Find an equation with 2 variables

[Apollo123]

I am currently calculating the radiation received by a surface for different orientations. The amount of light depends on 2 things:
(1) Solar Altitude (0-90)
(2) Azimuth different between the window and the sun (0-180)
By numerical method, I have found the radiation level for different (1) and (2) (91*181= 16341 no. of data). And now, I want to find a function for the radiation level - Function(solar altitude, azimuth difference)=VDF. Does anyone know how to find the function? I found a lot of books which only describes how to find the relation with only 1 variable ( y=f(x)). How to find the function y=f(x1,x2)?


Different lines represent radiation at different solar altitude.

[VBAhack]

Welcome to the forums!

Perhaps it would be helpful if you could provide the equations you are using.

I might be looking at this too simplistically, but it seems to me the amount of incident radiation is proportional to the effective area 'A' seen by the solar radiation. The effective area, I think, is purely a function of the 2 angles (and of course the surface geometry and orientation). For example, if you have a window with height 'h' and width 'w', the effective area will vary from 0 to h*w depending on the 2 angles. I think it is pure geometry.

If you have equations relating the incident radiation to either angle, I think it is possible to combine them into a single equation. Having a look at the equations you are using would be fruitful.

[Apollo123]

Nice to meet u VBAhack~~It's my first time to post in this forum. I just happened to find this site and ask for help. Actually, the irradiation received by the surface is the products of 3 quantities: 1)the sky radiance distribution 2)the solid angle of sky patch (which is actually how large the sky patch is) 3)the incident angle between the sky patch and the surface. (for a vertical surface, only half of the sky is "seen" by the surface)
The sky distribution varies according to some equations (we only need to input solar altitude and azimuth to get the distribution). I then used numerical method to calculate the irradiation (split the sky into small patches and then sum them up) and it's what u saw in the graph above. How to use an equation to summarize the results is my question.

For the sky distribution equation, it's a little bit complicated. It involves few exp functions. You can find it from the below website.
http://www.esim.ca/2002/documents/Pr...ngs/other2.pdf

[VBAhack]

it's what u saw in the graph above

Ah, that's part of the problem. I don't see any graph in your post (just an X). Maybe you can post it again as an attachment (e.g. jpg, gif, pdf).

If I understand correctly, you have numerically calculated the values of a function in 2 variables and now want to derive a 'simple' equation that fits the data, either exactly (probably not possible) or approximately (in a least squares sense).

If this is true, I could help you with the least squares part (though trying to do a least squares problem with 16k data points could prove to be a challenge) if you knew the nature of the fitting function, but I don't know how much help I could be in determining the fitting function - depends on what the graph looks like. My guess is the graph is a 2d plot with multiple curves. Have you tried producing a surface plot? Might provide some insight.

I'll also send you a PM with another suggestion.