Boundary-Layer Meteorology

, Volume 163, Issue 2, pp 327–350 | Cite as

Influence of the Surf Zone on the Marine Aerosol Concentration in a Coastal Area

  • Gilles Tedeschi
  • Alexander M. J. van Eijk
  • Jacques Piazzola
  • Jolanta T. Kusmierczyk-Michulec
Research Article

Abstract

Sea-salt aerosol concentrations in the coastal zone are assessed with the numerical aerosol-transport model MACMod that applies separate aerosol source functions for open ocean and the surf zone near the sea–land transition. Numerical simulations of the aerosol concentration as a function of offshore distance from the surf zone compare favourably with experimental data obtained during a surf-zone aerosol experiment in Duck, North Carolina in autumn 2007. Based on numerical simulations, the effect of variations in aerosol production (source strength) and transport conditions (wind speed, air–sea temperature difference), we show that the surf-zone aerosols are replaced by aerosols generated over the open ocean as the airmass advects out to sea. The contribution from the surf-generated aerosol is significant during high wind speeds and high wave events, and is significant up to 30 km away from the production zone. At low wind speeds, the oceanic component dominates, except within 1–5 km of the surf zone. Similar results are obtained for onshore flow, where no further sea-salt aerosol production occurs as the airmass advects out over land. The oceanic aerosols that are well-mixed throughout the boundary layer are then more efficiently transported inland than are the surf-generated aerosols, which are confined to the first few tens of metres above the surface, and are therefore also more susceptible to the type of surface (trees or grass) that determines the deposition velocity.

Keywords

Marine aerosol Numerical model Sea-salt aerosol source function Surf zone 

1 Introduction

Aerosol particles influence many processes in the marine boundary layer that are of importance to the global climate. Through scattering and absorption, they reduce the amount of solar radiation that reaches the Earth’s surface, and by acting as effective condensation nuclei, they aid cloud formation. This gain affects the amount of radiation reaching the surface, and hence the heat and moisture fluxes that affect local weather and eventually larger scale processes. Therefore, climate models need to take the aerosol component into account, which, as noted by the intergovernmental panel on climate change (IPCC 2007), remains one of the most poorly understood elements of climate modelling.

With 70% of the Earth’s surface covered by oceans, sea salt is the most abundant aerosol species in the atmosphere. Fifty years after Woodcock (1962) published extensive data on the sea-salt concentration as a function of altitude and wind speed, many authors have addressed the production of sea-salt aerosols at the surface and their subsequent dispersion through the atmosphere. Building on pioneering efforts by Blanchard and Woodcock (1980) and Monahan et al. (1986), an abundance of source functions (production flux at the surface per unit area) has been reported (see, e.g., Andreas 1992, 2002; Lewis and Schwartz 2004; O’Dowd and DeLeeuw 2007) and wind speed is generally used to parametrize the aerosol production in terms of environmental conditions. However, other authors prefer to base their expressions on whitecap coverage related to wave-breaking (e.g., Piazzola and Despiau 2002; Clarke et al. 2006; Shi et al. 2009; Piazzola et al. 2009), which is a phenomenon that is associated with the primary steps in aerosol production (see, e.g., Blanchard 1963; Monahan et al. 1986; Spiel 1994, 1997).

As breaking waves are especially abundant in the surf zone, Monahan (1995) hypothesized that more sea-spray aerosol per unit area and time is generated over the surf zone than over the open ocean. This hypothesis was supported by earlier work (Gathman and Hoppel 1970; Exton et al. 1985) and has been confirmed recently (Neele et al. 1998; Hooper and Martin 1999; Clarke et al. 2006; Van Eijk et al. 2011). While there appears to be no ambiguity in the abundance of the surf-generated aerosol, there is debate as to the significant environmental parameters responsible for its production. In the relatively sparse literature on this topic, several authors (DeLeeuw et al. 2000; Clarke et al. 2006; O’Dowd and DeLeeuw 2007) consider the surf zone as an extension of the open ocean and suggest wind speed as the key quantity for production. Others (Chomka and Petelski 1997; Van Eijk et al. 2011) adopt the hydrodynamical point of view that the surf zone consists of waves breaking onto a sloping beach. In that formalism, the ultimate driver for aerosol production becomes wave-energy dissipation, which can be expressed in terms of the bathymetric profile and the characteristics of the incident wave field (Francius et al. 2007).

Once generated, the surf-aerosol particles are mixed upwards by turbulent transport. Lidar observations over the surf zone at Scripps Pier, California revealed the presence of surf-aerosol plumes that extended up to 20 m (Hooper and Martin 1999). In contrast, Clarke et al. (2006) presented data obtained from Hawaii, suggesting that the surf-generated aerosol plumes remain much closer to the surface. Their results are also confirmed by lidar observations (Porter et al. 2003) and corroborate, e.g., Exton et al. (1985), Sievering et al. (2004).

In view of these contrasting results, it is understandable that modelling techniques have been applied to better understand the physical processes underlying the transport properties of surf-generated aerosols. Van Eijk et al. (2011) and Kusmierczyk-Michulec et al. (2013) applied the marine aerosol concentration model (MACMod) developed at the Mediterranean Institute of Oceanography (Toulon, France) by Tedeschi and Piazzola (2011). Numerical simulations by Kusmierczyk-Michulec et al. (2013) suggested that the vertical concentration gradients of surf aerosols, for the same downwind production-zone distance, are more pronounced in stable stratification than in unstable stratification due to reduced convection. As a result, aerosol plume heights in stable conditions may be three times smaller than those in unstable conditions, which may explain the difference between the observations of Hooper and Martin (1999) and Clarke et al. (2006).

For horizontal transport of surf aerosols remote from the production zone, viz. out to the sea or inland, the sparse literature differs even more. Petelski and Chomka (2000) found no salt particles \({>}10\,\upmu \hbox {m}\) in size further inland than 82 m from the shoreline of the Baltic Sea. In contrast, Kunz et al. (2002) concluded from lidar observations on the Irish west coast that surf-generated aerosols may be transported over distances of several km. In addition to these experimental efforts, Vignati et al. (1998, 2001) developed the numerical coastal aerosol-transport model to assess the horizontal transport of surf aerosols in offshore flow. By initializing the model with observations obtained during the electro-optical propagation assessment in coastal environments experiments in California from 1996 to 1997, DeLeeuw et al. (2000) and Vignati et al. (2001) predicted that the effect of the surf zone extended up to several tens of km from the shoreline, both for low and high surf production. Unfortunately, their experimental dataset did not allow for the experimental verification of the model results.

More recently, Van Eijk et al. (2011) assessed the horizontal transport properties of surf aerosols by measuring downwind concentrations up to 12 km from the shore from a boat. They expected that the high concentrations over the surf zone would quickly decrease with downwind distance, but rather they found a constant concentration away from the surf zone. While this may support the hypothesis that surf aerosols are transported over appreciable distances, it is also possible that the particles generated over the surf zone are replaced by particles generated over the ocean.

