Sky radiance measurements in the wavelength bands of ultraviolet-B (0.28–0.32 μm), ultraviolet-A (0.32–0.40 μm), and photosynthetically active radiation (0.40–0.70 μm) were made under obscured overcast skies in a rural area. Radiance distributions were modeled for seven measurement scans with solar zenith angles varying from 19° to 49°. For the seven scans, the atmospheric transmittance of photosynthetically active photon flux density varied from 0.16 to 0.25. The corresponding fraction of cloud-free sky photosynthetically active photon flux density ranged from 0.21 to 0.32. The corresponding fraction of ultraviolet-B cloud-free sky irradiance was between 0.20 and 0.34, with typically lower fractions of cloud-free sky irradiance in the ultraviolet-B than in the photosynthetically active photon flux density. The sky radiance was modeled from the ensembled measurements according to the standard overcast sky radiance distribution for each of the wavelength bands.
Although the ultraviolet wave bands had slightly greater normalized radiance at the zenith and smaller radiance at the horizon than has been found for the photosynthetically active radiation wave band, the differences between the photosynthetically active radiation and the ultraviolet-A and ultraviolet-B radiance distributions were not statistically significant. Therefore, the authors concluded that the normalized obscured overcast sky radiance distribution for all three wave bands could be satisfactorily described by the standard overcast sky model of the photosynthetically active radiation distribution.
The potential for increased solar ultraviolet radiation due to decreases in the atmospheric column thickness of ozone at all latitudes of the earth has increased the importance of understanding the distribution in time and space of solar ultraviolet (UV) radiation (Nunez et al. 1994). Ultraviolet radiation at the surface of the earth occurs in the wavelength bands 0.28–0.32 μm (UVB) and 0.32–0.40 μm (UVA), which together typically comprise about 3% of the total solar radiation under cloud-free skies. Although the amount of UV irradiance at the earth’s surface is relatively small, the photons at these wavelengths are biologically active and commonly detrimental to plant and animal health. The UVB wave band is important due to its adverse impacts on plant growth and development (Grant 1997), and its association with human skin cancers, photoaging, immunosuppression, and erythema (Taylor and Sober 1996). The UVA wave band is important due in part to the mitigating effects of UVA on UVB damage to plants (Grant 1997) and in part to its creating photosensitivity and tanning on the human skin (Taylor and Sober 1996). As a result, understanding the amount of UV radiation received by plant and animal organisms near the earth’s surface over the entire year is critical to assessing the potential impact of increased UV on biological systems. Since the shapes of UV-sensitive surfaces on organisms are typically not horizontal, calculation of the irradiance on the surfaces requires knowledge of the distribution of the sky radiance with and without cloud cover.
The scattering and transmission of radiation through the atmosphere varies with the wavelength of energy, the solar zenith angle (SZA), atmospheric turbidity, and the type and thickness of clouds. With cloud-free skies, intense single scattering in the forward direction in the circumsolar region causes definite asymmetry in the sky radiance distribution. Efforts to describe the cloud-free sky radiance distribution have been made from numerical (Stamnes et al. 1991) and empirical (Grant et al. 1996a) modeling approaches. Under translucent overcast skies (where the solar disk is visible through the cloud cover), UV radiation is entirely diffuse, although asymmetrical scattering results in considerable diffuse radiance in the circumsolar region of the sky, resulting in an individual being able to identify the location of the solar disk (Grant et al. 1997). Under obscured overcast skies (where the solar disk cannot be discerned through the cloud cover), the thickness of the clouds precludes being able to see the solar disk and the density of cloud droplets reduces the scattering asymmetry that occurs with cloud-free skies. Skies completely overcast with uniform, sun-obscuring clouds commonly have maximum radiance at the zenith because the preferred direction of multiple-scattered light exiting the cloud is perpendicular to the cloud base (van Weele et al. 1995) and the optical thickness is least for radiation perpendicular to the ground. It is often assumed that actual obscured overcast skies can be described as homogeneous, uniformly thick layers. This “homogeneity” of the cloud deck makes the obscured overcast sky a useful cloud condition for understanding the basic influence of clouds on various wavelengths of solar radiation.
