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Correlation analysis of solar constant, solar activity and cosmic ray

April 2017
Journal of Physics Conference Series 817(1):012045

DOI:10.1088/1742-6596/817/1/012045

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National Agency for Research and Innovation The Republic of Indonesia

Actually, solar constant is not constant but fluctuated by ±1.5% of their average value. Solar constant indicates that the value is not constant but varies with time. Such variation is correlated with solar activity and cosmic ray. Correlation analysis shows a strong correlation between solar activity and cosmic ray and between solar activity and solar constant. Solar activity indicates by sunspot number. Correlations between solar constant variations and sunspot number variations were found to be higher than ones between variations in cosmic ray and solar constant. It was also found a positive correlation between solar constant and sunspot number, with correlation coefficient about +0.77/month and +0.95/year. In other hand, negative correlation between solar constant and cosmic ray flux i.e. −0.50/month and −0.62/year were found for monthly and yearly data respectively. A similar result was also found for the relationship between solar activity and cosmic ray flux with a negative correlation, i.e. −0.61/month and −0.69/year. When solar activities decrease, the clouds cover rate increase due to secondary ions produced by cosmic rays. The increase in the cloud cover rate causes the decrease in solar constant value and solar radiation on the earth's surface. Solar constant plays an important role in the planning and technical analysis of equipment utilizing solar energy.

. Correlation between solar constant, sunspot number and cosmic rays.

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Correlation analysis of solar constant, solar activity

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Correlation analysis of solar constant, solar activity and

cosmic ray

Y S Utomo

Research Center for Electrical Power and Mechatronics, Indonesian Institute of Sciences, Jl.

Sangkuriang, Kompleks LIPI, Bandung 40135, West Java, Indonesia

E-mail: yustomo@gmail.com

Abstract. Actually, solar constant is not constant but fluctuated by ±1.5% of their average

value. Solar constant indicates that the value is not constant but varies with time. Such

variation is correlated with solar activity and cosmic ray. Correlation analysis shows a strong

correlation between solar activity and cosmic ray and between solar activity and solar constant.

Solar activity indicates by sunspot number. Correlations between solar constant variations and

sunspot number variations were found to be higher than ones between variations in cosmic ray

and solar constant. It was also found a positive correlation between solar constant and sunspot

number, with correlation coefficient about 0.77/month and 0.95/year. In other hand, negative

correlation between solar constant and cosmic ray flux i.e. 0.50/month and 0.62/year were

found for monthly and yearly data respectively. A similar result was also found for the

relationship between solar activity and cosmic ray flux with a negative correlation, i.e.

0.61/month and 0.69/year. When solar activities decrease, the clouds cover rate increase due

to secondary ions produced by cosmic rays. The increase in the cloud cover rate causes the

decrease in solar constant value and solar radiation on the earth’s surface. Solar constant plays

an important role in the planning and technical analysis of equipment utilizing solar energy.

1. Introduction

The sun is the main energy source for the earth and its environment. Through the emitted energy, the

sun acted as a climate controller is very important to the air movement (atmospheric circulation) and

ocean currents (ocean circulation) as well as to bio-instruments that processes photosynthesis in the

biosphere. Therefore, the climate also depends on variations in the flux of solar energy received by the

earth's surface. Variation in the solar energy flux is caused by variations in solar activity cycle. Thus

the climate is a manifestation of how solar radiation is absorbed, redistributed by the atmosphere, land

and oceans, and ultimately radiated back into space. Every variation of solar energy received at the

earth's surface and reradiated by the earth into space will have a direct impact on climate change on

Earth.

When reaching the upper limit of the atmosphere, the solar radiation is not actually attenuated but

when it passes through the layers of the Earth's atmosphere solar radiation it will be scattered and

absorbed by molecules and particles of dust clouds. Thus, only a small fraction of the solar radiation

reaches the earth. Radiation flux before attenuation by the atmosphere at an average distance of the

Sun - Earth (1.5  108 km) is called the solar constant which is defined as the total amount of solar

radiation of all wavelengths, which falls on a unit area of the surface normal to the Sun - Earth line on

a clear sky condition [1].

