Water Vapor vs CO2 for Planet Warming

Abstract
During the time period when water vapor (WV) and carbon dioxide (CO2) have been accurately measured worldwide, 1988-2018, WV increase has been responsible for the human contribution to Global Warming with no significant net contribution from CO2.

Introduction
A useful insight to the influence of WV on planet warming can be obtained from understanding why cloudless nights cool faster and farther when absolute water vapor content of the atmosphere is lower; especially when there is no dew or frost. This simple observation demonstrates that water vapor is infrared electromagnetic radiation (IR) active which makes it a so-called greenhouse gas (ghg), thermalization (ghg molecules absorbing radiant heat from the surface or other ghg and sharing the absorbed energy with surrounding molecules) takes place, and that the misleadingly named greenhouse effect (GHE) exists.

1. Atmospheric structure
At a scale of the size of atoms the atmosphere consists of spinning and vibrating gas molecules, with empty space between them, bouncing off surfaces and each other. Activity of all of the gas molecules determines properties which can be measured as temperature and pressure. Only certain gas molecules significantly contribute to radiation heat transfer. These are IR active in the wavelength range of earth temperatures, are misleadingly called greenhouse gasses (ghg) and include CO2 and WV. The radiation energy travels from ghg molecule to ghg molecule (or between surface and ghg) at the speed of light but dwells in each molecule for a few microseconds making the molecule warmer. The dwell time is also called the relaxation time and cumulative dwell time is what causes the GHE.

Approximately 99% of dry atmospheric molecules are non-ghg; nearly all nitrogen and oxygen with about 1% argon. Near the surface, they are substantially warmed by thermalization of the earth source thermal radiation energy absorbed by the ghg molecules and, at higher altitudes (starting a few meters above the surface), cooled by pressure decline and reverse-thermalization back to the ghg molecules. Increasingly with altitude, because of lower pressure and wider spacing between ghg molecules, outward directed radiation can make it all the way to space.

All molecule species are fairly well mixed throughout the atmosphere with the exception of WV. WV molecule population declines with altitude from average of about 10,000 ppmv (parts per million by volume) at sea level to, because of the low temperature (~ -50 °C), about 32 ppmv at the tropopause. The 10,000 ppmv (1%) average increases to about 4% in the tropics. The tropopause altitude averages about 10 km (32,808 ft) with up to 14 km or so at the equator. In addition to the population decline of WV molecules due to temperature decline, is the decline due to pressure decline. The combination results in an overall average WV molecule population decline up to the tropopause of about 1200 to 1.

2. Thermalization

Thermalization occurs continuously throughout the atmosphere. The combination of thermalization and the steep gradient of WV molecules causes much of the energy absorbed by CO2 to be shared with (redirected to) WV molecules which radiate it to space. This energy transfer and WV population decline produce the ‘hash’ and notch in Top-of-Atmosphere (TOA) graphs of radiation flux vs wavenumber/cm. A typical example of such a graph, showing 18 W/m^2 being redirected to WV, is at Figure 1.


Figure 1: Thermal radiation from below assessed from top-of-atmosphere. Lower wavenumber photons are lower energy. (Original graph is from NASA [1])

3. Relative influence of CO2 and WV on climate
Hitran [2] using Quantum Mechanics calculates, besides many other things, the relative absorb/emit intensity of water vapor molecules vs CO2 molecules. Comparison at zero altitude is shown in Figure 2. Comparison by the ratio of the summation of the multiplication products intensity times wavenumber for each transition (vertical lines on the graph) for each molecule species is 1520/46 = 33. On average at ground level, according to the comparatively low populations used by Hitran, WV molecules outnumber CO2 molecules by about 8,000/330 ≈ 24 to one. After accounting for molecule count, each WV molecule is still 33/24 ≈ 1.37 times more effective at warming (absorb/emit of thermal radiation) than a CO2 molecule. 
Figure 2: At zero altitude, CO2 absorb/emit is barely discernable compared to WV.


The relative effectiveness of the increases of WV and CO2 over the last 30 years is calculated as follows:
CO2 increase in 3 decades [3], 1988 to 2018: 407 - 348 = 59 ppmv

Average global water vapor increase trend from Figure 5, which is a graph of NASA/RSS TPW data, is 0.04268/28.9 * 100 * 10 = 1.47 % per decade.


