Design artifacts in eulerian air quality models: Evaluation of the effects of layer thickness and vertical profile correction on surface ozone concentrations

Pergamola

Atmospheric Enuironment Vol. 29, No. 1, pp. 105-126, 1995 Elsevier Science Ltd Printed in Great Britain

1352-2310(94)00225-8

DESIGN ARTIFACTS IN EULERIAN AIR QUALITY MODELS: EVALlJATION OF THE EFFECTS OF LAYER THICKNESS AND VERTICAL PROFILE CORRECTION ON SURFACE OZONE CONCENTRATIONS DAEWON

W. BYUN*

and ROBIN

DENNIS*

Atmospheric lSciences Modeling Division, Air Resources Laboratory, National Oceanic and Atmospheric Administration, Research Triangle Park, NC 27711, U.S.A. (First received 16 March 1994 and in final form 6 July 1994) Abstract-Previous studies on the regional acid deposition model (RADM) have revealed high bias of surface SO, and 0, concentrations by the model, especially during nighttime hours. Comparison of the RADM results with surface measurements of hourly ozone concentrations from the National Dry Deposition Network (NDDN) sites showed distinct diurnal variations in the model high bias. Here, we investigate what part of this phenomenon is influenced by the coarse vertical resolution of RADM in representing the deposition layer. For certain deposition species in the model, we apply the planetary boundary layer (PBL) similarity theory to predict the high bias of the model results (volume averages) to the surface observations (time series at a point) for the horizontally homogeneous case. Here, we applied the profile corrections to a secondary species O,, which is one of active reacting species even at night especially with NO. However, we attempted to separate the effect of deposition layer thickness from the effects of other horizontal and vertical resolution such as emissions source distribution during the NO-O, titration process for a clearer presentation of our hypothesis. The study ishows that there are situations when a considerable portion of the high bias of model 0, concentrations at night is explained by the coarse vertical resolution in the deposition layer. It is shown that the model needs to resolve, at least, the lower half of the PBL in order to predict surface deposition fluxes correctly. Comparison with several NDDN observations shows that for certain NDDN sites the present hypothesis cannot fully explain the model’s high bias of daily minimum 0,. In a companion paper, the effect of emission source distribution in representing the NO-O, titration process will be studied to investigate causes of the model bias further. Key word index: Model evaluation, ozone, deposition, vertical profile, PBL.

WOMENCLATURE

a2

=u +811/B

a”(P)

coefficient of the power-law term for momentum profile function coefficient of the power-law term for species profile function coefficient of the power-law term for 0 profile function concentrations in the parameterized sublayers concentration at the surface model concentration at z.,,, model concentration at zc = l/z,, --20 %’ C(z) dz concentration scale at the surface Coriolis factor profile c80rrection factor (=Cl-(1-G’ %(~1VVd&1)1~ flux of pollutant available for dry deposition

a.&) a&) ct., cc

Cs Cnl(r,,) &,) C* I F

k

F o(s), OV) P P

F f0P P” P0 Prc r

ri r2 ‘.

* On assignment to the Atmospheric Research and Exposme Assessment Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, NC 27711, U.S.A.

r.sr rsPBL

105

surface deposition flux PBL height the von Karman constant vertical eddy diffusivity the Monin-Obukhov length order of errors power of the power-law term for momentum profile function pressure at the level z surface pressure pressure surface at the model top (100 mbar) integrated PBL profile function for momentum integrated PBL profile function for potential temperature the turbulent Prandtl number for the neutral atmosphere power of the power-law term for scalar profile function (=(l-zi/h)“z) (=(l-zJh)“2) aerodynamic resistance surface-layer contribution to r* boundary-layer (above the surface layer) contribution to r,

106 rbrI,,rg r, SB ~tll 1 I 4n,hl u* %.h) v&d 44, Vdb. vdol vds w* Z Zo Z19 ZZ Zdcp Z&S

zF1 ZSL

D. W. BYUN and R. DENNIS resistances for the parameterized sublayers surface resistance (sum of r, and rs)

( = L(z,)

