Estimating Marine Aerosol Particle Volume and Number from Maritime Aerosol Network Data

As well as spectral aerosol optical depth (AOD), aerosol composition and concentration (number, volume, or mass) are of interest for a variety of applications. How- ever, remote sensing of these quantities is more difficult than for AOD, as it is more sensitive to assumptions relating to aerosol composition. This study uses spectral AOD mea- sured on Maritime Aerosol Network (MAN) cruises, with the additional constraint of a microphysical model for unpol- luted maritime aerosol based on analysis of Aerosol Robotic Network (AERONET) inversions, to estimate these quanti- ties over open ocean. When the MAN data are subset to those likely to be comprised of maritime aerosol, number and volume concentrations obtained are physically reasonable. Attempts to estimate surface concentration from columnar abundance, however, are shown to be limited by uncertain- ties in vertical distribution. Columnar AOD at 550 nm and aerosol number for unpolluted maritime cases are also com- pared with Moderate Resolution Imaging Spectroradiometer (MODIS) data, for both the present Collection 5.1 and forth- coming Collection 6. MODIS provides a best-fitting retrieval solution, as well as the average for several different solutions, with different aerosol microphysical models. The "average solution" MODIS dataset agrees more closely with MAN than the "best solution" dataset. Terra tends to retrieve lower aerosol number than MAN, and Aqua higher, linked with dif- ferences in the aerosol models commonly chosen. Collection 6 AOD is likely to agree more closely with MAN over open ocean than Collection 5.1. In situations where spectral AOD is measured accurately, and aerosol microphysical properties are reasonably well-constrained, estimates of aerosol number and volume using MAN or similar data would provide for a greater variety of potential comparisons with aerosol proper- ties derived from satellite or chemistry transport model data. However, without accurate AOD data and prior knowledge of microphysical properties, such attempts are fraught with high uncertainties.


Introduction
Columnar aerosol optical depth (AOD) has been mapped on a near-global basis for several decades from satellite measurements with varying degrees of accuracy (e.g. Husar et al., 1997, Hsu et al., 1999, Torres et al., 2002, Mishchenko et al., 2007, Remer et al., 2008, Thomas et al., 2009, Kahn 25 et al., 2010, Sayer et al., 2012a. There is a similar wealth of ground-based aerosol observation from techniques such as sun photometry, lidar, or multifilter rotating shadowband radiometers, with records approaching two decades at some locations (e.g. Holben et al., 1998, Michalsky et al., 2001, Campbell et al., 2002. The AOD represents the vertically-integrated extinction of light by aerosol particles, where τ λ is the AOD at wavelength λ, and β λ the aerosol extinction (sum of scattering and absorption) at that wavelength and altitude z, and as such is related to the aerosol mass loading of the atmosphere.
The spectral behaviour of AOD, frequently referred to in the context of theÅngström parameter is often evaluated across the visible region of the solar spectrum and used as a first-order indication of aerosol type , Dubovik et al., 2002. However, α is not a unique identifier of a particular aerosol composition, so additional constraints such as microphysical aerosol particle models 40 are necessary to infer physical aerosol amount from AOD. Further, particularly in low-AOD regimes, satellite and ground-based estimates of α can suffer from significant uncertainty (Wagner and Silva, 2008). These factors mean that estimating aerosol number or volume from remotely-sensed AOD is, at present, not straightforward. Remote determination of aerosol number or volume/mass rather than solely AOD is of interest to estimate, for example, the deposition flux of mineral dust aerosols (Kauf-over the ocean (Smirnov et al., 2009(Smirnov et al., , 2011, with typically four (sometimes five) channels in any individual measurement. Thus, the model can be used to infer columnar aerosol number and volume of maritime aerosol from the MAN AOD measurements (size distribution inversions as performed at the AERONET land sites are not possible from the hand-held measurements collected on MAN 60 cruises). The aim of this study is to perform such an exercise.
This is first a test of whether the model of Sayer et al. (2012b) is able to produce physicallyreasonable values of aerosol concentration. It also allows a comparison of derived aerosol number with the (unvalidated) aerosol columnar number concentration estimates provided in the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite aerosol product (Remer et al., 2005(Remer et al., , 65 2008). These open up further scope for evaluation of the aerosol parametrisation of chemistry transport models (CTMs) through comparisons with aerosol number or volume as well as AOD. This is important because CTM aerosol fields are diverse, and it is possible for the CTM to produce the right AOD but with the wrong aerosol composition (e.g. Kinne et al., 2006, Textor et al., 2006.
Uncertainties in the MAN-derived estimates are also discussed.