The relative effect of overcast skies on the spectral irradiance varies with wave band. In the shortest UVB wavelengths, below 0.3 μm, the influence of ozone scattering can reduce irradiance by more than an order of magnitude (Bais et al. 1993). When the entire UVB band is considered climatologically, the variability in irradiance is generally influenced more by the variability in cloud cover and consequent scattering than by the variability in the ozone column depth (τoz; Blumthaler et al. 1994; Frederick et al. 1993). Some studies suggest that cloud cover reduces the shortwave (SW) irradiance to a greater degree than the UV due to the radiation in the UV wavelengths having a higher diffuse fraction and more similar cloud-free atmosphere and cloud-scattering thicknesses than the SW (Spinhirne and Green 1978; Blumthaler et al. 1994; Bordewijk et al. 1995). Other studies have found similar relative reductions in UVB and SW irradiance by clouds (Frederick et al. 1993). Estupinan et al. (1996) found that the relative attenuation of UVB and SW depends on the SW atmospheric transmittance, with the difference in attenuation evident as the transmittance decreases below 0.2, which they assumed corresponds with thick cloud layers that include ice fractions.
Variation in cloud thickness appears to influence transmission of UV to a lesser degree than the SW. Modeling studies by Spinhirne and Green (1978) found this effect to increase with increasing SZA. Frederick and Snell (1990) found that the changes in optical thickness of the cloud cover were less important in explaining the UV irradiance variability than the fraction of sky covered with clouds. Frederick and Lubin (1988) suggested that thick clouds might cause an increase in absorption by ozone over that of thinner clouds due to the increased isotropy of the radiation field in the atmosphere with thick clouds. While unproved, this suggestion was used by Bais et al. (1993) and Blumthaler et al. (1994) to at least partially explain the large decrease in UV irradiance as cloud fraction increases from 9/10 to 10/10.
The obscured overcast sky has often been modeled as the standard overcast (SOC) distribution. The SOC distribution was initially developed by Moon and Spencer (1942) for luminance by assuming only diffuse radiation impinging at the cloud top. Fritz (1955) and Kasten (1961) expanded the theoretical underpinnings of the SOC by explicitly linking the distribution to the ground surface albedo. Since only a diffuse radiation field was considered, clearly the theory could be used only to approximate conditions when the optical thickness of the cloud was great. Previous studies have shown that the SOC distribution applies best to very thick cloud layers (Rosen and Hooper 1989; Kittler and Valko 1993). Although radiation models have improved since then, the SOC distribution continues to be used and has been extended to describe radiance distributions. The SOC distribution has been used to estimate the overcast sky distribution for illuminance (0.39–0.76 μm), as previously mentioned (Moon and Spencer 1942; Fritz 1955), photosynthetically active radiance (PAR, 0.40–0.70 μm; Grant et al. 1996b), and the total SW band radiance (0.29–3.50 μm; Steven and Unsworth 1980). Rosen and Hooper (1989) related the SOC model to their semiempirical, three-component continuous distribution model for SW sky radiance.
There are, to the knowledge of the authors, no analytical sky radiance distribution functions for radiation in UV wavelength bands under obscured overcast skies. This paper reports on the adaptation of the SOC distribution to the PAR, UVA, and UVB radiance distribution of obscured overcast skies as a first step in the process of describing the mean sky radiance distribution under partly cloudy skies. This paper also briefly examines the relative effect of obscured overcast skies on irradiance in the UV and PAR wavelengths.
