Correlation Between Total Solar Irradiance and Hematite Stained Grains During the Last 420 Years
By Nasif Nahle
Scientific Research Director of Biology Cabinet.

This article was ACCEPTED FOR PUBLICATION under the category DIDACTIC ARTICLE and it was subject to minor amendments.

  * The author is grateful to Dr. Jonathan M. Walsh for his kind assistance with the TSI extrapolation.
** Additional editing of this English text by TS.


Nahle, N. (2009). DIDACTIC ARTICLE: Correlation Between Total Solar Irradiance and Iron Stained Grains During the Last 420 years. Biology Cabinet. San Nicolás de los Garza, N. L., México. Obtained on (month) (day), (year) from


Biological processes and evolution of living beings are directly or indirectly affected by climate. (Sutton. 2000)

Biomes are distributed around the world according to prevailing climatic conditions at each biogeographic zone (Odum. 2006). Plants that succeed in warm and humid places encounter tremendous difficulties prospering in environments which are cold and dry. Species make migratory movements when climate changes become drastic in their original habitats. On the other hand, the evolutionary history of species has been determined mainly by pressures exerted by climate on their survival. (Jablonski et al. 1996)

Climate is continuously changing through time. We have records of climate changes throughout the geologic eras for periods of months, years, decades, centuries, millennia and for billions of years.

Direct measurements of climatic parameters began some 300 years ago, so instrumental measurements of climatic factors are not able to provide us with a long-term picture of changes in climate before the eighteenth century. For this reason, scientists often resort to documentary data provided by systems directly or indirectly affected by changes of environmental conditions, known as proxy variables.

There are proxies representing specific changes of determined environmental factors. For example, the concentration of aragonite, calcite and magnesium-calcite in fossil shells of diatoms, molluscs and foraminifera are analyzed to determine the environmental temperature. Other proxies are isotopes of determined elements; for example beryllium-10, Calcium-II and carbon-14, which are taken into account for calculating the intensity of solar irradiance or the temperature at an established epoch. (Kozdon et al. 2004)

For example, by simple calculation, 1 W/m^2 of solar energy incoming to Earth causes a change of temperature of 0.37 °C (Shaviv. 2004). From the reconstruction of Dr. Judith Lean (Lean et al. 2000) based on sunspot numbers and proxies, the change of TSI since 1610 AD up to 2000 AD was 3.293 W/m^2, which resulted in a change of temperature of 1.2 °C. In 1998, the deviation from the standard of total solar irradiance was 1.07 W/m^2, then the subsequent change of temperature due to this anomaly of TSI was 0.44 °C. The fluctuation of the Earth's temperature in 1998 was 0.51 °C; therefore, the solar irradiance effect on the Earth's temperature represents about 80% of the total fluctuation of temperature.

On the issue of total solar irradiance (TSI), we biologists tend to hesitate before serious obstacles because documented data goes back only four centuries, to the point in history when observers first began counting sunspots appearing on the visible disk of the Sun. We have reliable databases on TSI centred on the number of sunspots going back to 1610 AD.

Solar Irradiance (SI) is the main factor that affects the behaviour, evolution and distribution of living beings inhabiting the Earth (Odum. 2006). All the energy which sustains all living beings on Earth has been and is provided by the Sun (Sutton. 2000). Without the energy delivered by the Sun to Earth, life would not be possible on the planet. Therefore, it is especially important to know how small and large changes of the intensity of solar irradiance (ISI) have affected biosystems in the past and how those small or large changes of ISI might affect life on Earth in the future.

As for ISI and TSI, Beryllium-10 and Carbon-14 have proven to be excellent proxies for periods before the utilization of satellites for measuring solar variation. (White et al. 1997)

Objective of This Article

In 2001, Gerald Bond and colleagues discovered a correlation between quartz grains which had been stained with iron (Iron Stained Grains, or ISG) and the climatic conditions of the environment. The correlation from the ISG proxy that Bond found was negative, i.e. the higher the percentage of iron stained grains stacked up in a well-known geological sedimentary layer, the lower the temperature and humidity prevailing in that epoch.

