A new study of sea spray optical properties

Introduction Conclusions References


Introduction
Radiative forcing by sea spray aerosol (SSA) comprises a significant portion of the global energy budget. Studies have shown that SSA contributes an aerosol optical depth (AOD) of approximately 0. 15  Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | larization (CALIOP) onboard the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) platform has eliminated some of the assumptions made by the passive instruments and has provided a more complete picture of global aerosol distribution desirable by climate scientists. However, CALIOP is an elastic backscatter lidar with no molecular filtering capability and therefore requires the assumption of an 5 extinction-to-backscatter ratio, also known as the lidar ratio, to infer extinction from attenuated backscatter measurements. Depending on the microphysical properties of the aerosol, the lidar ratio can have a wide range of values and therefore a straightforward a priori solution within some reasonable uncertainty range is generally unobtainable without various assumptions or constraints. Theoretical calculations for the lidar ratio 10 can be performed, if the physicochemical properties and the size distribution of the particles at the different heights in the vertical column are known; although, the fulfillment of these requirements will make the lidar measurements unnecessary (Ackermann, 1998). The typical solution to this problem is to assign a vertically independent lidar ratio to aerosol retrievals that fit a specific aerosol model as outlined in Omar et al. (2009).
Since the uncertainty in the lidar ratio can significantly affect the accuracy of the aerosol extinction retrieval (see a detailed discussion below), lidar ratios have been constrained by numerous approaches. However, SSA size distribution, chemical composition and refractive index can change significantly with ocean surface wind speed (U 10 ), relative humidity (RH), temperature, salinity and chemical/biological composition 20 of surface sea water (de Leeuw et al., 2011;Lewis and Schwartz, 2004). Because of this, large disagreement exists in the literature regarding the value of maritime aerosol lidar ratio (S p ). For example, lidar measurements of Ansmann et al. (2001) over the North Atlantic showed S p = 24 ± 5 sr whereas measurements using a nighttime lidar measurements at a horizontal orientation off the northern coast of Queensland, Aus-25 tralia showed maritime aerosol lidar ratios as high as S p = 39 ± 5 (Young et al., 1993). Using the data from AERONET oceanic sites (Cattrall et al., 2005) derived a lidar ratio of 28±5 sr, the value that compared well with literature averaged value of S p = 29±5 sr (for 490 ≤ λ ≤ 550 nm) for maritime aerosols. Passive  to derive the lidar ratio using an alternative definition of S p as a function of single scattering albedo and the scattering phase function near 180 • (Bréon, 2013). Using the multi-directional measurements of the solar radiation from the polarization sensitive passive radiometer POLDER, typical values for clean marine aerosol S p were derived to be 25 sr at 532 nm (Bréon, 2013). The lidar ratio of 20 ±6 sr (at 532 nm) was selected 5 for the CALIOP retrieval algorithm based on parameters measured during the Shoreline Environmental Aerosol Study (SEAS) experiment (Masonis et al., 2003;Omar et al., 2009). The SEAS experiment reports a particulate lidar ratio S p = 25.4 ± 3.5 sr at 532 nm based on the optical size measurements of sea spray aerosol and a modeled value of S p = 20.3 sr (Masonis et al., 2003). Although the S p value used in the CALIOP 10 marine aerosol model is the same as the one derived using an average SSA size distribution measured on the beach (downwind of an offshore reef), modeling studies show a wide range of S p values (from 10 to 90 sr) depending on particle size (Masonis et al., 2003). Therefore, as size distribution (and chemical composition) of SSA may vary over the oceans, a constant lidar ratio used in CALIOP algorithms may lead to erroneous 15 retrievals of AOD.
In this study, we present a new method for deriving lidar ratios for individual CALIOP retrievals of single aerosol layer columns over the ocean. To estimate S p for a strictly defined subset of CALIPSO data we have used the Synergized Optical Depth of Aerosols (SODA) product ( only lidar that provides aerosol data at the vast spatiotemporal resolution required for global climate model comparison.

