Is the average photon energy a unique characteristic of the spectral distribution of global irradiance?

The average photon energy (APE) has become a popular index to qualitatively assess whether shorter or longer wavelengths are enhanced in a specific spectral distribution of irradiance when compared to the AM1.5G standard spectrum. According to some previous assessments, this index might uniquely distinguish individual global tilted irradiance and global horizontal irradiance spectra. This paper basically applies the same methodology as that used in these studies, i.e., a statistical analysis based on spectral distributions grouped in 0.02-eV APE bins and their standard deviation across all 50-nm bands into which the wavelength range under scrutiny (350-1050 nm) is divided. Two years of spectral global tilted irradiance datasets collected at two Spanish locations, 333 km apart, are analyzed here. The same brand and model of spectroradiometer is used in each site with identical experimental protocols. It is found here that the coefficient of variation-a more meaningful statistical coefficient than the standard deviation to quantify dispersion around the mean-remains below 3.3% over the 450-900-nm waveband, whereas values up to 5-11% occur outside of it. It is shown that these higher values can be explained by the separate or combined impacts of experimental uncertainty and the direct effect of aerosols and water vapor. Based on radiative transfer principles related to these two atmospheric constituents, it is argued that APE cannot be a unique characteristic of the complete spectrum, thus confirming previous results that pertained to direct irradiance only. In practical terms, however, it is reasonable to ascertain that APE may be considered approximately unique relative to the spectrum distribution under the climate of the two sites under scrutiny over the limited 450-900-nm spectral range. This conclusion presumably holds for most of Spain, or even for locations with sunny inland climates similar to those of Jaén and Madrid.