Aerosol NO3- and NH4+ concentration data were acquired for 2890 samples collected from > 120 ship-based studies over the period 1995–2012. The spatial distributions of these samples is shown in Fig. 1a and a description of the individual cruises, the data sources and contributors is given in the Supplement for this paper (Table S1). The database itself (aerosol concentrations and sample locations) is also available in the Supplement. In general, the data were accessed from publicly available data archives (i.e. the SOLAS aerosol and rain chemistry database (http://www.bodc.ac.uk/solas_integration/implementation_products/group1/aerosol_rain/), the NOAA-PMEL Atmospheric Chemistry Data Server (http://saga.pmel.noaa.gov/data/)), were provided directly by the originator or were unpublished results from the authors. Since the data originate from multiple sources, the samples were acquired using a variety of sampling devices (e.g. bulk filtration or in size fractions using cascade impactors), collection substrates (e.g. Whatman 41, glass fibre or quartz) and sampling intervals, and were analysed using different techniques (commonly, ion chromatography or automated spectrophotometry) in many different laboratories (a summary of the available information on sample collection procedures is given in Table S1). Standard procedures for aerosol inorganic N sampling and analysis have not yet been established, nor have interlaboratory intercomparison/intercalibration exercises (e.g. Morton et al., 2013) been commonly held. In the absence of such procedures, datasets were accepted into the database that had either already been published in the peer-reviewed literature or that originated from laboratories with established publication records. Under these conditions, the presence of biases within the observational database cannot be ruled out. Sampling intervals varied between 12 and 48 h, but the majority of samples were collected over ∼ 24 h. In cases where the observations were obtained for multiple size fractions for a given sample, the fraction concentrations were summed and stored in the database only as total NO3- or NH4+ concentrations for that sample.

The database contains ∼ 1420, ∼ 680 and ∼ 770 samples collected over the Atlantic, Indian and Pacific oceans, respectively. Overall, 81 % of the samples contain observations of both NO3- and NH4+, 16 % observations of NO3- only and 3 % of NH4+ only. The distributions of these samples are non-uniform with time (by year and by month) through the 18-year period that we examined, as illustrated for the major ocean basins in Fig. 1b and c.

Where possible, the observed aerosol concentrations (C: nmol m-3) for NO3- and NH4+ were compared directly with corresponding particulate concentrations simulated by the models (i.e. for the TM4 model; see below). Dry deposition fluxes from the models were also compared to the observational database. In order to do so, dry deposition fluxes (F: mg N m-2 d-1) were calculated from the observed concentrations of the two species using dry deposition velocities (vd: m d-1) (Eq. 1), with appropriate correction for the relative atomic mass of N. (Note that hereafter we quote vd in units of cm s-1.) F=vdC

Two approaches were used for the calculation of F. In one case, fixed values for vd of 0.9 cm s-1 for NO3- and 0.1 cm s-1 for NH4+ were used to calculate F in all grid cells (hereafter referred to as the “fixed vd” method). For NO3-, the relatively high vd value used reflects its association over the ocean with coarse sea-salt particles (and is similar to the vd for gaseous HNO3). The lower vd value of NH4+ is due to its association with fine aerosol fractions. Similar methods have been applied to the calculation of dry deposition fluxes in many previous studies (e.g. Markaki et al., 2003; Buck et al., 2013; Baker et al., 2016). Dry deposition fluxes were also calculated using wind-speed-dependent values of vd for particles of 7 µm (coarse mode) and 0.6 µm (fine mode) diameter using the parameterisation of Ganzeveld et al. (1998). This “variable vd” method is similar to the approach used previously to estimate dry deposition of N species to the Atlantic Ocean by Baker et al. (2010) and Powell et al. (2015). In this case, European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis dataset surface wind speeds were obtained for the years 1995–2012 and the mean wind speed for these years was used to calculate vd for each grid cell. In this case, the total NO3- and NH4+ concentrations in the database were artificially separated into coarse and fine modes using the median fractions of each species in coarse-mode aerosol reported for 210 aerosol samples collected over the Atlantic Ocean (Baker et al., 2010). These fractions were 0.90 and 0.14 for NO3- and NH4+, respectively. (For comparison, in TM4 on a global scale, these fractions were 0.92 and 0.08, respectively, for the year 2005.) The mean values of vd for NO3- and NH4+ calculated using the variable method over the global ocean were 0.81 and 0.15 cm s-1, respectively, and their distribution is shown in Fig. S1 of the Supplement. Hereafter, deposition fluxes derived from measured aerosol concentrations and dry deposition velocities are referred to as “calculated deposition” (CalDep).

