Short-Wave Solar Radiation in the Earth’s Atmosphere Part 9 pot

246 Analysis of Radiative Observations in Cloudy Atmosphere Fig. 7.7a,b. Spectral dependence of single scattering co-albedo 1 – ω 0 retrievedfromthe ground observation data: a in Arctic, 1979and b in St. Petersburg suburb (city Petrodvorets), 1996 Fig. 7.8. Spectral dependence of optical thickness τ 0 retrieved from the data of the ground observations in Arctic: experiment 11 – 13 August 1979 and experiment 12 – 08 October 1979 7.3.2 Data Processing of Satellite Observations Optical thickness τ 0 and single scattering co-albedo 1 −ω 0 for extended clouds were obtained with inverse asymptotic formulas [(6.13), (6.28)]. The approx- imate accounting of the horizontal inhomogeneity including the scattering of radiation by the upper atmospheric layers was accomplished with (6.36) and (6.39). Multidirectional reflected radiance measurements with the POLDER Optical Parameters from Ground and Satellite Observations 247 instrument were processed for the retrieval of cloud optical parameters. The pixels with the cloud amount exceeding 0.5 were only considered. The follow ing sequence of the procedures for every pixel is proposed for processing POLDER data: 1. At the first step the angular dependent functions are calculated. 2. The next step includes the calculation of the approximate optical thick- ness for every viewing direction with the simple formula, assuming theconservativescattering.Theobtainedvaluesshowthedegreeofthe shadowinginfluence(ortheinfluenceofthecloudtopdeviationfrom theplane)andgivethepossibilitytoevaluateparameterr with (6.39). Besides, they allow choosing the pairs of viewing directions where the optical thickness is approximately equal. 3. Thethirdstageconsistsoftheparameters 2 retrieval from the radiances at each pair of viewing directions with the equal optical thickness [(6.13)]. If the optical thickness defined at the previous stage without accounting of the absorption is more than 100, parameter s 2 is obtained according to (6.16). Then the averaging over all pairs of the viewing directions is accomplished, and the relative mean square deviation is estimated. 4. At the fourth stage optical thickness τ 0 is calculated for every viewing direction, assuming the true absorption, and the results are averaged. 5. Then, the similar procedure is repeated for every available wavelength. 6. At the sixth stage the res ults are prepared for mapping (inserting the missed pixels; inserting the values averaged over the neighbor pixels to the missed pixels or to the pixels with only one viewing directio n; rejecting the edge pixels). The uncertainties are calculated for every pixel using the formulas similar to (6.46). 7. Finally, the images of the single scattering co-albedo and optical thick- ness are figured with the GRADS editor. The space distribution of single scattering co-albedo (1 − ω 0 ) is shown in Fig. 7.9, optical thickness τ 0 is shown in Fig. 7.10 (Melnikova and Nakajima 2000a,b). The values of (1 − ω 0 ) are in the range 0.001–0.010; the optical thickness is about 15–25 and can reach 100 in the Tropics. Black gaps in the images cor- respond to the pixels with the cloud amount less than 0.5. Four images are presented in Figs. 7.9 and 7.10, the upper picture join three images registered during the successive satellite pass with time interval about one hour (i.e. these images are presenting one cloud field). Figure 7.11 demonstrates the values of (a) – single scattering co-albedo (1 − ω 0 ), and (b) – optical thickness τ 0 and shadow parameter r multiplied by 10 2 in three spectral channels ver sus pixel numbers. The latter turns not to depend on wavelength, and in con trast the spectral dependence of the optical thickness decreases with wavelength for all (!) processed pixels. Please remember that the processing has been accomplished for every wavelength