Estimating the Received Solar Radiation by Bird and Hulstrom Model in Isfahan Province

Solar energy is one the most important renewable energies in Iran, but according to Iran’s high potential of using this energy, it has not been seriously used. Iran has deserts so that it brings about a high capability of using solar energy. Nowadays, the growth of population in the world has led to the limitation of energy resources and many ecological effects have been occurred so the attraction of attentions to the renewable energies has increased. For example, the plan of using solar energy has been started in Germany, although it is located in high latitude. As Iran’s oil resources are non-renewable energy, by constructing solar power plants, the government can produce electricity, export to neighbor countries and increase its income. The main purpose of this study is to estimate and assess the time-spatial variation for the received radiation by earth surface in Isfahan province by using the optimized model of Bird and Hulstrom. This model considers most of the influential parameters on received radiation such as absorption and scattering, water vapor, atmosphere mass, atmosphere Albido and etc.
Methods and Material: In this study, the daily solar radiation amount has been estimated by considering climatic and Spatial features in Bird and Hulstrom model. Bird and Hulstrom (1981) have represented equations according to atmospheric parameters as shown in equation (1) (Safaripour and Mehrabian, 2011). To estimating the total daily received radiation by earth surface, equation (1) is used:Equation (1): H=(H_(B ) cos θ_DF)/(1-r_g r_s)
In equation (1), HB is the Direct daily global irradiation at earth’s surface, θ is Altitude Angle, HDF is Daily diffuse irradiation at earth’s surface, rs and rg are Ground albedo and Sky albedo. The value of HB (the Direct daily global irradiation at earth’s surface) is calculated by equation (2):Equation (2): HB = IB (n/N)
In equation (2), IB is the Direct beam irradiance for clear sky which is calculated in equation (3) as following:Equation (3): IB = 0.9662I_0 (T_M – a_w ) T_A
In the equation (3), I0 is the solar constant with the value of 1367 W/m2, TM is the Transmissivity of atmospheric gases except water vapor, TA is the Transmissivity due to absorption and scattering and aW is the Water vapor absorptance. The value of HDF is calculated by equation (4) as following:Equation (4): H_DF=I_DF (n/N)^* (1-(n/N))(I_B_DF)
The value of constant K* is equal to 0.32, n is Hours of measured sunshine, N is the Potential astronomical sunshine hours (within the day) that vary according to the season, year and solar angle. Diffuse irradiance for clear sky (IDF) is calculated based on equation (5) as following:Equation (5): 〖 I〗_DF= I_0 (cosθ)(0.79)T_0 T_W T_UM T_AA [0.5(1-T_R) B_a (1- T_AS)]/[1-m (m)^1.02]
In equation (5), T0 is the Transmissivity due to ozone, TW is the Transmissivity of water vapor, TUM is the Transmissivity due to oxygen and carbon dioxide, TA Transmissivity due to absorption and scattering by particles, TAA is the Transmissivity due to absorption by particles, and TR is the Transmissivity due to Rayleigh Scattering. Ba is the percentage of scattered radiation by earth surface under the effect of superficial suspended particles (constant value equal to 0.84). The Extraterrestrial daily irradiation is calculated by equation (6) as following:Equation (6): H_0=(24I_0 E_0)/π(cos∅cos⁡δ sin⁡〖ω_s(πω_s)/180〗 sin∅ sinδ
In equation (6), I0 is the solar constant equal to 1367 W/m2, δ is Declination angle, ωs is Sunset hour angle. The Direct Solar irradiance on horizontal surface, Solar irradiance on horizontal surface from atmospheric scattering and Total (global) solar irradiance on a horizontal surface (7), (8) and (9) respectively shown as following (Bird and Hulstrom, 1981):Equation (7): Id = I0 * cosθ * 0.9662 * Tr * T0 * TUM * Tw * TA
Equation (8): Ias =I_0*cosθ * 0.79 *T_A* a_w*T_0 * T_UM
Equation (9): IT = (Id↫)/(1-r_g*Ba)

Results And Discussion

The maximum received radiation in winter is for central, western and southern regions of Isfahan and this is because of these region’s altitudes. The minimum received radiation by earth surface is in January and February for Khorobiabanak station and in March for Kashan station. The maximum received radiation in January, February and March is for Daran and Kabutar Abad stations respectively. In spring, the radiation is a little different from winter. Generally, in spring, the sun latitude gets higher and more radiation is received by the earth. In April, the minimum radiation is for Shahreza and the maximum is for east Isfahan station. In May, the maximum radiation is for Golpayegan station and the minimum is for Kashan. In June, most regions of the province have high radiation and only Kashan station has lower radiation than the others. At the end of the spring and the beginning of the summer, with the sun latitude reaching to its most, desert regions have more radiation energy than High ones. In June and July, the maximum radiation energy is received in most regions and that is because of receiving direct radiation. The radiation reached to the surface of the earth in summer is influenced by sunshine and solar radiation angle. On the other hand, entering external factors such as air mass get cut and subtropical high pressure gets control of the region. Radiation angle in southern latitudes of Isfahan province is more and the atmosphere thickness is lower than northern latitudes. The amount of radiation weakness is dependent on the length of the path while passing the atmosphere. This is because the earth’s gas coverage absorbs an important part of the solar radiation and emits the rest of the radiation to the surroundings. In this season, the maximum radiation received is for eastern and southern regions of the province. After July, the Altitude Angle gradually decreases and in autumn, the maximum received radiation is for Khorobiabanak station.


The main purpose of this study is to estimating the received radiation on earth surface by using Bird and Hulstrom model in Isfahan province. The gained results from this model were using co-Kriging Interpolation Methods. The results of this study showed that Bird and Hulstrom model can estimate the radiation well in this province, so that the maximum Direct beam irradiance for clear sky (IB) is in July with the value of 36.77 MJ/m2. Diffuse irradiance for clear sky (IDF) has the minimum value in winter and autumn, so that the minimum received radiation in January is with the value of 5.68 MJ/m2 and the maximum is in July with the value of 6.43 MJ/m2.
The Direct daily global irradiation at earth’s surface (HB), the Daily diffuse irradiation at earth’s surface (HDF) and the Daily global irradiation at earth’s surface (H) received by earth surface have the maximum value in July and June respectively. It seems that the reasons caused the most radiation occur in summer are Altitude Angle, increase in sunshine and Iran’s location around subtropical high pressure. The estimated results showed that in December and January (autumn and winter), the received radiation is minimum and in June it is maximum. The average received radiation in winter, spring, summer and autumn is 16.91, 27.37, 27.04 and 15.93 MJ/m2 respectively.

Article Type:
Research/Original Article
Geography and Development Iranian Journal, Volume:16 Issue: 51, 2018
159 - 174  
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