The majority of human activities are confined to the lowest tens of meters of the atmosphere. Inevitably, the focus of air pollution problems that affect human health occurs in these lowest strata of the atmospheric column. There are many important physical and chemical processes that influence air quality in this portion of the atmosphere. The chemical processes of primary importance simulated in Air Quality (AQ) models include photolytic and hydrolysis reactions, radical chemistry, aqueous-phase chemistry, and gas-particle conversion. Similarly, the physical processes of primary importance simulated in an air quality model include source and sink term descriptions of surface exchange, such as emission and dry and wet deposition of gaseous and particulate pollutants; convection and advection; dispersion and diffusion; gradient and counter-gradient fluxes; fog and cloud and precipitation formation; and in-cloud and below-cloud scavenging of gaseous and particulate pollutants. The Planetary Boundary Layer (PBL), the lowest relatively well-mixed atmospheric layer that touches the earth's surface and is capped by a statically stable layer, is the most relevant to all the above issues.

In this study, the surface layer and air-surface exchange processes of five selected air quality forecasting models are compared with respect to their PBL and dry deposition schemes. All of these models are capable of resolving meso-scale features, but nonetheless are of regional to continental coverage and computationally viable for operational forecasting application. The selected models are: (a)The European Center for Medium range Weather Forecast meteorology model (ECMWF) coupled with CHIMERE [1,2]; (b) The Stanford Gas-Aerosol-TranspOrt-Radiation chemistry model (GATOR)— coupled with the General-Circulation-Mesoscale-and-Ocean-Model (GCMOM) [3–5]; (c) The Canadian Global Environmental Multi-scale meteorology model (GEM) coupled with the Modelling Air quality and CHemistry in 15 km horizontal grid resolution (MACH15) [6]; (d) The Weather Research and Forecasting (WRF)—Advanced Research WRF (ARW) dynamic core meteorology model coupled with Chemistry (Chem) model [7,8]; and (e) the WRF—Non-hydrostatic Meso-scale Model (NMM) dynamic core meteorology model [9] coupled with the Community Multi-scale Air Quality model (CMAQ) [10,11].

A brief historical background of these aforementioned models is as follows: CHIMERE stemmed from a box model chemical constituent study of the Paris Area in 1997. It acquired its current name in 2005 as it had incorporated many upgrades and became Europe's premiere tropo-spheric air chemistry model [2] the GATOR-GCMOM started with Gas-Aerosol-TranspOrt-Radiation code (GATOR) in 1990 [3,12], and it acquired fully inline coupled capability with meteorology and feedback of gases and size-resolved aerosols to meteorology through solar and thermal-IR radiative transfer in 1993. In 2001, a 2-D ocean model module was added reflecting the general capability of the General-Circulation-Mesoscale-and-Ocean-Model (GCMOM). GATOR-GCMOM has hitherto been upgraded with several chemistry and cloud-microphysical schemes [3,4,13–17]; GEM-MACH15 is the successor of the Canadian Hemispheric and Regional Ozone and NOx System (CHRONOS), the first Canadian air quality forecasting model that was operated by Environment Canada (EC) between 2001 and 2007. The replacement was a major change from 24 vertical layers [18] to 58 pressure and terrain-following hybrid layers as well as horizontal projection change from polar stereographic to rotated latitude-longitude projection. There are many science module upgrades throughout its decade of service [6] the WRF-Chem model was built by Grell et al. [19] as a fully online meteorological and tropo-spheric chemistry model. It has since added many state-of-science upgrades [8]; and the WRF-NMM-CMAQ model was a successor of the National Center for Environmental Prediction (NCEP) ETA-CMAQ model that provided incrementally enlarging geographical coverage for the U.S. between 2004 until 2006. WRF-NNM-CMAQ replaced ETA-CMAQ since 2007 [9,10].

