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Atmospheric Environment 147 (2016) 409e422

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Atmospheric Environment

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Parameterization of gaseous dry deposition in atmospheric chemistrymodels: Sensitivity to aerodynamic resistance formulations understatically stable conditions

Kenjiro Toyota a, *, Ashu P. Dastoor b, Andrei Ryzhkov b

a Air Quality Modelling and Integration Section, Science and Technology Branch, Environment and Climate Change Canada, Toronto, Ontario, Canadab Air Quality Modelling and Integration Section, Science and Technology Branch, Environment and Climate Change Canada, Dorval, Quebec, Canada

h i g h l i g h t s

* Corresponding author. Air Quality Modelling anronment and Climate Change Canada, 4905 DufferinCanada.

E-mail address: [email protected] (K. Toyo

http://dx.doi.org/10.1016/j.atmosenv.2016.09.0551352-2310/Crown Copyright © 2016 Published by Els

g r a p h i c a l a b s t r a c t

� Stability-correction algorithms for rashow notable discrepancies atRiB > 0.2.

� Some of the atmospheric chemistrymodels compute L, u* and rainconsistently.

� Choice of ra formulation impacts thesimulated surface chemical exchangerates.

a r t i c l e i n f o

Article history:Received 9 May 2016Received in revised form20 September 2016Accepted 23 September 2016Available online 25 September 2016

Keywords:Dry depositionAerodynamic resistanceStable boundary layerMonin-Obukhov similarity theory

a b s t r a c t

Turbulence controls the vertical transfer of momentum, heat and trace constituents in the atmosphericboundary layer. In the lowest 10% of this layer lies the surface boundary layer (SBL) where the verticalfluxes of transferred quantities have been successfully parameterized using the Monin-Obukhovsimilarity theory in weather forecast, climate and atmospheric chemistry models. However, there isa large degree of empiricism in the stability-correction parameterizations used to formulate eddydiffusivity and aerodynamic resistance particularly under strongly stable ambient conditions.Although the influence of uncertainties in stability-correction parameterizations on eddy diffusivity isactively studied in boundary-layer meteorological modeling, its impact on dry deposition in atmo-spheric chemistry modeling is not well characterized. In this study, we address this gap by providingthe mathematical basis for the relationship between the formulations of vertical surface flux used inmeteorological and atmospheric chemistry modeling communities, and by examining the sensitivity ofthe modeled dry deposition velocities in statically stable SBL to the choice of stability-correction pa-rameterizations used in three operational and/or research environmental models (GEM/GEM-MACH,ECMWF IFS and CMAQ-MM5). Aerodynamic resistances (ra) calculated by the three sets of parame-terizations are notably different from each other and are also different from those calculated by a “z-less” scaling formulation under strongly stable conditions (the bulk Richardson number > 0.2).Furthermore, we show that many atmospheric chemistry models calculate ra using formulations whichare inconsistent with the derivation of micro-meteorological parameters. Finally, practical implications

d Integration Section, Envi-St., Toronto, ON M3H 5T4,

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K. Toyota et al. / Atmospheric Environment 147 (2016) 409e422410

of the differences in stability-correction algorithms are discussed for the computations of dry depo-sition velocities of SO2, O3 and reactive bromine compounds for specific cases of stable SBL.Crown Copyright © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

Dry deposition is a process that transfers chemical constituentsin the atmosphere to the earth's surface through the actions ofdiffusion in air followed by the uptake onto the surface (Wesely andHicks, 1977, 2000). If the deposited substances are not lost irre-versibly on the surface, they can be re-emitted to the atmosphere,which is called bi-directional exchange (Pleim and Ran, 2011). Inboth cases, turbulent eddy diffusivity in the air is one of the keyparameters in determining the exchange rates of the transferredsubstances (Wesely and Hicks, 1977).

Turbulence plays a pivotal role in determining the verticaltransfer ofmomentum, heat andmass in the atmospheric boundarylayer (ABL) that usually encompasses the lowest tens to hundredsof meters in the atmosphere over the earth's surface (Garratt, 1992).In approximately the lowest 10% of the ABL, i.e. the surfaceboundary layer (SBL), the vertical fluxes of transferred quantitiesare nearly constant with height and can be represented quite suc-cessfully by formulations based on the Monin-Obukhov (M-O)similarity theory (H€ogstr€om, 1988, 1996; Foken, 2006). Turbulentmixing in the ABL is fostered through the energy cascading oftransient eddies generated by wind shear and buoyancy into mo-lecular dissipation (Stull, 1988). Under the assumption of steadystate between generation, dissipation and transport of the turbu-lent eddies across the SBL above the interfacial sublayer adjacent tosurface obstacles, the M-O similarity theory describes relationshipsbetween vertical profiles and fluxes for momentum and scalarquantities (i.e., heat and trace constituents), using a metric calledthe Obukhov length (L) (Garratt, 1992):

L ¼ u2�qvk g qv�

: (1)

Here, k is the von K�arm�an constant (0.4), g is the acceleration due togravity, qv is the mean state of virtual potential temperature, u* isfriction velocity which is related to the surface stress ts by

u* ¼ jts=rj1=2 where r is the density of air, and qv� ¼ �w0q0v=u�,namely, the turbulent fluxof virtual temperature divided by frictionvelocity. The flux-gradient relationships are then defined in termsof dimensionless universal functions (Fm,c), namely:

FmðzÞ ¼ k zu�

vuvz

(2)

for momentum (u) and

Fc zð Þ ¼ k zPrtN c�

vc

vz(3)

for scalar quantities (c) such as the concentrations of chemicalspecies, where z¼ z/Lwith z being height above the earth's surface,PrtN is the turbulent Prandtl number (the ratio of eddy diffusivityfor momentum, KM, to that for heat, KH) in the neutral static sta-bility and c� ¼ �w0c0=u�. It is normally assumed that all the scalarquantities have the same eddy diffusivity in the air. The universalfunctions, Fm and Fc, have been formulated by combining theo-retical considerations and empirical fitting to field observations

(H€ogstr€om, 1996; Beljaars and Holtslag, 1991; Delage and Girard,1992; Delage, 1997), where Fm ¼ Fc ¼ 1 at z ¼ 0 (neutral stratifi-cation), 0 < Fm < 1 and 0 < Fc < 1 at z < 0 (unstable stratification)and Fm > 1 and Fc > 1 at z > 0 (stable stratification).

One of the challenges in the modeling of vertical fluxes formomentum and scalar quantities is the formulation of eddy diffu-sivity in strongly stable air, where the occurrence of turbulenteddies is no longer continuous in space and time and is increasinglycontrolled by vortices associated with internal gravity waves(Webb, 1970; Hicks, 1976; Kondo et al., 1978; Zilitinkevich et al.,2008; Mahrt et al., 2012; Sun et al., 2012; Grachev et al., 2013).The grid resolution of models is generally too coarse to representthe wind shear at fine scales of relevance, needed to resolvelocalized, intermittent eddies in such conditions (Mahrt, 1987).Models of weather, climate and atmospheric chemistry have thusadopted eddy-diffusion parameterizations that allow for a persis-tence of weak diffusion in very strong stratification of air in the SBLand sometimes in the entire ABL, to circumvent issues such asunrealistic cooling under the surface inversion and much tooshallow ABL depth at night (Louis, 1979; Delage, 1997; King et al.,2001; Bechtold et al., 2008). It should be noted that the successof such diffusion parameterizations does not necessarily extend toall aspects of physico-dynamical behavior of the model, e.g.,insufficient strength of nocturnal jets (Cuxart et al., 2006; Holtslaget al., 2013). The problem is complicated by the potential involve-ment of additional processes in need of improved formulations andrepresentations. For example, Viterbo et al. (1999) find that a coldbias in the stable SBL is alleviated by a proper representation oflatent heat release due to the freezing of soil moisture in theirweather forecast model. Also, Makar et al. (2006) demonstrate thatthe incorporation of anthropogenic heat sources at the lowerboundary of a meteorological model enhances eddy diffusivity inurban ABL during nighttime.

Although the influence of uncertainties in stability-correctionparameterizations on eddy diffusivity is thus actively studied inboundary-layer meteorological modeling, its impact on drydeposition in the modeling of atmospheric chemistry is not wellcharacterized. As we describe in this study, conventions used inthe formulation of air-surface exchange are different between themeteorological and atmospheric-chemistry models. To representthe surface eddy fluxes of momentum and scalar quantities (heatand moisture), the meteorological models define bulk transfercoefficients, into which the effects of wind shear and thermalstability in the eddy diffusivity are included (Garratt, 1992). Onthe other hand, the models of atmospheric chemistry (by whichwe refer to air quality, chemical transport and chemistry-climatemodels collectively) compute dry deposition velocities forsimulating the surface fluxes of chemical constituents. The drydeposition velocity is defined as a reciprocal of the sum of “re-sistances” acting in series, namely, aerodynamic resistance,quasi-laminar layer resistance and canopy (or surface) resistance(Wesely and Hicks, 1977, 2000). Among these, the aerodynamicand quasi-laminar layer resistances account for the effects ofeddy diffusivity and are mathematically interchangeable with thebulk transfer coefficients used in meteorological models (seesection 2.2). Consequently, the computation of micro-meteorological parameters for dry deposition in the

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K. Toyota et al. / Atmospheric Environment 147 (2016) 409e422 411

atmospheric chemistry models takes advantage of equivalentparameters and/or algorithms present in their meteorologicalmodel components. The uncertainties in the stability-correctionformulations are therefore common to both models. Indeed,uncertainty in the computation of eddy diffusivity is noted as oneof the major factors influencing the performance of air-qualitymodels in the simulation of ambient concentrations of ozone(O3) and particulate matter in the statically stable ABL (Makaret al., 2014). This is because the eddy diffusivity controls thesupply of these substances from aloft as well as the dilution oftheir key precursors and scavengers emitted from the surface. Assuch, the assessment of this problem is confounded by concur-rent uncertainties in the emissions and the secondary reactions.Makar et al. (2014) also note algorithms employed for the drydeposition as an additional source of uncertainty in the compu-tation of the particulate matter concentrations at night. However,the aspect of uncertainty in the parameterization of aerodynamicresistance has not been included in such discussions.

