## 1. Introduction

[2] The size distribution and spectral complex refractive index of aerosols are needed to compute properties such as their scattering phase function, single scatter albedo, and extinction coefficient, which are in turn used to calculate quantities such as total aerosol optical depth (AOD) from column abundance. In general, the information content of measurements from current satellite radiometers is insufficient to unambiguously retrieve all these parameters, particularly when the (spectral and directional) behavior of surface reflectance is unknown [*Hasekamp and Landgraf*, 2007]. For this reason, aerosol retrieval algorithms employed by most of these sensors are required to make assumptions about aerosol microphysical properties, and rely on a set of predefined aerosol models or components. The assumptions in these aerosol retrieval algorithms contribute to differences in retrieved AOD, even in the idealized case of a black (non-reflecting) surface [*Kokhanovsky et al.*, 2010]. The Polarization and Directionality of the Earth's Reflectance (POLDER) sensor is much less restricted, as its measurement capabilities provide an increased information content as compared to most current sensors [*Dubovik et al.*, 2011; *Hasekamp et al.*, 2011].

[3] For other sensors, it is therefore of high importance that the models used are representative of real aerosol properties. The purpose of this study is to develop such a model for clean maritime aerosol, using Sun-photometer data from the Aerosol Robotic Network (AERONET) [*Holben et al.*, 1998]. A companion paper [*Sayer et al.*, 2012] describes the application of this model to aerosol retrievals from Sea-viewing Wide Field-of-view Sensor (SeaWiFS) measurements.

[4] The AOD over the open ocean is typically low (<0.1 in the midvisible [e.g., *Smirnov et al.*, 2009, 2011]). As such, a small absolute bias in a satellite AOD retrieval can translate into a large relative bias. As the Earth's oceans cover approximately two thirds of its surface, and natural marine aerosol is the primary source of cloud condensation nuclei in the remote marine atmosphere, accurate knowledge of the atmospheric aerosol burden is needed for climate modeling studies [e.g., *Forster et al.*, 2007]. Further, by understanding the contribution from pure marine aerosol, the contribution from other aerosol types (such as mineral dust or biomass burning) in conditions of mixed aerosol can be better characterized.

[5] The optical properties of marine aerosol can be determined from ground-based and aircraft in-situ measurements, or theoretical considerations, as well as remote sensing. A review of some of these is presented by *Smirnov et al.* [2002]. In particular, the models of *Shettle and Fenn* [1979] (from aircraft measurements) and *Gathman* [1983] (coastal towers, and ships) have been used widely. However, observational data sets are typically limited in time and space, and differences between the types of instrumentation used in these campaigns contribute to significant differences between the results [*Reid et al.*, 2006]. Advantages of AERONET data therefore include the opportunity to analyze a longer time series, with a wide global distribution, and consistency between different measurement sites. Such studies are also often coastal, such that there may be a non-maritime component to the aerosol. While still a factor for AERONET data, this can be minimized through choice of remote sites, and careful filtering of data. A previous AERONET-based analysis was performed by *Smirnov et al.* [2003a], although at that time the available data record was significantly shorter.

[6] The aerosol number size distribution *dN*(*r*)/*d*ln(*r*) describes the number of aerosol particles with radius in the infinitesimal size range *r* ± *d*ln(*r*). The distribution is also sometimes defined as *dN*(*r*)/*dr*, and these two distributions are easily related by

[7] The volume size distribution, calculable for spherical aerosol particles as

describing the aerosol particle volume over the same infinitesimal radius range, is also frequently used. The AERONET products are defined in terms of the columnar volume size distribution and so this convention is adopted in the analysis here. The total aerosol columnar particle number (*C*_{n}) and volume (*C*_{v}) are obtained by integrating these distributions over all ln(*r*).

[8] Frequently-used metrics to characterize aerosol size distributions include the logarithmic volume mean radius (*r*_{v}) as a measure of the size of the aerosol particles, where

and the geometric standard deviation (or spread) of the distribution (*σ*) as a measure of the dispersion:

[9] The mean radius of the number distribution *r*_{n} is defined analogously to equation (3), using *dN*(*r*)/*d*ln(*r*) in place of *dV*(*r*)/*d*ln(*r*). A third useful quantity is the effective radius (*r*_{eff}), the ratio of the third to second moments of the number size distribution:

[10] The effective radius is more closely related to aerosol extinction than the number mean radius. This is because scattering depends on aerosol cross-sectional area, and distributions with similar effective radii (and effective variances, although this quantity is less frequently used in aerosol studies) typically have similar scattering properties, even if the precise mean radii and spreads differ [*Hansen and Travis*, 1974; *Mishchenko et al.*, 1997].

[11] Aerosol size distributions are commonly represented as a combination of lognormally-distributed components, and the number size distribution is defined as a summation over these (*n*_{c}) components by

and the modal radius for each component is also its median and geometric mean. The equivalent distribution for aerosol volume is arrived at by substituting *r*_{n} with *r*_{v}, and *C*_{n} with *C*_{v}. The advantages of lognormal distributions include that their statistical properties are well-known, and many available radiative transfer codes are able to take as input lognormal distribution parameters. For individual lognormal components, the conversion between the volume and number distribution parameters is presented in Appendix A. Note that the spread *σ* remains the same for both number and volume distributions. *Hinds* [1999] presents some general results for moments of lognormal distributions, including that

[12] Section 2 describes the AERONET data used, and properties of average size distributions. Section 3 examines the effect of meteorology on the size distribution. Next, section 4 combines the size information with various refractive indices to define an average aerosol model which is best able to replicate the observed AERONET AODs. Following the definition of this model, section 5 tests the predictive power of the relationship observed between wind speed and aerosol volume on ship-borne AOD measurements, and section 6 presents calculated lidar ratios. Finally, section 7 summarizes the results of the study.