For Estimates of Cloud Optical Thickness, Simple Equation Is Good Enough

Barnard, J., University of Nevada Reno

Cloud Distributions/Characterizations

Cloud Properties

Barnard, J. C., and C. N. Long, (2004): A Simple Empirical Equation to Calculate Cloud Optical Thickness Using Shortwave Broadband Measurement, JAM, 43, 1057-1066.


Distributions of cloud optical thickness reveal that the empirical method (dashed line) closely replicates the Min algorithm (solid line), including the long tail that extends up to an optical thickness of 200. Both methods used observational data from the central facility at the ARM Program's Southern Great Plains site in 2000.


Distributions of cloud optical thickness reveal that the empirical method (dashed line) closely replicates the Min algorithm (solid line), including the long tail that extends up to an optical thickness of 200. Both methods used observational data from the central facility at the ARM Program's Southern Great Plains site in 2000.

In contrast to complicated algorithms and extensive computer time required to obtain cloud optical thickness from surface measurements, researchers funded by the DOE's Atmospheric Radiation Measurement (ARM) Program have developed a simple equation that does the job—as long as only reasonably close estimates are needed. Using data from several geographically diverse ARM sites, the researchers calculated cloud optical thickness from both their empirical method and a well documented transmission-based algorithm developed by Min and Harrison (1996). When compared, the median distributions were well within 10% of one another, and the shapes of the distributions were very similar. Because this new expression relies only on readily available solar flux measurements, it provides a much wider base of cloud optical depth values on a global basis than have previously been available.

Cloud optical thickness is the fundamental variable needed to understand the impact of clouds on the surface radiation budget. Measuring cloud optical thickness directly from the ground requires sophisticated and expensive instrumentation. Deducing optical thickness from solar flux measurements at the earth surface is possible, but requires additional measurements that are not generally available, as well as complex algorithms and computer time.

Transmission-based algorithms, such as that of Min and Harrison, use spectral or broadband irradiance measurements to infer cloud optical thickness. Though the Min spectral radiance algorithm runs relatively quickly on a desktop computer, the specific wavelength measurements it uses as input are not widely available, limiting its usefulness on a global scale. On the other hand, shortwave broadband irradiances are commonly measured, but the associated algorithms to infer cloud optical thickness require complex data about atmospheric state, not to mention considerable computer time to perform the calculations. In the new approach, only surface shortwave broadband irradiances are required. Additionally, sensitivity studies conducted by the researchers demonstrated another advantage of the simple equation: seasonal fluctuations of unknown atmospheric variables (e.g., water vapor, aerosol optical thickness) did not significantly degrade the method's accuracy.

The simple empirical expression computes cloud optical thickness as a function of solar zenith angle, surface albedo, broadband diffuse irradiance, and broadband "clear sky" total irradiance. Thus, it retains the flexibility of using widely-available broadband measurements, and virtually eliminates the computational time consideration. However, the simplicity comes with several caveats: (1) it is recommended for surface albedo values known to be less than 0.30; (2) it is only applicable to fully overcast sky conditions with cloud fractions greater than 0.99; (3) it is not designed for low solar elevation angles; and (4) clear sky total radiance should be obtained from fitting clear sky measurements rather than from model calculations. And most importantly, the equation should be used only when "routine" measurements of cloud optical thickness are needed. Because long-term statistics of cloud properties are more relevant to climate studies than point-by-point comparisons at an instant of time, the empirical formula does an adequate job for these purposes.