Accuracy of Solar Irradiation Models Based on Air Temperature Data

The results synthesized below are based on results reported in a lot of paper con­cerning the testing of temperature based models under Romanian climate.

The database here considered contains daily global solar irradiation, maximum and minimum air temperature, sunshine duration and daily mean of cloudiness, all recorded in the year 2000. The stations belong to the grid of Romanian Meteorolog­ical Agency: Bucuresti (44.5°N; 22.2°E; 131m), Constanta (44.2°N, 28.6°; at the Black Sea seacoast), Craiova (44.3°N; 23.8°E; 110m), Iasi (47.2°N; 27.6°E; 130m) and Timisoara (45.7°N; 21.2°E; 85.5m), Galati (45.48°N; 28.01°E; 72m).

The accuracy of different models is compared using two statistical indicators: Relative Root mean Square Errors (rrmse) and Relative Mean Bias Errors (rmbe) which are reading as:

where yi and Fi are the i-th measured and computed values of radiation quantities, while n is the number of measurement taken into account.

In Table 7.2, air temperature based models are compared with models that do not include air temperature as input. The models have been run with the fol­lowing parameters: a = 0.075, b = 0.428 and c = -0.283 in equation (7.1) be­ing appropriate for 45°N latitude; a = 0.71, b = 0.112, c = -6.72 • 10-3 and d = -0.283 in Eq. (7.11) as mean values at 45°N latitude, provided by the au­thor (http://www. isci. it). The empirical irradiance A model (Adnot et al. 1979) has been used for the clear sky global solar irradiation which was carried along in the Kasten and Czeplak (1979) equation for daily solar irradiation. The parametric Hy­brid model proposed by Yang et al. (2001) has been run with an Angstrom – Prescot type equation provided by them. The input used local recorded parameters with two exceptions: the depth of ozone layer equal to 0.35cm • atm and the Angstrom tur­bidity coefficient в = 0.089 computed as a mean value after Yang et al. (2001). We place these models in Table 7.2 because it was proved that they are appropriate for Romania (Badescu, 1997; Paulescu and Schlett, 2004).

The results from Table 7.2 demonstrate that the estimation of monthly mean of daily global solar irradiation can be performed with an acceptable accuracy using temperature based models. This is comparable with the accuracy of estimation us­ing classical models. The adding of air temperature to cloudiness in equations like Eq. (7.1) is not leading to significant improvements. But the solar irradiation can be computed via cloudiness and air temperature if sunshine duration data is miss­ing. The models which use only air temperature as parameter (including the fuzzy model) shows the same accuracy but have the merit to use for input the highest

Table 7.2 Range of statistical indicators of accuracy of monthly mean daily global solar irradia­tion. The models have been applied at the mentioned stations for the year 2000. Statistical indicator range includes results from Paulescu and Schlett (2004); Paulescu et al. (2006)


Input parameters



H/He, Eq. (7.1)

N, At


[-0.132, 0.123]

H/He, Eq. (7.7)

N, tmax, tmin


[-0.078, 0.064]

H/He, Eq. (7.11)a

At, Atw


[-0.129, 0.107]

H/H0, Eq. (7.12 a, b,c)

At, t


[-0.118, 0.094]


tmax, tmin

[0.082, 0.062]

[-0.020, 0.006]




[-0.029, 0.082]




[-0.045, 0.069]

arrmse range not includes data from the station of Constanta where it is >0.3

Fig. 7.9 Estimated with the fuzzy model and observed daily global solar irradiation at the station of Timisoara in the last six months of the year 2000

spatial recorded meteorological parameter. Since these models are close connected to the origin location need careful calibration when are applied in location with air temperature special regimes (seacoast or higher altitudes). Regarding the details of daily global solar irradiation, Fig 7.9 shows that the estimation of daily so­lar irradiation with a temperature model tracks actual measurements with good accuracy.

2 Conclusions

Simple formulae that can be used to calculate daily global solar irradiation based on air temperature data have been exposed. These models either using air temperature as additional parameter to cloudiness or using only air temperature are both viable alternatives to the classical equations based on sunshine duration. These equations may be useful in many locations where sunshine duration measurements are missing but air temperature measurements are available in many-year database. Thus, the number of sites where the estimation can be performed is much higher. The methods based on temperature database comparison are able in many cases to exceed the sensitivity of temperature models to origin location. A distinct case is the model built inside fuzzy logic, which may exhibit the flexibility needed in solar energy forecast. The readers can test the presented fuzzy model included on the CD and potential users are encouraged to modify the fuzzy procedures in order to customize particular applications.

Updated: August 4, 2015 — 3:32 am