Cloud forcing Directory UMM :Data Elmu:jurnal:A:Atmospheric Research:Vol55.Issue2.Oct2000:

result of the interception of solar radiation by the sides of the cloud elements. The sequence of panels shows results for increasing absorption with the bottom right panel indicating near-plane parallel behavior of cloud field properties. Although finite cloud effects dominate the reflectance, the absorptance of the entire cloudy layer can be modeled quite well with the simple linear weighting of cloud and clear absorption that is standard practice in model parameterizations. The non-linearity appears, of course, in the transmittance term. The point to note here is that the effective Ž . fraction defined by Eq. 2 in terms of the reflectance can be quite different from that Ž . defined by Eq. 3 in terms of the absorptance. This has important implications for extracting cloud forcing from measurements, as we shall show later. 4.2. Liquid absorption, water Õapor window In this second set of computations, we assume that there is no vapor absorption in the clear or cloudy portions, i.e., t s 0.0 in addition to √ s 0.0. The vertical extinction 2 2 optical depth of the cloud elements is fixed at 20.0 and several values of the single scattering albedo are chosen in turn. The aspect ratios and cloud fractions are as in the earlier runs. Here again, we assume a Henyey–Greenstein phase function with g s 0.843. Fig. 6 shows the system reflectance and Fig. 7 the system absorptance for four values of the droplet single scattering albedo. Since there is no vapor absorption, the clear portions are completely transparent and in addition do not scatter either because we have confined ourselves to the near-infrared portion of the spectrum. Although there are similarities between Figs. 3 and 6, there are some striking differences. For example, even for the highly absorbing case, there are non-linearities in the behavior of system reflectance vs. cloud fraction. This is because, unlike the vapor absorption case, the photon aspect ratio is identical to the geometrical aspect ratio. Radiation impinges on the portion of the sides of the cloud element that are not shaded by neighboring clouds since there is no gaseous absorption between cloud elements. The incident radiation will also be significantly greater than in the previous case because there is no absorption by vapor above the cloud layer. These wavelengths will contribute the most to cloudy layer absorption of total energy. The absorptance, shown in Fig. 7, shows a pronounced non-linear behavior and simple linear weighting will be grossly inadequate. This point is more explicitly made Ž . Ž . by Fig. 8, which shows the effective cloud fraction based on Eqs. 2 and 3 . The substantial variation of N and N with single scattering albedo and, more impor- e R e A tantly, the difference between N and N point out the inadequacy of effective cloud e R e A Ž parameterizations based on geometric considerations Harshvardhan and Thomas, 1984; . Welch and Wielicki, 1984 . There is simply no unique relationship that can encompass both reflection and absorption, and all wavelengths.

5. Cloud forcing

Some of the recent discussion regarding solar absorption in the atmosphere has Ž centered around the cloud forcing at the surface and top of the atmosphere Cess et al., . 1995; Ramanathan et al., 1995 . In the context of finite cloud fields such as the bar cloud array discussed here, the cloud forcing at the top of the atmosphere, C , is the st difference in the net downward solar flux at the top between a clear atmosphere and one in which the finite cloud array has been embedded. Likewise, the forcing on the surface, C , is the difference between surface solar absorption with and without the cloudy layer. ss Here we can address issues related to the near-infrared solar cloud forcing in the presence of broken clouds, a situation that was fairly common in some of the reported Ž . Ž . studies Pilewskie and Valero, 1995 . Following Lubin et al. 1996 , for a partially cloudy atmosphere with normal cloud fraction, N, the mean reflectance R and absorp- tance A of the atmospheric column is usually written as R s R 1 y N q R N 4 Ž . Ž . c o and A s A 1 y N q A N 5 Ž . Ž . c o where R and A are the clear sky reflectance and absorptance, respectively, R and A c c o o Ž . Ž . refer to the corresponding overcast quantities. Now we can modify Eqs. 4 and 5 by introducing the respective effective cloud fractions, such that the system reflectance and absorptance are ˆ R s R 1 y N q R N 6 Ž . Ž . c e R o e R and ˆ A s A 1 y N q A N 7 Ž . Ž . c e A o e A Note that the effective cloud fraction defined in terms of reflectance is different from that defined by absorptance following the results presented earlier. A parameter used widely to characterize atmospheric absorption is the ratio of the cloud forcing at the surface and top of the atmosphere, i.e., f s C rC 8 Ž . ss st where C and C have been introduced earlier. Strictly speaking, our results cannot ss st provide f because all computations have been performed for an isolated cloudy field, but as long as the incident radiation is not diffuse, our estimates of N and N would e A e R still be valid and this is the case in the near-infrared as long as there is no overlying cloud layer. Ž . Ž . Ž . Ž . Substitution of Eqs. 6 and 7 instead of the usual practice of using Eqs. 4 and 5 in the definition of f yields A y A N Ž . o c e A f s 1 q 9 Ž . R y R N Ž . o c e R Ž . Ž . which reduces to Eq. 3 of Lubin et al. 1996 A y A o c f s 1 q 10 Ž . R y R o c when N s N . Since overcast skies usually result in enhanced column absorption and e A e R Ž . R R , f is typically greater than 1.0, perhaps as large as 1.5 Cess et al., 1995 o c although modeling studies generally obtain somewhat lower values. Inspection of Eq. Ž . 9 shows that f is not simply a function of the difference in clear and overcast properties but also dependent on geometrical effects. The ratio N rN can amplify or e A e R dampen the positive departure of f from unity. The albeit limited simulations presented here indicate that N rN is neither a universal ratio nor easily parameterizable. It is a e A e R function of wavelength since it depends on whether there is liquid or vapor absorption and also on the geometrical aspect ratio. Therefore, a simple interpretation of measured Ž . values of f as in Eq. 10 is not possible when geometric effects are present.

6. Conclusion