- coIIcc(z0,,) - Cal)

layer mean wind speed in the direction of surface stress latitudinal and longitudinal components of the layer mean wind friction velocity (= l/r,) deposition velocity at height zi inverse of r,, rs, rs, and rp, respectively convective velocity scale= k/e, h u*e+y’3 a height in the PBL surface roughness length arbitrary integration limits height of the deposition-layer top height at which measurements are made height at the top of the lowest model layer surface layer height. = - 9/L = 4.1 h/0.14 L = 4.7jo.14 L

concentration gradient at the top of PBL I:,, k,(5)) dC

l;. AX’) 4

a small number a stability parameter for the surface layer ( = z/L) (=20/L)

nondimensional height = z/h =zdh = zdh =z,e,fh =z,/h =z,dh

layer-mean potential temperature surface potential temperature potential temperature scale nondimensional concentration gradient (=yhlC,) scale-height ratio (= IfI h/u,) a stability parameter for the PBL(= h/L] a normalized nressure coordinate f\ = TP &

- pt0pllcps”rf-‘P,0,1)

h&3 h(4-) 4,(C)

top of deposition layer in o-coordinate surface layer profile-function for momentum surface layer profile function for potential temperature surface layer profile function for the passive scalar integrated profile function for momentum

( = j;64,(f) W)

integrated profile function for potential temperature=$, 4JJ di integrated profile function for species concentration =jiO 4#‘) dc.

1. INTRODUCIION

most frequently used to evaluate air quality models are surface concentrations of pollutants measured at several air pollution monitoring sites. Usually, volume-averaged concentrations from the lowest model layer are compared with the observed data, expecting that the former are representative of the surface measurements. However, a surface measurement represents a value only at a given horizontal Data

location and height, while the concentration predicted by the grid model represents a volume-averaged value. There has been a lack of studies to quantify how these two different values can be compared. We can consider two possible causes for this difference: (1) the model assumes horizontally homogeneous conditions for a given cell while the observation may not be horizontally representative, and (2) the model concentrations represent vertically averaged values over the depth of the given model layer while the observations represent values at the measured altitude. Although Lenschow and Delany (1987) discussed cases of vertical profiles of reactive species that can be modified in the surface layer due to fast reaction time, often, we can determine what species can be treated as a passive scalar by comparing their time scales of vertical mixing and chemical reactions. During a clear day, the time scale of vertical mixing can be much shorter than the chemical time scales of certain trace gas reactions due to vigorous vertical mixing. We can therefore expect that even some of the photochemically active species will maintain vertical profiles similar to a passive scalar, as required by the PBL similarity theory. At night, vertical mixing of the atmosphere is very slow, causing a large time scale for the vertical mixing. However, some photochemical species that react vigorously under the sun’s ultraviolet lights will behave as passive scalars at night when there are no other significant reaction pathways. Some others, such as the NO-O, titration reaction, are very reactive day and night. For species that may be considered as passive scalars, we can apply the PBL similarity theory to predict the high bias of the model results (volume averages) to the surface observations (time series at a point) for the horizontally homogeneous case. Due to limited time resolution of observations and lack of regional representativeness, it was difficult to compare some observations directly with the RADM results of coarse horizontal resolution of 80 x 80 km*. For species such as SO, which varied rapidly with time and species, more detailed descriptions (high resolution in time and space) of emission sources and meteorological fields are needed in the model. In this paper, we apply the profile correction to a secondary species, O,, which is one of active reacting species, especially with NO even at night. Although the profile correction method is based on the profile functions for passive scalars, it is to account for the simulated deposition processes in the model. Therefore, we need to apply the correction to all the depositing species in the model for comparing with observations at 10 m. Also, the secondary species is known to have more horizontal homogeneity than the primary species. Diurnal behavior of 0, concentration is very regular and its amplitude is sensitive to the model inputs (meteorology and emissions) and model grid structure. We attempt to isolate the effect of deposition layer thickness from the effects of other horizontal and vertical resolution such as emission

Vertical profile correction source distribution during the NO-O9 titration ‘process for a clearer presentation of our hypothesis. We quantify how much of the systematic model bias can be explained by the: subgrid scale vertical profile for the case when surface removal processes are estimated by deposition velocity and the lowest layer concentration. In this study, we do not take into account changes in the vertical profiles of the trace gases by local sources and subgrid-scale fast-reaction conditions. We concentrated our study on how well the deposition process is described in the model and on how to compare model concentrations with available surface measurements. In a companion paper the effect of emission source distribution in representing the NO-O3 titration process will be studied to investigate causes of the lmodel bias further.