For the TM4 model, surface-level particulate NO3- and NH4+ concentrations and dry deposition fluxes of these species were simulated for the nominal year 2005 (for details, see Kanakidou et al., 2016; Myriokefalitakis et al., 2015). The model's lowest level has a mid-level height of 40 m and its native resolution is 2∘ (lat.) × 3∘ (long.), but for this study the model output was interpolated to a grid scale of 1∘ × 1∘ . The TM4 model also applies the Ganzeveld et al. (1998) parameterisation to compute vd for each grid cell using ECMWF ERA-Interim meteorology for the year 2005 and accounts for organic nitrogen sources and fate in the atmosphere (see Kanakidou et al., 2012). TM4 also assumes dry mass diameters of 0.34 µm (1σ 1.59) and 6.71 µm (1σ 2.00) for sea-salt aerosol and 0.68 µm (1σ 1.59) and 3.5 µm (1σ 2.00) for dust aerosol that are in agreement with those used here to calculate dry deposition based on measured aerosol concentrations. Furthermore, TM4 accounts for 8.15 Tg-N yr-1 of NH3 emissions from the ocean to the atmosphere, taken from the Bouwman et al. (1997) emission inventory, which are used in the model based on annual mean fluxes. Although this reduced nitrogen is of marine origin and thus does not constitute an external source of N to the ocean, its consideration is needed when comparing to atmospheric aerosol observations in the marine environment. TM4 also accounts for marine emissions of amines as discussed in Kanakidou et al. (2016). The present TM4 model configuration explicitly considers the atmospheric iron cycle (Myriokefalitakis et al., 2015) and uses the ISORROPIA II thermodynamic equilibrium module (Fountoukis and Nenes, 2007) to calculate the partitioning of NH3/NH4+ and HNO3/NO3- accounting for the impact of sea-salt and dust elements on this partitioning (Myriokefalitakis et al., 2015) assuming stable conditions (Karydis et al., 2016).

The ACCMIP products used in this comparison were based on emissions for the year 2000 and average meteorology for the decade 2000–2009 (Lamarque et al., 2013a). The fields used were MMM dry deposition from 10 (for NOy) or 5 (for NHx) individual atmospheric chemical-transport models, generally with surface mid-level heights of 20–40 m, and were reported by ACCMIP on a grid scale of 0.5∘ × 0.5∘, although the resolution of individual models was coarser. NOy and NHx dry deposition estimates were also available for TM4. (Neither particulate concentration nor dry deposition fields were available for NO3- or NH4+ from ACCMIP.) For both ACCMIP and TM4 model results, NHx corresponds to the sum of NH3 and NH4+. Most models in the ACCMIP product included marine emissions of NH3 based on Bouwman et al. (1997). However, NOy differs between the two model products. NOy is derived from TM4 results as the sum of all inorganic oxidised N species in the model, i.e. NO, NO2, NO3-, N2O5, HONO, HNO4 and HNO3 (Kanakidou et al., 2016), since organic oxidised N is explicitly studied (Kanakidou et al., 2012). For the ACCMIP models, NOy also contains some gas-phase organic nitrates and peroxyacyl nitrates (PANs) (Lamarque et al., 2013a). Thus, the NOy and NHx deposition estimates from both models include contributions from gas-phase, as well as particulate, deposition. On a global scale, TM4 simulates that particulate NO3- and NH4+ account for 80 and 35 % of inorganic NOy and NHx deposition, respectively, while particulate NH4+ deposition comprises ∼ 25 % of NHx deposition in the ACCMIP MMM (Lamarque et al., 2013a). Note that these global numbers are dominated by deposition over continents, where particulate NH4NO3 is a much more significant component of aerosol N than over the oceans. Particulate NO3- was not simulated by all of the models contributing to ACCMIP, and hence the fractional contribution of NO3- to NOy deposition was not reported by Lamarque et al. (2013a). In models without a specific simulation of particulate NO3-, this species is likely to have been simulated as gas-phase HNO3, whose dry deposition velocity is similar to that of particulate NO3- (Pryor and Sorensen, 2002). Thus, the dry deposition flux of NOy in the multi-model mean was not greatly affected by this factor. The ACCMIP NOy dry flux was not substantially different from that computed in the TM4 model, which does specifically simulate dry particulate NO3- deposition (Kanakidou et al., 2016). Therefore, in the present study, TM4 speciated results are more appropriate for comparison to the observations and are put in context when used jointly with the more robust, but less speciated, ensemble model results of ACCMIP. Modelled NOy and NHx deposition estimates are therefore not directly comparable to the observationally derived deposition estimates examined here. For information, Table S2 presents the total annual emissions of NOx and NH3 (and their emissions from Africa, India and southeast Asia/Japan) used by the ACCMIP models and by TM4 for the present study.