CALIPSO satellite
The CALIPSO mission was launched on April 28, 2006. CALIPSO has been able to 5 provide the scientific community with vertically resolved measurements of both aerosol and cloud optical properties like depolarization ratio (a measure of particle sphericity), AOD, and ice/water phase since June 2006. The CALIPSO payload includes a high-powered digital camera, an infrared radiometer, and a two-wavelength (532 and 1064 nm), near nadir, polarization sensitive, elastic backscatter lidar, CALIOP.

10
The level 1 data algorithms are responsible for the geolocation and range determination of the satellite and produce profiles of attenuated backscatter coefficients. Data in this work were obtained from the 5 km, level 2 operational products version 3.01. Level 2 products have undergone various processing algorithms from the Selective Iterated BoundarY Locator (SIBYL), the Scene Classification Algorithm (SCA), 15 and the Hybrid Extinction Retrieval Algorithm (HERA). First, SIBYL identifies layers, then the SCA identifies the type of feature (i.e., aerosol or cloud) and the subtype (i.e., aerosol type, ice/water phase), and finally, the HERA generates extinction profiles for the feature. The theoretical basis of the algorithm can be found online at www-calipso.larc.nasa.gov/resources/project_documentation.php.

Synergized Optical Depth of Aerosols (SODA)
CloudSat was launched in 2006 with CALIPSO and was positioned in sun-synchronous orbit as part of the A-Train satellite constellation. CloudSat and CALIPSO have paved the way for new multi-sensor data products like SODA to be developed. The main instrument on CloudSat is the Cloud Profiling Radar (CPR), a nearly nadir looking Introduction The CPR signal is mostly attenuated by water vapor; however, for cloud free regions over the ocean, the CPR data can be used to retrieve AOD. A method developed by Josset et al. (2008) and later expanded by Josset et al. (2010a) uses a combination of 5 CALIOP and CPR measurements of the ocean surface reflectance to derive AOD. The design of SODA utilises the ratio of the ocean surface scattering cross section of the radar over the lidar to infer column optical depth for non-cloudy atmospheric columns. The radar signal attenuates mostly due to water vapor, while the lidar signal weakens mostly due to aerosols. Therefore, once the radar signal is corrected for attenuation by water vapor and oxygen, the change in the radar-to-lidar signal ratio is directly related to aerosol abundance (Josset et al., 2008(Josset et al., , 2010a. Therefore, by using observations from two different sensors, SODA can eliminate uncertainties induced by the CALIOP aerosol extinction algorithm over oceans. SODA AODs have been shown to be in very good agreement with MODIS AOD retrievals (Josset et al., 2008). More detailed de- 15 scription of the SODA technique and its application is given in Josset et al. (2008Josset et al. ( , 2010aJosset et al. ( , b, 2011Josset et al. ( , 2012

Lidar ratio definition
One of the biggest advantages of the SODA product is that it removes the dependence of the prescribed lidar ratio while still utilizing the active sensors to retrieve 20 an AOD, thereby providing a means for independent evaluation of the lidar ratio. In the current study we use Eq. (4) from Josset et al. (2011) to estimate lidar ratio from CloudSat/CALIOP measurements of AOD values. Following Fernald et al. (1972), the particulate two-way transmittance at height Z can be written as: where the lidar ratio at height Z can be defined as the ratio of the particulate extinction to backscatter (S p = σ p (Z) β p (Z) ). Differentiating Eq.