The main objective of this study is to explore the uncertaintiesin the formulations of aerodynamic resistance in stable SBL andits implications for atmospheric chemistry modeling. Section 2begins with the description of the mathematical foundationupon which the surface eddy fluxes are formulated for meteo-rological quantities (bulk transfer coefficients for momentum,heat and moisture; section 2.1) and for chemical constituents(aerodynamic resistance and dry deposition velocity) and therelationship between these two conventions (section 2.2). To aidwith discussions in this study, we also introduce the formulationof the eddy diffusivity in the M-O similarity theory and itsrelationship with the aerodynamic resistance (section 2.3). Insection 2.4, we discuss the nature of the problem with stability-correction parameterizations used in surface eddy flux algo-rithms under statically stable conditions in models and itsimportance (sections 2.4.1e2.4.2). In addition, there often existsinconsistency between the stability-correction formulations andthe calculation of aerodynamic resistance in atmosphericchemistry models, which is described in section 2.4.3. In section3, we first demonstrate the relevance of strongly stable condi-tions in which the model calculations of surface eddy fluxes canbe notably different to each other (section 3.1). Next, we discussthe impacts of using different empirical formulations of staticstability corrections taken from selected operational/researchweather forecast and atmospheric chemistry models on thecalculation of aerodynamic resistance and dry deposition veloc-ities for trace gases such as sulfur dioxide (SO2), O3 and reactivebromine species (section 3.2). Section 4 gives conclusions of thisstudy and some remark on the limiting values of aerodynamicresistance in stable SBL.

2. Formulation of surface fluxes on the basis of the M-Osimilarity theory and its approximations

This section begins with the description of basic formulationsused for the modeling of surface fluxes of meteorological quan-tities (momentum, and sensible and latent heat) and gaseousconstituents of interest in air quality and tropospheric chemistry.By this, we demonstrate the connections between the surfaceeddy flux formulations generally used in the disciplines ofmeteorological/climate models and air quality/troposphericchemistry models. We then describe the problem of parameter-izing stability correction functions to be addressed in this study.

2.1. Basic formulations in use for meteorological modeling

From a practical standpoint of numerical modeling, one major

strength of the M-O similarity theory is that its governingequations (Eqs. (2) and (3)) can be integrated over the depth ofthe SBL where the turbulent fluxes of transferred quantities areassumed to be constant. This provides a great advantage to themodeling of the surface fluxes, as the flux calculation then re-quires the information of state variables only at two levels in this“constant-flux” layer within the SBL. After rearranging Eq. (2) bydividing with kz/u* on both sides and then integrating over z, theintegral form of flux-gradient relationship for momentum isobtained (Garratt, 1992):

uðzÞ ¼ u�k

�ln�zz0

��Jm

�zL

�þJm

�z0L

��(4)

where z0 is the roughness length, at which height above the earth'ssurface wind speed is mathematically required to vanish, viz.u(z0) ¼ 0, under the assumption of continued validity of the M-Oflux-gradient relationships down into the interfacial sublayer, andJm is the integrated stability-correction term for the wind profiledefined as follows:

JmðzÞ ¼Zz0

1� FmðxÞx

dx: (5)

For the sake of simplicity, our formulation ignores the zero-planedisplacement, which represents the role of bulk surface struc-tures such as vegetation in raising the effective height above whichturbulent eddies are deemed to behave according to the M-Osimilarity theory (Garratt, 1992; Campbell and Norman, 1998).Large-scale meteorological models often define a drag coefficient(CD):

CD ¼ k2�ln�zrefz0

��Jm

�zrefL

�þJm

�z0L

��2 (6)

so that the surface kinematic momentum flux (ts=r ¼ �u2� ) iscalculated by �CDu2ref (Garratt, 1992). Here, zref is a referenceheight, normally taken as the lowest prognostic vertical level of themodel where its governing equations for dynamics and physics aresolved, and uref ¼u(zref).

The integral form of flux-gradient relationships for scalarquantities can be obtained similarly by rearranging Eq. (3):

Dc ¼ c zð Þ � c0 ¼ PrtNc�k

"ln

zz0c

!�Jc

�zL

�þJc

�z0cL

�#(7)

where z0c is scalar roughness length, c0 is the value of c at thebottom of the air in contact with the surface and Jc is the inte-grated stability-correction term for the profiles of scalar quantitiesdefined as follows:

Jc zð Þ ¼Zz0

1� Fc xð Þx

dx: (8)

A thorough review of existing field data indicates PrtN to be in therange of 0.90e0.95, slightly lower than unity (H€ogstr€om, 1996),whereas, in practice, meteorological models often employ PrtN ¼ 1(Beljaars and Holtslag, 1991; Delage, 1997). We adopt the lattervalue for the discussions in this study unless otherwise noted.

It should be noted that, in terms of physical reality, the windspeed does not vanish exactly at the height z0. Nor does the


quantity c0 in Eq. (7) represent the value of c at the height z0cbut at the very bottom of free air in contact with the surfacesubstrates, as stated above. Although z0 and z0c provide a mea-sure of the aerodynamic efficiency of surface obstacles in causingthe eddy diffusion of momentum and scalar quantities, respec-

C0c ¼ k

ln�z0ref.z0��Jm

�z0ref.L�þJmðz0=LÞ

� k

PrtNhln�zref.z0c��Jc

�zref.L�þJc

�z0cL i ; (11)

tively, in the SBL, these length scales are introduced basically asmathematical constraints for the vertical integration of Eqs. (2)and (3) down into the interfacial sublayer where the M-O flux-gradient relationships are no longer valid (Campbell andNorman, 1998). In addition, the Reynolds analogy, which isinvoked to assume the equivalence of eddy diffusivity betweenmomentum and scalar quantities, is not valid in the interfacialsublayer. This is because pressure fluctuations around roughnesselements act only on momentum transfer and also there aredifferences between the distributions of the sources and sinks ofmomentum and scalar quantities at the surface (Garratt, 1992).As such, the value of z0c should, in general, differ from that of z0.For several natural land surface types, the following relationshipis known to work as a reasonable approximation for the sensibleand latent heat transfer (Garratt and Hicks, 1973; Wesely andHicks, 1977):

k B�1 ¼ lnðz0=z0T Þzln�z0z0qz2; (9)

where z0T and z0q are roughness lengths for temperature (sensibleheat) and specific humidity (latent heat), respectively, and B�1 is anempirical constant. This relationship between z0 and z0T provides abasis for the commonly-used formulation of quasi-laminar layerresistance for gaseous constituents (Wesely and Hicks, 1977; Pleim,2006) described in section 2.2. However, significant deviationsfrom Eq. (9) can occur for the relationship between z0 and z0T (i.e.,variations in the plausible value of B�1) over aerodynamicallysmooth surfaces, surfaces with bluff elements and surfaces withinhomogeneous land-use characteristics and/or topography withina few kilometers (Brutsaert, 1982; Garratt, 1992; Andreas, 1987;Holtslag and de Bruin, 1988; Beljaars and Holtslag, 1991; Fairallet al., 2000). It is beyond the scope of this study to delve intoempirical relationships between z0 and z0T more suitable for suchcases.

As with the momentum transfer, large-scale meteorologicalmodels define a transfer coefficient (Cc) for scalar quantities byrearranging Eqs. (4) and (7):

Cc ¼ k

ln�zref.z0��Jm

�zref.L�þJmðz0=LÞ

� k

PrtNhln�zref.z0c��Jc

�zref.L�þJc

�z0cL i ; (10)

by which the surface scalar fluxes (¼ �u* c*) can be expressed as

eCc uref (cref e c0) where cref ¼ c(zref). Since the constant-fluxassumption (i.e., u* and c* do not change with height) is madein the SBL, different reference heights can be chosen for mo-mentum and scalars. Using zref as the reference height for scalarswhile using z0ref (s zref) as the reference height for momentum,the formulation for the scalar transfer coefficient is adapted to

by which the surface scalar fluxes can be expressed as�C0

c u0ref ðcref � c0Þ where u0ref ¼ uðz0ref Þ. Eq. (11) is useful whenthe model employs a vertical grid structure which is staggeredbetween momentum and thermodynamic variables.

2.2. Basic formulations in use for atmospheric chemistry modeling

In atmospheric chemistry applications, the vertical fluxes (Fc)of trace gases in the SBL are normally formulated by using aresistance-in-series approach (Wesely and Hicks, 1977; Pleim andRan, 2011). In a case where the constituent can be assumed not toaccommodate on the underlying surface for a reversible ex-change with the atmosphere, Fc can be calculated as follows:

Fc ¼ �vd cref ; (12)

where cref is the concentration of a constituent at the referenceheight zref and vd is the dry deposition velocity given at the samereference height zref by

vd ¼ ðra þ rb þ rcÞ�1: (13)

Here, ra is the aerodynamic resistance to the top of the canopy(or the earth's surface) at the reference height (zref) where vd iscalculated, rb is the quasi-laminar layer resistance to account forthe differences in transport behavior between momentum andscalar quantities in air adjacent to the surface, and rc is thecanopy (or surface) resistance to account for the rate of net lossof the chemical species within the canopy or on the earth'ssurface. The mathematical formulations of ra and rb build uponthose of surface fluxes for momentum, heat and moisture fromthe M-O similarity theory employed in weather forecast andclimate models as described below. The formulation of rc buildsupon the models of the water and carbon cycles on the landsurface which take into account physiological behavior of vege-tation, and has been expanded on its own right to address thevarying reactivity and solubility of trace gases on the substrates

in contact with air. It is beyond the scope of this study to reviewthe details of the existing rc parameterizations, for which readers


may refer to the literature (Baldocchi et al., 1987; Wesely, 1989;Wesely and Hicks, 2000; Erisman et al., 1994a, b; Zhang et al.,2002b, 2003; Fairall et al., 2007; Pleim and Ran, 2011; ValMartin et al., 2014) and references cited therein.

