Far Shadings: Horizon

What this step does

The row measures the light that distant hills and buildings take from the plane irradiance. The direct sunlight and the circumsolar light are removed for the part of each timestep during which the sun sits behind the skyline. The sky light is reduced by the share of the sky the skyline hides. The ground-reflected light is reduced by a factor that falls with the height of the skyline, a convention of the method: the skyline also hides sky and sun from the ground in front of the modules, which then reflects less. The Model tab's Far shading (horizon) step sets how these fractions are found.

The math

1. Running total
2. Loss at a timestep

$$E_{after} = E_{before} - E_{row},\qquad E_{row} = \frac{\Delta t}{1000}\sum_i L_i \tag{1}$$ $$L_i = (1-f_{b,i})(B_i + C_i) + (1-F_{dif})\,D_i + (1-F_{alb})\,G_{gnd,i} \tag{2}$$

where

Symbol	Meaning	Unit
$E_{before}$	the running total of the loss diagram before this row	kWh/m²
$E_{after}$	the running total after this row	kWh/m²
$E_{row}$	the row taken as a loss	kWh/m²
$\Delta t$	the length of one timestep	hours
$L_i$	the irradiance lost at timestep $i$	W/m²
$f_{b,i}$	the fraction of timestep $i$ during which the sun is above the skyline	—
$B_i$	the direct sunlight on the plane	W/m²
$C_i$	the circumsolar part of the diffuse light on the plane	W/m²
$F_{dif}$	the fraction of the sky light that the skyline leaves visible, constant over the year on a fixed plane	—
$D_i$	the sky diffuse light on the plane	W/m²
$F_{alb}$	the fraction of the ground-reflected light kept: 1 for an open horizon, falling linearly to 0 for a skyline 20° high, averaged over the ground the plane sees and multiplied by the fraction of albedo taken into account (Site tab); constant over the year on a fixed plane	—
$G_{gnd,i}$	the ground-reflected light on the plane	W/m²

Reading the number

A loss, negative. A flat horizon costs nothing. A skyline of 10° to the east and west costs about 2 % of the plane irradiance at a mid-latitude site, on utility and rooftop systems alike. The loss grows with the height of the skyline in the directions where the sun rises and sets.

References

1. Quaschning & Hanitsch 1998, Irradiance calculation on shaded surfaces, Solar Energy 62(5) 369–375

API

loss.horizon

Symbols follow the symbol registry.