the passive scalars in the literature are defined for the atmospheric surface layer. In order to estimate the concentration at the observation height (10 m) from the model prediction represented at a height above the surface layer, we need to have a profile function covering the whole PBL. Byun (1991) introduced an extension of the surface-layer similarity of wind components and potential temperature to describe the resistance laws for the whole PBL. By assuming the profile has a shape of the surface similarity function with an added power-law in terms of nondimensional height q = z/h, as in Byun (1991), where z is a height in the PBL and h is the PBL height, we introduce a similarity function for a passive scalar in the PBL as follows:

wlkCo= 2. PBL

Pr0C, -

k

CWl’to)+~x(~vo)

-~,(~tl)+a,(~)(?-tlorl,

SIMILARITY THEORY

The regional acid deposition model (RADM) is an Eulerian grid model. that simulates atmospheric transport, chemical transformation, emissions input, and deposition processes (Chang et al., 1987). Vertical layers of RADM are defined in a sigma-coordinate similar to its meteorological driver known as Mesoscale Model Version 4 (MM-4) (Anthes et al., 1987). For the National Acid Precipitation Assessment Program (NAPAP), we used both 6-layer and 15layer versions of RADM for the evaluation and aggregation studies (Dennis et al., 1990). In spite of an attempt by Chang et al. (1990) to make the layered diffusion flux exchange comparable for the 6-layer and Slayer models by introducing vertically integrated eddy diffusivity, the lowest model layers for both 6- and 15layer versions showed quite different concentration values. Here we quantify and explain this difference. In RADM, dry deposition is simulated as a lower boundary condition in the diffusion process and is treated as a part of the transport step, which is assumed to have larger time-step than the chemistry computation. In the model, trace gases are assumed to be well mixed before they go through chemical transformations. Total chemical production or destruction is computed based on the layer mean concentrations. In reality, profiles o!f the trace gas concentration can be affected by the locatl sources, chemical production or loss within a plume, availability of pollutant mixtures for reactions, as well as removal processes. For the slowly reacting chemicals, influence of chemical production or loss on the vertical profile can be small where there are no significant local sources. For such a situation, the surface removal process will influence the shapes of concentration profiles considerably. Then, we can approximate profiles of the trace gases to behave similar to that of potential temperature or humidity. The lowest RADM layer can include not only the surface layer, but allso part of the upper PBL depending on the time of day. Most of the profile functions for

107

(1)

where the coefficient of the added power-law term is given as

1 1 r(l-qoYel

(2)

and the power r in the equation is estimated by applying an asymptotic magnitude comparison of the surface- and outer-layer profiles (the value r may depend on the atmospheric stability and concentrations in the upper layers). K is the nondimensional concentration,_~adient at the PBL top. For the descriptions of the notations in equations (1) and (2), refer to the Nomenclature. Figure 1 presents a schematic of the similarity profile function for a passive scalar. The coefficient of the added power-law term, equation (2), satisfies the upper boundary condition for the scalar (continuity of concentration profile above the boundary layer). Although there is no guarantee that the expression will represent the universal shape of species profile functions in the PBL, it is a simple representation of the PBL profile that reflects several important features: (1) it conforms with the surface similarity theory for small z/h, (2) it represents well the stabilitydependency in the flux-profile relations, and (3) it satisfies the bottom and top boundary conditions for fluxes and mean values. Because no alternative analytical profile formula exists, we will rely on this formula for the description of the similarity function for a deposition species.

3. THEORETICAL BY THE LIMITED

ESTIMATION VERTICAL

OF MODEL RESOLUTION

DEPOSITION

BIAS CAUSED OF THE DRY

LAYER

Using equation (l), the ratio of concentration at the center of the lowest layer to that at the measurement height can be estimated for the horizontally homogeneous conditions and away from large point source

108

D. W. BYUN and R. DENNIS

Free Atmosphere

+Nk-Gl 0

*

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

q=l

Outer Layer I

Surface Layer

Fig. 1. Schematic of the similarity profile function for a passive scalar.

regions. Since the model predicts the vertically averaged concentration of the lowest layer, rather than the value at the center of the layer, bias of the model to the observation should be estimated by treating model prediction as the vertically integrated value. Therefore, we define the bias of layer-averaged concentration compared to the concentration at a height z.~ due to the deposition process as S =G(z1)-Ccl

(3)

B C(z,,)-C,’ where =F,

1 C,(z,)=zFl-zO

s

To make use of the above analysis for the estimation of systematic model bias with respect to the measured surface concentration, we need to know the reference concentration at zo. For the deposition velocity concept to be valid, concentration at the ground should be much smaller than the concentration in the air, assuming there is no ground source. Figure 3 shows relationships among the concentrations at different heights during the deposition process. F is the flux of pollutant available for dry deposition by turbulent atmospheric transport. F. is the deposition flux, or the flux of pollutant actually taken out of the air. For the lowest model layer, we can estimate the available flux F from

C(z) dz.

