Hello Frank,

This is an excellent observation; based on the recent review of the literature it is evident that the most commonly used (and the most accurate until now) is the estimate provided in my first answer. The issue of errors with respect to the spherical approximation is still in the center of an active debate. The most important element in this discussion is selection of a coordinate system for modeling of the atmosphere (both for weather and climate applications).

The interesting paper addressing the nuances of the problem was published recently in the QJRMS:

“Spheroidal coordinate systems for modelling global atmospheres”

Q. J. R. Meteorol. Soc. 134: 261–270 (2008)

https://rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/qj.208

In many of our current estimates there is a discrepancy between the spherical shape used in the dynamic models and the ellipsoidal formula used in JGR paper. There are definitely numerous justifications of this fact but certainly it is worthwhile to perform the corresponding estimates of errors in calculations related to atmospheric chemistry, mass balances and heating rates.

Sincerely,

Janusz

https://www.quora.com/How-is-the-volume-of-earths-atmosphere-determined

No idea sir...

Well,

Troposphere size = Earth and troposphere size with radius (6371 km + 12 km) - Earth size with radius (6371 km).

Sincerely

What do you mean by "accurately"?

The altitude of the tropopause varies with location (latitude, longitude) and time.

The accurate calculations are rather complicated considering the fact that the Earth is a triaxial ellipsoid, with an extremely complex terrain, varying shorelines and changing sea level. Over the years I was attempting to perform these calculations exactly and each time some additional elements were added. Considering the fact that the perfect is the worst enemy of good, I would suggest to start from the classical work:

“The Total mass of the atmosphere, J. Geoph. Res., Volume 99, Issue D11, 20 November 1994”

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/94JD02043

The authors apply a simple ellipsoidal model to evaluate the mass of the atmosphere. In order to obtain an expression for the volume we can use Eq. (4) from the above paper setting $\rho$ to one, there is of course a problem with determination of the upper limit for r, this fact shows that the tasks of estimating the volume and the mass of the atmopshere are intimately connected.

Thanks folks for all your answers.

It seems to me that estimating the volume of the troposphere, is a complex matter. Still however, a lot of scientist come up with atmospheric volume estimates. I wonder how they proceed and what typical errors are made? All in all the error on the atmospheric (tropospheric) volume estimation methods determines the absolute error on the heat balance of the Earth doesn't it?

Thanks again.

Frank

Hello Frank,

This is an excellent observation; based on the recent review of the literature it is evident that the most commonly used (and the most accurate until now) is the estimate provided in my first answer. The issue of errors with respect to the spherical approximation is still in the center of an active debate. The most important element in this discussion is selection of a coordinate system for modeling of the atmosphere (both for weather and climate applications).

The interesting paper addressing the nuances of the problem was published recently in the QJRMS:

“Spheroidal coordinate systems for modelling global atmospheres”

Q. J. R. Meteorol. Soc. 134: 261–270 (2008)

https://rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/qj.208

In many of our current estimates there is a discrepancy between the spherical shape used in the dynamic models and the ellipsoidal formula used in JGR paper. There are definitely numerous justifications of this fact but certainly it is worthwhile to perform the corresponding estimates of errors in calculations related to atmospheric chemistry, mass balances and heating rates.

Sincerely,

Janusz

The atmoshere does not really have a volume since you need to know at what altitude it ends, The mass of the atmosphere is easier to calculate since it is set by the atmospheric pressure at the surface.

If the tropause was at a constant pressure, then it would be relatively easy to calculate the mass of the troposphere, but the pressure at the tropopause varies with latitude.

Frank,

What the modellers do is use pressure rather than height to specify the altitude coordinate.

Alastair,

The modern non-hydrostatic models are coded in the height coordinates. The mass based vertical coordinates are still relevant in some studies but the future is definitely in the height coordinates. Please see for example the information about NICAM model from Japan:

https://progearthplanetsci.springeropen.com/articles/10.1186/s40645-017-0127-8

As far as the volume vs mass issue is concerned the subject is elaborated in the JGR paper mentioned in my first answer.

With my best regards,

Janusz

Thanks Alastair,

Seems to be the standard representation of atmospheric properties indeed.

Cheers,

Frank

But Janusz makes a point too. When the atmosphere has no volume, how do we calculate for example the mass of carbon dioxide (and other heat absorbing chemical species) in the atmosphere and hence the heat balance?

A bit enigmatic no?

Cheers,

Frank

Frank,

In the NICAM model it says "... we used NICAM with horizontal grid spacing of 14 km and 38 vertical layers "

For the layers to have an equal mass you need to know the pressure at each altitude. But you can specify the levels for each layer in pressure or in height.