2nd International Symposium on Frontier of Applied Physics (ISFAP 2016) IOP Publishing

IOP Conf. Series: Journal of Physics: Conf. Series 817(2017) 012045 doi:10.1088/1742-6596/817/1/012045

International Conference on Recent Trends in Physics 2016 (ICRTP2016) IOP Publishing

Journal of Physics: Conference Series 755 (2016) 011001 doi:10.1088/1742-6596/755/1/011001

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution

of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Published under licence by IOP Publishing Ltd

Solar activity was also influenced by variations in solar irradiance received at the earth's surface.

Simulation of solar irradiance variability over 113 years (1880-1993) showed a variation of 0.5 %.

While satellite observation during one cycle showed a variation of 0.1 % between the minimum and

maximum activity [2, 3]. Determination of the solar constant and its variations over time is needed in

climate research [4]. Solar constant plays an important role in the planning and technical analysis of

equipment utilizing solar energy [5].

The results of this study are expected to use as an input and consideration in the planning and

technical analysis of renewable energy, in particular the utilization of solar energy will be intensified

and expanded in line with increasing energy needs. The utilization of solar energy is one step in the

development of energy diversification. However its field operations should be supported with

adequate information about the potential and availability of solar energy at a given location. By

knowing the potential and availability of solar energy, then the site selection mistakes can be avoided.

2. Basic Theory

2.1. Solar Constant

Solar constant is defined as the total amount of solar radiation of all wavelengths, which falls on a unit

area of the surface normal to the sun - earth line on a clear sky condition [1]. Until now, the absolute

value of the solar constant uncertainty is both theoretically and observationally high enough.

Determination of the solar constant has experienced a long history, has began by Smithsonian Institute

in the early 20th century [6]. Solar constant measurement data obtained at that time were large, but the

results did not provide a convincing value of solar constant [7].

The average value of solar constant ranges from 1364.61 to 1371.67 Wm-2. Nimbus-7/ERB

measurement is differed by 4.31 to 6.86 Wm-2 compared to the three other measurement results. It is

caused by the problem of directing the telescope, correction calculation the average distance of the

earth-sun and the sensitivity of instruments. Sensor Nimbus-7/ERB has an accuracy of 0.5 Wm-2 [8].

2.2. Solar Activity

Fluctuation of turbulence in the surface of the sun is related to the term of what we called as a solar

activity. The combination of radiation activity and magnetic activity plays a major role in the cycle of

solar activity. One indicator of solar activity is the appearance of black spots on the sun's surface

called sunspots. The numbers of sunspots indicate the activity level of the sun. Variations in solar

activity can affect the geomagnetic properties of ionosphere and stratosphere layer. Rapid changes in

the region of UV radiation and X-rays due to solar activity can affect the ionosphere and the

atmosphere through a system of coupling the magnetosphere-ionosphere-atmosphere [9, 10].

Solar activity was also influenced by variations in solar irradiance received at the Earth's surface.

Simulation of solar irradiance variability over 113 years (1880-1993) showed a variation of 0.5%,

while satellite observation during one cycle showed a variation of 0.1% between the minimum and

maximum activity [2, 3]. Determination of the solar constant and its variations over time is needed in

climate research [4]. Solar constant plays an important role in the planning and technical analysis of

equipment utilizing solar energy [5].

2.3. Cosmic Ray Flux

Cosmic rays are energetic particles originating from space and spread until it reaches the Earth's

atmosphere equal in all directions. The composition of cosmic rays consists of protons (90%), a

helium nucleus (9%) and electrons (1%). Cosmic rays or the full name of Galactic Cosmic Rays

(GCR) has a high energy level in the range of 300 MeV to 10 GeV. The main cause modulation of the

cosmic rays is not the activity level of the sun, but the variation in the magnitude of the solar wind.

The amount of solar wind is not constant, but varies with changes in solar activity during the 11

annual cycles [11].