Dry deposition fluxes simulated by the TM4 and ACCMIP model products are referred to below as “modelled deposition” (ModDep).

Observations and model products were compared using a 5∘ × 5∘ grid. This represents a compromise between the desire to undertake the comparison at a high spatial resolution and the need to ensure that the amount of observational data available in each grid cell was sufficient to adequately represent the deposition in that cell.

For the observations, means of all available NO3- and NH4+ concentrations were calculated for each grid cell. Values of CalDep for each species were then calculated from these mean concentrations using the methods described above. Annual mean model products were prepared for comparison by removing outputs from grid cells that contained land using a (0.5∘ × 0.5∘ or 1∘ × 1∘, as appropriate) land-mass mask. This was done in order to prevent high deposition fluxes of N species over land from biasing the comparison to the marine observations for grid cells along continental margins. The model outputs were then averaged from their input resolution to the same 5∘ × 5∘ grid that was used to bin the observational data.

The following parameters were then compared: observed aerosol concentrations of NO3- and NH4+ with their simulated concentrations from TM4; CalDep for NO3- and NH4+ with their respective ModDep from TM4 and with ModDep of NOy and NHx from ACCMIP and TM4. Comparisons over regions larger than individual grid cells were made using the area- and sample-number-averaged ratio (RA,n) of modelled to observation-based parameters (concentration or deposition flux), as shown in Eq. (2), and normalised mean bias (NMB; Eq. 3) (where M is the modelled concentration or ModDep, O is the observed concentration or CalDep, A is the surface area and n is the number of observations for each grid cell). RA,n=∑(M/O)An∑AnNMB=100∑M-O∑O Thus, the value of RA,n would be equal to unity in the ideal case of perfect agreement between the model annual average and observations in the region in question. When the model deviates from observations, the ratio reflects the model-to-measurement agreement, favouring the grid cells where most measurements exist compared to the grid cell areas with fewer measurements. Ratios larger than unity indicate overestimation of observations and lower than unity an underestimation of the observations.

While the database contains observations that cover wide regions of the global ocean (Fig. 1), for NO3- only 550 grid cells (∼ 28 % of oceanic grids cells) contain observations. Of those grid cells containing observations, only 65 contained 10 or more NO3- observations, and 72 contained observational data acquired over 4 or more calendar months. For NH4+, there were observations in 478 grid cells (∼ 24 % of oceanic cells), with 57 of those containing 10 or more observations, and 50 with observations acquired over 4 or more months (Table 1). Summaries of the data available for each grid cell over the global ocean (number of observations, number of calendar months with observations, mean and relative standard deviation aerosol concentrations) are shown in Figs. S2 and S3 for NO3- and NH4+, respectively.

In the following, the global dataset was retained, but detailed analysis focused on the TEAtl, NInd and NWPac study regions (the number of NO3- or NH4+ observations in each cell and the number of calendar months represented by those observations for these regions are shown in Figs. 9–14). Data coverage was best in the TEAtl region (Fig. 2a), where many grid cells had both relatively large numbers of observations and observations covering 6 or more months of a calendar year. In the NInd region (Fig. 2b), there were several grid cells containing many observations, but only one grid cell with observations spanning more than 6 months. Data coverage in most of the NWPac region (Fig. 2c) was poor compared to the other two regions, with high sample numbers and relatively good temporal coverage only in cells close to the coast of China. The NWPac region had the additional benefit that it is adjacent to the Acid Deposition Monitoring Network in east Asia (EANET) that has already been used to assess the skill of the ACCMIP- and TM4-modelled wet deposition products (Lamarque et al., 2013a; Kanakidou et al., 2016). The observational data available in these three regions were considered most likely to be representative of the annual N concentration and deposition fields represented by the models, although even here it is apparent that the distribution of observations is non-uniform in and between individual grid cells (Fig. 2). Where possible, the ship-based observations were compared to longer-term records obtained at remote island sites located in specific grid cells (see Sect. 3.2). Observation–model comparisons outside of the three study regions (i.e. for the global database) are subject to higher uncertainties.

