ATMOSPHERIC RADIATION FROM CLOUDY SKY

Abstract

In the earlier paper (Nakagawa, 1977), the author has published the optimum Brunt type experimental formula for atmospheric radiation from a cloudless sky at Tateno based on theoretical calculations; _??_ where e0=RA/σT04 is the apparent atmospheric emissivity, RA is downward flux of atmospheric radiation from the sky, 6 is Stefan-Boltzmann constant, To is absolute surface air temperature, and e0 is surface water vapor pressure in mb. In reality, the sky is, however, nearly always cloudy. If clouds are present, the amount of downward longwave radiation from clouds is greatly increased and the cooling of the ground is correspondingly reduced. Consequently, when using the experimental formula for estimating atmospheric radiation, it is general practice to introduce the influence of cloudiness. The general solution for the equation of longwave radiation transfer in the atmosphere is given by _??_ where Bv (T) is Planck's function, _??_f is the transmission function of a slab, v is wave number, ni and Ti are, respectively, apparent fractional cloudiness and cloud base temperature of the i-th cloud layer. Subscription ∞ represents the top of the atmosphere. In the special case of n1=n2=n3=0, which denotes a cloudless sky condition, the numerical calculation scheme of the solution has been established (Nakagawa, 1977). Therefore, it is of importance to determine ni and Ti. In this paper, ni is determined from the result of surface visual observation of clouds, Tl is assumed to be equal to the temperature of the convective condensation level, and T2 and T3, follow Katayama (1966). Values computed with the program developed in this paper are in good agreement with directly observed values at Tateno (see Fig. 1). At four points in Japan, atmospheric radiation is calculated everyday in 1975 (see Fig. 2). After parameterizing the computed values, a new type experimental formula is determined as follows ; _??_ The coefficient aij is determined by the least square method (see Table 2). These formulae explain more than 99% of total variance. Consequently, whichever formula may be used, the resulting estimated values are about the same. Since the above equation contains several layers of clouds, it is necessary to obtain cloudiness at several layers for the calculation of the emissivity en. In practice, the accurate data of multiple layer cloudiness are not available, for this reason, the above equation is not suitable for the climatological studies. Another type formula with a use of total cloud cover is determined as follows; _??_ The coefficient aij determined is given in Table 3. The values of percent of reduction decrease, these formulae explaining from 96 to 90% of total variance. This formula derived from data at Tateno or Kagoshima systematically underestimates downward flux of atmospheric radiation during winter at Wakkanai or Wajima which is located in the districts along the Japan Sea. If only one formula is applied throughout the country, one for Wajima is the most appropriate. With a use of the formula for Wajima, monthly normals of net longwave radiation at 78 points in Japan are estimated (see Table 4). The isolines in the distribution map of annual normals of net longwave radiation (see Fig. 6) run parallel to the central mountain range, having a tendency to decrease from the districts along the Japan Sea to ones along the Pacific Ocean.