Direct solar radiation is the amount of solar radiation received by a plane perpendicular to the vector of the incident solar beam. In 1932, when JMA commenced observation of direct solar radiation, silver-disk pyrheliometers were used. Silver-disk pyrheliometers had excellent precision and stability, and the accumulated data measured with pyrheliometers were highly reliable (Sekine, et al., 1973), but the disadvantages in their use were that observation requires manual work, and continuous observation was not possible. Silver-disk pyrheliometers were replaced one after another from 1978 by electric pyrheliometers on an equatorial mounting, making continuous observation of direct solar radiation possible. Furthermore, completely automated observation began in 1992, with a pyrheliometer mounted on an automated sun tracker. Figure 188.8.131.52 shows a view of the observation system.
From 31 March 2010, JMA observes not only direct radiation but also diffuse radiation and long-wave downward radiation using a precise radiation observing system (Fig. 184.108.40.206) at five locations: Sapporo, Tsukuba, Fukuoka, Ishigakijima and Minamitorishima.
Whereas there are various definitions of the atmospheric turbidity coefficient, JMA calculates turbidity coefficients as defined by Feussner and Dubois. The atmospheric turbidity coefficient is calculated from instantaneous solar radiation (irradiance) that are measured in the periods defined by 30 minutes before and after 9:00, 12:00, and 15:00 in local apparent solar times in the condition of no clouds between the observing system and the sun.
Direct solar radiation per unit wavelength at wavelength decreases exponentially with increases in optical air mass and optical depth. The direct solar radiation reaching the ground at wavelength per unit wavelength is expressed by the following equation based on Beer's Law:
where, is the intensity of extra-terrestrial solar radiation per unit wavelength at wavelength , is the atmospheric optical depth, or attenuation cofficient of direct solar radiation for a vertical column, when the optical air mass is 1, and is the optical air mass which represents the depth of the atmospheric layer through which solar radiation passes defined to be 1 on the vertical plane. Beerfs Law is a theory stating that solar radiation of a single wavelength, and are wavelength-dependant. On the other hand, the wavelength range of interest in observations of direct solar radiation carried out by JMA is between about 0.3 and 3.0 µm. However, the atmospheric turbidity coefficient is calculated with the next equation below, with the assumption that the above equation holds approximately when it is integrated over wavelength.
The attenuation equation for direct solar radiation is expressed using the following equation by integrating equation (1) with respect to wavelength:
where in equation (2) is expressed by the following equation, dividing solar radiation attenuation into its different components:
where is the optical depth averaged over the wavelength range due to Rayleigh scattering in an ideal atmosphere at standard pressure with no water vapor, O3, CO2, aerosol, or other such gases, and an optical air mass of 1. is the optical depth averaged over the wavelength range due to absorption of gases (e.g., water vapor, O3, and CO2) when the optical air mass is 1 at atmospheric pressure ; is the optical depth averaged over the wavelength range due to scattering and absorption by aerosol when the optical air mass is 1 at pressure ; is the local pressure at the observation site at the time of observation; and is the standard atmospheric pressure. By substituting equation (3) into equation (2)
Further, by letting Linkefs turbidity coefficient be , equation (4) is expressed as:
and the equation for calculating Linkefs turbidity coefficient can be expressed as:
Linke's turbidity coefficient is a quantity expressing multiples of the optical depth of an ideal hypothetical atmosphere (Rayleigh atmosphere), where only air particles are assumed to be present, present in the optical depth of the actual atmosphere containing water vapor, O3, CO2, aerosol, and other gases. The value is necessary to obtain and is given as a function of absolute optical air mass . The observed optical depth can therefore not be compared to each other if the pressures differ from each other, even if the values are the same. Because of this, Feussner-Dubois proposed that be corrected for standard atmospheric pressure. Feussner-Dubois' turbidity coefficient can be expressed by the following equation:
where is the optical depth averaged over the wavelength range due to Rayleigh scattering in an ideal atmosphere at standard atmospheric pressure containing no water vapor, O3, CO2, aerosol, or other gases, and the optical air mass is .