Solar radiation controls the temperature and moisture profile of soil and provides energy for photosynthesis. For assessing the potential productivity in agriculture recently there are proposals for modeling seed germination, crop-weed interaction and crop growth (Sirotenko, 2001; Cheeroo-Nayamuth, 1999) where solar energy is a major variable. This is a segment of solar energy computation where the most popular models have been developed using only minimum and maximum air temperature as input parameters.
Bristow and Campbell (1984) established an empirical equation for daily global irradiation using air temperature amplitude At = tmax — tmin:
The coefficients a, b and c have been found to be distinct for every location. Moreover this model demands calibration which involves a solar energy database – or such models are applied just to search out this quantity. Despite the disadvantage of requiring local calibration, the Bristow and Campbell scheme has been used as a core by many other models. Thornton and Running (1999) refine the Bristow and Campbell model over a wide geographic area with the aim to eliminate the need for locally calibration. A comprehensive evaluation of different 14 variations of the Bristow and Campbell method can be read in Wiss et al. (2001). We note here the updating done by Donatelli and Bellocchi (2001) which accounts for seasonal effects on cloudless transmittance using a sine function:
j is the Julian day, Atw is the weekly At and a, b, c, d are empirical constants. This model is one of the basic in the RadEst3.00 application (Donatelli et al. 2003), a useful tool to estimate global solar radiation in a given location.
In Eqs. (7.10) and (7.11) the clear sky model is implicitly embedded. But the usual modeling approaches for solar irradiation run in two steps: first the solar irradiation under clear sky condition H0 is computed and second, cloud cover is accounted via the Angstrom-Prescott equation. For H0 the integration of a clear sky model between sunrise and sunset and summing up these results to daily, monthly or yearly irradiation is the ordinary approach. There is a large number of solar irra – diance models elsewhere reported, having either empirical or physical basis that can be used in the computation of the daily solar irradiation with a reasonable level of accuracy. Apart from the Eqs. (7.10) and (7.11), in the following model daily global solar irradiation is related to its maximum possible value using daily air temperature extremes. The input is the daily temperature amplitude range At and the 5-day average of daily mean air temperature t computed as t = (tmax + tmin) /2. A range of several days for the calculation of average air temperature, centered in the day for which H is estimated, is introduced as for a good estimation of daily mean air temperature in a certain period of the year. In addition to At, the deviation of tfrom t5 is an appropriate measure of weather condition on the day: higher At and t «t5 indicate a sunny day while a lower At and t < t5 an overcast day.
Practically the model considers a linear dependence of H with respect to H0, having slope and interception as functions of At and t5, respectively.
H = H0f1(At )+f2(t5)
f1(At) = a1 + b1(At )c>
f2 (<5) = a2 + b2sin(^nl + c^ (7.12 a, b,c)
Figure 7.4 displays a 3D graph of the solar irradiation estimated with Eq. (7.12) showing the way in which the functions f1(At) and f2(t) act on H0. Two surfaces are plotted corresponding to H0 = 2kWh/m2 (in the winter days) and H0 = 8kWh/m2 (in the summer days) between which H are enfolded when (At, t) vary in the usual
Fig. 7.4 Plots oftheEq. (7.12 a, b,c) in the usual range of temperature for H0 = 2kWh/m2 (lower surface) and H0 = 8kWh/m2 (upper surface)
range. The graphic points out the role of sine function as a seasonal adaptor for H0 depending only on t.
The coefficients used are a1 = —0.324, b1 = 0.366, c1 = 0.424, a2 = 0.00576, b2 = 0.372, c2 = 1.832 and d2 = 26.35 which particularize the model for Western Romania (Paulescu et al. 2006). The sensitivity to origin location is due to the fact that the daily amplitude of air temperature and daily mean air temperature are parameters influenced in a complex manner by local meteo-climate. An increase of the model generality concerning the application area is possible by introduction a factor, denoted |, which adapt the coefficients in Eqs. (7.12 a, b,c) taking into account the behaviour At = At(t) over a period extending to several years. The approach has been introduced in (Paulescu et al. 2006) and points out that the corrective factor is characteristic to each location. This coefficient in its simplest form can be considered a constant. A practical implementation of | will be described in the next sub-section for fuzzy models.
The greatest benefit of the model (7.12 a, b,c) results from the synergism among the possibility of using simplified but accurate clear sky empirical irradiance models which require as input only geographical and temporal coordinates, and an Angstrom type equation which require at input air temperature, a worldwide measured parameter.