"The globally averaged non-blackbody incident solar radiation entropy flux at the top of the Earth’s atmosphere equals 0.31Wm−2 K−1. This value is about 4 times larger than that estimated from the conventional blackbody approach"

A proper citation would be to where Wu et al list the values.
Spectral solar irradiance and its entropic effect on Earth’s climate (PDF) published in 2011 by Wu et. al.
If we assume that the TOA SSI outside [200 nm, 2400 nm] wavelengths corresponding to the SIM-based TOA SSI observations is equal to a constant fraction of the TSI of 1361Wm−2, we obtain the overall Earth’s incident solar radiation entropy flux of 1.24Wm−2 K−1
corresponding to the SIM-based TOA SSI through Planck expression. This value is surprisingly very close to the overall Earth’s incident solar radiation entropy flux of 1.23Wm−2 K−1 5 by applying the blackbody Sun’s TOA SSI into Planck expression.
Both amount to a global averaged Earth’s incident solar radiation entropy flux of 0.31Wm−2 K−1.
On the other hand, using the same blackbody Sun’s brightness temperature (TSun =5770 K), and assuming the global averaged cosine of solar zenith angle 10 cos0 =0.25 and solar solid angle Ò0 =6.77×10−5 sr to the planet as in Stephens and O’Brien (1993), the conventional expression (5) yields the Earth’s incident solar radiation entropy flux of 0.08Wm−2 K−1, 4 times smaller than that by using Planck expression and the SIM-based TOA SSI (or the blackbody Sun’s TOA SSI).
It is isn't it? You interject with some copypasta from a propaganda website that you don't really understand. It shows to me you aren't interested in learning anything. You have blind faith in what you read on blogs is correct.
That is idiotic, 3bodyproblem.
I am learning things by reading the papers that are listed on that blog.
I (mostly) understand what they post and the papers that they link to.
I have no blind faith - I analyze what they present in light of what I know about physics. This is a lot in general but not so much in climate science. The last thing I did that is even remotely related to climate was a post-graduate course on oceanography where the role of oceanic oscillations like El Nino was mentioned.
It is idiotic to label a blog a "propaganda website" when its purpose is clearly stated - to list the scientific evidence about climate change.
I've asked a relatively straightforward question and presented you with peer reviewed literature to support the fact that the incident solar flux has been severally underestimated.
I have given you a straightforward answer to your question.
But maybe you can understand this
I do not know how. Tell me how to calculate the % of global warming from the incident solar entropy flux and I will calculate that. Maybe subtracting this from the observed global warming will be the percentage of anthropogenic warming from CO2.
You are wrong: The Wu et. el. paper calculates the incident solar
entropy (you misses that vital word) flux from the incidence solar radiation flux.
Using the standard model of a black body Sun they get the usual result.
Using another model of the Sun they get an incident solar entropy flux that is 4 times higher.
They give a possible cause for the large discrepancy in the estimates.
The satellite was launched in 2003!
I am not ignorant enough to think that observations of the Sun started with the launch of a satellite in 2003!
I checked and I was wrong: It was 1983

:
Entropy productions on the earth and other planets of the solar system (1983, Aoki, I.)
The entropy flux of incident solar radiation at the top of the earth atmosphere is given as 0.000031 J/sq cm per sec per deg K. The entropy production on the earth is calculated from balance equations of radiation energy and entropy and shown to be 0.000012 J/sq cm per sec per deg K. Those for other planets of the solar system are also given.