Solar Energy, Clear Sky Effects

Date : 4 May 1997

Before I discuss how clouds influence solar energy (S), I first discuss the influence of a clear sky. This topic maybe a little dull, but for those who are reading these articles weekly, it is a necessary topical transition.

For calculation of direct S, the concept of transmittance is often used. Transmittance of a medium is the fraction of incident electromagnetic (EM) radiation which passes thru it. Thus, it is all neither scattered nor absorbed. Monochromatic (single wavelength) transmittance can be expressed as

T_l = R_l / R_0l ,

in which R_0l represents incident EM radiation intensity (S flux per unit wavelength) at wavelength l, and R_l that after passing thru a medium. When the medium is our atmosphere, an optical depth (t_l) is typically defined such that transmittance is 1/e (e = 2.718281...) for a value of 1. I.e.,

I_l = I_0l e ^{- t_l} ,

in which I_0l & I_l are expressed as for R_0l & R_l, except for S intensity. Because our atmosphere is very rarely standard, an attenuation coefficient is defined as

t_al = t_l m ,

in which m represents optical air mass :

Thus, more air penetration means more attenuation (less transmittance). Optical depths can be defined for specific atmospheric constituents. Their combined transmittance affects are assumed multiplicative :

I_l = I_0l T₁ T₂ T₃ ...

in which 1, 2, 3 ... refer to specific constituents. Thus

I_l = I_0l e ^{- t_a₁l} e ^{- t_a₂l} e ^{- t_a₃l} ... ,

I_l being direct S intensity after penetration thru our atmosphere.

Total direct S can be calculated, integrating spectral contributions (among wavelengths) :

I = I_l d_l

Detail of such calculations is dependent on number of constituents, many sometimes considered. A standard simplification is representation of the primary atmospheric affects, each as 'constituents' : e.g., molecular scattering, aerosol scattering, aerosol absorption, water vapor absorption, ozone absorption, and 'uniformly mixed' gas absorption. The latter category includes many of the constituents previously mentioned. Their total attenuation is relatively small, thus calculation is greatly simplified. Affects of aerosol scattering and absorption are often combined, transmittance represented with an aerosol optical depth. Quite often the entire atmosphere is considered as a 'constituent', all S wavelengths simultaneously considered. I.e.,

I = I₀ e ^{- t_a} ,

in which t_a is a single atmospheric attenuation coefficient.

A person may ask how such coefficients are determined. The process is the reverse of what I just wrote - S must first be measured to determine coefficients. As a simple example, suppose that during a clear day, extraterrestrial S flux is 900 W/m², direct S flux is 500 W/m², and optical air mass is 1.5. Thus,

I₀ = 900 , I = 500 , m = 1.5

I = I₀ e ^{- t_a} = I₀ e ^{- t}^m ,

t m = - ln(I/I₀) = -ln(900/500) = .165 ,

t = .165/m = .165/1.5 = .11 ,

an atmospheric optical depth .11. Optical depth for specific constituents are thus defined. When considering many constituents, the problem is obviously more difficult than this simple example, since each significantly contribute at many wavelengths. The situation is more complicated for diffuse S flux, consisting of complex directionally-dependent scattering from air molecules and aerosols of various sizes and shapes and including ground reflection and multiple backscattering. A helpful concept though, is definition of the 3 basic S components - global, direct, and diffuse. If 2 of the components can be specified (e.g., measured), the 3^rd is known, a concept often utilized in practical applications. An example is the Atmospheric Radiation Measurement Program's Multi-Filter Rotating Shadowband Radiometer. Using a rotating band for shadowing direct sunlight (shadowband), it allows global and diffuse S measurements for 6 wavelengths, specifically chosen to yield info regarding aerosol, water vapor, and ozone attenuation. Corrections must be made for how the shadowband influences diffuse S measurement. Particularly, circumsolar radiation is blocked, which can be a very significant portion of diffuse. A sample of diffuse S distribution (actually, visible light) during a clear day nicely illustrates this. Among features you may notice are

The circumsolar area - a very bright sky near the solar disc (which is occulted)

The dark area at middle to high sky elevations opposite the solar disc

Horizon brightening, caused mainly by ground reflection

From many measurements and a few clever ideas, researchers have quantified these affects, making broadband diffuse S estimation accurate for well-known terrain and atmospheric conditions.

Active sensing is useful for determination of clear sky S distribution. An example is Atmospheric Radiation Measurement Program's Cloud and Radiation Testbed Raman Lidar imager. Similarly for standard meteorological radars, a laser pulse is sent in the atmosphere, and the return signal provides info regarding atmospheric water vapor, aerosol content, and radiation polarization. The instrument is particularly useful for continuous water vapor soundings, as comparisons of LIDAR and balloon sounding data illustrate. Those are daytime measurements, including some corruption of data because of solar radiation. Nighttime images are more impressive ! Water vapor quite significantly influences clear sky S, its absorption occurring mainly in near infrared EM radiation bands. Clouds are sensed particularly well, but such discussion is for next week.

Text and embedded graphics are copyright of Joseph Bartlo, though may be used with proper crediting.

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