To the Editor:

In their response to my comments published in the January 2010 edition of Physics & Society, David Hafemeister & Peter Schwartz repeat some of the statements I commented upon, and refer to other sources to fill the gaps in their original tutorial. In summary, I insist that their simplified treatment, or for that matter the results of General Circulation Models, do not give convincing arguments for anthropogenic carbon dioxide being an essential factor behind the climate changes that have occurred over the last 100 years. The GCM’s at best, offer a fit to sea level data, but the parameter values required for this agreement results in poor agreement with independent measurement at higher altitudes [1-4]. I add some further comments:
  1. The authors claim that “The large natural fluxes of CO2 are approximately balanced. The increase in CO2 emissions from humans raises the CO2 atmospheric concentration.” This is claimed although the natural fluxes of CO2 are more than 10 times larger than the anthropogenic contribution. No comment is made to the fact that they are coupled and dependent on the concentration in the atmosphere, that is, that the fluxes depend on the atmospheric CO2 content such that if is higher, more is consumed both in photosynthesis (see below) and absorption by sea-water. IPCC has acknowledged this effect in their concern for CO2 “sinks” which have systematically caused the measured CO2 content to stay below their predictions. It is, for example, well-known, and even utilized as a source of fertilization, that that the photosynthetic process is more efficient and consumes more CO2 if the atmospheric content of CO2 is increased well beyond the present level. A further bonus is that plants that grow in an CO2-enriched atmosphere have a lower density of stomata cells and therefore consume less water [5]. This may be a reason for the present shrinking of deserts [6]. It is also the background reason behind the use of stomata cell density as a proxy for atmospheric CO2-content in past atmospheres [5].

  2. My second remark was that Hafemeister & Schwartz’s equations only treated radiative transport, leaving out important contributions from convection and phase change. The authors agree that these missing contributions exist, but mention that they have been considered in other treatments. This naturally raises the question of why their “radiation only” treatment gives the correct total result. It is hard to avoid the impression that their use of atmospheric emissivity as an adjustable parameter, just after eq. 17 in their tutorial, “By adjusting ea to 0.76, we obtain the ‘correct’ surface temperature, Ts = 287 K”, is the reason for such a coincidence. I mentioned in my comment that the adiabatic model - without adjustable parameter – also gives the right end result. Yet, it is not correct.

  3. Hafemeister & Schwartz repeat the mistake of considering only solar variations at the top of the atmosphere. The more relevant factor is the variation of solar intensity at the surface of earth, which is strongly modulated by low clouds. It is well-known that only a few percent change in this cloud cover is enough to change local and global average temperatures more than the increase of 0.6 – 0.8 C that we have observed over the past 100 years. IPCC admits poor basic knowledge about cloud formation mechanisms, and the formation of clouds occurs on a spatial scale that is smaller than cell size of the numerical models.

  4. Finally, I am disappointed that Hafemeister & Schwartz have no comments to the four references [1-4] that give measured results challenging the high climate sensitivity values used in the numerical models. After their statement “It is our belief that ‘theory leads experiment’ on climate change”, such comments should be of interest to the visitors of Physics & Society.

Carl G. Ribbing
The Ångström Laboratory, Uppsala University, Sweden


1. R. W. Spencer et al., “Cloud and radiation budget changes associated with tropical intraseasonal oscillations.” Geophys. Res. Lett. 34, L15707, (2007)

2. David H. Douglass et al., “A comparison of tropical temperature trends with model predictions.” Int. J. Climatol. 28, 1693–1701, (2008)

3. R. S. Lindzen et al., “On the determination of climate feedbacks from ERBE data,” Geophys. Res. Lett. 36, L16705, (2009). doi:10.1029/2009GL03962.

4. G. Paltridge et al., “Trends in middle- and upper-level tropospheric humidity from NCEP reanalysis data.” Theor. Appl. Climatol, doi 10.1007/s00704-009-0117. (2009).

5. L. Kouwenberg, et al. ”Atmospheric CO2 fluctuations during the last millenium reconstructed by stomatal frequency analysis of Tsuga heterophylla needles.” Geology 33:1, 33 (2005).

6. Eklund L. and Olsson L. “Vegetation index trends for the African Sahel 1982-1999” Geophysical Res. Lett. 30:10.1029/2002GL016772 (2003)

David Hafemeister replies:

We thank Professor Ribbing for his continued interest in our work. As we pointed out in our January 2010 response, our three-page paper contained some simple climate models, which were obtained from my text Physics of Societal Issues (Springer 2007). Let us take a moment to consider an even simpler model. In the building sciences we know that there will be a heat flow (dQ/dt) when there is a temperature difference between surfaces (delta) over an area (A) with thermal resistance (R),


The necessary temperature difference needed to expel the internal heat power through the thermal resistance in the steady state is


Note that an increase in R from increased carbon dioxide and other gases (absorption and re-radiation, convection) requires an increased surface temperature to force the heat power through the atmosphere to space. This is the basic cause of the warming: more thermal resistance requires a greater temperature difference to dispatch a given heat source in the steady state. To this, one must add positive feedbacks (more water vapor, less ice to reflect, methane release, IR absorption in clouds), which are larger than the negative feedbacks (reflecting clouds). Aerosols and volcanic dust lower surface temperatures, but these particles leave the atmosphere after a few years.