Bond and colleagues attributed the staining of quartz grains to insolation and deduced that at higher insolation, the higher the percentage of ISG in geological layers. They were right, the intensity of the insolation, or the intensity of the incident solar radiation upon the surface, is indirectly linked to the number of iron stained quartz grains.

However, insolation is influenced by many factors; for example, cloudiness, angle of incidence of solar rays, Earth’s axial tilt, precession, translational orbit of the Earth (orbital radius), prevailing vegetation, etc. From that conclusion which had been identified also by Bond and colleagues, I wondered if there could be a way of demonstrating that insolation was also correlated directly to ISI more than to previously mentioned local variables. So the collection of databases on ISG, also known as hematite stained grains (HSG), and TSI constituted my fundamental task of assessing a possible correlation between the percentages of HSG and TSI.


I found two problems with TSI and HSG databases. The first problem consists of the total time covered by each database. HSG databases cover a period of 11550 years, while databases of TSI comprehend only the last 300 years in Svalgaard's database and the last 420 years in Lean's database. The second problem has to do with the incomplete computation of the proportion of HSG for the most recent period of 70 years. Bond's database reports only 2% of HSG, which is not the total percentage of hematite stained grains computed for the period mentioned.

The first problem was solved out by comparing instantaneous values of each database, so the period comprehended was long enough as to formulate a valid conclusion. I also compared the 70 years scale of Svalgaard's database with both HSG percentages and Stacked proxies.

I have solved the second problem, related to the incomplete computation of HSG for the recent period of 70 years, and have eliminated the period from my assessment. This means a lower degree of freedom; nevertheless, this is compensated by the resolution of the samples, each one representing the proportions of the population of HSG in every stratum, i.e. 0.5 cm/year. Take into account that as the size of the sample decreases, the correlation coefficient increases.

On this comparison, I considered the reconstructions of TSI, one made by Dr. Leif Svalgaard who based his reconstruction only on sunspots number (Svalgaard. 2008), and another TSI database calculated by Dr. Judith Lean (Lean et al. 2000). For the reconstruction of HSG, I made use of Dr. Gerald Bond’s databases published in 2005 (Bond et al. 2001). Lean’s TSI reconstruction includes both proxies and sunspots, so her database covers a period longer than the period covered in Svalgaard’s TSI reconstruction.

The next graph compares the instantaneous values of the complete databases of Dr. Bond on HSG, of Dr. Lean on TSI and of Dr. Svalgaard on TSI:

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The above graph shows positive correlations among the three databases. Notice the presence in the graph of a Medieval Global Warming of which the temperature fluctuation was higher than the temperature fluctuation that took place in the last century (i.e. along the red line for HSG from age 490 to age 350).


The next graph shows the average per each 70 years from Svalgaard’s TSI reconstruction plotted together with the percentages of HSG:


The graph shows a negative correlation between the 70 years TSI scale and the percentages of HSG.


In the next graph, I compared the stacked proxies — specifically, glass, HSG and detrended Carbon-14 — with Lean’s TSI reconstruction and Svalgaard’s TSI reconstruction for all the seven periods, comprehending 70 years each, covered by the longest-term TSI database (Lean’s reconstruction) and the corresponding-in-time HSG database:


The correlation among the three databases is positive, which means there is a direct correlation between the intensity of solar irradiance and the percentage of stacked proxies. The correlation coefficient between Lean's TSI reconstruction and HSG is very low.


In the next graph, I have plotted only the TSI and the HSG for the corresponding period covered by Lean’s and Svalgaard’s TSI databases and the corresponding period for Bond’s HSG:


The graph above shows a positive correlation between the TSI reconstructions and the percentage of Iron Stained Grains taken at various sites in the North Atlantic.


The next graph shows the correlation between the 70-years average of Svalgaard's TSI reconstruction and the stacked proxies’ database of Bond:


The graph above shows a negative correlation coefficient between the 70-years scale from Svalgaard's TSI reconstruction and Bond's Stacked Proxies database.


Correlation Coefficients

  • The correlation coefficient on Lean’s TSI reconstruction and Bond’s HSG database is -0.15.

