Mastering Methane Mania

Methane alarm is one of the moles continually popping up in the media Climate Whack-A-Mole game. An antidote to methane madness is now available to those inquiring minds who want to know reality without the hype.

Methane and Climate is a paper by W. A. van Wijngaarden (Department of Physics and Astronomy, York University, Canada) and W. Happer (Department of Physics, Princeton University, USA) published at CO2 Coalition November 22, 2019. It is a summary in advance of a more detailed publication to come. Excerpts in italics with my bolds.

Overview

Atmospheric methane (CH4) contributes to the radiative forcing of Earth’s atmosphere. Radiative forcing is the difference in the net upward thermal radiation from the Earth through a transparent atmosphere and radiation through an otherwise identical atmosphere with greenhouse gases. Radiative forcing, normally specified in units of W m−2 , depends on latitude, longitude and altitude, but it is often quoted for a representative temperate latitude, and for the altitude of the tropopause, or for the top of the atmosphere.

For current concentrations of greenhouse gases, the radiative forcing at the tropopause, per added CH4 molecule, is about 30 times larger than the forcing per added carbon-dioxide (CO2) molecule. This is due to the heavy saturation of the absorption band of the abundant greenhouse gas, CO2. But the rate of increase of CO2 molecules, about 2.3 ppm/year (ppm = part per million by mole), is about 300 times larger than the rate of increase of CH4 molecules, which has been around 0.0076 ppm/year since the year 2008.

So the contribution of methane to the annual increase in forcing is one tenth (30/300) that of carbon dioxide. The net forcing increase from CH4 and CO2 increases is about 0.05 W m−2 year−1 . Other things being equal, this will cause a temperature increase of about 0.012 C year−1 . Proposals to place harsh restrictions on methane emissions because of warming fears are not justified by facts.

The paper is focused on the greenhouse effects of atmospheric methane, since there have recently been proposals to put harsh restrictions on any human activities that release methane. The basic radiation-transfer physics outlined in this paper gives no support to the idea that greenhouse gases like methane, CH4, carbon dioxide, CO2 or nitrous oxide, N2O are contributing to a climate crisis. Given the huge benefits of more CO2 to agriculture, to forestry, and to primary photosynthetic productivity in general, more CO2 is almost certainly benefitting the world. And radiative effects of CH4 and N2O, another greenhouse gas produced by human activities, are so small that they are irrelevant to climate.

Radiative Properties of Earth Atmosphere

On the left of Fig. 2 we have indicated the three most important atmospheric layers for radiative heat transfer. The lowest atmospheric layer is the troposphere, where parcels of air, warmed by contact with the solar-heated surface, float upward, much like hot-air balloons. As they expand into the surrounding air, the parcels do work at the expense of internal thermal energy. This causes the parcels to cool with increasing altitude, since heat flow in or out of parcels is usually slow compared to the velocities of ascent of descent.

Figure 2: Left. A standard atmospheric temperature profile[9], T = T (z). The surface temperature is T (0) = 288.7 K . Right. Standard concentrations[10], C {i} = N {i}/N for greenhouse molecules versus altitude z. The total number density of atmospheric molecules is N . At sea level the concentrations are 7750 ppm of H2O, 1.8 ppm of CH4 and 0.32 ppm of N2O. The O3 concentration peaks at 7.8 ppm at an altitude of 35 km, and the CO2 concentration was approximated by 400 ppm at all altitudes. The data is based on experimental observations.

If the parcels consisted of dry air, the cooling rate would be 9.8 C km−1 the dry adiabatic lapse rate[12]. But rising air has usually picked up water vapor from the land or ocean. The condensation of water vapor to droplets of liquid or to ice crystallites in clouds, releases so much latent heat that the lapse rates are less than 9.8 C km−1 in the lower troposphere. A representative lapse rate for mid latitudes is dT/dz = 6.5 K km−1 as shown in Fig. 2.