2nd International Symposium on Frontier of Applied Physics (ISFAP 2016) IOP Publishing

IOP Conf. Series: Journal of Physics: Conf. Series 817(2017) 012045 doi:10.1088/1742-6596/817/1/012045

Cosmic ray particles that had such high energy enter the Earth's atmosphere at speeds approaching

3  108 m.s-1. With this speed and high energy, the cosmic ray particles are possible to collide with

molecules of atmospheric when cosmic rays entering Earth's atmosphere. This collision is able to

break the composition of the molecules in the atmosphere and induced the formation of secondary ions

which serve as condensation nuclei to increase the formation rate of high clouds (at an altitude of 12-

15 km). Because cosmic rays have an impact on the formation rate of cloud which further affects the

amount of solar radiation to reach the Earth's surface, the contribution of cosmic rays on the Earth's

climate cannot be ignored [11].

2.4. Correlation between Solar Constant, Solar Activity and Cosmic Ray Flux

Solar Constant is actually not constant but fluctuated by ±1.5% of their average value [1]. Direct

observation via satellite indicates the same that the solar constant value is not constant but varies with

time. The variation of solar constant that occurs as a result of changes in the form of solar activity such

as sunspots dark or faculae bright in the Sun's surface [4, 10].

Solar activities have close correlation with the solar constant whose inconstant values. Therefore,

in addition the sunspots, faculae are also an important source of solar constant variations [10]. The

amount of solar energy emitted from the entire surface of the Sun is not the same, but varies with time.

Hoyt and Kyle studies (1990) indicated that the solar constant will decrease with an increase in the

sunspot area and will increase with the presence of the excellent faculae area on the solar disc. Based

on Lean’s research (1991) solar constant value at the time of minimum solar activity in 1986 is about

1367±3 Wm-2, and showed a variation of 0.1% [2, 8].

3. Methodology

To determine whether there is a relationship between solar constant and solar activity, in this study the

effect of solar activity (with indicators of the sunspot numbers) on the solar constant were analyzed

using data with a 39-year period (1978-2016). Daily data for global solar constant were obtained from

ftp://ftp.ngdc.noaa.gov/STP/solar_data/solar_irradiance/composite_42_65_1611.dat. Daily data of

solar constant were processed into monthly average data, and then compared to monthly average data

of sunspot numbers, which were obtained from

ftp://ftp.ngdc.noaa.gov/STP/solar_data/sunspot_numbers/ridaily.plt with a 39-year period (1978-

2016). These data were used in the analysis of solar activity’s influence on the solar constant variation.

Monthly Cosmic rays data (Galactic Cosmic Rays - GCR data) were obtained from

ftp://ftp.ngdc.noaa.gov/STP/solar_data/cosmic_rays/huancayo.dat with a 39-year period (1978-2016).

Furthermore, correlation analysis using a linear regression to determine the degree of influence of

solar activity on the solar constant was employed and the effect of cosmic rays on the solar constant

variation and its relation to solar activity was studied. In correlation analysis, it can be estimated a

sample correlation coefficient which is denoted by r, ranges between 1 and 1. This coefficient

quantifies the direction and strength of the linear association between the two variables. The

correlation between two variables can be positive or negative. The sign of the correlation coefficient

indicates the direction of the association. The magnitude of the correlation coefficient indicates the

strength of the association.

4. Analysis and discussion

4.1. Correlation analysis

As already known, that the value of the solar constant is not constant, but varies with time despite

minor amendments. The change might be related to solar activity and cosmic rays. Therefore, all three

parameters i.e. solar constant, solar activity (which is indicated by the number of sunspots) and cosmic

rays) have a relationship or correlation between one parameter with another. Correlation analysis was

done by calculating the correlation coefficient and the results are summarized in Table 1.

