tag:blogger.com,1999:blog-4142988674703954802.post2541595645155193530..comments2021-05-10T09:31:50.012-07:00Comments on THE HOCKEY SCHTICK: Why Atmospheric Temperature is a Linear Function of Mass & Gravity, and Not Influenced by Greenhouse Gas ConcentrationsUnknownnoreply@blogger.comBlogger9125tag:blogger.com,1999:blog-4142988674703954802.post-6171198770834470952015-09-01T15:05:32.556-07:002015-09-01T15:05:32.556-07:00Apologies Willis, I just now noticed that the 2nd ...Apologies Willis, I just now noticed that the 2nd part of your detailed reply was published, lost in moderation somehow, but now remedied :-)<br /><br />"Now, note several things. First, there are seven successive layers in the US Standard Atmosphere (visible in their Figure 3). The temperature is calculated as a series of seven similar linear equations, with different tuned parameters for each equation. These parameters control the trend and the height of each layer.<br /><br />Second, there is no derivation of these parameter values from first principles. They are rounded off values which have been fitted to the known heights of the layer boundaries like the tropopause, and the known trends of each layer.<br /><br />Third, they say clearly that the definition of temperature as a linear function of height is simply a tradition, one which this study follows."<br /><br />The seven lapse rates, as verified by observations, are relatively linear in all the atmospheric layers, so this is a valid assumption, especially since the lapse rate eqn. is<br /><br />dT/dh = -g/Cp<br /><br />and since Cp is close to a constant for each layer, the linear assumption is entirely reasonable. Obviously Cp varies significantly between the 7 layers due to much different compositions, etc., but they did derive the Cps of the constituent layers, so the use of the 7 linear lapse rates is justified both on first principles and on the basis of observations. <br /><br />"Note that the temperatures in the seven different sections are completely defined by the parameters T0 (ground temperature), the seven altitudes of the changes in temperature H0 through H6, and the seven lapse rates Lm0 through Lm6."<br /><br />It's true that they start with the assumption of Ts = 15C, and they say they had to do so because by official international agreement Ts is defined as 15C! <br /><br />That's why I came up with the HS greenhouse equation, which doesn't know the Ts in advance, only the 255K equilibrium T with the Sun located exactly at the center of mass, "proving" that it is not necessary to observe the surface T to determine the gravito-thermal GHE. <br /><br />Getting back to US Std, yes they start from surface T, and as I discussed above the linear rate rate function/assumption is reasonable in each layer, so they just connect those 7 line segments/lapse rates together. This is to be expected of course to not have a discontinuity. <br /><br />"obviously, those are not calculated values"<br /><br />They are calculated values. If you look at the ~150 pages of their computer model printout at the end of the doc for every single 200 feet increment from 0-100km it is clear that all of the values they determined were calculated using the perfectly reasonable linear lapse rate assumptions due to the change of Cp in each layer. <br /><br />Willis, even though the US Std didn't do it, the one contribution I've made to this endeavor is to show that by triangulating the ERL at the center of mass, one can calculate the temperature profile without knowing any temperature in advance other than Te=equilibrium T with the Sun=255K= a constant, thus "proving" the gravit0-thermal GHE can be derived from first principles using a single equation!<br /><br />http://hockeyschtick.blogspot.com/search?q=greenhouse+equation<br /><br />Thanks very much for your input Willis, very helpful as always!<br /><br />My best regards,<br /><br />MS/HSMShttps://www.blogger.com/profile/06714540297202434542noreply@blogger.comtag:blogger.com,1999:blog-4142988674703954802.post-90850250540619865152015-08-31T23:22:38.544-07:002015-08-31T23:22:38.544-07:00COMMENT PART DEUX
So according to the authors, th...COMMENT PART DEUX<br /><br />So according to the authors, they assume temperature is linear with height because a) while not true, it is not far from the truth, and b) it makes the calculations simpler. Which makes perfect sense ... but which is also about as far from calculating temperature from "first principles" as you can get.<br /><br />They go on to say:<br /><br /><em>The general form of these linear equations is<br /><br />Tm = Tm,b + Lm,b * (H-Hb) (23)<br /><br />with the value of subscript b ranging from 0 to 6<br />in accordance with each of seven succe.ssive layers.<br /><br />The value of Tm,b for the first layer (b = 0) is<br />288.15K, identical to T0, the sea-level value of T,<br />since at this level M = M0. With this value of Tm,b<br />defined, and the set of six values of H, and the six<br />corresponding values of Lm,b defined in table 4, the<br />function Tm of H is completely defined from the<br />surface to 84.8520 km. (86 km)."</em><br /><br />Note that the temperatures in the seven different sections are completely defined by the parameters T0 (ground temperature), the seven altitudes of the changes in temperature H0 through H6, and the seven lapse rates Lm0 through Lm6. Note also that these parameters are not calculated anywhere in their paper. They are the simplified and rounded averages of countless observations of the atmosphere over the US. So for example in Figure 4, the temperature takes a very sharp turn at the tropopause at exactly 11,000 metres, and the lapse rate goes to exactly 0.0 ... obviously, those are not calculated values. As far as I know the height of the tropopause and its thickness are a) not nice round numbers like 11,000 metres, and 0K/metre, and b) not calculable from first principles, and c) they don’t have nice sharp corners at even thousand-meter altitudes.<br /><br />So no, the temperature of the US Standard Atmosphere is absolutely not calculated from first principles. The paper itself says that even its calculation of temperature as a linear function of height is done solely because of tradition, which is enough to disprove your claim right there ... and by tradition it is a parameterized set of seven linear equations, one for each of the seven atmospheric layers, with the parameters obviously NOT calculated from first principles, but carefully chosen rounded-off values that match the real atmosphere as closely as is reasonable and can still be mathematically tractable.<br /><br />My regards to you,<br /><br />w.<br />Willis Eschenbachhttps://www.blogger.com/profile/14276840691598976175noreply@blogger.comtag:blogger.com,1999:blog-4142988674703954802.post-42938370457175781862015-08-31T23:20:58.714-07:002015-08-31T23:20:58.714-07:00MSAugust 31, 2015 at 5:08 PM