The tropospheric lapse rate is familiar to vacationers who leave hot areas near sea level for cool vacation homes at higher altitudesin the mountains. On average, the temperature lapse rates are small enough to keep the troposphere buoyantly stable[13]. Tropospheric air parcels that are displaced in altitude will oscillate up and down around their original position with periods of a few minutes. However, at any given time, large regions of the troposphere (particularly in the tropics) are unstable to moist convection because of exceptionally large temperature lapse rates.

The vertical radiation flux Z, which is discussed below, can change rapidly in the troposphere and stratosphere. There can be a further small change of Z in the mesosphere. Changes in Z above the mesopause are small enough to be neglected, so we will often refer to the mesopause as “the top of the atmosphere” (TOA), with respect to radiation transfer. As shown in Fig. 2, the most abundant greenhouse gas at the surface is water vapor, H2O. However, the concentration of water vapor drops by a factor of a thousand or more between the surface and the tropopause. This is because of condensation of water vapor into clouds and eventual removal by precipitation. Carbon dioxide, CO2, the most abundant greenhouse gas after water vapor, is also the most uniformly mixed because of its chemical stability. Methane, the main topic of this discussion is much less abundant than CO2 and it has somewhat higher concentrations in the troposphere than in the stratosphere where it is oxidized by OH radicals and ozone, O3. The oxidation of methane[8] is the main source of the stratospheric water vapor shown in Fig. 2.

Fluxes and Forcings

How greenhouse gases affect energy transfer through Earth’s atmosphere is quantitatively determined by the radiative forcing, F, the difference between the flux σT4 of thermal radiant energy from a black surface through a hypothetical, transparent atmosphere, and the flux Z through an atmosphere with greenhouse gases, particulates and clouds, but with the same surface temperature, T0.

Figure 3: Left: The altitude dependence of temperature from Fig. 2. Right The flux Z increases with increasing altitude as a result net upward energy radiation from the greenhouse gases H2O, O3, N2O and CH4, and CO2.

The forcing F and the flux Z are usually specified in units of W m−2. The radiative heating rate, dF R = , (3) dz is equal to the rate of change of the forcing with increasing altitude z. Over most of the atmosphere, R < 0, so thermal infrared radiation is a cooling mechanism that transfers internal energy of atmospheric molecules to space or to the Earth’s surface. Forcing depends on latitude, longitude and on the altitude, z. The right panel of Fig. 3 shows the altitude dependence of the net upward flux Z and the forcing F for the greenhouse gas concentrations of Fig. 2. The temperature profile of Fig 2 is reproduced in the left panel. The altitude-independent flux, σT 4 = 394 W m−2, from the surface with a temperature T0 = 288.7 K, through a hypothetical transparent atmosphere, is shown as the vertical dashed line in panel on the right. The fluxes for current concentrations of CO2 and for doubled or halved concentrations are shown as the continuous green line, the dashed red line and dotted blue line.

At current greenhouse gas concentrations the surface flux, 142 W m−2, is less than half the surface flux of 394 W m−2 for a transparent atmosphere because of downwelling radiation from greenhouse gases above. The surface flux has nearly doubled to 257 W m−2 at the tropopause altitude, 11 km in this example. The 115 W m−2 increase in flux from the surface to the tropopause has been radiated by greenhouse gases in the troposphere. Most of the energy needed to replace the radiated power comes from convection of moist air. Direct absorption of sunlight in the troposphere makes a much smaller contribution.

