Sky Definition Part 2

Hi Francesco,

Thanks so much for your input. I need to apologize, when I started this thread I narrow mindedly thought the IESNA equations were all part of what's defined as the "CIE standard sky". I had no idea there were so many differing equations to determine the magnitudes of the sun and sky components. I believe IES uses the CIE 110-1994 luminance distribution functions but I could not track down a copy of this at the moment. Is it the same function from his 1967 studies and then adopted by CIE in 1973? or was it changed in 1994? IES still lists the refence as Kittler 1967.

First, a note on sun/sky efficacies. The 94.2 lm/W efficacy I had said IES gives is for extraterrestrial solar. Which, along with the solar irradiation/illumination constants are the same for the entire world. It can then range from ~95 - 120 lm/W or whatever depending on the amount of particles it has to travel through, which is a function of elevation, solar angles, and turbidity and as Santiago pointed out a function of the eccentricity of the earth orbit which just slightly varies the extraterrestrial values throughout the year. I'm guessing air particles absorb more heat then light, hence the more particles the direct solar travels through the more efficacious it becomes. Given this, it does not seem like the determination of solar illuminance or solar efficacy should be that difficult as long as it is a function of extraterrestrial solar, eccentricity, elevation, solar angles (day, time, lat etc), and turbidity. This is partly why I trust the IES equation for direct solar at sea level because its a function of extraterrestrial solar, eccentricity, and sun angles. It falls short by not including elevation or just estimating a turbidity. Also, this is why I think direct solar estimates can be fairly accurate and not a matter of guesswork, since every input variable is extremely accurate except for perhaps the turbidity, which in the IES equations is assumed to be a constant value and probably based off weather data for north america. But given an accurate turbidity value there is no reason why an accurate estimate of the direct solar component can't be made. Also, it seems more logical to be able to vary the turbidity (and have it affect the solar component) as input to gensky rather than vary the solar radiance.

Furthermore, the sky estimate shouldn't be too much harder to achieve since, for one, it can not exceed the difference between ground level and extraterrestrial direct solar. It is also a function of the same variables listed above and is distributed according to either the kittler distribution function or perez or whatever.

If we only specify location and time, gensky uses the following formula:

solarbr = 1.5e9/SUNEFFICACY*sin(sunaltitude)
                        if (1.147 - .147/sin(sunaltitude) > .16), otherwise
         (could anybody give any reference about this equation?)

SUNEFFICACY = 208 /* illuminant B (solar dir.) */

Given what I just said above, from what I can tell, this equation only takes into account the sun angles with perhaps an estimate for ext. solar radiance. Hence, I'm more inclined to believe the IES equations which estimate a turbidity value and only misses an elevation factor.


If neither zenith radiance (zenithbr) nor horizontal diffuse irradiance (eed)
are given, the Krochmann equation is used for the CIE OVERCAST SKY:

zenithbr = 8.6*sin(sunaltitude) + .123 [kcd/m^2] (Krochmann)

CIE 110-1994 also reports equations by Kittler and Nakamura, Oki et al. for this

IES's equation for cloudy sky zenith luminance (Lz) is this;

Lz = (0.3 + 21.0*sin (sunaltitude))*0.409

For comparison on summer solstice at 12:00PM at 40 lat., the Krochmann equation gives 8,366 cd/m2 and IES equation gives 8,356 cd/m2. Pretty close!!!

For the CIE CLEAR SKY the LBL equation (Karayel, Navvab, Ne'eman, Selkowitz) is used
(here the Linke Turbidity appears for the first time):

zenithbr = (1.376*turbidity-1.81)*tan(sunaltitude)+0.38 [kcd/m^2]
(Karayel, Navvab, Ne'eman, Selkowitz)

For comparison on the same day and lat. etc., the IES equation, which I listed earlier, gives roughly 8,147 cd/m2 and this equation gives 7,023 cd/m2.

CIE 110-1994 also reports a lot of equations that should be chosen according to
the climate condition in the location of interest (Kittler, Dogniaux, Krochmann,
Liebelt, Gusev, Nagata, Nakamura Oki et al.), but gensky only uses the LBL one.

For the CIE CLEAR SKY, CIE 110-1994 suggests two different polynomial approximations
by Kittler (as said, "for practical purposes") and by Gusev (for polluted
both of them are not used by gensky.

I'd be interested how these other equations compare.

Part 2: proposal(s)

As we've seen, gensky is compliant with the CIE standard for the CIE CLEAR and
CIE OVERCAST skies when the user gives solar and zenithal radiances.

When the user only specifies time and location, gensky uses only some of the
equations suggested by CIE. It would be useful to be able to switch between
those equations for practical reasons.
As I've already said, in Italy there is only a few directly measured illuminance
some illuminance data series have been derived by using the Perez model.
Berin and Vio (University of Venice) have shown that the Doginaux equation
approximates very well the Italian luminous conditions, that's why I'm proposing
this integration inside the gensky code ...

Yes, I would prefer not to have to input solar and zenithal radiances in lieu of some of the more accurate estimates discussed here. Actually, I would prefer to just be able to adjust the turbidity to get my desired values as that should be the only less than accurate input variable.

There is no standardised intermediate sky luminance distribution model at the
moment, but
CIE 110-1994 cites the Nakamura, Oki et al. intermediate sky (does anybody know
recent works of CIE commissions about this topic?)
Zack (hi Zack!) showed interest in being able to use the IESNA (Kittler) sky model.

It would be very useful to have a sort of "plug in" method to insert new sky models,
for instance simply via .cal files (at the moment sky definition is splitted between
a program and a .cal file).

Does anybody else think that this could be useful and feasible?
Probably it would be better to develop another program to generate skies and
leave gensky
as it is now ... and to add a sky library of .cal files to it ...

Good idea. I think this is a good approach, that way old stuff reliant on gensky will not be affected.

Thanks again Francesco, that was some great info to add to the discussion! Again, please correct me if I am wrong in any of this thinking.



Zack Rogers
Staff Engineer
Architectural Energy Corporation
2540 Frontier Avenue, Suite 201
Boulder, CO 80301 USA

tel (303)444-4149 ext.235
fax (303)444-4304