2nd International Symposium on Frontier of Applied Physics (ISFAP 2016) IOP Publishing

IOP Conf. Series: Journal of Physics: Conf. Series 817(2017) 012045 doi:10.1088/1742-6596/817/1/012045

Table 1 shows the correlation coefficient both per month and year between solar constant, sunspot

number and cosmic rays. The values are all above 0.50 which can be categorized as high value. The

high correlation coefficient indicates that cosmic rays and sunspot numbers have strong relationships

with the solar constant. There are two types of correlation between the solar constant with both

parameters, namely the positive and negative correlations. The correlation coefficient between the

solar constant and sunspot numbers are very high with positive number, i.e. 0.77/month and

0.95/year. The correlation coefficient between the solar constant and cosmic rays is high with

negative number, i.e. 0.50/month and 0.62/year, while the correlation coefficient between sunspots

number and cosmic rays were 0.61/month and 0.69/year. Therefore, if the value of cosmic rays

increases then solar activity decreases, indicated by the reduction in sunspot numbers and the solar

constant value.

Table 1. Correlation between solar constant, sunspot number and cosmic rays.

Parameter Relation

Correlation coefficient - r

per month

per year

Solar Constant – Sunspot Number

0.77

0.95

Solar Constant – Cosmic Rays

0.50

0.62

Sunspot Number – Cosmic Rays

0.61

0.69

The influence of solar activity on the solar constant variation has been proposed by previous

researcher [2, 3]. A previous researcher simulated the variability of solar irradiance over 113 years

(1880-1993) and found the variation of solar constant at 0.5% [2], while another researcher found a

variation of 0.1% based on satellite observations during a solar cycle, i.e. the 21th cycle (1976 to 1986)

[3]. Determination of the absolute value of the solar constant and its variations over time is needed in

climate research. Solar constant plays an important role in the planning and technical analysis of

equipment utilizing solar energy. Another researcher reported a correlation between temperature and

global cloud coverage with the cosmic rays [12]. The influence of cosmic rays on cloud coverage,

could also affect the solar constant [4, 5].

4.2. Influence of solar activity on the solar constant

For purposes of analysis influence of solar activity on the solar constant, the daily data of solar

constant and solar activity in the period of November 1978 to November 2016 were used. Solar

activity is indicated by the number of sunspots.

Figure 1 shows the pattern of the yearly average value of solar constant is similar with the pattern

of the yearly average number of sunspots. The figure also shows the 21th solar cycle (1976-1986) and

the 22th cycle (1987-1997). In the 21th solar cycle, the yearly average value of the solar constant

reached its maximum value of 1366.56 Wm-2 in 1979. This coincided with the peak period of 21thsolar

activity cycle which reached the maximum yearly average sunspot number of 155.3. Start from 1980,

the value of the solar constant was gradually reduced following the reduction in solar activity. Solar

constant value reached minimum when the sun was quiet in 1985-1986 with the average value of

1365.54 Wm-2. The lowest value occurred in 1986, i.e. 1365.54 Wm-2 in conjunction with solar

activity reached a minimum value. At the beginning of 22th solar cycle (19871997), a constant value

increases exponentially with the increment of solar activity. The sun reaches its maximum solar

constant value in 1989 with the amount of 1365.39 Wm-2 in conjunction with solar activity reached its

maximum with yearly average sunspot number of 157.8. Solar constant value remained high during

the years of 1989-1992 with small variations from year to year ranged from 0.04 to 0.32 Wm-2. When

the 23th solar cycle began in 1998, the value of the solar constant grew significantly following the

increase in solar activity which was peaked in 2000. The yearly solar constant values were ranging

from 1365.43 to 1366.60 Wm-2 or varied by 0.09% against the average value of 1366.01 Wm-2 [10,

1315].

2nd International Symposium on Frontier of Applied Physics (ISFAP 2016) IOP Publishing

IOP Conf. Series: Journal of Physics: Conf. Series 817(2017) 012045 doi:10.1088/1742-6596/817/1/012045

Figure 1. Yearly average of solar constant and sunspot number.

4.3. Influence analysis of cosmic ray on the solar constant

For the influence analysis of cosmic rays on the solar constant, the daily average cosmic ray data of

Huancayo, Peru (12o S, 75o W) and solar constant data in the period of November 1978 to November

2016 were used. Huancayo was chosen with consideration that it has the lowest latitude among several

other locations on Earth. Figure 2 shows the effect of cosmic rays on the solar constant.