independently. The size of every pixel is about 60 km. 248 Analysis of Radiative Observations in Cloudy Atmosphere Fig. 7.9. Images of single scattering co-albedo (1 − ω 0 ) of the cloud pixels, retrieved from POLDER data Fig. 7.10. Images of optical thickness τ 0 ofthecloudpixels,retrievedfromPOLDERdata General Analysis of Retrieved Parameters of Stratus Cloudiness 249 Fig. 7.11a,b. Cloud optical parameters versus pixel numbers: a – single scattering co-albedo (1−ω 0 ), and b – optical thickness τ 0 (solid line)andshadowparameterr×10 2 (dashed line) for three wavelength channels 443 nm – black line; 670 nm – red line; 865 nm –blueline;1– latitude 58.75 ◦ N and longitude 23 ◦ W–75 ◦ ; 2 – latitude 44.75 ◦ N and longitude 24 ◦ W–30 ◦ E; 3 – latitude 8.75 ◦ N and longitude 120 ◦ E–140 ◦ E 7.4 General Analysis of Retrieved Parameters of Stratus Cloudiness 7.4.1 Single Scattering Albedo and Volume Absorption Coefficient Molecular absorption bands are apparent in the figures illustrating the spectral dependence of single scattering co-albedo (1 − ω 0 )buttheyareexpressed differently in different cloud layers. The molecular band at wavelength 0.42 µ appears in experiments 1, 2 and 4. I t can be identified as an absorption by hematite (see Sect. 3.3, Fig. 3.14 and studies by Ivlev and Andreev 1986 and Sokolic and Toon 1999) contained in flue sand escapes from the Kara-Kum and Sahara deserts. One can see the weak bands of the aerosol absorption at wavelengths around 0.5 and 0.8 µm in the curves obtained from the data of experiments 3 and 4, accomplished above the sea surface. I t could be attributed 250 Analysis of Radiative Observations in Cloudy Atmosphere to sea salt (namely to NaCl) content in the atmospheric aerosols according to the study by Ivlev and Andreev (1986). The atmosphere in the Arctic regions is purer – the conservative scatter- ing becomes apparent within a large range of wavelength (Fig. 7.2d, experi- men t 11). Spectral values (1– ω 0 ) retrieved from airborne experiments 3 and 7 (Fig. 7.2b,c) and from the satellite experiments (certain parts of the curves in Fig. 7.11, 3) demonstrate a monoton ic increase with wavelength that can be attributed to organic fuel combustion (Sokolic 1988). The values of single scattering co-albedo (1– ω 0 )obtainedfromairborneexperiments1,2and5 and most pixels of the sat ellite images show no spectral dependence, which is typical for the black carbon and dust aerosols. Consideration of volume absorption coefficient κ of the s eparate cloud sub- layers (Fig. 7.4) indicates strong vertical inhomogeneity. The upper curves in Fig. 7.4b demonstrate significant absorption by two upper cloud sublayers cor- responding either to the oxygen and water vapor absorption bands (0.68, 0.72, 0.76 µm) or to the ozone Chappuis molecular absorption band (0.65 µm). Two lower sublayers show the opposite spectral dependence. It could be explained with the higher content of ozone in the upper tropospheric layers compared with the lower ones. The results of exper iment 7 show the monotonic increase of the absorption coefficient with wavelength in the bottom layer (1.0–1.1 km). A similar result has been mentioned above for the cloud, considered as a whole layer. Inspiteofsignificantuncertaintiesoftheretrievalofvalues(1− ω 0,i )and especially τ i the obtained result demonstrates the r ather real magnitudes and spectral dependence coinciding with the results of considering the cloud layer as a whole. Using the spectral dependence of the irradiances promotes dimin- ishing the uncertainties of the retrieval because the results obtained for the neighbor wavelengths do not distinguish stro ngly fr om each other. Smoothing over spectral values out of the absorption bands could be rather effective for obtaining the real values of the optical parameters. Several pixels of the satellite images (in Fig. 7.11, 1) are characterized with magnitude 0.05 for value (1 − ω 0 ). It could be concl uded that the observational errors increases at the edges of the image, especially for the single pixels with the strong absorption. However, the other parts consist of several pixels with the higher absorption and could correspond to the industrial regions with the increasing content of the soot aerosols. Only some rare pixels above the ocean are characterized with the conservative scattering of radiation. 