Wednesday, February 14, 2018

rev 1/24/22,9/15/22,1/19/23,6/30/23,8/15/23,3/7/24
Theory of Redirected Energy

Top-of-atmosphere (TOA) graphs of radiation flux from earth show ‘notches’ (‘ditches’?) centered at the nominal wavenumbers of long wavelength infrared (LWIR) active gas molecules, mostly CO2, which do not condense in the atmosphere. Figure 1 appears to be a typical mid-latitude TOA graph. Radiation flux intensity is plotted vs. wavenumber at any one geometric location. Wavenumber is simply the number of radiation wavelengths per centimeter. Wavenumber, cm-1 and wavelength in microns are easily converted: Divide 10,000 by either to get the other.


Figure 1: Typical mid-latitude TOA emission of radiation from earth. (original graph is from NASA [1])


Areas on these graphs represent power which for any elapsed time is energy. If there was no CO2, the average height of the black curve between 600 and 740/cm would be approximately 330 mW/m2 which results in an area of about 330 * (740 – 600)/1000 = 46 W/m2 while the actual area remaining is only about 140 * 200/1000 = 28 W/m2. The notches represent, for any time increment, energy that is ‘missing’. The first law of thermodynamics mandates that energy cannot simply disappear so where (and when) did the energy represented by the ‘missing’ 18 W/m2 go?

On average, radiation from the liquid and solid surfaces of the earth is very closely described by the Planck spectrum for a black body at 288 K (15° C, 59° F) (The colors you see are reflected sunlight). The red trace on Figure 1 shows the Planck spectrum for a black body at 294 K (69.5 F). Part of this radiated energy goes directly to space through an ‘atmospheric window’ in the approximate wavenumber range 770-1230 (13-8.13 microns) where no gas molecules (except O3) significantly absorb radiation. Over the rest of the total range of significant terrestrial radiation (6.5-200 microns, wavenumber 1538-50 cm-1) the radiation is absorbed by LWIR active gases (which, including water vapor, are misleadingly called greenhouse gases (ghg)).

Logic mandates that the elapsed time between when a molecule absorbs a photon and when it emits one must be more than zero or there would be no indication the photon had been absorbed. This elapsed time, called the decay time, averages about 1.1 second in the atmosphere where people are [2, 3]. The summation of decay times in outward directed radiation flux, especially from water vapor (WV) molecules, accounts for the so called Greenhouse Effect (GHE)


At the scale of atoms, the atmosphere can be visualized as molecules bouncing elastically (no energy loss) off each other in empty space. At sea level conditions, the time between collisions for the air molecules (molecule diameter 4E-10 m) is extremely short, less than 0.0002 microseconds [4]. Among other properties, these collisions are the basis for thermal conduction in the gas. Therefore, electromagnetic radiation (EMR) energy absorbed by ghg molecules is immediately shared with surrounding molecules both ghg and non-ghg. The sharing is thermal conduction in the gas. The process of absorbing radiation and sharing it with surrounding molecules is called thermalization.

A common observation which shows that water vapor increase contributes to global warming is that cloudless nights cool faster and farther when absolute water vapor content of the atmosphere is lower. Clear nights cool faster and farther in the desert than where it is humid.

Below the tropopause (below about 8 to 16 km depending mostly on latitude; more at the equator) WV decreases from an average of about 10,000 ppmv (1%, 4% near the equator) at ground level to, because of the low temperature (about negative 50 °C), 203 ppmv at the tropopause (assume about 12 km). Saturation vapor pressure of ice at -­50 C/total pressure at 12 km = 3.94 Pa/19400 Pa = 0.000203 = 203 ppmv (at saturation).

 In addition to the decline in ppmv is the decline resulting from pressure decline with altitude of 19.4/101.1 = 0.191. The total WV molecule population gradient from surface to tropopause is thus about 10000/203 * 101.1/19.4 = 257 to 1.