Spectral Forcings

Planck’s formula (7) for the spectral intensity of thermal radiation is one of the most famous equations of physics. It finally resolved the paradox that classical physics predicted infinite fluxes of heat radiation, in clear contradiction to observations, and it gave birth to quantum mechanics [16].  As one can see from Fig. 3, the flux at the top of the atmosphere, 277 W m−2 is only 70.3% of the flux σT 2 = 394 W m−2 emitted by a black surface at a temperature of T0 = 288.7 K. So without greenhouse gases, the surface would only need to radiate 70.3% of its current value to balance the same amount of solar heating. Since the Stefan-Boltzman flux is proportional to the fourth power of the surface temperature, without greenhouse gases the surface temperature could be smaller by a factor of (0.703)1/4 = 0.916. For this example, the greenhouse warming of the surface by all the greenhouse gases of Fig. 2 is ∆T = (1 0.916)T0 = 24.3 K. The warming would be different at different latitudes and longitudes, or in summer or winter, or if clouds are taken into account. But 20 C to 30 C is a reasonable estimate of how much warming is caused by current concentrations of greenhouse gases, compared to a completely transparent atmosphere.

Instantaneous forcing changes due to changes in the concentrations of greenhouse gases, but with no other changes to the atmosphere, can be calculated accurately for a given temperature profile. The next step, using instantaneous forcing changes to calculate temperature changes, is fraught with difficulties and is a major reason that climate models predict much more warming than observed[18]. As shown in Fig. 3, increasing the concentration of greenhouse gases (doubling the CO2 concentration for the example in the figure) slightly decreases the radiation flux through the atmosphere. In response, the atmosphere will slightly change − its properties to ensure that the average energy absorbed from sunlight is returned to space as thermal radiation. Since both the surface and greenhouse molecules radiate more intensely at higher temperatures, temperature increases are an obvious way to restore the equality of incoming and outgoing energy.

But the amount of water vapor and clouds in the atmosphere will also change, since water vapor is evaporated from the oceans and from moist land. Water is also precipitated from clouds as condensed rain or snow. Low, warm clouds reflect more sunlight and reduce solar heating, with little hindrance of thermal radiation to space. High, cold cirrus clouds reduce the thermal radiation to space, but are wispy and do little to hinder solar heating of the Earth.

The simplest response to changes in radiative forcing would be a uniform temperature increase dT , at every altitude and at the surface. The rate of increase of top-of-the atmosphere flux with a uniform temperature is then [1] dZ = 3.9 W m−2 K −1. (9) dT For a uniform temperature increase, the forcing increase ∆F = 0.23 W m−2 after 50 years, that would result if methane concentrations continued to rise at the rate of the previous 10 years as shown in Fig. 9, would cause a surface-temperature increase of ∆T = ∆F/(dZ/dT ) = 0.05 C. The forcing increase ∆F = 2.2 W m−2 after 50 years, if carbon dioxide concentrations continued to rise at the rate of the previous 10 years, would cause a surface-temperature increase of ∆T = ∆F/(dZ/dT ) = 0.59 C.

Both temperature increments are small and probably beneficial.

But there are persuasive reasons to expect that the temperature changes will be altitude dependent, like the forcing changes shown in Fig. 3, and that the water-vapor concentrations and cloud cover will change in response to changes in the surface temperature. Fig. 6 illustrates a more complicated “feedback” calculation.

Figure 6: Left. An initial temperature profile T (continuous blue line), the mid latitude profile of Fig. 3. The dashed red line is the adjusted temperature profile T ′ , after a doubling of the CO2 concentration. Right. The continuous blue line is the altitude profile of the “instantaneous” flux change ∆Z, caused by doubling CO2 concentrations.

On the left panel of Fig. 6, the continuous blue line labeled T is the midlatitude temperature profile of Fig. 3. The dashed red line labeled T ′ is the adjustment of the temperature profile in response to doubling the concentration of CO2, with a simultaneous increase in the concentration of water vapor in the troposphere The right panel of Fig. 6 summarizes forcing increments, with and without feedbacks. The continuous blue line is the instantaneous flux change from doubling CO2 concentrations, with no other changes to the atmosphere. It is the difference between the dashed red curve and the continuous green curve on the right of Fig. 3, but plotted on an expanded scale. The instantaneous forcing, ∆F = ∆Z, is 5.5 W m−2 at the tropopause altitude of 11 km, and 3.0 W m−2 at the 86 km altitude of the top of the atmosphere. The dashed red curve on the right of Fig. 6, labeled δZ is the “residual forcing” for the dashed-red temperature profile T ′ on the left, for doubled CO2 concentrations, and for the same relative humidity as before doubling CO2.

