Amplitude of Solar Irradiance and Change of Temperature

Authors: Nasif S. Nahle,* Adip S. Nahle, Esther Velazquez.
Published on ©19 June 2008. Updated: 19 December 2009 (minor grammar errors and lost links). Please, read Addenda.

* To whom correspondence should be addressed.

The authors declare no conflict of interest. This article is a BIOCAB direct submission. (Additional editing of this English text by TS)


When assessing the influence of solar irradiance on the Earth’s climate, we sometimes fail to compare the total solar irradiance with the variation of temperature. The solar irradiance magnitudes refer to absolute values, while the change of temperature refers to a deviation from a standard value of change; for example, if the average temperature yesterday was 307.15 K and the standard temperature is 300.15 K, the amplitude of change of temperature is:

A = Tcurrent – Tstd = 307.15 K - 300.15 K = 7 K

7 K is the amplitude of the change of temperature averaged throughout 24 hours.

If the temperature is 297.35 K, the amplitude would be:

A = Tcurrent – Tstd = 297.35 K - 300.15 K = -2.8 K

The records released by NOAA (1) and other institutions (2) dedicated to assessing climate are magnitudes that refer to anomalies. For example, we determined that the average of global temperature on 2 February 2008 was 290.45 K when the global average for the same position of the Earth with respect to the Universe had averaged 290.68 K in the last 100 years. To obtain the anomaly on 2 February 2008, we subtract the centennial average of temperature from the current average of temperature on the same date:

290.45 K - 290.68 K = -0.23 K

Which means that the change of temperature on 2 February 2008 was -0.23 K.

The magnitudes of oscillations of temperature are simulated because it is impossible for us to know what the standard change of temperature is, given that the Earth is 4.8 billion years old and has undergone millions of global oscillations, most of them larger than the current ones. Consequently, we cannot assert that recent warming has been unprecedented or atypical. The examination of iron stained grains (3, 4) and other proxies like diatoms, foraminifera, growth tree-rings and Ca-II shows that the Holocene Epoch has been characterized by fluctuations of temperature of 6 degrees Celsius or more (4). The global fluctuation detected throughout the last 100 years has been no higher than 0.52 degrees Celsius (5).


We have a highly ambiguous set of data referring to the equilibrium point for solar radiation hitting the outer layer of the Earth’s atmosphere. Some solar physicists take 1371 W/m^2 as the equilibrium point, others take 1366 W/m^2, some say that the equilibrium is 1364.5 W/m^2 and others that it is 1360.5 W/m^2. Thus, given the state of things, we decided to consider the median of each database as the equilibrium point in all datasets of Total Solar Irradiance (TSI). For example, the median of Lean’s complete database (6) on the intensity of solar irradiance is 1364.67865 W/m^2 (taking into account the number of sunspots and proxies). With this value, we can calculate the amplitude of the intensity of solar irradiance for each set of data; for example, the amplitude of the intensity of solar irradiance in 1610 was:

A = 1364.7338 W/m^2 - 1364.67865 W/m^2 = 0.05515 W/m^2

The subtraction is contemplated as a deviation from the median; however, the median in all these cases is the magnitude of equilibrium for any particular database of TSI. The greater the amplitude, the greater the energy it carries. If the amplitude is below the standard deviation, then the energy would be low. If the amplitude is above the standard deviation, then the energy would be high.

Let’s try graphing the data from Lean’s 2001 reconstruction (6):


Notice that the deviations (red spots) have been higher than the standard deviation (violet horizontal band) since 1916 AD.


IMPORTANT: The databases on Total Solar Irradiance used for the graphs below are the intellectual property of Dr. Leif Svalgaard and have been included here by kind permission. Use of these data without permission, in writing from the author, is not permitted. *

Now, let us try the same thing with Dr. Svalgaard's reconstruction (7). Dr. Svalgaard has calibrated his reconstruction with respect to sunspots only (7).

