It was recently found that spectral solar incident flux (SIF) as
a function of the ultraviolet wavelengths exhibits

As is well known, electromagnetic radiation is continuously emitted by every physical body. This radiation is described by Planck's law near thermodynamic equilibrium at a definite temperature. There is a positive correlation between the temperature of an emitting body and the Planck radiation at every wavelength. As the temperature of an emitting surface increases, the maximum wavelength of the emitted radiation increases too. Smith and Gottlieb (1974) re-examined the subject of photon solar flux and its variations vs. wavelength and showed that variations in the extreme ultraviolet (UV) spectrum and in the X-ray of solar flux may reach high orders of magnitude causing significant changes in the Earth's ionosphere, especially during major solar flares (Kondratyev et al., 1995; Kondratyev and Varotsos, 1996; Ziemke et al., 2000; Varotsos et al., 2001; Melnikova, 2009; Tzanis et al., 2009; Xue et al., 2011; Cracknell et al., 2014).

Solanki and Unruh (1998) proposed simple models of the total solar irradiance variations vs. wavelength showing that variations on solar flux are mainly caused by magnetic fields at the solar surface. Solar observations may be reproduced by a model of three parameters: the quiet Sun, a facular component and the temperature stratification of sunspots.

Tobiska et al. (2000) developed a forecasting solar irradiance model, called
SOLAR2000, covering the spectral range of 1–1 000 000

Very recently, Varotsos et al. (2013a, b) suggested the existence of strong
persistent long-range correlations in spectral space of the solar flux
fluctuations for UV wavelengths in the range 278–400

However, Varotsos et al. (2013a) tried to formulate the above-shown finding,
i.e., that the solar spectral irradiance obeys

In the present study, focusing on these fluctuations, we examine whether the

As mentioned above, the solar incident flux data for WL ranging from 115.5 to
629.5

Furthermore, we calculated the power spectrum for the detrended SIF data set using the Fast Fourier Transform (FFT) algorithm as well as the maximum entropy method (MEM) (Hegger et al., 1999).

A brief description of DFA-

Consider the SIF data set

We split the integrated data set into non-overlapping boxes of
equal length,

The root mean square fluctuations

where

In case the signals involve scaling, a power-law behavior for the
root mean square fluctuation function

The above is fine for the nonintermittent, quasi-Gaussian case, but in the
general (multifractal) case – which is of interest here – it is more
convenient to define the mean fluctuation of the running sum

For uncorrelated quasi Gaussian data, the scaling exponent is

Finally, the scaling properties of SIF-WL data set were also studied using
Haar fluctuation analysis (Lovejoy and Schertzer, 2012a, b). In the DFA
method above, fluctuations are defined by the standard deviation of the
residues of the polynomial regressions of the integrated process (the

Power spectral density of the detrended SIF data set together
with the least squares fit with power-law exponent

Varotsos et al. (2013a) studying the high-resolution observations of SIF
reaching the ground and the top of the atmosphere, suggested that SIF vs. UV
WL exhibits

In the present study, the scaling dynamics of a wider spectrum of SIF vs. WL
data set was studied, for wavelengths between 115.5 and
629.5

In the following we plotted the power spectral density (using FFT) of the
detrended SIF data set. The derived power spectral density showed that the
power-law fitting gives an exponent

Next, to summarize our results we analyzed the detrended SIF-WL data set by
using Haar analysis (Lovejoy and Schertzer, 2012a, b) using the software
available at

To clarify this aspect, we revisited the results of DFA-1 (see Fig. 4a) and
calculated the power spectrum for the detrended SIF-WL data set, using the
MEM (see Fig. 4b). In Fig. 4a, we plot the root mean square fluctuation
function

We observe that the DFA method gives results similar to those of the Haar
analysis, but obscures the break that is clearly seen in the Haar analysis
(Fig. 3). Finally, we have to recall that the

The main conclusions of the present survey were:

DFA-

Power spectral density for the detrended SIF data set showed
that the power-law fitting gives

To better understand our results we analyzed the detrended
SIF-WL data set by using Haar analysis. As it was derived, the
intermittency of SIF data set was very high and the data were far
from Gaussian. Specifically, the parameter characterizing the intermittency
near the mean

The results of the power spectral density for the detrended
SIF-WL data set (using the MEM) vs. frequency are compatible with
the aforementioned two

This study was partly funded by Greek General Secretariat for Research and Technology (GSRT) through the project 12CHN350. Edited by: A. Hofzumahaus