From Figure 3, at 30 degrees latitude (area to pole = area to equator) average global WV ≈ 10,000 ppmv. WV increase in 3 decades = .0147 * 10,000 * 3 = 441 ppmv.
Figure 3: Water vapor declines with latitude and rapidly with altitude. [4] (original from NASA)

Therefore, WV increase has been 441/59 * 1.37 ≈ 10 times more effective at increasing ground level temperature than CO2 increase 1988-2018. (Much of the world human population has been falsely indoctrinated)


Well above the tropopause, radiation emitted from molecules there to space is primarily from CO2 molecules (indicated in Figure 1 by the spike at wavenumber 667. If you ignore the increase in water vapor (big mistake), near the surface, WV averages about 10,000 ppmv. The increase in absorbers at ground level since 1900 is then about 10,410/10,295 ≈ 1%. WV above the tropopause is limited to about 32 ppmv because of the low temperature (~ -50 °C) while the CO2 fraction remains essentially constant with altitude at (in 2019) about 410 ppmv; up from about 295 ppmv in 1900. The increase in emitters to space at high altitude (~> 20 km, 0.055 atm), and accounting for the lower atmospheric pressure, is (410 + 32)/(295 + 32) * 0.055 ≈ 7.4%. This explains why CO2 increase does not cause significant warming (except at the poles). The result being that Climate Sensitivity (the temperature increase resulting from doubling the CO2 level) is not significantly different from zero. 

The exception at the poles is because it’s cold there at ground level so WV molecule count is already low. Therefore, transfer of energy to WV molecules which radiate it to space does not occur.

4. Water vapor increase is a cause and also a result of warming
WV increase is a cause of warming because it is a ghg. WV increase is a result of warming because its vapor pressure increases with temperature. The vapor pressure increase causes an increase in the number of WV molecules in the atmosphere.

Liquid water has a vapor pressure which depends ONLY on the temperature of the liquid water. The relation is available from multiple sources. Numerical values are graphed at Figure 4 along with the fractional rate of change vs. temperature (dp/dT/p vs. T) over the temperature range of interest for earth climate.
Figure 4: Vapor pressure of water and fractional rate of change vs liquid water temperature.

The rate-of-change of vapor pressure is a measure of the ‘extra’ vapor pressure increase from temperature increase resulting from the warming from added water vapor. It is fairly constant, reaching a maximum of 0.0687 at 13.4 °C. This is most effectively calculated by fitting a quadratic (second order polynomial) to the vapor pressure vs. temperature data and then taking the derivative (as in calculus) of the quadratic. The per unit change (%/100 = 1/1) is obtained by dividing by the vapor pressure at that temperature.

This shows that, although the VP of water increases progressively with temperature, the percent increase of VP is limited and therefore the influence of increasing temperature is also limited.


5. Measured water vapor increase
Average measured global atmospheric water vapor (total from surface to TOA) over the years is provided here at Figure 5.
Clear sky water vapor measurements over the non-ice-covered oceans in the form of total precipitable water (TPW) have been made since 1988 by Remote Sensing Systems (NASA/RSS) [5]. A graph of this measured ‘global’ average anomaly data, with a reference value of 28.73 added, is shown in the left graph of Figure 5. This data is extrapolated earlier using CO2 level as a proxy, with the expression kg/m^2 TPW = 4.5118 * ppmvCO2^0.31286. The result is the right-hand graph of Figure 5 which shows approximately 7% increase 1960-2005.
 Figure 5: Average clear air Total Precipitable Water over all non-ice-covered oceans as measured by NASA/RSS using satellite based instrumentation and with extrapolation by me. (Left graph is by month, right graph is by year average.). Estimated near future minimum is the average since mid-2016. Estimated near future maximum is the slope of the recent monthly trend.

6. World Sources of Increased Water Vapor
Irrigation, industrialization, and, increasing population have been causing the rise in atmospheric WV above that from feedback due to liquid water temperature increase. A survey of available on-line literature provides direct and indirect quantification of significant global sources of the extra increase.

Transportation fuel, linearly interpolated to 2017, amounts to 113E15 BTU/y [6]. Energy content of a typical liquid fuel is 115,000 BTU/gal [7]. Liquid fuels weigh about 6.073 lb/gal = 2.75 kg/gal. Therefore transportation fuels amount to
113E15 * 2.75/115000 = 2.7E12 kg fuel/y                 (a)

About 1.42 kg of WV is produced for each kg of liquid fuel [7] so the amount of WV produced by transportation is
2.7E12 * 1.42 = 3.8E12 kg WV/y                  (b)

World electricity generation is now about 25,000 TWH/y [8]. At an average efficiency of 50% and ignoring non-thermal sources this requires a thermal input of 50,000 TWH/yr. Fuel source fractions of energy [9] in 2017 are approximately 0.38 coal, 0.36 natural gas and 0.26 non fossil fuel.