F=uda(zi) C,(z,),

IO

Figure 2a and b present the bias estimates between the layer-averaged concentrations and concentration at specific heights. In the figures, we assumed that the observed height relative to the PBL height, h, is large (v,,,,~=z.,,Jh =O.ll) at nighttime (stable conditions) and small (ttob.=O.O1) at daytime (unstable conditions). For the stable case (Fig. 2a), the bias factor increases with increasing value of qF=zF1/h. For example, for the U-layer RADM, the bias can be as high as a factor of 2 when the lower PBL top is as low as the top of the lowest model layer. For the unstable case (Fig. 2b), the bias is within f 20% from a factor of unity for the range 0.01-0.1 of tfF values. Here, it is assumed that there is no significant concentration gradient at the top of the PBL. However, from equation (l), it is expected that the bias estimates will be larger if there exists a strong positive concentration gradient at the top of PBL.

(4)

and (5) where K, is the vertical eddy diffusivity, and r, the aerodynamic resistance. Formulations for K, and r, used in RADM are described in Appendix A. Note that the resistance concept is valid for the regime where K, increases monotonically with height, or at least in the lower half of the PBL. In RADM, the deposition layer is defined as a part of the lowest model layer below the center of mass. The PBL height shows significant diurnal changes and the assumption of a fixed-depth deposition layer can cause errors in estimating deposition fluxes during very stable conditions when the’model cannot resolve the surface layer from the PBL. In a well-defined deposition layer, the deposition flux in

Vertical profile correction

I, I

2.5 - STABLE

I I I 11 I

109

I I I I,,,, I

9obs=o.1

___*_._.-.-0 - . .._-_..)--“-- b _*________.-.-‘-’ :._-_-.__c_--e-h-_,___...+.__...-----’

-50

-40

-30

-20

-10

0

P Kg. 2. Concentration bias factor estimates between the model and observed values for deposition species (a) for stable atmosphere, (b) for unstable atmosphere. In the figure, v0b = z,&, qF = zpl /h, A = (f) h/u,, and p = h/L. Other symbols are described in the text.

the model is estimarted by F~F,:=v,(z,)(C,(z,)-C,)

=%(~1)C(Cm(Z1)-CO)+(CO-Cb)

F, =

ud(zl)

(‘&&I

b

c,)

+wtl-c,)+(c,-ql

(6)

where CO is not zero. The magnitude of surface deposition flux, F,,, is less than that of the available flux F. Deposition velocity u,, is determined based on the following relations for the case C,(z,) > C1 > C, > C, > C,, (see Fig. 3 for definitions):

=u,(z,) =

Fsud(zi

S+S+$+S [ Od. udb

uds

) cr. + rb + r. + rgl

1 (7)

where r. is the aerodynamic resistance, r, is the resistance in the quasi-laminar layer, and r,, which is

D. W. BYUN and R. DENNIS

110 __---__--_______-_--.

Top of First Model Layer

Q

W-q) \k

fa__

PBL

F = F(z)

_________-_-________~-~~~~~~-~~~~~-~.

Quasi-Laminar

Boundary Layer

Fig. 3. Relationship among the concentrations at different heights in the dry-deposition process.

the sum of rc and rg, represents the surface resistance. Refer to Fig. 3 for schematics of the deposition process that are based on the assumption of constant fluxes in the surface layer. When we assume C,(z,)BC,, the concentration C, at the height z0 can be estimated by

(8) ~s=~,(zl)G&l).

(9)

Then, model concentration at the measurement height can be estimated from the layer values:

G&,Ll*) 1

&Jz,) co+cm(z,)-co=~

where

ti(z1) u&d 1

I-

1

r,

r,+rb+r,

1

is the profile correction factor. Equation (10) states that the amount of concentration correction for the vertical profile depends not only on the shape of the vertical profile of a species but also on the relative magnitude of the surface resistance (r,) and aerodynamic resistance (rJ because u,=