Figure 3 shows box-and-whisker plots of NO3- and NH4+ concentrations grouped according to calendar month for cells containing relatively high numbers (16–73) of observations for each of the TEAtl, NInd and NWPac study regions. For two of these cells, the monthly and annual mean concentrations are directly compared to observations from remote island monitoring sites situated within those cells (see below). Similar independent records have not been identified in any other grid cell that also contains high numbers of observations in the database.

In the TEAtl region, the data obtained for the 15–20∘ N, 25–20∘ W cell were compared to results reported for the Cape Verde Atmospheric Observatory (CVAO: 16∘51′49′′ N, 24∘52′02′′ W) for the years 2007–2011 (Fomba et al., 2014). Here, agreement between the ship-based observations and the island station was rather good for NO3-, with the range of the 42 ship-based concentrations falling entirely within the range of the 671 observations at CVAO (Fig. 3a). The mean NO3- concentration for the ship observations was 20.7 nmol m-3, compared to the 5-year mean concentration of 17.7 nmol m-3 for the island observations, with neither dataset showing significant seasonal variation. There was also generally good agreement between the ship and island observations of ammonium in this cell, with the exception of July, where the ship data (2 samples) were approximately a factor of 2 higher than the upper limit of the island data (Fig. 3g). Mean NH4+ concentrations were 13.9 nmol m-3 for the ship observations (n=35) and 5.0 nmol m-3 (5-year average) for the island observations. Fomba et al. (2014) reported a small seasonal cycle for NH4+ at CVAO, with higher concentrations during March–June than during the rest of the year. There were not enough ship data available to independently confirm this seasonal pattern.

In the NWPac region, there was also good agreement between the 73 ship-based observations from 2005 to 2008 in the 25–30∘ N, 120–125∘ E cell and the 173 daily observations made during 2010 at Pengchiayu Island (25∘37′44′′ N, 122∘4′4′′ E) in the East China Sea (Hsu et al., 2014). The Pengchiayu dataset indicated that there was some seasonality in aerosol NO3- concentrations at this site (Fig. 3e), with mean concentration values being approximately twice as high during the months of December to April than during May to October. Mean NO3- concentrations were 67.8 nmol m-3 for the ship-based observations and 71.0 nmol m-3 at Pengchiayu Island. Except for January and September, there was little monthly variation in NH4+ concentrations at Pengchiayu (Fig. 3k). Mean NH4+ concentrations were 88.7 and 91.4 nmol m-3 for the ship and island observations, respectively.

Comparisons of observed aerosol concentrations for NO3- and NH4+ with modelled surface-level particulate concentrations from TM4 for these species are shown in Fig. 4. The sample number weighting included in the calculation of RA,n is illustrated in Fig. 4 using crosses of different sizes to represent the amount of data available in each cell.

For NO3-, TM4 generally overestimated aerosol concentrations (RA,n=6.6 for the global dataset), although the model appears to significantly underestimate NO3- concentrations in the Atlantic sector of the Southern Ocean (see Fig. S4a; note that there were relatively little observational data in this region). Overestimation of aerosol NO3- concentrations was particularly noticeable over the Bay of Bengal, the northwest Pacific around Japan and for some areas of the northwest Atlantic, including a number of coastal grid cells around North America that contained relatively large numbers of observations (Fig. 4a). Spatial gradients in aerosol concentrations over coastal areas are likely to be strong, and this may contribute to the large observation–model discrepancies for these grid cells. For the TEAtl region, TM4 reproduced the regional average aerosol NO3- concentration better than for the global comparison (RA,n=1.4). However, TM4 did not reproduce the spatial distribution of NO3- in this region, particularly around the margins of west Africa (Fig. 5). Regional concentration overestimates by TM4 in the NInd (RA,n=2.9) and NWPac (RA,n=2.6) regions appear to be due to overestimation over the Arabian Sea and Bay of Bengal and the seas around the Korean Peninsula and Japan, respectively (Fig. 5).

