Absorption correction and phase function shape effects on the closure of apparent optical properties

We present a closure experiment between new inherent optical properties (IOPs: absorption a, scattering b, backscattering b_b) and apparent optical properties (AOPs: remote-sensing reflectance R_rs, irradiance reflectance R, and anisotropic factor at nadir Q_n) data of Ionian and Adriatic seawaters, from very clear to turbid waters, ranging across one order of magnitude in R_rs. The internal consistency of the IOP-AOP matchups was investigated though radiative transfer closure. Using the in situ IOPs, we predicted the AOPs with the commercial radiative transfer solver Hydrolight. Closure was limited by two unresolved issues, one regarding processing of in situ data and the other related to radiative transfer modeling. First, different correction methods of the absorption data measured by the Wetlabs ac-s produced high variations in simulated reflectances, reaching 40% for the highest reflectances in our dataset. Second, the lack of detailed volume scattering function measurements forces us to adopt analytical functions that are consistent with a given particle backscattering ratio. The analytical phase functions named Fournier-Forand and two-term Kopelevich presented reasonable angular shapes with respect to measurements at a few backward angles. Between these phase functions, induced changes were within 4% for R_rs, within 11% for R, and within 10% for Q_n. Additionally, closure of Q_n was generally not successful considering radiometric uncertainties. Simulated Q_n overestimated low values and underestimated high values, especially at 665 nm, where Hydrolight was unable to predict measured Q_n values greater than 6 sr. The physical nature of Q_n makes this mismatch almost independent of the measured IOPs, thus precluding Q_n tuning by varying the former. The non-closure of Q_n might be caused by an inaccurate phase function and, to a lesser extent, by the modeling of the incoming radiance. For the future, this remains the task of accurate absorption and phase function measurements, especially at red wavelengths.