Figure 2 shows yearly averages of solar constant and cosmic rays which has the same pattern but in

the opposite direction. Yearly average of solar constant variation cycle was seemed to follow the cycle

of the yearly average variation of cosmic rays in the opposite direction. When cosmic rays increased,

the solar constant actually declined. As mentioned before, cosmic ray particles that have high energy

(10 GeV) enters the Earth's atmosphere at speed approaching to 3  108 ms-1. With its high speed and

high energy, it is possible to collide with molecules of atmospheric and to break the composition of the

molecules in the atmosphere forming the secondary ions which acts as condensation nuclei. The

increase in the formation rate of cloud would affect the decrease in the intensity of solar radiation

reaching the Earth's surface. The relationship between cosmic rays and solar constant is a "opposite"

relationship because of the negative correlation type (r < 0). The phenomenon of "opposite" is in a

good agreement with the result by Svensmark (1997) who found a correlation between temperature

and global cloud coverage with the cosmic rays [12].

Figure 2. Yearly average of solar constant and cosmic ray.

4.4. Influence analysis of solar activity on the cosmic ray

For the influence analysis of the of solar activity on cosmic rays, a daily average of cosmic rays and

sunspot numbers data during the period November 1978 to November 2016 were used. Figure 3

shows the effect of solar activity on cosmic rays.

In figure 3, variation of yearly average cosmic rays is in opposite to the pattern of sunspot numbers.

When solar activity is maximum (indicated by the high number of sunspots), cosmic rays is minimum.

2nd International Symposium on Frontier of Applied Physics (ISFAP 2016) IOP Publishing

IOP Conf. Series: Journal of Physics: Conf. Series 817(2017) 012045 doi:10.1088/1742-6596/817/1/012045

This phenomenon of "opposites" is in accordance with what is stated by Svensmark (1997) who found

a correlation between temperature and global cloud coverage with the cosmic rays. Physically,

particles of cosmic rays when it enters the Earth's upper atmosphere are suffered from modulation

caused by two things, namely the solar wind and Earth's magnetic field. The solar wind affects cosmic

ray particles to decelerate. According to Yamada (1998), the size of the solar wind is not constant, but

varies with changes in solar activity during the 11st annual cycles. The relationship between solar

activity and cosmic rays is an "opposite" relationship because of negative correlation type (r < 0). The

solar activity influenced on cosmic rays has an impact on the cloud formation rate [11, 12].

Figure 3. Yearly average of sunspot number and cosmic ray.

5. Conclusion

Correlation analysis showed that there was a relationship between the variation of the solar constant

with the variation in solar activity and the flux of cosmic rays. A positive correlation (r = 0.95) was

found between the solar constant and solar activity, a negative correlation (r = 0.62) was for the

relationship between the solar constant and cosmic rays, and also a negative correlation (r = 0.69)

between solar activity and cosmic rays.

The results of this study are expected to be used in the consideration in the work of planning and

technical analysis of renewable energy, particularly in the utilization of solar energy that will be

intensified and expanded in line with increasing energy needs. The utilization of solar energy is one

step in the development of energy diversification, but its application should be supported with

adequate information about the potential and availability of solar energy at a given location. By

knowing the potential and availability of solar energy, mistake in choosing the site selection can be

avoided.

Acknowledgments

The author gratefully acknowledgment the support of the Research Center for Electrical Power and

Mechatronics, Indonesian Institute of Science (LIPI) for funded and has given encouragement and

opportunity to work in the field of conversion and conservation energy research.

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2nd International Symposium on Frontier of Applied Physics (ISFAP 2016) IOP Publishing

IOP Conf. Series: Journal of Physics: Conf. Series 817(2017) 012045 doi:10.1088/1742-6596/817/1/012045

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2nd International Symposium on Frontier of Applied Physics (ISFAP 2016) IOP Publishing

IOP Conf. Series: Journal of Physics: Conf. Series 817(2017) 012045 doi:10.1088/1742-6596/817/1/012045