(1) with respect to vertical coordinate (z) gives the particulate backscatter at height Z: Since atmospheric constituents (molecules and different particle types) can interact with the lidar beam at different heights, the lidar ratio using remotely sensed data cannot be uniquely defined for a given atmospheric column. However, the lidar ratio is a particle intensive property (i.e., dependent on particle type and not on the amount). So, if we assume that there is only a single type of aerosol and it is homogeneously 10 distributed throughout the atmospheric column and that molecular scattering is sufficiently removed by the CALIOP level 2 algorithms, then the column lidar ratio (S p ) can be expressed as the ratio of the particulate column integrated extinction (τ p = AOD) to the attenuated backscatter (Γ p ). With these assumptions in mind, integration of Eq. (2) with respect to vertical coordinate gives the particulate lidar ratio as: In Eq.
(3) if we substitute the definition for two-way transmittance as T 2 p = e −2τ p , the total particulate attenuated backscatter signal retrieved by the lidar as Γ p = Z 0 β p (z)T 2 (z)dz, and consider that T 2 p (0) = 1, we get an equation for a columnar partic-20 ulate lidar ratio as: This equation allows us to calculate SSA lidar ratio from two independent sources: the AOD (i.e., τ p ) from SODA and the integrated attenuated backscatter (Γ p ) from CALIOP. It should be noted that CALIOP estimation of Γ p is difficult for layers that are not bounded by clear air (Vaughan et al., 2004) and therefore require carefully designed data screening algorithms. In Sect. 4 we carry out an error analysis to verify 5 that uncertainties in Γ p have a minimal effect on the retrieved lidar ratio.

Data selection method
As different aerosol sub-types have different lidar ratios, application of Eq. (4) to episodes when aerosols other than sea spray are present in the atmospheric column may lead to erroneous results for the calculated S p . To minimise the contamination of 10 sea spray AOD and therefore S p by aerosol types other than SSA (e.g., anthropogenic pollution, biomass burning, and dust), we developed a strict scene selection algorithm. The algorithm first uses the feature classification flags in the CALIOP aerosol layer product. We start with clean marine aerosol that is identified based on surface type (as determined by the location of the satellite), total integrated attenuated backscat- 15 ter γ > 0.01 km −1 sr −1 , and volume depolarization ratio δ < 0.05 (Omar et al., 2009). As multiple types of aerosols can be found within retrieved vertical profiles (e.g., dust above sea spray), aerosol feature types that have been identified as marine in a given atmospheric column are not enough to carry out the analysis. Therefore, when determining the lidar ratio of SSA using Eq. (4), the algorithm only retains the data in 20 which sea spray is the only type of aerosol present in the entire atmospheric column. To further reduce the uncertainty, we constrain the analysis to single layer profiles and remove profiles in which marine aerosol layers are vertically stacked within an atmospheric column. Therefore, the vertically integrated particulate attenuated backscatter Γ p is replaced by Γ p . Similarly, the column lidar ratio S p is reduced to S p for the re-25 mainder of the paper. Note also that all quantities discussed are particulate quantities (denoted by subscript p) and therefore, molecular scattering is removed using gridded 221 Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | molecular and ozone number density profile data from the Goddard Earth Observing System Model, version 5 (GEOS-5) analysis product available from the NASA Global Modeling and Assimilation Office (GMAO) (Winker et al., 2009). Operationally, particulate scattering is determined to be where the ratio of the CALIOP 532 nm scattering profile normalised by the GEOS-5 molecular scattering profile is greater than one In this study, CALIOP and SODA nighttime data are collected globally for a period of three years from December 2007 to February 2011. The global data are then binned into 2 • × 5 • latitude and longitude, respectively, grid cells. The data is binned according to season and ocean surface wind speed (taken from the Advanced Microwave 10 Scanning Radiometer-Earth (AMSR-E) observing system). To identify distinct features associated with the variability in sea spray aerosol lidar ratio over different parts of the oceans, the selected data is examined in relationship with other variables such as season, spatial location, and wind speed.