My simple models have been successful for non-climate physicists to understand the basic physics, but they clearly are not sufficient to determine policy, compared to the work of the professional atmospheric and climate scientists [1]. The IPCC global circulation model calculations agree with the time dependent temperature data over the past century ONLY if CO2 absorption is taken into account [2]. The blue curves (natural forcing due to solar activity and volcanoes) remain relatively constant in temperature over the century. On the other hand, the red curves (both natural and anthropogenic forcing) separate from the blue curves in 1955, with an increased temperature of about 0.7 oC in 2000.

Some climate skeptics say the Earth is cooling: But many skeptics plot temperature starting in 1997, where they should begin the plot 50 to 100 years earlier. The IPCC stated in 2007 that “eleven of the past 12 years (1995 to 2006 – the exception being 1996 – rank among the 12 warmest years on record since 1850.” In the last few decades we have seen the area of the Artic Icecap reduced 7.5%/decade (from 8.5 Mkm2 in 1979 to 6.5 Mkm2 in 2009), the rapid rise in the melting of Greenland, twelve fewer days of frozen lakes, and a doubling of the ocean level rise rate. Our Alaska and your Lappland have increased in temperature by 1-2 oC. It is unclear how skeptics can say the Earth’s climate is cooling.

Other climate skeptics say the Earth is warming but argue that, rather than the warming being due to carbon dioxide, it is caused by a sun that is emitting more ultraviolet photons or increasing the flux of galactic cosmic rays that make clouds. This has been refuted by a variety of authors [3]. The main argument is that the 11-year solar cycle has been quite constant, not showing a trend over the past 30 years. The amount of extra ultra-violet photons and cosmic rays has been minimal; the sun did not cause significant warming of the Earth at the end of the 20th century.

Some climate skeptics say that CO2 additions are irrelevant because its effect is saturated by the exponential absorption from a collimated beam of infrared photons. But this is not true for the atmosphere. Each micro-layer absorbs IR photons and re-radiates new IR photons, both up and down. As one goes higher in the atmosphere it is cooler, thus reradiating fewer IR photons upwards. It is this physics that produces considerable forcing from carbon dioxide; it is logarithmic in concentration and it is not a negative exponential with concentration. For today’s increase of 2 ppm/year for a decade, the thermal forcing increases linearly with time. For a doubling of CO2, the forcing is not doubled but increased by a factor of 1.69. Temperature increases (direct and feedbacks) are approximately proportional to the additional thermal forcing.

Some climate skeptics ignore the fact that carbon dioxide is now at 390 ppm, which is over 100 ppm above the pre-industrial revolution level of 280 ppm, and rising 2 ppm/year. This level will double somewhere in the next century, it is already the highest level in the past 650,000 years, which has always been less than 280 ppm. Carbon dioxide cycles in and out of the atmosphere over past ice age cycles, but at lower levels and a much slower rate. At the same time methane is now at 1800 ppb, compared to its pre-industrial value of about 600 ppb. It is the rate of change of carbon dioxide and methane that is worrisome since they are exploding the natural norms.

Ribbing holds out the hope that increased photosynthesis from raised CO2 levels will help (with water), but not in all ecosystems, and the additional sequestering of carbon is far, far smaller than global emissions of 30 billion tons of CO2 per year (now) to 50 billion tons in 2050. I wish there was an easy fix, but it will be difficult.

David Hafemeister
Physics Department
Cal Poly University, San Luis Obispo, CA

[1] G. Schmidt, “The Physics of Climate Modeling,” Physics Today 60, 72-73 (January 2007)

[2] Climate Change 2007: The Physical Science Basis (IPCC, Geneva, 2007), Fig. Summary-4.

[3] J. Lean, G. Rottman, J. Harder and G. Kopp, Solar Physics 230, 27 (2005). J. Lean, “Living with a variable Sun,” Physics Today 58, 32-38 (June 2005), P. Duffy, B. Santer, and T. Wigley, “Solar variability does not explain late-20th century warming,” Physics Today 62, 48-49 (January 2009).

This contribution has not been peer refereed. It represents solely the view(s) of the author(s) and not necessarily the views of APS.