The selected five models, except for GATOR-GCMOM, are run operationally in forecast mode with single or multiple cycles each day in national or international government institutes or laboratories. WRF/Chem is not run continuously all year round but is run quasi-operationally when there is a specific need such as during field campaigns [20,21]. Among these five models, two are offline coupled (ECMWF-CHIMERE and WRF/NMM-CMAQ) and three are online coupled (GATOR-GCMOM, GEM-MACH15 and WRF/Chem). It is worth noting that ECMWF-CHIMERE is a member of the forecasting model ensemble under the Monitoring Atmospheric Composition and Climate (MACC) initiative [22]. The offline models' lack of feedback in particulate matter (PM) mass loading results in deficiencies in updating the PM direct effect on photolysis rate attenuation and the indirect effect on cloud-microphysical processes.

A substantial review paper by Zhang [23] surveyed online coupled models with both historical and forward-looking perspectives. Although her discussion focused on using online models for regional-to-global chemical climate research, valuable information on the chemistry-PM-cloud-radiation feedbacks of interest to AQ modelers was also provided. The PM-radiation feedbacks are obviously important to regional air quality. Climate change and regional chemical weather inter-relationships are becoming increasingly important research areas for air quality modelers. The differentiation between regional, hemispheric and global air quality-chemistry-climate modeling will inevitably become less distinct. Regional and near continental-scale modelers will continue to simulate beyond medium-to-long range and extend to fully-continental to multi-continental scales, while the global modelers are nearly or already achieving meso-scale resolutions. Long range transport of gaseous and particle-phase pollutants with various source origins have been modeled and measured, rendering convincing evidence that regional pollution is significantly influenced by trans-boundary, inter-continental transport of pollutants [24–27].

The choices of grid staggering of both the horizontal and vertical grids are different among the five models considered. The issue of grid staggering does not apply to the spectral models of ECMWF and GEM-MACH15. In the horizontal direction, GATOR-GCMOM and WRF-NMM use Arakawa B grid staggering and WRF/Chem uses Arakawa C grid staggering. The Arakawa C grid staggering in horizontal space is superior to A- and D-grid staggering in simulating inertial gravity wave processes due to its prevention of spurious energy cascades in incompressible flows [28].

There are two rather strict criteria judging the usefulness of an air quality operational forecast system. These are accuracy and timeliness. The latter is response-driven, since a reasonable lead time is required for the AQ forecast to be disseminated to the end-users so that appropriate actions such as raising an alert can be performed for certain sensitive residents in the affected areas. There are several ways to advance the system's timeliness, among them the following three are often adopted: (a) prolong the forecast-duration of the infrequent model outputs—typically once or twice daily; (b) rapidly refresh the current forecast system by issuing output more frequently—typically hourly or three-hourly [29]; and (c) optimize or modify the AQ code and/or allocate more processing elements to execute the model. The accuracy of the first two strategies depends heavily on the accuracy of initial conditions. In the coming years, Data Assimilation (DA) will likely be used to adjust the first initialization field of AQ models. The importance of this capability will be enhanced by the continuing trend of strengthening standards, such as the US National Ambient Air Quality Standards (NAAQS) for O₃ and PM_2.5. The strengthened standards inevitably tighten the margin of error for AQ forecast models and for AQ impact assessment studies. For regulatory applications, the computational speed of AQ models is not as important.

In an operational setting, both run time memory and model speed are strong constraints. One way to reduce both burdens is to reduce the vertical layers of the AQ model. The AQ model often is designed to have a lower model-top and a set of coarsened layers than those of the meteorological model. In the five models considered here, all of them except WRF/Chem practice such layer-collapsing techniques to reduce the overall computational burden. However, reduction of the number of the vertical layers results in a loss of model accuracy. All four of these models attempt to collapse layers where the impact is as minimal as possible and keep one-to-one corresponding layers wherever the atmospheric column typically exhibits strong gradients in meteorological variables, such as gradients in lapse rates, temperature, humidity, wind speed and direction. Even with optimal selection, a reduction in model accuracy invariably occurs. It is the burden of the modeler to assure that the loss of accuracy is minimal and the mass consistency characteristics of the AQ model are not compromised. For the CMAQ model, a recent study by Otte and Pleim [30] has shown that to ensure mass conservation, the resultant thicker layers obtained by collapsing adjacent layers together should not collapse more than two layers for each resultant layer and layer interfaces of the collapsed layers are chosen from the existing interfaces of the original un-collapsed ones. In addition, running the AQ model in tracer mode studies is essential during the engineering design phase to assure preservation of the model's mass consistency characteristics. One important consideration is the time evolution of layer and domain total mass (see Appendix B).

