Relationship between the sub-micron fraction (SMF) and fine mode fraction (FMF) in the context of AERONET retrievals

The sub-micron (SM) aerosol optical depth (AOD) is an optical separation based on the fraction of particles below a specified cut off radius of the particle size distribution (PSD) at a given particle radius. It is fundamentally different from spectrally separated FM (fine mode) AOD. We present a simple (AOD-normalized) SM fraction versus FM fraction (SMF vs FMF) linear equation that explains the well-recognized empirical result of SMF generally being greater than the FMF. The AERONET inversion (AERinv) products (combined inputs of spectral AOD and sky radiance) and the Spectral Deconvolution Algorithm (SDA) products (input of AOD spectra) enable, respectively, an empirical SMF vs FMF comparison at similar (columnar) remote sensing scales across a variety of aerosol types. SMF (AERinv derived) vs FMF (SDA derived) behavior is primarily dependent on the relative truncated portion (εc) of the coarse mode (CM) AOD associated with the cutoff portion of the CM PSD and, to a second order, the cutoff FM PSD and FM AOD (εf). The SMF vs FMF equation largely explains the SMF vs FMF behavior of the AERinv vs SDA products as a function of PSD cutoff radius ("inflection point") across an ensemble of AERONET sites and aerosol types (urban industrial, biomass burning, dust, maritime and a mixed class of Arctic aerosols). The overarching dynamic was that the linear SMF vs FMF relation pivots clockwise about the approximate (SMF, FMF) singularity of (1, 1) in a "linearly inverse" fashion (slope and intercept of approximately 1 − εc and εc) with increasing cutoff radius. SMF vs FMF slopes and intercepts derived from AERinv and SDA retrievals confirmed the general domination of εc over εf in controlling that dynamic. A more general conclusion is the apparent confirmation that the optical impact of truncating modal (whole) PSD features can be detected by a SMF vs FMF analysis.