Supplementary Material 2. Additional figures and algorithms to calculate daily mean global insolation on an inclined and obstructed surface (Hβ)

-  Fig. ESM2-1 – Simulated changeability of the beam shading factor (BSFβ,h) and the beam radiation tilt factor (Rb) for all research sites within Dupniański Stream valley

-  Fig. ESM2-2 – Simulated variations in daily total insolation on an inclined surface (Hβ) calculated at all investigated sites in Dupniański Stream valley

-  An algorithm to calculate theoretical daily mean total insolation on an inclined surface (Hβ, Fig. ESM2-2):

1.  assume daily mean clearness index, KT

2.  calculate daily average total insolation on an extraterrestrial horizontal surface, H0 (ESM1-11)

3.  compute daily average total insolation on a terrestrial horizontal surface, Hh=KT⋅H0 (ESM1-10)

4.  evaluate daily mean insolation of the diffuse component on a horizontal surface, Hd,h (ESM1-13) – use an appropriate equation for your region

5.  integrate values of Ib (ESM1-9) to estimate the daily mean insolation of beam component on a horizontal surface, Hb,h

6.  estimate values of BSFβ,h and SVF for a given, inclined surface

7.  determine daily mean total insolation on an inclined surface based on equation (8), Hβ=BSFβ,h⋅Hb,h+SVF⋅Hd,h

-  An algorithm to calculate daily total insolation on an inclined surface, Hβ, based on field measurements:

1.  numerically integrate recorded data of global solar irradiance, It (Fig. 4 in the manuscript), to obtain daily average total insolation on a terrestrial horizontal surface, Hh – also denoted as Hi or HM1 in (9)

2.  estimate daily average total insolation on an extraterrestrial horizontal surface, H0 (ESM1-11)

3.  calculate daily mean clearness index KT (ESM1-10)

4.  evaluate daily mean insolation of the diffuse component on a horizontal surface, Hd,h (ESM1-13) – use an appropriate equation for your region

5.  estimate values of BSFβ,h and SVF for a given, inclined surface

6.  determine Hβ by Eq. (8): Hβ=BSFβ,h⋅KT⋅H0-Hd,h+SVF⋅Hd,h

Fig. ESM2-1 Changeability of the beam shading factor (BSFβ,h) and the beam radiation tilt factor Rb for all research sites within Dupniański stream catchment (calculated at the height of tree stands or at ground level for sites placed in open fields: M1, M2 and S5). The values of coefficients heavily depended on season, aspect and tilt angles of an analysed plane (especially for sites S1 and S2 which was situated on southern slopes) and shading effect caused by the topographic relief of adjoining mountains as well as surrounding tree stands. In winter direct solar radiation did not reach site M2 which was located in the valley bottom as it took the sun’s disk less than 2 weeks to be completely hidden behind the densely-forested mountain range, positioned to the south of the site. The significant reduction of beam solar insolation resulting from the contour of the adjacent tree stand at site S5 was also very noticeable (see also Fig. 3 in the manuscript).

Fig. ESM2-2 Daily solar insolation on an incline surface, Hβ [kWh∙m-2], absorbed by tree stands calculated at all investigated sites in Dupniański Stream catchment. Calculations were performed for three days with the most characteristic solar elevations (the winter solstice, the vernal/autumnal equinox and the summer solstice) for different sky conditions based on Iqbal’s (1983) classification (KT=0.1 cloudy sky day, KT=0.4 partially cloudy sky day, KT=0.7 clear sky day). Daily total insolation consisted of two main components: beam, Hb,β, and diffuse Hd,β, which largely depended on season, weather conditions, aspect and tilt angle of the analysed plane and shading effect caused by the topographic relief of adjoining mountains as well as the contour of surrounding tree stands. Reflected radiation from the neighbouring terrain was omitted.

Supplementary References

Iqbal M., 1983. An introduction to solar radiation. Academic, Toronto

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