Sky radiance measurements in the UVA, UVB, and PAR and were made simultaneously during the summer of 1993 at the Purdue Agronomy Research Center located in West Lafayette, Indiana (latitude 40.5°). This paper presents an analysis of only the sky condition in which cloud cover obscures the view of the solar disk. Other portions of the total sky radiance dataset have already been reported in the literature: UVA and UVB radiance distributions under cloud-free and translucent overcast sky conditions have been analyzed and reported in Grant et al. (1996a) and Grant et al. (1997), respectively, while PAR radiance distributions under cloud-free, translucent overcast, and obscured overcast conditions have been reported in Grant et al. (1996b). While the UVA and UVB wave bands are of primary interest in this analysis, the PAR wave band was included here both because it is the source of energy for plant carbon fixation and subsequent plant growth and because the wave band corresponds closely to the visible wave band (0.39–0.77 μm), in which the SOC model was first established.
The UVA and PAR sky radiances were measured with silicon-photodiode (SED033) sensors and the UVB with a vacuum silicon photodiode sensor (SED240), all of which were produced by International Light, Inc.1 The UVA and UVB radiance sensors were calibrated at the factory in February 1993 and November 1992, respectively. The PAR radiance sensor was calibrated at the factory in November 1992. The spectral bandwidth of response for the UVB sensor was achieved by use of an interference filter, while the bandwidths of the UVA and PAR radiance sensors were achieved using color-absorption filters. The spectral bandpasses of the three radiance sensors are illustrated in Fig. 1. The UVB sensor response decreased by a factor of 150 between 0.294 and 0.310 μm. The field of view (FOV) of the radiance sensors was 16° (95% cutoff) (Grant et al. 1996a).
The hemispheric distribution of the sky radiance was measured over 12- to 20-min scan periods by inclining the sensor at approximately 10° zenith angle increments and rotating the sensors about the 360° of azimuth at each inclination, as reported in Grant et al. (1996a, b). The conditioned sensor responses and the sensor orientation were sampled by a CR7X data logger (Campbell Scientific) at 2-s intervals. Measurements were quality assured by comparison of the beginning and ending scan dark current after the application of sensor temperature coefficients. Measurements were then corrected for the photodiode dark current (Grant 1996). No postseason calibration of the radiance sensor responses was conducted.
The global radiation in the PAR and UVB was also measured during each sky scan. Photosynthetically active photon flux density (PPFD) measurements were made with a LiCOR quantum sensor. The PPFD sensor had a slightly different spectral response than the PAR radiance sensor (Fig. 1), with the 50% response bandwidth of the PPFD sensor between 0.4 and 0.695 μm and that of the PAR radiance sensor between 0.415 and 0.76 μm. The PPFD sensor was factory calibrated in 1987, intercalibrated with a sensor calibrated in 1991, and used only for short periods in the field from then until the current study. UVB irradiance measurements were made with a SED240 sensor with a UVB filter and a quartz diffuser. The UVB irradiance sensor was factory calibrated in February 1993 and had identical temperature and spectral response characteristics to the UVB radiance sensor. UVB irradiance measurements were corrected for temperature and cosine response of the sensor according to Grant (1996). PPFD sky transmittance was defined as the ratio of measured PPFD to the extraterrestrial PPFD derived from the modified extraterrestrial solar spectrum reported in Bird and Riordan (1986). No correction was made for the difference in the measured PPFD wave band (0.4–0.695 μm) versus that reported in Bird and Riordan (1986) (0.4–0.69 μm).