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The notation adopted in this work follows that of Sayer et al. (2012b), in which various identities and derivations are presented. A summary of relevant notation is presented here. The aerosol number size distribution dN (r)/dln(r) describes the number of aerosol particles with radius in the infinitesimal size range r ± dln(r); for spherical particles, this is related to the volume size distribution dV (r)/dln(r) by 75 dV (r) dln(r) = 4πr 3 3 dN (r) dln(r) . ( In this work and many others (Sayer et al., 2012b, and references therein) aerosol particle size distributions are represented as a sum of n c lognormally-distributed components, where r n and σ are the mode's modal (also median and geometric mean) radius and geometric 80 standard deviation respectively, and C n the total number of aerosol particles in the mode. The equivalent aerosol volume distribution is given by the same expression, except substituting r n with the volume median radius r v , and C n with the total aerosol volume C v . The relationships between these quantities for a lognormal component (Sayer et al., 2012b) are r v = r n e 3σ 2 (5) 85 and C v = 4π 3 r n 3 e 4.5σ 2 C n , enabling the conversion between number and volume radii, and calculation of aerosol number-tovolume ratio. In this work bimodal aerosol distributions are used (i.e. n c = 2), with the smaller mode denoted 'fine' with a subscripted f, and larger mode 'coarse' with a subscripted c.

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The remainder of the manuscript is organised as follows. Section 2 describes the MAN data and the method whereby aerosol number and volume can be estimated, along with derived maps of these data. Aerosol mass is not explicitly discussed (for a given density, it is a simple scaling of aerosol volume). Section 3 provides a comparison with MODIS estimates, and Section 4 looks at the relationship between total columnar and surface concentrations. Finally, Section 5 provides a 95 summary and outlook.
2 Estimating columnar volume and number

MAN data
The AOD measurements on MAN cruises (Smirnov et al., 2009(Smirnov et al., , 2011 are made with hand-held Microtops II Sun-photometers, which allow measurement of AOD with a total (one standard deviation) 100 uncertainty of order ±0.015 for typical oceanic conditions (Porter et al., 2001, Knobelspiesse et al., 2003. The instruments have five filters which can be adjusted to observe the Sun at different wavelengths; typically on MAN cruises one is used to retrieve columnar water vapour, leaving four for AOD, in the spectral range 340 nm-1020 nm. The overwhelming majority of measurements consist of the combination τ 440 , τ 500 , τ 675 , and τ 870 (subscripted wavelengths are in nanometres 105 throughout). TheÅngström parameter α is calculated in MAN from a least-squares fit (in logarithmic space) of AOD and wavelength over the spectral range 440 nm-870 nm.
Two MAN datasets are used in this work. The first is the 'series average' product, where one measurement series is defined as the set of AOD measurements taken with a gap of no more than 2 minutes between an individual pair. The second is the 'daily average' product, which is the average 110 of all measurement series on a given day. Frequently multiple series are obtained on a given day in identical or very close locations, so visual interpretation is typically clearer using daily data, while statistical analysis benefits from the larger sample size of the series average data. In practice the results change negligibly if only one or the other data product is used, suggesting that most of the observations collected on a MAN cruise over the course of a single day sample similar aerosol 115 regimes. In all cases, only level 2.0 (cloud-screened and quality assured) data are used.