7.4.2 Optical Thickness τ 0 and Volume Scattering Coefficient α The values of volume scattering coefficient α vary strongly in different exper- iments. Spectral dependence α(λ) demonstrates the strong vertical inhomo- geneity of the cloud, and both the magnitudes and the spectral dependence are different in different cloud sublayers. It reflects the inhomogeneity of the mi- crophysical cloud structure. The volume scattering coefficient obtained for the cloud as a whole coincides with the averaged values obtained for the separate Influence of Multiple Light Scattering in Clouds on Radiation Absorption 251 sublayers within the uncertainty range. The scattering coefficient is maximal for the inner sublayers close to the cloud top. The obtained vertical profile of thevolumescatteringcoefficientissimilartotheairborneresultsaccomplished in stratus-cumulus cloudiness in the Southern hemisphere (Boers et al. 1996) and to the results of the FIRE experiment in the Arctic (Curry et al. 2000). The same values are cited in the book by Mazin and Khrgian (1989) for stratus clouds. Thus, our results could be assumed to be the quite real ones. Figure 7.10 illustrates that most pixels are characterized with optical thick- ness τ 0 about 10–25, while i n some regions consisting of several pixels the optical thickness reaches 70–80 and even 100 (in the Tropical latitudes). Space variation s of the optical thickness seem rather monotonic in images obtained from the satellite data, and this obstacle points to the low enough uncertainty of either observatio ns or da ta processing. The presented results of the retrieval of optical thickness τ 0 and single scat- tering albedo ω 0 fromthe airborne, ground, and satellite radiative observations demonstrate the similar values and spectral features in spite of using different observational methods and different formulas. It shows the inverse asymptotic formulas to be quite suitable for obtaining the cloud optical parameters. The elaborated method has more advantages comparing with the other methods (Rosenberg et al. 1974; Asano 1994; Nakajima TY and Nakajima T 1995; Rublev et al. 1997) because it pr ovides obtaining two parameters for every wavelength in the shortwave spectral range and for every pixel of the satellite images independently and with no additional restricting assumptions. The approximate account of the cloud top inhomogeneity turns out to be rathereffectiveeither forinverse orfor directproblems.The introducedshadow parameterturnsouttotakeintoaccounttheupperatmosphericlayersinfluence together with the uncer tainty of the phase function approximation with the Henyey-Greenstein function. It will be promising to analyze the results of similar data processing in the global scale. It should be mentioned that the more accurate presentation of the phase function would change the numerical magnitudes of the results because it has to retrieve the phase function parameter for substituting its real value instead of the model one to the formulas. 7.5 Influence of Multiple Light Scattering in Clouds on Radiation Absorption 7.5.1 Empirical Formulas for the Estimation of the Volume Scattering and Absorption The results discussed in the previous section have common features, namely: 1. magnitudes of the single scattering albedo are lower than the values calculat ed with Mie theory, 2. and the existence of the spectral dependence of the optical thickness con tradicted Mie theory r esults. 