The median from the Svalgaard’s database (7) is 1365.92 W/m^2. And the graph derived from his database is

Nahle, N. S., Nahle, A. S., Velazquez, E. Amplitude of Solar Irradiance and Change of Temperature. ©19 June 2008. Biology Cabinet Magazine Online.
This Website created and kept up by Nasif Nahle et al.
Copyright© June 2008 by Biology Cabinet Organization

The red line represents the correlation between the asymmetries of Solar Radiation calculated from the database of Judith Lean (6) and the fluctuations of temperature from 1970 AD taken from the databases of the University of Alabama in Huntsville (2). Notice the solid correlation between the intensity of solar radiation and the changes of temperature. The peaks of the line (value = 1) represent a positive correlation, which means that the increase of solar radiation generated an increase of the atmospheric temperature. The troughs of the red line (value = -1) represent a negative correlation, which means that the atmospheric temperature decreased when the intensity of the solar radiation increased, denoting an inversely proportional correlation. Notice the absence of values equal to zero, which means that the factors did not change independently of one another.

The green squares represent the correlation between the asymmetries of Solar Radiation calculated from the database of Leif Svalgaard (7). Observe that the graph does not have values of zero; for this reason, the correlation is similar to the correlation calculated from Lean’s reconstruction. (6)

Although different in length and frequency, both reconstructions of the Intensity of Solar Radiation reflect the physical sensibility of the terrestrial climatic system to the changes in the flux of solar radiation. The negative correlations observed year to year are due to the increase in cloudiness (negative feedback) by effect of the heating up of the oceanic surface by incident solar radiation and consequential evaporation.


This evaluation, which takes into consideration the amplitudes, asymmetry coefficients and correlation coefficients obtained from the total solar irradiance reconstructions of Dr. Judith Lean(6) and Dr. Leif Svalgaard(7), is evidence for the theories on the increase of solar irradiance over the last three centuries immediately following the end of the Maunder Minimum.

The connection of Solar Irradiance with the temperature of the Earth’s atmosphere complement other climate theories. It is of considerable value to note that very small changes in the intensity of Solar Irradiance lead to severe changes of the Earth’s climate.(8) The influence of “greenhouse gases” on the climate is irrelevant. (9)

P. S. Standard Temperature is the temperature and pressure where the equilibrium constant for the auto-ionization of water is 1.0x10^14. For the Ambient Standard Temperature (AST) the value is 300.15 K (27 °C).

Esther Velazquez




2. Monthly reports of temperature from the National Space Science and Technology Center (NSSTC) of the University of Alabama in Huntsville.

3. Broecker, Wallace S. Was the Medieval Warm Period Global? Science. 23 February 2001. Vol. 291. No. 5508, pp. 1497 – 1499.

4. Bond, Gerard et al. Persistent Solar Influence on North Atlantic Climate During the Holocene. Science 7 December 2001: Vol. 294. no. 5549, pp. 2130 – 2136.

5. Nahle, N. S. Temperature Variations from 1979 up to Date. ©April 2007. Biology Cabinet Magazine Online. Reviewed in 19 June 2008.

6. Lean, J. 2004. Solar Irradiance Reconstruction. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2004-035. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA.

7. Svalgaard, L. 2008. Reconstruction of Total Solar Irradiance. Research Analysis. Last reading on May 12, 2008.

8. Cowen, Ron. Stormy Weather - When the Sun's Fury Maxes Out, Earth May Take a Hit. Science News. January 13, 2001. Vol. 159, Pp.26-28.

9. Perkins, Sid. Pinning Down the Sun - Climate Connection-Solar Influence Extends Beyond Warm, Sunny Days. Science News. January 20, 2001. Vol. 159, Pp. 45-47.

10. Scafetta N., R. C. Willson. ACRIM-gap and TSI Trend Issue Resolved Using a Surface Magnetic Flux TSI Proxy Model. 2009. Geophys. Res. Lett., 36, L05701, doi:10.1029/2008GL036307.



