## 1 Introduction  
The radiation budget at the ground surface is important to understand the climate system and its variability. Net radiation (\(R_{n}\)) is the sum of the net shortwave radiation (0.3-3.0 \(\mu\)m) (\(R_{ms}\)) and the net longwave radiation (0.3-100 \(\mu\)m) (\(R_{nl}\)). The net shortwave is the difference between the incoming global solar radiation (G) and the reflected radiation (R) from the ground, while the net longwave radiation is the difference between the downward (\(L_{th}\)) and upward (\(L_{up}\)) radiation components. Therefore, the net radiation (\(R_{n}\)) is generally defined as the difference between incoming and outgoing radiation of both short and long wavelengths and it is expressed as follows [1]:  
\[R_{n}=R_{ms}+R_{nl}=G(1-\rho_{S})+L_{th}-L_{up} \tag{1}\]where \(\rho_{g}\) is the surface albedo (fraction of Reflected radiation to Global radiation). Net radiation represents the effective energy provided by sun to heat soil and air as well as to evaporate soil surface water. The downward longwave radiation originates from gases present in the atmosphere such as water vapor, carbon dioxide, and ozone. About 90% of the downward longwave radiation at the ground surface comes from the first 800-1600 m of the atmosphere [2]. Therefore, the water vapor pressure and the air temperature are closely related to \(L_{dn}\). The role of clouds is also significant for the amount of the emitted downward irradiance [3,4]. On the other hand, the upward longwave radiation depends on the emittance/absorptance properties of the material at the ground surface and its temperature and is always higher than the downward irradiance. Therefore, the longwave radiation balance is normally negative. The knowledge of this radiation is important for agricultural meteorology and building heating/cooling systems, energy budget studies, frost forecasting and environmental applications [5, 6, 7]. Furthermore, the downward longwave radiation has shown a remarkable increase during the process of global warming [8]. The longwave radiation components can be estimated by four different methods [9], i.e., (1) direct measurements by pyrgeometers in meteorological stations, which is the most accurate method; (2) simple physical or empirical models which are the most popular and use mainly temperature and relative humidity and follow the Stefan-Boltzmann equation with recalibration of the coefficients under local conditions; (3) radiative transfer models which are data demanding and use meteorological observations from different layers of the atmosphere; and (4) through satellite observations where their accuracy needs to be improved. As outlined earlier, most of these empirical equations follow the Stefan-Boltzmann law:  
\[F=\epsilon*\sigma*T_{s}^{4} \tag{2}\]  
where \(F\) is the longwave radiation flux emitted by any surface which depends on the absolute surface temperature \(T_{s}\) and on the longwave emittance \(\epsilon\). The constant \(\sigma\) is the Stefan-Boltzmann constant (\(\sigma=5.66697*10^{-8}\)Wm\({}^{-2}\)K\({}^{-4}\)). The total emissivity can be estimated from clear-sky effective emissivity (\(\epsilon_{c}\)) and the emissivity which is modulated by clouds (\(\epsilon_{cl}\)). Dozens of parameterization formulas have been developed in which clear-sky effective emissivity is calculated as a function of the screen-level air temperature (\(T_{a}\)) and water vapor pressure (e), since about half the longwave radiation comes from the lowest 100 m of the atmosphere [1]. Details about the formulae for estimating emissivity are given by various authors [10, 11, 12]. [PERSON] [13] found that the precipitable water content was much better to represent the effective emissivity of the atmosphere than the water vapor pressure. Other authors [14,15] have extended the calculations of emissivity by adopting the effect of land use. [PERSON] [16] has estimated the effect of clouds on the longwave irradiance. The downward longwave radiation can be increased up to 34% with an overcast sky of low clouds [17].