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The X-ray sources of the universe are the extraterrestrial in nature which emit X-ray photons. The closest strong X-ray source is the Sun, which is followed by various compact sources such as neutron stars, black holes, the Crab pulsar, etc. In this paper, we analyze the data received from several low-cost lightweight meteorological balloon-borne missions launched by the Indian Centre for Space Physics. Our main interest is to study the variation of the vertical intensity of secondary cosmic rays, the detection of strong X-ray sources, and their spectra in the energy band of ∼ 10 − 80 keV during the complete flights. Due to the lack of an onboard pointing system, low exposure time, achieving a maximum altitude of only ∼ 42 km, and freely rotating the payload about its axis, we modeled the background radiation flux for the X-ray detector using physical assumptions. We also present the source detection method, observation of the pulsation of the Crab (∼ 33 Hz), and spectra of some sources such as the quiet Sun and the Crab pulsar.

Study of secondary cosmic rays using small stratospheric balloon missions

Article

Jul 2023
J ASTROPHYS ASTRON

Secondary cosmic rays are produced from the interaction of primary cosmic rays, which are high-energy (

\sim

GeV) particles originating from outer space, primarily, protons (

\sim

89%) and alpha particles (

\sim

10%) with atoms (mainly nitrogen and hydrogen) present in our Earth’s atmosphere. Such rays are dependent on solar activity and geomagnetic latitude through magnetic rigidity and are found to be modulated by these factors. For analysis of secondary cosmic ray data, we use the Indian Centre for Space Physics’s data obtained through small stratospheric balloon-borne experiments. In the present paper, we have measured the secondary cosmic ray intensity at low geomagnetic latitude of

\sim

14.50

^\circ

N in the low energy range of 25–60 keV from the ground to 30 km altitude for different detectors used in various balloon missions because such missions are almost detecting the X-ray sources above 30 km till 42 km. We also calculated background flux of the detector with the help of some justifiable physical assumptions, secondary cosmic gamma-ray component measurements, and assumed internal background functions. Finally, using our data of 2012–2019, which falls in the 24th solar cycle, we have shown that there is a clear anti-correlation between cosmic ray intensity at Regener–Pfotzer maximum and the solar activity.

Spatio-temporal dynamic clustering modeling for solar irradiance resource assessment

Article

Sep 2022
RENEW ENERG

Nowadays, with the development of international policies and agreements to promote the integration of renewable energy sources, mainly solar and wind, modeling the solar resource by including the spatio-temporal variability is crucial to determine future PV power plant locations and estimate potential power generation performances. However, contributions involving long–term periods and different time windows to explore such potential solar resource variability are generally scarce. Under this framework, the present paper proposes a methodology focused on characterizing and clustering the spatio–temporal solar resource variability through the global horizontal irradiance analysis. Hierarchical clustering technique is firstly used to classify the spatial data. Different time windows —from short-term to long-term data— can be subsequently evaluated by using various sources of information. The Spanish territory is selected as case study, considering 22–year period data (1999–2020) and 1,936,917 observations from online satellite database. Spatial variability and geographical clustering differences are discussed and compared depending on the selected time windows, identifying relevant spatial variations for some specific months. Additionally, some years present more variability as well, in line with the sunspot peak of the solar cycles. The proposed approach gives an alternative comprehensive spatio–temporal clustering and characterization of GHI evolution, providing a suitable methodology to help the current European sustainable energy transition.

Spatio-Temporal Dynamic Clustering Modeling for Solar Irradiance Resource Assessment

Article

Jan 2022

Solar Proton Activity over the Solar Cycle 24 and Associated Space Radiation Doses

Chapter

Full-text available

Apr 2022

Wellen Rukundo

The least number of proton events and ground-level enhancements was recorded in the solar cycle 24 which corresponds with the least smoothed sunspot number compared to the last three previous solar cycles. This was attributed to the weak sun’s polar field and decreasing strength of the interplanetary magnetic field at the start of the solar cycle. The majority contribution to background radiation dose within our earth’s atmosphere is galactic cosmic rays and trapped particles in the Van Allen Belts. However, solar proton events cause sudden spikes in radiation doses, and this depends on the fluence and energy spectra of the events. While these doses are least detected in the lower atmosphere, they have significant radiation damage to spacecraft electronic components and astronauts on long space missions and at higher atmospheric altitudes. Therefore, the prediction of such events and estimation of their effective radiation damage is an important consideration for planning long space missions and spacecraft design materials.

