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ATTENUATION OF VISIBLE SUNLIGHT BY LIMITED VISIBILITY AND CLOUDINESS
Impact/Purpose:
A Multi-Filter Rotating Shadowband Radiometer (MFRSR) operated from the roof of the Hinds Geophysical Sciences Building on the University of Chicago campus for much of calendar year 2005. The measurements analyzed here are total (direct plus diffuse) solar irradiances incident on a horizontal surface in five narrow wavelength bands extending from λ = 416 nm to 868 nm, covering the visible portion of the spectrum and a small segment of the near-infrared. Interpretation of the datasets provides a comprehensive description of the roles of cloudiness and limited visibility on solar irradiance reaching the ground. Issues of particular interest center on (1) characterizing the attenuation associated with limited horizontal visibility under clear skies; (2) determining the extent to which measures of cloud cover that are widely available in meteorological datasets constrain the attenuation provided by prevailing cloudiness; (3) identifying situations where fractional cloudiness leads to surface irradiances in excess of the values for clear skies; and (4) identifying any wavelength dependence associated with the attenuation provided by cloudy skies.
Description:
Variability in the irradiance measurements arises from systematic changes in the solar zenith angle (SZA), cloudiness and changing visibility. Measurements in the wavelength band centered on 612 nm serve as a reference for the initial characterization of the effects of cloudy skies and limited visibility. It is essential to develop an index of the influences of cloudiness and visibility that is insensitive to changes in SZA. The “irradiance ratio” defined as:
T(λ) = EM(λ)/EC(λ) (1)
accomplishes this, where EM(λ) is the measured irradiance and EC(λ) is the clear-sky irradiance that would have existed at the time of the measurement. Although both the numerator and denominator vary with SZA, the ratio is nearly independent of this quantity. A clear sky with high visibility corresponds to T(λ) = 1.0 for any SZA.
To determine the clear-sky irradiance EC(λ) as a function of SZA, we selected a subset of 1,304 data points at each wavelength that coincided within 5 minutes with meteorological data recorded at Midway Airport, located approximately 12 km west of the observation site. Of these, 73 points correspond to totally clear skies and a visibility, V, of 10 miles (which is the largest value recorded). A quadratic fit to these points produced the estimated clear-sky irradiance as a function of SZA (θ) at each wavelength. As an example, at λ = 612 nm, the fit EC(612) = -0.0975 + 1.427 cos θ + 0.1167 cos2θ explains 99.2 percent of the variance the observations, where cos θ varies in the range from 0.15-0.70. The derived clear-sky irradiances at all five wavelengths allow the calculation of irradiance ratios via Equation 1.
The attenuation associated with cloudy skies is far more important than that associated with restricted visibility. However, it is possible to isolate the influence of visibility by focusing exclusively on clear skies. With the 612 nm signal as an example and letting Tc refer to transmission ratios derived for clear sky conditions, the regression Tc = a0 + a1(V-10) yields the values a0 = 1.010 (0.012) and a1 = 0.0235 (0.0065), where values in parentheses represent two standard errors, approximately corresponding to 95 percent confidence limits. Although the derived value of a1 is significant at better than the 1 percent level of confidence, the regression explains only 36 percent of the variance in the clear-sky Tc-values. This is not surprising since visibility is an imprecise quantitative measure of the horizontal optical depth associated with particulates and small droplets. The attenuation of irradiance depends on the vertical profile of the opacity, which is correlated with visibility, although a simple one-to-one relationship will not exist. Still, the statistical results demonstrate that routinely available visibility data provide useful information on the excess attenuation provided by particles and droplets. The best estimates of the regression coefficients indicate that a reduction in visibility from 10 miles to 5.7-5.8 miles reduces the irradiance under clear skies by 10 percent. Results deduced for other wavelengths in the MFRSR dataset differed insignificantly from those stated above.
Table 1 summarizes the distribution of computed irradiance ratios at 612 nm based on all 1,304 measurements, where the sorting is according to the index of cloudiness contained in the coincident meteorological data set. The designations are “clear”, “scattered”, “broken”, and “overcast”, which correspond to fractional sky covers of 0/8, 1/8-4/8, 5/8-7/8, and 8/8, respectively. The “central 50 percent range” in Table 1 is defined such that 25 percent of the irradiance ratios lie above the maximum reported value, and 25 percent lie below the reported minimum.
