Comments by Gerhard Kramm On Nicola Scafetta’s Paper “A Shared Frequency Set Between The Historical Mid-Latitude Aurora Records And The Global SurfaceTemperature”

Let me start with a quotation of Eddy’s (1976) famous paper on the Maunder Minimum. In the section “Aurorae” of his paper Eddy stated:

 »Records of occurrence of the aurora borealis and the aurora australis offer an independent check on past solar activity since there is a well-established correlation between sunspot numbers and the number of nights when aurorae are seen. The physical connection is indirect: auroral displays are produced when charged particles from the sun interact with the earth’s magnetic field, resulting in particle acceleration and collision with air molecules in our upper atmosphere.«

From this point of view it could be possible that the records of mid-latitudes of the occurrence of aurorae reveal a physical link between climate change and astronomical oscillations, as argued by Dr. Scafetta. Generally, I do not decline that the observations of aurorae and sunspot numbers provide useful information about the sun’s activity. However, I challenge the physical link between climate change,characterized by the variation of the globally averaged near-surface temperature, and the astronomical oscillation.

There were various attempts to directly relate the solar constant to the number of sunspots (e.g., Ångstrøm 1922, Solanki et al. 2005) because the solar constant is a measure for the annually mean irradiance at the top of the atmosphere, and hence, indispensable for global energy balance studies. As illustrated in Figure 1 recently published by Butler et al. (2008), such a relationship seems to be likely (see also Liou, 2002).

Schneider and Mass (1975) reported about such an attempt because they tried to relate the variation of the global surface temperature trend to the variation of the solar constant. They used the empirical formula proposed by Anders Ångstrømin 1922 to express the solar constant as a function of the sunspot number and mentioned that Kondratyev and Nikolsky get good agreement with this formula. Ångstrøm’s empirical formula is shown in Figure 2. I inserted the formula into his figure for the purpose of convenience.

Apparently, the data base is small (205 data for 1915 – 1917). Note that a value of 1.903 cal cm-2 min-1 corresponds to 1327 W m-2 and the maximum of 1.953 cal cm-2 min-1 to 1362 W m-2.For 2003, when TIM was launched,Ångstrøm’s formula provided a solar constant of S = 1361.6 W m-2. This value is in substantial agreement with the TIM value (see Figure 1). This means that Dr. Scafetta’s remark “that the solar irradiance reconstruction proposed by Schneider and Mass in 1975 is considered today to be severely obsolete” is not justified.The results of Schneider and Mass may be obsolete, but the true reason is that their global energy balance model will reflect a planetary radiative equilibrium for the earth’s surface if steady-state conditions are achieved. Such a planetary radiative equilibrium does not exist in case of the earth-atmosphere system.

Ångstrøm’s figure suggests that a threshold value exists beyond that the solar constant decreases with increasing sunspot number. Based on the empirical formula the threshold value is of about 84. Ångstrøm, therefore, discussed two different phenomena working in opposite directions. It seems that Ångstrøm’s formula is unsuitable for low sunspot numbers as the concurrent observations of sunspot numbers and the satellite observations of the total irradiance (TSI) document.

The observational data used by Ångstrøm may, therefore, not be accurate enough compared with to current day information, but his hypothesis regarding the two different phenomena working in opposite directions is worth to discuss. If we try to relate the solar constant to sunspot numbers, then it is important to confirm or falsify Ångstrøm’s hypothesis.Based on Ångstrøm’s formula, I calculated the results illustrated in Figure 3. Also shown in this figure is the global temperature anomaly with respect to the climate normal 1961 – 1990 (HADCRUT3 data, see Brohan et al., 2006). It seems that there is some similarity between the minimum values in the predicted solar constant and the maximum values of the temperature anomaly. However, the correlation is not sufficient. Figure 4 shows another attempt performed by Solanki (2002) to relate the global temperature anomaly to the reconstructed solar constant.