Over the global dataset, agreement between the observations and TM4 concentrations was better for NH4+ than for NO3- (RA,n=0.9, indicating a slight model underestimation). However, underestimation of NH4+ concentrations by TM4 was greater in all of the three study regions, and the global value of RA,n appears to be influenced by model overestimation in regions with low observed NH4+ concentrations (Fig. 4b). Specifically, TM4 appears to overestimate NH4+ concentrations in the western South Atlantic and equatorial Pacific oceans, while underestimation occurred in the NWPac region and southeastern South Atlantic (Fig. S4b). Although TM4 appeared to underestimate NH4+ concentrations across the TEAtl (RA,n=0.7) and NWPac (RA,n=0.5) regions, the spatial distributions of NH4+ in the observations and model were similar (Fig. 6). In the NInd region (RA,n=0.7), TM4 did not appear to reproduce the spatial distribution of NH4+, with observed concentrations in the Bay of Bengal and in the cells around 5∘ S–10∘ N, 65–80∘ E being higher than those simulated by the model.

Note that, over land, NO3- and NH4+ levels are affected by the vicinity of the sources. In particular, biomass burning and dust emissions affect the partitioning of NO3- and NH4+ to the aerosol phase. Even small inaccuracies in the model simulations of this partitioning can lead to higher discrepancies between model results and observations over land than over the ocean. Indeed, Kanakidou et al. (2016) have compared NO3- and NH4+ concentrations in PM10 over Europe and found an overestimate in NO3- PM10 content of about 115 % and an underestimate in NH4+ in PM10 of about 55 % (Fig. S4 in the Kanakidou et al., 2016, their Supplement), results that are consistent with but larger than the 70 and 44 %, respectively, reported here for oceanic regions (Fig. 4 of the present paper).

Figure 7 shows the comparison between CalDep from the variable vd method for NO3- and NH4+ and ModDep of NOy/NO3- and NHx/NH4+ from the models for all grid cells which contained observations. (A similar figure for CalDep from the fixed vd method is shown in Fig. S5.)

The comparison to NO3- CalDep for the global oceanic dataset indicates that the models generally overestimated the flux (Table 2), with values of RA,n of at least 4 in all cases (Figs. 7 and S5). The ACCMIP simulation appeared to overestimate NOy deposition in the Northern Hemisphere and underestimate it in the Southern Hemisphere, while TM4 showed a less pronounced difference in performance between the Northern Hemisphere and the Southern Hemisphere with overestimates and underestimates in both hemispheres and a clear underestimate in NOy/NO3- deposition over the Southern Ocean (Fig. S6). Values of RA,n for the global TM4 deposition comparison (4.4–5.6) were all slightly lower than that for the TM4 concentration comparison (6.6). This must be due to differences between the average dry deposition velocity used for NOy/NO3-, which is lower in TM4 than in either CalDep method. For NO3-, the use of the variable vd CalDep method led to lower observation-based deposition fluxes and higher values of RA,n (i.e. generally worse overall agreement to the models), when compared to the fixed vd method. This indicates that the average deposition velocity for NOy/NO3- used by the models was closer to the value used in the fixed vd case (0.9 cm s-1) than to the average deposition velocity used in the variable vd case, but does not necessarily imply that the models or fixed vd case are more accurate representations of aerosol nitrate dry deposition. For TM4, values of RA,n were generally closer to unity for simulated NO3- than for NOy (i.e. agreement was better when the simulation more closely matched the measured parameter).

For NH4+, the global comparison (Figs. 7 and S5) indicates that the modelled NHx deposition results were considerably higher than NH4+ CalDep (RA,n= 3.0–5.4). This is primarily due to the large component of gas-phase NH3 deposition in the modelled NHx fluxes (for ACCMIP NHx : NH4+=∼ 4 (Lamarque et al., 2013a), while in TM4 this ratio is ∼ 2.5). The greatest disagreement between NHx ModDep and CalDep was at the lowest NH4+ deposition fluxes (< 0.01 mg N m-2 d-1), which were overestimated in the models by 1–2 orders of magnitude, generally over the tropical open oceans (Fig. S7). This mismatch between NH4+ CalDep and NHx ModDep makes meaningful comparison between these fields rather difficult. Therefore, NH4+ CalDep – NHx ModDep comparisons for the three study regions are not discussed below. TM4 NH4+ ModDep fluxes agreed better (in the global comparison) with the corresponding CalDep fluxes (RA,n=  1.1–1.4; Figs. 7f and S5f) than the NHx ModDep results. Use of the variable vd method led to higher CalDep fluxes for NH4+ and hence lower values of RA,n and better overall agreement to the models, when compared to the fixed vd method. The fixed vd flux comparison for TM4 was also worse (RA,n was higher) than the TM4 concentration comparison, which was caused by the value of vd used in the calculation being higher than the average deposition velocities used in TM4 or the variable vd calculation.

