If you're just interested in the irradiance at the top of the atmosphere, then you can use the temperature of the Sun surface (approx. 5772 K) to obtain the so-called solar constant or an approximate spectrum with Planck's law. But that would not give you the irradiance incident at the surface anywhere on this planet...

What you describe as "flux" is not clear: do you mean shortwave or longwave?

The formula Qrad = A*sigma*T4 you mention is about the latter, but this has nothing to do with the usable energy incident on the collector and that can produce heat or power.

Dear Chris Gueymard :

Thank you for your reply.

As a first approximation I would like to determine all the Electromagnetic radiation coming from the Sun, and arriving to a tilted surface placed on the surface of Earth (meaning, all the spectrum from radio waves to gamma rays) it is possible ?

additionally, can you explain to me why the formula Qrad = A*sigma*T4 does just work for the long wavelengths of this radiation, and no the other wavelengths.

As a first approximation I would like to know how to express or calculate all the Radiation Flux (in W/m2) coming from the Sun and arriving to a tilted surface placed here on Earth.

Regards !

I believe that this scientific contribution will be useful for your research.

A simple yet more accurate model to calculate solar radiative flux in the inhomogeneous atmosphere.

Abstract

A simple yet more accurate semiempirical model is developed to calculate solar radiative flux in the optically inhomogeneous atmosphere. In the model a parameterized expression of spherical reflectance and transmitance of the atmosphere is confirmed, and the weighted single scatter albedo and weighted asymmetric factor are introduced to fit four empirical correction factors responsible for radiative fluxes in the inhomogeneous atmosphere. For both clean and turbid models, there are 120060 sets of radiative flux simulations for accuracy checks of the model, which cover 0-50 cloud optical depths, 0-0.8 surface reflectance, Junge and Log-normal aerosol size distributions, and 0-0.05 imaginary parts of aerosol refractive indexes. In case of the homogeneous atmosphere, standard errors of the 120060 upward fluxes from the present model are 1.08% and 1.04% for clean and turbid aerosol models, respectively; and those of the downward fluxes are 4.12% and 3.31%. In case of the inhomogeneous atmosphere, standard errors of the upward fluxes from the present model are 3.01% and 3.48% for clean and turbid aerosol models, respectively; and those of the downward fluxes are 4.54% and 4.89%, showing a much better accuracy than the results calculated by using an assumption of the homogeneous atmosphere.

You need to look at the solar spectrum. Most of the energy is concentrated in the 0.3 to 4 µm spectral range, called "shortwave". That's what can be used by solar collectors as the fuel, and thus this should be your main (or only) focus.

The longwave (beyond 4 µm) is only of interest if you are into radiative cooling. There is upward and downward longwave radiative transfer, more or less in net balance.

Dear Chris Gueymard :

I understand Sir.

So. Can the Radiation Solar Flux (lambda between 0.3 and 4 um) arriving to a surface on Earth be calculated by the Eq :

Q = A*sigma*(T4sun - T4sup ) or Q = A*sigma*(T4sky - T4sup ) ?

Thank you for your reply ,

Regards !

There are a lot of on-line models and experimental data on the energy of solar radiation taking into account the time of day, season, geographical location, panel orientation and cloud cover.

For example:

https://re.jrc.ec.europa.eu/pvg_tools/en/tools.html

https://www2.pvlighthouse.com.au/calculators/solar%20spectrum%20calculator/solar%20spectrum%20calculator.aspx

https://power.larc.nasa.gov/data-access-viewer/

If you are interested in the total energy, and there is data only for photovoltaic panels, then you can recalculate it from the energy of photovoltaic panels, dividing it by the efficiency of the panels - 0.13 ... 0.17.

If you want to take into account heat transfer with the environment, then in addition to radiative heat transfer, you should take into account convective heat transfer, which in some cases is much more significant. For example, consider wind speed.

Dear Vladimir Kubov, thank you for your advice and explanation,

However, I am interested in a more accurate calculation.

I.e., to compute the Solar Irradiation flux arriving to my surface, although corresponding to my particular case of : exact plate's geometry and tilt, exact location, exact altitute, with the precise atmospherical conditions at the place, etc.

This is to say, that I don't want to use an empirical model, I want to do it from "first principles".

I though this could be possible since the Irradiance from the sun is Radiation Heat Transfer, which is described by the Stefan-Boltzmann's Law.

