Bn sin Hn

Thus the mean daily solar flux (W m~2) on day n can be calculated from f©„ = Sqfi,ndn (j-^j . (5.65)

We note that at the equinoxes S = 0 and so H = n/2 so that d = 1/2. In the polar regions it is possible for H to be zero, d = 0, i.e. polar night (or winter) that can last up to six months depending on latitude. At this time the other pole has H = n, d =1 polar day (or summer). The polar night can happen for latitudes that satisfy tan 0 = — cot S for S = 0. This occurs for 0 > 90° — S = 66.56°. During the polar day H = n and j > 0 for 24 hours and the sun simply remains above the horizon circling the sky in an upward spiral motion, beginning at the spring equinox, with an elevation S above the horizon reaching a maximum value of e at the summer solstice for the Pole (0 = 90°).

5.6.6 Global distribution of incoming radiation Zonal-seasonal variation The zonal-seasonal variation of the daily (24-h) average in W m~2, mean monthly incoming solar radiation is given in Fig. 5.16. We note that the seasonal variability of ISR increases as we move towards the poles. Latitudinal variation The long-term (1984-1997) latitudinal variation of mean annual TOA incoming solar radiation is given in Fig. 5.17 for a solar constant of 1367 W m~2. Mean monthly 10-degree latitude zonal fluxes were computed by averaging along 2.5-degree latitude zones, taking into account the

FlG. 5.16. Long-term (1984-1997) zonal-seasonal variation of incoming solar radiation (W m~2) at the top of the atmosphere (TOA) for the Northern Hemisphere (dotted lines) and Southern Hemisphere (solid lines).

fraction of surface area contained in each 2.5-degree zone. The fraction of surface area in each zone can be taken, to a very good approximation, to be Ej = sin j50 — sin(j — 1)50 where 50 is the width of each latitudinal zone, for j = 1, 2,..., 36 zones in the case of 2.5-degree zones spanning from equator to pole, assuming the Earth is a perfect sphere. Subsequently, annual mean quantities can be computed by summing the corresponding monthly means for each 10-degree latitudinal zone over the 12 months of the year. Seasonal variation The yearly averaged incoming solar radiation has a maximum value of about 425 W m~2 along the equator, decreasing rapidly to about 175 W m~2 towards the poles, due to the latitudinal variation of solar zenith angle. However, note that the equator-to-pole decrease in ISR is associated with a corresponding increase in ISR seasonal variability. The mean hemispherical ISR fluxes have opposite seasonality (Fig. 5.18 with values ranging between about 200 and 475 W m~2, resulting in a mean global ISR ranging from 330 to 352 W m~2 throughout the year. The ISR seasonal range for the Southern Hemisphere is slightly larger than for the Northern Hemisphere as perihelion occurs in January, corresponding to a slightly larger incoming solar flux during summer in the Southern Hemisphere.

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FIG. 5.17. Long-term (1984-1997) mean annual latitudinal variation of computed incoming shortwave radiation (W m~2) at the top of the atmosphere. (Hatzianas-tassiou et al. 2004)



- m









iat di








h s




mi o


o n

----North hemisphere

South hemisphere

FlG. 5.18. Long-term (1984-1997) latitudinal average seasonal variation of incoming shortwave radiation (W m~2) at the top of the atmosphere. (Hatzianastassiou et al. 2004)

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