Global Warming Appears Likely
As countless papers have demonstrated, the increased opacity from increased carbon dioxide tends to impose a surplus of radiative energy which, if not reversed by strong negative feedback, would tend to accumulate, raising temperatures until radiative balance is again restored. This appears to be the case when calculated for nearly all the various vertical atmospheric profiles, with the possible exception of the high Antarctic where increased carbon dioxide leads to net radiative deficit. There are ways other than warming in which the atmosphere might reverse some of the radiative imbalance imposed by GHGs, but the fact that the vast majority of observed atmospheric profiles appear radiatively sensitive to GHG increase appears to make continued warming likely with continued increases in carbon dioxide.
What then of Climate Change? It bears first considering the definition of climate being the statistical properties of weather over some duration or region. Most qualitative descriptions of weather and climate begin with the ultimate source of energy, sunshine, as it encounters earth:
Such an arrangement of sunshine on a sphere leads to a surplus of net radiative energy at the equator and deficit of net radiative energy at the poles in the annual average:
The pattern of polar deficit, tropical surplus is important for two reasons: 1.) it determines the temperature distribution of cold poles and warm tropics, and 2.) Because the pattern appears in the annual mean, it implies annual exchange of energy accomplished by exchange of mass between the tropics and poles, otherwise, the tropics would be much hotter and the poles would be much colder than they are observed to be.
“Averaged over the year, there is a net energy surplus at the equator and a net energy deficit at the poles. This equator-versus-pole energy imbalance is the fundamental driver of atmospheric and oceanic circulation.”
As for 1. above, the gradient of temperatures creates the gradient in pressure that causes atmospheric motion:
Implied Exchange of Heat and Mass
As for 2. above, the exchange of energy between the poles and equator is conceived of as in this single cell circulation idealization:
And when accounting for the effects of earth’s rotation, and observations of average climate, a generalized three cell conceptual model arose:
In reality, though the annual average implies pole-and-equator air mass exchange, the mechanism ( and physical formulation ) is baroclinic instability, or waves in the imposed pressure gradient which exchange air mass across latitude bands. These waves manifest as air masses in the lower atmosphere. These air masses pass all the way from pole to equator ( and beyond across the equator ) and are not bound by the depicted cells at all, so the model is flawed. But the conceptual model does serve as a reminder of the forces of climate, in this case earth’s rotation. Another important force with respect to climate is also a pressure force in addition to the pressure gradient created by radiative imbalance, namely the pressure of mountain ranges on air masses, which tend to channel air masses in the lowest levels of the atmosphere.
Calculating Global Imbalance Using CRM
I set out to emulate the annual radiation budget by latitude as above. As with previous calculations, I used the Column Radiation Model (CRM) as applied to CFS analysis data to calculate the annual net radiance ( using the 21st day of each month for 2010 ) and compared the result with the mean annual net radiance from the CERES data. Here is the result:
The pattern is similar, though there are differences between data. These differences may come from the age of the CRM model which has been improved over the decads. Also, the CRM calculations include approximations of surface albedo, both longwave and shortwave, and both specular and diffuse and a fixed value is applied depending only on whether the surface is ocean, land, or snow covered. Also, because of prohibitive calculation time, the CFS data is 12 different snapshots of atmosphere rather than full monthy means of radiance. Further, the CFS data does include estimates of cloud liquid water content, but a rule of thumb relationship between relative humidity and cloud amount is used to approximate the value of cloud cover. Further, the CRM calculations include other approximations for fraction of ice versus supercooled water in clouds and particle distributions. These effects appear to be greater on the shortwave rather than longwave calculations. With all these assumptions in mind, the general pattern of equatorial surplus and polar deficit are clear.
How Might The Global Imbalance Change?
With the basic calculation, I ran similar calculations for scenarios of future CO2 emissions. I compared the 2010 monthly snapshot atmospheres for:
- 1x CO2 ( 400ppm )
- 2x CO2 ( 800ppm )
- 2x CO2, existing atmosphere warmed uniformly by 2°C
- 2x CO2, warmed, humidified per constant RH, and Arctic Sea Ice reduced one ninth
This resulted in the following comparison:
In this comparison, the forcing imposed by 2x CO2 is apparent ( the blue trace compared with the black trace ). So too are the effects of warming and humidifying the atmosphere. While there are changes, the changes are small with respect to the overall pattern of polar deficit and equatorial surplus.
Further comparisons of
- 1x CO2
- 2x CO2, Warmed, Humidified, One-Ninth less Arctic Sea Ice
- 2x CO2, Warmed, Humidified, Half less Arctic Sea Ice
- 2x CO2, Warmed, Humidified, No Arctic Sea Ice, and twice the warming in the Arctic
The effects of Arctic Amplification appear small with respect to the overall pattern of polar deficit and equatorial surplus.
Quadrupling and Octupling
Further comparisons of
- 1x CO2
- 2x CO2, warmed 2°C with Arctic amplification, humidified, no Arctic sea ice
- 4x CO2, warmed 4°C with Arctic amplification, humidified, no Arctic sea ice
- 8x CO2, warmed 6°C with Arctic amplification, humidified, no Arctic sea ice
Again, these conditions impose changes, but small ones with respect to the polar deficit and equatorial surplus. Two interesting features of note: 1.) the notional value of 2°C warming per doubling with humidifying appears to somewhat under compensate for the first doubling, but over compensate for the last doubling. Also, 2.) Arctic Amplification appears to create a negative feedback, at least for these proscribed conditions ( twice as much warming in the Arctic as the global average change ).
Relatively Constant Climate Factors
Within limits, the climate factors which should remain relatively constant, even with increasing carbon dioxide concentrations include the forces which determine atmospheric motion and the resulting weather:
- pole to equator radiative imbalance which creates a pressure gradient
- the rate of earth’s rotation
- and the size, shape, position, orientation of the mountain ranges and oceans
The relative constancy of the factors determining motion are significant because motion determines weather and climate is the statistical description of weather over time or for an area.
- Thunderstorms, including severe thunderstorms
are all determined by the dynamics of fluid flow, the main determinants of which will not change significantly.
Average temperatures would appear likely to increase, and temperature is an important statistic of climate. Absolute humidity would also appear likely to increase in the global mean with increasing temperature. There are considerations for increases in humidity. While an increase in humidity does not imply a big change in the frequency of precipitation, it might imply an increase in the average amount of precipitation. Also, an increase in absolute humidity means a unit mass of atmosphere contains greater latent heat, so a lesser amount mass exchange between the poles and tropics would amount to the same amount of energy exchange. This could conceivably somewhat reduce the amount of mass exchange or the amount of temperature variability, or both.
Natural ‘Climate Change’
Climate does vary, of course, and some of that variation is from variation in the fluid flow when the broad global factors appear to remain constant. Identified El Niño and La Niña events remind us of this every few years. How can this be? It would appear that there are an infinite number of mathematically possible configurations of wave patterns that can and do occur. Beyond this, longer term variations occur because of the oceans large heat capacity means certain regions of the sea surface may be a longer term source or sink of energy.
It would appear that global warming is likely and that natural climate change will continue but there does not appear to be a large source of change from increased carbon dioxide.