Total Solar Irradiance Trend During Solar Cycles 21 and 22

Article

Full-text available

Oct 1997

Richard C Willson

Results from Active Cavity Radiometer Irradiance Monitor (ACRIM) experiments show an upward trend in total solar irradiance of 0.036 percent per decade between the minima of solar cycles 21 and 22. The trend follows the increasing solar activity of recent decades and, if sustained, could raise global temperatures. Trends of total solar irradiance near this rate have been implicated as causal factors in climate change on century to millennial time scales. Total solar irradiance (TSI), a measure of the climate-driving radiative energy received by Earth from the sun, has been monitored by satellite experiments with adequate precision to detect intrinsic solar variability since 1978 (1). A direct association between solar magnetic activity and climate has been inferred from historical records of climate, solar activity indicators, and time series analyses of cosmogenic isotopes (2, 3). Data from the first ACRIM experiment (ACRIM I) on the Solar Maximum Mission (SMM) showed that solar activity during a solar cycle was directly related to TSI. This was confirmed by the Nimbus 7 Earth Radiation Budget (ERB) and Earth Radiation Budget Satellite (ERBS) experiments during solar cycles 21 and 22 (4-6). On the basis of this result, it has been suggested that the a TSI decrease during the Maunder Minimum of solar activity (1650-1715) may have been a contributing factor to the Little Ice Age climate anomaly (2, 7). The ERB, ACRIM I, ERBS, and Upper Atmosphere Research Satellite (UARS) ACRIM II (1) experiments have provided the overlapping, complementary data essential for establishing and sustaining a precision, long-term TSI database (Fig. 1) (8). Of these experiments, only ACRIM I and II are able to calibrate degradation of their monitoring sensors (9). The larger uncertainties of the ERB and ERBS are the result of their limited observing opportunities and their inability to calibrate sensor degradation (10).

The total solar radiation time series simulation in Athens, using neural networks

Article

Full-text available

Aug 2000

The present study describes a neural network approach for modeling and making short-term predictions on the total solar radiation time series. The future hourly values of total solar radiation for several years are predicted, by extracting knowledge from their past values, using feedforward backpropagation neural networks. The results are tested using various sets of non training measurements, the findings are very encouraging and the model is found able to simulate the future values of total solar radiation time series based on their past values. “Multi-lag” output predictions are performed using the predicted values to the input database in order to model future total solar radiation values with sufficient accuracy. Furthermore, an autoregressive model is developed for analysing and representing the total solar radiation time series. The predicted values of solar radiation are compared with the observed data series and it was found that the neural network approach leads to better predictions than the AR model.

A stochastic view of the solar modulation phenomena of cosmic rays

Article

Jul 1998
GEOPHYS RES LETT

We report on a numerical method for solving the Fokker-Planck equation (FPE) which describes the solar modulation of cosmic rays using Ito^'s stochastic differential equations (SDEs) and discuss on it's power and profound implications not easily attainable by standard methods. It is shown how easily the modulated energy spectrum of cosmic rays is calculated from the interstellar spectrum utilizing the momentum distribution function obtained by SDE method for particles with a fixed momentum of various values at 1 AU. The resultant modulated spectra are compared with the results by the standard numerical technique using the Crank-Nicholson method to demonstrate the validity of our method.

Variability of the solar 'constant' on time scales of minutes to years

Article

Jan 1987

Claus Fröhlich

The power of the irradiance variability spectrum from about 70 nHz (150 days) to 5 mHz (3.3 min) can be divided into three major domains with the following characteristics: (1) From 70 nHz to 2 muHz (5.8 - 150 days) the spectrum is dominated by solar activity, the power of which changes during the course of the solar cycle by up to 1 order of magnitude. (2) From 2 to 20 muHz (14 hours to 5.8 days) the spectrum follows a 1/nu2 law, which may be due to g modes. (3) From 20 muHz to 5 mHz (14 hours to 3.3 min) the spectrum follows a 1/nu law, with a broad peak around 5 min which is due to p modes yielding amplitudes of several ppm. As to the long-term changes, trends of the order of 0.02% per year seem to exist. The question whether the up and down trends with a peak around 1980 belong to an oscillatory modulation of the solar output can only be answered in the future.