 Radiation from WV molecules below about wavenumber 600/cm can only be absorbed by other WV molecules. This steep WV molecule population gradient means that much of the outward directed radiation from WV molecules will make it all the way to space. This is demonstrated by the ‘hash’ in flux intensity observed in this wavenumber range measured at the top-of-atmosphere as shown on Figure 1. At about 2 km and higher, outward directed photons from WV molecules can make it all the way to space. Gaseous conduction causes energy absorbed by CO2 molecules to be conducted to replenish the energy radiated to space by WV molecules.

The redirection mechanism is summarized as follows: Much of the radiation energy that is absorbed by CO2 below the tropopause (18W/m^2 in the example shown in Fig 1) is shared with all molecules (thermalization) and emitted to space by WV molecules. This is discussed further in Sect 10 of Ref [10].


At high altitude (above about 20 km), the remaining energy is conducted from non-ghg molecules to ghg molecules for radiation towards space. For lack of a better term, call the conduction of energy from non-ghg to ghg molecules and radiated from them reverse-thermalization.


Ghg in the warmed air can emit photons only at a limited number of wavelengths (or wavenumbers) characteristic for each molecule species. Furthermore, all theoretically possible wavenumbers are not equally likely. 

The Water Vapor Factor

Water vapor is a transparent gas that, molecule for molecule, is more effective at absorb/emit of earth-temperature infrared radiation (IR) than carbon dioxide. From Jan 1988 thru Dec 2022 NASA/RSS accurately measured and reported monthly the global average water vapor as Total Precipitable Water (TPW). The anomaly data are reported at [11]. The nominal value is about 29 kg/m^2 so the trend from Jan 1988 thru Dec 2022 is 1.36 % per decade. Given that at ground level average global water vapor is about 0.8% or 8,000 ppmv (parts per million by volume), the increase in water vapor molecules in 3.5 decades is about 0.0136 * 8000 * 3.5 = 381 ppmv. From Mauna Loa data at [12] the CO2 increase in that time period is 420 - 350 = 70 ppm. Per ideal gas laws, ppm = ppmv. With that, water vapor molecules have been increasing 381/70 = 5.4 times faster than CO2 molecules. Thus, regardless of the initial source of warming, water vapor molecules have been increasing about 5.4 times faster than CO2 molecules. The idea that CO2 starts the increase is ludicrous.

Further analysis shows that the determination by molecule count that increased CO2 influence on the climate has been only about 1/7 as much as the increased water vapor influence is still high. Radiation from water vapor molecules can be in any direction but, because of the steep decline with altitude of the population gradient of water vapor molecules, the distance traveled by a photon before it encounters another water vapor molecule is greater towards space than towards earth so the prevailing direction of IR flux is towards space. This is shown on a Top of Atmosphere (TOA) graph of radiation flux vs wavenumber (wavenumber is the number of wavelengths in a centimeter) by the jagged line below about wavenumber 600. Because of the characteristic absorb/emit signature of every gas no other gas can significantly absorb or emit radiation in the wavenumber range occupied by water vapor. The line is jagged because radiation that reaches TOA/space is from water vapor molecules at different temperatures/altitudes.

Fig 1.5 is TOA graph with overlaid constant temperature curves for black body radiation at noted temperatures. For any specified atmosphere, these are also constant elevation curves. The temperature and associated altitude for standard atmosphere are shown in the upper right corner of Fig 1.5.


Figure 1.5: Typical TOA radiant emission.

At about 2 km and higher, the outward directed radiation from water vapor can make it all the way to space. In this altitude range energy absorbed by CO2 and other IR active molecules is redirected with respect to wave number via gaseous conduction to replenish the substantial energy radiated to space by water vapor molecules. This eliminates any warming from increased CO2 (or any other IR active gas that does not condense at earth temperatures) in the troposphere.

At the tropopause (about 8 to 16 km altitude depending mostly on latitude; higher at the equator) and above, water vapor molecules are greatly diminished because of low temperature so radiation to space is mostly from CO2 and other IR active molecules that do not condense in the atmosphere. Increased CO2 in the extremely thin air there actually counters warming.