Here, we aim at resolving the above question by applying the model MACMod. This two-dimensional aerosol-dispersion model is unique because it contains separate source functions for the surf zone and for the open ocean. This allows the model to differentiate between sea-salt aerosols generated over the surf zone and those from the open sea—a differentiation that experimentalists find difficult to achieve. In other words, the model MACMod assesses the relative contribution of surf-zone generated aerosols to the total marine aerosol concentration as the airmass advects away from the production zone. We emphasize that the model MACMod is a numerical testbed that provides insight into the fundamental physical processes governing aerosol transport in the atmospheric surface layer. The model is not configured for numerical weather prediction or for a detailed analysis of atmospheric dynamics, nor is this the aim of the present study.

We apply the model MACMod to a 2-day time frame from an experimental campaign held in Duck, North Carolina in autumn 2007, as part of a surf-zone aerosol experiment (Van Eijk et al. 2011). During the 2-day time frame, aerosol concentrations were measured as a function of distance to the coast (the relevant details are summarized in Sect. 2), and these data serve as a gauge for the model simulations. Note that the two-dimensional approach of the model MACMod implies that the domain is considered as laterally homogeneous, which is a good approximation for the coastline at Duck.

The model MACMod requires tuning with two aerosol source functions: one for the open ocean and one for the surf zone. Since the literature on the latter type of source function is sparse, Sect. 3 presents a review of the current source functions used to estimate the production of sea-salt aerosols in the surf zone. The numerical framework for the model MACMod and the numerical settings used for the present study are discussed in Sect. 4. The model simulations are compared to the experimental data in Sect. 5, and in particular, we discuss the effect of atmospheric stratification on the horizontal transport of surf-generated sea-salt aerosols. The extent of the surf-zone influence is calculated both for offshore and onshore flows, and under various environmental conditions. Finally, Sect. 6 summarizes the main results.

2 Experimental Campaign

The surf-zone aerosol experiment took place in Duck, North Carolina from October–November 2007 and is described extensively in Van Eijk et al. (2011). The experiment aimed at assessing the generation and transport of aerosol particles generated over the surf zone. This was accomplished by deploying seven optical-particle counters, along with standard meteorological equipment, a sun photometer and instrumentation to characterize the wave field.

The equipment was installed at the 560-m long pier of the field research facility of the US Army Corps of Engineers (http://www.frf.usace.army.mil/), extending well beyond the surf zone. The pier is equipped with a sensor insertion system—a crane-like device with two arms that can reach 15–25 m out from the side of the pier. This system can move the full length of the pier, and thus can always be positioned downwind of the surf zone: close to the beach for onshore flows and near the end of the pier during offshore flows. Aerosol optical-particle counters were mounted in four locations: near the base of the pier, on the upper and lower arms of the sensor insertion system (about 16 and 6 m above the water, respectively) and at the end of the pier. This set-up allowed for the assessment of surf-aerosol concentrations in both onshore and offshore flows.

The surf-aerosol transport experiment took place during a 2-day offshore flow event on 5 and 6 November 2007, during which period relatively constant wind speed and wave height were observed. A commercial tuna-fishing boat was chartered and aerosol probes were mounted on the top of the boat’s main cabin, at 3 m above sea level, with the intake horns pointing forwards. A small portable meteorological station was used next to the probes to measure standard parameters while aerosol data were being recorded. The boat travelled from the end of the pier along the offshore wind vector to a distance of 15 km. Ten stops were made during the outbound and inbound runs and the aerosol distribution was sampled for 15 min at each waypoint. The aerosol concentrations on the boat could be compared to data acquired near the shore, in particular, to the data collected on the lower arm of the sensor insertion system. This latter concentration served as a baseline for the amount of aerosol leaving the surf zone.

Aerosol data were acquired by four optical-particle counters manufactured by particle measuring systems. There were two classical aerosol spectrometers CSASP-200 (with a radius ranging from 0.21 to 18.5 \(\upmu \hbox {m}\)), a CSAP-100HV (with a radius ranging from 0.75 to 45.5 \(\upmu \)m), and a CSAP-100HV-ER (with a radius ranging from 1.5 to 92 \(\upmu \)m). The four probes were paired two by two, with one CSASP-200 paired with one CSAP-100HV, which yielded a larger size range. Data from the two individual probes were mixed into a single size distribution and the data were accumulated and averaged over 15 min, i.e., corresponding to the on-station time at each waypoint. The probes had been calibrated for absolute sizing prior to the experiment and all probes had been inter-calibrated for relative concentrations.

3 Modelling of Sea-Spray Aerosol Particles Generated in the Surf Zone

3.1 Review of Current Models

Numerical modelling of the marine aerosol concentration over the sea requires a source function that represents the number of particles of specific radius produced at the sea surface per unit area and time. The expressions found in the literature have been generally determined on the basis of experimental observations. Two major mechanisms have been identified for the generation of sea-spray aerosols: jet and film droplet production from air bubbles created from breaking waves, entrained in the water and then bursting on the sea surface (Blanchard 1963); and spume droplet production by direct tearing from wave crests by turbulence (Monahan et al. 1986). As the wave breaking and the extraction from the crest are dependent on the wind speed, this parameter is generally used to characterize the aerosol production (Andreas 2002). Source functions apply wind speed either directly or indirectly, e.g., by means of the whitecap coverage, which is then parametrized in terms of wind speed. While the strong correlation between aerosol generation and wind speed may occur for deep waters and for well-developed wind-generated wave fields, the dependence is much less pronounced in coastal areas and for short fetches.

In the surf zone, wave breaking is a complex process that depends both on the energy flux of the incident waves (linked to the wind speed) and on the bathymetry profile (acting on the wave steepness). With the knowledge of the incoming wave field and of the bathymetric profile of the surf zone, the wave energy dissipation can be determined. According to Van Eijk et al. (2011), the wave energy dissipation is a more relevant parameter for aerosol production in the surf zone than the local wind speed, especially during offshore flow conditions when the flow is in the opposite direction to the waves.

While many studies have addressed a parametric source function for the open ocean, only a few have been dedicated to the surf zone. DeLeeuw et al. (2000, 20l1) proposed an expression that was dependent on wind speed, deduced from experiments conducted at La Jolla, California in 1996 and 1997 during onshore flow. Thus,
$$\begin{aligned} \frac{\hbox {d}F}{\hbox {d}D_0 }=1.1 \times 10^{6}\exp (0.23U_{10})D_0^{-1.65} \end{aligned}$$
(1)
is the number of particles produced at the sea surface per diameter range per unit area and time (expressed in \(\upmu \hbox {m}^{-1}\,\hbox {m}^{-2}\,\hbox {s}^{-1})\) and \(U_{10}\) is the wind speed at a height of 10 m. Equation 1 is valid for diameters at formation \(D_{0}\) between 1.6 and \(20\,\upmu \hbox {m}\) and \(U_{10} < 9\,\hbox {m s}^{-1}\). It is implicitly assumed here that the surf zone is completely covered with whitecaps; in other words, the fractional whitecap coverage \(W = 1\). This allowed O’Dowd and DeLeeuw (2007) and DeLeeuw et al. (20l1) to extend their source function to open-ocean conditions by multiplying it by the whitecap ratio. To this end, they applied the empirical formulation given by Monahan et al. (1986),
$$\begin{aligned} W=3.84\times 10^{6}U_{10}^{3.41}. \end{aligned}$$
(2)
Clarke et al. (2006) undertook sea-salt aerosol measurements at Oahu, Hawaii, during onshore flow, at various heights on a 20-m tower on the beach. By differentiating the 5- and 20-m measurements, they isolated the contribution from the waves breaking in the surf zone. This allowed them to create a source function for the surf zone, expressed as three fifth-order polynomials that together cover a size range between 0.01 and 8 \(\upmu \hbox {m}\),
$$\begin{aligned} \frac{\hbox {d}F}{\hbox {d}\log _{10} D_{\mathrm{p}} }=10^{6}\sum _{j=0}^5 {\beta _{ij} D_{\mathrm{p}}^j }, \end{aligned}$$
(3)
expressed (for a given range interval i) in \(\hbox {m}^{-2}\,\hbox {s}^{-1}\), where \(D_{\mathrm{p}}\) is the dry diameter of the aerosol particle (which is supposed to be attained around a relative humidity of 40%) and the values of the three sets of \(\beta _{ij}\) can be found in the original paper.