Variation in the UV irradiance and PPFD during each 15- to 20-min sky radiance scan period (Fig. 2a) was accounted for by the adjustment of the radiance measurement by the variation in the PPFD from the mean PPFD for the entire scan period. Under overcast conditions, the solar spectral irradiance differs from that of the clear sky with relatively more irradiance in the UV and blue wavelengths and more pronounced water vapor and droplet absorption in the near-infrared wavelengths (Nann and Riordan 1991). This results in only small changes in the relative spectral irradiance in the PAR, but relatively large differences in the relative spectral irradiance in the UV. Therefore, the PPFD sensor was detecting approximately the same proportion of the photons under clear as under overcast skies, while the UVB irradiance sensor was detecting a different (and unknown) proportion of the incident energy in the UVB. Comparisons of the instantaneous PPFD and UVB irradiances during the individual sky scans showed a nearly constant ratio of UVB irradiance to PPFD (Fig. 2b), with a coefficient of variation [CV; (standard deviation divided by mean)100] of between 1.5% and 8.3%. All measured radiance values (PAR, UVA, and UVB) were adjusted for varying irradiance during the scan using the changes in the PPFD since the signal-to-noise ratio of the PPFD measurements was higher than that of the UVB irradiance and the spectral quality of radiation in the PAR was more consistent with changes in cloud cover than in the UVB. Thus, for any waveband radiance measurement Nm(θ, Φ, t), the normalized radiance was defined according to
where θ and Φ are zenith and azimuth angles of the radiance, IPAR(t) is the instantaneous PPFD at measurement time t, and IPAR is the mean PPFD during the scan. No spectral correction factor was needed in this transformation since the ratio of the PPFD is used to normalize Nm(θ, Φ, t) rather than IPAR(t).
Mean normalized radiance values were computed from the measurements made during each 360° azimuth rotation for nine zenith angles in a given scan. Further analyses of the influence of the cloud cover on the sky radiance distributions were based on these mean normalized values.
Cloud transmittance was estimated by the ratio between measured overcast irradiance and estimated cloud-free sky irradiance. The measured overcast-to-estimated cloud-free UVB irradiance or PPFD ratio for each measurement scan period (Iovc/Îclear) was calculated by dividing the mean measured overcast UVB irradiance or PPFD Iovc for each scan period by a predicted cloud-free value Îclear, given the SZA of the measurement period and regression equations of Iclear on SZA; Iclear PPFD values were reported in Grant et al. (1996a). The corresponding Iclear UVB irradiance was measured (but not reported) at the time of the cloud-free PPFD measurements, and sky UV radiance measurements were reported in Grant et al. (1996b). The Iclear UVB irradiance and PPFD measurements used in the regressions spanned an SZA of 15° to 75° (Grant et al. 1996a) and aerosol turbidities of 0.18 to 0.37. The τoz during the measurements was unknown since there were no satellite measurements made at the time of the sky radiance measurements. This methodology introduces a source of error in the ratio since there was no means to ratio Iovc by an Îclear for identical aerosol turbidity or τoz.
Hemispheric (180° FOV) photographs of the sky were taken before and after each complete scan of the sky (Fig. 3). The developed slides were then projected onto a polar grid with a 10°-interval azimuth and zenith angle line. Cloud cover was determined by counting the number of intersections that fell on clouds, according to the methodologies described in Grant et al. (1996a). Only scans taken when the atmospheric PAR transmittance was less than or equal to 0.25, and the photographic analysis indicated complete cloud cover were used in this analysis. The type of cloud cover was determined by the method of Humphreys (1964) from the height to cloud base measured by the National Oceanic and Atmospheric Administration National Weather Service (NWS) observer at the Purdue University airport and from cloud structure evident in the photographic slides. The airport is 10 km from the radiance measurement site, but the intervening terrain is flat, with no major bodies of water or land cover differences that would lead to systematic local-scale cloud differences.
The normalized PAR, UVA, and UVB radiance of the obscured overcast sky was modeled using the SOC sky radiance functional form. The ratio of radiance at some zenith angle to radiance at the zenith provides the generalized SOC formulation
where N(0) is the normalized radiance at the zenith.