By using Eq. (7), Fc (¼ w0c0 ¼ �u�c�) can be reformulated on thebasis of the M-O similarity theory:

Fc ¼ �ku��cref � c0

�

PrtN

"ln

zrefz0c

!�Jc

�zrefL

�þJc

�z0cL

�# : (14)

Now, the flux Fc can be conceived as the product of the concen-tration increment (cref e c0) from the air at the canopy top (or incontact with the earth's surface) to the reference height zref and theinverse of the serial resistance (ra þ rb) acting between the twoheight levels. By assuming Jcðz0=LÞzJcðz0c=LÞ in Eq. (14), wearrive at the third expression for Fc:

Fc ¼ �cref � c0ra þ rb

(15)

where

ra ¼ PrtNku�

�ln�zrefz0

��Jc

�zrefL

�þJc

�z0L

��; (16)

rbzPrtNku�

ln

z0z0c

!: (17)

For simulating the dry deposition of gaseous constituents, rb iscustomarily formulated on the basis of the empirical relationshipbetween momentum and scalar roughness lengths (Eq. (9)) withadaptation to account for the difference between the moleculardiffusivities of temperature (sensible heat) and gaseous constitu-ents (Wesely and Hicks, 1977; Pleim, 2006):

rb ¼ PrtN B�1

u�

�ScPr

�2=3

z5 PrtNu�

�ScPr

�2=3

: (18)

Here, Pr (¼ n/kT) is the Prandtl number, namely, a ratio between thekinematic viscosity (n) and molecular thermal diffusivity (kT) of air,and Sc (¼ n/Dg) is the Schmidt number, namely, a ratio between n

and the molecular diffusivity (Dg) of a gaseous species of interest.Typical values in the lower atmosphere are: Sc ¼ 0.60 for watervapor and Pr¼ 0.71 (Garratt, 1992). The expression for rb as definedabove is equivalent to extending Eq. (9) for a general relationshipbetween z0 and z0c as follows (Wesely and Hicks, 1977):

ln�z0z0c ¼ k B�1 ðSc=PrÞ2=3z2 ðSc=PrÞ2=3: (19)

The approximation of k B�1 z 2 becomes rather inaccurate forsurfaces such as sparse vegetation and water, where the aero-dynamic characteristics of the surface are far from those of densevegetation (Wesely and Hicks, 1977; Tuovinen et al., 1998; Fairallet al., 2000); however, the error introduced by this approxima-tion in the calculated vd is small, because rb is often much smallerthan the sum of ra and rc (Ganzeveld and Lelieveld, 1995).

The flux Fc at the canopy top (or at the earth's surface) can beformulated as the product of the concentration c0 in air at thecanopy top and the inverse of the canopy resistance rc:

Fc ¼ �c0rc

: (20)

In the framework of the M-O similarity theory, the vertical flux isassumed to be constant within the SBL; hence, by comparing theformulations of Fc between Eqs. (15) and (20), one obtains

c0 ¼ rc crefra þ rb þ rc

; (21)

which can be used to eliminate c0 from Eq. (15), or from Eq. (20),leading to the formulation of dry deposition fluxes normally rep-resented by Eqs. (12) and (13). This simple formulation needs to beadapted for modeling the situations where the gaseous species ofinterest interacts with multiple substrates (e.g., soil, stomata,cuticle) in different parts of the canopy and/or undergoes bi-directional exchange, but even then the net vertical fluxes of thetransferred species depend on ra formulated as described here (e.g.,Nemitz et al., 2001).

It is important to note that the sum of ra and rb used in thecalculation of chemical dry deposition is mathematically inter-changeable with the bulk transfer coefficients used in the calcula-tion of surface eddy fluxes in meteorological models. By using Eqs.(4) and (10e11) from the previous subsection and Eqs. (16) and (17)from the present subsection, the following relationship can bederived (Garratt, 1992):

Ccuref ¼ C0cu

0ref ¼ ðra þ rbÞ�1: (22)

2.3. Eddy diffusivity in the SBL and above

Using the M-O flux-gradient relationships (Eqs. (2) and (3)) andFick's law of diffusion (u0w0 ¼ �u2� ¼ �KM vu=vz andw0c0 ¼ �u� c� ¼ �Kc vc=vz), we can derive eddy diffusivity for mo-mentum (KM) and scalar quantities (Kc), respectively (Garratt,1992):

KM ¼ k z u�FmðzÞ ; (23)

Kc ¼ k z u�PrtNFc zð Þ : (24)

It follows that the turbulent Prandtl number (Prt) with allowancefor changes with z can be represented by

Prt ¼ KM

Kc¼ PrtNFc zð Þ

Fm zð Þ : (25)

It is useful to note the mathematical relationships of ra and rb to theeddy diffusivity Kc from Eq. (24) (Baldocchi, 1988; Garratt, 1992):

ra ¼Zzrefz0

K�1c dz; (26)

rbzZz0z0c

K�1c dz: (27)

For simulating the eddy diffusion of momentum and scalars inthe outer boundary layer above the SBL, the M-O similarity theorycan be expanded for the derivation of eddy diffusivity, where Eqs.


(23) and (24) are adapted by the multiplication of a scaling factor toaccount for changes in the vertical fluxes with height up to the topof the ABL (Brost andWyngaard,1978; Nieuwstadt,1984; Troen andMahrt, 1986):

KM ¼ k z u�FmðzÞ

�1� z

H

�p; (28)

Kc ¼ k z u�PrtNFc zð Þ

�1� z

H

�p(29)

with H being a diagnosed height for the top of the ABL and p ~ 1e2.Both the operational and research models of weather predictionnow use more advanced approaches for calculating KM and Kc inthe outer boundary layer without assuming a direct correspon-dence to the surface fluxes (Cuxart et al., 2006). However, thesimple parametric representation of height-dependent momentumand heat fluxes, as in Eqs. (28) and (29), is sometimes employed inthe case of the stable ABL to adjust the M-O universal functionsused in the calculation of surface fluxes through the lowest prog-nostic model layer, when its thickness (several tens of meters) is ofthe same order as H (Delage, 1997).

2.4. The M-O universal functions and their approximations for thestable stratification of air

2.4.1. The Richardson number: a metric for determining flowregimes

For diagnosing the steady-state balance between the growthand decay of turbulence and its resultant intensity in a fluid, thegradient Richardson number (Ri) is widely used as a metric forthermal stability (Garratt, 1992). By ignoring small changes in winddirection in the SBL, Ri can be given by

Ri ¼ gqv

vqv=vz

ðvu=vzÞ2: (30)

Since Eqs. (1)e(3) are assumed to hold in the SBL, Ri can be also

Table 1A list of the selected M-O universal functions and their integral forms for momentum, viz.relationships in the statically stable case (z > 0) within the SBL or the lowest atmospher

Model name and reference Fm, Fc, Jm and

ECMWF IFS, Beljaars and Holtslag (1991) Fm ¼ 1þ azþ b

Fc ¼ 1þ azð1þJm ¼ �½azþ bðzJc ¼ �½ð1þ 2azwhere a ¼ 1, b ¼

GEM, Delage (1997)a,b Fc ¼ Fm ¼ 1þ a

Jc ¼ Jm ¼ �12

�where Ri is the gC ¼ D/h�1/h2, D

CMAQ-MM5, Pleim (2006) Fm, Fc: Not avai

Jm ¼ Jc ¼�1

where b ¼ 1/Ricr

z ¼

8>>><>>>:

ln�zz0

�1

ln�zz0

�1�

“z-less” scaling, Dyer (1974) Fm ¼ Fc ¼ 1 þ 5

Note,a For deriving J from F, an assumption is made in that the quadratic decrease of mom

the eddy fluxes are assumed to vary across the lowest model layer unlike the normal asb The top height (h) of the ABL is diagnosed according to Zilitinkevich (1972): h ¼ 0:7

forced to ensure the real finite numbers in some of the terms in the Jm, c formula.

formulated as follows (Garratt, 1992):

Ri ¼ PrtN z Fc zð ÞF2m zð Þ

: (31)

It has been deduced theoretically that the dynamic instability oftravelling waves does not occur in an inviscid fluid until the value ofRi goes below a critical value (Ricrit) of 0.25, which marks a transi-tion of flow regime from laminar to turbulent (Miles, 1961; Garratt,1992). On the other hand, the transition from turbulent to laminarflow regimes occur only at Ri > 1, known as hysteresis in the flow-regime transition (Stull, 1988; McTaggart-Cowan and Zadra, 2015).Field observations in the SBL indicate a termination of fully tur-bulent flow at Ri z 0.2 and an occurrence of intermittent turbu-lence at Ri ≳ 0:2 (Webb, 1970; Hicks, 1976; Kondo et al., 1978). It is achallenge to represent the intermittent turbulence inmodels. In thestrongly stable stratification of air, the vertical and horizontal scalesof the turbulent patches of air are often smaller than the grid res-olution feasible in models (Mahrt et al., 2012; Grachev et al., 2013);hence, it is likely that the local values of Ri in such small-scaleturbulent patches are in fact below Ricrit (0.2e0.25), even if themodel-resolved values of Ri are notably higher than Ricrit (Mahrt,1987). As discussed in section 2.4.2, these practical limitationshave been addressed in a semi-empirical manner for representingstrongly stable conditions in the calculation of surface eddy fluxeswithin the large-scale models of meteorology and atmosphericchemistry.

For large-scale model applications, it is also useful to define thebulk Richardson number (RiB) (Garratt, 1992):

RiB ¼gzref

�qv; ref � qv0

�qvu2ref

(32)

where qv, ref and qv0 are the virtual potential temperatures at thereference height zref and at the canopy top (or at the earth's sur-

face), respectively, and qv is their mean value. By using Eqs. (1) (4)and (7), Eq. (32) can be reformulated as follows:

Fm(z) andJm(z), and for scalars, viz. Fc(z) andJc(z), for modeling the flux-gradientic model layer on top of the earth's surface.

Jc

zð1þ c� dzÞexpð�dzÞ2az=3Þ1=2 þ bzð1þ c� dzÞexpð�dzÞ� c=dÞexpð�dzÞ þ bc=d�=3Þ3=2 þ bðz� c=dÞ expð�dzÞ þ bc=d� 1�0.667, c ¼ 5 and d ¼ 0.35Ri

A� zh � ln

�1þ Bz

2 þ A�� B

2ffiffiffiC

p sin�1�B�2Cz

D

�� 1þ lnð2Þ þ B

2ffiffiffiC

p sin�1�

BD

� radient Richardson number, a ¼ 12, A ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ Bzþ Cz2

p, B ¼ D�2/h,

¼ 4a/L and h ¼ (diagnosed ABL height)lable�bz ð0< z � 1Þ� b� z ðz>1Þit, Ricrit ¼ 0.25 and z is approximated by using the bulk Richardson number (RiB):

RiB� RiB=Ricrit

ð0<RiB <Ricut; 0< z � 1Þ

RiBRicut=Ricrit

ðRiB >Ricut; z>1Þwith Ricut ¼ ½lnðz=z0Þ þ 1=Ricrit ��1.

z, Jm ¼ Jc ¼ e5z

entum and scalar fluxes occurs with height up to the top of the ABL. In other words,sumption of constant fluxes in the SBL.ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

u�L=jf jp

, where f is the Coriolis parameter. However, h > z and h > L/(4a) must be

Fig. 1. : Changes in the ratios of the bulk transfer coefficients of heat to those in theneutral stratification of air (Cc/CcN) with the bulk Richardson number (RiB). The rangeof the Cc/CcN values for each set of the M-O formulation (gray shade: Dyer (1974), redshade: Beljaars and Holtslag (1991), blue/purple shade: Delage (1997) and greenshade: Pleim (2006)) is calculated by using the ratios between the reference heightand the momentum roughness length varied over 102 � zref/z0 � 105. The Delageformulation requires the input of a diagnosed ABL height (see footnote b in Table 1),which is calculated here by assuming uref ¼ 2.5 m s�1, zref ¼ 40 m and the Coriolisparameter at the latitude of 75� . The values of Cc/CcN for the three HadAM2 formulae(King et al., 2001) are directly given by fc(RiB) in Eqs. (40)e(42), which depend only onRiB and independent of zref/z0 (black, red, and blue dashed lines).