New Findings Support our Theory:

Last week, Nicola Scafetta and Richard C. Wilson published a peer reviewed paper in which they revealed a considerable Total Solar Irradiance (TSI) increase of 0.033 % per decade between the solar activity minima of 1986 and 1996, which is comparable to the 0.037 % found in the ACRIM composite. The data gathered by satellites, which were reported by Scafetta and Wilson, coincide with my theory of a correlation between the Amplitude of TSI and the Change of the Earth’s Tropospheric Temperature until 1998. In my article “Heat Stored by Greenhouse Gases”, I concluded that the fluctuation of the TSI of the last 300 years had been 1.25 W/m^2, causing a change of the Earth's temperature of 0.56 °C, which is the maximum averaged change in tropospheric temperature achieved in the 1990s (the average of change of temperature in 1998 was 0.51 °C). The correlation resides in the total change since 1610 AD, which I had calculated was 1.25 W/m^2. The new findings fix the change at 1.32 W/m^2 which would produce a change of temperature of 0.594 °C, while the change I had calculated would produce a change of temperature of 0.56 °C. Nonetheless, both calculations of the changes of temperature based on the fluctuation of the TSI coincide with the natural change observed in 1998 (0.52°C) and with the total natural oscillation of temperature of -3 °C to 3 °C in the Holocene Period.

Nasif Nahle
Scientific Research Director-Biology Cabinet



The dark blue line represents the asymmetry of each magnitude from Lean’s database with respect to the equilibrium magnitude, 1364.5 W/m^2. Dr. Lean's 2001 reconstruction (6) which considers the number of sunspots and proxies, shows symmetry with respect to the equilibrium magnitude from 1700 to 1880 AD, which means about 180 years. The asymmetry is negative after 1880, which means that the Solar Irradiance has been increasing since that date.

The red line represents the asymmetry of each magnitude from Svalgaard’s database (7) with respect to the equilibrium magnitude, 1364.5 W/m^2. Notice that the lapse for asymmetries from Svalgaard’s reconstruction of Total Solar Irradiance (TSI) is shorter than the asymmetries obtained from Lean’s database, and that the period it covers, from 1705 to 1825 AD, is about 120 years. This means that the solar irradiance, considering Svalgaard’s database (7), has been increasing since 1825, which is 25 years before the start of the industrial revolution.

The violet line is the correlation coefficient between Lean’s (6) and Svalgaard’s (7) reconstructions. Notice that the correlation is solid from 1940 to 2000. The strongest correlation corresponds to the period 2001-2007 because the data magnitudes were provided by satellites. The combination of both databases in one correlation coefficient indicates indirectly that the increase of solar irradiance started in 1870 AD.


The following graph combines the correlation coefficients between the asymmetries of solar irradiance from Lean’s reconstruction (6) with respect to the change of temperature and the asymmetries of solar irradiance from Svalgaard's reconstruction (7) with respect to the change of temperature:


Notice that the positive deviations from the standard are larger (above zero) than the negative deviations (below zero) from the standard. The graph drawn from Svalgaard's database (7) gives the impression that the Sun has been quite stable throughout the period it covers and has nothing to do with the load of energy absorbed by the surface. The deviation from average (violet horizontal band) is ample and encloses almost all amplitude magnitudes (red spots), and the negative amplitudes go no lower than -0.32 W/m^2, while the negative amplitudes from Lean’s database (6) goes down to -1.244 W/m^2. The divergence in Svalgaard’s database (7) is that he has dismissed the reconstructions derived from isotopes and other proxies for calibrating magnitudes. An explanation for ice ages from Svalgaard’s reconstruction (7) would rely on internal unknown effectors and drivers of climate without minimal connection with the Sun and/or other external sources.

Let’s find the asymmetries and the correlation coefficient from the databases of Lean and Svalgaar (7):