Atmospheric modeling systems that simulate meteorology, chemistry, or climate include model algorithms for air-surface exchange processes. Surface fluxes of heat, moisture, and momentum are critical elements of meteorology and climate models while chemistry/air quality models also require algorithms for surface fluxes of trace chemical species. Vertical flux of any quantity in the atmospheric surface layer is well described by gradient turbulent diffusion. Momentum flux can be modeled simply by means of turbulent surface layer similarity theory since momentum goes to zero at some finite height, known as the roughness length (z_o), which depends on the characteristics of the surface and vegetation. Sensible heat flux is slightly more complex than momentum flux since thermal exchange processes must interact directly with the surface and turbulent flow cannot extent all the way to the surface because of the “no-slip” condition. Thus, for heat there is an additional consideration of laminar molecular diffusion over a very thin layer in contact with all ground and canopy surfaces. Modeling moisture fluxes adds another element of complexity because of the multiple sources of surface moisture, via evapotranspiration (ET), which is regulated by leaf stomata, soil moisture, which requires diffusion through soil, and surface wetness from rain and dew. The surface fluxes of many chemical species that are involved in air quality modeling have similarities to moisture fluxes, since they may also involve multiple pathways for exchange with the surface, including stomatal, ground, water, built surfaces, and leaf cuticles. For example, in two different field experiments where both moisture fluxes and ozone fluxes were measured by eddy covariance, one for a vineyard and cotton field in California [1] and another for a soybean field in Kentucky [2], the stomatal pathway for ozone and water vapor fluxes were shown to be highly correlated. Thus, modeling chemical dry deposition and bi-directional surface fluxes involve many of the same physical processes and can use many common algorithms with moisture flux calculations in the land surface models of meteorology and climate models, especially for the stomatal component.

While chemical constituents of the atmosphere can undergo a variety of chemical and physical transformations, dry and wet deposition are the ultimate removal mechanisms of mass emitted to the atmosphere. Surface fluxes of some chemical species, notably ammonia [3–5], mercury [6,7], and certain volatile organic compounds (VOCs) [8] are often bi-directional, such that the surface may be alternately a source or sink of atmospheric mass. For other chemicals, particularly biogenic VOCs such as isoprene, terpenes, and alcohols the surface emissions from biological processes are very important atmospheric sources [9].

In addition to their roles as sources and sinks of atmospheric constituents, surface fluxes also have important effects on vegetation, ecosystems, and human health. Risk assessments and setting standards for protecting vegetation and ecosystems from damage by air pollutants has usually involved concentration based indexes such as AOT40 (Accumulated Over a Threshold of 40 ppb) which is used for assessing ozone impacts. A new flux based index called AFstY (Accumulated stomatal Flux above a flux threshold Y) has been proposed to estimate O₃ dose to leaf interiors where damage occurs rather than in the air outside the leaf [10]. A recent study in Europe used the Deposition of Ozone and Stomatal Exchange (DO3SE) model to compute the AFstY index to assess the O₃ impacts on key European tree species [11,12]. Their results showed that the AFstY index differed significantly from the AOT40 over different regions and species.

Until recently, secondary standards for protecting ecosystems from damage caused by NOx and SOx in the U.S. have been based on ambient concentrations even though flux based standards were proposed more than 10 years ago [13]. Recently, however, new SOx-NOx secondary standards are being considered to protect both terrestrial and aquatic ecosystems from acidification and nutrient enrichment. Although the U.S. Clean Air Act requires that regulations must be based on ambient concentration levels, the newly proposed standards include linkages to deposition of SOx and NOx [14] to be computed by the Community Multiscale Air Quality CMAQ model [15]. Therefore, chemical surface flux modeling has become a more important process in air quality models used for regulation assessment and enforcement because environmental standards are now being promulgated that include assessments of deposition effects on ecosystems.

