Clear sky irradiance refers to the total irradiance (GHlclear) and direct irradiance (DNlclear) of the solar radiation incident on the ground surface at a location and time period without clouds. The clear sky irradiance represents the boundary condition of the superposition of the cloud attenuation signal received by the satellite (see Figure 1 for details).
Clear sky irradiance is a function of the following parameters:
· Extraterrestrial irradiance (a function of distance between the sun and the earth);
·The position of the sun in the sky represented by the sun’s zenith angle;
·Atmospheric gas composition, especially water vapor content and ozone content;
· Atmospheric aerosol content.
The sun’s zenith angle and altitude dictate the length of the path of extraterrestrial radiation incident on the earth’s surface (that is, the mass of the atmosphere). The length of the path affects the amount of solar radiation. The amount of solar radiation will be scattered when the radiation reaches the earth, or absorbed by atmospheric gas molecules and other components.
The term turbidity is often used to describe the mixing effect of aerosols and water vapor, which defines the transparency of the atmosphere. The most transparent atmosphere is probably the Rayleigh atmosphere, which contains only air molecules (oxygen, nitrogen, and trace gases). Atmospheric turbidity is superimposed on this ideal situation and is the main function of atmospheric aerosol content, and to some extent, it is also a function of atmospheric water vapor content and ozone content.
Aerosols are formed by small solid particles or small liquid particles in the air. The sources of these particles are diverse, such as sea salt, biomass burning, pollen, sand and dust, industrial pollution, traffic pollution and other particles produced by human activities. Aerosol has great variability in time and space, and its radiation effect is expressed by aerosol optical thickness (AOD). AOD depends on the size, type and chemical composition of the aerosol, and changes with the wavelength of the incident radiation. The solar radiation model described in this paper considers the average influence of aerosols on the entire solar spectrum, but ignores the degree of spectral dependence. Therefore, the average influence of broadband AOD on the entire solar spectrum can be used to express. It should be noted that the 700nm spectral AOD is regarded as an acceptable estimate of broadband AOD. Generally, under low atmospheric turbidity conditions, the AOD value ranges from 0.05 to 0.20; and in several regions of Central Africa, West Africa, Southwest Asia, Central Asia, North India and China, the AOD value sometimes reaches 0.8 or above (See Figure 2 and Figure 6 for details).
Water vapor absorbs incident solar radiation in the near-infrared region of the solar spectrum, thereby affecting the irradiance of clear sky. It should be noted that the water vapor content in the atmosphere will affect the condensation nuclei around the aerosol, thereby affecting AOD. Under normal circumstances, the total atmospheric column water vapor W can be used to represent water vapor. The annual value of water vapor (precipitable) in 2009 is shown in Figure 3 (the profile of annual precipitation in Ouagadougou, Burkina Faso, West Africa, see Figure 5 for details).
The ozone layer absorbs ultraviolet rays in the solar spectrum and thus has an impact on solar radiation. The ozone content is expressed in Dobson units (du), that is, in standard atmospheric conditions, the thickness of the 0.01mm ozone layer is one Dobson unit. Although ozone absorption is important for spectral resolution models or models for ultraviolet radiation in solar radiation, broadband irradiance is not very sensitive to ozone. Therefore, many broadband models do not consider the variability of ozone and use constant values. In temperate climates, the content of ozone is generally in the range of 250-350du, but in the winter polar regions it can only reach 150du or even lower.
In addition to the solar zenith angle, the factors that have the greatest impact on clear sky irradiance are AOD, W, and ozone. Ground elevation has the least influence on clear sky irradiance. Figure 4 compares the effects of doubling the above factors on the clear sky irradiance DNIclear.
Both the SolarGIS model and the SUNY/SolarAnywhere model adopt the simplified clear sky model established by Ineichen (2006, 2008), which are expressed as GHIclear and DNlclear in equation (1) and equation (2), respectively.
I’, Z, τg, and α represent the modified normal incident irradiance (including the influence of precipitation and site elevation), the solar zenith angle, the aerosol attenuation coefficient (also including the site elevation effect), and the factor α (which is the elevation And AOD function). Ineichen (2008) gave a detailed introduction to the model and its coefficients.
Without DNI, τb and b in equation (2) are similar to τg and α.
Another commonly used model of clear sky irradiance DNI is the broadband model of Bird (1981) [as shown in equation (3) and solar transmittance benchmark evaluation] and the dual-band (REST2) broadband model established by Gueymard (2008) [as in equation (4) and equation (5)].
In equation (3), lo, TR, To, TUM, TW, and TA represent the normal incident irradiance outside the earth, Rayleigh scattering transmittance, ozone absorption transmittance, uniform mixed gas absorption transmittance, water vapor absorption, respectively Transmittance and aerosol absorption and scattering transmittance. As mentioned above, Bird and Hulstrom have detailed the above-mentioned coefficients and their correlation as a function of atmospheric composition, site elevation, and solar orientation.
The REST2 model proposed by Gueymard reverses the performance of DNIclear and clear sky diffuse irradiance DIFclear. GHlclear can be derived from the sum of DNIclear and DIFclear. DNIclear‘s formula is similar to Bird’s formula (which contains one item of TN and-nitrogen dioxide absorption rate). In addition, the REST2 model contains two spectral bands with completely different transmission characteristics and scattering characteristics [that is, the subscript i in equation (5)].
Ba, BRi and Fi in equation (5) represent aerosol forward scattering factor, Rayleigh forward scattering fraction and multiple scattering correction coefficient, respectively. Gueymard gave a detailed introduction to the various coefficients.
It should be noted that early clear sky models used Link turbidity factor (TL) to represent all non-Rayleigh effects in clear skies (aerosol, water vapor, and ozone). Up to now, some satellite models still use this unit. On the physical level, the turbidity factor indicates the amount of superimposed Rayleigh atmosphere. In fact, this means that the attenuation of extraterrestrial radiation on the earth’s surface is the same as the attenuation of the turbid atmosphere. Based on the early clear sky model using TL and the clear sky equation proposed by Kasten, Ineichen and Perez, GHIclear and DNlclear [Equations (6) and (7)] are derived.
The m in equation (6) represents air quality, while fh1 and fh2 are functions of site elevation, in meters, which are equal to e(﹣alt/8000) and e(﹣alt/1250), respectively.
It should be noted that the accuracy of the clear sky irradiance at any particular moment mainly depends on its input parameters, firstly AOD (or TL), and secondly the model formula itself. Normally, the monthly climate values of AOD, W, and O3 representing the current location are used in models (such as NRELCSR, HelioClim, and 3-Tier databases). Recently, through the combination of ground monitoring and satellite remote sensing monitoring, the emergence of new data sources has created new characteristics of monthly/annual AOD and W values (Gueymard, 2012a; AEROCOM2012; see Figure 5 for details).
The recently developed atmospheric transport model and spaceborne model (Papadimas et al., 2009) can provide the day’s AOD (such as MACC 2012, MATCH 2012; see Figure 6). It has been observed that the model driven by AOD and W on the day can capture the dynamic changes of atmospheric transmittance related to weather fronts, pollution conditions and sand and dust transport activities, so it is better than the monthly weather model. However, since the model is still in the development stage, it is still important to verify its accuracy and perform local calibration if necessary.