Sabbagh model

An empirical formula was obtained which relatesthe daily total solar radiation to the sunshine duration, relativehumidity, maximum temperature, latitude, altitude and thelocation of the place  relative to the water surfaces.

Solar energyGlobal solar radiation model



Initial contribute: 2021-09-07


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Application-focused categoriesIntegrated-perspectiveGlobal scale

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Quoted from:J.A. Sabbagh, A.A.M. Sayigh, E.M.A. El-Salam,Estimation of the total solar radiation from meteorological data,Solar Energy,Volume 19, Issue 3,1977,Pages 307-311,ISSN 0038-092X,

The estimation of the performance of any solar energy utilizingequipment necessitates the knowledge of the solar radiation datawhich have been gained over a long period of time. Investigatorshave developed many empirical formulas to estimate the solarradiation using various parameters. These parameters are,the climatological data which has been measured for prolongedtime in various locations including sunshine hours: relativehumidity; maximum and minimum temperatures; cloud cover andgeographical location. Angstrom,Black,Glover andMcCullock and Sabbagh-Sayigh and El-Salam used thesunshine hours to estimate the mean solar radiation. Lui and Jordan,KreithSharma and Pal and Whillier used the declination angle and the latitude in their formulas.Bennett and Mateer combined the sunshine duration, thedeclination angle and the latitude to develop their formula.Swartman and Ogunlade used the relative humidity in additionto the sunshine duration in establishing their formula. Reddy etal. obtained their formula by using sunshine duration, therelative humidity and mean temperature, while in another formula Reddy suggested the use of the number of rainy days,sunshine duration and a factor which depends on the latitude andthe location of the place relative to the sea, in computing the dailytotal shortwave solar radiation.
In this paper an empirical formula was obtained which relatesthe daily total solar radiation to the sunshine duration,relativehumidity,maximum temperature,latitude,altitude and thelocation of the place relative to the water surfaces.
Sabbagh proposed following equation to estimate the monthly average daily global radiation that might be applicable to dry arid and semi-arid regions:
\( 𝐻=0.06407(𝐾_𝑔 )exp⁡[𝐿(𝑆/12−(𝑅𝐻^0.333)/100−1/𝑇_𝑚𝑎𝑥 )] \)
where Kg is geographical and seasonal factor and can be calculated from the following equation:
\( 𝐾_𝑔=100(0.2/(1+0.1𝐿) 𝑆_0+𝜓_𝑚 cos⁡𝐿) \)
where \( 𝜓_𝑚 \)  is a seasonal factor in month that is suggested by Reddy. The model is only reliable for locations with an average mean sea level of about 300 m and needs to be modifified for arid regions with higher altitudes.
The formula proposed in this study can be used to estimate thesolar radiation intensity fairly accurately in areas lacking suchdata. It relates the solar radiation intensity to the well establishedclimatological data, i.e. sunshine duration,relative humidity andmaximum temperature. Also to the geographical parameters, i.e.altitude,latitude of the location. The formula can be appliedaccurately to different locations with the same average best fittedcoefficient. This makes the formula ready to be applied even inareas where there is no data available.
Yearly and monthly total solar radiation were estimated withinan average error of ±5 per cent. This is clearly shown in Figs.8-11which demonstrate the validity of such formula and its accuracy incomparison with other existing forrnulae.Therefore using theappropriate K and the coefficient of 1.53, the formula can be used to predict total solar radiation on flat surface at anylocation. However it should be noted that the accuracy of thisformula was tested in arid and semi-arid zones only.


J. A. SABBAGH, A. A. M. SAYIGH, E. M. A. EL-SALAM (2021). Sabbagh model, Model Item, OpenGMS,


Initial contribute : 2021-09-07



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