Calculation and uncertainty
Size distribution parameters and refractive indices for the bimodal model of Sayer et al. (2012b) are given in Table 1. The free parameters, C v,f and C v,c , are determined from a least-squares fit of each set of MAN spectral AOD to the spectral extinction per unit volume modelled using Mie theory 120 (values at the common reference wavelength of 550 nm are also given in Table 1), with the constraint that the volumes cannot be negative. Aerosol number can then by calculated using the ratio C n /C v , from Equation 6. This process is shown conceptually in Figure 1. In this case, the observed spectral AOD (black diamonds) is best reproduced by the combination C v,f =0.005 µm 3 µm −2 and C v,c =0.04 µm 3 µm −2 (total AOD given by the red curve). Note that as previously mentioned a real MAN observation would have five or fewer spectral AOD measurements, rather than the seven shown here, but this serves to illustrate the spectral dependence of the fine and coarse mode extinction across the Microtops bands. Table 2 provides statistics on the quality with which the model is able to reproduce the spectral 130 MAN AOD. At all wavelengths, the bias and scatter are small (<0.01), particularly over the wavelength range (440 nm -870 nm) which was used during development of the model. Note that some of the MAN measurements contain an interpolated rather than measured 500 nm AOD: in these cases, this interpolated AOD was used for the statistics in Table 2 but not when performing the least-squares fit (as it did not correspond to a real measurement).

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Clearly, not all of the observations in the MAN database will represent unpolluted maritime aerosol, and therefore derived aerosol volume and number may be significantly biased when this is not the case. For this reason, the MAN data have been stratified in a simple attempt to discriminate according to aerosol type, based on the AOD and α. Three broad classes have been defined based on typical values for these parameters (e.g. Eck et al., 1999, Smirnov et al., 2004 2012b): pure maritime (τ 500 ≤ 0.2, α ≤ 1), dust-influenced (τ 500 > 0.2, α ≤ 0.6), and fine continental (e.g. pollution/smoke or land organic)-influenced (all other points, referred to hereafter as 'continental' for brevity). Additionally, as in Smirnov et al. (2012), to minimise the likelihood of continental influence in the 'maritime' subset it was further required that such points be at least 200 km from land, using a coarse (1 • ) land mask as a basis (to eliminate large land masses, but not small 145 remote islands).
Maps of these classes and fit volumes from the daily MAN data are shown in Figure 2; the points cluster in generally expected regions, suggesting that as a first-order attempt this classification is reasonable, although there is inherently a degree of ambiguity in this type of classification. Altering these thresholds within sensible ranges does not significantly affect the spatial distribution or inter-150 pretation of results. Additionally, if the more conservative set of 'pure maritime' MAN points used by Smirnov et al. (2012) is used, the results do not significantly change for this subset (which is the main focus of the analysis). Information on the sampling of these subsets is given in Table 3.
The latitudinal distribution of the number of measurement series in these three classes is shown in Figure 3. The large abundance of the 'continental-influenced' class is not suggesting that the 155 majority of the open ocean is influenced significantly by continental outflow. Rather, this happens because of the fact that the MAN cruises begin and end on the coast, and often spend much of their time in coastal regions ( Figure 2). For example, the spike in this class at high southern latitudes comes from data collected near Antarctica. It is important to note that this 'continental-influenced' classification is not purely an indicator of urban or smoke aerosol mixed with maritime aerosol 160 (although it may contain these), but rather a catch-all for aerosol which, due to its proximity to the coast, has the potential to be influenced by land masses, and is additionally unlikely to be dominated by dust. The intent of this classification is to 'protect' the 'pure maritime' subset as much as possible. The reduced χ 2 statistic is used to measure the goodness of fit, where τ λ,MAN indicates the MAN-observed AOD, σ λ,MAN its uncertainty (assumed to be 0.015 and uncorrelated spectrally), τ λ,pred the AOD predicted by the model, and n λ the number of wavelengths in the measurement series (or daily average). The factor n λ − 2 arises as two free parameters are fit; typically n λ = 4, leading to 2 degrees of freedom. The expectation of the reduced χ 2 over a large 180 number of samples is 1. Figure 2 also shows χ 2 for each of the three aerosol type subsets: this is almost always less than 1, even for those cases where the aerosol is likely not pure maritime in origin.
There are two important implications of this. First, this highlights limitations in inferring aerosol type from spectral AOD (it is possible to obtain an acceptable quality of fit even if the microphysical model is incorrect). Second, this suggests that σ λ,MAN = 0.015 is not necessarily a good metric 185 for the random error of the MAN AOD, i.e. systematic error is likely a significant component of the total uncertainty. This is also consistent with the results in Table 2, that the maritime model is able to reproduce spectral AOD with greater accuracy and precision than 0.015. Porter et al. (2001) and Knobelspiesse et al. (2004) estimate that among the largest uncertainty on Microtops AOD is the calibration gain coefficient. For a set of measurements taken on a single cruise with a single 190 Microtops sun photometer, this is likely a systematic error, although over the whole MAN dataset (multiple instruments and calibration tests) biases may cancel out such that the errors are random.
The least-squares fit provides estimates of the uncertainty on C v and hence C n , under the assumption that σ λ,MAN represents the random error on the MAN AOD. Scaling these uncertainty estimates by χ 2 provides a lower bound on the estimated uncertainty, which is under the assumption that 195 the true value of σ λ,MAN is unknown and the uncertainty is therefore related to the residuals on the fit AOD. The true error on derived C v or C n is therefore likely in between these two estimates.
Relative uncertainty on C v is shown as a function of C v for the maritime subset of daily-average MAN AOD for both these methods in Figure 4. As, for a given microphysical aerosol model, the aerosol number is a simple scaling to the aerosol volume (rightmost column of Table 1), these rel-200 ative uncertainties also apply to the equivalent aerosol numbers. The 'unscaled' points (i.e. taking σ λ,MAN = 0.015) typically fall into one of several curves, dependent on the selection of bands available for a particular MAN data point. The absolute uncertainty is fairly constant as a consequence of the fact that, for a given set of microphysical model parameters, AOD is linearly proportional to aerosol amount. If instead σ λ,MAN is assumed to be 0.01 or 0.02, the uncertainty estimates decrease 205 and increase by approximately 50 % respectively. The 'scaled' uncertainties are much more diverse but generally lower by a factor of 2-5. For the unscaled uncertainty estimates, uncertainty on volume is around 100 % for low aerosol loadings. However, the 'scaled' uncertainty estimates are much lower, suggesting better sensitivity.