The end result is that CO2 does not cause significant climate change, sequestering it is an expensive mistake and the Green New Deal will have no significant effect on climate.


Radiance calculated by MODTRAN6
MODTRAN6 [5] is a computer program developed for the Airforce Research Laboratory which (besides other things) can calculate the radiation flux at selected elevations in the atmosphere for specified constituents and conditions. It contains default values for several environments including the tropics and the 1976 Standard Atmosphere. Values for water vapor change rate and atmospheric temperature vary with altitude for different latitudes and seasonal conditions as shown in MODTRAN documentation [7].

Figures 2 and 3 are typical graphs showing how radiation flux absorbed by ghg other than WV is redirected to WV with increasing altitude. The redirection is quantified by the progressively increasing depth of the ‘notches’ at the characteristic wavenumber ranges for each ghg (except WV). Note that, at 20 km, redirection from CO2 is greatest and at 50 km and higher some of the flux has returned to the CO2 molecules. Somewhere in the vicinity of 20 km the energy that has not yet radiated to space is directed by gaseous thermal conduction to replenish the energy radiated to space by the sparse CO2 molecules there.

 The ‘notches’ are evidence of energy redirection. Redirection is possible because of thermalization and reverse-thermalization in the gaseous atmosphere.

Energy absorbed by ozone begins to be significantly redirected to CO2 and WV above 10 km, reaches a maximum below 50 km and stays at the maximum level above 50 km where radiation from O3 itself can make it to space.


 Figure 2: 1976 Standard Atmosphere at MODTRAN6 default values.


Figure 3: Tropics atmosphere at MODTRAN6 default values.


Figures 2 and 3 are somewhat misleading; especially below the tropopause. Approximately 161 W/m2 of solar energy reaches the solid and liquid surfaces of the planet [8]. Another ~16 W/m2 is radiated from clouds through the ‘atmospheric window’ [9]. The energy leaving the surface includes about 78 W/m2 from heat of vaporization of water (annual rainfall averages about a meter and what comes down had to have gone up). Another 17 W/m2 has been added by convective heat transfer, leaving 161 + 16 – 78 – 17 = 82 W/m2 in net thermal radiation. This compares favorably to up radiation minus down radiation of 345 – 271 = 74 W/m2 at zero altitude for MODTRAN6 but is only about 73% of 382 – 269 = 113 W/m2 for MODTRAN.

With increasing altitude, the non-radiant flux is replaced with radiant flux and the solar energy that was absorbed by the atmosphere and clouds is incorporated. Most of this takes place by about 10 km so the graphs at 20 km and higher should be reasonably valid.

Most of the photons emitted by the water vapor molecules are at wavelengths different from the comparatively narrow band that CO2 molecules can absorb. Effectively, much of the terrestrial thermal radiation energy absorbed by CO2 (and other non-condensing ghg) is thermalized, redirected to, and radiated to space from water vapor.

At very high altitudes, temperature, molecule spacing and time between collisions increases to where reverse-thermalization to CO2 (and O3) molecules becomes significant as does radiation from them to space.

Figures 2 and 3 answer the question posed above of where (and when) the energy went which is ‘missing’ at the notches in TOA graphs. In Figure 1, the 18 W/m2 ‘notch’ is permanently redirected to water vapor and radiated to space. The 28 W/m2 radiates to space from the 600-740 cm-1 wavenumber range. At low altitude the tiny amount of energy absorbed by CO2 and much greater amount absorbed by water vapor are thermalized; warming the low altitude atmosphere.

The water vapor content of the atmosphere diminishes rapidly as the temperature decreases with increasing altitude. Above the tropopause it has declined to a level where emission from water vapor ceases to dominate and emission from CO2 molecules becomes significant. The result is most of the residual energy not emitted to space by water vapor at low altitude is, at high altitude, redirected back to the wavenumber range 600-740 cm-1 and emitted to space by CO2. The ’redirection’ is not geometric because all wavenumbers refer to photons at essentially the same physical location.