For the data analyses conducted in this study, the single layer columns that have 15 been identified by CALIPSO as clean marine aerosol were isolated and binned when the following conditions were met: (i) the vertical feature mask found one layer in the entire column, (ii) the vertical feature mask ranked the layer as type: aerosol and subtype: clean marine, (iii) the layer top was < 2 km, (iv) the relative error in Γ p due to random noise in molecular backscatter was < 50 %, (v) the collocated SODA 5 km layer was 20 composed of at least 70 % shot-to-shot data (therefore increasing the signal to noise ratio), (vi) the total number of retrievals per 2 • × 5 • grid cell ranked above the first quartile of the grid cell frequency distribution (i.e., grid cells with frequency data in the lower 25 % of the distribution have not been included in the data analysis and are masked in the subsequent figures), and (vii) only nighttime data was used. Such strict quality 25 controls, although reducing the total number of data points, considerably increase the reliability of the selected episodes. It should be noted that even after all the quality control and quality assurance tests have been conducted, a large number (over 260 000) of data points allowed a robust statistical analysis to be conducted. To further minimise the effect of outliers on the estimated value, statistical medians were calculated for each grid cell. Regions where grid cells fail criteria (vi) indicate low confidence in the reported median value due to a low number of observations and are removed. This also ensures that global means are not heavily biased by outliers resulting from grid cells with a low number of retrievals. This procedure allows the 5 removal of the non-physical positive skewness of the distribution observed by Josset et al. (2012). Despite such rigorous quality control criteria, readers should be cautioned when interpreting data near coastlines as the CALIOP scene classification algorithm may mistakenly identify continental pollution as clean marine aerosol (Burton et al., 2012;Oo and Holz, 2011;Schuster et al., 2012) causing an overestimation in the lidar 10 ratio inferred from Eq. (4). Further discussion of error analysis is given in Sect. 4 below.

Global distribution of retrieved AOD and lidar ratio
Active detectors like CALIOP require knowledge of the lidar ratio for retrieval of aerosol optical properties. Incorrect estimates of the S p values for a given aerosol type can 15 lead to significant errors in the retrievals of particulate extinction and AOD. Past studies using collocated CALIOP and MODIS retrievals have shown that, over the marine regions, CALIOP underestimates the AOD values relative to MODIS (Oo and Holz, 2011). As MODIS data over the ocean has been extensively evaluated with numerous field campaigns (e.g. Levy et al., 2005), it was suggested that the primary source of 20 discrepancy between the two sensors was the low value of the SSA lidar ratio used by CALIOP (Oo and Holz, 2011). Figure 1 shows seasonally averaged maps of CALIPSO and SODA SSA median optical depth at 532 nm and the differences between SODA and CALIOP retrieved AODs. White regions on Fig. 1  in sea spray AOD. Although the largest values of AOD seem to occur over regions with higher surface wind speed (i.e., the northern and southern oceans), elevated AOD values can also be seen over the regions downwind from dust and/or pollution sources such as the mid-latitude North Atlantic Ocean and the Bay of Bengal (BoB) and over the major oceanic gyres. The former is believed to be just a retrieval artifact. Large 5 disagreements between SODA and CALIOP reported AODs for these regions suggest that some dust/pollution aerosols might have been misclassified by CALIOP as sea spray. Higher S p values for dust and pollution compared to SSA would produce a higher AOD retrieval in SODA compared to CALIOP. Elevated AOD values over the oceanic regions with lower surface wind speed, on the other hand, could point to changes 10 in sea spray particle size distribution to smaller sizes. Sub-micron sea salt aerosols (with particle diameter, D p < 1 μm) are believed to be characterised with larger lidar ratios than super-micron ones (e.g., Masonis et al., 2003;Oo and Holz, 2011). In general, Fig. 1 shows positive differences between SODA and CALIOP retrieved seasonal median AOD values. Recalling that CALIOP retrieved extinction is the product of the 15 prescribed lidar ratio and the measured column integrated particulate backscatter, positive differences between SODA and CALIOP median AODs at 532 nm over most of the oceans suggest underestimation of the SSA lidar ratio prescribed in the CALIOP clean marine aerosol model. Figure 2 shows that over most of the ocean surfaces, the calculated lidar ratio is higher than the default (S p = 20 sr) used in the CALIOP clean marine 20 aerosol model. Global means and standard deviations for AOD and lidar ratio are given in Table 1. CALIOP retrievals in this study