(r, +r,,+rs)-

I. For a species with very little surface resistance, such as HNO,, the ratio u,(z,)/u,,(z,) is larger than that for a species with significant surface resistance, such as SO, or 0,. Therefore, the profile correction for HNO, is much more significant than the profile correction for SO, or 0,. Figure 4 provides an example of the differences in the concentration correction factor for different species vs the cumulative frequency (in percentage) for Pennsylvania State Scotia Range, PA, one of the EMEFS (The Eulerian Model Evaluation Field Study) special chemistry sites. Because the surface resistance depends on the land-use as well as several other environmental parameters, the amount of corrections needed to be applied would be significantly different across time and place. Although the correction method was developed based on the profile functions for passive scalars, the correction needed to be applied to all the depositing species in the model. It should be noted that the profile correction is to account for the simulated deposition processes in the model for comparing model results with observations. It should not be considered as a replacement for the modeling needs of detailed subgrid-scale treatment of reactive species. Especially, if one wants to simulate the effect of subgrid scale reactions on the vertical profiles of reactive species, for which the current regional model is not designed, a high resolution PBL numerical model for reactive trace ‘gases, such as reported by Gao and Wesley (1993), should be used.

Vertical protie correction ---.o---

Fc(O3) Day

-

Fc(O3) Night

----I+--

Fc(SO2) Day

-

Fc(SO2) Night

---.A-----

Fc(HN03)

-

Fc(HN03)

I

I

1 .i!

Day

/I

II

SCOTIA 1.I

111

I

II

1988

Ii

Night

I

SO2(day) ,___.

Summer

-

:

--

-

HN03 I

0.!5 .oi

I

.l

(ngt) I

1

II

5

II

10

2030

Cumulative

I

50

II

II

7080

9095

Probability

I

99

I

99.9

99.99

(Percent)

Fig. 4. Concentration profile correction factors for SO,, HNO,, and 0, vs cumulative probability in percentage for Scotia Range, PA (1988 Summer).

4. MODEL

DATA FOR THR RADM EVALUATION

l.OZu,,,>0.995. Table 1 shows the full and half ulevels and standard heights for the 6- and 15.layer versions of RADM. For model evaluations and de4.1. 6- and U-layer RADM tailed episodic studies, both the 6- and 15-layer Both Mesoscale Model, Version 4 (MM4) and versions have been used (Dennis, 1990). In RADM RADM use the 0 as the vertical coordinate system, version 2.6, the lowest PBL height is limited td the top defined by of the lowest layer of the 15.layer MM4. Therefore, for 15.layer RADM, the height at which the surface P-P,, IT=_ _ , (11) concentration is represented (center of mass of the Psurf -4, bottom layer) is within the well-defined deposition is the top layer regardless of the atmospheric stability. However, where P,,,is the surface pressure, Ptop pressure surface of the model top, selected at for the 6-layer RADM, the representative height of the 100 mbar, and P is lthe pressure at the level where u is concentration in the bottom layer could be outside the well-defined deposition layer for very stable atmoevaluated (Chang et al., 1990). Chang et al. (1990) describe versions of RADM spheric conditions. Another objective of this study is having vertical grids of 6 and 15 layers. Layers of the to quantify inadequacies in estimating deposition 6-layer model are obtained by collapsing layers of fluxes in the 6.layer RADM. the U-layer model. For example, the lowest layer of 6-layer RADM (defined in u-coordinate as 4.2. 1988 summer evaluation study period As part of the Eulerian Model Evaluation Field l.O>a, >0.98) combines the bottom two layers of the U-layer model (1.0 > ui > 0.99 and 0.99 > Q~> 0.98). Study (EMEFS, 1991), a three-month period was Because the u-coordinate is a mass-consistent co- chosen for the 1988 summer evaluation period. The ordinate; the deposition layer, which is below the period includes July 15 to September 30 (78 days) center of mass of the lowest layer, is defined for 6-layer when both RADM runs and NDDN data are availmodel as 1.02 udc. > 0.99 and for 15.layer model as able. AND

STUDY

D. W. BYUN and R. DENNIS

112

Table 1. Full and half u-levels and standard heights for 6-layer and 1%layer versions of RADM Level Index (6)

u-Level Half (6) Full (6)

Level Index (15) 15

0.0

C-Level Full (15) Half (15)

Standard height (m) Full (15) Half (15) 16,069

0.0

0.05 6

14

0.1

13

0.2

12

0.3

11

0.4

10

0.5

9

0.6

8

0.7

7

0.78

6

0.84

5

0.89

4

0.93

3

0.96

2

0.98

1

0.99

0

1.0

0.15

13,712 11,998

0.15

10,649 9512

0.25 0.3

8513 7621

0.35 0.45

5

6813 6073

0.45

5390 4754

0.55 0.6

4159 3600

0.65 0.72

4

3071 2570

0.74

2187 1818

0.81 0.84 0.885

3

1550 1289

0.865

1077 868

0.91 0.93 2

705 544

0.945

0.955

425 307

0.97 0.98 1

0.99

230 152

0.985

114 76

0.995 0

1.0

38 0

Table 2. NDDN sites used in the present study Site No. 104 110 115 117 119 121

128 130 133 140 146 157

Initial reporting date

Latitude

Longitude

Elevation (m)