Often, it is argued that the satellite-observed TSI data are the most trustful data we have. As illustrated in Figure 1, there is a variation of the satellite-observed TSI from up to S = 1374 W m-2 in 1978 (ERB) to S = 1361 W m-2 in 2005 (TIM). It seems that this variation can only be attributed to an improvement in sensor calibration, rather than to the sun’s activity. Dr. Scafetta mentioned this uncertainty in the satellite observations, but this uncertainty is much larger as illustrated by his figure.

So far, so bad. Let me explain what “bad” means. We try to indirectly relate the number of sunspots and/or the frequency of their occurrence recorded over four centuries to the globally averaged near-surface temperature and/or its variability with respect to time. To me, it is like looking for a black cat in a dark room, but we do not know whether this cat is inside or not.

The reasons are two-fold. On the one hand, we have to consider the sun as the energy spender, the characteristics of the earth’s elliptical orbit (i.e., the orbit of the Earth-Moon barycenter)around the sun, and the orientation of the earth’s equator plane. Since we know the laws of celestial mechanics in an appropriate manner, we can predict the TSI at the TOA, and, hence, the corresponding solar insolation as a function of Julian day, longitude, and latitude. Such a prediction can also be extended to Millions of years as done, for instance, by Bergerand Loutre, (1991).

The solar insolation is the dominant energy input into the system earth-atmosphere. This radiative input is affected by the atmosphere in various ways (e.g., absorption and scattering). Only a portion of about 47 percent (@ 161W m-2), on global average, is absorbed by the earth’s surface (strictly spoken, in the layers of the land masses and oceans directly beneath the surface). This percentage was already mentioned by Fortak (1971) and recently confirmed by Trenberth et al. (2009). Note, however, that Fortak assumed a planetary albedo of 36 percent (Trenberth et al. 30%) and an absorption of solar radiation by gaseous and particulate atmospheric constituents of 17 percent (Trenberth et al. 23%). The results of Trenberth et al. suggest that only 239 W m-2, on global average, are energetically relevant for the earth-atmosphere system and 78 W m-2are directly absorbed by gaseous and particulate atmospheric constituents. Globally averaging of flux densities (called fluxes hereafter) for the TOA and the earth’s surface is in substantial agreement with physical laws.

On the other hand, the near-surface temperature at a station of a meteorological network is governed by the local energy conversion and the advection of air masses. This local energy conversion is customarily characterized by an energy flux budget in which the absorption of solar radiation and down-welling infrared radiation at the earth’s surface is approximately balanced by the fluxes of sensible and latent heat, the emission of infrared radiation, and the transport of heat in the soil layers and water layers, respectively.Note that the difference between the infrared radiation emitted by the earth’s surface and the down-welling infrared radiation is called the IR net radiation. Furthermore, a portion of the solar radiation reaching the earth’s surface is reflected, where the reflectivity depends on the surface conditions and the zenith distance of the sun. This means that the solar radiation absorbed at the earth’s surface also depends on the surface conditions. Moreover, the fluxes of sensible and latent heat are usually not directly observed because eddy covariance measurements of wind vector, temperature, and humidity would be required. Thus, these fluxes have to be parameterized for using mean observations of wind vector, temperature and humidity. These parameterizations are only valid on a local scale.Consequently, any attempt to link the near-surface temperature observed at a network station to the physical processes of local energy conversion and the advection of air masses is not a simple one.

If we consider a column of air at such a meteorological station reaching from the earth’s surface to the TOA, then we have to recognize that an energy flux balance at the bottom of this column may exist, but not at its top. This means that a radiation balance (it means the energetically relevant solar radiation is balanced by the infrared radiation emitted into the space) at the TOA only exists, if at all, in the sense of a global average, where, in addition, an averaging period of, at least, one year is required. We may also find global averages for the solar radiation absorbed by the earth’s surface (@ 161 W m-2), the IR net radiation (@ 63 W m-2), and the fluxes of sensible and latent heat (@ 97 W m-2, in total). Note that the numbers are taken from the paper of Trenberth et al. (2009). As already mentioned, globally averaging of fluxes for the TOA and the earth’s surface is in substantial agreement with physical laws.