RiB

¼ zrefL

PrtNhln�zref.z0T��Jc

�zref.L�

þ Jcðz0T=LÞi

hln�zref.z0��Jm

�zref.L�

þ Jmðz0=LÞi2 :

(33)

Similarly to Eq. (31), this mathematical relationship indicates thatthermal and mechanical stability of the flow as set out in the M-Osimilarity theory uniquely defines the corresponding values of RiB.In this study, we consistently use RiB as a reference for the flowregimes when we compare stability-dependent behaviors in thevariables associated with surface eddy fluxes between differentmodel formulations.

Also, RiB is explicitly used in many (but not all) model applica-tions for defining analytical functions that represent the stabilitycorrections in the calculation of surface eddy fluxes (e.g., Louis,1979; Pleim, 2006) (see section 2.4.2). This approach compro-mises the exact correspondence of the calculated fluxes to the M-Osimilarity theory (e.g., van den Hurk and Holtslag, 1997), but avoidslaborious iteration algorithms in finding the numerical solution ofunknowns (u*, L, etc.) in the governing equations of the flux-gradient relationships (e.g., Deardorff, 1972; Delage, 1997; Pleim,2006).

2.4.2. Stability correction functions used in this studyTable 1 lists a set of the M-O universal functions (Fm and Fc)

and/or their integral forms (Jm andJc) selected for this study fromthree models of atmospheric chemistry and/or weather forecast:the Integrated Forecasting System developed at the EuropeanCentre for Medium-rangeWeather Forecasts (ECMWF IFS) (Beljaarsand Holtslag, 1991), the Global Environmental Multi-scale model(GEM) developed at the Canadian Meteorological Centre (CMC)(Delage, 1997) and the Community Multi-scale Air Quality modelwith the fifth-generation Pennsylvania State UniversityeNationalCenter for Atmospheric Research Mesoscale Model (CMAQ-MM5)(Pleim, 2006). The M-O universal functions in these models areformulated not to terminate the eddy diffusion at Ricrit z 0.2, but toallow for a weak eddy diffusion even at Ri[Ricrit.

ECMWF IFS employs formulae developed by Beljaars andHoltslag (1991) based on the analysis of field observations in theNetherlands; their formulae account for the assertion that, in theregime of intermittent turbulence (z > 5e10), the transfer of scalarquantities is far less efficient than that of momentum (Prt[PrtN,hence Fc[Fm; see Eq. (25)), unlike in the regime of continuousturbulence whereFczFm (Hicks, 1976; Kondo et al., 1978; Grachevet al., 2013). In contrast, the formulae employed in GEM and CMAQ-MM5 assume Jc ¼ Jm, hence Prt ¼ PrtN, for the entire range ofz > 0. Delage (1997), whose formulae are employed in GEM, for-mulates the dependence of Fm and Fc on the Richardson numberby adjusting the Louis (1979) formulae, whereas approximating thequantitative behaviors of Fm and Fc in the limit of a very strongstratification of air similar to that of Fc formulated by Beljaars andHoltslag (1991). An assumption is then made that the shallownessof the ABL thickness leads to notable changes in the eddy fluxeseven within several tens of meters from the surface, namely, overthe thickness of the lowest model layer. A quadratic decrease withheight is thus assumed for both the momentum and scalar fluxessuch that they drop to zero at the top height of the ABL diagnosedempirically (e.g., Zilitinkevich, 1972; Aliabadi et al., 2016). This isequivalent to assuming p ¼ 1 in Eqs. (28) and (29). CMAQ-MM5employs the Pleim (2006) formulae, which behave similarly tothe Dyer (1974) formulation (see below) between 0 < z � 1 butrelax the slope of changes with z in Jm and Jc above z ¼ 1.

TheJm, c formulae employed in ECMWF IFS and GEM call for aniterative approach to find numerical solutions of u*, L, Jm and Jcfrom the input values of wind speed and virtual potential tem-peratures at z ¼ 0 and z ¼ zref. There is a realm of algorithms thatavoid this iterative process by approximating z with formulaeexplicitly dependent on RiB (Byun, 1990; Byun et al., 1999;Launiainen, 1995; Uno et al., 1995; van den Hurk and Holtslag,1997; Pleim, 2006). Pleim's approach belongs to this category.PrtN ¼ 0.95 is assumed in the Pleim (2006) model.

Table 1 also lists the functional form of Fm, c given by Dyer(1974), which is known to be valid at 0 < z � 1 where the contin-uous occurrence of turbulence is expected (Webb, 1970). Byextrapolating beyond this range, Eq. (31) yields Ri/ 0.2 in the limitof z / ∞; this implies the absence of eddy diffusion at Ri > 0.2.Also, the use of the Dyer functions in Eqs. (23) and (24) leads toeddy diffusivities independent from z in the limit of z / ∞(Wyngaard and Cot�e, 1972; Garratt, 1992; Grachev et al., 2013),namely:

KM/0:2 k L u�; (34)

Kc/0:2 k L u�=PrtN: (35)

Therefore, Dyer's formulation is known as a “z-less” scaling


formulation. Fig. 1 demonstrates the difference between the foursets of the M-O universal functions mentioned above (ECMWF IFS,GEM, CMAQ-MM5 and “z-less” scaling in red, blue/purple, greenand gray shades, respectively) by examining the decrease in thebulk transfer coefficients (Cc) of a scalar quantity (sensible heat) ascalculated by Eq. (10) from those in the neutral stratification of air(CcN, see Eq. (39)) with increasing RiB.

Also shown in Fig. 1 is the behavior of the same quantity (theratio between Cc and CcN) as calculated by yet another realm ofsurface flux algorithms used in meteorological models which arefurther simpler and more directly dependent on RiB (Louis, 1979;Louis et al., 1982; King et al., 2001; Bechtold et al., 2008) than thetype of algorithms employed by Pleim (2006). In this family ofsurface flux formulations, the drag coefficient (CD) for momentumand the transfer coefficient (Cc) for scalars are formulated in thefollowing general forms:

CD ¼ CDN fmðRiBÞ; (36)

Cc ¼ CcN fcðRiBÞ (37)

where

CDN ¼ k2�ln�zrefz0

��2; (38)

Fig. 2. Area-weighted cumulative relative frequency distributions of the bulk Richardson nCanadian Meteorological Centre (CMC) for the months of January (light-blue lines), April (grgridded data of surface temperatures for each of the four surface types (land, glaciers, oprognostic layer of the atmosphere (i.e., h ¼ 0.995 in the s-pressure hybrid vertical coordinglaciers surfaces in the northern hemisphere, (b) openwater surfaces in the northern hemispin the southern hemisphere, (e) the same as (b) but in the southern hemisphere and (f) thdenotes RiB ¼ 0.2.

CcN ¼ k2"PrtN$ln

�zrefz0

�$ln

zrefz0c

!#�1

(39)

are the momentum drag and scalar transfer coefficients for theneutral stratification of air. The scaling factors fm(RiB) and fc(RiB)represent corrections to CD and Cc due to departure from neutralstatic stability as a function of RiB. Note here that fm and fc havebeen formulatedwith additional dependence on zref/z0 for staticallyunstable conditions (Louis, 1979; Louis et al., 1982), which are notaddressed in this study. In Fig. 1, we show how fc(RiB) (¼ Cc/CcN) isprescribed to change with RiB for three variant expressions thathave been tested in the atmosphere-only version of the UnifiedClimate Model developed at the Hadley Centre of the UKMet Office(HadAM2) (King et al., 2001), namely, the “long-tail” function

fcðRiBÞ ¼ ð1þ 10 RiBÞ�1; (40)

the Louis (1979) function:

fcðRiBÞ ¼ ð1þ 5 RiBÞ�2; (41)

and the SHARP function:

fcðRiBÞ ¼� ð1� RiB=aÞ2 for RiB < a=2

b ða=RiBÞ2 for RiB a=2(42)

with a ¼ 0.25 and b ¼ 0.0625. In HadAM2, the Louis and SHARP

umber (RiB) among the cases of RiB > 0 in the 6-hourly global objective analyses at theeen lines), July (red lines) and October (blue lines) in the year 2010, calculated from thepen water and ice-covered water) and wind speeds and temperatures in the lowestate, globally averaged, z40 m above the surface, see Charron et al., 2012): (a) land andhere, (c) ice-covered water surfaces in the northern hemisphere, (d) the same as (a) bute same as (c) but in the southern hemisphere. The vertical dashed line in each graph


functions have been found to be more successful than the long-tailfunction in the simulation of surface heat fluxes in stable ABL (Kinget al., 2001; Bechtold et al., 2008).

As is evident in Fig. 1, all the stability-correction functions beingused in weather forecast and climate models are designed to pro-duce weak eddy fluxes well beyond RiB z 0.2, which is the criticalvalue for the existence of turbulent eddies as set out by the “z-less”scaling. In the range of strong stability, i.e., RiB ≳ 0.2, the values ofCc/CcN calculated with the formulations by Beljaars and Holtslag(1991) and by Delage (1997) both remain generally within a fac-tor of three from the values of fc(RiB) calculated with the HadAM2Louis function, except that the Beljaars and Holtslag formulationfalls off to approach the HadAM2 SHARP function at RiB ≳ 5. ThePleim (2006) formulation behaves similarly to the HadAM2 long-tail function at RiB ≳ 0.2.

In section 3.2, we discuss the impacts of using different M-Ouniversal functions listed in Table 1 on the calculation of aero-dynamic resistance and dry deposition velocities. As mentionedbelow, there is another source of potential problems in the calcu-lation of micro-meteorological parameters in the modeling of drydeposition which is often inconsistent between host meteorolog-ical models/data and atmospheric chemistry models. For demon-strating the impact of this inconsistency, the HadAM2 Louisfunction introduced above in Eq. (41) is also used for some of thecalculations in section 3.2.