Since industrialization, atmospheric reactive nitrogen concentrations and deposition have increased tremendously [16–18]. Deposition of reactive nitrogen including, ammonia, NO₂, nitric acid, ammonium and nitrate containing aerosols, and organic nitrates has serious deleterious impacts on terrestrial and aquatic ecosystems [19–21]. Thus, modeling anthropogenic and natural emissions, chemical transformations, wet deposition, and surface fluxes is important not only for air quality studies but also for ecosystem impact assessments. Ammonia from fertilizer and livestock operations contribute the largest portion of excess nitrogen emissions to the environment [22]. Accurate accounting of fertilizer sources of ammonia requires development of new modeling techniques such as bi-directional surface fluxes, as well as integration with agricultural management models (see Section 3.3).

This article presents an overview of the current state of science and modeling for surface flux processes in air quality modeling systems. We start with a presentation of the governing principles and equations of air-surface exchange that are applicable to moisture, heat, and momentum in meteorology models and chemical surface fluxes in chemical transport models in Section 2. Then, in Section 3 we focus on modeling techniques for chemical surface fluxes, including gas and aerosol dry deposition and bi-directional fluxes. Section 4 gives an overview of recent advances in dry deposition and bi-directional modeling along with a few examples of model results. Section 5 contains a concluding discussion of limitations of current models and future research and model development directions. As developers of land surface models (LSM) [23,24], dry deposition [25], and bidirectional models [26] we often use the formulation of these models as they are applied in the Weather Research and Forecast (WRF) model [27] and the CMAQ model as examples of parameterization techniques and to illustrate some of the characteristics of model results. Note that much of the description of the dry deposition model used in CMAQ has not been previously published.

Turbulent fluxes of any atmospheric quantity, including heat, moisture, momentum and trace chemical species, can be computed according to Monin-Obukov similarity theory in the atmospheric surface-layer which relates fluxes at height z near the surface to the mean vertical profile: (1) F α ( z ) = w ′ α ′ ¯ = u * k z ϕ h ( z L ) ∂ α ∂ zwhere F_α is the vertical flux of any quantity α, which can be measured as the mean value of the turbulent covariance of w and α wherever stationarity and horizontal homogeneity can be reasonably assumed. Also, u* is the surface friction velocity, k is the von Karman constant, ϕ_m and ϕ_h are non-dimensional profile functions derived empirically from observed data, and L is the Monin-Obukov length scale which is defined as: (2) L = T o u * 3 g k < w ′ T o ′ > )where <w′T_o′> represents the kinematic heat flux and T_o represents the average temperature in the surface layer. Assuming constant flux between some reference height z_r within the surface layer and the surface, Equation 1 can be vertically integrated to give: (3) F α = u * k ( α ( z r ) − α o ) ϕ h n [ ln ( z z o ) − ψ h ( z L , z o L ) ]where ϕ_hn is the non-dimensional temperature profile constant for neutral conditions, ψ_h is the stability correction function for heat, and α_o is the value of α at a micro-distance above the surface where turbulence cannot penetrate. Equation (3) can be rewritten as: (4) F α = ( α ( z r ) − α o ) R a , R a = ϕ h n u * k [ ln ( z z o ) − ψ h ( z L , z o L ) ]where R_a is generally known as the aerodynamic resistance. However, Equation (4) by itself is not very useful because of the difficulty in measuring or modeling quantities at a tiny distance above the surface. We would rather replace α_o with α_s (the quantity at the surface) which can be measured, estimated from surface properties, or assumed to equal zero, as for dry deposition. Again assuming that the flux is constant down to the surface, we can define two more resistances for the quasi-laminar boundary layer (R_b), which is the non-turbulent micro layer adjacent to all surfaces, and a surface resistance (R_s): (5) F α = ( α o − α δ ) R b = ( α δ − α s ) R swhere α_δ represents the quantity α in the air at the surface. Combining Equations (4) and (5) yields: (6) F α = ( α ( z r ) − α s ) R a + R b + R sFor dry deposition α _s is assumed to be zero and Equation 6 is expressed as: (7) F α = V d α ( z r ) , V d = 1 R a + R b + R sFor bi-directional surface flux Eq 6 can be more complicated because α_s may be different for various components of the surface such as the ground and vegetation canopy as described in section 3.3.