cannot be directly compared to MODIS since we only use nighttime data. Nevertheless, SODA retrievals of AOD have been shown to agree well with MODIS (Josset et al., 2008) suggesting that the corrected lidar ratios will bring CALIOP retrievals close to MODIS data. Figure 2 also reveals that the value 25 of the lidar ratio calculated using Eq. (4) changes considerably over different parts of the remote oceans, pointing to the variability in sea spray aerosol optical properties. It has long been known that meteorological and/or environmental factors and ocean chemical/biological composition influence SSA production, entrainment, transport, and removal processes (Lewis and Schwartz, 2004), that can ultimately affect S p . Moreover, due to atmospheric transport of SSA, satellite retrieved AOD values may also be related to the upwind processes. Despite the complexity of the mechanisms controlling SSA mass concentration over the oceans, surface wind speed has always been considered as the major parameter governing the production, chemical composition, and 5 life cycle of SSA (Lewis and Schwartz, 2004). Therefore, in the next section we will investigate the effect of wind speed on calculated temporal variability of marine aerosol lidar ratio.

Wind speed dependence
Numerous investigators have examined the effect of sea surface wind speed and sea 10 state on marine aerosol optical properties. There are two production mechanisms for sea spray particles: bursting of bubbles at the water surface, and mechanical tearing of water drops (spume) from wave crests (for surface wind speeds U 10 > 9 ms −1 , (Anguelova et al., 1999). Ocean bubbles are generated by the entrainment of air due to wave action. As bubbles rise due to their buoyancy, they burst at the surface producing 15 SSA (Blanchard and Woodcock, 1957). In this study we have selected seven different wind speed regimes (see Table 2). The lowest wind speed regime, 0 < U 10 ≤ 4 ms −1 , was chosen to represent aerosols not generated via wind driven processes over the ocean. In general, ocean waves break at wind speed values above ∼ 4 ms −1 (initiating the white cap formation and bursting of the entrained bubbles) (Lewis and Schwartz,  tamy et al., 2003). Although CALIOP retrieval counts for sea spray aerosol in each 2 • × 5 • grid cell are also influenced by the presence of clouds, Fig. S1 shows the global distributions of CALIOP retrieval frequencies for different wind speed regimes. Figure  3 shows the scatterplots for SODA and CALIOP retrieved AOD values for the wind 5 speed regimes of Table 2. As expected, Fig. 3 shows that increases in wind speed are typically associated with higher values of SSA optical depth (note the center of the scatter distribution shifts to higher AODs for larger wind speed values). However, as the majority of the SODA AODs exist above the 1 : 1 line, this figure also indicates the underestimation of CALIOP retrieved SSA optical depth values. When averaged over the entire globe, CALIOP retrieved clean marine AOD is roughly 32 % lower compared to SODA. According to Fig. 3 the largest discrepancies between SODA and CALIOP retrievals are observed at lower wind speed values. One easy explanation for this is greater chance for CALIOP misclassification over the oceanic regions where long-ranged continental aerosols can contribute a larger fraction of the MBL particles 15 (e.g., Blot et al., 2013). Terrestrial particles (e.g. mineral dust, anthropogenic pollution) are typically characterised by the larger lidar ratio values, leading to underestimation of the CALIOP retrieved AODs. However, measurements also show that changes in surface wind speed values can cause a considerable shift in the SSA size distribution. For optically active sea spray particles, the residence time decreases considerably with 20 increasing size. Thus the aerosol population is increasingly controlled by the smaller end of the particle size spectrum as wind speeds decrease over the ocean (Hoffman and Duce, 1974). Conversely, as wind speed increases, fine mode aerosol volume size distribution changes slightly (with mixed trends), while the coarse mode volume size distribution exhibits a large and positive response to the increase in wind speed (Lewis 25 and Schwartz, 2004;Smirnov et al., 2003). Such variability in SSA volume size distribution is expected to have an effect on the aerosol lidar ratio. As sub-micron sea salt aerosols are characterised with much larger lidar ratios than super-micron ones (e.g., Masonis et al., 2003;Oo and Holz, 2011), shifting SSA size distribution spectra to ACPD Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | smaller particles will cause an increase in total aerosol lidar ratio. Therefore, for clean marine aerosols, AODs and lidar ratios are expected to have opposite dependences on wind speed: high wind speed regions are characteristic of high AODs and low lidar ratios while lower wind speeds favor higher lidar ratios and lower AODs (Smirnov et al., 2003;Sayer et al., 2012).