Variations in the Sun's radiative output

Article

Nov 1991

Judith Lean

During the past decade, satellite instruments have measured, simultaneously, both the sun's spectrally integrated radiative output and its ultraviolet spectrum. These data have been analyzed in terms of their relationships to ground-based observations that characterize different aspects of the sun's 11-year activity cycle, allowing estimates of solar radiative output variations over time-scales from days to decades and interpretations of these variations in the broader context of the variable sun.

Variation of cosmic ray ﬂux and global cloud coverage—a missing link in solar-climate relationships

Article

Jul 1997
J ATMOS SOL-TERR PHY

In the search for a physical mechanism that could account for reported correlations between solar activity parameters and climate, we have investigated the global cloud cover observed by satellites. We find that the observed variation of 3–4% of the global cloud cover during the recent solar cycle is strongly correlated with the cosmic ray flux. This, in turn, is inversely correlated with the solar activity. The effect is larger at higher latitudes in agreement with the shielding effect of the Earth's magnetic field on high-energy charged particles. The observed systematic variation in cloud cover will have a significant effect on the incoming solar radiation and may, therefore, provide a possible explanation of the tropospheric and stratospheric 10–12 year oscillations which have been reported. The above relation between cosmic ray flux and cloud cover should also be of importance in an explanation of the correlation between solar cycle length and global temperature, that has been found.

The interplanetary and solar causes of geomagnetic activity

Article

Feb 1990
PLANET SPACE SCI

Recent data on the interplanetary and solar causes of geomagnetic activity are reviewed. Emphasis is given to the interplanetary source of southward Bz for magnetic storms, the solar sources of magnetic storms, and the roles of 'great' solar flares, substorms, the magnetopause boundary layer, and the dayside aurora in causing geomagnetic activity. A background information for interplanetary phenomena is also provided.

Solar Constant: First Direct Measurements

Article

Sep 1968

The solar constant was directly measured from an altitude of about 82 kilometers-apparently the first such determination. The total solar intensity was 136.1 milliwatts per square centimeter, or 1.952 calories per square centimeter, per minute-about 2.5 percent less than Johnson's derived value. Energy in the ultraviolet and visible regions (for λ less than 607 nanometers) was 7.0 percent less than that obtained by integration over Johnson'Scurve; for integral flux of λ greater than 607 nanometers there was almost perfect agreement. Seven supporting series of measurements from lower altitudes agreed extremely well with these results after correction for atmospheric extinction.

An alternative derivation of the Nimbus 7 total solar irradiance variations

Article

Sep 1990

Nimbus 7 solar irradiance values have been made available to the scientific community through the open literature (e.g., Hickey et al., 1988) and through NASA data centers. A comparison of these measurements to the Solar Maximum Mission/Active Cavity Radiometer Irradiance Monitor (SSM/ACRIM) time series indicated differences which might be caused in part by the method of converting the Nimbus 7 raw data counts to solar irradiance values. In an effort to see if the derivation of the solar irradiance could be improved, the raw counts were extracted from the tapes and analyzed to see how a new algorithm could be constructed. The basic form of the calibration remains the same as in the previous solar irradiance derivations. However, the input values to the equation differ from what was used before. In particular, improved values of the Earth-sun distance are incorporated and new temperature sensitivities were derived. Several problems with the instrument were uncovered which previously had not been noticed. The sun did not appear to cross the center of field of the radiometer but was systematically off by 1.5 to 2.5 degrees. The analog to digital convertor changed its properties in July 1980. The gain of the electronics apparently increased by 0.03 percent in September 1987. Applying these and other changes in the processing, the day to day variations appear much more like the SMM observations. In fact, the Nimbus 7 observations are sufficiently stable that a problem with the SSM observations in the spin mode period of 1981 to 1984 can be detected when the two time series are compared.