R_a represents the resistance to flux by turbulent diffusion through the turbulent surface layer while R_b represents molecular or Brownian diffusion across a very thin quasi-laminar boundary layer adjacent to the surface. A general form of R_b for any scalar quantity was recommended by Wesely and Hicks [28] as: (8) R b = B − 1 u * ( S c P r ) 2 / 3where Sc is the Schmidt number (Sc = v/D), with ν representing the kinematic molecular viscosity, and D is the molecular diffusivity of the scalar quantity. Pr is the Prandtl number, which is the analogous quantity for heat (Pr = v/v_θ), where v_θ is the molecular thermal diffusivity. The parameter B⁻¹ is the inverse Stanton number, a dimensionless heat transfer coefficient. The value of B⁻¹ may depend on the Reynolds number as well as the type of surface roughness. For example, Garratt and Hicks [29] suggested a value of kB⁻¹ = 2 for fully turbulent flow over fibrous vegetative canopies.

Note that, since R_a represents the aerodynamic properties of the turbulent surface layer which depends purely on meteorological parameters and surface characteristics (i.e., surface roughness) it is independent of the chemical or physical properties of the transported scalar. Thus, R_a,once computed, can be used in the surface flux calculations of any scalar. R_b, however, combines meteorological and fluid flow parameters (i.e., u_* and B) with properties of the transported scalar (i.e., molecular diffusivity) and must be computed individually for each chemical species.

Chemical surface fluxes are partially analogous to moisture fluxes, especially for the stomatal conductance, which can be adapted to any gas by scaling by the ratio of molecular diffusivity of the chemical species to the molecular diffusivity of water vapor.

In the early 1980s, two comprehensive reviews of gas and particle dry deposition were published by Hosker and Lindberg [117] and Sehmel [118]. Later, Wesely and Hicks [119], reviewed the state of knowledge on dry deposition. At that time the major processes controlling the deposition of the major inorganic species such as SO₂, O₃ were well understood because of the relative abundance of flux measurement studies of these species. For example, many flux measurements, mostly of ozone but also some of SO₂ and NO₂, have been made by gradient and eddy correlation methods going back several decades, starting in the 1970s [120,121], with many more in the 1980s and 1990s [122–126]. Note that reliable eddy correlation measurements over forest canopies were not feasible until the 1990s [127–129]. Because of the extensive measurement data in the published record the modeling of these species has been somewhat constrained. Significant improvements in the modeling gas dry deposition in recent years have resulted from advances in land surface modeling and closer coupling between air quality and meteorology models. Since stomatal resistance, aerodynamic resistance, quasi-laminar boundary layer resistance, surface and canopy wetness, and snow cover are important parameters for both latent heat flux and dry deposition of many gases, air quality modeling systems that are comprised of meteorology and chemical transport models, such as the WRF-CMAQ system, can use the same parameters for both dry deposition and land surface modeling [25].

Examination of dry deposition velocities modeled by CMAQ along with concurrent parameters from the LSM in WRF demonstrates the close relationships between these processes. Figure 6 shows ozone dry deposition on a 12 km grid simulated by CMAQ for a summer afternoon (19 UT), which is within the range usually measured in the field with peak values of about 1.1 cm/s. The spatial pattern illustrates that ozone deposits primarily through the stomatal pathway since the highest values are in the most vegetated areas. It is interesting that high deposition velocities are simulated for both heavily forested areas in the East and agricultural areas in the Midwest because forests generally have higher LAI than crops but crops have much lower minimum stomatal resistance. Thus, ozone dry deposition velocity closely follows the latent heat flux (Figure 7) except where there is evaporation from rain wetted canopies. Note, however, that there is some enhancement of V_d for wet canopies (e.g., in southern Quebec) because the cuticular resistance for ozone is set to a lower value than would result from Henry's law scaling (also lower than dry cuticular resistance) on the basis of a study comparing measured ozone flux and latent heat flux [2]. CMAQ's dry deposition model has been evaluated through comparison to measurements over soybeans in Kentucky and mixed forest in upstate NY [130] as shown in Figure 8. While there is some lag in the morning increase of V_d for the soybeans, and overprediction at night, the gradual afternoon decline which is caused by stomatal response to lower RH is well represented.