252 Analysis of Radiative Observations in Cloudy Atmosphere TheinterpretationoftheUVradiationobservationsinthecloudyskyby(Mayer et al. 1998) also demonstrates the strong extinction: the cloud optical thickness in the UV region has been retrieved to be equal to several hundreds. Mie theory calculations yield volume scattering coefficient α (and optical thickness τ 0 )forensembleoftheparticleswithsize> 5 µm independent of wavelength in the shortwave region, and the magnitude of the volume absorp- tion coefficient in the cloud has to be in range 10 −5 –10 −8 (single scattering albedo ω 0 is about 0.99999–1.0). Here we propose a possible explanation of this contradiction. It links with the multiple scattering within clouds. Qualitatively the similar assumption has been proposed in the book by Kondratyev and Binenko (1984), while considering the airborne observational data. The cloud layer is considered to consist of droplets, sometimes with addi- tion of aerosols within the droplet. The molecular scattering is accounted for with summarizing the scattering coefficients and as the molecular scattering coefficientismuchlower(byafactorof10 3 ) than the cloud scattering coef- ficient, its yield turns out to be negligible. It’s known that the mean number of the scattering events in the cloud with optical thickness τ 0 is proportional to τ 2 0 owing to the multiple scattering (Minin 1981,1988; Yanovitskij 1997); forreflectingphotonsitisproportionalto τ 0 . Thus, the photon path within the optically thick cloud significantly increases compared to the photon path within the clear sky, and the number of collisions with air molecules (more rigorous with fluctuations of the molecular density) increases as well. The radiation absorption removes the part of photons and weakens the increasing effect of the molecular sca ttering. Since it is necessary to tak e into account tha t the cloud layer does not simply superpose to the molecular atmosphere, but it increases the molecular scattering. We should mention that the increasing of the molecular absor ption within oxygen absorption band λ = 0.76 µm due to the increasing of the photon path within the cloud has been considered in various studies (Dianov-Klokov et al. 1973; Marshak et al. 1995; Kurosu et al. 1997; Pfeilsticker et al. 1997; Wagner et al. 1998; Pfeilsticker 1999). The same reasons are also valid for radiation scattering and absorption by the aerosol particles between droplets. It is clear that the multiple scattering theory and the radiative transfer equa- tion takes in to a ccount all processes of scattering and absorption, but it is right only, if they are accurately put in the model of scattering and absorbing medium. Usually the averaging values of scattering and absorption coefficients over the elementar y volume are substituted to the transfer equation and then the solving is accomplished with one of the radiativ e transfer methods. How- ever, from the physical point it is incorrect to average the initial parameters over the elementary volume befo re solving. The incorrectness is intensified with the essentially different scales of the elementary v olumes for different particles (molecules, aerosols and droplets), whose sizes distinguish by an or- der of magnitude and much more (look Sect. 1.2) and the transfer equation is derived in a phenomenological way for this incorrect elementary volume. Strictly speaking, the equation of the radiative transfer for the complex multi- component medium is to be inferred from Maxwell equations accounting all Influence of Multiple Light Scattering in Clouds on Radiation Absorption 253 its components. However, we don’t aim here to consider the mathematical aspectoftheproblem,thusweproposetheempiricalapproach,presentedin several studies (Melnikova 1989, 1997; Kondratyev et al. 1997; Melnikova