## A4 Energetic Factors Solar Radiation

The most important factor driving the evolution of the ecosystem is the energy flow and the main source of energy for ecosystems is solar energy. For this reason, modelling solar radiation is of great importance because it is the principal forcing function for models of heat budget, photosynthesis, primary productivity and photolysis. Solar energy reaching the earth's surface depends on the day, the hour and the latitude of the place because of the earth's rotation on its axis and around the sun. Table 3.2 shows the energy entering the troposphere with different wavelengths and its fate. As we can simply understand from the table, only 46% of the energy entering the troposphere reaches the earth's surface and the major part of this energy has wavelengths in the ranges ultraviolet and visible. After utilization by ecological systems, an equal quantity of energy leaves the planet. Unfortunately, during the last century, human activities have increased the concentration of CO: and other gases in the atmosphere. These gases have generated the well known greenhouse effect and the related global warming. Because the energy balance, at the earth scale, is no longer in equilibrium, the flow of energy through the atmosphere changes, both in quantity and quality, in terms of wavelengths, and we can roughly say that each photon entering the surface with short wavelengths generates about 20 outgoing photons with long wavelengths. This fact is explained by the formula

where the energy of a photon E is inversely proportional to the wavelength, so shorter wavelengths have higher energy than longer ones. This degradation of energy quality supports life on earth.

An important variable in the model of solar radiation is the longest duration, P, of light in a day, commonly named the photoperiod, expressed as part of the 24 hours. Equation (3.16) indicates a way of calculating the photoperiod for a given day, n, of the year and for a given latitude (J)

where 8, the solar declination (angle between the line connecting sun and earth and the equatorial plane) is expressed by the following function

4- 0.36958 cos(2v) + 0.10868 sin(2y) + 0.01834 cos(3y) - 0.00392 sin(3y) - 0.00392 cos(4v) - 0.00072 sin(4y) -0.00051 cos(5v) + 0.00250 sin(5y)

Physical Processes: Energetic Factors 117

Table 3.2. Fate of solar radiation flowing through the troposphere and reaching the earth's surface

Total Energy rf Band Wave length

Absorbed bv about 1360 W nr:

9 r/c ultraviolet

partially by O,

41 rr visible

50CÎ infrared

46r; almost entirely reaching the earth's surface and reflected after utilization by ecosystem and wavelength degradation

50rr absorbed and reflected by CO,, N.O at 10 km (2)

(1) Reduction of O, in the troposphere due to the increased CFC concentration is reducing the quantity of the energy with this wavelength that is reflected, increasing the global warming and the damages due to ultraviolet rays.

(2) The increase of CO, generates the greenhouse effect, reduces the reflected infrared energy and increases the global warming.

wherey, the yearly angle in degrees, is given by the following relation (3.17) (France and Thornley, 1984) with the convention that the first day of the year is the Is" March to avoid the problem of leap-years.

The absolute value of the argument of the arcos. (/g<t>rg5), must be less than 1. In fact the maximum solar declination (5) is 23.5° and tg(23.5) = 0.434, the maximum absolute value for latitude (\$) is 66.5°, because #(66.5) = 2.2998 < (1/0.434) = 2.3041. This justifies the fact that for latitudes larger than the latitude of polar circles (66.5°) the day (or night) can be 24 hours long and consequently the photoperiod 1

The daily solar radiation at a given latitude is modelled by a sinusoidal formula for the clear sky condition and is calculated by multiplying the clear sky solar radiation (W rrr2) times the photoperiod. Attention must be paid to the photoperiod when the unit is expressed per hour or second and to the unit of solar radiation.

Usually, solar radiation is measured in W rrf; but sometimes other units are used, such as, for instance, the English system unit BTU (British Thermal Unit) ft~: day"1 (= 0.131 W m 2) or the Langley day(Ly = 1 cal cm"2 which means 1 Ly = 0.483 W m~2) and Kcal rrf2 h"' (= 1.16 W rrf2) or cal nr2 s"1 (= 4.18 W rrf2) or in MJ rrf2 day1 (= 86.4 W rrf2).

