Why clear days are not alike: What's the atmospherical science of a clear day? I was hoping for an ideal clear day (synoptically clear sky) to see the maximum power output for my solar setup at my latitude (43.5804° N, 7.1251° E). Simple enough I thought weeks ago.
Well over the past 6 weeks things turned out to not be black and white.

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*I've had a super clear sky (not synoptically clear) without even a slight fog/haze buildup during the entire day which still felt cold and the energy yield of that day verified this. Pmax was 267W and energy yield 1,08kWh. The sea pressure level dropped just during 24h by 70mbar.


*The next day was 25% cloud covered but visibly covered 75% of the time. Pmax was 400W and the yield even higher with 1,11kWh.


*Today was a super clear sky and the slightest visible fog/haze buildup over 10h and I got 1,82kWh and a Pmax of 364.


*Two days ago (part. cloudy) I had a Pmax of 479W and energy yield of 1,15kWh
Outside temperatures are all comparable at btw. 6 - 12degrees Celsisus. I don't know the temperature of the panels, but of course the will differ slightly judging from the Pmax values.
It's not the batteries State of Charge at 60% (which was comparable anyways), as I am pretty familiar with the LifePo4 chemistry and their C-Rate and the capacity is way higher than the solar Power capacity, notwistanding that it is Winter. But to be sure I also switched on loads, which didn't have any effect on the momentary Power yield. So nothing is saturated. The batteries are climatized and always around 30 degrees Celsius.
In other words I am pretty certain that this irradiance is a purely atmospheric effect. Lastly I have a small greenhouse and the data I get there is quite consistent with the power levels of the solar setup.
A caveat: Many people in the northern hemisphere know this from intuition. There are clear days in winter that still feel cold, whereas one in a few days or weeks feels super warm. While due to the sine nature (of mean shortwave solar irradiation throughout the months for regions in earths hemispheres) there is an exponential increase over time, that behavior wanes at the peaks and troughs.
I always thought some clear days feel cold due to my metabolism.
There are virtually no planes or visible pollution due to the Corona lockdown.
I am one kilometer away from the land / sea (mediterranean) boundary.
There is a difference of 40%-60% in power output from one 100% visible clear day to another with the same declination angle of the sun!
Sorry for all the long text, I just would like to lay it all out in hopes that someone knows what is going on and can shed some light on the issue.
Because I am a chemist and know about the absorption of molecular water, my only explanation is that this has to do with the infrared or atmospheric window to be more general. As there is no fogging or haze seen over the entire day - but neither do I know the entire chemical setup of the atmosphere right above me.
Unfortunately without some atmospheric terminology it is hard to google. I found this, but don't think it applies:
Over Côte d'Ivoire... ...Consequently, the effective window as seen from the cloud-top altitudes is more open, with the result that the cloud tops are effectively strong sources of window radiation; that is to say, in effect the clouds obstruct the window only to a small degree
https://en.wikipedia.org/wiki/Infrared_window
Can someone lead me to a paper or book or tell me everything I need to know to understand what is going on.
Further reading:
https://www.e-education.psu.edu/eme810/node/684
The Historical Backdrop: the Clearness Index
*In the 1960s, Liu and Jordan found that for different US locations with the same value of K¯¯¯T , the cumulative distribution curves of KT were identical, almost irrespective of latitude and elevation.\marginnote{A cumulative distribution describes the frequency or fraction of occurrence of days in the month below a given daily clearness index, KT}. This work was expanded into equations by Bendt et al.,\cite{Bendt81} using 20 years of real measurements in 90 locations in the USA. However, it was determined that the data sets were not so similar from region to region (e.g., the tropics had different correlations than the temperate USA, India was different from Africa, etc.) This work was followed by Hawas and Muneer for India and Lloyd for the UK, among others.\cite{Hawas85,Lloyd82}
Remember this! KT distributions are not universal---they are regional and empirically derived. For all of our future work, we will only rely on hourly kT values, and the manner in which kT is used to back out a value of Ib, the hourly beam irradiation component on a horizontal surface.*
 A: The reason why up to 10% more energy and up to 25% or more Pmax values are achieved on a slightly (scatter) cloudy day compared to one perfectly clear day, is "light soaking" and other less prominent effects like for instance the voltage dependent https://en.wikipedia.org/wiki/Potential-induced_degradation
Many of these effects follow a saturation curve whose peaks are reached after minutes. Most of these effects influence the https://www.pveducation.org/pvcdrom/solar-cell-operation/collection-probability
I didn't intend to give an answer here but luckily the very next day I had some scattered clouds and enery yield was about 10Wh more than the previous day which was perfectly unobstructed. Pmax showed a difference of about 431Watts compared to 364W to the previous perfectly clear day.
Considering that during cloud coverage, the Power temporarily reduced to 100W or less the power yield is remarkable!
The explanation is mostly due to https://en.wikipedia.org/wiki/Light_soaking
The details and behavior of monocrystalline silicone based cells (that I use) differ based on the exact doping-blend of the silicone material. Consult the specs of your solar panels. But they too leave some stuff out for reasons of inellectual property safeguarding.
Finally other individual effects matter such as that the parallel solar panels in my setup don't all exactly match up in internal resistance and in Vcc and Voc. There is a difference of about 1-2Volts thus temporally stretching some of the aforementioned effects.
Also note that clouds can during particular constellations lead to a short-lasting light concentration effect!
Secondly: correlation does not equal causation. This is the case with two independent
devices: A greenhouse and a solar panel setup.
There are two different atmospheric windows: the infrared and the visible window that are effected by different gasses and at different layers of the atmosphere. For the greenhouse temperature the infrared window is of greater importance.
There was a +8 Degrees temperature difference on two clear days of comparable sun declination angle. The solar panels also showed markable differences but these are only slightly correlated, as the power yield of mono-Si solar panels is mostly from visible photons of much higher energy per photon:
Sunlight energy that reaches the ground is around 4% ultraviolet, 43% visible light, and 53% infrared.  Solar panels mostly convert visible light into electrical energy, and they also can make use of almost half the infrared energy.  But solar panels only use a small portion of ultraviolet.
https://www.solarquotes.com.au/blog/uv-solar-panels/ (just don't take this as a scientific source)
Even though the human eye cannot really compare intraday or extraday differences in luminosity, if a clear sky in the same region and time would differ in visible luminosity, the literature should be full with this by now. I am not an expert, but from what I've gathered this is not the case.