and Mikhailov 2000). Usually the scattering or absorption coefficients of the whole medium are presented as a sum of the corresponding coefficients of separate components. Specify the optical parameters relating to the molecular component with M, relating to the aerosol component with A, and relating to the droplets with D. Then the usual notation looks like: α = α M + α A + α D , κ = κ M + κ A . (7.1) Accounting for the mutual influence of the scattering and absorption by dif- ferent components, we propose the empirical relations: α = (α M + α A )Cτ p D ω q 0 + α D , κ = (κ  M + κ  A )Cτ p D ω q 0 , (7.2) where ω 0 isthesinglescatteringalbedo,C isthefactorofproportionality, τ D and α D are the optical thickness and the volume scattering coefficient caused only by scattering by droplets (value of τ 0 in Fig. 7.1 and value of α in Fig. 7.12a for λ > 0.8 µm), α  M , α  A , κ  M , κ  A are the values of scattering and absorption coefficientsof molecules and aerosol particles in theclear sky ( α  M is a coefficient of Raleigh scattering) at corresponding wavelength and altitude of the atmosphere;pand q are the empiric coefficients, estimated inseveral studies (Melnikova 1989, 1992, 1997; Kondratyev et al. 1997; Melnikova and Mikhailov 2000). The coefficient of scattering by droplets α D has no factor because the Fig. 7.12a,b. Spectral dependence of the volume coefficients (a –scatteringandb –absorp- tion) of the stratus cloud, retrieved from the data of the experiments, numbered as per Table 3.2 254 Analysis of Radiative Observations in Cloudy Atmosphere Fig. 7.13a,b. Volume c o effi c i ents o f a –scatteringandb – absorption, transformed using (7.2). The curve numbering corresponds to the experiments, listed in Table 3.2. The curve marked with letter R characterizes the molecular scattering at altitude 1 km equation of radiative transfer and corresponding asymptotic formulas solving it are written for one component – droplet (in some cases for the droplet with the absorbing particle within it). Item κ  M τ p D ω q 0 in the second of (7.2) differs from zero only within the molecular absorption bands. Remember that the problem is considered only for τ 0 >> 1. Factor C turns out to be equal to unity. Powers p and q are equal to: p = 2and q = τ 2 0 , as per the estimations in several studies (Melnikova 1989, 1992, 1997; Kondratyev et al. 1997; Melnikova and Mikhailov 2000). These magnitudes correspond to the above-mentioned fact that the mean number of scattering events in the cloud of optical thickness τ 0 is proportional to τ 2 0 (Minin 1981; Yanovitskij 1997). We should point out that powers p and q were obtained from the analysis of the magnitudes of volume scattering and absorption coefficients for the data of two experiments at two wavelengths. Transform values [ α(λ)−α(0.8)] and κ(λ) (Tables A.8, Appendix A) using (7.2) leads to the values obtained with Mie theory and usually attribut ed to the cloud elementary volume (Grassl 1975; Nakajima et al. 1991). The spectral dependence of the transformed values of both difference [ α(λ)−α(0.8)] and the volume absorption coefficient is presented in Fig. 7.13a,b. It is seen that the magnitudes of the volume absorption coefficient demonstrated in Fig. 7.13b practically coincide with the ones usually calculated with Mie theory for cloud droplets (Grassl 1975). The molecular absorption bands become sharper. The values of the single scattering albedo corresponding to the absorption coeffi- cients presented in Fig. 7.13b are about 0.99998 that is close to the standard magnitudes for the cloud layer. Difference [ α(λ)−α(0.8)] converted with (7.2) does not distinguish much from Raleigh scattering coefficient for the clear sky. The presented consideration concerns the external mixture,i.e.thecase, when aerosol particles are situated between the cloud droplets. When aerosol References 255 particles are situated within the droplets (the internal mixture)theaerosol absorption is correctly accoun ted for in calculation with the formulas for one-component medium. Basing on the obtained results one could conclude that the anomalous absorption by clouds points to the external mixture of the atmospheric aerosols and cloud droplets because in the opposite case the radiation absorption by clouds coincides with the theoretical values. 