Using a parameter optimization study, Timin et al. [31] proposed that the most important parameters in controlling surface pollutant concentration in AQ models are: (1) h, PBL height; (2) K_z, eddy diffusivity for heat; and (3) V_d, dry deposition velocity of both gaseous and PM species. Lee et al. [32] studied the importance of h, K_z and its parameterization approach on the surface concentration of ozone. Their study reiterated the findings of many other recent investigations [33,34], described in detail later, that the entire diurnal evolution of the PBL, from its nocturnal shallowness to its increase to a maximum late-afternoon depth, are contributing factors to the surface concentrations of airborne pollutants. In Section 2, we will discuss the PBL modeling approaches of the selected five AQ models.

The PBL is intimately related to heat exchange at the air-surface interface. Evaporation is the primary process that governs the partitioning of exchange rates between the sensible and latent portions of the surface energy budget. Therefore, PBL modeling is strongly coupled with land surface modeling (LSM). Since soil moisture and evaporation processes are key parameterizations needed to model surface latent heat fluxes accurately, identifying the uncertainties in modeling these items is important. These are the main questions for LSM. Xiu and Pleim [35] summarized that the primary goal of LSM is to parameterize surface moisture flux.

The same can be said for the strong coupling between dry deposition modeling and LSM, but for mass fluxes. Dry deposition is recognized as an important pathway among the various removal processes for atmospheric trace species. Among many ongoing investigations to understand and quantify this pathway, recent reinforced research efforts in this area by the U.S. Environmental Protection Agency have already shed light on these many related topics [36-38]. Section 3 will discuss the dry deposition velocity modeling of the selected five AQ models.

It is the surface fluxes that produce the PBL. As incident sunlight is absorbed by the earth's surface, radiant energy is transformed into sensible and latent heat fluxes from the surface. This heating from the bottom of the atmospheric column produces convective eddies that transport heat and water vapor to warm and moisten air parcels above them. Such a convective eddy also consists of a downward element of heavier and cooler air which accelerates the displacement of the ascending element of buoyant air within the eddy. During the growth phase of the PBL, the ascending eddies penetrate the thermal inversion capping the layer top. They transport heat, moisture and kinetic energy upwards in a counter-gradient manner forming the so-called entrainment zone [39]. The ascending air parcel soon equilibrates itself with the penetrated environment through redistribution of momentum, heat and moisture. In doing so, the air parcel expands the PBL top with its penetration height. This growth phenomenon continues until the PBL height attains its maximum height defined by the height of the capping thermal inversion, and reaches its maximum height at hundreds or even thousands of meters Above Ground Level (AGL) in the late afternoon.

However, the PBL is not always well defined, whenever frontal boundaries, deep convection, or multiple levels thermal inversions are involved [40]. In addition, Dabberdt et al. [40] recommended the establishment of a high-resolution nation-wide observing network to monitor the diurnal variation of PBL heights. Their recommendation stemmed from the conclusion that Air Quality modeling accuracy is significantly limited by the lack of knowledge of the PBL structure and dynamics.

At the approach of sunset, the rapid weakening and eventual loss of incident solar flux at the surface causes a second thermal inversion to form in the bottom of the atmospheric column. This second inversion together with the capping inversion defines the so-called nighttime residual layer, and the second inversion caps the lowest layer to form the stable nocturnal boundary layer [39].

The layers prevailing at night pose different challenges for AQ forecasting. The residual layer may have sustained part of its turbulent mixing mechanically with wind shear. A nocturnal low-level jet may form just above the stable boundary layer as surface friction is de-coupled from the residual layer, giving rise to the potential emergence of a strong horizontal wind. Therefore, the residual layer can behave both as a vertical capped reservoir of pollutants, such as ozone, trapped aloft and as a conduit for the rapid transport of these pollutants to destinations far from their origin [41].

