The calculations that were undertaken to determine the solar insolation for each of the point is described below. They are based on the American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) building heat gain calculations.

Incident Solar Flux on a Surface

Total Solar Radiation, Gt:

Gt = GD + Gd + GR
GD is the direct incidence of solar radiation on a surface, W/m2
Gd is the diffuse incidence of solar radiation on a surface, W/m2
GR is the ground/surroundings reflected incidence of solar radiation on a surface, W/m2
solar flux diagram

Direct Solar Radiation, GD:

GD = CNGNDcosθ
CN is the sky clearness number (CN=1 for clear sky)
θ is the solar incident angle (angle between the suns rays direction and normal to the surface)
GND is the normal direct irradiation, W/m2
GND = A / (e(B/sinβ))
A is the apparent solar irradiation outside the atmosphere, W/m2
β is the solar altitude angle
B dimensionless atmospheric extinction coefficient
*for values of A, B, and C refer to Table 7, ASHRAE-F-31.14, 2005

Diffuse Solar Irradiation, Gd:

Gd = CGND((1+cos∑) / 2)
C is the ratio of diffuse to direct normal irradiation on a horizontal surface
∑ is the surface tilt angle (slope)

Reflected Solar Irradiation, GR:

GR = GtHρg((1 − cos∑) / 2)

ρg is the solar reflectance of ground or horizontal surfaces (albedo)
GtH is the total solar radiation (direct + diffuse) on horizontal surface:
	GtH = GNDsin(β +C)

Solar Angles

∑: Surface tilt angle (vertical ∑=90°; horizontal ∑=0°)
ψ: Surface orientation (azimuth) angle 
(for surface faced South, ψ=0°; faced W, ψ=90°;faced E, ψ= −90°)
θ: Solar incident angle (angle between the sun's rays direction and normal to the surface)
β: Solar altitude above the horizontal
φ: Solar azimuth measured from south (at West, φ=90°; at East, φ= −90°)
γ: Surface − Solar azimuth measured from the south; γ=φ − ψ
H: Hour angle (angle between the meridian passing the surface and the sun's rays direction);
	H=15(LST − 12); (Morning H<0 and afternoon H>0)
L: Local Latitude; (North, L>0)
δ: Solar declination; 
	δ=23.45sin((360(284+n)) / 365); n is the day of the year (n=1 for 1st of Jan.)

Local Solar Time Calculation

LST = (CT - DT) + (1/15)∘(Lstd − Lloc)+E

LST: Local Solar Time, hr
CT: Clock Time, hr
DT: Daylight Savings Time Correction 
	(DT=0 if not on daylight savings time, DT equals to the number of hours advanced)
Lstd: Standard Meridian for local time zone 
	(60° Atlantic, 75° Eastern, 90° Central, 105° Mountain, 120° Pacific, and 135° Alaska)
Lloc: Local longitude, degree
E: Equation of Time, hr
	E=0.165sin(2B) − 0.126cos(B) − 0.025sin(B)
	B=(360 / 364)∘(n − 81), n is the day of the year

Solar Angle Relations

Solar Altitude:
	sinβ=cosLcosδcosH + sinLsinδ
Solar Azimuth:
	cosφ=(sinβsinL− sinδ)/cosβcosL
Solar Incident Angle: