The Attenuation of Sunlight by High-Latitude Clouds: Spectral Dependence and Its Physical Mechanisms

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JOHN E. FREDERICK AND CARYNELISA ERLICK Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois (Manuscript received 7 August 1996, in ®nal form 14 March 1997)

ABSTRACT Measurements of the ground-level solar irradiance from Palmer Station, Antarctica, and Ushuaia, Argentina, reveal a systematic wavelength dependence in the attenuation provided by cloudy skies. As wavelength increases from 350 to 600 nm, the measured cloudy-sky irradiance, expressed as a fraction of the clear-sky value, decreases. Results from Ushuaia for a solar zenith angle of 45Њ show that a cloudy sky that reduces the spectral irradiance at 500 nm to 50% of that for clear skies is accompanied by irradiances at 350 and 600 nm, which are approximately 59% and 49%, respectively, of the clear sky value. A weaker wavelength dependence appears in the data for Palmer Station. The observed behavior can arise from Rayleigh backscattering of sunlight beneath the cloud, followed by re¯ection of this upwelling radiation from the cloud base back to the ground. This sequence of events is most effective at short wavelengths and leads to cloudy skies providing less overall attenuation as wavelength decreases.

1. Introduction the ultraviolet than in total wavelength-integrated sun- This paper addresses a question related to the atten- light (Frederick and Steele 1995). The authors suggest uation of sunlight by cloudy skies. Speci®cally, does a that the discrepancy between these results could arise cloudy sky attenuate incoming sunlight by the same from the very different sensitivities of the Robertson± percentage at all wavelengths, or is there a spectral de- Berger meter and Eppley ultraviolet sensor to ozone pendence in the attenuation? For example, if the solar located in the lower atmosphere. irradiance observed at a wavelength of 500 nm under In this work we analyze ground-level solar irradiances a cloudy sky is reduced to 50% of the value expected at selected wavelengths obtained by spectroradiometers for clear skies, is the irradiance at other wavelengths located at Palmer Station, Antarctica, latitude 64.8ЊS, reduced by the same, or by a different, fraction? The and Ushuaia, Argentina, at latitude 55.0ЊS. Each instru- spectral region considered extends from 350 nm in the ment is a Model SUV-100 scanning spectroradiometer near ultraviolet to 600 nm in the visible. provided by Biospherical Instruments, Inc. Once per Previously published results indicate that clouds pro- hour the sensors scan the solar spectrum from the ul- vide somewhat less attenuation in the ultraviolet than traviolet, shortward of 290 nm, into the visible and rec- in the visible. This comes from a comparison of data ord the sum of direct and diffuse irradiance striking a obtained by a total sunlight pyranometer and a Robert- horizontal surface. Lubin et al. (1992) have described son±Berger ultraviolet meter (Blumthaler and Ambach the instrumentation in more detail, so no further dis- 1988). These datasets were obtained in the Austrian cussion is required here. The measurement sites are, for Alps, at a site removed from sources of pollution. Using practical purposes, free of air pollution, allowing us to data from a large urban area, Frederick et al. (1993) focus on the effects of clouds alone. These data have found that cloudy skies provided essentially the same an advantage over previous work in that they refer to attenuation of irradiance as measured by a Robertson± speci®c wavelengths rather than being broadband mea- Berger meter and an Eppley pyranometer. However, sub- surements. We can therefore isolate any wavelength de- sequent data from an Eppley ultraviolet monitor, whose pendence in the attenuation associated with cloudy spectral response is shifted to longer wavelengths than skies. the Robertson±Berger meter, implied less attenuation in 2. The characterization of clouds We characterize the in¯uence of clouds on ground- Corresponding author address: Dr. John E. Frederick, Department level spectral irradiance E(␭) at wavelength ␭ by the of the Geophysical Sciences, University of Chicago, 5734 South Ellis ``attenuation factor'' T(␭), de®ned by Avenue, Chicago, IL 60637. E-mail: [email protected] E(␭) ϭ T(␭)ECLR(␭), (1)

᭧ 1997 American Meteorological Society

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TABLE 1. Regression coef®cients derived from irradiance mea- where ECLR(␭) is the ground-level irradiance, including direct and diffuse components, that would have pre- surements at Palmer Station; t is the ratio of the standard error in derived coef®cient to the best estimate of that coef®cient. vailed under clear skies. All quantities in Eq. (1) are functions of the solar zenith angle (SZA). As de®ned ␭ (nm) a0(␭) t(a0) a1(␭) t(a1) above, T(␭) depends on the properties of the prevailing Solar zenith angle ϭ 40Њ±50Њ clouds, the atmosphere in which the clouds reside, and 350 4.98 ϫ 10Ϫ1 203.4 Ϫ1.20 ϫ 10Ϫ2 5.3 the albedo of the lower boundary. Physically, the at- 400 8.37 ϫ 10Ϫ1 317.4 Ϫ5.51 ϫ 10Ϫ3 2.3 tenuation factor is simply the measured ground-level 600 7.82 ϫ 10Ϫ1 319.8 1.12 ϫ 10Ϫ2 5.0 irradiance expressed as a fraction of the clear-sky ir- Solar zenith angle ϭ 60Њ±70Њ radiance. The analysis seeks to determine if a detectable 350 5.02 ϫ 10Ϫ1 199.5 Ϫ3.16 ϫ 10Ϫ2 6.8 wavelength dependence exists in T(␭). 400 8.41 ϫ 10Ϫ1 330.2 Ϫ3.19 ϫ 10Ϫ2 6.8 1 2 The irradiance E(␭) is measured by the spectroradi- 600 7.53 ϫ 10Ϫ 386.2 3.70 ϫ 10Ϫ 10.2 ometers, but the corresponding clear-sky irradiance, E (␭), is not in general known. One approach would CLR 3. Measurements and statistical analysis be to compute ECLR(␭) using a radiative transfer code, but this could introduce model-dependent uncertainties We sorted irradiances measured from Palmer Sta- into the analysis. Instead we develop an approach to tion and Ushuaia during September through Decem- detecting a wavelength dependence in T(␭), which is ber 1990 into bins of SZA 10Њ wide. The smallest free of model-based assumptions. We select a reference range of SZA considered is 40Њ±50Њ, corresponding wavelength ␭* and consider the ratio to times close to local noon near summer solstice for Palmer Station. The various panels refer to the SZA [T(␭)E (␭)] E(␭)/E(␭*) ϭ CLR . (2) ranges 40Њ±50Њ and 60Њ±70Њ for wavelengths of 350 [T(␭*)ECLR(␭*)] nm, 400 nm, and 600 nm. The regression model of Eq. (4) was ®tted to the data, and the resulting co- The ratio E (␭)/E (␭*) on the right-hand side of Eq. CLR CLR ef®cients appear in Table 1. The slopes derived for (2) is constant for a ®xed SZA, and when the sky is each panel in Fig. 1 are signi®cantly different from clear it is obvious that T(␭)/T(␭*) ϭ 1. If cloudy skies 0.0, as indicated by the t statistic associated with each provide the same attenuation at both wavelengths ␭ and value of a exceeding a value of 2.0. ␭*, then we should also ®nd that T(␭)/T(␭*) ϭ 1 for 1 Although there is considerable scatter in the mea- all cloudy conditions. However, if a wavelength depen- surements, Fig. 1 and Table 1 show that the irradiance dence exists in the attenuation associated with cloudy ratios are dependent on the degree of cloudiness, in- skies, then the ratio T(␭)/T(␭*) should depart from unity dicating a wavelength dependence in the attenuation as the degree of cloudiness increases. factors. The irradiance ratios for 350 and 400 nm de- For a ®xed SZA, the absolute irradiance at ␭* is itself cline slightly as E(500 nm) increases, while the ratio a valid index of the degree of cloudiness. The simplest for 600 nm has the opposite behavior. This demon- relationship one could adopt in seeking a wavelength strates that cloudy skies over Palmer Station provide dependence associated with cloudiness is then less attenuation as wavelength decreases. Further-

T(␭)/T(␭*) ϭ c 0(␭) ϩ c1(␭)E(␭*), (3) more, as the clouds become thicker, cover a greater fraction of the sky, or preferentially block the direct where the wavelength-independent case corresponds to solar beam, as indicated by a shrinking value of E(500 c0(␭) ϭ 1 and c1(␭) ϭ 0. The combination of Eqs. (2) nm), the difference in attenuations experienced at two and (3) plus that ECLR(␭)/ECLR(␭*) is a constant for ®xed wavelengths increases. SZA yields Figure 2 and Table 2 present the measurements and E(␭)/E(␭*) ϭ a (␭) ϩ a (␭)E(␭*), (4) derived regression coef®cients for Ushuaia. The pat- 0 1 tern is qualitatively similar to that for Palmer Station, where the regression coef®cients a0(␭) and a1(␭) are to and all of the slopes, a1 , are signi®cantly different be determined by a least squares ®t of measured irra- from zero. However, a comparison of the plots and diances to Eq. (4). We use the three wavelengths ␭ ϭ coef®cients for the two locations reveals a stronger 350, 400, and 600 nm with the reference wavelength wavelength dependence at Ushuaia than at Palmer ␭* ϭ 500 nm. A wavelength dependence in T(␭) will Station. appear as a value of a1(␭) signi®cantly different from The irradiance ratios in Figs. 1 and 2 display con- zero. Blumthaler and Ambach (1988) used a relationship siderable scatter. This can arise from temporal vari- similar in form to Eq. (4), although in place of E(␭*) ations in irradiance over the time period of a spectral on the right-hand side, they used fractional cloud cover scan from 350 to 600 nm. Many of the points in the in tenths as the index of cloudiness. In addition, the ®gures refer to partly cloudy conditions. Under these numerator on the left-hand side was the output of a circumstances the direct solar beam, which comprises Robertson±Berger meter, and the denominator was from a large fraction of the total irradiance for clear skies, a total sunlight pyranometer. may or may not be present. For example, there will

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FIG. 1. Irradiance ratios E(␭)/E(500 nm) presented as functions of the absolute irradiance at 500 nm based on measurements from Palmer Station during 1990. The wavelengths are, from top to bottom, 350 nm, 400 nm, and 600 nm. Panels on the left refer to solar zenith angles of 40Њ± 50Њ. Panels on the right refer to the range 60Њ±70Њ. Arrows on the horizontal scales denote the clear-sky irradiance at 500 nm. be cases when the solar disk is obscured by clouds as when fractional cloud cover is present, but the solar the spectroradiometer records irradiance at 500 nm, disk is in the clear portion of the sky as seen by the but the disk has become visible when the reading at spectroradiometer. 600 nm occurs. This circumstance would lead to The combination of Eqs. (1) and (4) provides an ex- anomalously large ratios, as appear in the lower left pression that relates the attenuation factor at any wave- panel of Fig. 2. length ␭ to that at 500 nm. This is The arrows on the horizontal scales in Figs. 1 and 2 [a (␭) ϩ a (␭)E (500 nm)T(500 nm)] are estimates of the clear-sky irradiance at 500 nm based T(␭) ϭ 0 1 CLR on a radiative transfer calculation. Note that measured [a0(␭) ϩ a 1(␭)E CLR(500 nm)] irradiances exist that exceed the clear-sky computation, ϫ T(500 nm), (5) and these differences far exceed any uncertainties in the data and model-based results. These large irradiances where the computed 500-nm clear-sky irradiances are are especially prevalent at Palmer Station. As shown in 1.24 and 0.704 W mϪ2 nmϪ1 for SZAs of 45Њ and 65Њ, the following section, enhanced irradiances can exist respectively. These values combined with the regression

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FIG. 2. Irradiance ratios E(␭)/E(500 nm) presented as functions of the absolute irradiance at 500 nm based on measurements from Ushuaia, Argentina, during 1990. The wavelengths are, from top to bottom, 350 nm, 400 nm, and 600 nm. Panels on the left refer to solar zenith angles of 40Њ±50Њ. Panels on the right refer to the range 60Њ±70Њ. Arrows on the horizontal scales denote the clear-sky irradiance at 500 nm.

coef®cients in Tables 1 and 2 lead to the attenuation factor of 0.25 at 500 nm, the computed attenuation fac- factors in Fig. 3 for Palmer Station and Fig. 4 for Us- tors increase from 0.232 at 600 nm to 0.350 at 350 nm. huaia. Labels on each curve indicate the attenuation factor at a wavelength of 500 nm. The results for Palmer 4. Physical mechanisms Station are indistinguishable from horizontal lines. In the most extreme case shown, being a SZA of 65Њ and This section addresses the physical mechanisms re- an attenuation factor of 0.25 at 500 nm, the computed sponsible for the wavelength dependence identi®ed in attenuation factors range from 0.244 at 600 nm to 0.259 Figs. 1 and 2. The features to be explained are ®rst, the at 350 nm. The wavelength dependence at Ushuaia is origin of the nonzero slopes and, second, the reasons more pronounced. For a SZA of 65Њ and an attenuation for the difference in slopes between Palmer Station and

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TABLE 2. Regression coef®cients derived from irradiance measurements at Ushuaia; t is the ratio of the standard error in a derived coef®cient to the best estimate of that coef®cient.

␭ (nm) a0(␭) t(a0) a1(␭) t(a1) Solar zenith angle ϭ 40Њ±50Њ 350 5.12 ϫ 10Ϫ1 102.7 Ϫ1.09 ϫ 10Ϫ1 18.5 400 8.98 ϫ 10Ϫ1 131.5 Ϫ1.16 ϫ 10Ϫ1 14.5 600 8.77 ϫ 10Ϫ1 126.2 2.67 ϫ 10Ϫ2 3.3 Solar zenith angle ϭ 60Њ±70Њ 350 5.20 ϫ 10Ϫ1 88.4 Ϫ2.56 ϫ 10Ϫ1 19.3 400 9.12 ϫ 10Ϫ1 117.3 Ϫ2.87 ϫ 10Ϫ1 16.4 600 8.33 ϫ 10Ϫ1 134.1 1.25 ϫ 10Ϫ1 8.9

Ushuaia. Based on the radiative transfer model of Fred- erick and Erlick (1995), we consider a cloud to be a nonabsorbing surface with an albedo A and a transmission, 1 Ϫ A, located at a prescribed altitude. For sim- plicity we apply the same albedo to both direct and diffuse components of the solar radiation ®eld. Physical reasoning shows that a cloud whose albedo is independent of wavelength will still have a wavelength-dependent effect on solar irradiance at the ground. The physical mechanism involves a coupling between wavelength-dependent Rayleigh scattering and FIG. 3. Attenuation factors computed for Palmer Station based on wavelength-independent re¯ection of upward moving the regression coef®cients in Table 1. Top panel refers to solar zenith radiation from the base of the cloud. Consider down- angles of 40Њ±50Њ; bottom panel is for 60Њ±70Њ. Labels on the curves indicate the attenuation factor at 500 nm. ward moving irradiances at two wavelengths, ␭L and ␭S, where ␭L Ͼ ␭S. A cloud may or may not be present at an altitude zc. At altitudes less than zc Rayleigh backscattering has a larger in¯uence on irradiance at the shorter wavelength, ␭S, than at the longer wavelength ␭L, owing to the variation of the cross section being 1/␭ 4. Although Rayleigh backscattering occurs at both wavelengths, the fraction of radiation scattered is great- est at ␭S. Under clear conditions much of the back- scattered upward radiation will escape the atmosphere. Now assume that a cloud whose albedo and transmission are independent of wavelength is placed at altitude zc, as depicted in Fig. 5. The cloud transmits the same fraction of incident downward irradiance at both wavelengths. However, Rayleigh backscattering beneath the cloud has a greater in¯uence at the shorter wavelength. Owing to this, a larger fraction of the transmitted irradiance at ␭S later upwells to strike the base of the cloud from below, where part of it is re¯ected back downward. This re¯ection of upwelling radiation back into the downward direction preferentially reinforces the ground-level irradiance at the shorter wavelength. The result is that cloudy skies appear to provide less attenuation as wavelength decreases, at least when absorption is absent. This behavior appeared in early calculations presented by Frederick and Lubin (1988), although the authors did not discuss the phenomenon or the physical mechanism at work. FIG. 4. Attenuation factors computed for Ushuaia, Argentina, based The reasoning outlined above can be quanti®ed using on the regression coef®cients in Table 2. Top panel refers to solar the radiative transfer model of Frederick and Erlick zenith angles of 40Њ±50Њ; bottom panel is for 60Њ±70Њ. Labels on the (1995). Figure 6 presents calculations of the ratio E(350 curves indicate the attenuation factor at 500 nm.

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creases and ground-level irradiances that exceed the clear-sky value. Different ground albedos at Palmer Station and Us- huaia provide a mechanism for the different slopes in Tables 1 and 2. The wavelength dependence associated with cloudy skies arises from Rayleigh scattering beneath the cloud. However, some of the upwelling radiation that strikes the cloud from below has re¯ected from the ground. The larger the ground albedo, the greater the upwelling irradiance from the surface be- comes relative to the contribution from Rayleigh scattering. If the ground albedo is the same at the two wavelengths being compared, or at least has a much weaker FIG. 5. Schematic illustrating the physical mechanism responsible spectral variation than Rayleigh scattering, this process for a wavelength dependence in the attenuation provided by cloudy acts to suppress the wavelength dependence in the at- skies. More ef®cient Rayleigh backscattering at the shorter wavelength plus re¯ection from the cloud base leads to less overall attenuation factor. tenuation of the irradiance at the ground. Figure 7 presents calculated ratios E(350 nm)/E(500 nm) versus E(500 nm) for an SZA of 45Њ and surface

albedos of AG ϭ 0.05 and AG ϭ 0.50. The results refer nm)/E(500 nm) plotted against E(500 nm) for SZAs of to 100% cloud-covered skies and cloud albedos, from

45Њ and 65Њ and a ground albedo of AG ϭ 0.05. The left to right, of 0.9, 0.7, 0.5, 0.3, and 0.1. A difference open circle in each panel refers to clear skies. Points in the slopes of the two curves is evident, with the that lie to the left of the clear-sky result represent several weakest slope associated with the largest ground albedo. combinations of cloud albedos and fractional cloud cov- Since snow cover is more persistent at Palmer Station ers. Points to the right refer to fraction cloud cover than at Ushuaia, it is likely that a larger ground albedo values from 0.2 to 1.0, but subject to the condition that applies to the former site. This accounts qualitatively the direct solar beam comes from a clear spot in the for the different slopes in Tables 1 and 2. sky. In this case, the total 500-nm irradiance at the ground increases as fractional cloud cover increases, so 5. Discussion and conclusions long as the direct component of solar irradiance is un- altered by the clouds. The mechanism behind the en- Measurements in the high-latitude Southern Hemi- hancement is straightforward; part of the direct solar sphere show a wavelength dependence in the effect of irradiance is scattered upward in the atmospheric layer cloudy skies on solar irradiance at ground level. Spe- beneath the cloud and re¯ects back downward off the ci®cally, the irradiance expressed as a fraction of the cloud base. The result is a total irradiance at the ground clear-sky value decreases as wavelength increases. that exceeds the clear-sky value. In summary, the cal- However, the observed spectral dependence does not culations reproduce two major features of the measure- necessarily require the albedo or transmission of a cloud ments, namely, a weaker attenuation as wavelength de- layer to vary with wavelength. A spectral dependence

FIG. 6. Computed irradiance ratio, E(350 nm)/E(500 nm), presented as a function of the absolute irradiance at 500 nm. The ground albedo is 0.05. Left panel refers to a solar zenith angle of 45Њ; the right panel refers to 65Њ. The open circles are for clear skies.

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presence of ozone below the cloud would oppose the mechanisms discussed in this paper. Absorption beneath the cloud would inhibit the ¯ow of radiation from the point of backscattering, up to the cloud base, and back to the ground. Furthermore, ozone located in the air within a cloud will act to absorb the multiply scattered radiation contained therein. Under these circumstances, the albedo and transmission of a cloud will not be independent of wavelength. Depending on the ozone abundance in the lower troposphere, the attenuation factor may undergo a maximum at some wavelength shorter than 320 nm.

Acknowledgments. This work was supported by the National Science Foundation, Of®ce of Polar Program, under Grant OPP-9314616. We thank C. Rocky Booth of Biospherical Instruments, Inc., for providing us with FIG. 7. Computed irradiance ratio, E(350 nm)/E(500 nm), presented the datasets analyzed in this paper. as a function of the absolute irradiance at 500 nm for a solar zenith angle of 45Њ. Solid points refer to a ground albedo of 0.05; open circles refer to a ground albedo of 0.50. REFERENCES

Blumthaler, M., and W. Ambach, 1988: Human solar ultraviolet ex- in the attenuation arises naturally from Rayleigh back- posure in high mountains. Atmos. Environ., 22, 749±753. scattering in the atmosphere beneath a cloud layer fol- Frederick, J. E., and D. Lubin, 1988: The budget of biologically active ultraviolet radiation in the earth±atmosphere system. J. Geophys. lowed by re¯ection of this radiation from the cloud base Res., 93, 3825±3832. toward the ground. A ground albedo independent of , and C. Erlick, 1995: Trends and interannual variability in er- wavelength acts counter to the mechanism described ythemal sunlight, 1978±1993. Photochem. Photobiol., 62, 476± above. The different spectral sensitivities found at Palm- 484. er Station and Ushuaia are consistent with a larger , and H. D. Steele, 1995: The transmission of sunlight through cloudy skies: An analysis based on standard meteorological in- ground albedo at the former location. formation. J. Appl. Meteor., 34, 2755±2761. This work has considered wavelengths longer than , A. E. Koob, A. D. Alberts, and E. C. Weatherhead, 1993: 350 nm, where absorption by ozone is not strong. In Empirical studies of tropospheric transmission in the ultraviolet: addition, the irradiance measurements refer to a rela- Broadband measurements. J. Appl. Meteor., 32, 1883±1888. Lubin, D., B. G. Mitchell, J. E. Frederick, A. D. Alberts, C. R. Booth, tively unpolluted region of the world. If one extended T. Lucas, and D. Neuschuler, 1992: A contribution toward un- the analysis to wavelengths shorter than 320 nm, Ray- derstanding the biospherical signi®cance of Antarctic ozone de- leigh scattering would be still more important, but the pletion. J. Geophys. Res., 97, 7817±7828.

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