This expression is limited to wind speeds where wave tearing and spume production are not active (roughly \(U_{10}< 10\,\hbox {m s }^{-1})\). Following DeLeeuw et al. (2000), the authors extended their source function to the open ocean by multiplying this function by the Monahan whitecap ratio (Eq. 2). We note, with interest, that both DeLeeuw et al. and Clarke et al. extended their surf source function to open-ocean conditions through multiplication by the whitecap ratio. This implies that the production mechanisms in the surf zone and open ocean are the same and only separated by a scale factor. This does not corroborate the fundamental changes in wave breaking as one approaches the shallow coastal waters and the sloped beach.

New experimental results were obtained during the surf-zone aerosol experiment in La Jolla, California in November 2006 and in Duck, North Carolina in October–November 2007. Van Eijk et al. (2011) measured aerosol concentrations simultaneously both upwind and downwind from the surf zone, as in the experiments of DeLeeuw et al. (2000). However, in contrast to the latter authors, measurements were also made during offshore flow and a source function in terms of wave-energy dissipation \(\in \) rather than wind speed was crafted,
$$\begin{aligned} \frac{\hbox {d}F}{\hbox {d}D_0 }=10^{10(1-\in ^{-0.35})}D_0 ^{-1.5}, \end{aligned}$$
(4)
expressed in \(\upmu \hbox {m}^{-1}\,\hbox {m}^{-2}\,\hbox {s}^{-1}\). This equation is considered valid for diameters at formation \(D_{0}\) between 0.5 and \(10\,\upmu \hbox {m}\) and \(10< \in < 200\,\hbox {W m}^{-2}\). Since the evaluation of \(\in \) requires knowledge of the incoming wave field and the bathymetric profile of the surf zone (cf. Francius et al. 2007), which may not always be readily available, Van Eijk et al. (2011) suggested an approximate relation between \(\in \) and the height of the waves entering the surf zone \((H_{rms})\),
$$\begin{aligned} \in =-3+35H_{rms}, \end{aligned}$$
(5)
where \(H_{rms}\) is the root-mean-square wave height and Eq. 5 is valid for \(0.1< {H}_{rms}< 5\) m.

3.2 Comparison Between Models

The flux formulations presented above are given either for the diameter at formation \(D_{0}\) or for the dry diameter \(D_{\mathrm{p}}\), and they are expressed either as the micron range or as the logarithm of the micron range. In order to compare the various source functions for surf-generated sea-salt aerosols, the various expressions are normalized to the diameter \(D_{80}\) at a relative humidity of 80% and expressed as the number flux by micron range \((\hbox {d}F{/}\hbox {d}D_{80})\). Using the approximate relation \(D_{0} \approx 2D_{80} \approx 4D_{\mathrm{p}}\) (O’Dowd and DeLeeuw 2007), and the relationship,
$$\begin{aligned} \frac{\hbox {d}F}{d\log _{10} D}=2.3D\frac{\hbox {d}F}{\hbox {d}D}, \end{aligned}$$
(6)
the three surf source functions can be rewritten as: from DeLeeuw et al. (2000)
$$\begin{aligned} \frac{\hbox {d}F}{\hbox {d}D_{80} }= & {} 7.11 \times 10^{5}\exp (0.23U_{10} )D_{80} ^{-1.65} (0.8<D_{80} <10\,\upmu \hbox {m}), \end{aligned}$$
(7a)
from Clarke et al. (2006)
$$\begin{aligned} \frac{\hbox {d}F}{\hbox {d}D_{80} }=0.217\sum _{j=0}^5 {\beta _j \left( {\frac{D_{80} }{2}} \right) } ^{j-1} \quad (0.02<D_{80} <16\,\upmu \hbox {m}), \end{aligned}$$
(7b)
from Van Eijk et al. (2011)
$$\begin{aligned} \frac{\hbox {d}F}{\hbox {d}D_{80} }=0.707\times 10^{10(1-\in ^{-0.35})}D_{80} ^{-1.5} \quad (0.25<D_{80} <5\,\upmu \hbox {m}). \end{aligned}$$
(7c)
Fig. 1

Surf-zone sea-salt aerosol flux \(\hbox {d}F/\hbox {d}D_{80}\) for various wind speeds (U) and wave heights (H); \(\hbox {d}L\) denotes the DeLeeuw et al. (2000) source function and vE the Van Eijk et al. (2011) source function

Flux data obtained from the three expressions are plotted in Fig. 1 as a function of aerosol diameter. As the DeLeeuw et al. (2000) formulation is dependent on wind speed, and the Van Eijk et al. (2011) function on the incident wave height, the environmental conditions have been roughly matched by assuming that the waves are fully developed as wind waves, which is clearly a simplification for the near-shore wave field. For example, a wind speed of \(7\,\hbox {m s}^{-1}\) then yields waves of 1 m in height. Since the Clarke et al. (2006) expression does not depend on the wind speed or waves, only a single curve is plotted.

Figure 1 shows that the three expressions react in a more or less well-pronounced manner to changes in environmental conditions. For the considered wind-speed range of \(4{-}10\,\hbox {m s}^{-1}\), the sea-salt aerosol fluxes predicted by Van Eijk et al. (2011) vary by more than three orders of magnitude, those predicted by DeLeeuw et al. (2000) vary by less than one order of magnitude and those predicted Clarke et al. (2006) show no variation. Furthermore, Fig. 1 shows that the flux curves obtained from the DeLeeuw et al. (2000) expression for a \(10\,\hbox {m s}^{-1}\) wind speed, the Van Eijk et al. (2011) flux function at 1 m wave height (equivalent to a \(7\,\hbox {m s}^{-1}\) wind speed), and the Clarke et al. (2006) equation almost coincide. Since Clarke et al. (2006) made their measurements for a wind speed of \(7.3\,\hbox {m s}^{-1}\), it thus seems that the DeLeeuw et al. (2000) source function is somewhat conservative with respect to wind speed as compared to the functions given by Clarke et al. (2006) and Van Eijk et al. (2011).