2.4.3. Formulation inconsistencies introduced in atmosphericchemistry modeling

If the coefficients of momentum drag (CD) and scalar transfer(Cc) are formulated in a simple manner, i.e., independent of u* and Las in Eqs. (36)e(39), the values of u* and L can be derived by usingthe following analytical relationships that do not require iterationto find their numerical solution:

u� ¼ urefffiffiffiffiffiffiCD

p; (43)

L ¼ zref C3=2D

k Cc RiB: (44)

These relationships are often useful for transferring information onthe SBLmicro-meteorological parameters from host meteorologicalmodels (or from objective analyses data) to atmospheric chemistrymodels (e.g., Walcek et al., 1986).

It should be noted, however, that an inconsistency can existbetween the computations of stability corrections for the deriva-tion of micro-meteorological parameters (u* and L) and the sub-sequent calculation of aerodynamic resistance. Quite often, themicro-meteorological parameters are calculated by a formulationthat prescribes weak eddy diffusion beyond the limit of the “z-less”scaling, whereas the aerodynamic resistance itself is formulatedbased on the “z-less” scaling (Walcek et al., 1986; Padro et al., 1991;Jacob et al., 1993; Ganzeveld and Lelieveld, 1995; Kerkweg et al.,2006). For example, Walcek et al. (1986) use the Louis (1979)formulation for deriving u* and L from the mean state variables(uref, qv,ref and qv0) via equations equivalent to Eqs. (43) and (44),followed by the calculation of aerodynamic resistance using Jcbased on Dyer's “z-less” scaling formulation. As noted in section2.4.2, the Louis formulation allows for the persistence of weak eddydiffusion at RiB[0:2 where the “z-less” scaling formulation as-sumes the termination of turbulent eddies (see Fig. 1). Impacts ofthis type of inconsistency on the calculation of aerodynamicresistance and dry deposition velocities are also discussed in sec-tion 3.2.

3. Relevance and impacts of using different formulations ofstability corrections for aerodynamic resistance

3.1. Frequency distributions of the bulk Richardson number in theCMC global analyses

To demonstrate the relevance of strongly stable conditionsbeyond the limit of the “z-less” scaling (RiB > 0.2) to the simulationsof weather and atmospheric chemistry, we calculated RiB by Eq.(32) in the lowest layer of the atmosphere using CMC's 6-hourlyglobal objective analyses of meteorological and surface fields forselected months (January, April, July and October) in 2010. Theseanalyses retain the horizontal and vertical grid structure of theGEM weather forecast model employed in the global deterministicprediction system, consisting of 800 � 600 horizontal grid pointsspaced uniformly in longitude and latitude (33-km resolution inlatitude) and 80 vertical levels from the earth's surface up to 0.1 hPain a s-pressure hybrid coordinate (Charron et al., 2012). In GEM, thesurface fluxes are calculated over four types of surfaces (land, gla-ciers, open water and ice-covered water) (B�elair et al., 2003a, b;2009) and thus up to four independent values of RiB are obtainedon each grid tile as a result of varying surface temperatures amongthe surface types.

Fig. 2 shows area-weighted cumulative relative frequencies forthe value of RiB under statically stable conditions (RiB > 0) in eachselected month and each hemisphere and for different surfacetypes (albeit the statistics for the land and glaciers surfaces areaggregated). For each selected month, 51e57% and 26e40% of thestatically stable lowest atmospheric layer over the land and glacierssurfaces can be beyond the limit of the “z-less” scaling (i.e.,RiB ¼ 0.2) in the northern and southern hemispheres, respectively.Proportions of RiB becoming greater than 0.2 are also quite highover ice-covered water surfaces, namely, 12e30% of the surfaces instatically stable conditions for each selected month in each hemi-sphere. On the other hand, RiB exceeds 0.2 over openwater surfacesmuch less frequently, viz. generally less than 10% of the surfaces instatically stable conditions except in the northern hemisphere forJuly 2010.

Fig. 3 shows the cumulative relative frequencies of RiB sorted bythe wind speed (uref) at the reference height (~40 m above thesurface), where we use the same global analyses data as those usedfor producing Fig. 2 but aggregate the data over the four selectedmonths (January, April, July and October 2010) and both hemi-spheres. At uref ( 5 m se1, the lowest atmospheric layer is char-acterized by RiB > 0.2 onmore than half of the land, glaciers and ice-covered surfaces under the stable stratification of air. On the otherhand, at uref > 8 m s�1, the strong stability conditions of RiB > 0.2rarely occur on any of the four surface types considered in the GEMmodel.

3.2. Sensitivities of the dry deposition velocities to the choice ofstability correction algorithms

3.2.1. Changes in the aerodynamic resistance with algorithmselection

We now examine the impacts of using different stability-correction algorithms for the calculation of aerodynamic resis-tance (ra) on the rates of air-surface exchange of reactive gases.Fig. 4(a) and (b) show variations in the calculated values of raamong Dyer's “z-less” scaling formulation (Dyer, 1974), the Beljaarsand Holtslag (1991) formulation, the Delage (1997) formulation andthe Pleim (2006) formulation (see Table 1). Based upon our findingon the proportions for the occurrence of RiB greater than 0.2 inCMC's global objective analyses (section 3.1), we calculate changes

Fig. 3. The same as Fig. 2 but aggregated over the four selected months (January, April, July and October 2010) and both hemispheres, while being sorted by the wind speed ath ¼ 0.995 for each bin of 1 m s�1 between 0 and 10 m s�1 and disregarding cases where the wind speed is beyond 10 m s�1.


in ra with RiB from 10�2 to 101 at the reference-height wind speedsof 1 and 5 m s�1. In accordance with the trends in changes ofvarious bulk transfer coefficients with RiB (Fig. 1), the calculated

Fig. 4. Changes with RiB in the aerodynamic resistance (ra) of scalar transfer at the referenceby Dyer's “z-less” scaling formulation (gray shade) (Dyer, 1974), the Beljaars and Holtslag (1employed in GEM (blue/purple shade) and the Pleim (2006) formulation employed in CMformulation (“Delage-Dyer hybrid” in light-blue shading) or HadAM2's Louis formulation bderive u* and L, which subsequently enter Dyer's “z-less” scaling formulation to obtain ra. As102 � zref/z0 � 105. Corresponding changes in the calculated dry deposition velocities with RiBand Abbatt, 2002) (c, d) and for O3 on snow-covered surfaces in polar regions where rc ¼ 10with RiB are calculated for SO2 using ra obtained at zref/z0 ¼ 102 along with rc ¼ 50 s m�

respectively (Erisman et al., 1994b) (g, h).

values of ra diverge notably beyond RiB z 0.2 between Dyer's “z-less” scaling formulation and the rest of the formulations. Ascalculated by Dyer's “z-less” scaling formulation, the values of ra

height (zref) where the wind speed is assumed at 1 m s�1 (a) or 5 m s�1 (b), as calculated991) formulation employed in ECMWF IFS (red shade), the Delage (1997) formulationAQ-MM5 (green shade). Also shown are the cases where either the Delage (1997)

ased on Eq. (41) (King et al., 2001) (“Louis-Dyer hybrid” in yellow shading) is used towith Fig. 1, the range of the ra values for each set of the formulation is calculated overare shown for HOBr on the salty snow surface in polar regions where rc ¼ 1 s m�1 (Huff4 s m�1 (Helmig et al., 2007) (e, f). Changes in the calculated dry deposition velocities1 (solid lines) and 103 s m�1 (dashed lines) on “wet” and “dry” heathland surfaces,


start going up sharply at RiB z 0.1 and eventually increase towardinfinity at RiB z 0.2. In contrast, ra continues to grow graduallybeyond RiB z 0.2 as calculated by the other three formulations. Thevalues of ra calculated by using these three formulations divergesignificantly only at RiB ≳ 3, where the discrepancies between thehighest (Beljaars and Holtslag) and lowest (Pleim) values exceed anorder of magnitude.

Fig. 4(a) and (b) also show the values of ra calculated by hybridapproaches employed in some of the atmospheric chemistrymodels, where ra is formulated based on the “z-less” scalingformulation but uses the input values of u* and L derived fromformulations that allow for weak eddy fluxes beyond the limit ofthe “z-less” scaling (section 2.4.3). The curves denoted as “Louis-Dyer hybrid” represent the results based on HadAM2's Louisformulation (Eq. (41)) for the derivation of u* and L followed by theuse of Dyer's “z-less” scaling formulation for the calculation of ra inEq. (16). This algorithm simplifies the root-finding process byavoiding iteration. However, owing to inconsistent application ofstability corrections within the formulations, the calculated valuesof ra end up in between those derived purely by the “z-less” scalingformulation and those calculated by formulations permitting theoccurrence of eddy diffusion at RiB > 0.2. Environment and ClimateChange Canada's operational air quality model, GEM-MACH (GlobalEnvironmental Multi-scaleeModelling Air quality and CHemistry),employs a “Delage-Dyer hybrid” approach where the Delage (1997)formulation is used to calculate u* and L and Dyer's “z-less” scalingformulation is subsequently used to calculate ra under stable con-ditions (Moran et al., 2012; Robichaud and M�enard, 2014; Voldneret al., 1986). The curves for ra obtained by the “Delage-Dyer hybrid”approach follow the same trends as those obtained by the “Louis-Dyer hybrid” approach (Fig. 4(a) and (b)). This confirms that thealgorithms using inconsistent stability corrections between thecalculations of u*, L and rawill likely obtain intermediate values of rabetween those calculated by using one of the consistently formu-lated algorithms. The formulation of aerodynamic resistanceadopted in the models of air quality and atmospheric chemistry byWalcek et al. (1986), Padro et al. (1991), Ganzeveld and Lelieveld(1995) and Kerkweg et al. (2006) falls under the category of the“Louis-Dyer hybrid” approach. A correction to the inconsistency inthe stability-correction algorithm for the determination of ra isbeing sought along with revisions in more fundamental aspectssuch as representation of plant physiology in the next-generationdry deposition scheme for GEM-MACH.

3.2.2. Impacts on dry deposition velocitiesNext, we demonstrate the impact of changing the stability-

correction algorithms on the computation of dry deposition ve-locities (Fig. 4(ceh)). Since it is not our purpose to deal with all thecomplexity in the canopy resistance parameterizations (e.g.,Wesely, 1989; Wesely and Hicks, 2000; Zhang et al., 2003), weselect three ideal cases among which the representative values of rcvary by four orders of magnitude in a simple manner: the exchangeof reactive bromine compounds across salty snow surfaces in thespringtime polar region, dry deposition of O3 on surfaces largelycovered with snow and/or ice during thewinter, and dry depositionof SO2 at night on land surfaces.