Derived volume and number concentration 210
For all three classes, coarse-mode volume tends to be larger than fine-mode volume by approximately a factor of 5-10 ( Figure 2); the maritime subset typically has 80 % or more of total aerosol volume in the coarse mode. Relatively higher fractional coarse-mode volumes are found for the dust subset, and relatively higher fractional fine mode volumes for the continental subset, which is expected from the α-based classification. Histograms of aerosol volume for these three cases appear 215 to follow approximate lognormal distributions, illustrated in Figure 5 (using the series average MAN dataset). This is not surprising, as AOD distributions have also been observed to be lognormal (e.g. O'Neill et al., 2000 and reference therein), and was also noted by Heintzenberg et al. (2000). The modes and spreads (geometric mean and geometric standard deviation, analagous to r n and σ in Equation 4, respectively) are given in Table 4, and are reasonably robust to small changes in his-220 togram bin size. The median value of all points is also shown. As mentioned previously, volumes for the dusty and continental classes are likely to be qualitatively reliable but absolute values may have a bias of order 20 %.
The fine mode distribution for the continental-influenced class shows two peaks (or a very long tail); the lower-volume segment is similar to the maritime class's peak, and likely corresponds to 225 maritime aerosol which narrowly missed the τ 500 , α, and/or land distance thresholds for inclusion in the maritime class. Both the maritime and dust-influenced distributions, however, are more distinct. were collected in the tropical Atlantic and fall into the 'dusty' subset, and so it is possible that the small negative AOD fitting bias at these wavelengths (Table 2) and elevated fine mode volume for this subset are related to the real aerosol being more absorbing than the maritime model.