The dry deposition velocity for SO₂ is far more influenced by surface wetness as shown in Figure 2a because of its high effective Henry's law solubility. The highest values of V_d for SO₂ are all in the same areas where LE is high from evaporating surface wetness (see also Figure 2b). In these areas, where rain is occurring currently or recently, peak values are 3–4 cm/s, which indicates that there is very little surface resistance in these areas. Dry deposition of NO₂ and NO were studied in relationship to O₃ and ET in a series of gas exchange experiments involving tobacco and sunflower plants described by Neubert et al. [131]. These experiments showed that NO₂ deposition is almost entirely stomatal with negligible mesophyll resistance, while NO had considerable mesophyll resistance that changed with light intensity. These experiments also showed that ozone deposition occurs by stomatal uptake with negligible mesophyll resistance and destruction at cuticle surfaces. A field measurement study of PAN fluxes over grassland by Doskey et al.[67] found that PAN deposition is mostly via the stomatal pathway but with a non-zero mesophyll resistance resulting in V_d values 0.5−0.3 of V_d for O₃, which is in concurrence with previous studies. However, leaf level measurements reported by Sparks et al. [132] suggest unimpeded stomatal uptake of PAN, indicating insignificant mesophyll resistance and higher deposition velocities. Furthermore, recent eddy covariance flux measurements over loblolly pine by Turnipseed et al. [133] show total surface conductance about twice the stomatal conductance, which suggests significant cuticular uptake. On the basis of these measurement studies the CMAQ was revised in 2007 with higher values of surface reactivity scaling parameter for PAN resulting in maximum deposition velocities close to the values for O₃.

Recently, many more chemical species are being added to dry deposition models as measurement techniques improve in detection capability and response time and the needs of the modeling community extend to more environmental issues such as air toxics and ecosystem impacts. For example, many toxic gases have been added to the CMAQ model in recent years, thereby requiring estimates of dry deposition velocity for these chemicals. However, the lipid solubility scaling discussed in Section 3 has yet to be applied to the CMAQ dry deposition model. A recent study by Karl et al. [134] promotes the importance of the dry deposition of oxygenated VOCs, many of which are oxidation products of biogenic VOCs. They found that Methyl vinyl ketone (MVK) and Methacrolin (MAC), which account for about 80% of the initial oxidation products of isoprene, have deposition velocities of similar magnitude as O₃. On the basis of this study CMAQ is being updated to include dry deposition of MVK and MAC. The dry deposition model in AURAMS described by Zhang et al.[46] already includes dry deposition of these species although with small values of V_d than suggested by Karl et al. [134].

Modeling of surface fluxes for air quality modeling involves micrometeorology, plant physiology and biology, surface chemistry, soil hydraulics and physics, agricultural management, spatial descriptions of geophysical characteristics, and most importantly, surface flux measurements for a variety of chemical substances over a variety of landscapes. Uncertainties in parameterizations, incomplete knowledge of processes, limitations to theory, and paucity of detailed data and measurements, combine to limit the realism and accuracy of surface flux models used in large-scale (mesoscale to global) air quality modeling systems. Progress is being made on many of these fronts but significant uncertainties remain. Even for ozone dry deposition, which is the most widely measured substance, current model results still show substantial errors compared to observations (Figure 8). Some of the errors in chemical fluxes have their source in common with the meteorological fluxes (heat, moisture, and momentum), such as the aerodynamic resistance, while other errors are due to incomplete understanding of chemical interactions with surfaces and leaf tissue. Further errors can be attributed to insufficient detail and accuracy in the spatial and temporal representations of landscape, land use, and vegetation in meso to global scale grid models.