Coal combustion produces about 0.4 kg WV/kg coal [10]. Energy content of bituminous coal is about 8200Wh/kg [11]. The amount of WV resulting from burning coal to generate electricity is then
50E15 * 0.38 * 0.4/8200 = 0.93E12 kg WV/y                       (c)

The amount of WV produced by natural gas (nearly all methane, CH4) is readily calculated from the dominant chemical reaction
CH4 + 2O2 => CO2 + 2H2O                (d)

Where a mole of methane weighs about 16 g and the two moles of WV weigh about 18 g each.
Natural gas energy content is about 15,400 Wh/kg [11]. The amount of WV resulting from burning natural gas to generate electricity is then
50E15 * 0.36 *36/16/15400 = 2.6E12 kg WV/y                    (e)

The total WV from all fossil fuel used to generate electricity is then
0.9E12 + 2.6E12 = 3.5E12 kg WV/y                         (f)

Waste energy during electricity generation can be approximately accounted for by evaporation of water in cooling towers, etc. At 50% efficiency the waste energy is the same as the energy in the electricity produced, 25,000 TWH/yr = 25E12 kWh/y.
Latent heat of water = 2257 kJ/kg = 0.627 kWh/kg = 1.594 kg/kWh.
The amount of WV from waste heat (cooling tower, etc.) during electricity generation is then
25E12 * 1.594 = 39.8E12 kg WV/y                           (g)

Irrigation is by far the largest source of WV. The increase in irrigation is indicated by the increase in withdrawal for agriculture as shown in Figure 6 [12].
Figure 6: Global water withdrawal includes both ground water and surface water [12]

The total agricultural area equipped for irrigation in 2012 was 324E10 m2 [13]. Estimate 80% were actually being irrigated. Estimating an increase of 2% to 2017, the total area being irrigated is now about
324E10 * 0.8 * 1.02 = 266E10 m2                              (h)
This is more than 4 times the area of France.

Total annual fresh water withdrawal (both ground and surface) is now 3,986 km3 = 3.986E15 kg/y [14]. Of this, about 70% is for agricultural use [15]. This works out to
3.986E15 * 0.7/266E10 = 1052 kg/m2/y ≈ 1 m/y                   (i)
which appears reasonable because average rainfall for the planet is about 1 m/y.

Evapotranspiration, WV from plants and landscape, is discussed in the ‘thematic discussion’ of Aquastat [12]. From there, the amount of precipitation on land is 110,000 km3 /y of which the fraction evapotranspirated is 0.56 + 0.05 = 0.61. Given the planet surface area of 510.1E6 km2, and land fraction of 0.29 this results in the equivalent liquid depth of the total amount of water leaving the surface as WV as
110,000 * 0.61/0.29/510.1E6 = 0.00045 km = 0.45 m/y                    (j)

Water weighs 1000 kg/m3 so evapotranspiration amounts to 450 kg/m2 /y.

Worldwide about 86% of the irrigated area is flood irrigated [20]. To simplify calculation, assume all irrigation is flood irrigation approximated as furrow type [16]. Optimum frequency is to flood the furrows about every 10 days [17]. Thus about half the area is covered by water 10% of the time where evaporation from the water is about one meter per year [18] and the rest of the time, the additional evaporation is assumed to be according to the calculated evapotranspiration. Evapotranspiration prior to irrigation must have been low or irrigation would not be done. Evapotranspiration with irrigation, to be cost effective, is most likely to be much more than calculated. These two uncertainties are assumed to approximately cancel each other. The total amount of WV resulting from irrigation is then
(0.1 * (1 + 0.45)/2 + 0.9 * 0.45) * 266E10 = 127.0E10 m3 = 127.0E13 kg/y            (k)

These calculations are summarized in Table 1

Water vapor source
E13 kg/y
%
Irrigation
127.0
96.4 %
Transportation fuel
0.4
0.3 %
Fossil fuel for electricity generation
0.4
0.3 %
Cooling towers, etc. for electricity generation
4.0
2.9%
Total
131.8
100 %

Table 1: Summary of contributions to atmospheric water vapor.

WV increase above that due to feedback from liquid water temperature increase results about 96 % from irrigation. WV added by irrigation might be particularly influential because it is added at locations where natural WV is low.

The area of the oceans, much of them quite cold, produced the WV responsible for the basic GHE temperature increase of 33 K. The added WV, mostly from irrigation in previously warm dry areas, has contributed an additional approximately 0.8 K [19] of the total average global temperature increase since 1700.

Given the earth area of 510E12 m^2 and average annual precipitation of about a meter or 1000 kg/m^2 the increased water use, mostly for irrigation, results in 131.8E13/5.1E17 = 0.0026 kg/m^2 or only about 0.0026/1000 * 100 =  0.00026 % equivalent increase in global precipitation.