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Maps of derived aerosol number (for the maritime subset only) are shown in Figure 6, and histograms in Figure 7. The histogram are again approximated well by a lognormal distribution (parameters in Table 4). The aerosol number:volume ratio, C n /C v =190 µm −3 for the fine mode (Table 1), is in good agreement with previous studies in the range 167-225 µm −3 for marine aerosol (Hegg and Kaufman, 1998, van Dingenen et al., 1999, Kaufman et al., 2001, Dusek 240 et al., 2004. Dusek et al. (2004) note that in previous studies this ratio has been defined in different ways, often the ratio of total number of particles above a certain size to total volume of particles below a certain cutoff size, dependent often on the available instrumentation. As the coarse mode total aerosol number is generally only 1 % or so of the fine mode number, and the coarse mode volume below the typical cutoff size used in these studies (around 1µm) is small, it makes little difference 245 to C n /C v in this case (although C n /C v would become slightly smaller and depend on the weighting between fine and coarse modes for each situation).
3 Comparison with MODIS data

Data description and methodology
The MODIS aerosol algorithm retrieves spectral AOD and α over ocean by mixing two aerosol 250 components (one fine mode and one coarse mode, each from Table 1) to find the combination which matches the observed top-of-atmosphere (TOA) reflectance in six bands between 470 nm and 2.1 µm (Tanré et al., 1997, Remer et al., 2005. Two solutions are reported in the product: namely, the combination of fine and coarse modes which most closely fit the observed TOA reflectance (hereafter the 'best solution'), and the average (hereafter the 'average solution') of either all solutions with a 255 root mean square fitting error of less than 3 %, or the three solutions with the smallest fitting error if none are less than 3 %. From this, the algorithm also derives an estimate of the total columnar number of aerosol particles of radius 0.03 µm or larger (Remer et al., 2005). The effect of this minimum size on the comparison is minor, as the maritime model applied to the MAN data results in less than 4 % of the fine mode particles having a radius smaller than 0.03 µm.

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The MODIS aerosol number estimate is to the authors' best knowledge an unvalidated quantity, although it has been used, examined, or compared with other data in several studies (Gassó and Hegg, 2003, Li et al., 2010, Kaskaoutis et al., 2011, Krüger and Graßl, 2011. In contrast, the AOD over ocean has been compared more thoroughly with other satellite and ground-based datasets and its strengths and limitations are fairly well-understood (e.g. Zhang and Reid, 2006, Mishchenko 265 et al., 2007, 2010, Remer et al., 2008, Kahn et al., 2009, Shi et al., 2011, Smirnov et al., 2011, Kleidman et al., 2012, Sayer et al., 2012a. The MAN-derived data here are also subject to some uncertainties as discussed previously, so while a comparison between aerosol number from these two datasets cannot be considered a validation against ground truth, it does allow for an examination of their consistency and, hopefully, an understanding of their differences. Matchups between MODIS and the MAN data are performed by averaging MODIS retrievals within 25 km of a MAN measurement separated in time by 30 minutes or less. In almost all cases, variability in MODIS AOD in this 25 km circle was small, and the same aerosol model was chosen as the 'best solution' for each retrieval. Only MAN data defined previously as belonging to the maritime subset are considered, as C n from others is expected to be less reliable. The AOD is compared at 275 the standard reference wavelength of 550 nm, as provided in the MODIS product; interpolation of the MAN data to this wavelength using theÅngström power law (Equation 2) introduces negligible uncertainty.
As well as the present Collection 5.1 (hereafter C5.1), results are presented using the forthcoming Collection 6 (C6) algorithm. C6 products should become available around the end of 2012.

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The over-ocean algorithmic concept is the same in C6 as C5.1, but there are changes related to gaseous transmittance corrections, improved masking of cirrus clouds, accounting for wind-speed dependence of Sun glint and oceanic whitecaps (which will decrease retrieved AOD in high-wind environments; Sayer et al., 2010, Shi et al., 2011, Kleidman et al., 2012, and definitions of quality flags. Sensor calibration will also be updated for C6 but final coefficients are not available at the 285 time of writing (i.e. these results use C5 radiometric calibration coefficients), and the impact over open ocean (on retrieved AOD at least) is expected to be small.

