## 1. Introduction

[2] Interpretation of remotely-sensed ocean colour radiometry (OCR) requires knowledge of the bidirectionality of the upward radiative flux. The *Q* factor that relates upwelling radiance (*L*_{u}) to upwelling irradiance (*E*_{u}), *Q* = *E*_{u}/*L*_{u}, has been studied extensively [*Siegel*, 1984; *Morel and Gentili*, 1991, 1993; 1996; *Åas and Højerslev*, 1999; *Loisel and Morel*, 2001; *Zibordi and Berthon*, 2001; *Morel et al.*, 2002; *Bulgarelli et al.*, 2003; *Sathyendranath et al.*, 2004].

[3] *Morel and Gentili* [1991, 1993, 1996] developed a parameterisation of the *Q* factor as a function of chlorophyll-a concentration, solar zenith angle and viewing angle, based on Monte Carlo simulations. Limitations of this parameterisation, as acknowledged by the authors, were: (1) the model was designed for case-1 waters (optical properties covary with chlorophyll-a concentration); (2) use of a single volume scattering function regardless of the particle size distribution; and (3) the narrow range of chlorophyll-a concentration (0.03 to 3 mg m^{−3}). The last two limitations were addressed in a subsequent work [*Morel et al.*, 2002] using a phase function that was related to chlorophyll-a concentration and a range of chlorophyll concentrations extending to 10 mg m^{−3}. This work also incorporated Raman scattering, which improved the parameterisation at low chlorophyll-a concentration. *Loisel and Morel* [2001] studied the *Q* factor as a function of the total scattering (*b*) and absorption (*a*), *Q* = *f*(1 + *b*/*a*), based on radiative transfer simulations that included case-2 waters (waters in which phytoplankton, detrital and other suspended particles and dissolved organic matter vary independently of each other).

[4] Here, we present a new parameterisation of the *Q* factor as a function of total backscattering (*b*_{b}) and absorption coefficients. The use of those two variables is motivated by the following: (1) reflectance is related to *a* and *b*_{b} [*Morel and Prieur*, 1977; *Sathyendranath and Platt*, 1997]; and (2) many procedures are available to retrieve inherent optical properties (IOP) from reflectance data, in particular total absorption and backscattering coefficients [*International Ocean-Colour Coordinating Group* (*IOCCG*), 2006].

[5] In this paper, a bivariate polynomial regression is performed on simulated *Q* data for open-ocean and coastal waters, at various wavelengths and two solar zenith angles. The performance of the new parameterisations is tested against in situ data. Total backscattering at 555 nm is retrieved using the reflectance model of *Sathyendranath and Platt* [1997] and the new *Q*-factor parameterisation. Our results are also compared with derivations from the method of *Morel et al.* [2002], which is designed for case-1 waters.