7. Comparison of measured WV with WV increase calculated from feedback over a long time period.
As described in Section 4, as the temperature of liquid surface water increases, its vapor pressure increases which forces more WV molecules into the atmosphere. This contributes to a net feedback from all factors which caused the temperature to increase. A conservative value for WV increase (actual WV increase from feedback will be less than calculated) can be calculated from available measured data. The percent increase is obtained from the measured WV per-unit increase (%/100) as shown in Figure 4. With compounding (arguable because of time delay due to effective thermal capacitance) the 6.87 % increases to 0.0687 + 0.6872 + 0.6873 + … = 0.0737 = 7.37 %.

The file for calculated change is generated in EXCEL where each row contains:

WVn = WV(n-1) + (Tn – T(n-1) * R * A

Where:
WVn = WV in month n, kg/m^2
Tn = temperature anomaly in month n, K
R = effective rate of WV increase resulting from temperature increase, 0.0737/K = 7.37 %/K
A = Average WV over the period of study = 28.9 kg/m^2

The starting calculated WV is adjusted to make the starting point of the trends the same.


The results of this are shown in Figure 7 along with the actual measured WV anomaly measured and reported by NASA/RSS [5].
 Figure 7: Measured WV vs calculated WV based on HadCRUT4 reported average global temperatures.

The observation that the actual measured trend is steeper than the calculated trend demonstrates that, on the long term, measured WV is increasing faster than possible from feedback.

8. Over a short time period, water temperature drives WV.
Surface water temperature fluctuates as shown in an animation [21]. A particularly dominant fluctuation is in the equatorial Pacific and is tracked and reported weekly as el Nino. Fluctuations in el Nino affect short term global average WV and average global temperature as shown in Figure 8.
Figure 8: On the short term, local temperature fluctuations drive WV and average global temperature.

9. Influence of WV increase on HadCRUT4 average global temperature.
Figure 9 is a plot of the measured WV vs measured HadCRUT4 data. It shows the short term scatter as well as the long term trend of the influence of WV on average global temperature.
Figure 9: Scatter graph of WV vs HadCRUT4 measured data.

This provides fertile ground for those motivated to mislead to cherry-pick periods where the increasing side of fluctuations drives both WV and outgoing-longwave-radiation up.

Conclusion
Humanity’s contribution to planet warming is from increased atmospheric water vapor resulting nearly all from increased irrigation. The increased CO2 has negligible effect on warming. Climate Sensitivity, the temperature increase from doubling CO2, is not significantly different from zero.


References:
5. NASA/RSS TPW http://www.remss.com/measurements/atmospheric-water-vapor  (they only report data which includes the latest month available, 201910 means thru October, 2019) http://data.remss.com/vapor/monthly_1deg/tpw_v07r01_198801_201910.time_series.txt
9. Fuel sources for electricity generation https://www.eia.gov/outlooks/ieo/exec_summ.php
11. Energy content of bituminous coal https://en.wikipedia.org/wiki/Energy_density
17. Frequency of furrow irrigation https://naldc.nal.usda.gov/download/54786/PDF
19. Climate change drivers http://globalclimatedrivers2.blogspot.com
20. Surface irrigation 86%: http://www.fao.org/3/I9253EN/i9253en.pdf
21. Ocean surface temperature animation https://www.youtube.com/watch?v=1ir1w3OrR4U




Comments

  1. Very interesting paper and thanks for sharing it Dan.

    ReplyDelete
  2. Agree, very important investigation.
    The key is to simplify.
    We know the black body temperature steady state temperature of the earth which can easilly be calculated to -18 Celsius, meaning without atmosphere.
    We know aveage earth temperature today which is + 14 C Celcius.
    I am trying to corelate the two and need discussion about CO2 and WV H2O. Most important how many Watt -1 Tonn of each backscatter..

    ReplyDelete
  3. Without the Atmosphere as we know today, the black body steady state temperature of the earth would be different from -18 C due to Oceans.

    ReplyDelete
    Replies
    1. The -18 C assumes albedo of 0.3 which would not hold if no atmosphere. Also, if no atmosphere there would be no water vapor and no oceans.

      Delete
  4. So what do we do about the irrigation problem?

    ReplyDelete
    Replies
    1. Water vapor, and warming from increased WV, is limited by how much WV the atmosphere will hold. The amount of warming possible from increased WV appears to be less than a degree K and not a problem. Global cooling, portended by the quiet sun, is a far greater threat. The warming from increased WV is countering that, will slow and possibly prevent it

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