Results
Some statistics of the comparison of AOD and aerosol number are presented in Table 5, considering both the MODIS sensors on board the Terra and Aqua platforms, and for either the highest quality 290 assurance (QA) flag (QA=3) or the looser criteria of QA=1,2, or 3 (almost no retrievals were assigned QA=2). Scatter plots of the QA=3 data are shown in Figure 8, and maps for the 'best' solution in Figure 9, both for C5.1 data. Table 6 shows the fraction of MODIS-MAN matchups with an AOD at 550 nm within the expected MODIS absolute error (Remer et al., 2008)  AOD by 20 %, the MODIS C n would be decreased by a corresponding amount). This 'scaled' C n allows a first-order separation between the effects of differences in AOD and differences in aerosol microphysical model assumptions on the comparison. Tables 5 and 6 also show that restricting the data to QA=3 (the retrievals with highest confidence) results in a poorer agreement of AOD (and also C n ) between the datasets. However, these results should not necessarily be expected to apply to the MODIS dataset as a whole, as the QA=3 subset is comparatively small (about a factor of 3 fewer points than the QA=1,2,3 case for C5.1), and these comparisons only consider MAN data from the maritime subset, which is a small proportion of the total dataset. The MODIS over-ocean data usage recommendation is that retrievals of QA 1,2, or 3 are likely of similar quality and all suitable for analysis, which is consistent with these comparisons (Remer et al., 2005(Remer et al., , 2008. The total number 310 of C6 points is smaller than C5.1, likely due to stricter cloud screening, and QA=3 becomes more common. Irrespective of QA threshold, the differences between best and average solutions, and scaled and unscaled QA, are broadly similar. Relative to MAN-derived data, MODIS Terra tends to underestimate and Aqua to overestimate C n ( Table 5). The regional sampling of the two datasets is similar (Figure 9), suggesting these dif-315 ferences are more related to the retrieval than spatial sampling. Performing the AOD-based scaling tends to reduce the absolute and root mean square differences between MAN and MODIS data; however, significant differences remain in this case, indicating microphysical model assumptions play a role. Further, large differences of either sign between the datasets are not confined to continental outflow areas, suggesting that errors in MAN C n from non-maritime influences are not the primary 320 cause for difference. Table 1 shows that, as is the case for the maritime aerosol model of Sayer et al. (2012b), the fine mode per-particle extinction is around two orders of magnitude larger than the coarse mode, and so the total C n will be determined largely by fine mode abundance. MODIS fine mode #2 has a similar per-particle extinction and C n : C v to the model of Sayer et al. (2012b), so if the two datasets report 325 the same AOD and this fine mode is picked in the MODIS dataset, the two estimates of C n should be close (although the partition between fine and coarse modes to the total AOD in both datasets will remain a factor).
However, Figure 9 shows that MODIS fine mode #2 is rarely picked as the 'best' solution by either Terra or Aqua. Instead, Terra has a tendency to more frequently pick #3 or #4, and Aqua #1, which 330 have lower (for Terra) or higher (for Aqua) C n : C v (and the reverse for per-particle extinction) than the maritime model applied to MAN data. This will be responsible for the relative overestimate of Aqua and underestimate of Terra as compared to MAN. As the same algorithm is applied to both MODIS sensors, it seems reasonable to suspect that the differences in typical model choice between the two sensors could be linked with small systematic differences in their radiometric calibration; 335 as the AOD is low for these cases, determination of size-related aerosol information is an inherently difficult task which is more sensitive than total AOD to uncertainties and errors. These conclusions hold for both C5.1 and C6 (although it is likely that aerosol model selection will be more sensitive than total AOD to radiometric calibration changes which may be applied in the final C6 data).
The 'average' MODIS solution matches MAN data closer than the 'best' solution, for both AOD 340 and C n (Table 5), with higher correlations and smaller biases/absolute differences. This is likely because the averaging of several solutions reduces both retrieval noise and the effect of aerosol microphysical model assumptions on the retrieval. Although the MAN-derived C n are not a 'ground truth' for the satellite retrievals, these results suggest that the MODIS 'average' solution may provide a better estimate of AOD and C n for unpolluted maritime aerosol than the 'best' solution. The 345 differences between these two solutions are generally smaller for C6 than C5.1.