Results and discussion
Seven sky radiance scans were made under the obscured sun conditions defined in this study, with SZAs ranging from 19.2° to 48.8°. For six of the seven scans, the cloud deck was comprised of primarily cumuloform clouds with cloud bases at 2.7 km or less (Fig. 3, Table 1). The remaining scan (221-9) was made under an altostratus cloud deck (Fig. 3) with an estimated cloud base of 7.6 km (Table 1). There was a linear relationship between PPFD and UVB irradiance during each scan; however, there was no single linear relationship applicable for all scans (Fig. 2b). The CV in the irradiance ratio was on average 5.0% for all scans, with a high CV of 8.3% and a low CV of 1.5%. The relatively low mean CV may be a result of relatively low variability in the type, thickness, and vertical distribution of the cloud layers during scans since all measurements were made during the summer. The high CV scan corresponded to the one scan (221.9) in which the NWS cloud cover estimate was much less than the overcast (Table 1), while the hemispheric photographs showed an obscured overcast sky (Fig. 3a). The similarity of the UVB irradiance ratio for the scans on day 196 regardless of SZA and the nearly constant ratio of PPFD to UVB irradiance (Fig. 2b) was probably because the τoz was approximately constant throughout the day, while the thickness of the cloud layer(s) and the consequent aerosol concentration and size distribution during the day varied (Fig. 2a, Table 1).
The Nr in each wave band differed greatly between scans but showed consistency between wave bands for a given scan. The Nr–PAR and Nr–UVA were similar to one another, while both differed significantly from the Nr–UVB. For all scans, the Nr–UVB had a greater scatter than that of the UVA and PAR (Fig. 4). Variability in Nr–UVA and Nr–PAR was comparable to that reported by Kittler and Valko (1993) for a similar number of scan replicates of sky luminance under a variety of overcast sky conditions. Results clearly show that obscured overcast skies are not homogeneous in sky radiance.
While cloud type would be expected to influence the Nr distribution, no consistent trends were identified. Four scans, representing cloud layers of stratocumulus only, stratocumulus and altocumulus, and altostratus only, were very similar. Two scans made under cloud layers of cumulus, stratocumulus, and altocumulus (196-6 and 196-7; Table 1) showed the tendency for a maximum Nr at a θ of 40° to 50° (Fig. 5, closed diamond and open inverted triangle). Although the θ of Nr maximum was at approximately the same zenith angle as the SZA, no apparent brightening of the cloud deck at the location of the sun was evident in the hemispheric photographs. Therefore, the difference in Nr distribution with or without a layer of cumulus may be due to scattering off the sides of cumulus enhancing the medium-range zenith angle radiance, as suggested by Estupinan et al. (1996). Kittler and Valko (1993) reported two scans of stratocumulus cloud decks that also had an Nr maximum at θ of approximately 40°, although the presence of multiple cloud layers was not discernible from the ground. The remaining scan in this study (Fig. 5, open circle) showed a nearly linear decline in Nr with increasing θ for cloud conditions identical to 196-4 (Table 1) but with relatively large changes in irradiance during the scan (Fig. 2a). It is believed that the linear decline may be an artifact of the scan Nr normalization process.
While the number of cloud layers may also be expected to influence the Nr distributions, insufficient scans were made to discern such an influence. If anything, one would expect the number of cloud layers to have increased between the time of 196-4 and 196-5, given the layers identified in 196-7 2 h later. The increase in UVB irradiance ratio between 196-4 and 196-7 was associated with a decrease in the PPFD ratio and a decrease in total cloud cover (Table 1). This suggests that the reflection of radiation off the cloud sides may have enhanced the UVB irradiance over the PPFD.