We now need to select one of these three source functions as input into the model MACMod. In our opinion, the source function should depend on the wave properties rather than on the wind speed. While one could argue that wind speed drives the wave-breaking process for onshore flow, offshore flow reduces the wave breaking that is incident on the beach. At that time, wind speed and wave breaking are inversely related, as demonstrated by Van Eijk et al. (2011). Since the DeLeeuw et al. (2000) source function is based on wind speed, and the Clarke et al. (2006) function is invariant with respect to wave parameters, the Van Eijk et al. (2011) function is selected as the primary choice for the surf-generation function in the model MACMod.

4 Modelling of Horizontal Aerosol Transport

4.1 The Model MACMod

The model MACMod (Tedeschi and Piazzola 2011) is an unsteady two-dimensional model resolving the budget equation for the sea-salt aerosol concentration over a Cartesian grid (regular in the horizontal direction and stretched in the vertical direction), using the finite-volume method (Patankar and Spalding 1972; Patankar 1980). It evaluates the classical aerosol concentration \(C = {\hbox {d}N/\hbox {d}r}_{80}\) (in \(\hbox {m}^{-3 }\upmu \hbox {m}^{-1})\) for a particle of radius r at 80% relative humidity (RH). The governing equation for C at a given radius r, is given by,
$$\begin{aligned} \frac{\partial C}{\partial t}+(\mathbf{v}\nabla )C=-\nabla \mathbf{F}+S, \end{aligned}$$
(8)
where \(\partial C/\partial t\) is the rate of change of the concentration, v is the velocity, \((\mathbf{v}\nabla )C\) represents the advection flux, S is the volume source-sink term accounting for condensation, evaporation, coagulation and nucleation (not activated in the present simulations), and F is the combined horizontal \((F_{\mathrm{h}})\) and vertical \((F_{\mathrm{z}})\) aerosol flux excluding advection. The horizontal aerosol flux \(F_{\mathrm{h}}\) can be neglected compared to the horizontal advection flux, noting that the vertical flux \(F_{\mathrm{z}}\) includes both gravitational settling and the turbulent dispersion flux.

Aerosol emission (production) and removal (deposition) at the sea surface are taken into account as additional terms for the vertical flux in the first layer. The deposition flux (downward from the domain) is proportional to the concentration and the deposition velocity \(V_{\mathrm{d}}, F_{\mathrm{d}} = -V_{\mathrm{d}}C\). The deposition flux at the sea surface is taken from Vignati et al. (2001), which predominantly depends on the particle radius and the drag coefficient \(C_{\mathrm{d}}\) at the sea surface. Alternatively, the deposition process over non-water surfaces can be modelled using a constant deposition velocity.

Sea-salt aerosols enter the model domain in the bottom (horizontal) layer, within the cells that are located over water. The production flux is described by two source functions: a surf-aerosol source function for the cells corresponding to the surf zone (see Sect. 3 for this expression), and an oceanic source function in the remaining over-water cells. The oceanic source function is taken from Monahan et al. (1986) (specified in \(\upmu \hbox {m}^{-1 }\hbox {m}^{-2 }\hbox {s}^{-1})\),
$$\begin{aligned} \frac{\hbox {d}F}{\hbox {d}r}=1.373\times U_{10}^{3.41} r^{-3}\left( {1+0.057r^{1.05}} \right) \times 10^{1.19\exp (-B^{2})}, \end{aligned}$$
(9)
with \(B=\frac{0.38-\log _{10} (r)}{0.65}\). The Monahan et al. (1986) source function is generally considered applicable for particles with radii around \(1\,\upmu \hbox {m}\), and has been incorporated by Gong et al. (1997) into a single one-dimensional sea-salt model. It was found to produce a reasonable emission rate for particles down to \(0.1\,\upmu \)m in size. For coastal seas, Piazzola et al. (2009) confirmed its appropriateness for onshore flow, and a modified version was suggested for offshore flow (Demoisson et al. 2013). However, simulations with this modified source function (plots not shown) did not significantly change the results presented herein.
An upwind scheme is used for the advection term and an implicit scheme is used for time integration. Turbulence closure uses the classical first-order eddy diffusion coefficient K, taking into account the atmospheric stratification and the surface roughness. For the first few tens of metres above the surface (the surface layer), K is given by,
$$\begin{aligned} K=\frac{\kappa \;u_{*} z}{\phi (z/{L)}}, \end{aligned}$$
(10)
where \(\kappa = 0.4\) is the von Karman constant, z is the height above the surface, L is the Obukhov length, \(u_{*} \) is the friction velocity, and the stability function \(\phi (z/L)\) is given by Businger et al. (1971). The parameter z / L can be determined from the bulk Richardson number \({Ri}_{\mathrm{b}}\), which is based on an approximate expression given by Graf et al. (1984), applicable over the ocean,
$$\begin{aligned} Ri_{\mathrm{b}} =\frac{gZ(T_{air} -T_{sea)} }{T_{air} U_{10}^2 }, \end{aligned}$$
(11)
where \(\Delta T=T_{air} -T_{sea} \) is the air–sea temperature difference. The parameter z / L is then calculated according to Deardorff (1968),
$$\begin{aligned} \frac{z}{L}= & {} \beta Ri_{\mathrm{b}} \qquad \hbox { (unstable)}, \end{aligned}$$
(12a)
$$\begin{aligned} \frac{z}{L}= & {} \frac{\beta Ri_{\mathrm{b}} }{1-\alpha Ri_{\mathrm{b}} }\qquad (\mathrm{stable}), \end{aligned}$$
(12b)
where \(\beta \) is in the range of 4–13 (Hsu 1989). For the marine atmospheric boundary layer, experiments have shown an optimum \(\beta \approx 10\) (Grachev and Fairal 1997); the parameter \(\alpha \) has a value \({\approx }5\) (Dyer 1974). The expression for stable stratification cannot be used for values of \({Ri}_{\mathrm{b}} \ge 0.2\), and we then assume that \(\phi \) becomes large enough (and K small enough) so that turbulent diffusion can be neglected.

4.2 Numerical Settings

We used the model MACMod to perform numerical simulations of aerosol concentration up to tens of km downwind of the surf zone. The horizontal (x coordinate) calculation domain was 30 km, divided into 300 cells of 100 m in length. In the vertical (z) direction, the domain extended by 600 m, divided into 23 cells with an irregular height step, with smaller steps close to the sea surface. The height of the lowest grid cell was chosen as 0.5 m. The atmospheric surface layer (i.e., up to 40 m) was represented by 11 grid cells and the remaining 12 grid cells were used to describe the atmosphere aloft.

The numerical boundary conditions were as follows: at the top boundary, the concentrations were forced to zero, and we verified that concentrations at the higher altitudes were marginal, i.e., that the upper boundary was high enough to allow unforced vertical dispersion of the aerosol. At the bottom boundary, deposition and source fluxes were assumed to be constant with time. The upwind boundary conditions varied for onshore and offshore flow. For onshore flow, an advection component was specified using the Mediterranean extinction aerosol model (MEDEX, Piazzola et al. 2003), whereas an aerosol-free atmosphere (no advection component) was assumed during offshore flow. While this is obviously a simplification, Van Eijk et al. (2011) have shown that the surf-generated aerosol concentrations largely exceed the background concentrations arriving from overland.