The formulation of aerodynamic resistance described here forthe modeling of dry deposition of scalars is also applicable tosimulating bi-directional exchanges and/or heterogeneous chemi-cal conversions that occur between the near-surface air and theunderlying surface for gaseous species, such as ammonia (NH3),elemental mercury (Hg(0)), nitrous acid (HONO), methanol(CH3OH) and reactive bromine species (HOBr, Br2, etc.) (Nemitzet al., 2001; Bash et al., 2007; Bash, 2010; Massad et al., 2010;

Zhang et al., 2009; Pleim and Ran, 2011; Carpenter et al., 2004;Huff and Abbatt, 2002; Cao et al., 2014; Toyota et al., 2011, 2014;Karamchandani et al., 2015). Here, we refer to one simpleexample, i.e., modeling of the autocatalytic build-up of reactivebromine gases (“bromine explosion”) that are released into thestable ABL from polar snowpacks containing halide anions (Br� andCl�) (Huff and Abbatt, 2002; Cao et al., 2014):

HOBrðgÞ þ Br� þ Hþ/Br2ðgÞ þ H2O; (45)

HOBrðgÞ þ Cl� þ Hþ/BrClðgÞ þ H2O: (46)

In this chemical scheme, the dry deposition of hypobromousacid (HOBr) on the snow surface results in the production andsubsequent release of Br2 and/or BrCl back to the ambient surfaceair. The vertical flux of HOBr (FHOBr) is assumed to be either iden-tical to or greater than the sum of the fluxes of Br2 (FBr2) and BrCl(FBrCl) in magnitude and opposite in sign, namely, FBr2 ¼ eaBr2FHOBrand FBrCl ¼ eaBrClFHOBr where aBr2 and aBrCl are the fractions of thedeposited HOBr being converted to Br2 and BrCl, respectively, viareactions (45e46). If HOBr is converted to other products orretained in the snow without chemical conversion, the total yieldsof Br2 and BrCl are less than unity; therefore, 0 � aBr2 þ aBrCl � 1.The canopy resistance, rc, for HOBr is formulated based upon itsuptake coefficient (g) on the surface of a frozen solution of sea saltand the mean thermal speed of the HOBr molecule (vt):

rc ¼ 4g vt

: (47)

In their application of this formulation, Huff and Abbatt (2002)selected a couple of their experimental values of g (of the order of10�3) for HOBr at 233 K, along with vt ¼ 2.25� 103 m s�1 estimatedat the same temperature, obtaining rc of the order of 1 s m�1. Thisimplies that the rate of the dry deposition of HOBr on the snowsurface over sea ice is determined largely by aerodynamic resis-tance, as presumed and/or estimated in models simulating the“bromine explosion” (Lehrer et al., 2004; Toyota et al., 2011, 2014;Cao et al., 2014). Hence, using rc ¼ 1 s m�1, we calculate the drydeposition velocities (vd) for HOBr on the salty snow/ice surfacescorresponding to the values of ra plotted in Fig. 4(a) and (b), seeFig. 4(c) and (d). Since the values of rb þ rc are much lower thanthose of ra in this scenario, variations in vd due to the choice ofstability-correction algorithms essentially mirror those obtainedfor ra. We note that the momentum roughness length (z0) for snowcover on sea ice is in the range of 10�3e10�4 m with somedependence on u* (Andreas, 2011); thus, the realistic value of zref/z0is on the order of 105 on the sea ice for zref ¼ 40 m, which corre-sponds to the lower end of each shaded band for the calculatedvalues of vd in Fig. 4(c) and (d). Now, if we assume that all thefraction of HOBr deposited from the ambient air to the salty snowsurface is converted to Br2 and then released back to the air(aBr2 ¼ 1) and the volumemixing ratio of HOBr at 20 pmol mol�1 asmeasured in the springtime Arctic boundary layer (Liao et al., 2012),FBr2 z 5 � 107 cm�2 s�1 at vd ¼ 0.1 cm s�1 in the 1-atm pressure ofair. Models simulating the “bromine explosion” estimate that thefluxes of total Br-atoms released in the form(s) of Br2 and/or BrClfrom the snowpack are required to be on the order of 108 cm�2 s�1

or greater for a partial or major depletion of O3 (a ubiquitousphenomenon in polar spring) to occur in the springtime polarboundary layer within 1e4 days (Piot and von Glasow, 2009; Toyotaet al., 2011, 2014). Thus, the simulation of the “bromine explosion”is likely to be sensitive to the choice of the stability-correction al-gorithm for ra, because it considerably changes the range of RiBvalues (i.e., stability regime) where vd for HOBr is calculated to


become lower than 0.1 cm s�1.Fig. 4(e) and (f) show the sensitivity of vd for O3 on the surfaces

covered with snow and/or sea ice during the winter to the choice ofstability-correction algorithms for ra. For these calculation, we as-sume rc ¼ 104 s m�1, based on the evaluation of simulated ground-level O3 concentrations in a global three-dimensional chemicaltransport model by Helmig et al. (2007). They concluded that thedry deposition velocities of O3 on the snow and ice cover should bebetween 0.00 and 0.01 cm s�1 inwinter. Compared to the precedingscenario for the deposition of HOBr on the salty snow surface,variations in the values of vd for O3 on snow/ice surfaces are limitedby the large value of rc. Beyond the limit of the “z-less” scaling(RiB > 0.2), however, the choice of the stability-correction algorithmmakes a notable difference in the values of vd.

According to the CMC global analyses, RiB > 0.2 occurs over landsurfaces in spring, summer and autumn nearly as frequently as inwinter (see Fig. 2). Therefore, dry deposition velocities simulatedon the land surfaces without snow cover in warm seasons at nightare also expected to be quite sensitive to the choice of parameter-izations for aerodynamic resistance in stable SBL. The formation ofdew on the surface of vegetation and soils, typically associated withcooling under the stable stratification of air at night, often de-creases the values of rc below those without the dew on the samesurface (Erisman et al., 1994b; Zhang et al., 2003). For example,Zhang et al. (2002a) estimate the median nighttime values of rc forO3 over several types of vegetated surfaces to decrease from735e1831 sm�1 under dry conditions to 244e1055 sm�1 under theconditions of dew formulation. The impact of wet surface condi-tions on rc is even larger for more soluble species; for the drydeposition of SO2 on heathland surfaces, the nighttime value of rc isestimated to decrease from 1000 s m�1 under dry conditions(relative humidity less than 60%) to less than 50 s m�1 under humidconditions (relative humidity greater than 80%) (Erisman et al.,1994b). Also, in their model calculation above a deciduous forestduring the summer in Canada, Padro et al. (1991) find that thecanopy wetness reduces the cuticle resistance to a degree that rabecomes a dominant factor for the determination of vd for SO2 atnight and early in themorning. Fig. 4(g) and (h) show the variationsin vd with RiB for different formulations of stability corrections inthe case of SO2 deposition on dry and wet heathland surfaces. AtRiB ( 0.2, the changes in the calculated values of vd are largely dueto switching the value of rc from 1000 s m�1 representing the drysurface condition to 50 s m�1 representing the wet surface condi-tion. At RiB ≳ 0:2, however, the uncertainty associated with thechoice of the stability-correction algorithm is as critical as theparameterization of rc related to the surface wetness in the deter-mination of vd, particularly at the lower end of wind speed.

4. Concluding remarks

In this study, we have reviewed the uncertainty present in theformulations of aerodynamic resistance (ra) in stable SBL used inlarge-scale models of weather and atmospheric chemistry.We haveshown that different stability-correction algorithms employed inexisting operational and/or research models can estimate thevalues of ra and dry deposition velocities in notable disagreementwith each other under strongly stable conditions at RiB > 0.2. Im-pacts associated with this discrepancy among the algorithms maynot be negligible in the simulation of chemistry in the ABL, asdiscussed through a few examples in section 3.2. Given the highdegree of empiricism involved in the construction of stability-correction formulations under statically stable conditions, it isimportant to examine the skills of model parameterizations foreddy fluxes in the ABL and the impact of their uncertainties on

meteorology and chemistry, especially in online models of weatherand atmospheric chemistry.

One of the major topics of interest in weather forecast andclimate modeling is the uncertainty in the stability corrections forcalculating the surface fluxes of heat and momentum under stableconditions, because it is often associated with biases in the surfacetemperatures simulated at night and can even impact the simula-tion of atmospheric dynamics such as the development of cyclones(Holtslag et al., 2013). On the other hand, there has not been muchstudied on how much impact the uncertainty translated to theparameterization of ra will have on the simulation of atmosphericchemistry. However, air-quality models are seeking improvementin their skills for simulating the surface air concentrations ofgaseous pollutants and particulate matter during both the daytimeand nighttime (e.g., Makar et al., 2014). It thus seems to beworthwhile asking whether the changes in the stability-correctionalgorithm for ra (and hence vd) can improve (or degrade) thesimulation of the pollutant concentrations at night and whetherthe changes in vd at night can impact the simulated deposition ofthe pollutants to the ecosystem over a full diurnal cycle.

On a final note, the values of ra much in excess of 106 s m�1 canviolate a physical realism that the sum of the aerodynamic andquasi-laminar layer resistances (ra þ rb) must remain below thelimit of molecular diffusion for gaseous compounds in air. Forexample, molecular diffusivities (Dg) of O3 and SO2 in air at 0 �C and1 atm are 1.4 � 10�5 m2 s�1 and 1.1 � 10�5 m2 s�1, respectively(Massman, 1998), from which we can deduce that upper limits forra þ rb (z zref/Dg, cf. Eqs. (26) and (27)) are around 3� 106 s m�1 forthese compounds at zref ¼ 40 m. The violation of this constraint canbe avoided simply by applying an upper limit for ra þ rb at zref/Dg,because the models of dry deposition calculate Dg for gaseouscompounds of interest as required for deriving rb. However, thelength scale of relevance for Dg at 10�5 m2 s�1 over a day (t1d ¼ 8.64

� 104 s) is no more than 0.93 m ð¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffit1d Dg

p Þ. The problem arising

from the violation of the molecular-diffusion limit is thereforenegligible for the calculation of ra at the temporal and spatial scalesof general interest in atmospheric chemistry simulations. On theother hand, some air-quality models assume the ad-hoc lowerlimits of eddy diffusivity for pollutants to be as high as 0.01 m2 s�1

and 1 m2 s�1 in the outer boundary layer over the non-urban andurban surfaces, respectively, to improve a practical skill of themodels in simulating the ground-level concentrations of the pol-lutants at night (Makar et al., 2014). The length scales of relevanceare between 29.4 and 294 m for the diffusivities between 0.01 and1 m2 s�1 at the timescale of a day, which raises a question as towhether the values of ra in the SBL should be reconciled to thelower limits of eddy diffusivity in the outer boundary layerempirically imposed on the simulations of atmospheric chemistry.