Estimating surface concentration
The previous sections have dealt with columnar aerosol number and volume, as the MAN AOD measurements represent the column extinction. Determination of surface concentration requires knowledge of the vertical profile. Marine aerosol is often observed (e.g. Table 7) to show an exponentially 350 decreasing number profile with height, where n(z) is the number concentration at altitude z, n 0 the surface concentration, and h the characteristic scale height. As by definition ∞ 0 n(z)dz = C n , simple integration of Equation 8 yields n 0 = C n /h. Table 7 suggests h ≈ 1.5 km as a reasonable default assumption, although the typical 355 range in Table 7 (1-2 km, a few around 0.5 km) will lead to around a factor of 2 variability in derived n 0 , highlighting the uncertainty in estimating surface concentration. Additionally, Table 8 shows that profiles other than exponentially-decreasing with height are also observed for marine aerosol.
Finally, the assumption is required that the aerosol composition is invariant through the column, which may not always be true. Still, taking h = 1.5 km can provide a first-order estimate to examine 360 average behaviour.
Unfortunately, direct comparison of MAN-derived estimates with in situ data is difficult due to a paucity of directly colocated data. However, general tendencies can be examined. Figure 10  shown here are multiannual median values and standard deviations for three low-lying island sites (Samoa, 14.5 • S; Cape San Juan, 18.3 • N; Sable Island, 43.9 • N). Medians are used as it is likely these sites sometimes sample non-maritime air masses (so the median is likely a better estimate of the baseline maritime than the mean).
Finally, bimodal lognormal fits to median AERONET size distribution inversions representing 380 maritime conditions at eleven sites were used by Sayer et al. (2012b) to constrain the maritime aerosol microphysical model applied in this work. These distributions have been used to calculate total columnar and hence surface number concentration (again assuming h = 1.5 km), and also shown in Figure 10. The error bars for these points are taken using the relative standard deviation of τ 440 at each site scaled to the total aerosol particle number, the rationale being that this wavelength 385 is most sensitive to fine-mode particles. One site (Graciosa, 39.1 • N) falls outside the scale at an estimated surface aerosol particle concentration of 3,000 cm −3 ; Sayer et al. (2012b) noted a higher fine-mode abundance here than at other sites, and speculated some contribution from a local aerosol source.
Poleward of 20 • S, there is good agreement between the datasets. However, through the tropics 390 and northern hemisphere the MAN-derived estimates are generally higher than the in situ data. There are multiple reasons why this could be the case. For the points poleward of 20 • S, it could be that the scale height chosen is appropriate and the aerosol is maritime in nature. Further north of this, land means there may be an increased influence of continental air masses and so the maritime model is less appropriate. Table 1 shows that discrepancies of this magnitude are possible due to uncertainty 395 in aerosol microphysical properties. Non-coincidence of sampling (both spatial and temporal) is likely an important factor, as variabilities within each latitude range, and at individual sites averaged over time, are large. A further possibility in the tropics is contamination by thin cirrus, which can be widespread and not always detected by ground-based instrumentation, leading to a positive bias in the MAN AOD (Chew et al., 2011).

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Earlier reviews of field campaign data by Podzimek (1980) and Fitzgerald (1991) Williams et al. (2007) reported similar high aerosol number concentrations along the coast of Europe and northern Africa, but generally less than 1,000 cm −3 in marine air masses in the southern Atlantic at mid-and high latitudes. These results are also similar to recent CTM simulations, although such models are sensitive to e.g. emission and nucleation schemes (Spracklen et al., 2010).

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Tables 7 and 8 show significant variability in vertical profile shape. If the bulk of the profile follows an exponential decrease with height but the near-surface layer is well-mixed and uniform, this would mean that assuming a relationship of the type of Equation 8 overestimated surface con-centration, as is observed. Instrumental artefacts such as incomplete sampling of the aerosol size distribution can also be a factor leading to underestimates of aerosol number in the in situ data (e.g. 415 Reid et al., 2006), although Heintzenberg et al. (2000) performed additional filtering on their input data to minimise the likelihood of this.
The main conclusion from this exercise is therefore to illustrate the difficulties inherent in inferring near-surface quantities from columnar ones. This difficulty is also present when, for example, trying to estimate ground-level particulate matter concentrations from satellite measurements of AOD for 420 air quality assessment (e.g. Hoff and Christopher, 2009, and references therein).