The best-fit b coefficients from the nonlinear regression fits of Eq. (2) were 1.27 and 1.61 for the Nr–UVA and Nr–UVB, respectively (Fig. 4). Using the normalization and regression methodology described in this paper, the Nr–PAR b coefficient was determined to be 1.23. This is identical to that determined for the SW wave band by Steven and Unsworth (1980), but in contrast to the 4.6 value reported for PAR under obscured overcast skies in Grant et al. (1996b). The b coefficient values for the two UV wave bands fall between the 1.23 determined for the SW wave band by Steven and Unsworth (1980) and the 1.89 determined by Rosen and Hooper (1989). The difference in the PAR b coefficient value determined in this analysis versus that determined in Grant et al. (1996b) is due primarily to differences in the sample size and, hence, the range of conditions nominally described as “obscured overcast.” This analysis was based on seven scans chosen on the basis of the photographic analysis of cloud cover and for periods when the atmospheric PAR transmittance was less than or equal to 0.25, while the analysis in Grant et al. (1996b) was based on three scans chosen on the basis of the NWS cloud cover assessments. The additional scans used in this analysis include all scans where the NWS-reported opaque cloud cover was less than 10/10 (Table 1). In addition to this difference, different normalization and averaging methodologies were used. This analysis corrected the radiance measurements by temporal changes in the PPFD during the scan, while the Grant et al. (1996b) analysis did not correct for temporal changes in PPFD during the scan.
Numerically, the greater magnitude of the b coefficient results in a greater rate of decrease in Nr as the horizon is approached (Fig. 4). The radiance at the horizon under obscured overcast conditions was estimated to be 44% and 38% of the radiance at the zenith for the UVA and UVB wave bands, respectively.
The combined effect of atmospheric and cloud attenuation on the irradiance under obscured overcast conditions was estimated by comparing the measured irradiance for the obscured overcast conditions to those predicted for cloud-free sky conditions. The mean ratio for UVB irradiance was 0.24 (standard deviation 0.05). This was lower than the 0.30 (standard deviation 0.03) found by Schafer et al. (1996). Values of the PPFD ratio under the obscured overcast skies had a mean of 0.26 and a standard deviation of 0.05. Both irradiance ratios were within the range of the normalized irradiance found by Bais et al. (1993) and Lubin and Frederick (1991). The slightly greater UVB irradiance ratio over the PPFD ratio is consistent with, but not a confirmation of, the wavelength dependence in cloud transmittance reported by Seckmeyer et al. (1996). The irradiance ratios for skies with multiple layers of cloud were typically lower than those with a single layer (Table 1). The effect of clouds on UV attenuation can be separated from ozone attenuation influence by comparing the measured irradiance for the obscured overcast conditions to those predicted for cloud-free sky conditions over a wave band, such as PAR, that is not affected by ozone (Stamnes et al. 1991). The UVB irradiance ratio was less than the PPFD ratio in five of the seven scans (Table 1). However, since the differences between the mean irradiance ratios were not significant at the 0.05 level (based on a paired t test), no ozone influence on attenuation could be confirmed, suggesting that the UVB irradiance under overcast skies can be predicted from the reduction in PPFD.
The irradiance ratios were influenced by both SZA and the height of the lowest cloud layer. Kondratyev (1969) stated that for the total solar spectrum, the SZA does not influence the irradiance ratio for low cloud cover of stratus and stratocumulus but does influence the ratio for middle and high cloud cover. The low cloud cover scans occurred on Julian day 196, with cloud bases of less than 0.7 km and SZA ranging from 19° to 36° (Table 1). For these scans, the SZA did not appear to influence the UVB ratio but did appear to influence the PPFD ratio (Fig. 6a). This lack of influence of SZA on the UVB ratio is in agreement with the findings of Schafer et al. (1996). There was a tendency for greater reduction in the UVB irradiance than the PPFD at low SZA and for less reduction at high SZA (Fig. 5a). For the three lowest SZA scans, the PPFD ratios were significantly higher than the UVB (paired t test), which is in agreement with the predictions of Spinhirne and Green (1988) and Frederick and Lubin (1988) who state that cloudy skies attenuate UV irradiance to a greater degree than total short wave. Only the ratio for the highest SZA agreed with the results of Frederick and Steele (1995) and Blumthaler et al. (1994), which state that UVB irradiance is reduced less by clouds than the total SW. This scan (221-9) differed from the other scans in that the NWS-reported cloud fraction was less than 10/10 for the hour of measurements while the hemispheric photographic analysis indicated obscured overcast conditions—suggesting that the obscured overcast condition was due to the visual sky cover including both cloud base and cloud sides. However, the UVB irradiance and PPFD did not vary greatly during the time of the radiance measurement scan (Fig. 2) and the hemispheric photographs did not show a variable optical thickness of the cloud cover (Fig. 3). Therefore, this scan does not in any way deviate from the expected conditions of obscured overcast skies. It is important to remember that differences in the UVB irradiance and PPFD ratios exclude the near-infrared radiation included in comparisons of the total SW and UVB irradiance made by Spinhirne and Green (1978), Frederick et al. (1993), Blumthaler et al. (1994), Bordewijk et al. (1995), and Estupinan et al. (1996), in part because the total SW includes the near-infrared wavelengths excluded in the PAR wave band.