Heterogeneity in Land-Use Land-Cover (LULC) can have strong effects on the PBL both in its development and collapse in the diurnal cycle and in its interactions between the various LULC boundaries in affecting pollutant transport characteristics. For instance, a sea- or lake-breeze can suppress PBL growth. Melas et al. [42] concluded from measurements that under specific conditions a sea-breeze can rapidly decrease the growing maritime PBL height soon after the onset of the breeze.

Banta et al. [43,44] provided valuable insight into the intricate interactions among synoptic flow, land-sea-breeze, and PBL diurnal evolution by studying the air quality data collected in the Houston, TX, area where two consecutive intensive field studies were carried out in August and September of 2000 and 2006, respectively. The latter campaign reinforced and extended what was understood by studies made from the first. The daytime sea-breeze in the Houston-Galveston area often starts with an easterly and southeasterly Galveston Bay breeze around 3:00 pm local time. Then within one to two hours, a larger-scale southerly to southeasterly Gulf of Mexico breeze strengthens and reinforces the easterly, southeasterly flows. The diurnal cycle manifests itself in coastal temperature contrast and produces a steady 24-h rotation of the wind direction about the larger-scale synoptic flow of gradient wind. Banta et al. [43] suggested that if the geotropic gradient wind was light to moderate and was not able to prevail over the bay breeze, a stagnant wind condition would arise just within the coastline around the late afternoon hours resulting in high surface concentration of pollutants. Furthermore, the convergence of these countering flows produces intermittent updrafts that often results in detached pollutant plumes which are transported aloft high above the marine boundary layer and which can be subject to a different wind direction. These pollution plumes strongly affect morning rush hour surface pollutant concentration as the thermal inversions break and eddies entrain the plumes down to the surface. However, Banta et al. [43] also report from measurements that h is not strongly correlated with maximum concentration of surface O₃. Other factors, such as the pre-existing stratification condition of the previous night, pose an equally importance influence on the rapid rise of surface O₃ concentration in late morning as well as the eventual daily O₃ peak concentration [43,44].

Soil moisture governs surface evaporation and thus critically controls the PBL characteristics [35,45]. Deep soil moisture has a large inertia and influences longer-term PBL behaviors. The Pleim and Xiu [46] (hereafter PX) LSM includes soil moisture and soil temperature nudging utilizing a four-dimensional data assimilation (FDDA) scheme using model analysis [46-48]. This scheme yields high quality meteorological fields, especially those within the PBL, to enable longer duration forecasts than those LSMs which have no DA capability such as the U.S. National Centers for Environmental Prediction; Oregon State University; Air Force; Hydrological Research Laboratory (Noah) LSM [49,50]. This resonates with the discussion on prolonging current operational AQ forecast in the previous section.

Table 1 summarizes basic model configurations which directly affect the outcome of PBL parameterization results either due to grid structure alignment between the meteorological model (MET) and the chemical transport model (CTM) or other numerical artifacts. Table 1 states the domain map projection and grid structure, the models' overarching assumptions to their primitive equations; microphysical, radiative parameterization; and removal schemes for air pollutants. In the case of land/sea breezes, the thermally driven processes such as the microphysical and radiative processes are likely to be the major drivers. Table 2 continues Table 1 but focusing on turbulent mixing parameterizations within the PBL itself. The choice of schemes and their interplay with other important physical processes are listed for further discussion. Chemical mechanisms and parameterizations that are deemed to have a less direct affect on the PBL scheme outcomes on turbulent mixing of pollutants are not listed here. A thorough listing of such items for the five selected models are available elsewhere: ECMWF-CHIMERE [1,51]; GATOR-GCMOM [17]; GEM-MACH15 [52,53]; WRF/Chem [7]; and WRF-NMM/CMAQ [54,32]. In grid structures, the inter-leaving, “layer-collapsing” practices of ECMWF-CHIMERE, GATOR-GCMOM, GEM-MACH15 and WRF-NMM/CMAQ introduce potential inaccuracies in coupling between the MET and CTM, especially in upper tropo-spheric layers where the jump in inter-leaving selection of layers in MET is the largest. Appendix B presents a study by Ngan [55] where it was shown that the CTM (in this case, CMAQ) layers preserve the domain total mass over time but layer-specific total mass fluctuates temporally.