West Point, NY Connecticut Hill, NY Ann Arbor, MI Laurel Hill State Park, PA Cedar Creek State Park, WV Lilley Comett Woods,

01/06/87

41.35

74.05

203

Forested

Complex

09/14/87 06/30/88 12/10/87

42.40 42.42 40.00

76.65 83.90 79.25

515 267 616

Forested Forested Forested

Rolling Flat Complex

1l/09/87

38.83

80.90

274

Forested

Complex

KY Ardentsville, PA Bondville, IL Salamonie Reservoir, IN Vincennes, IN Argonne NL, IL Alhambra, IL

01/19/88 06/30/88 02/09/88

37.08 39.92 40.05

82.99 77.30 88.37

335 210 212

Forested Agricultural Agricultural

Complex Rolling Flat

06/30/88 08/05/87 07/01/87 06/30/88

40.81 38.74 41.70 38.87

85.68 87.49 87.99 89.62

219 134 229 164

Agricultural Agricultural Urban-agricultural Agricultural

Flat Rolling Flat Flat

Site name

4.3. National dry deposition network (NDDN) data In the NDDN (Edgerton and Lavery, 1990: Clarke and Edgerton, 1993), the dry deposition is estimated by an inferential measurement technique (Hicks et al.,

Land use

Terrain

1991; Meyers et al., 1991), which uses air concentrations and surface meteorological parameters. Most of the atmospheric samples measured at each NDDN site are integrated over a weakly period using a three-stage filter pack (SO*, SO:-, NH,, NOs, and

Vertical profile correction

HNO,). However, only ozone concentrations measured at 10 m above the surface are recorded continuously and reported as hourly averages. Although we prefer to consider rlelatively nonreactive species such as HNO, for studying model bias caused by the coarse vertical resolution, here we employ only ozone concentration which c;an be affected by transport and chemical reactions at night. Surface ozone concentration is affected considerably by the NO titration throughout the day. Table 2 lists twelve NDDN sites used in the analysis as reported in Clarke and Edgerton (1993).

5. COMPARISON

BETWEEN d AND H-LAYER RADM

Here, we provide a quantitative analysis on the differences in the predictions of the 6- and 15layer model concentrations and depositions showing effects of deposition layer thickness. For demonstration purpose, we analyzed model output from two RADM cells, one close to am urban area and the other in a rural area, corresponding to two selected NDDN sites. 5.1. Characteristics of RADM cells corresponding to NDDN Site 104 and Site 133 Site 104 (West Point, NY) represents a suburban site with considerable surface NO, emissions and Site 133 (Salamonie, IN) a rural site with very little NO, emissions. The majority of the NDDN sites, including the West Point Site and the Salamonie Site, were selected to be regionally representative and, consequently, were well removed from major population centers, transportation corridors, and point sources of pollutants (Clarke and Edgerton, 1993). In RADM, the 80 x 80 km2 New York City cell is comprised of 40% urban, 30% water, 21% deciduous forest, and 3% for other land-use categories. The roughness length is estimated to be about 20 cm. The West Point Site is categorized as “forested and complex” land-use. In RADM, the 80 :X80 km2 Salamonie cell is comprised of 99% agricultural and 1% urban land-use categories. The roughness length is estimated to be about 25 cm. In the NDDN database, the Salamonie site is categorized a,s “agricultural and flat” land-use. Because each NDDN site is characterized by the land-use and land cover (surveyed plant species information within 1.0 km of the site), deposition characteristics for each site are quite different from that of the corresponding RADM cell containing the site. Therefore, we just compared ozone concentrations at the NDDN measurement height and did not attempt to compare local depositions at NDDN sites to RADM predicted depositions in this study. 5.2. Ozone concentration difference between the 6- and 15-layer RADM As shown in Figs 5a, b and 6a, b, the predicted firstlayer OJ concentrations by 6- and 15-layer models are distinctively different. For the New York City cell,