The UVB irradiance ratio and PPFD ratio tended to increase with the height of the cloud base. A linear correlation of the height of the cloud ceiling and the UVB irradiance ratio had a coefficient of determination of 0.92 (Fig. 6b). A linear correlation of the height of the cloud ceiling and the PPFD ratio had a lower coefficient of determination of 0.31 (Fig. 6b). These results are consistent with the analysis of Kondratyev (1961) that showed that the irradiance ratio was directly (but nonlinearly) related to the height of the cloud base. The difference in influence of cloud ceiling on the UVB irradiance ratio and PPFD ratio agreed with the model analysis of Spinhirne and Green (1978) and empirical regressions developed by Frederick and Steele (1995). This relationship, however, relies on the previously mentioned highest solar zenith scan period measurements of 221-9 (Table 1). The sky condition during this scan consisted of a deck of relatively uniform cloud thickness (Fig. 3), which resulted in a fairly consistent UVB irradiance and PPFD (Fig. 2). The relatively high CV of the UVB irradiance to PPFD (Table 1) for 221-9 was due to the increasing thickness of the cloud layers.
Since our sky radiance measurements were made simultaneously in the UVA, UVB, and PAR, direct comparisons between the normalized radiance values under the cloud cover was possible. A tendency for the Nr–UVB to be less than the Nr–UVA and Nr–PAR was suggested by the measurements (Fig. 5), but the significance of this difference was difficult to assess due to the small number of replicate scans. A comparison of the paired differences in Nr between the PAR and the UVA wave bands showed a significant difference at the 0.05 level (paired t test: tPAR-UVA = −5.29 and Δ = −0.038); Nr–PAR tended to be consistently slightly less (less than 5% of Nr–PAR) than Nr–UVA for θ less than 50° (Fig. 7). This supports the regression result that the b coefficient for the UVA is slightly greater than that for the PAR. The close relationship between UVA and PAR may be expected since there are no common molecular absorbers in the UVA that do not absorb in the PAR. The paired differences in Nr between the PAR and UVB wave bands also showed a significant difference at the 0.05 level (paired t test: tPAR-UVB = 2.16 and mean difference Δ = 0.004), with the differences in ΔNr consistently higher for Nr–UVB than for Nr–PAR for θ less than 45° and with Nr–UVB alternating from higher than Nr–PAR to lower than Nr–PAR for θ greater than 45°—suggesting random errors overwhelming the signal strength as radiance measurements approached the horizon (Fig. 7). The tendency for the Nr–UVB to be less than Nr–PAR for most Θ suggested greater attenuation of UVB by the clouds or cloud–atmosphere combination, indicative of additional attenuation of UVB by ozone in the atmosphere.