Four sets of simulations were performed:
  1. (A)

    The capabilities of the model MACMod were assessed by comparing the model results to aerosol concentrations measured during the transport experiment (see Sect. 2). The simulations were made for three radii (0.5, 1 and \(2.5\,\upmu \)m) and by using both the Van Eijk et al. (2011) and the DeLeeuw et al. (2000) surf source functions. The model was run for the environmental conditions observed during the transport experiment: \(U_{10} = 5\,\hbox {m s}^{-1}\), unstable atmospheric stratification with \(\Delta T = -6\,\hbox {K }(T_{air}= 14\,^{\circ }\hbox {C}\), \(T_{sea} = 20\,^{\circ }\hbox {C}\)), \(H_{rms} \approx 0.45\,\hbox {m}\) and a surf-zone length of 20 m. Figure 2 shows that the environmental conditions were fairly constant during the experiment.

     
  2. (B)

    In order to estimate the effect of the atmospheric stratification on the horizontal (offshore) transport of surf-generated sea-salt aerosol and the extent of the surf-zone influence, a series of numerical simulations were defined. Three values of \(U_{10} \) (5, 10 and 15 m s\(^{-1})\), one radius value \((1.0\,\upmu \hbox {m})\) and three values of \(\Delta T ({-}6\) K, zero, \(-6\) K, corresponding to unstable, near-neutral and stable stratifications) were used.

     
  3. (C)

    For near-neutral stratification, the offshore aerosol concentration was further considered as a function of the sea-salt aerosol source function. Three simulations were undertaken: surf-zone production only (using the flux function from Van Eijk et al. 2011), open-ocean production only (using the expression given by Monahan et al. 1986) and simultaneous surf-zone and open-ocean production (using both expressions).

     
  4. (D)

    Finally, simulations were undertaken for near-neutral stratification and onshore flow. At the upwind boundary, a vertical concentration profile for marine aerosols was specified as a function of the environmental conditions. Two constant deposition velocities were used (for grass and tree cover), accounting for aerosol removal at the flat land surface downwind of the surf zone.

     
Fig. 2

Transport experiment on 5 November 2007. Time series for the air temperature, the sea temperature (a) and the wind speed (b)

5 Results and Discussion

5.1 Comparison Between the Measured and Modelled Concentrations (Simulation Set A)

Figure 3 shows the experimental and numerical aerosol concentrations downwind of the shoreline at 3 m above sea level for particles with radii of 0.5, 1 and \(2.5\,\upmu \hbox {m}\). In the figure, the offshore flow is oriented from left (shoreline at \(x = 0\)) to right (out to sea). Both the DeLeeuw et al. (2000) and Van Eijk et al. (2011) source functions were used for the sea-salt aerosol surf-zone production.
Fig. 3

Transport experiment on 5 November 2007. Aerosol concentration downwind of the shoreline at 3 m above sea level for \(r = 0.5\,\upmu \hbox {m}\) (a), \(r = 1\,\upmu \hbox {m}\) (b), \(r = 2.5 \upmu \hbox {m}\) (c). Experimental data are represented by black triangles, the blue solid line denotes the Van Eijk et al. (2011) source function (abbreviated to vE), and the dashed green curve denotes the DeLeeuw et al. (2000) source function (abbreviated to \(\hbox {d}L\))

Focussing first on the experimental data, a small decrease in the concentration (30–40% for the three radii) is observed in the first 2 km downwind of the surf zone, after which the concentration remains fairly constant until 12.5 km, the longest distance taken by the boat. Van Eijk et al. (2011) estimated that the uncertainty in their measurements is about a 0.3 logarithmic unit or a factor of 2. This uncertainty results from the inherent inaccuracy of the instrument (evaluated from an inter-comparison between several identical instruments), the slight changes in environmental conditions during the 4-h time frame of a single transport experiment, and the difficulty in making the observations on a small boat in high-wave conditions. The estimated uncertainty implies that the near-shore concentration peak is at the limit of being statistically significant and that the concentration must essentially be considered constant with distance. This behaviour may seem surprising at first, as one would expect a strong concentration peak close to the shoreline where sea-salt aerosol production in the surf zone is thought to be several orders of magnitude higher than that over the open ocean (DeLeeuw et al. 2000). One would then expect a sharp decrease with an increase in the distance offshore because of the gravitational settling of the surf-generated particles as they move out over the open ocean.

Two explanations can be put forward for the absence of this expected behaviour: (1) the influx of a large background concentration at the upwind boundary of the domain, consisting of aerosols generated over the land or over the sound west of Duck; and (2) the generation of a large amount of sea-spray particles over the open ocean, which replace the surf-generated particles as they settle due to gravitation.

We rule out explanation (1), since the aerosol concentrations were measured upwind and downwind of the surf zone, and the concentration added by the surf zone was clearly visible in the data (0.3–0.4 logarithmic units for particles of \(0.5{-}2.5\,\upmu \hbox {m}\) radius for the conditions during the transport experiments). Furthermore, an advected component would likely exhibit differences in gravitational settling for smaller and larger particles, whereas the trends in Fig. 3 are identical. On the other hand, during offshore flow conditions, the surf zone is relatively shallow and the wave height increases with distance offshore. It may thus be that open-ocean production was relatively strong compared to surf production. This hypothesis is further discussed in Sect. 5.3.

When considering the model data and measurements, Fig. 3 shows that the DeLeeuw et al. (2000) source function yields 2–3 times higher aerosol concentrations than the Van Eijk et al. (2011) source function. This corroborates the finding on the difference between the DeLeeuw et al. (2000) flux computed with a \(5\,\hbox {m s}^{-1}\) wind speed and the Van Eijk et al. (2011) flux computed with a 0.45-m wave height (cf. Sect. 3.2 and Fig. 1). The Van Eijk et al. (2011) flux matches the experimental data well for the 1-\(\upmu \hbox {m}\) particles (panel b) and relatively well (within the measuring error) for the 2.5-\(\upmu \hbox {m}\) particles (panel c). In contrast, the Van Eijk et al. (2011) flux underestimates the 0.5-\(\upmu \hbox {m}\) particles (panel a) by a factor of 3–4. This may be due to the relatively weak surf-production strength at this radius (Van Eijk et al. 2011), which causes the background concentration originating from upwind regions to dominate the total concentration.

Upon closer inspection, Fig. 3 reveals that the behaviour of the numerical aerosol concentration with increasing fetch depends on use of either Van Eijk et al. (2011) or DeLeeuw et al. (2000) source functions. The numerical concentration increases with the Van Eijk et al. (2011) source function, but decreases with the DeLeeuw et al. (2000) function. This reflects the difference in aerosol production of the two functions: at a wind speed of \(5\,\hbox {m s}^{-1}\) (as existed during the experiment, see Fig. 2), the DeLeeuw et al. (2000) function injects more particles into the domain over the surf zone than the Van Eijk et al. (2011) function (see Fig. 1). In accordance with our hypothesis that the surf-generated particles are replaced by ocean-generated particles, we may expect that the numerical concentration tends towards the open-ocean equilibrium concentration at unlimited fetch. Apparently, this lies between the initial concentrations at shorter fetch obtained with the Van Eijk et al. (2011) and DeLeeuw et al. (2000) functions. The comparison between the Van Eijk et al. (2011) and DeLeeuw et al. (2000) source functions should be regarded as a sensitivity analysis: the choice of a particular source function may thus change the absolute numerical concentrations and/or the detailed behaviour of the concentration with fetch. Nevertheless, these differences do not hamper our goal of explaining the (initially surprising) absence of a strong peak in the experimental concentration at short fetch.

