting with the surrounding air, at all, neither energy or mass is being exchanged … I understand there are other reasonable assumptions that be made … I’m just not clear why you think my assumption is unreasonable … I’m simplifying this to just the vertical dimension and considering just the vertical forces involved … as this is what the OP is asking about …
I hope I’ve made clear above that I’m not considering environmental conditions, or if you like the surrounding air is under the exact conditions as our column … and these exact conditions conform to the dry ALR … then we are in equilibrium … there will be no motion in the air …
Now extend this initial condition down another 3.5 km and compare to what our thermometer down there says … I don’t think they’ll be the same in an actual mine …
Of course I don’t think your assumption of an adiabatic process is unreasonable - provided that you’re applying this simplifying assumption to an appropriate process that behaves approximately adiabatically. From the initial conversation, I agree that the ALR describes what would happen if we just pumped air at ambient pressure from the surface down to the bottom of the mine, i.e. this method would be ineffective.
But this is what I was disputing:
The last phrase “adiabatic characteristics are lost” does not rescue this misleading picture of the radiative-convective equilibrium process that leads to the environmental lapse rate (ELR) observed in the atmosphere. There is no simplifying assumption or theoretical model in which in the ELR in the Grand Canyon or anywhere else tends toward the ALR, because the ALR is the opposte of an equilibrium state, it describes the short-term dynamics of a packet of air that does not reach equilibrium with its surroundings. And the ELR most especially does not equal or tend toward the ALR in vertically stationary air, in which (absent convection) the ELR would tend toward unstable radiative equilibrium.
Maybe it’s just semantics, but then your semantics are wrong!
“At equilibrium” or “tending toward equilibrium” in this context implies the medium- or longer-term process of exchanging heat with the surroundings, i.e. undergoing convective mixing and not adiabatic.