113

higher-end ozone concentrations from the 6-layer model show slightly lower values than those from the 15-layer model (Fig. 5b). This can be explained with the fact that the hydrocarbon and NO, emissions injected into the 6-layer model are diluted in a deeper layer compared to the same injected into the 15-layer model; thus, the 6-layer RADM produces less ozone from the photochemical reactions. Where the PBL height is above 100 m, RADM/6 predicted slightly higher ozone concentrations in the morning. For the Salamonie cell, the differences in the higher-end concentrations between the 6- and 15-layer RADM results are minor (Fig. 6b). This is somewhat expected because the photochemical ozone production is much subdued in the rural cell; thus, the relative contribution from the different emissions is not as significant as in the New York City cell. The species concentrations at the lowest model layers are expected to be similar between the two versions of RADM for unstable conditions due to the vigorous mixing in the boundary layer for similar starting concentrations and chemical productions. For both the New York City cell (Fig. 5a) and the Salamonie cell (Fig. 6a) the lowerend concentrations from the 6-layer model are still consistently higher than those from the 15-layer model. Several possibilities that account for the difference in high-end and low-end concentrations are: representative heights, layered emissions, transport winds, and mass budget and contributions from such chemical reactions as titration of ozone by nitrogen oxide. Among these, some may contribute to the model bias while others may not. 5.3. Difference in atmospheric resistance Among other things, we focus on the difference in the lower-end values, especially, those that come from the different surface removal of fluxes between the two versions of RADM. As will be seen later, the vertical resolution of the 6-layer model is too coarse to estimate aerodynamic resistance adequately for stable atmospheric conditions. In RADM, the PBL parameters such as surface fluxes, friction velocity, and PBL height are estimated using the wind and temperature profiles of the 15-layer MM4 predictions. Therefore, there are no differences in the PBL parameters between RADM/6 and RADM/lS. The PBL height for the stable atmospheric conditions are estimated as a maximum of the top height of the lowest MM4 layer and the mechanical turbulence height estimated by the Zilitinkevich’s (1989) formula. For very stable atmospheric conditions, the estimated PBL heights are mostly determined by the lowest layer-top height of 15-layer MM4. The deposition layer of the 6-layer model (lower half of the lowest layer in sigma coordinate, or about 76 m) could well extend to the top of the PBL at night when there are very low eddy-diffusivity values. Refer to Fig. 7 showing the schematics of the deposition layers for RADM/6 vs RADM/lS. For RADM/6 the max-

114

D. W. BYUN and R. DENNIS

RADM/15 vs. RADM/G (New York City cell) I I ( 7 3 II I ” ’

120

- (a) x

O0

”

PBL ht. < 100 m (R26)

20

40

80

60

120

100

03 at Layer 1 of RADWlS (ppb) /

120 _ (b)

0

“’

I

“’

I,

*,

I

“’

I

”

PBL ht. >= 100 m (R26) /

20

I

” 0

20

40

60

80

100

120

03 at Layer 1 of RADWlS (ppb)

Fig. 5. Scatter plots comparing hourly ozone concentrations predicted by RADM/6 and RADM/lS for the New York City cell for the 1988 summer evaluation period: (a) for PBL height less than 100 m, and (b) for PBL greater than 100 m. imum height of the deposition layer has to be limited to 0.9h to avoid a singularity in the integration of the

inverse of eddy ditfusivity integrated over the depth of the deposition layer. Therefore, the resulting depos-

eddy diffusivity. This causes a serious problem in estimating the aerodynamic resistance, which is the

ition velocities for various species become very small for the stable conditions.

Vertical profile correction

115

RADtW15 vs. RADM/6 (Salamonie cell)

(a)

x

PBL ht. < 100 m (R26)

““’ 3

/

100

B u’ $j

80

a 6 r 6oi

I.

O0

20

8,

I,

40

.,

,

,

,

60

03 at Layer 1 of RADWlI

,

,

,

80

,

,

,

,

,

100

120

100

120

(ppb)

120 o

PBL ht. >= 100 m (R26)

20

O 0

20

40

60

80

03 at Layer 1 of FtADMIlti (ppb) Fig.. 6. Scatter plots comparing hourly ozone concentrations predicted by RADM/6 and RADM/IS for the Salamonie cell for the 1988 summer evaluation period: (a) for PBL height less than 100 m, and (b) for PBL greater than 100 m.