In view of the above results, the model MACMod using the Van Eijk et al. (2011) surf source function appears to simulate the aerosol concentration that was measured downwind of the shoreline at Duck with sufficient accuracy. This configuration is thus used further to investigate the physical processes acting during sea-salt aerosol transport. In hindsight, this conclusion may not be surprising, since the Van Eijk et al. (2011) source function was developed with measurements in the same general area and time frame. However, the transport experiment involved a different configuration with measurements from a boat, and the resulting data were not used in the development of the Van Eijk et al. (2011) function. This explains why this function does not exactly reproduce the measurements at very short fetch (cf. Fig. 3). The observed differences of 0.2–0.5 logarithmic units are within the uncertainty range of the Van Eijk et al. (2011) function, as inferred from Fig. 8 in their publication.

5.2 Influence of Atmospheric Stratification (Simulation Set B)

Atmospheric stratification is a governing parameter for the vertical variation of aerosol concentration in the marine atmospheric boundary layer, where unstable conditions induce more efficient vertical turbulent aerosol mixing and stable conditions confine the sea-salt aerosols to a thin layer close to the production zone. The stratification depends on the sensible and latent heat fluxes and the wind speed. The air–sea temperature difference \(\Delta T\) may therefore serve as an indicator for the stratification since it controls the sign of the sensible heat flux: sufficiently large positive or negative values of \(\Delta T\) (in our simulations \({+}\)6 and \({-}\)6 K) thus signal stable or unstable conditions. A value \(\Delta T \approx 0\) indicates near-neutral stratification.
Fig. 4

Aerosol concentration of \(1\,\upmu \hbox {m}\) particles downwind of the shoreline at 3 m above sea level for \(U_{10} = 5\,\hbox {m s}^{-1}\) (a), \(U_{10} = 10\,\hbox {m s}^{-1}\) (b), \(U_{10} = 15\,\hbox {m s}^{-1}\) (c)

The effect of stratification on vertical turbulent aerosol mixing was previously studied with the model MACMod by Tedeschi and Piazzola (2011) for the open ocean. Now, the model is used with both the open ocean and the surf source functions. Sea-salt aerosol concentrations were modelled for a radius \(r = 1\,\upmu \hbox {m}\), and results are shown in Fig. 4, which depicts the aerosol concentration at 3 m height downwind of the surf zone for \(U_{10} = 5\), 10 and \(15\,\hbox {m s}^{-1}\). The wind speed affects the amount of aerosols produced over the surf zone (through the approximate relations between wind speed, wave height and wave-energy dissipation in the Van Eijk et al. (2011) source function), which is reflected in the concentration peaks near the shoreline (Fig. 4): \(8.2\times 10^{5}\) particles \(\upmu \hbox {m}^{-1 }\,\hbox {m}^{-3}\) for \(U_{10} = 5\hbox { m s}^{-1} (H_{rms} = 0.45\,\hbox {m}), 3.4\times 10^{7}\) particles for \(U_{10} = 10\,\hbox {m s}^{-1} (H_{rms} = 2.3\,\hbox {m})\) and \(6.1\times 10^{7}\) particles for \(U_{10} = 15\,\hbox {m s}^{-1}(H_{rms} = 4.2\,\hbox {m})\).

In passing, we note that the highest wind speed of \(15\,\hbox {m s}^{-1}\) is outside the validity regime of the open-ocean source function given by Monahan et al. (1986). Furthermore, at this wind speed, the height of 3 m at which we monitor the numerical results is only just above the wave crests, which are not taken explicitly into account by the model MACMod. In this respect, our numerical results at \(15\,\hbox {m s}^{-1}\) may be less realistic than at lower wind speeds and they are only used to establish trends in comparison with simulations at lower wind speeds.

Figure 4 shows that, as expected, in all cases the stable thermal layer tends to restrict the aerosols close to the sea surface, resulting in an increase compared to the near-neutral case. In contrast, thermal instability tends to decrease the aerosol concentration as particles are lifted upwards by turbulence dispersion.

As noted from the \(Ri_{\mathrm{b}}\) expression (Eq. 11), the wind speed also affects vertical dispersion. This is illustrated in Table 1, which lists the concentration ratios 25 km offshore between the stable and near-neutral, and between the unstable and near-neutral, stratifications. The Table shows that the ratios approach unity for high wind speeds where the stability tends to approach neutral conditions. The bulk Richardson number values are \(Ri_{\mathrm{b}} =\pm 0.08\), \(Ri_{\mathrm{b}} =\pm 0.02\) and \(Ri_{\mathrm{b}} =\pm 0.01\) for \(U_{10} = 5\), \(U_{10} = 10\) and \(U_{10} = 15\,\hbox {m s}^{-1}\), respectively.
Table 1

Sea-salt aerosol concentration ratios between stable and near-neutral (S/N) and between unstable and near-neutral (U/N) stratifications, 25 km offshore at 3 m height for \(r = 1 \upmu \hbox {m}\)

\(U_{10} (\hbox {m s}^{-1})\)

5

10

15

S/N

1.63

1.3

1.15

U/N

0.79

0.87

0.92

Fig. 5

Aerosol concentration downwind of the shoreline at 3 and 10 m heights above sea level for \(r = 1\,\upmu \hbox {m}\) and \(U_{10} = 5\,\hbox {m s}^{-1}\) for stable \((Ri_{\mathrm{b}} = 0.08)\) and unstable \((Ri_{\mathrm{b}}={-}0.08)\) conditions

Figure 5 shows longitudinal profiles of the sea-salt aerosol concentration for the first few km offshore for \(U_{10} = 5\,\hbox {m s}^{-1}\), at 3- and 10-m heights, and for stable and unstable stratifications. At 3-m height, the concentration is initially lower in stable conditions than in unstable conditions, because turbulent dispersion from the surf-production zone at the surface to the probe height of 3 m is less efficient. Further away from shore, the concentration at the height of 3 m in stable conditions becomes respectively higher, as the more efficient vertical dispersion in unstable conditions mixes more particles upwards. At 10-m height, the same behaviour can be observed, but the cross-over point is at a greater distance from the shore as the particles must now be dispersed up to 10 m, which also causes the initial concentration difference to be more pronounced. This behaviour corroborates Kusmierczyk-Michulec et al. (2013). At higher wind speeds (not shown here), the effect becomes less marked as the stratification has a smaller influence with respect to the increased mechanical turbulence.
Fig. 6

Aerosol concentration downwind of the shoreline at 3-m height for \(r = 1\,\upmu \hbox {m}, U_{10} = 15\,\hbox {m s}^{-1}\) (a), \(U_{10} = 10\,\hbox {m s}^{-1}\) (b), \(U_{10} = 5\,\hbox {m s}^{-1}\) (c). The abbreviations SZ and OO denote surf zone and open ocean, respectively

5.3 Influence of the Surf Zone on the Offshore Sea-Salt Aerosol Concentration (Simulation Set C)

This section focuses on the individual contributions of surf-zone and open-ocean aerosol production. The characteristics of the Duck site and of the previous simulations (i.e., the width of the surf zone, slope of the beach, wave heights and associated wind speeds, and representative particle diameters) have all been retained to allow for a comparison with the results reported in Sects. 5.1 and  5.2. Three sets of simulations were performed: one with only surf-zone production, one with only open-ocean production and one with both. The offshore concentration profiles for 1-\(\upmu \hbox {m}\) particles at 3-m height in near-neutral stratification are shown in Fig. 6 for the usual wave-height/wind-speed values.

