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Summary

Horizon shading accounts for losses when the sun is blocked by distant terrain features, tree lines, buildings, or other obstructions far beyond the solar array field. Users define a horizon profile as a series of - pairs describing the apparent horizon line around the site. At each timestep, the algorithm compares the solar position to the interpolated horizon elevation at that azimuth and determines whether the sun is visible. When sunrise or sunset occurs within a timestep, the shading factor is prorated based on the duration of terrain blockage. Diffuse horizon shading (sky-view reduction from far-field obstructions) is currently not implemented in PlantPredict.

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Inputs

NameSymbolUnitsDescription
Horizon Profile(γi,ei)(\gamma_i, e_i)degreesList of azimuth-elevation pairs defining horizon
Solar Zenith Angleθz\theta_zdegreesAngle between sun and vertical
Solar Azimuth Angleγs\gamma_sdegreessun azimuth measured clockwise from north
Sunrise/Sunset Timetrise,tsett_{rise}, t_{set}—Times when sun crosses geometric horizon (0°)

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Outputs

NameSymbolUnitsDescription
Horizon Shading FactorUhorizonU_{horizon}—Unshaded fraction of beam irradiance (0-1)

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Detailed Description

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Horizon Profile Definition

The horizon profile is a user-defined list of obstruction elevations at specified azimuths around the site: Horizon={(γ1,e1),(γ2,e2),…,(γn,en)}\text{Horizon} = \{(\gamma_1, e_1), (\gamma_2, e_2), \ldots, (\gamma_n, e_n)\} where:
  • γi\gamma_i is the azimuth direction (0° to 360° measured clockwise from north)
  • eie_i is the elevation angle of the obstruction at that azimuth (degrees above horizon)
Points should cover the full 360° azimuth range and be ordered by increasing azimuth.

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Horizon Elevation Interpolation

The horizon elevation at the current solar azimuth γs\gamma_s is determined by linear interpolation between the two nearest profile points: ehorizon(γs)=ei+(γs−γi)(γi+1−γi)(ei+1−ei)e_{horizon}(\gamma_s) = e_i + \frac{(\gamma_s - \gamma_i)}{(\gamma_{i+1} - \gamma_i)} (e_{i+1} - e_i) where (γi,ei)(\gamma_i, e_i) and (γi+1,ei+1)(\gamma_{i+1}, e_{i+1}) are the profile points immediately before and after the solar azimuth.

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Sun Visibility Determination

The shading factor depends on whether the sun is above or below the horizon obstruction at the current azimuth. The solar elevation is es=90°−θze_s = 90° - \theta_z: Uhorizon={1if es≥ehorizon(γs)0if es<ehorizon(γs) for entire timestepproratedif sun crosses horizon within timestepU_{horizon} = \begin{cases} 1 & \text{if } e_s \geq e_{horizon}(\gamma_s) \\ 0 & \text{if } e_s < e_{horizon}(\gamma_s) \text{ for entire timestep} \\ \text{prorated} & \text{if sun crosses horizon within timestep} \end{cases}

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Prorated Shading Calculation

When sunrise or sunset occurs within a timestep, the shading factor is prorated based on obstruction duration. The algorithm interpolates solar position from adjacent timesteps in 1-minute increments to find when the sun clears the horizon obstruction. The shading factor is then: Uhorizon=1−ΔtblockedΔtintervalU_{horizon} = 1 - \frac{\Delta t_{blocked}}{\Delta t_{interval}} where:
  • Δtblocked\Delta t_{blocked} is the time between sunrise/sunset and when the sun clears the horizon obstruction
  • Δtinterval\Delta t_{interval} is the portion of the timestep when the sun is above the geometric (0°) horizon
Example: For a 60-minute timestep with sunrise at minute 20, the sun is above the geometric horizon for 40 minutes (Δtinterval=40\Delta t_{interval} = 40). If a mountain blocks the sun until minute 35, then Δtblocked=15\Delta t_{blocked} = 15 minutes and Uhorizon=1−15/40=0.625U_{horizon} = 1 - 15/40 = 0.625. The horizon shading factor UhorizonU_{horizon} is applied only to the beam irradiance component. Diffuse and ground-reflected components are not modified by this algorithm.