The same lapse rate, dT/dz = 6.5 K km−1, was used before and after doubling CO2 concentrations, as proposed by Manabe and Wetherald[19] in their model of “radiative-convective equilibrium.” This feedback prescription approximately doubles the surface warming, compared to a uniform temperature adjustment and no change in water vapor concentration. There is stratospheric cooling and surface warming. Variants of the radiative-convective equilibrium recipes illustrated in Fig. 6 are widely used in climate models. Unlike forcing calculations, which can be uniquely and reliably calculated, there is lots of room for subjective adjustments of the temperature changes caused by forcing changes.

Future Forcings of CH4 and CO2

Methane levels in Earth’s atmosphere are slowly increasing.  If the current rate of increase, about 0.007 ppm/year for the past decade or so, were to continue unchanged it would take about 270 years to double the current concentration of C {i} = 1.8 ppm. But, as one can see from Fig.7, methane levels have stopped increasing for years at a time, so it is hard to be confident about future concentrations. Methane concentrations may never double, but if they do, WH[1] show that this would only increase the forcing by 0.8 W m−2. This is a tiny fraction of representative total forcings at midlatitudes of about 140 W m−2 at the tropopause and 120 W m−2 at the top of the atmosphere.

Figure 9: Projected mid-latitude forcing increments at the tropopause from continued increases of CO2 and CH4 at the rates of Fig. 7 and Fig. 8 for the next 50 years. The projected forcings are very small, especially for methane, compared to the current tropospheric forcing of 137 W m−2.

The per-molecule forcings P {i} of (13) and (14) have been used with the column density Nˆ of (12) and the concentration increase rates dC¯{i}/dt, noted in Fig. 7 and Fig. 8, to evaluate the future forcing (15), which is plotted in Fig. 9. Even after 50 years, the forcing increments from increased concentrations of methane (∆F = 0.23 W m−2), or the roughly ten times larger forcing from increased carbon dioxide (∆F = 2.2 W m−2) are very small compared to the total forcing, ∆F = 137 W m−2, shown in Fig. 3. The reason that the per-molecule forcing of methane is some 30 times larger than that of carbon dioxide for current concentrations is “saturation” of the absorption bands. The current density of CO2 molecules is some 200 times greater than that of CH4 molecules, so the absorption bands of CO2 are much more saturated than those of CH4. In the dilute“optically thin” limit, WH[1] show that the tropospheric forcing power per molecule is P {i} = 0.15 × 10−22 W for CH4, and P {i} = 2.73 × 10−22 W for CO2. Each CO2 molecule in the dilute limit causes about 5 times more forcing increase than an additional molecule of CH4, which is only a ”super greenhouse gas” because there is so little in the atmosphere, compared to CO2.

Footnote: On Playing Climate Whack-A-Mole

Dealing with alarmist claims is like playing whack-a-mole. Every time you beat down one bogeyman, another one pops up in another field, and later the first one returns, needing to be confronted again. I have been playing Climate Whack-A-Mole for a while, and if you are interested, there are some hammers supplied at the link above.

The alarmist methodology is repetitive, only the subject changes. First, create a computer model, purporting to be a physical or statistical representation of the real world. Then play with the parameters until fears are supported by the model outputs. Disregard or discount divergences from empirical observations. This pattern is described in more detail at Chameleon Climate Models

A series of posts apply reality filters to attest climate models.

 

2 comments

  1. Bob Greene · 9 Days Ago

    Gosh, all the things I missed from the undergrad chemistry and infrared spectroscopy I learned half a century ago. I guess I was distracted by stretches, rocks, wags, scissors, etc.

    Like

  2. rogercaiazza · 9 Days Ago

    Ron,
    I love our apt description of the media Climate Whack-A-Mole game. Perfect!

    Like

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