Practical spectral radiance distributions
In practice, a sky radiance distribution model should be representative of the possible sky conditions included in the model. Although a small statistically significant difference in sky radiance between the UVA and PAR wave bands was indicated in this study, the differences were much smaller than the variability found in each wave band for the range of sky conditions collectively defined as obscured overcast. Likewise, the smaller statistically significant difference in sky radiance between the UVB and PAR wave bands had high variability in the difference with respect to θ, suggesting that the results could be different with a different set of measurements for analysis. Therefore, wave band differences in the b coefficient of Eq. (2) found in the study are only suggestive of the relationship between the wave bands. This is especially clear when one considers the change in b for the PAR from that reported in Grant et al. (1996b) to that found in the current study—in part due to the greater number of (and variability in) obscured overcast cases used in the current study.
The inability to discern differences in the sky radiance distributions for the obscured overcast sky condition may be inherent in the variability in cloud types, ozone column thicknesses, cloud-base heights, and coverage of individual cloud layers creating an obscured overcast sky. Such variability can be seen to confuse the issue when one considers the relatively wide range in SW and UVB irradiance ratios reported in the literature for obscured overcast skies. As previously stated, the variability in sky radiance found in the current study is comparable to that found by Kittler and Valko (1993) for luminance under obscured overcast skies. We therefore conclude that one distribution function should be adequate to model the radiance distribution for all three wave bands. Since the sky radiance in the PAR is the greatest of the three wave bands (and consequently the signal-to-noise ratio in the radiance measurements), the PAR model should be used to describe both the UVA and UVB Nr radiance distributions.
Summary and conclusions
The obscured overcast sky radiance in the PAR, UVA, and UVB wavelength bands were measured during the summer of 1993 and fit to the SOC-type model of sky radiance distribution. Results showed that the shorter wavelength bands had higher zenith radiance, more rapid declines in radiance with approach to the horizon, and lower horizon radiance than the SW band as a whole.
Comparison of the calculated normalized radiances in the UVA and UVB to those measured in the PAR showed that the differences in distribution of radiance in the three wave bands were statistically, but not practically, significant. This suggests that the rate of change in radiance with zenith angle can be considered identical for the three wave bands, and the distribution for PAR, UVA, and UVB radiance with obscured overcast skies can be modeled as
where θ is the zenith angle.
Global PPFD and UVB irradiance were also monitored during the obscured overcast conditions. Results showed that the absolute UVB irradiance under the overcast skies could be estimated from the PPFD reduction ratios since the relevant reductions in cloud-free sky irradiance in the UVB and PAR were not significantly different for most of the various times and days of sky radiance scans. Replication of low SZA scans provided evidence for the greater attenuation of the UVB irradiance relative to the PPFD under the overcast skies, as predicted by theory and models. Variability in the UVB irradiance during individual scans was similar to that of the PPFD.
The distributions developed here provide a means of describing the obscured overcast sky radiance distributions in the UVB and UVA wave bands over natural surfaces. The wide variability in measured radiance resulted from the wide range of cloud conditions producing obscured overcast skies. Additional measurements under obscured overcast skies are needed to determine whether the range of conditions modeled in this study is indeed representative of the natural range. The sky radiance distribution under greater surface albedos such as snow cover may be expected to differ from those described since albedo strongly influences the radiance distribution under overcast skies.
The authors thank Wei Gao and Thomas Sperback for their help in collecting and processing the radiance measurements. This research was funded in part by the Purdue Agricultural Experiment Station and the USDA Forest Service Northern Global Climate Change Program under Cooperative Agreement 23-793 of the Northeastern Forest Experiment Station. Thanks also go to the Institüt für Meteorologie and Physik, Universität für Bodenkultur, Vienna, Austria, for providing support during the analysis. This is journal paper 15 212 of the Purdue Experiment Station.
Corresponding author address: Dr. Richard H. Grant, Dept. of Agronomy, Purdue University, West Lafayette, IN 47907.
Mention of a commercial or proprietary product does not constitute endorsement by the U.S. Department of Agriculture, Purdue University, or the Forest Service.