Of course, we may use the temperature observations of the meteorological network and satellite observations to compute a global surface temperature.Unfortunately, this temperature cannot be related to global energy balance schemes for the earth-atmosphere system in a thermodynamic manner. From a physical point of view, this globally averaged near-surface temperature is a bloodless quantity. Neither the globally averaged fluxes of sensible and latent heat nor the emission of infrared radiation by the earth’s surface can be related to this global surface temperature. Probably, many climate scientists will strongly disagree with the latter. However, it is true. The power law of Stefan and Boltzmann must not be applied to a mean temperature. The reasons are simple. This power law requires a local formulation because its derivation is not only based on the integration of Planck’s blackbody radiation law, for instance, over all frequencies (from zero to infinity), but also on the integration of the isotropic emission of radiant energy by a small surface element(like a hole in the opaque walls of a cavity) over the adjacent half space. It is indisputable that the latter corresponds to the integration over the vector field of radiation intensities. In Dines-type two-layer models of the global energy flux balance the IR net radiation flux is related to the global surface temperature and a global temperature for the atmosphere. It can simply be shown that many different temperature pairs provide the same IR net radiation of 63 W m-2.Therefore, a physical link between climate change and the astronomical oscillation, as suggested by Dr. Scafetta, is, at least, doubtful.

Since a couple of years I wonder why this bloodless quantity “global surface temperature” seems to be so important. There is only one reason: It is used to define the so-called atmospheric greenhouse effect, but this definition is not a unique one.Thus, the trend of the global surface temperature is related to the notion ‘global climate’ the debate on climate change is mainly focused on global climate change.Let me quote a paper of Kramm and Dlugi (currently in press):

»The notion ‘global climate’, however, is a contradiction in terms. According to Monin and Shishkov[11], Schönwiese[12] and Gerlich[13], the term ‘climate’ is based on the Greek word ‘klima’ which means inclination. It was coined by the Greek astronomer Hipparchus of Nicaea (190 – 120 BC) who divided the then known inhabited world into five latitudinal zones – two polar, two temperate, and one tropical – according to the inclination of the incident sunbeams, in other words, the Sun’s elevation above the horizon. Alexander von Humboldt in his five-volume ‘Kosmos’ (1845 -1862) added to this ‘inclination’ the effects of the underlying surface of ocean and land on the atmosphere [11]. From this point of view one may define the components of the Earth’s climate system: Atmosphere, Ocean, Land Surface (including its annual/seasonal cover by vegetation), Cryosphere, and Biosphere. These components play a prominent role in characterizing the energetically relevant boundary conditions of the Earth’s climate system.«

Note that the bibliography numbers are related to the paper of Kramm and Dlugi. What I described before about the local and global energy flux schemes is in substantial agreement with this cited paragraph. It characterizes the scope of the discipline of physical climatology. I strongly recommend reading the paper of Monin and Shishkov (2000). (Monin was on of the five dozens scientists who took part on the climate conference on which the GARP Report # 16 is based).  A global surface temperature plays no role in these considerations.

The final question is the following: Does the global surface temperature play a role in the discipline of statistical climatology? To find an answer it is reasonable consider the definition of climate by the World Meteorological Organization (International Meteorological Vocabulary, Sec. ed. WMO-No. 182. Geneva, 1992, p. 112):

»Synthesis of weather conditions in a given area, characterized by long-term statistics (mean values, variances, probabilities of extreme values, etc.) of the meteorological elements in that area.«

What are the weather conditions of the whole earth? Even in the discipline of statistical climatology the notion global climate is unfavorable. Therefore, I do not recommend the use of the global surface temperature in discipline of physical climatology.