Thanks Willis,
The ...MSAugust 31, 2015 at 5:08 PM<br /><br /><em>Thanks Willis,<br /><br />The US Std Atmosphere did calculate the dynamic and kinematic viscosities on the basis of temperature, and the temperatures were in turn calculated on the basis of pressure/mass/gravity. After they derived their gravito-thermal mathematical model, it was then verified with million of observations, so I don't agree with your statement that the dynamic viscosity is "calculated from OBSERVED temperatures." </em><br /><br />Thanks, MS, but I fear you've misread the document. Here's how they say that they calculated the temperature. Here's the first part of their statement:<br /><br /><em>Traditionally, standard atmospheres have<br />defined temperature as a linear function of height<br />to eliminate the need for numerical integration in<br />the computation of pressure versus height. This<br />Standard follows the tradition to heights up to 86<br />km, and the function Tm versus H is expressed as<br /><strong>a series of seven successive linear equations.</strong> </em><br /><br />Now, note several things. First, there are seven successive layers in the US Standard Atmosphere (visible in their Figure 3). The temperature is calculated as a series of seven similar linear equations, with different tuned parameters for each equation. These parameters control the trend and the height of each layer.<br /><br />Second, there is no derivation of these parameter values from first principles. They are rounded off values which have been fitted to the known heights of the layer boundaries like the tropopause, and the known trends of each layer.<br /><br />Third, they say clearly that the definition of temperature as a linear function of height is simply a<strong> tradition</strong>, one which this study follows.<br /><br />So I fear that your claim of "first principles" is totally contradicted their statement that the linear relationship of T with H is NOT calculated from first principles, but is done because of "tradition". And why is it done that way?<br /><br />Because it simplifies the further calculations greatly. As they explain:<br /><br /><em>... when Tm is expressed as a<br />linear function of H, the resulting differential<br />equation has an exact integral. Under these conditions,<br />the computation of P versus H becomes a<br />simple process not requiring numerical integration.</em><br /><br />>>> Continued because your site only allows 4,096 characters ... and I don't tweet, even at that length ...>>>Willis Eschenbachhttps://www.blogger.com/profile/14276840691598976175noreply@blogger.comtag:blogger.com,1999:blog-4142988674703954802.post-34520675975547377302015-08-31T17:28:33.670-07:002015-08-31T17:28:33.670-07:00Actually there's over 30 dimensionless combina...Actually there's over 30 dimensionless combinations between just mass/pressure/kinematic viscosity alone!:<br /><br />I think that overwhelmingly proves the point that the 3 are un-questionably intimately related upon first principles, and from which the physical quantities of pressure and temperature may then be derived. <br /><br />http://www.wolframalpha.com/input/?i=kinematic+viscosity%2C+mass%2C+pressureMShttps://www.blogger.com/profile/06714540297202434542noreply@blogger.comtag:blogger.com,1999:blog-4142988674703954802.post-46054894277241902352015-08-31T17:20:09.561-07:002015-08-31T17:20:09.561-07:00Also should have said that kinematic viscosity is ...Also should have said that kinematic viscosity is a linear function of geometric altitude, rather than pressure/mass/gravity, thanks for pointing that out. <br /><br />Dimensional Analysis (posted above and below) relates mass/pressure/weight and dynamic/kinematic viscosities: <br /><br />http://4.bp.blogspot.com/-CD6yAwO2nTU/VeTuc_G3guI/AAAAAAAAHWg/yXNc9dCg4iM/s1600/kinematic%2Bviscosity%2B%2Bdynamic%2Bviscosity%2B%2Bmass%2B%2Bpressure%2B%2Bdensity%2B%2Btemperature%2B%2B%2BWolfram%2BAlpha.pngMShttps://www.blogger.com/profile/06714540297202434542noreply@blogger.comtag:blogger.com,1999:blog-4142988674703954802.post-43740446865773319722015-08-31T17:08:18.359-07:002015-08-31T17:08:18.359-07:00Thanks Willis,
The US Std Atmosphere did calculat...Thanks Willis,<br /><br />The US Std Atmosphere did calculate the dynamic and kinematic viscosities on the basis of temperature, and the temperatures were in turn calculated on the basis of pressure/mass/gravity. After they derived their gravito-thermal mathematical model, it was then verified with million of observations, so I don't agree with your statement that the dynamic viscosity is "calculated from OBSERVED temperatures." It was calculated by first principles using gravity/mass/pressure/density/specific heats/etc. which then provided T, which then provided the viscosities. Obviously, that's why the shape of the dynamic viscosity graph looks almost the same as the derived temperature profile graph. <br /><br />The main reason for showing kinematic viscosity is a semi-linear function of gravity/mass/pressure is because I'm constantly being told that all the US Std Atm is is a curve-fitting exercise to observations. That is false and it is clear from that 241 page document and physical derivation that the entire atmosphere 1D mathematical model was derived from first principles and then verified with millions of observations.<br /><br />Best regards,<br /><br />MS/HSMShttps://www.blogger.com/profile/06714540297202434542noreply@blogger.comtag:blogger.com,1999:blog-4142988674703954802.post-70343997733627915242015-08-31T16:47:06.913-07:002015-08-31T16:47:06.913-07:00HS, thanks for a thought-provoking article.