Energy redirection helps explain why average global temperature tracks average global water vapor and not CO2 [6].

References:

1. NASA/GISS TOA graph https://www.giss.nasa.gov/research/briefs/2010_schmidt_05/

2. Average elapsed time to emit a photon https://sealevel.info/Happer_UNC_2014-09-08/Another_question.html

3. Average elapsed time to emit a photon http://rabett.blogspot.com/2013/04/this-is-where-eli-came-in.html

4. Time between gas molecule collisions http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/frecol.html

5. MODTRAN6 calculator http://modtran.spectral.com/modtran_home#plot

6. Climate change drivers http://globalclimatedrivers2.blogspot.com

7. MODTRAN6 defaults http://modtran.spectral.com/modtran_faq

8. K & T chart http://chriscolose.wordpress.com/2008/12/10/an-update-to-kiehl-and-trenberth-1997/

9. Mistakes made by the ‘consensus’: http://consensusmistakes.blogspot.com

10. Water Vapor vs CO2 for Planet Warming: https://watervaporandwarming.blogspot.com

11. NASA/RSS measurements thru Dec 2023 of Total Precipitable Water anomalies https://data.remss.com/vapor/monthly_1deg/tpw_v07r02_198801_202312.time_series.txt

12. Mauna Loa data for CO2:  https://www.co2.earth/monthly-co2

 

8 comments:

  1. This comment has been removed by a blog administrator.

    ReplyDelete
  2. Malicious nonsense.
    CO2 Science - Pruitt, proof is in the pudding! Impossible Modern Marvels
    https://confrontingsciencecontrarians.blogspot.com/2018/01/pruitt-proof-isin-modernmarvels.html

    ReplyDelete
    Replies
    1. Your lack of engineering/science skill has made you gullible to the "malicious nonsense" group think by people with an agenda. Take the blinders off and learn what happens at the scale of molecules in the atmosphere. The molecule action mandates that CO2 has no significant effect on climate. Much more is at Ref 6.

      Delete
    2. Here is sample from the website you linked to:

      "Lasers wouldn't work if we had radiative physics wrong".

      No one said you had radiative physics wrong. The question is whether radiative heat transfer is the dominant process in the removal of heat from our atmosphere. Your linked website makes no attempt to establish this.

      Delete
    3. Anyone who understands heat transfer phenomena is aware that radiative heat transfer is the ONLY way that heat leaves the atmosphere and goes to space.

      Delete
  3. And your ego has disconnected you from reality. You got words, this guy can teach you the physics http://forecast.uchicago.edu/lectures.html
    and ignoring this https://confrontingsciencecontrarians.blogspot.com/2018/01/pruitt-proof-isin-modernmarvels.html - doesn't make it any less valid. Our modern marvels alone are proof that you got something very wrong.

    And before calling me gullible, how about you?
    Does confirmation bias mean anything to you?

    ReplyDelete
    Replies
    1. You are indeed gullible and I have done my own research and challenge it. My only interest is reality and in fact believed CO2 was the culprit until proven otherwise.

      Listening to people like in your link contributes to your lack of understanding. I saw no mention of thermalization. Thermalization results from the fact that the porbability of absorbed radiation energy being shared with other molecules is thousands of times more likely than the molecule that absorbed the photon will emit a photon.

      No mention of the vapor pressure of water. Unfortunately, many so-called experts appear to be unaware water has a vapor pressure that depends only on the temperature of the liquid water.

      Implication that atmospheric water vapor depends only on air temperature which would require that it rains everywhere all the time.

      And, no explanation for the 'notch' in graphs of TOA radiation flux.

      A simple demonstration of misinformation in that series is the assertion that water vapor is essentially constant. It has been increasing 1.5% per decade for at least 30 years. Measured and reported by NASA/RSS it is graphed as Figure 3 in my Ref 6 link.

      If you care to actually learn about this stuff spend some time with the link at Ref 6. Otherwise, I can't help you.

      Delete