  • The correlation coefficient on Svalgaard’s TSI reconstruction and Bond’s HSG database is 0.99.

  • The correlation coefficient on Lean’s TSI reconstruction and Bond’s database of stacked proxies is -0.17.

  • The correlation coefficient on Svalgaard’s TSI reconstruction and Bond’s database of stacked proxies is 0.4.

  • The correlation coefficient between a 70-years scale from Svalgaard’s TSI reconstruction and Bond’s database on stacked proxies is -0.34.

  • The correlation coefficient between a 70-years scale from Svalgaard’s TSI reconstruction and Bond’s database on HSG is -0.55.


Extrapolation of Data

The more extensive database is Lean's reconstruction of the intensity of total irradiance which comprehends about 420 years. For the next graph, I extrapolated the Total Solar Irradiance from the proportion of Iron Stained Grains. Given that the correlation between ISG and TSI is logarithmic, I have used the next formula:

TSI = 2.052 [ln(ISG)] + 1361.5 W/m^2

For example, the sedimentary layer for the period which corresponds to 7000 years ago contains a proportion of iron stained grains of 7%. Introducing magnitudes, we have:

TSI = 2.052 [ln(7)] + 1361.5 = 1365.49 W/m^2

Comparing the intensity of the SI from 7000 years ago with the modern satellite database, we had a similar solar activity in 1975.


The resolution of the proportions of ISG is 20 years; consequently, the resolution of TSI is also 20 years for periods previous to 1700 AD.

The extrapolation of the TSI based on the proportion of HSG clearly illustrates that the Total Solar Irradiance (TSI) has been declining during the Holocene. The Holocene Optimum is visibly delineated by a proportion of Iron Stained Grains (HSG) much higher than for other periods before and after the Holocene Optimum. There is no doubt about the occurrence of the Holocene Optimum.


Arguments and Conclusion

The correlation between TSI reconstructions and the HSG database allows us to deduce that there is an influence of the Intensity of Solar Irradiance on the rate of staining of grains by iron. Given that the staining of grains by iron depends also on the environmental temperature and relative humidity, we are able to conclude that the climate changes which propitiated the staining of grains by iron were caused by changes of solar irradiance. This is the best connection we can infer from the correlation coefficients.

The low correlation coefficient for TSI reconstructions and the stacked proxies database shows that there are some proxies which are affected more by local environmental conditions than by the intensity of solar irradiance.

The correlation coefficient for Svalgaard’s magnitudes of TSI shows an inverse correlation with respect to the population of iron stained grains accumulated through periods of 70 to 100 years. The correlation coefficient is -0.55.

The period comprehended by the HSG database is long enough to conclude that this kind of proxy is highly suitable for obtaining approximate TSI values for ages before the start of satellite technology and direct observations of sunspots. Notice the high correlation between the total solar irradiance and the proportion of hematite stained grains, which is almost 1.00; nevertheless, the low degree of freedom does not allow us to conclude a definite so high correlation. If the six non-iterated points are included, the correlation coefficient drops to 0.63, which is also a feasible correlation.

The iron stained grains index is a scientific methodology for assessing the climate prevailing in the geological timescale and stands in opposition to the carbon dioxide concentration proxy for Earth’s temperatures—the ambiguity of which has been clearly demonstrated by the levels of atmospheric carbon dioxide continuing to increase long after the occurrence of climate warming and so does not correspond with climatic changes.

There is a weak correlation (-0.34) between the Stacked Proxies of Bond et al and the 70-years scale of TSI reconstruction by Svalgaard. This constitutes evidence of an indirect correlation between the percentage of stacked iron stained grains, glass and carbon-14 proxies and the intensity of solar irradiance, although it is very low. It is quite clear that Svalgaard's database on Total Solar Irradiance is incomplete and highly biased, while Lean's database on TSI is more congruent with reality because Judith Lean included all the available results from proxies besides the sunspots number.

Iron stained grains, glass and carbon-14 are proxies whose response to solar irradiance is consistent and relatively regular through the geological eras. These proxies, if stacked, can be used to calculate the total solar irradiance striking the upper layers of the atmosphere.


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The Sun Today. Image: SOHO; 18 June 2009