Acknowledgments

We thank Ayrton Zadra, Mike Moran, Amir Aliabadi, Ralf Stae-bler, Paul Makar and Alain Robichaud for useful information anddiscussions. We are also grateful to two anonymous reviewers fortheir detailed and useful comments to the manuscript. This studywas supported by funding from the Clean Air Regulatory Agenda(CARA) at Environment and Climate Change Canada.

References

Aliabadi, A.A., Staebler, R.M., de Grandpr�e, J., Zadra, A., Vaillancourt, P.A., 2016.Comparison of estimated atmospheric boundary layer mixing height in theArctic and southern Great Plains under statically stable conditions: experi-mental and numerical aspects. Atmos.-Ocean 54, 60e74.

Andreas, E.L., 1987. A theory for the scalar roughness and the scalar transfer

http://refhub.elsevier.com/S1352-2310(16)30773-7/sref1








coefficients over snow and sea ice. Bound.-Layer Meteorol. 38, 159e184.Andreas, E.L., 2011. The fallacy of drifting snow. Bound.-Layer Meteorol. 141,

333e347.Baldocchi, D., 1988. A multi-layer model for estimating sulfur dioxide deposition to

a deciduous oak forest canopy. Atmos. Environ. 22, 869e884.Baldocchi, D.D., Hicks, B.B., Camara, P., 1987. A canopy stomatal resistance model for

gaseous deposition to vegetated surfaces. Atmos. Environ. 21, 91e101.Bash, J.O., 2010. Description and initial simulation of a dynamic bidirectional air-

surface exchange model for mercury in Community Multiscale Air Quality(CMAQ) model. J. Geophys. Res. 115, D06305.

Bash, J.O., Bresnahan, P., Miller, D.R., 2007. Dynamic surface interface exchanges ofmercury: a review and compartmentalized modeling framework. J. Appl.Meteorol. Clim. 46, 1606e1618.

Bechtold, P., K€ohler, M., Jung, T., Doblas-Reyes, F., Leutbecher, M., Rodwell, M.J.,Vitart, F., Balsamo, G., 2008. Advances in simulating atmospheric variabilitywith the ECMWF model: from synoptic to decadal time-scales. Quart. J. R.Meteorol. Soc. 134, 1337e1351.

B�elair, S., Brown, R., Mailhot, J., Bilodeau, B., Crevier, L.-P., 2003a. Operationalimplementation of the ISBA land surface scheme in the Canadian regionalweather forecast model. Part II: cold season results. J. Hydrometeor 4, 371e386.

B�elair, S., Crevier, L.-P., Mailhot, J., Bilodeau, B., Delage, Y., 2003b. Operationalimplementation of the ISBA land surface scheme in the Canadian regionalweather forecast model. Part I: warm season results. J. Hydrometeor 4,352e370.

B�elair, S., Roch, M., Leduc, A.-M., Vaillancourt, P.A., Laroche, S., Mailhot, J., 2009.Medium-range quantitative precipitation forecasts from Canada's new 33-kmdeterministic global operational system. Weather. Forecast. 24, 690e708.

Beljaars, A.C.M., Holtslag, A.A.M., 1991. Flux parameterization over land surfaces foratmospheric models. J. Appl. Meteorol. 30, 327e341.

Brost, R.A., Wyngaard, J.C., 1978. A model study of the stably stratified planetaryboundary layer. J. Atmos. Sci. 35, 1427e1440.

Brutsaert, W., 1982. Evaporation into the Atmosphere. Reidel, Dordrecht, Holland.Byun, D., Pleim, J., Tang, R., Bourgeois, A., 1999. Science Algorithms of the EPA

Models-3 Community Multiscale Air Quality (CMAQ) Modeling System, Chapter12. EPA/600/R-99/030.

Byun, D.W., 1990. On the analytical solutions of flux-profile relationships for theatmospheric surface layer. J. Appl. Meteorol. 29, 652e657.

Campbell, G.S., Norman, J.M., 1998. An Introduction to Environmental Biophysics,second ed. Springer-Verlag, New York, USA.

Cao, L., Sihler, H., Platt, U., Gutheil, E., 2014. Numerical analysis of the chemicalkinetic mechanisms of ozone depletion and halogen release in the polartroposphere. Atmos. Chem. Phys. 14, 3771e3787.

Carpenter, L.J., Lewis, A.C., Hopkins, J.R., Read, K.A., Longley, I.D., Gallagher, M.W.,2004. Uptake of methanol to the north atlantic ocean surface. Global Bio-geochem. Cycles 18, GB4027.

Charron, M., Polavarapu, S., Buehner, M., Vaillancourt, P.A., Charette, C., Roch, M.,Morneau, J., Garand, L., Aparicio, J.M., MacPherson, S., Pellerin, S., St-James, J.,Heilliette, S., 2012. The stratospheric extension of the Canadian global deter-ministic medium-range weather forecasting system and its impact on tropo-spheric forecasts. Mon. Weather. Rev. 140, 1924e1944.

Cuxart, J., Holtslag, A., Beare, R., Bazile, E., Beljaars, A., Cheng, A., Conangla, L., Ek, M.,Freedman, F., Hamdi, R., Kerstein, A., Kitagawa, H., Lenderink, G., Lewellen, D.,Mailhot, J., Mauritsen, T., Perov, V., Schayes, G., Steeneveld, G.-J., Svensson, G.,Taylor, P., Weng, W., Wunsch, S., Xu, K.-M., 2006. Single-column model inter-comparison for a stably stratified atmospheric boundary layer. Bound.-LayerMeteorol. 118, 273e303.

Deardorff, J.W., 1972. Parameterization of the planetary boundary layer for use ingeneral circulation models. Mon. Weather. Rev. 1972, 93e106.

Delage, Y., 1997. Parameterising sub-grid scale vertical transport in atmosphericmodels under statically stable conditions. Bound.-Layer Meteorol. 82, 23e48.

Delage, Y., Girard, C., 1992. Stability functions correct at the free convection limitand consistent for both the surface and Ekman layers. Bound.-Layer Meteorol.58, 19e31.

Dyer, A.J., 1974. A review of flux-profile relationships. Bound.-Layer Meteorol. 7,363e372.

Erisman, J.W., van Elzakker, B.G., Mennen, M.G., Hogenkamp, J., Zwart, E., van denBeld, L., R€omer, F.G., Bobbink, R., Heil, G., Raessen, M., Duyzer, J.H., Verhage, H.,Wyers, G.P., Otjes, R.P., M€ols, J.J., 1994a. The Elspeetsche Veld experiment onsurface exchange of trace gases: summary of results. Atmos. Environ. 28,487e497.

Erisman, J.W., Van Pul, A., Wyers, G.P., 1994b. Parameterization of surface resistancefor the quantification of atmospheric deposition of acidifying pollutants andozone. Atmos. Environ. 28, 2595e2607.

Fairall, C.W., Hare, J., Edson, J.B., McGillis, W., 2000. Parameterization and micro-meteorological measurement of air-sea gas transfer. Bound.-Layer Meteorol. 96,63e105.

Fairall, C.W., Helmig, D., Ganzeveld, L., Hare, J., 2007. Water-side turbulenceenhancement of ozone deposition to the ocean. Atmos. Chem. Phys. 7, 443e451.

Foken, T., 2006. 50 years of the Monin-Obukhov similarity theory. Bound.-LayerMeteorol. 119, 431e447.

Ganzeveld, L., Lelieveld, J., 1995. Dry deposition parameterization in a chemistrygeneral circulation model and its influence on the distribution of reactive tracegases. J. Geophys. Res. 100 (D10), 20999e21012.

Garratt, J.R., 1992. The Atmospheric Boundary Layer. Cambridge Univ. Press, Cam-bridge, UK.

Garratt, J.R., Hicks, B.B., 1973. Momentum, heat and water vapour transfer to andfrom natural and artificial surfaces. Quart. J. R. Meteorol. Soc. 99, 680e687.

Grachev, A.A., Andreas, E.L., Fairall, C.W., Guest, P.S., Persson, P.O.G., 2013. Thecritical Richardson number and limits of applicability of local similarity theoryin the stable boundary layer. Bound.-Layer Meteorol. 147, 51e82.

Helmig, D., Ganzeveld, L., Butler, T., Oltmans, S.J., 2007. The role of ozoneatmosphere-snow gas exchange on polar, boundary-layer tropospheric ozone ea review and sensitivity analysis. Atmos. Chem. Phys. 7, 15e30.

Hicks, B.B., 1976. Wind profile relationship from the Wangara experiment. Quart. J.R. Meteorol. Soc. 102, 535e551.

H€ogstr€om, U., 1988. Non-dimensional wind and temperature profiles in the atmo-spheric surface layers: a re-evaluation. Bound.-Layer Meteorol. 42, 55e78.

H€ogstr€om, U., 1996. Review of some basic characteristics of the atmospheric surfacelayer. Bound.-Layer Meteorol. 78, 215e246.

Holtslag, A.A.M., de Bruin, H.A.R., 1988. Applied modeling of the nighttime surfaceenergy balance over land. J. Appl. Meteorol. 27, 689e704.

Holtslag, A.A.M., Svensson, G., Baas, P., Basu, S., Beare, B., Beljaars, A.C.M.,Bosveld, F.C., Cuxart, J., Lindvall, J., Steeneveld, G.J., Tjernstr€om, M.,Wiel, B.J.H.V.D., 2013. Stable atmospheric boundary layers and diurnal cycles:challenges for weather and climate models. Bull. Am. Meteor. Soc. 94,1691e1706.

Huff, A.K., Abbatt, J.P.D., 2002. Kinetics and product yields in the heterogeneousreactions of HOBr with ice surfaces containing NaBr and NaCl. J. Phys. Chem. A106, 5279e5287.

Jacob, D.J., Logan, J.A., Yevich, R.M., Gardner, G.M., Spivakovsky, C.M., Wofsy, S.C.,Munger, J.W., Sillman, S., Prather, M.J., Rodgers, M.O., Westberg, H.,Zimmerman, P.R., 1993. Simulation of summertime ozone over North America.J. Geophys. Res. 98 (D8), 14797e14816.

Karamchandani, P., Emery, C., Yarwood, G., Lefer, B., Stutz, J., Couzo, E., Vizuete, W.,2015. Implementation and refinement of a surface model for heterogeneousHONO formation in a 3-D chemical transport model. Atmos. Environ. 112,356e368.