7.5.2 Multiple Scattering of Radiation as a Reason for Anomalous Absorption of Radia tion by Clouds in the Shortw ave Spectral Region The aerosols consisting of hydrophobic particles such as sand, soot etc. could exist within the cloud between droplets with higher probability than the hy- drophilic ones (salt, sulfates); hence, they increase the shortwave absorption of radiation by the cloud. Hydrophilic particles, being the nuclei of conden- sation increase the droplet number. This obstacle in turn increases the cloud optical thickness and causes the cloud cooling. The aerosol absorption by the cloud increasing up to 15% has been app roximately estimated basing on the proposed mec hanism with the mean values of the aerosol volume absorption coefficient equal to 0.08 km −1 and of the volume scattering coefficient equal to 30 km −1 with geometrical thickness ∆z = 1 km and within spectral range 0.4– 1.0 µm. The molecule absorption within the ozone Chappuis band increases up to 6–10% and the molecule absorption within oxygen band 0.76 µm increases up to 10% that coincides with the results of the study by Dianov-Klokov et al. (1973). This effectturns out strongerfor the thicker clouds, andit quantitatively explains the anomalous absorption by clouds. Experimental studies (Boers et al. 1996; Bott et al. 1996) actually indicate the higher content of the carbonaceous and mineral compound in the atmospheric aerosols than has been assumed before together with their significant yield to forming the radiative regime of the atmosphere. The hydrophobic particles could be injected into the atmosphere as the result of industrial escapes, sand storms, volcanic eruptions, and fires. These sources do not seem enough to ac- count for the cloud anomalous absorption display ed on a global scale, however the aerosols flue escapes extend up to 3000 km keeping their radiation activity in the optical range (Mazin and Khrgian 1989). In the remainder of this chapter, we would like to point out that careful accounting of the optical properties of all atmosphericcomponentsis necessary for the construction of optical models (Vasilyev and Ivlev 2002). References Asano S (1994) Cloud and Radiation Studies in Japan. Cloud Radiation Interactions and Their Parameterization in Climate Models. In: WCRP-86 (WMO/TD No. 648), WMO, Geneva, pp 72–73 Binenko VI, Kondratyev KYa (1975) Vertical profiles of typical cloud forms. In: Main Geo- physical Observatory Studies 331, pp 3–16 (in Russian) [...]... 1000 90 0 800 700 600 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 26.7 35.0 47.8 48 .9 51.2 69. 9 74.3 82.2 61.2 75.6 93 .0 94 .3 93 .2 98 .5 92 .0 90 .7 94 .7 87.7 93 .8 90 .5 92 .9 90.8 91 .4 91 .8 87.1 89. 3 88 .9 29. 8 33.3 51.6 51.7 53 .9 73.1 77.5 85.3 64.4 79. 3 96 .8 97 .8 96 .5 102.0 95 .0 93 .5 97 .4 90 .3 96 .4 92 .9 95.2 93 .0 93 .6 94 .1 89. 2 91 .2 90 .7 33.3... 59. 8 59. 7 85.1 86.3 90 .1 78.1 93 .6 106.0 1 09. 0 108.0 113.0 107.0 105.0 108.0 101.0 106.0 102.0 104.0 102.0 103.0 102.0 98 .6 99 .0 98 .0 97 .3 93 .9 93.1 90 .3 87.0 88.5 86.1 78 .9 79. 6 71.8 67.5 24.4 35.1 41.0 43.0 59. 4 61.4 61.1 86.8 87 .9 91 .9 79. 5 95 .1 108.0 111.0 110.0 115.0 108.0 106.0 1 09. 0 102.0 107.0 103.0 105.0 103.0 103.0 102.0 99 .3 99 .7 98 .6 97 .9 94.4 93 .6 90 .8 87.5 89. 0 86.6 79. 9 80.0 73.0 68 .9. .. 76.5 81.0 88.6 67 .9 83.3 101.0 102.0 100.0 105.0 98 .3 96 .7 100.0 93 .1 99 .2 95 .5 97 .7 95 .5 96 .1 96 .5 91 .6 93 .4 92 .7 21.6 25 .9 42.6 43.4 46.0 64.6 68.8 76.5 55.7 69. 