Howev...HS, thanks for a thought-provoking article.<br /><br />However, when you say:<br /><br />>>>>>This proves that only kinematic viscosity effects, not radiative effects, of any gases including greenhouse gases, are what determine the kinematic temperatures at all locations, not "greenhouse gas radiative forcing.>>>><br /><br />i fear you are reversing the calculations. You seem to think that because the the log of the kinematic viscosity graph versus altitude somewhat resembles a straight line, that this means that there is no <em>"significant "radiative forcing," "heat trapping," or "radiative imbalance" from any greenhouse gases."</em><br /><br />Nothing could be further from the truth. The problem is that you have the situation backwards. The kinematic viscosity shown at the bottom of page 19 is calculated from the temperature of the standard atmosphere, not the other way around. <br /><br />This is because at a given pressure (or "geopotential height"), <strong>the kinematic viscosity of a given gas is purely a function of temperature</strong>, and temperature is NOT a function of kinematic viscosity. To be more precise, the dynamic viscosity µ, is a function of temperature alone plus two constants beta and S.<br /><br />µ = beta * T^3/2 / (T+S)<br /><br />where T is temperature in kelvins.<br /><br />So the dynamic viscosity µ is calculated from the OBSERVED temperatures. It is not derived from first principles.<br /><br />The kinematic viscosity, in turn, is the dynamic viscosity divided by the density. The density of the air above the US drops off as exp(-altitude_km/7.44). So it is calculated from the previously determined dynamic viscosity, which in turn was calculated from the observed temperature.<br /><br /><br />So what the authors of the US Standard Atmosphere paper have done is to calculate the kinematic viscosity based on the temperature, and graphed the log of kinematic viscosity versus altitude. It turns out that it graphs somewhat as a straight line, which should come as no surprise given the above equation. However, it does in fact vary significantly from a straight line. It doesn't look like a lot, but that is a log plot on the right so every unit is ten times as large.<br /><br />And it is the SHAPE of that line that is unknown. Without knowing the exact shape of the line, you cannot make the inverse calculation from kinematic viscosity to temperature.<br /><br />I say that because if you take a straight-line kinematic viscosity and you use that to calculate the other way, you get dynamic viscosity equal to kinematic viscosity times density. But with respect to altitude, density and kinematic viscosity vary inversely to each other. So you will get a straight line for the variation of dynamic viscosity with altitude ... in total contradiction to the actual graph of dynamic viscosity versus altitude shown at the bottom of page 19.<br /><br />So no, we absolutely cannot calculate the temperature structure of the atmosphere from first principles as you propose. Instead, all of the graphs in your paper are calculated based on a long-term average of the OBSERVED variations of temperature and pressure over the US.<br /><br />Sorry, but it can't be done the way you think.<br /><br />Best regards,<br /><br />w.<br /><br />Willis Eschenbachhttps://www.blogger.com/profile/14276840691598976175noreply@blogger.comtag:blogger.com,1999:blog-4142988674703954802.post-25748631528190837472014-12-15T03:23:30.623-08:002014-12-15T03:23:30.623-08:00It is worth to make us realize once again how thes...It is worth to make us realize once again how these calculations are important for spaceflight and whether they are still in use. If so, then we have a contradiction to the theory of greenhouse gases.rennoreply@blogger.comtag:blogger.com,1999:blog-4142988674703954802.post-1773613066461378372014-12-11T13:54:03.405-08:002014-12-11T13:54:03.405-08:00I've said elsewhere that all the different act...I've said elsewhere that all the different actual lapse rates within the vertical temperature profile of an atmosphere must net out to the 'ideal' lapse rate determined only by mass and gravity in order for the atmosphere to be retained.<br /><br />Whenever the actual lapse rates net out to anything different to the 'ideal' lapse rate then convection changes in order to negate any such disequilibrium.<br /><br />Stephen Wildenoreply@blogger.com