5 Figure 4 shows that on average, the calculated aerosol lidar ratio is inversely related to the surface wind speed. According to this figure, aerosols retrieved in the wind speed regime 0 < U 10 ≤ 4 ms −1 depict the largest variability in the lidar ratio as indicated by the spread of the distribution. As discussed above, aerosols in this regime likely include both sea spray particles produced upwind and advected into the satellite field of view 10 (with S p ∼ 20 to 30 sr), as well as dust/pollution particles (with S p ∼ 40 to 70 sr (Omar et al., 2009) that may have been misclassified by CALIOP as sea spray. As shown in Table 2, SSA lidar ratio distribution in this regime is characterised by the largest standard deviation (σ = 17.4 sr) indicating that for the lowest wind speed values, a wide range of sea spray particle sizes can be present over the ocean. Since for the wind 15 speed values less than 4 m s −1 , the sea spray production is minimal, such large spread could also indicate that under low wind conditions there is greater probability for natural continental and human-induced pollution aerosols be miss-classified by CALIOP as clean marine. For the higher wind speed values (4 < U 10 ≤ 15 m s −1 ) lidar ratio generally decreases 20 with the increase in the wind speed and approaches the lidar ratios prescribed by CALIOP retrieval algorithms (i.e., 20 sr) at the highest wind speed regime. According to Fig. S1, the most common wind values in CALIOP SSA retrievals over the ocean are in the 8 < U 10 ≤ 10 m s −1 regime (26 % of all available data) followed by the 6 < U 10 ≤ 8 ms −1 regime (23 % of all available data). For the higher wind speed regimes 25 (U 10 > 6 ms −1 ), surface winds play a decisive role in the determination of the lidar ratio (indicated by the narrow standard deviation, see Table 2). This is an important result as the distributions shown on Fig. 4  Analysis of data indicates that a mean lidar ratio of 26 sr is the most probable value that occurs for the majority of CALIOP retrievals over the oceans. This new lidar ratio reduces discrepancy between CALIOP-prescribed and SODA-derived lidar ratios from about 30 % to 4 %. Although the mean S p = 26 sr value for SSA proposed in this study considerably improves relationship between SODA and CALIOP retrievals for a wide 5 range of ocean surface wind speed values, the added advantage of the current analysis is the ability to correct individual CALIOP retrievals of sea spray AODs. The correction to the lidar ratio can be prescribed using Eq. (4) as: where the subscripts C and S stand for CALIOP default (S p,C ) and suggested (S p,S ) lidar ratios, respectively. In future studies we intend to examine limited number of parameters (in addition of wind speed) to construct a look-up table with a wind speed dependent, spatiotemporal distribution of SSA lidar ratios for use in CALIOP clean marine aerosol retrievals.