Figures 8–13 show the spatial distribution of CalDep for each of the three study regions, together with the corresponding ModDep fields from ACCMIP and TM4. From these figures, it is clear that the CalDep calculation method (fixed and variable vd methods) influences both the magnitude and spatial distribution of N deposition estimates, and that this will, in turn, influence assessments of the impacts of that deposition on the marine environment.

Inertial segregation of larger particles at inlets of aerosol sampling systems, particularly at higher wind velocities, can result in relatively low passing/collection efficiencies and thus negative bias for supermicron aerosol constituents including NO3-. Cascade impactors are associated with significant internal losses (typically ranging from 25 to 40 %) of large particles (e.g. Young et al., 2013; Marple et al., 1991). Because virtually all NO3- in marine air is associated with supermicron diameter particles, NO3- concentrations summed over all impactor size fractions correspond to lower limits for ambient concentrations and dry deposition fluxes estimated from those concentrations.

The pH of marine aerosol varies significantly as a function of size. In addition, based on their thermodynamic properties, the gas–aerosol phase partitioning of nitric acid (HNO3) and NH3 varies as a function of pH. HNO3 partitions preferentially with the less acidic supermicron size fractions, while NH3 partitions preferentially with the highly acidic submicron size fractions. When chemically distinct aerosol size fractions are sampled in bulk, the pH of the bulk mixture differs from that of the size fractions with which HNO3 and NH3 partition preferentially in air. This drives artefact phase changes of both HNO3 and NH3, resulting in negative measurement bias. Because of their relatively short atmospheric lifetimes, low surface-to-volume ratios and corresponding slow rates of thermodynamic equilibrium, the upper end of the marine aerosol size distribution is often undersaturated with respect to gaseous HNO3. Following collection on filters, HNO3 can continue to condense from the sample air stream into these particle deposits, resulting in positive measurement bias. In addition, a number of aerosol collection media have been reported to be susceptible to uptake of gas-phase species such as HNO3 and NH3 (e.g. Keck and Wittmaack, 2005).

Thus, there are various processes, particularly in the marine environment, that can lead to positive and negative biases in measured aerosol NO3- and NH4+ concentrations, and the extent to which a given dataset is affected by these processes is greatly influenced by sampling methodology. If such effects have influenced the database used here, biases are unlikely to be uniform across all the observations, since the observations come from a very wide variety of sources with many different sample collection protocols (see Table S1).

Uncertainty in analysed meteorology introduces uncertainty into deposition velocities derived for the variable vd CalDep calculation. This uncertainty was assessed by calculating vd from mean ECMWF wind speeds for each of the individual years (1995–2012) and the relative standard deviations of these annual vd values. Standard deviations were relatively high over the tropical oceans (up to ∼ 25 %) and lower elsewhere (< 10 % for coarse particles and < 5 % for fine particles); see Fig. S8. While ECMWF wind fields are themselves subject to uncertainty, weather product skill continues to improve as a result of extensive use of global-coverage satellite observations (Bauer et al., 2015). Dry deposition velocities, however derived, are subject to high levels of uncertainty (up to a factor of 2–3; Duce et al., 1991) due to their strongly non-linear variation with parameters such as particle size, wind speed and deposition surface properties (Slinn and Slinn, 1980). Their use to estimate CalDep fluxes here therefore introduces substantial uncertainty into the CalDep–ModDep flux comparison.

In addition to the sampling-related biases discussed above, differences between observations and model calculations for a given grid cell can originate from several other interrelated processes. These include differences between the following modelled and actual processes: upwind emissions (including long-term trends in emissions) of NOx and NH3 and associated transport regimes; upwind chemical transformations and removal; phase partitioning of HNO3 and NH3 with size-resolved particles in near-surface marine air; and the corresponding size distributions of particulate NO3- and NH4+. In the latter case, if simulated concentrations of total NO3 (HNO3+ NO3-) and NH3 (NH3+ NH4+) were in agreement with actual concentrations but gas-phase concentrations were overestimated, particulate-phase concentration (and dry fluxes) would be underestimated. In addition, even if the total concentrations of particulate NO3- and NH4+ were modelled correctly, incorrectly simulated or assumed size distributions would lead to incorrect dry deposition fluxes, because dry deposition velocities vary greatly as a function of particle size. Gas–aerosol phase partitioning is highly parameterised in most global models. For particulates with deposition velocity of the order of 1 cm s-1 (i.e. NO3-), the short vertical turnover time of the surface atmospheric layer can lead to strong surface concentration gradients. This can lead to biases in the comparison of vertically averaged (for instance, over 50 m in TM4) modelled surface layer concentration (or deposition flux) with observations made at heights that vary depending on the ships used for sampling (typically 10–20 m).