Surface flux modeling relies on flux-profile relationships in accordance with Monin-Obukov similarity theory (MOST) in the atmospheric surface layer [135] (Equation 1). The MOST relationships are defined by dimensionless universal profile functions that have been empirically determined from the 1968 KANSAS experiment [136]. Thus, the validity of MOST is limited to flat terrain with uniform landscape and landcover [137]. Not only are MOST-based model calculations less accurate in non-ideal conditions, but also flux measurements are generally unreliable in complex landscapes. For substances that are mainly limited by surface resistances (e.g., O₃, NO₂, PAN), the limitation of MOST and resulting inaccuracies in estimates of R_a in non-ideal conditions such as sloping terrain or patchy land-use will have relatively small effects on V_d calculations [119]. However, for species not limited by surface uptake, such as HNO₃ or other highly soluble species such as H2O₂ or SO₂ when surfaces are wet, V_d estimates should be considered especially suspect in hilly or patchy landscapes.

There are distinct advantages to an integrated or coupled approach to LSM and chemical flux modeling. As meteorology and air quality models become more integrated such as, WRF-Chem [138], WRF-CMAQ [139], COSMO-ART [140], GATOR [141], to name a few, there is more opportunity for integrated surface flux algorithms that share key parameters like R_a, R_st, and R_b between meteorological and chemical flux models. Such integrated approaches not only ensure consistency but also potentially benefit the chemical flux calculations by using a more realistic stomatal conductance estimates from the ET modeling in the meteorological LSM. For example, in the WRF-CMAQ system the latent heat flux is optimized by an indirect soil moisture data assimilation scheme that effectively tunes the stomatal conductance through its dependence on soil moisture [41]. Thus, the resulting stomatal conductance is more constrained and generally more accurate than estimates by stand-alone dry deposition models. In this way, chemical flux models and air quality models automatically benefit as land surface models are improved.

Advancements in land surface and chemical surface flux modeling will depend on improved descriptions of land use and vegetation characteristics. For example, high resolution land use and land cover data from the NLCD, based on 30 m resolution LANDSAT thematic mapper, have recently been incorporated into the WRF-CMAQ system for land surface and chemical flux modeling [142]. Furthermore, a more detailed vegetation dataset is being developed by combining the high spatial resolution land use data from NLCD with county-level tree species data from the Forest Inventory Analysis (FIA) and crop data from the National Agricultural Statistical Service (NASS) [113]. By combining with ecoregion information this dataset will be able to better define key parameters such as minimum stomatal conductance, LAI, and canopy height across continental gridded modeling domains. Ultimately, the same data set with high spatial and vegetation-type resolution will be used for chemical surface fluxes, meteorological land surface modeling, and biogenic emissions.

Chemical, meteorological, and hydrological surface fluxes are key interface processes that link the atmosphere to the terrestrial, aquatic, and marine components of the Earth system. The dry deposition components of air quality models are expanding in scope to include many more chemical species that are important not only for atmospheric constituents but also as inputs to terrestrial and aquatic ecosystems. In addition, there is growing interest in the deposition of toxic contaminants that enter the food chain via air-surface exchange and subsequently impact human health. There has also been an extension to modeling substances that have surface compensation points (e.g., ammonia and mercury) necessitating the development of bi-directional flux capability. The new bi-directional systems often require adjunct land models such as agricultural management models (e.g., EPIC) that are used for ammonia from fertilizer. All of these extensions to the traditional dry deposition models urgently need evaluation and constraint from field and laboratory measurements.