Conclusions
The remote sensing of spectral AOD from space is not a solved problem. Ground-based measurements by techniques such as sun photometry are able to make more direct inferences about AOD, but with poorer spatial coverage. Remote sensing of aerosol number, volume, and mass would provide 425 useful and important information about the Earth system, but is more complicated than retrieval of AOD, as it is more sensitive to assumptions relating to aerosol composition. Using a microphysical model derived from AERONET inversions as a constraint, this study has attempted to determine columnar aerosol number and volume from ship-borne measurements of spectral AOD of fairly low uncertainty (∼ 0.015) for cases where this microphysical model can be 430 reasonably assumed to be appropriate (unpolluted maritime aerosol). Even with these constraints, the estimated uncertainty on the derived quantities can be significant (10 %-100 %), which probably precludes use of the technique with less accurate AOD data. Despite these uncertainties, the estimated concentrations are physically sensible. It is suggested that, in conditions where a microphysical model for the dominant aerosol type can be prescribed with some confidence, accurate and 435 precise spectral AOD measurements, such as from sun photometers deployed by the AERONET and MAN programs, could be used to estimate aerosol number or volume.
Potential applications of this method include an additional tool for comparison with CTM aerosol fields, and examining the fine/coarse partitions retrieved or assumed in satellite AOD retrieval algorithms. Currently, AERONET size distribution inversions are sparse at some locations due to 440 the requirement for clear skies and homogeneity over a period of one hour while almucantar scans necessary for the inversion algorithm are collected, plus a low Sun angle for high air mass factor (Dubovik and King, 2000). Although probably less accurate than these full inversions, estimates based on spectral AOD with the constraint of a microphysical model would expand the potential data volume for comparison. In estimating volume/number from spectral AOD, this is complemen-445 tary to the AERONET spectral deconvolution algorithm product (O'Neill et al., 2003), which uses a more generalised set of microphysical assumptions to estimate fine and coarse contributions to midvisible AOD (but not explicitly number or volume).
An attempt was made to convert MAN-derived columnar number concentrations into surface number concentrations, which were compared to typical values from in situ datasets and AERONET 450 estimates. From around 20 • S and poleward, similar values were obtained (∼ 300-600 cm −3 ). However, in the tropics and northern hemisphere, the MAN-derived data tended to produce higher values than the in situ measurements. This poorer agreement is expected to be due to a combination of reasons including spatio-temporal variability of aerosol loading, uncertainties in aerosol microphysical properties, and, in particular, uncertainties in vertical profile shape.

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Columnar aerosol number and AOD at 550 nm were also compared with the current Collection 5.1 product from both MODIS sensors, and results using the forthcoming Collection 6 algorithm.
Consistent with previous studies, MODIS was found to overestimate AOD as compared to the MAN data, with this overestimate being larger for MODIS Terra. The number to volume ratios and perparticle extinction of the different aerosol modes used in the MODIS retrieval over ocean can lead to 460 significant differences in derived number concentration. It was found that Terra tended to estimate lower aerosol number than MAN, and Aqua higher, linked to differences between the sensors in the aerosol fine modes which are typically found to provide the best solution. The MODIS 'average solution' dataset agreed more closely with the MAN data than the 'best solution', likely because some of the uncertainty associated with retrieval noise and microphysical model assumptions is 465 averaged out. The results suggest that, at least for cases of pure maritime aerosol, quality assurance flags of 1, 2, and 3 are all of similar quality, and the 'average solution' dataset is better than the 'best solution' dataset. Collection 6 showed closer agreement with MAN AOD than Collection 5.1, but otherwise conclusions drawn were similar.  Table 1. Aerosol microphysical model parameters. rn is the modal radius, σ the geometric standard deviation, m the complex refractive index at 550 nm, and Cn/Cv the ratio of aerosol particle number to volume. The extinction coefficient at 550 nm is denoted β550, given both per µm 3 and per particle.  ∼0.8 Canary Islands Fig. 2; also Figs. 3 and 6 of Gassó et al. (2000).
Little vertical variation. Coarse mode particles only. Sebacher et al. (1967) US coast (Virginia) Fig. 3 (top); peak around 1 km.    and (c, f) the index of the fine aerosol mode (Table 1) MODIS reported as providing the 'best' solution.