I still haven't fully figured out why two clear days differ so much in Shortwave incident infrared radiation and emitted longwave infrared radiation ("thermal photons") all heating up the immediate envionrment (On IR see: https://earthobservatory.nasa.gov/features/FalseColor/page5.php).
However the reason has to do with the atmospheric pressure, which is obvious (more molecules interacting with an incident ray of photons means more absorption). And it has to do with water molecules i.e. humidity.
This is particularly pronounced near the seashore because when the sun shines onto a body of water it causes evaporation mingling with the atmosphere above the drier land mass.
Relative humidity depend on the pressure and temperature. The point at which moisture nucleates and forms droplets above the diameter of the wavelength of light in order to allow scattering of light and make the moisture "visible" is described here:
https://en.wikipedia.org/wiki/Water_vapor
https://en.wikipedia.org/wiki/Cloud_physics
https://en.wikipedia.org/wiki/Humidity#Climate
The complexity is illuminated somewhat here: https://journals.ametsoc.org/view/journals/clim/10/7/1520-0442_1997_010_1601_tescsr_2.0.co_2.xml
Once I have the answer I will update this one, hopefully replacing this text soon for something more informative.
Related reading: https://www.researchgate.net/figure/Absorption-of-solar-irradiance-on-a-horizontal-radiative-cooling-surface-a-Air-mass_fig1_332459395