Cannot I start from this law to perform this calculation? That is my question.

I want to do start from the governing equations, so I can arrive to compute the Solar Irradiation (W/m2) corresponding exactly to my case, or to the general case.

I think this time I finally made myself clear :)

Thank you for replying !

No, the formula you mention is only for the longwave, which is essentially a function of T. For the shortwave, you would need to investigate the abundant literature on the solar resource, starting with this handbook: https://www.nrel.gov/docs/fy18osti/68886.pdf

Dear Chris Gueymard :

Thank you very much for the resource.

If you're just interested in the irradiance at the top of the atmosphere, then you can use the temperature of the Sun surface (approx. 5772 K) to obtain the so-called solar constant or an approximate spectrum with Planck's law. But that would not give you the irradiance incident at the surface anywhere on this planet...

Dear All,

You can use this reference for a solar spectrum at the top of the atmsophere at one astronomical unit:

https://www.aanda.org/articles/aa/full_html/2018/03/aa31316-17/aa31316-17.html

Then, you can use model to obtain solar irradiation at the surface. ERA5 is an example of model.

https://apps.ecmwf.int/codes/grib/param-db/

Dear Chris Gueymard :

Thank you for the explanatio. And what would I have to do to calculate the incident Irradiance (W/m2) on a tilted surface placed on the surface of Earth ?

Regards !

Hi, Franklin Uriel Parás Hernández

If you want to calculate the solar radiation flux on a solar collector, which is placed on the surface of the Earth, you can follow three methods for this, whether you can calculate from the empirical mathematical correlation, which has given in all solar energy books, you may also like Duffy and Backman Solar Engineering of Thermal Process Books, another way you can use pyrometers and other solar radiation measurement devices, where you want to measure, you can measure the scope. It will provide global solar radiation directly (W/m^2) or can measure direct and diffuse solar radiation separately. The third way is that you can take it directly from the meteorological department which is near your station or download it from different energy sources, as mentions above it, for understanding all these basic to you first read all the fundamentals things which is mention Chris Gueymard Sir, in a given book.

Best Regards;

Franklin Uriel Parás Hernández "And what would I have to do to calculate the incident Irradiance (W/m2) on a tilted surface placed on the surface of Earth ?"

First of all, you need to decide on a set of factors that affect this Irradiance. And more clearly formulate your question ;-)

Some simplified approaches are available in my work (link below). Maybe will be useful for you.

Article On Determination of the Optimum Tilt of Solar Installations

Mr. Franklin Uriel Parás Hernández

greeting

There are many references referring to the equations that employing to determine the solar intensity (heat flux) to the solar collector depending on the altitude from the see level , location and orientation with angle for the solar collector.

I list the some of the depending references

1-Solar Engineering of Thermal Processes (by John A. Duffie)

2-SOLAR ENERGY USE (ASHRAE Applications Handbook)

3- Solar energy engineering (Soteris Kalogirou)

To calculate the radiation flux, you can use the Angström Prescott formula that need some grown (in-situ) data.

If you have an e-mail adress I can have it to you.

Use a integração da irradiancia em função da área.

agree with Chhotelal Prajapati answer

the question you ask does not have an exact answer by an equation, as it a random parameter, So you need the device to justify your results.

problems: you can't find the parameter of clouds (Density, thickness, area, time of shading, soil seeding ) and air flux (water vapour and dust ) so it is not possible to achieve on the ground but you can assume on the surface of the extraterrestrial surface to be 1367w/m2.

Solution: still you need to do so, make an experimental device.

step 1: take a LUX sensor (Max Reading 56000LUX)

Step 2:take a translucent material and reduce it by 4 times.

Step 3: take a bulb of 100w, 500w,1000w and 1500w and calibrate your sensor on python or any software handy to work for you.

Step 4: build astronomical tracker and mount a simple Arduino camera with the help of x-ray sheet and calibrate your tracker using image processing.

Step 5: mount your sensor and have your real-time solar flux with the exact result.

Still have an issue please mail me on [email protected]

Article Analysis of Hourly Global, Direct and Diffuse Solar Radiatio...

You need to be more specific in your question because it is too vast:

- Clear-sky or all-sky conditions?

- What temporal resolution?

- Which region(s)?

- What time period?

- Global and/or direct radiation?