Assessing the validity and sensitivity of Γ p
The method used to derive the lidar ratio in this study depends on two parameters: the CALIOP integrated attenuated particulate backscatter (Γ p ) and the SODA aerosol optical depth (τ p ). Uncertainties in both Γ p and τ p retrievals are expected to propagate through the calculations of the particulate lidar ratio. Josset et al. (2008Josset et al. ( , 2010a in-20 vestigate the domain of validity for τ p through an extensive calibration procedure and find that the SODA product, for retrievals at wind speeds between 3 and 10 m s −1 is in very good agreement (R > 0.89) with MODIS AOD and has calibration errors less than 15 %. Calibration errors in τ p are expected to be even lower for nighttime retrievals used in this study (Josset et al., 2008 Since ocean is the source of SSA, clean marine aerosol layers typically extend to the ocean surface. This makes it more difficult to determine molecular and particulate backscatter components of the signal separately using satellite measurements alone. To assess the uncertainty in lidar ratio introduced for the surface connected layers (i.e., layers whose bottom bound is defined as the ocean surface), here we estimate the 5 error in CALIOP retrieved Γ p values. The total attenuated backscatter signal measured by the lidar consists of molecular and particulate components: with subscripts m and p representing molecular and particulate quantities, respectively.

10
From the definition of Γ p it follows that: where the integration is from the surface to the top of the layer. β p is the particulate backscatter and e −2τ p accounts for the attenuation of the lidar signal by the particles. 15 Substituting Eq. (6) into Eq. (7) gives: The molecular component of the signal in Eq. (8) can be derived from the GMAO modeled temperature and pressure profiles (Bloom et al., 2005). However, to solve 20 this equation and determine the particulate attenuated backscatter value, particulate column integrated extinction is required. To get τ p the CALIOP algorithm is using a prescribed value of the lidar ratio, making Eq. (4) circularly dependent on the lidar ratio.
Here we estimate the error in CALIOP retrieved Γ p associated with the prescribed lidar 229 Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ratio by substituting the τ p value from SODA. If the error is large, that would imply that the uncertainty in CALIOP prescribed lidar ratio would introduce sizable corrections to Γ p , making Eq. (4) unsuitable for the estimation of SSA lidar ratio. The relative error in Γ p can be defined as: where Γ p,S and Γ p,C are columnar integrated attenuated backscatter values for SODA and CALIOP, respectively. From the theoretical basis documents for CALIOP level 1 algorithms, the molecular backscatter is estimated as where height dependent T (z) and P (z) profiles from the surface (1000 hPa) to top-of-atmosphere (0.1 hPa) pressure levels were obtained from the GMAO Modern-Era Retrospective analysis for Research and Applications dataset. The molecular lidar ratio, S m is defined as 8π/3 and C s is a constant equal to 3.742 × 10 −6 K hPa −1 m −1 (Hostetler et al., 2006). When considering all of the parameters, our analysis shows that the average error in Γ p is approximately 1.5 %. Compared to the systematic uncertainty in the SODA product 15 (< 15%), the uncertainty in Γ p is much lower indicating that, on average, errors in Γ p do not dominate S p retrievals. Since an average discrepancy between CALIOP-prescribed and SODA-derived lidar ratios (∼ 30 %) is more than an order of magnitude higher than uncertainty in Γ p , we conclude that the uncertainty in the CALIOP column integrated backscatter has a minor effect on the Eq. (4) calculated lidar ratio. 20 Furthermore, because in our study we use feature integrated products for a single aerosol layer, it is important to evaluate the relationship between Γ p and aerosol layer thickness (ΔZ). Figure 5 shows the normalised column attenuated particulate backscatter Γ p as a function of layer depth. For uniformly distributed aerosols throughout the column, Γ p is likely to be proportional to ΔZ. The spread of Γ p /ΔZ ratio is Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Γ p /ΔZ ratio at the higher ΔZ values would indicate that the lidar signal is strongly attenuated throughout the layer reaching a sensitivity limit. On the other hand, considerable increase of the ratio for the thin layers may indicate contamination of the backscattered signal by the surface reflectance. According to Fig. 5 for the vast majority of the data, signal attenuation and surface reflectance do not seem to be major 5 issues for the surface connected layers, suggesting that the quality control algorithm described in Sect. 2.4 was sufficient to remove the majority of erroneous measures of Γ p .