The difference in irradiance between clear conditions and a sky with scattered clouds is small. In these circumstances the solar disk is most likely not obscured, resulting in average irradiances very close to the clear-sky values. Significant attenuation appears under broken clouds and overcast skies. In these cases the solar disk is most likely, but not always, obscured. In an average sense, a totally overcast sky reduces the 612 nm irradiance to 30-40 percent of its clear-sky value.
Table 1. Distribution of Computed Irradiance Ratios at 612 nm, Sorted According to an Index of Fractional Cloud Cover
Cloud Cover |
Number Points |
Mean |
Median |
Central 50% Range of T(612) |
|
|
|
|
|
Clear |
94 |
0.99 |
1.00 |
0.96-1.03 |
Scattered |
453 |
0.92 |
1.00 |
0.90-1.04 |
Broken |
410 |
0.73 |
0.73 |
0.49-0.98 |
Overcast |
347 |
0.36 |
0.32 |
0.22-0.45 |
An examination of the individual points summarized in Table 1 reveals that irradiance ratios in excess of the value for clear skies appear in all categories of cloud cover. More than 10 percent of the measurements corresponded to values T(612) > 1.05. To examine these measurements in more detail, Table 2 sorts this subset of the dataset according to the corresponding degree of cloudiness.
Table 2. Distribution of Irradiance Ratios for a Subset of the Data Where T(612.3) > 1.05, Sorted According to Fractional Cloud Cover
Cloud Cover |
Number Points |
Mean |
Median |
Central 50% Range of T(612) > 1.05 |
|
|
|
|
|
Clear |
16 |
1.09 |
1.08 |
1.06-1.12 |
Scattered |
75 |
1.09 |
1.07 |
1.06-1.11 |
Broken |
53 |
1.16 |
1.14 |
1.07-1.22 |
Overcast |
4 |
1.18 |
1.13 |
1.07-1.34 |
Table 2 shows that, contrary to the behavior shown by the entire data base, the mean irradiance ratios actually increase slightly with fractional cloudiness. A series of radiative transfer calculations showed that this behavior is consistent with theoretical expectations provided that the solar disk resides in the clear portion of the sky. In this circumstance, the ground still experiences the large contribution of the direct solar beam, while the highly reflective clouds act to direct upward radiation scattered from the lower boundary back toward the ground. The four points listed as referring to overcast skies must represent rare cases where the solar disk lies in a small clear portion of an otherwise cloud-covered sky.
The final issue centers on wavelength dependence in the attenuation provided by cloudy skies. To examine this, it is desirable to remove the large variation in irradiance associated with the SZA. The sample data presented in Figure 1 refers to the band of SZA defined by 0.5 < cos θ < 0.6. A total of 9,875 measurements exist at each wavelength in this range. At a fixed SZA, the absolute irradiance measured at 612 nm is itself a measure of the influence of clouds. If the attenuation was independent of wavelength, then a plot of the ratio EM(λ)/EM(612) versus EM(612) would be a horizontal line. This is true since the irradiances in both the numerator and denominator would change by the same multiplicative fraction under a cloudy sky. Figure 1 is a sample plot for λ = 416 nm, indicating the true observed behavior.
Figure 1. E(416)/E(612) Versus E(612) for 0.5<cos(SZA)<0.6
Large values on the horizontal axis in Figure 1 correspond to nearly clear skies, while many of the smaller 612 nm irradiance arise from partly cloudy or totally cloud covered conditions. It is apparent that the envelope of points slopes downward as EM(612) increases, indicating less attenuation at 416 nm than at 612 nm. A simple linear fit of the form EM(416)/EM(612) = b0 + b1EM(612) yields b0 = 0.941 (0.004) and b1 = -0.273 (0.006) where the values in parentheses represent two standard errors. The value of b1, being significantly different from 0.0, demonstrates the existence of a wavelength-dependent attenuation.
The most prominent feature in Figure 1 is the set of unusually large ratios in the vicinity of EM(612) = 0.2 W m-2 nm-1. A set of radiative transfer calculations demonstrated that these anomalously large ratios occur when the sky is partly cloudy (fractional cloud covers typically 2/8 to 4/8) and the solar disk is obscured by these clouds. In this circumstance, the diffuse Rayleigh scattered background makes a large fractional contribution to the measured irradiance. Owing to its λ-4 dependence, the result is an enhancement in the short wavelength irradiance relative to that at 612 nm. Consistent with this explanation, plots analogous to Figure 1, but for λ > 612 nm, reveal positive slopes (b1 > 0) and a scatter of data below the primary envelope of points near EM(612) = 0.2 W m-2 nm-1.