CIE standard general Sky type identification for Delhi during winter and summer

Abstract

Computer simulation of day lighting depends on mathematical model of sky luminance distribution. Fifteen Standard Sky Luminance Distribution (SSLD) model is recommended by CIE which are applicable for wide range of sky types all over the world. S. Darula and R. Kittler proposed a method to identify prevailing sky type(s) based on measured data for any location. In this paper this method is applied to identify SSLD model matching sky with prevailing sky types at Delhi during Winter and Summer seasons. To find out the best fit sky type(s), statistical test of significance (95 % confidence level) has been carried out for the ratio of zenith luminance to horizontal diffuse (or sky) illuminance distributions for different CIE skies with the same for Delhi data as reference. Statistical analysis of the computed results show that CIE Standard General intermediate sky type III.2 described as “Partly cloudy sky, no gradation towards zenith, slight brightening towards the sun” is the best fit for winter season, whereas sky type III.4 described as “Partly cloudy sky, no gradation towards zenith, distinct solar corona” is the best-fit for summer season in Delhi.

Appendix

Determination of Solar altitude (γ _s ) for different day time [9]

Equation of time ET

The Equation of Time describes variation between clock time and solar time due to eccentricity in the earth’s orbit. ET is positive when sun time is before clock time. Like solar declination, ET depends on the leap year cycle, but the following equation is accurate to within 40 s.

Input Day number, J

J = 1 on 1 January, J = 365 on 31 December. February is taken to have 28 days.

Equation Day angle(τ_d):

$$ {\tau}_{\mathrm{d}}=2\pi \left(\mathrm{J}-1\right)/365\ \mathrm{radian} $$

(15)

Solar declination (δ_s):

$$ {\updelta}_{\mathrm{s}}=0.006918-0.399912\ \cos {\tau}_{\mathrm{d}} + 0.070257 \sin {\tau}_{\mathrm{d}}\hbox{--}\ 0.006758\ \cos 2{\tau}_{\mathrm{d}} + 0.000907 \sin 2{\tau}_{\mathrm{d}}-\kern0.5em 0.002697 \cos 3{\tau}_{\mathrm{d}}+0.001480 \sin 3{\tau}_{\mathrm{d}}\ \mathrm{radian} $$

(16)

Equation

$$ \mathrm{ET}=0.170\mathrm{Sin}\left[4\pi \left(\mathrm{J}-80\right)/373\right]-0.129\mathrm{Sin}\left[2\pi \left(\mathrm{J}-8\right)/355\right]\mathrm{hours} $$

(17)

Note The argument of the sine function is in radians.

Input Local clock time, LT hours from midnight

Longitude of site (positive west of Greenwich)

Latitude of site phi

$$ \mathrm{TST}\left(\mathrm{True}\ \mathrm{solar}\ \mathrm{time}\right)=\mathrm{LT}+\mathrm{ET} $$

(18)

$$ \zeta\ \left(\mathrm{Solar}\ \mathrm{hour}\ \mathrm{angle}\right)=\left(\pi\ /12\right)\ \mathrm{TST}\ \mathrm{radian} $$

Solar altitude (γ _s ):

$$ \sin \left({\gamma}_s\right)= \sin \left(\phi \right) \sin \left({\updelta}_{\mathrm{s}}\right)- \cos \left(\phi \right) \cos \left({\updelta}_{\mathrm{s}}\right) \cos \left(\upzeta \right) $$

(19)

$$ {\gamma}_s=\mathrm{arc}\ \sin \left( \sin \left(\phi \right) \sin \left({\updelta}_{\mathrm{s}}\right)- \cos \left(\phi \right) \cos \left({\updelta}_{\mathrm{s}}\right) \cos \left(\upzeta \right)\right) $$

(20)

The value of different solar altitude for different solar time γ _S are obtained from sunpath diagram of Delhi [29.0167° N, 77.3833° E] from Fig. 15

Fig. 15

Sunpath diagram of Delhi