The truncated model top for ECMWF-CHIMERE, GATOR-GCMOM, GEM-MACH15 and WRF-NMM/CMAQ also incurs some loss of accuracy. Especially for ECMWF-CHIMERE, the model top of CHIMERE is rather low—topped around 3 km AGL.

The lowest mid-layer thicknesses of the five selected models are comparable. They are obviously too high for direct comparison with AQ monitors which are often situated at about 2–10 m Above Ground Level (AGL). Byun and Dennis [56] showed that model mid-layer values should be extrapolated to monitor levels for matched verification.

All five selected models except WRF-NMM/CMAQ use the classic Mellor and Yamada second order level 2.5 closure model to parameterize the turbulent mixing in PBL. Mellor and Yamada [59] used a local closure scheme to calculate turbulence fluxes. WRF-NMM/CMAQ uses Asymmetric Convective Model (ACM) 2 [62], a combined non-local closure and local gradient diffusion scheme to model mixing processes in the PBL. ACM2 is built on the original ACM non-local convective mixing scheme [64]. The extended scheme now includes an eddy diffusion component. A stability regime specific weighting factor governs the partition of mixing between a nonlocal and local diffusion scheme. For instance, for stable and neutral stabilities, all diffusion is attributed to the local diffusion scheme.

In all the turbulent mixing schemes listed in Table 2, considerable parameterization uncertainties warrant methodological procedures to fine tune the various coefficients and empirical constants employed in the schemes. Among these efforts, Nielsen-Gammon et al. [58] performed a rather vigorous parameter optimization study of the new local convection scheme of ACM2 [62]. Equation 1 states the PBL scaling form of K_z, the vertical eddy diffusivity for heat, within the layer.

(1) K z ( z ) = k u ∗ φ h z ( 1 − z / h ) pwhere k is the von Karman constant; φ_h is the similarity function for heat; z is height above ground level; u_*is friction velocity. Their conclusion is that the most sensitive parameter governing Equation 1 is p, the positive exponent to the normalized height. The optimal value of p was found to be 2, dictating a parabolic characteristic of K_z over height. The smaller the value of p, the stronger is the turbulent mixing; and vice versa [58].

Deep soil moisture and temperature govern the slowly varying evaporative component of the soil surface. In all five models, multiple layer soil models are used to calculate heat diffusion and moisture transport of heat and moisture profiles in the top soil stratum. The large inertia of these two quantities makes them attractive variables to be assimilated by observational data. Pleim and Xiu [46] followed the Interactions between Soil, Biosphere, and Atmosphere (ISBA) model [65] to develop an indirect soil moisture nudging algorithm. The scheme uses model biases of the 2 m air temperature to nudge soil moisture. More recently, Pleim and Gilliam [47] added a new technique using biases of the 2 m air temperature to nudge deep soil temperature only during nighttime.

Dry deposition velocities of gaseous species and sedimentation velocities of particulate species are sensitive parameters that influence surface concentrations of atmospheric constituents. Table 3 presents the parameterization schemes used by the five models in this study.

Parameter optimization is critical for the applicability of the dry deposition schemes to capture the characteristics of the resistances that are keys in the Wesely and Hicks [68] electrical analog model. The analog is applied to the three resistances in a series circuit, namely: R_a, aerodynamic resistance; R_b, laminar sub-layer resistance; and R_c, canopy resistance. There are large uncertainties in quantifying these resistances, especially R_c where stomatal, and highly variable leaf and twig coverage conditions of the soil surface are subject to parameter optimization. The research work on sub-modeling of these resistances by Erisman et al. [69]; Baer and Nester [72]; Sander [73] and Hall et al. [74] has increased the usefulness of the analog model.