As stated above, dry deposition velocities are highly uncertain. If modelled and observed aerosol concentrations were in agreement, differences between modelled dry deposition velocities for size-resolved particles and those used to calculate dry deposition fluxes from observed aerosol concentrations would lead to model–observation divergence. In addition, bias in estimated deposition velocities for gases also impacts lifetimes of modelled total NO3 and NH3, which would in turn influence the concentrations and dry fluxes of particulate N. Differences in the temporal scales of observations and model time steps can also lead to biases. For instance, the variable vd method for CalDep and dry particulate deposition in TM4 are both based on the parameterisation of Ganzeveld et al. (1998). The CalDep calculation involves the use of mean observed aerosol concentration and ECMWF wind speeds averaged over the period 1995–2012. In TM4, wind fields (also based on ECMWF meteorology) are updated every 3 h in order to calculate vd for each time step. In order to compare deposition velocities over similar timescales, it is possible to calculate “effective mean deposition velocity” for NO3- and NH4+ in TM4 (the ratio of the annual deposition fluxes to the respective annual mean concentrations), but these values are not representative of the deposition velocities used at each model time step. Maps of variable vd used in CalDep calculations and effective deposition velocity for TM4 and areal average values of these for the study regions can be found in the Supplement (Fig. S1 and Table S3).

Differences between modelled and actual deposition modes for HNO3/NO3- and NH3/NH4+ can also influence model–observation comparison. For instance, overestimation of modelled wet fluxes of total NO3 and NH3, would lead to underestimation of their modelled dry fluxes. Wet deposition is also highly parameterised in most global models.

The extent to which the available observations represent the actual conditions of the areas studied will also influence the effectiveness of the model–observation comparison. Ideally, the observations should capture the spatial variability of aerosol concentrations across the area to be compared (particularly for regions with large gradients, such as those across coasts), and should also be representative of temporal variations (i.e. observations distributed throughout the year are required to capture the annual mean concentration for species/regions with high seasonality). The 18-year period over which the observational database was acquired may also influence the effectiveness of the comparison to the shorter timescales represented by the model products.

Because there were few grid cells for which the observational data covered the majority of a calendar year, it was possible that unrepresentative sampling of seasonal variations in aerosol concentrations might lead to apparent biases in the annual-based observation–model comparisons reported in this paper.

The potential impact of seasonality was examined for the TEAtl, NInd and NWPac study regions by comparing monthly mean NO3- and NH4+ concentrations simulated by TM4 to observations in individual grid cells that contained relatively large numbers of observations (Fig. 3). For most cells, the TM4 simulation of both N species was very similar to the available ship- and island-based observations. However, in the Indian Ocean cells (C and D), there appeared to be relatively strong seasonality that was not always well reproduced by the model. For instance, TM4 appeared to underestimate observed median NH4+ concentrations in cell C during the months of January to March by factors of 2–3 (Fig. 3i) and overestimated observed median NO3 concentrations in cell D by factors of at least 4, with the seasonal changes indicated by the model not being evident in the observations (Fig. 3d).