Conclusions
A new method is applied here that shows that it is possible to infer lidar ratios of sea 10 spray aerosol over the ocean using two independent sources: the AOD from Synergized Optical Depth of Aerosols (SODA) and the integrated attenuated backscatter from Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP). The proposed equation calculates particulate lidar ratio for individual CALIOP retrievals of single aerosol layer columns as a correction to achieve the best agreement between SODA and 15 CALIOP retrievals. The new method allows calculating sea spray lidar ratio and assessing its spatiotemporal variability and dependence on ocean surface wind speed. Analyses were carried out using CALIOP level 2, 5 km aerosol layer and collocated SODA nighttime data from December 2007 to December 2009. During the data analysis over 260 000 data points passed various quality-control and quality-assurance tests 20 to reduce errors associated with the clean marine aerosol retrievals. The calculated lidar ratios have been analyzed over the global ocean covering a wide range of wind speed and AOD conditions. Data analysis shows that over most of the ocean surfaces, the calculated lidar ratio is higher than the default lidar ratio of 20 sr used in the CALIOP clean marine aerosol model. Such reduction was explained by the shift in aerosol volume size distribution with the wind speed; however, it was also emphasised that future studies should explore the role of meteorological and/or environmental factors and ocean chemical/biological composition for sea spray aerosol intensive properties. Our data analysis showed that changes in wind speed also affect the probability density function for sea spray aerosol (SSA) 5 lidar ratio distribution. The largest standard deviation calculated for the lowest wind speed regime suggested that under low wind conditions, a wide range of sea spray particle sizes can be present over the ocean and there is greater probability for naturalcontinental and human-induced pollution aerosols to be classified by CALIOP as clean marine. Overall, our data analysis shows that an average value of 26 sr for SSA lidar 10 ratio provides the best agreement between the SODA product and CALIOP retrieved global mean sea spray aerosol optical depth values. However, our study also shows large spatiotemporal variability in SSA lidar ratios, suggesting that a single constant value of the lidar ratio is not suitable for a wide range of sea spray aerosols and can lead to large uncertainties at different locations and seasons. 15 We have estimated the error in CALIOP retrieved column integrated attenuated particulate backscatter. Calculations suggest that the average error in particulate backscatter is more than an order of magnitude lower compared to the actual value. Data analysis also showed no clear indication for either approaching a sensitivity limit (due to strong attenuation of the lidar signal throughout the layer) or the contamination 20 of the backscattered signal by the surface reflectance. Based on the conducted error analysis we conclude that the strict quality control criteria developed in this study is adequate to remove the majority of erroneous retrievals.
Finally, even though calculations here were carried out for SSA, the technique used in this study is broad and can be used to infer lidar ratios of different species of atmo-25 spheric aerosols (i.e., mineral dust, biomass burning, etc.) advecting over the ocean. Because our data analysis shows that it is possible to derive a correction to the CALIOP prescribed sea spray lidar ratio, future studies should also consider conducting case studies over different oceanic regions to examine the possible effects of meteorologi-    20 40 60 80 100 Lidar R atio, S p ( λ = 532nm ) 0 < U 10 ≤ 4, μ = 32.3 4 < U 10 ≤ 6, μ = 26.8 6 < U 10 ≤ 8, μ = 26 8 < U 10 ≤ 10, μ = 25.8 10 < U 10 ≤ 12, μ = 25.6 12 < U 10 ≤ 15, μ = 24.5 U 10 > 15, μ = 22.3 . 0 The normalised integrated attenuated backscatter as a function of the layer depth. The solid line shows the 3rd order least squares fit to the data while the dotted lines show ±1σ; the hatched area shows the layer depth data frequency: cross hatch between the 25th and 75th percentiles and straight hatch between 5th and 95th percentile.