Ångstrøm, A. (1922), Solar constant, sun-spots and solar activity, Astrophysical Journal55, 24-29.

Berger A. and M.F. Loutre (1991), Insolation Values for the Climate of the Last 10000000 Years. Quaternary Science Reviews 10, 297-317.

Brohan P., J. J. Kennedy, I. Harris, S. F. B. Tett, and P.D. Jones (2006), Uncertainty estimates in regional and global observed temperature changes: A new data set from 1850, J. Geophys. Res.111, D12106,21pp.,doi:10.1029/2005JD006548.

Butler J.J., B.C. Johnson, J.P. Rice, E.L. Shirley, and R.A. Barnes (2008), Sources of differences in on-orbital total solar irradiance measurementsand description ofa proposed laboratory intercomparison,J. Res. Natl. Inst. Stand. Technol.113, 187-203.

Eddy J.A. (1976), The Maunder Minimum, Science192,1189-1202.

Fortak H. (1971) Meteorologie. Deutsche Buch-Gemeinschaft, Berlin/Darmstadt/Wien (in German).

Gerlich G. (2005), Zur Physik und Mathematik globaler Klimamodelle, in Presentation before the Theodor-Heuss-Akademie: Gummersbach, Germany.

Kramm G. and R. Dlugi (2011), Scrutinizing the atmospheric greenhouse effect andits climatic impact (in press).

Liou K.N. (2002) An Introduction to Atmospheric Radiation – Second Edition, Academic Press, San Diego, CA.

Monin A.S. and Y.A. Shishkov (2000), Climate as a problem in physics,Uspekhi Fizicheskikh Nauk.170, 419-445.

Schneider S.H. and C. Mass (1975), Volcanic dust, sunspots, and temperature trends,Science 190.741-746.

Schönwiese C.-D. (2005), Globaler und regionaler Klimawandel – Eine aktuelle wissenschaftliche Übersicht. J.-W. Goethe University: Fankfurt, Germany.

Solanki S.K. (2002), Solar variability and climatechange: is there a link? (Harold Jeffreys Lecture). Astronomy & Astrophysics43, 5.9-5.13.

Solanki S.K., N.A. Krivova, and T. Wenzler (2005), Irradiance models, Advances in Space Research35, 376–383

Trenberth K.E., J.T. Fasullo, and J. Kiehl (2009), Earth’s global energy budget,Bulletin of the American Meteorological Society, 311-323.

Figure 1: The 2005 TIM value for absolute TSI was about 1361 W/m^ whereas the ACRIM III and VIRGO (DIARAD + PM06V) absolute TSIvalues are about 1366 W/m^ during the same time. The proposed work aims to understand this difference. (Graphic adapted from Greg Kopp’spresentation entitled “TIM Accuracy,” presented at TSI Uncertainty Workshop atr NIST, July 2005.) This diagram is adopted from Butler et al. (2008).

Figure 2: Solar constant vs. sunspot numbers (adopted from Ångstrøm, 1922).

Figure 3: Solar constant as a function of year. Three cycles of sunspot numbers can be seen in Figure 1, but the data used were taken from the website of the Solar Influences Data Analysis Center (SIDC) at the Royal Observatory of Belgium. Ångstrøm’s formula given in Figure 2 was used for predicting the solar constant. Also shown is the record of the global temperature anomaly with respect to the climate normal 1961-1990 (HADCRUT3 data; see Brohan et al., 2006).

Figure 4: Two reconstructions of total solar irradiance combined with measurements, where available (inclosing the red shading) and two climate records (inclosing the yellow shading) spanning roughly 150 years (adopted from Solanki, 2002).

Comments Off on Comments by Gerhard Kramm On Nicola Scafetta’s Paper “A Shared Frequency Set Between The Historical Mid-Latitude Aurora Records And The Global SurfaceTemperature”

Filed under Climate Change Forcings & Feedbacks, Guest Weblogs

Comments are closed.