2 86.3 88.1 87.5 92 .9 86.8 85.8 90 .0 83.3 89. 4 86.6 89. 2 87.1 87.7 88.1 83.5 86.2 86.1 24.0 28.1 45.7 46.1 48.6 67.1 71.4 79. 3 58.3 72.2 89. 5 91 .0 90 .2 95 .6 89. 2 88.1 92 .2 85.4 91 .5 88.4 90 .9 88.8 89. 5 89. 8 85.2 87.7 87.4 Upwelling irradiance... µm−1 500 1000 90 0 800 700 600 500 37.0 39. 5 57.5 57.3 59. 2 80.2 84.8 92 .2 71.7 87.6 106.0 106.0 104.0 1 09. 0 102.0 100.0 104.0 96 .2 102.0 98 .3 101.0 98 .2 98 .7 99 .2 94 .2 95 .7 94 .9 1.48 2. 09 3 .96 4.87 5.70 7.86 8.30 9. 33 7.24 9. 97 13.7 15.0 15.5 17.4 16 .9 17.7 19. 8 19. 4 22.1 22.7 24.6 25.4 26.6 27.8 27.2 28.6 29. 3 3.41 4.10 7. 09 7.64 8.31 10.4 10 .9 12.2 9. 47 12.5 16.6 17.6 17 .9 19. 8 19. 1 19. 7 21.8 21.1... 88.6 90 .1 93 .9 81.1 97 .0 110.0 113.0 112.0 116.0 110.0 107.0 111.0 103.0 1 09. 0 104.0 106.0 104.0 104.0 104.0 100.0 100.0 99 .4 98 .7 95 .1 94 .2 91 .5 88.2 89. 6 87.2 81.1 81.0 74.6 70.7 Upwelling irradiance mW cm−2 µm−1 500 30.5 40.5 46.1 47.4 63 .9 64.8 64.7 90 .6 92 .8 96 .9 82 .9 99. 0 113.0 115.0 113.0 118.0 111.0 1 09. 0 112.0 104.0 110.0 106.0 107.0 105.0 105.0 105.0 101.0 101.0 100.0 99 .6 96 .6 95 .0 92 .3 89. 0... Characteristics and Optical Parameters of the Atmosphere Table A.2 (continued) λ (nm) Downwelling irradiance mW cm−2 µm−1 P (mbar) 1000 90 0 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 90 0 91 0 92 0 93 0 94 0 95 0 96 0 97 0 1000 90 0 62 .9 63 .9 65.1 66.7 68.6 70.8 25.6 25 .9 26.4 26.8 27.3 27.8 64 .9 64.3 39. 1 48.5 59. 6 58.6 56.8 55.5 49. 9 49. 1 49. 9 49. 3 48.0 47.7 47.6 46.8 40.8 35.1 36.6... 123 .97 122.14 1 19. 8 116.68 112.77 111.73 1 09. 90 107.30 106.78 105.48 95 .50 96 .44 96 .56 94 .23 87. 89 89. 65 88 .95 Upwelling irradiance mW cm−2 µm−1 1.3 1.2 1.1 0 .9 0.8 1.4 1.3 1.2 1.1 0 .9 0.8 57.70 64.81 81.02 72.38 74.86 104.84 106. 09 99. 78 100.11 105.34 118.52 126.44 125. 49 126.31 120 .97 1 19. 99 117.02 114.41 113.35 116.44 117.31 116.67 113.06 111.50 111.46 1 09. 80 107.64 104. 79 101. 39 100.41 98 . 89 96.32... 42.26 54.86 43.54 43.40 61.7 65.24 59. 76 59. 87 62.47 69. 04 73.32 72. 79 71 .96 68.30 67.24 65.24 63.70 62.66 64.08 64.25 63 .94 61.03 59. 62 59. 32 57.51 56.86 55.21 53.17 52.07 51.06 49. 48 49. 59 49. 24 43.26 44. 09 43 .97 42.81 38.84 40.07 40 .91 30.34 33.76 43.40 34.68 36.02 49. 86 51 .99 49. 13 49. 00 51.36 57.18 60.26 59. 96 58. 89 56.17 55.40 53.08 52.11 50.78 52. 19 51 .99 51.78 49. 29 47.88 47.57 45.81 45.40 44.03... 80 43 8 70 81 20 9 17 5 31 0 71 5 58 0 73 5 92 0 77 6 26 0 82 6 57 0 86 6 91 0 93 7 34 1 01 7 81 1 11 8 19 1 20 8 54 1 26 8 91 1 36 9 21 1 45 9 49 1 51 9 80 1 60 17 6 69 0 60 7 18 0 59 7 93 0 83 8 85 0 62 9 34 0 65 9 34 0 65 9 26 0 65 9 00 0 63 8 98 0 88 9 34 0 75 10 04 0 80 10 79 0 86 11 33 0 91 11 62 0 93 18 2 90 0 26 3 08 0 25 3 42 0 27 4 06 0 32 4 91 0 36 5 59 0 39 5 92 0 41 5 98 0 42 5 75 0 40... 0.35 λ (µm) 16 11 49 1 41 7 38 0 61 6 83 0 55 8 49 0 84 9 91 0 91 10 48 1 01 10 87 2 27 10 59 2 59 10 30 1 67 11 23 1 17 12 77 1 13 13 92 1 19 14 92 1 25 16 10 1 31 15 60 75 10 64 48 46 8 10 50 88 8 29 58 94 8 59 61 64 10 55 58 95 11 02 47 39 6 88 46 58 6 27 50 24 6 53 56 75 6 64 62 69 6 49 66 49 6 38 69 49 6 42 72 48 6 76 4 49 1 40 3 44 0 79 3 10 0 73 3 52 0 91 3 73 0 97 3 79 0 93 3 18 0 64 3 05 0 . 49. 2 610 97 .3 97 .6 98 .0 98 .6 99 .4 100.0 45 .9 46.2 46.6 47.2 48.0 49. 0 620 96 .7 96 .9 97.3 97 .9 98.7 99 .6 45.4 45.7 46.1 46.7 47.4 48.4 630 93 .3 93 .5 93 .9 94.4 95 .1 96 .6 43.2 43.3 43.7 44.2 44 .9. 27.5 29. 3 31.1 550 89. 2 90 .9 92 .9 95.2 97 .7 101.0 24.6 26.1 27.7 29. 4 31.1 32 .9 560 87.1 88.8 90 .8 93 .0 95 .5 98 .2 25.4 26.8 28.2 29. 7 31.3 33.0 570 87.7 89. 5 91 .4 93 .6 96 .1 98 .7 26.6 27 .9 29. 2. 105.0 49. 2 49. 6 50.2 50 .9 51 .9 53.1 580 101.0 101.0 102.0 102.0 104.0 105.0 48.1 48.4 48 .9 49. 6 50.3 51.2 590 97 .9 98.2 98 .6 99 .3 100.0 101.0 46.6 46.8 47.3 47 .9 48.7 49. 7 600 98 .3 98 .6 99 .0 99 .7