Figure 6 shows that the ratio of surf-generated and ocean-generated aerosol particles changes with increasing offshore distance x. However, the horizontal scale on which this occurs depends strongly on the environmental conditions. For higher wind speeds/higher wave heights (panels a and b), the surf-zone production is several orders of magnitude higher than that in the open ocean. Hence, the total concentration exhibits a peak over the surf zone. Away from the shoreline, there is no more production of surf-aerosol particles and their concentration starts to decrease. At the same time, the production of the oceanic aerosol commences and a build-up of the oceanic concentration with increasing offshore distance is observed. The oceanic contribution cannot fully compensate for the loss of surf particles and the total concentration thus decreases for the first 5–10 km offshore before reaching a more or less constant value. The surf and oceanic contributions become equal at approximately 30–35 km downwind of the shoreline. This corroborates well with the results reported by Vignati et al. (2001), who placed the break-even point at 40 km offshore for a wind speed of \(8\,\hbox {m s}^{-1}\).

For a lower wind speed/lower wave height (Fig. 6c), the production over the surf zone is less intense and the aerosol concentration produced over the ocean equals the decreasing surf-aerosol concentration already at 6 km offshore. Eventually, the oceanic production results in a larger concentration offshore than was initially present over the surf zone. Hence, the overall horizontal concentration profile does not exhibit a clear peak over the surf zone or a decrease with increasing offshore distance. Instead, a constant or even slightly increasing concentration is observed. This behaviour of the overall concentration curve corresponds quite well with the experimental observations (Fig. 3b), which were obtained for a wind speed of \(5\,\hbox {m s}^{-1}\) (Fig. 2). It can thus be concluded that the simulations by the model MACMod reveal the relative role of surf-zone and open-ocean production and thereby provide an explanation for the absence of the behaviour expected by Van Eijk et al. (2011), i.e., a rapid decrease of the aerosol concentration as the boat sails away from the coast.

Figure 7 shows the relative contribution of surf aerosol to the total concentration as a function of distance to the shore. \(R_{SZ/T}\) is defined as the ratio of surf-generated particles and the total concentration. The break-even points between the surf-generated sea-salt aerosol and oceanic sea-salt aerosol are reached at 30 km offshore for a wind speed of \(15\,\hbox {m s}^{-1}\), at 35 km for a wind speed of \(10\,\hbox {m s}^{-1}\) and at 7 km for a wind speed of \(5\,\hbox {m s}^{-1}\). Furthermore, Fig. 7 shows that the decrease in the relative contribution of surf-generated sea-salt aerosol is more rapid and more pronounced for a wind speed of \(5\,\hbox {m s}^{-1}\). This difference in behaviour and unexpected reversal of the break-even distance reflects the interplay of multiple processes that depend differently on wind speed and wave height, whereas the variation in wave height over the three cases is much larger (by a factor of 10) than the variation in wind speed (by only a factor of 3). The model MACMod provides the overall result of these interacting processes (generation, turbulent dispersion, horizontal transport, deposition) and Fig. 7 shows that these overall results are not linearly related to wind speed or wave height.
Fig. 7

Ratio of surf-generated particles and the total concentration \(R_{SZ/T}\) for 1-\(\upmu \hbox {m}\) particles downwind of the shoreline at 3-m height

5.4 Influence of the Surf Zone on the Onshore Sea-Salt Aerosol Concentration (Simulation Set D)

Simulations were also undertaken for an onshore flow, with the main flow from the open sea to the land. This implies that the background component entering the upwind boundary of the domain is maritime in nature. The magnitude of the background component was evaluated by the parametric aerosol model MEDEX (Piazzola et al. 2003) that gives the concentration at 10-m height \(\hbox {d}N_{10}/\hbox {d}r\) as a function of various environmental parameters, including wind speed. For near-neutral stratification and the usual wind-speed/wave-height values (\(U_{10} = 5\), \(U_{10} = 10\), \(U_{10} = 15\,\hbox {m s}^{-1}\) and \(H_{rms} = 0.45\,\hbox {m}, H_{rms} = 2.3\,\hbox {m}, H_{rms} = 4.2\,\hbox {m}\), respectively), the model MEDEX yielded \({\hbox {d}N}_{10}/{\hbox {d}r} = 4.2\times 10^{6}\) particles \(\upmu \hbox {m}^{-1}\,\hbox {m}^{-3}, \hbox {d}N_{10}/\hbox {d}r = 7\times 10^{6}\) particles \(\upmu \hbox {m}^{-1}\,\hbox {m}^{-3 }\) and \({\hbox {d}N}_{10}/{\hbox {d}r} = 1.17\times 10^{7}\) particles \(\upmu \hbox {m}^{-1 }\,\hbox {m}^{-3}\), respectively. A vertical profile of the concentration \(\hbox {d}N(z){/}\hbox {d}r\) was then crafted using,
$$\begin{aligned} \frac{\hbox {d}N(z)}{\hbox {d}r}=\frac{\hbox {d}N_{10} }{\hbox {d}r}\;\exp \;\left( {\frac{z-10}{H}} \right) , \end{aligned}$$
(13)
where H is the mixed-layer depth, which was set to 1000 m.
Fig. 8

Aerosol concentration downwind of the shoreline for onshore flow at 3-m height and for \(r = 1\,\upmu \hbox {m}, U_{10} = 5\,\hbox {m s}^{-1}\) (a), \(U_{10} = 10\,\hbox {m s}^{-1}\) (b), \(U_{10} = 15\,\hbox {m s}^{-1}\) (c). The abbreviations SZ and OO denote the surf zone and the open ocean, respectively

The model MACMod further requires the surf-zone width and the deposition velocity. On the basis of observations made during the surf-zone experiment, the surf width for onshore flow was set to a value of 100 m (compared to 20 m that was used for offshore flow). Obviously, this value will differ with the environmental conditions and bottom topography. A constant deposition velocity was set to account for aerosol removal over a flat land surface consisting of grass or trees. According to Petroff et al. (2008), the roughness lengths for grass and tree cover are \(z_{0} = 0.01\) and \(z_{0}= 1\,\hbox {m}\), and the deposition velocities for 1-\(\upmu \hbox {m}\) particles are \(V_{\mathrm{d}} = 10^{-3}\) and \(V_{\mathrm{d}} = 10^{-2}\,\hbox {m s}^{-1}\), respectively.
Fig. 9