Kerkweg, A., Buchholz, J., Ganzeveld, L., Pozzer, A., Tost, H., J€ockel, P., 2006. Technicalnote: an implementation of the dry removal processes DRY DEPosition andSEDImentation in the Modular Earth Submodel System (MESSy). Atmos. Chem.Phys. 6, 4617e4632.

King, J.C., Connolley, W.M., Derbyshire, S.H., 2001. Sensitivity of modelled Antarcticclimate to surface and boundary-layer flux parametrizations. Quart. J. R.Meteorol. Soc. 127, 779e794.

Kondo, J., Kanechica, O., Yasuda, N., 1978. Heat and momentum transfers understrong stability in the atmospheric surface layer. J. Atmos. Sci. 35, 1012e1021.

Launiainen, J., 1995. Derivation of the relationship between the Obukhov stabilityparameter and the bulk Richardson number for flux-profile studies. Bound.-Layer Meteorol. 76, 165e179.

Lehrer, E., H€onninger, G., Platt, U., 2004. A one dimensional model study of themechanism of halogen liberation and vertical transport in the polar tropo-sphere. Atmos. Chem. Phys. 4, 2427e2440.

Liao, J., Huey, L.G., Scheuer, E., Dibb, J.E., Stickel, R.E., Tanner, D.J., Neuman, J.A.,Nowak, J.B., Choi, S., Wang, Y., Salawitch, R.J., Canty, T., Chance, K., Kurosu, T.,Suleiman, R., Weinheimer, A.J., Shetter, R.E., Fried, A., Brune, W., Anderson, B.,Zhang, X., Chen, G., Crawford, J., Hecobian, A., Ingall, E.D., 2012. Characterizationof soluble bromide measurements and a case study of BrO observations duringARCTAS. Atmos. Chem. Phys. 12, 1327e1338.

Louis, J.-F., 1979. A parametric model of vertical eddy fluxes in the atmosphere.Bound.-Layer Meteorol. 17, 187e202.

Louis, J.-F., Tiedtke, M., Geleyn, J.F., 1982. A short history of the operational PBL-parameterization of ECMWF. In: Workshop on Planetary Boundary LayerParameterization, 25e27 November 1981, Shinfield Park, Reading, Berkshire,UK, European Centre for Medium Range Weather Forecasts, pp. 59e79.

Mahrt, L., 1987. Grid-averaged surface fluxes. Mon. Weather. Rev. 115, 1550e1560.Mahrt, L., Richardson, S., Seaman, N., Stauffer, D., 2012. Turbulence in the nocturnal

boundary layer with light and variable winds. Quart. J. R. Meteorol. Soc. 138,1430e1439.

Makar, P.A., Gravel, S., Chirkov, V., Strawbridge, K.B., Froude, F.J.A., Brook, J., 2006.Anthropogenic heat flux, urban properties, and regional weather. Atmos. En-viron. 40, 2750e2766.

Makar, P.A., Nissen, R., Teakles, A., Zhang, J., Zheng, Q., Moran, M.D., Yau, H.,diCenzo, C., 2014. Turbulent transport, emissions and the role of compensatingerrors in chemical transport models. Geosci. Model Dev. 7, 1001e1024.

Massad, R.-S., Nemitz, E., Sutton, M.A., 2010. Review and parameterisation of bi-directional ammonia exchange between vegetation and the atmosphere.Atmos. Chem. Phys. 10, 10359e10386.

Massman, W.J., 1998. A review of the molecular diffusivities of H2O, CO2, CH4, CO,O3, SO2, NH3, N2O, NO, and NO2 in air, O2 and N2 near STP. Atmos. Environ. 32,1111e1127.

McTaggart-Cowan, R., Zadra, A., 2015. Representing Richardson number hysteresisin the NWP boundary layer. Mon. Weather. Rev. 143, 1232e1258.

Miles, J.W., 1961. On the stability of heterogeneous shear flows. J. Fluid Mech. 10,496e508.

Moran, M.D., M�enard, S., Pavlovic, R., Anselmo, D., Antonopoulos, S., Robichaud, A.,Gravel, S., Makar, P.A., Gong, W., Stroud, C., Zhang, J., Zheng, Q., Landry, H.,Beaulieu, P.A., Gilbert, S., Chen, J., Kallaur, A., 2012. Recent advances in Canada'snational operational air quality forecasting system. In: 32nd NATO-SPS ITM,7e11 May, Utrecht, the Netherlands.

Nemitz, E., Milford, C., Sutton, M.A., 2001. A two-layer canopy compensation point


























































































































































































































































model for describing bi-directional biosphere-atmosphere exchange ofammonia. Quart. J. R. Meteorol. Soc. 127, 815e833.

Nieuwstadt, F.T.M., 1984. The turbulent structure of the stable, nocturnal boundarylayer. J. Atmos. Sci. 41, 2202e2216.

Padro, J., den Hartog, G., Neumann, H.H., 1991. An investigation of the ADOM drydeposition module using summertime O3 measurements above a deciduousforest. Atmos. Environ. 25A, 1689e1704.

Piot, M., von Glasow, R., 2009. Modelling the multiphase near-surface chemistryrelated to ozone depletions in polar spring. J. Atmos. Chem. 64, 77e105.

Pleim, J.E., 2006. A simple, efficient solution of flux-profile relationships in theatmospheric surface layer. J. Appl. Meteorol. Clim. 45, 341e347.

Pleim, J.E., Ran, L., 2011. Surface flux modeling for air quality applications. Atmo-sphere 2, 271e302.

Robichaud, A., M�enard, R., 2014. Multi-year objective analyses of warm seasonground-level ozone and PM2.5 over North America using real-time observationsand Canadian operational air quality models. Atmos. Chem. Phys. 14,1769e1800.

Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer AcademicPress, Dordrecht.

Sun, J., Mahrt, L., Banta, R.M., Pichugina, Y.L., 2012. Turbulence regimes and tur-bulence intermittency in the stable boundary layer during CASES-99. J. Atmos.Sci. 69, 338e351.

Toyota, K., McConnell, J.C., Lupu, A., Neary, L., McLinden, C.A., Richter, A., Kwok, R.,Semeniuk, K., Kaminski, J.W., Gong, S.-L., Jarosz, J., Chipperfield, M.P., Sioris, C.E.,2011. Analysis of reactive bromine production and ozone depletion in the Arcticboundary layer using 3-D simulations with GEM-AQ: inference from synoptic-scale patterns. Atmos. Chem. Phys. 11, 3949e3979.

Toyota, K., McConnell, J.C., Staebler, R.M., Dastoor, A.P., 2014. Air-snowpack ex-change of bromine, ozone and mercury in the springtime Arctic simulated bythe 1-D model PHANTAS e Part 1: in-snow bromine activation and its impacton ozone. Atmos. Chem. Phys. 14, 4101e4133.

Troen, I., Mahrt, L., 1986. A simple model of the atmospheric boundary layer;sensitivity to surface evaporation. Bound.-Layer Meteorol. 37, 129e148.

Tuovinen, J.-P., Aurela, M., Laurila, T., 1998. Resistances to ozone deposition to a flarkfen in the northern aapa mire zone. J. Geophys. Res. 103, 16953e16966.

Uno, I., Cai, X.-M., Steyn, D.G., Emori, S., 1995. A simple extension of the Louismethod for rough surface layer modelling. Bound.-Layer Meteorol. 76,395e409.

Val Martin, M., Heald, C.L., Arnold, S.R., 2014. Coupling dry deposition to vegetationphenology in the Community Earth System Model: implications for the

simulation of surface O3. Geophys. Res. Lett. 41, 2988e2996.van den Hurk, B.J.J.M., Holtslag, A.A.M., 1997. On the bulk parameterization of

surface fluxes for various conditions and parameter ranges. Bound.-LayerMeteorol. 82, 119e134.

Viterbo, P., Beljaars, A., Mahfouf, J.-F., Teixeira, J., 1999. The representation of soilmoisture freezing and its impact on the stable boundary layer. Quart. J. R.Meteorol. Soc. 125, 2401e2426.

Voldner, E.C., Barrie, L.A., Sirois, A., 1986. A literature review of dry deposition ofoxides of sulphur and nitrogen with emphasis on long-range transportmodelling in North America. Atmos. Environ. 20, 2101e2123.

Walcek, C.J., Brost, R.A., Chang, J.S., Wesely, M.L., 1986. SO2, sulfate and HNO3deposition velocities computed using regional landuse and meteorological data.Atmos. Environ. 20, 949e964.

Webb, E.K., 1970. Profile relationships: the log-linear range, and extension to strongstability. Quart. J. R. Meteorol. Soc. 96, 67e90.

Wesely, M.L., 1989. Parameterization of surface resistances to gaseous dry deposi-tion in regional-scale numerical models. Atmos. Environ. 23, 1293e1304.

Wesely, M.L., Hicks, B.B., 1977. Some factors that affect the deposition rates of sulfurdioxide and similar gases on vegetation. J. Air Pollut. Control Assoc. 27,1110e1116.

Wesely, M.L., Hicks, B.B., 2000. A review of the current status of knowledge in drydeposition. Atmos. Environ. 34, 2261e2282.

Wyngaard, J.C., Cot�e, O.R., 1972. Cospectral similarity in the atmospheric surfacelayer. Quart. J. R. Meteorol. Soc. 98, 590e603.

Zhang, L., Brook, J.R., Vet, R., 2002a. On ozone dry depositiondwith emphasis onnon-stomatal uptake and wet canopies. Atmos. Environ. 36, 4787e4799.

Zhang, L., Brook, J.R., Vet, R., 2003. A revised parameterization for gaseous drydeposition in air-quality models. Atmos. Chem. Phys. 3, 2067e2082.

Zhang, L., Moran, M.D., Makar, P.A., Brook, J.R., Gong, S., 2002b. Modelling gaseousdry deposition in AURAMS: a unified regional air-quality modelling system.Atmos. Environ. 36, 537e560.

Zhang, L., Wright, L.P., Blanchard, P., 2009. A review of current knowledge con-cerning dry deposition of atmospheric mercury. Atmos. Environ. 43,5853e5964.

Zilitinkevich, S., Elperin, T., Kleeorin, N., Rogachevskii, I., Esau, I., Esau, I.,Mauritsen, T., Miles, M.W., 2008. Turbulence energetics in stably stratifiedgeophysical flows: strong and weak mixing regimes. Quart. J. R. Meteorol. Soc.134, 793e799.

Zilitinkevich, S.S., 1972. On the determination of the height of the Ekman boundarylayer. Bound.-Layer Meteorol. 3, 141e145.






















































































































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