A compact algebraic representation of all-sky shortwave and longwave optical depths from surface radiometry

This work establishes a compact and physically grounded representation of the broadband all-sky optical depth, for both shortwave (solar) and longwave (terrestrial) radiation, that can be evaluated entirely from quantities routinely measured at the surface. Using six years of one-minute observations from seven stations of the Surface Radiation Budget Network (SURFRAD) across the continental United States (CONUS), totaling more than seven million daytime samples, we show that the optical depth in each band separates additively into a clear-sky baseline and a cloud term. The shortwave cloud optical depth is found to be a single universal function of the diffuse fraction, read through the extraterrestrial clearness index and independent of station and climate, because cloud shortwave extinction is governed by elastic scattering and is therefore insensitive to temperature; the cloud term takes the compact form 1 − 2 3 ( k d SW ) 3 / 2 . The longwave cloud term carries the entire station dependence through a single multiplicative factor, the fourth power of the ratio of cloud-base to surface temperature, attenuated with elevation on the same atmospheric scale height that adjusts the clear-sky emissivity; both are constructed from the same surface variables that govern the clear-sky emissivity. Reconstructing each station’s mean shortwave clearness and longwave cloud emissivity from surface variables alone reproduces the measurements to within 0.8 % and 4.6 % , respectively. The result is a closed set of algebraic correlations for the all-sky optical depths over the continental interior that requires no satellite input and no information beyond the surface record.