Choi et al. [75] addressed the uncertainty of roughness length used in CTMs. In their study an upper bound value for z_o was set to the canopy height in Xiu and Pleim [35] formulation for R_a, as follows: (2) R a = 1 k u ∗ ( ln z 1 z 0 + ϕ h )where k is the von Karman constant; u_* is friction velocity; z₁ is lowest mid-layer height above ground level; z_o is the roughness length; φ_h is the similarity function for heat. Figure 1 shows satellite observed canopy height and density [76] and how R_a changes during daytime and nighttime when the meteorology model derived z_o was replaced by satellite observed canopy height multiplied by 0.136 [77]. Figure 2 depicts the model-predicted monthly averaged surface ozone concentration difference between that obtained by using MET-given z_o in Equation 2, and that z_o replaced with satellite observed canopy height multiplied by 0.136 for night and day time scenarios. The monthly averaged maximum difference lies around 2.5 ppb. It is rather significant, as shown on Figure 2(A).

Physical processes within the PBL contribute important factors governing the characteristics of the diurnally varying surface concentration of the major air pollutant components; such as ozone and particulate matter. Air Quality models that are capable of resolving meso-scale features yet efficient enough to simulate large areas; e.g., continental scale or larger, are the focus of scrutiny in this review. Five models were selected to reveal the various challenges of meeting the accuracy and timeliness of these models in a real-time operational setting.

They are: (a) The European Center for Medium range Weather Forecast meteorology model (ECMWF) coupled with CHIMERE; (b) The Stanford Gas-Aerosol-TranspOrt-Radiation chemistry model (GATOR)—coupled with the General-Circulation-Mesoscale-and-Ocean-Model (GCMOM); (c)The Canadian Global Environmental Multi-scale meteorology model (GEM) coupled with the Modelling Air quality and CHemistry in 15 km horizontal grid resolution (MACH15); (d) The Weather Research and Forecasting (WRF)—Advanced Research WRF (ARW) dynamic core meteorology model coupled with Chemistry (Chem) model; and (e) the WRF—Non-hydrostatic Meso-scale Model (NMM) dynamic core meteorology model coupled with the Community Multi-scale Air Quality model (CMAQ). Among them (a) and (e) adopted offline coupling between its meteorological and chemical transport models; whereas (b), (c), and (d) adopted various degrees of inline coupling. (d) is probably the closest to fully inline coupled, as horizontal and vertical grid structures as well as dynamics and physical packages for the meteorological and chemical transport models are identical and the two-way feedbacks between them are fully functional. Some potential aerosol loading feedbacks have the direct effect of radiation attenuation, and indirect effects, such as increase in concentration in cloud condensation nuclei and precipitation modification.

The focus of this review study is on the two main physical processes within the PBL: turbulent mixing and dry depositions of gaseous and particulate phase constituents among the five models. Three of them used level 2.5 closure models to calculate turbulent mixing within the PBL. The key to model performance in capturing the characteristics of turbulent mixing within the PBL is often attributed to systematic efforts in parameter tuning and optimization of the model or sub-models used. This study quoted a rather thorough parameterization optimization study by Nielsen-Gammon et al. [58] performed for the local convective mixing parameterization scheme within ACM2 [62]. It illustrates the uncertainties involved and the well-invested optimization study utilizing variational methods, which can significantly improve model performance.

This study also revealed that the short-term trend for future AQ model improvement is the emphasis of data assimilation. A case in point is deep soil moisture data assimilation. Literature had repeatedly shown that this large inertia term is critical in understanding its medium- to long-range AQ forecast. The Pleim-Xiu [46] indirect soil moisture nudging algorithm exploits this possibility.

Dry deposition velocity (V_d) parameterization involved an intricate set of sub-modeling, such as: stomatal and land-surface conditions. Therefore, parameter optimization to generate universally applicable parameters for V_d models is the key to versatility and accuracy. This reinforces the importance of uncertainty quantification and parameter optimization mentioned for the model performance for turbulent mixing parameterization schemes.