Figure 3.15 shows a simple plot to estimate the daily clear sky solar radiation Qx due to the short waves, as a function of latitude and day of the year (30 to 300 Kcal nr2 h1).

 Latitude /^pf nI^sX / A// \V / / j 50° / : \

Jan Feb Mar Apr May Jun Jul Aug Sep Oct No\ Dec-Fig. 3.15. Clear sky radiation due to short wavelengths, according to Hamon et al. (1954).

Jan Feb Mar Apr May Jun Jul Aug Sep Oct No\ Dec-Fig. 3.15. Clear sky radiation due to short wavelengths, according to Hamon et al. (1954).

The net short-wave radiation Qsn = Q^- Q^ (£>sr = reflected short-wave radiation) is lower than the clear sky radiation (Q^) because of clouds and can be estimated by the following relation due to Ryan and Harleman (1973)

where C is the fraction of sky covered by clouds and the constant 0.94 roughly accounts for reflected short-wave radiation Q^. usually ranging from 4 to 20 W nr:.

Even if this model is easy to be set up, it is very dependent on the average cloud coverage of the site and for this reason it can be unreliable.

The example in Fig. 3.16 shows how it can work for one site yet fail for another when the clouds are not uniformly distributed over the year. Fortunately, average solar radiation does not change too much from point to point in a site and measured data of such a forcing function are usually available from the weather forecasting offices. This is the reason why, in environmental models, the solar radiation is simulated by regression on measured data by the formula

where a and b are parameters that have to be estimated on real data and_y is given by relation (3.17).

Figure 3.16a shows a set of daily radiation data gathered at Venice (Italy) during 1985 and the simulation obtained by relation (3.18). Figure 3.16b shows similar data for Manila (Philippines): it is easy to compare and appreciate the different agreement of the model with solar radiation data for a temperate and tropical place and to conclude that for the latter, the model would be changed and adapted. Days Days

Fig. 3.16. Daily radiation data gathered (a) at Venice (Italy) and (b) at Manila (Philippines) and the relative simulation curve, obtained by Eq. (3.18).

Days

Fig. 3.16. Daily radiation data gathered (a) at Venice (Italy) and (b) at Manila (Philippines) and the relative simulation curve, obtained by Eq. (3.18).

Gi„=0.-OM + OL--Olr-Ghr is the sum of two positive terms, the gross short-wave radiation, Qw, and the gross long-wave, Qk (260 to 420 W m~2), both with a wide range of values, and of three negative terms the two reflected £>sr, Qh (6 to 17 WrrT:) and a back radiation Qbr (255 to 400 W rrr2), numerical values are valid for a latitude close to that of the Mediterranean sea. This budget shows how a quantity of energy equal to that entering as long wavelengths is almost totally reflected as long wavelength radiation and the rest is leaving the earth after degradation as heat reflection and other radiation.

The long-wave incident radiation, Qk. is due to atmospheric radiation, the major emitting substances are water vapour, carbon dioxide and ozone. The approach generally adopted to compute this flux is the empirical estimation of an overall atmospheric emissivity of Swinbank (1963) (in BTU ft"2 day-1)

where Ta is the dry bulb air temperature in Fahrenheit.

The long-wave back radiation Qbr is the largest back flux of energy and a water body is evaluated according to the water surface emissivity (in cal m": s-')

where a is the Stefan-Boltzman constant (= 5.667 10 K W nT2 Kr4) and 7"w is the surface water temperature in Kelvin. A good linearization of relation (3.19) in the range from 0 to 30°C is given by the U.S. Army Corps of Engineers (1974) where Qb! is expressed in cal rrr2 s"1 and is the water temperature in °C

Solar radiation varies during the day as a sinusoidal curve, and relation (3.20) describes the variation of the intensity / as a function of t (hours of the day)

t can range over the photoperiod that is a fraction of the day and if we normalize the day length to 1, t can range between 0.5 - {P{ns|>)/2) and 0.5 + (P(/?,<t>)/2), out of this interval the light is zero because of night, due to the fact that the intensity is always positive the cos is shifted up by 1, relation (3.20) is finally normalized to the total daily solar radiation I(n) given by relation (3.18). 