On the scale of the whole study regions, observed seasonality was reproduced best by TM4 in the TEAtl region (Fig. 14a and d). In the NInd region, TM4 predicted a strong seasonal cycle for NO3- (particularly in the Arabian Sea; Fig. S9) which was not entirely reflected in the observed concentrations (Fig. 14b). Observed NH4+ seasonality in the NInd appears to be more pronounced than what was simulated in the model (Fig. 14e). Note that the uneven distribution of sample numbers through the year is a potential source of bias in the monthly mean observed concentrations used to infer seasonal cycles here. Since the comparisons of annual mean observed concentrations with those simulated by TM4 indicated differences over the Arabian Sea and Bay of Bengal (Figs. 5 and 6), observed and TM4 monthly concentrations and monthly total number of observations for these two regions (5–25∘ N, 55–75∘ E and 5–25∘ N, 80–90∘ E, respectively) are shown in Fig. 15. This shows clear differences in the temporal distribution of sample collection between the Arabian Sea and Bay of Bengal, with sampling over the latter dominated by the period of outflow from the Indo-Gangetic Plain (Srinivas et al., 2014). There were also differences in the extent to which the model predicted seasonal variations in NO3- and NH4+ concentrations (Fig. 15). For NO3-, TM4 simulated a strong seasonal variation over the Arabian Sea (and the observed months cover the full range of predicted concentration change) but a much weaker seasonality over the Bay of Bengal. The available observations suggest that the NO3- seasonal cycles are more pronounced than predicted for the Arabian Sea and Bay of Bengal, and that TM4 overpredicts mean NO3- concentrations in the Bay of Bengal by factors of 2–25 in all months with observations. For NH4+, there was strong seasonality in the TM4 concentration over both areas, but almost all the observations from the Arabian Sea were from months when TM4 predicted low concentrations, while the period of lowest concentrations predicted over the Bay of Bengal was almost entirely missing from the observations. Differences in N deposition seasonality between models and observations in this region might arise as a result of a number of factors. These include seasonal variations in N emissions used in the models (see, for instance, the discussion in Daskalakis et al., 2015, for seasonal and spatial differences in biomass burning emission databases, in Figs. 1 and S2 of that paper), biases in seasonal variations in meteorology (e.g. in precipitation rates, Srinivas and Sarin, 2013a, and wind fields) and seasonal changes in mineral dust composition, in particular calcium content, over the region (Srinivas and Sarin, 2013a) affecting the uptake of NOx onto dust particles.

Thus, it seems very likely that seasonality contributed to divergence between the models and observations over the NInd region for NH4+ but was less important for NO3- there. (Note that these analyses of seasonality at the regional scale allow investigation of the model–observation comparison but cannot provide assurance that either the ship-based observations, or the model, accurately reproduce the annual mean aerosol concentrations, especially in the NInd region, where there are no independent seasonal records available).

It is not entirely coincidental that all three of the study regions examined in this paper are impacted strongly by transport and deposition of mineral dust. Interest in the impact of dust deposition on marine productivity (Jickells et al., 2005) has stimulated a great deal of research on aerosol chemistry at the outflows of the world's major deserts over the past few decades (e.g. Gao et al., 2007; Baker et al., 2013; Srinivas and Sarin, 2013b; Srinivas et al., 2014; Powell et al., 2015). Much of the observational work on dust has generated data on aerosol N concentrations, augmenting the data available in these regions, but the presence of dust adds extra complexity to the comparison performed here. Uptake of nitric acid onto suspended mineral dust particles alters the size distribution and deposition velocity of aerosol nitrate, and changes the gas-phase composition of N (Hanisch and Crowley, 2001; Rubasinghege and Grassian, 2009). Atmospheric chemical-transport models for N must therefore also incorporate effective simulations of mineral dust. This is itself a considerable challenge. Dust emissions in TM4, simulated for the year 2008 using ECMWF meteorology, were 1181 Tg yr-1 (Myriokefalitakis et al., 2016), while Kanakidou et al. (2016) simulated emissions almost 30 % higher for the year 2005. In the case of ACCMIP, not all of the models involved included simulations of mineral dust aerosols (Lamarque et al., 2013b). In general, modelled dust deposition fluxes to remote ocean regions have been shown to vary by factors of 10 or more (Huneeus et al., 2011; Schulz et al., 2012) and to not reproduce key aspects of the dust cycle even in well-characterised regions (Prospero et al., 2010).

As noted above, dry deposition velocities are probably the largest sources of uncertainty in estimates of dry deposition fluxes of aerosol components. Thus, the comparisons of observed and modelled aerosol concentrations presented in Figs. 4–6 are preferable to comparisons of dry deposition flux because they avoid the uncertainty associated with conversion of measured aerosol concentrations into CalDep. However, modelled aerosol concentrations at a given location are dependent on the parameterisation of dry deposition velocity (together with a number of other factors of varying degrees of uncertainty) applied by the model all along the simulated aerosol transport pathway. Uncertainty in modelled vd therefore also impacts the effectiveness of the concentration comparison, although gross errors in vd in models are unlikely to result in good agreement between observed and simulated aerosol concentrations.