Ratio of surf-generated particles and the total concentration \(R_{SZ/T}\) of 1-\(\upmu \hbox {m}\) particles at 3-m height over grass (a), over trees (b)

Figure 8 shows the results of the model MACMod simulations for onshore flow for the three usual wind-speed values and the two categories of land cover. In the figure, the onshore flow is oriented from left (shoreline at \(x = 0.1\,\hbox {km}\)) to right (inland). Each panel shows the total concentration, as well as the surf-zone contribution only, at 3-m height as a function of the downwind distance from the shoreline. All panels show that the concentration decreases with downwind distance, and more so over an efficient deposition surface (trees). In that last case, at least 90% of the surf-produced sea-salt aerosol is deposited on the ground in the first km downwind. Furthermore, the concentration decrease is more pronounced for the aerosol generated over the surf zone (especially visible for advection over tree cover or at low wind speed). This is explained by the extent of vertical mixing that takes place. The surf-aerosol particles are still close to their production zone (at downwind range 0–0.1 km) and vertical mixing has just started, whereas the open-ocean aerosol particles entering the domain at the upwind boundary are well mixed throughout the boundary layer. Consequently, there is a downward flux of oceanic aerosols from aloft that replenishes the deposition loss near the surface, leading to a less pronounced concentration decrease.

The impact of the surf zone on the total sea-salt aerosol concentration downwind varies with wind speed/wave height and land-surface roughness. Figure 9 depicts the ratios between the surf contribution and the total concentration \(R_{SZ/T}\) over grass and tree land cover. At low wind speed (low wave height), the surf production is not very efficient and consequently, the maximum ratio is only 50–60% and it falls off quickly with increasing onshore distance. When surf production becomes more important (higher waves), the surf-produced sea-salt aerosol can dominate the total concentration (up to 95%) and over a surface with low deposition velocity (grass), the contribution remains close to 90% at 20 km onshore. Over a surface with a high deposition velocity (trees), the contribution decreases more strongly, but it remains at approximately 40% at 15 km onshore.

6 Summary and Discussion

The contribution of the surf zone to the sea-salt aerosol concentration in coastal areas has been investigated using the numerical model MACMod. The model MACMod used the Monahan et al. (1986) aerosol source function for the open ocean (dependent on wind speed) and the Van Eijk et al. (2011) aerosol source function for the surf zone (dependent on wave-energy dissipation). The latter choice was based on a review of the existing literature and a comparison of the various flux equations in terms of diameter \(D_{80}\) and number flux \({\hbox {d}F/\hbox {d}D}_{80}\) (Fig. 1). For low wind speeds, the model MACMod results are compared to experimental data reported by Van Van Eijk et al. (2011). Figure 3b demonstrates that the model correctly reproduces the shape of the horizontal concentration profile, and that the absolute concentrations are best reproduced when using the surf source function of Van Eijk et al. (2011) that is driven by wave-energy dissipation, rather than by wind speed.

The relative magnitude of the two source functions in terms of aerosol produced per unit surface and per unit time affects the simulations. Unfortunately, there is a significant uncertainty introduced here by the formulation of the Van Eijk et al. (2011) source function in terms of wave-energy dissipation, which necessitated adopting approximate relations between wave-energy dissipation and wave height (Eq. 5), and wave height and wind speed. For the latter, the existence of fully-developed waves was assumed, which is questionable for a near-shore environment with offshore flow. However, at the time of the measurements, in the aftermath of an autumn storm, the wave-field propagation was opposite to the wind field, which, to some extent, justifies our choice. Furthermore, sensitivity studies with the model MACMod (not shown here) demonstrated that minor modifications in the wind-speed/wave dependencies of the two aerosol production functions did not significantly alter the conclusions presented below.

In a series of numerical simulations, the effect of atmospheric stratification on the offshore transport of surf-generated sea-salt aerosol was assessed (Fig. 4). While the absolute amount of particles does not change, particles distributed differently in the atmosphere. Stable stratification tends to confine particles to the lower atmosphere, resulting in a local concentration peak compared to the near-neutral case. The concentration of 1-\(\upmu \hbox {m}\) particles increases by approximately 63% at 3-m height for a wind speed of \(5\,\hbox {m s}^{-1}\), and when the air–sea temperature difference \(\Delta T = 6\,\hbox {K}\). In contrast, unstable stratification decreases the near-surface concentrations as the particles are dispersed upwards. The concentration decrease is approximately \({-}\)21% for \(\Delta T = -6\,\hbox {K}\). At higher wind speeds \((15\,\hbox {m s}^{-1})\), mechanical turbulence dominates, the stability tends to the neutral case, and the concentration increase and decrease are only \({+}\)15 and \({-}\)8%, respectively.

Furthermore, the model MACMod was able to numerically demonstrate that the aerosol particles generated over the surf zone are gradually replaced by oceanic particles as the distance to the land–sea interface increases. For strong winds and high waves, the abundance of surf aerosol creates a concentration peak close to the land–sea interface and a decrease in concentration with increasing offshore distance as the oceanic source function cannot fully compensate for the deposition of the surf particles (Fig. 6a). In contrast, for low winds and small waves, there are less surf particles and the initial concentration peak is absent. With increasing offshore distance, the oceanic particles more than compensate for the surf fraction, resulting in a nearly constant or slightly increased concentration (Fig. 6c).

Finally, simulations with the model MACMod were performed for onshore flow. At the upwind boundary of the numerical domain, a vertical concentration profile of marine aerosol generated over the open ocean was imposed. Then, the oceanic and surf-generated aerosol particles were advected over a land surface. Two types of surfaces were considered: grass with low roughness and hence inefficient deposition, and trees with high roughness and hence efficient deposition. As with offshore flow, the effects of the surf zone are more apparent for strong winds, high waves and (in this case) inefficient deposition. Over grass, the surf contribution accounts for 90% of the total concentration up to 30 km inland (the numerical boundary). In contrast, low winds, small waves and efficient deposition cause the surf contribution to diminish rapidly. When advected 1 km inland over a tree surface, the surf contribution accounts for only 20% of the total aerosol concentration, while for grass, this percentage is attained at 15 km inland.

In conclusion, the model MACMod successfully gives insight into fundamental aerosol processes in the coastal region near the land-sea interface: vertical dispersion as a function of stability and horizontal transport during onshore and offshore flow.

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Gilles Tedeschi
    • 1
  • Alexander M. J. van Eijk
    • 2
    • 3
  • Jacques Piazzola
    • 1
  • Jolanta T. Kusmierczyk-Michulec
    • 4
  1. 1.Mediterranean Institute of Oceanography (MIO) - UM 110University of Toulon - CNRS/INSU - IRDToulon cedex 9France
  2. 2.TNOThe HagueThe Netherlands
  3. 3.LHEEA UMR CNRS 6598LUNAM Université - Ecole Centrale de NantesNantesFrance
  4. 4.CTBTOVienna International CentreViennaAustria

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