We prepared scatter plots in Figs 8a and b comparing model-estimated aerodynamic resistance from RADM/6 and RADM/lS for the New York City cell. The figures show that for low resistance conditions

are high due to atmospheric instability) there are no significant differences in the aerodynamic resistance values other than the one we may expect from the difference in the thickness of

(i.e. when PBL heights

D. W. BYUN and R. DENNIS

116

I

RADWOG

RADMll5

“4 !

Layer 4

Layer 2

2ayer

3

Layer 1

Deposition Layer Layer

Deposition Layers in RADM/G vs. 15 Layer Model

Fig. 7. Schematics of deposition layers for RADM/6 and RADM/lS. In RADM, the deposition layer is defined as lowest half (in terms of Au) of the model’s first layer. To prevent singularity, the top of deposition layer is set to be always less than 0.9h, where h is the PBL height, which changes significantly during the course of a day.

deposition layers. For high resistance conditions (i.e. when PBL heights are low; less than 100 m for typical stable conditions) the resistance values for the 6-layer

model are about 4-times or more higher than those for the 1Slayer model. We see similar differences between RADM/6 and RADM/lS for Salamonie cell (not shown here). The ratio can be verified by applying typical parameter values in equations (A13) and (A14) for stable conditions as follows: Atmospheric stability: h/L - 1.5. Nondimensional surface layer height (we assumed that surface layer is one-tenth of the PBL): VSL= z,,/h - 0.1. Nondimensional height for the deposition layer top (for RADM/6, the value is limited to 0.9 to avoid numerical singularity in the integration): tldcp = Zdcp/h qdep -

Ratio of aerodynamic

0.5

-

0a9

(for RADM/lS).

resistance:

r,(RADM/6)/r,(RADM/l5)-4.4.

The strong discrepancy in the aerodynamic resistance between the two models shows that the deposition layer in the 6-layer model is too thick. It is clear that the deposition layer concept should only apply to the layer above the surface-roughness length and below the height of the maximum vertical eddydiffisivity value in the PBL. We consider this to be a serious concern in estimating regional-deposition amounts although the nighttime (when PBL height is less than 1OOm) deposition is much smaller on an absolute scale than daytime deposition. Because nighttime deposition occurs in a thinner layer and thus may have a large effect on the concentrations even though V, is smaller. 5.4. D#erence in ozone dry deposition jlux The predicted geographical patterns of the cumulative deposition are very similar, but the deposition amounts are somewhat different between the two model versions (about 15% in certain areas for the four-and-half-day simulation of a typical summer case). For unstable conditions, the relative importance of the aerodynamic resistance in determining drydeposition velocity is the same for both’ RADM/6 and RADM/lS. However, for stable conditions, the abnormally large aerodynamic resistance greatly

117

Vertical profile correction Aerod namlc Resistance RADW15 vs. k ADMIB: New York Ctty Cell

F%Lht.elOOm

1

10

100

R, for RADWl5

10000

loo0 (s/m)

looca

Eulerian air quality models which compute drydeposition velocities at some reference height, such as 10 m, would not show similar errors as described above. However, when dry deposition is computed using the layer-averaged concentration that represents a layer-averaged value and the deposition velocity estimated at 10 m, the total deposition flux will be greatly over-estimated. This computation amounts to assuming that there is no aerodynamic resistance in the layer from the center of the lowest model layer to the reference height at which deposition velocity is estimated. One could argue that the concentration in the lowest layer has no vertical gradient to justify the inconsistency in the representative heights. In such a case, the deposition velocity concept, which requires a strong vertical concentration gradient, could not be applied to represent the surface removal process.

6. COMPARISON P6Lht.e1OOm

BETWEEN

SURFACE

15LAYER

RADM AND NDDN

MEASUREMENTS

To compare the model predictions with the NDDN surface measurements, we estimated the model predicted concentration at the measurement height, 10 m, using equation (10). Figure 10a shows the resulting profile corrections for the selected NDDN site, West Point Site 104 (New York City cell for RADM). As expected, for the case with low aerodynamic resistance (unstable conditions, i.e. daytime) the corrections were very small; while for the case with high aerodynamic resistance (stable conditions, i.e. nighttime), the profile 1 corrections were as high as 90% of the layer-mean 1 10 100 1000 10000 concentration. The Salamonie cell (Fig. lob) shows R1for RADM/lS (s/m) somewhat larger corrections because the atmospheric conditions were more stable during nighttime than Fig. 8. Aerodynamic resistance values for RADM/6 and RADM/lS deposition layers for the New York City cell: (a) for those in the New York City cell. Figure 11 shows an PBL height less than lOOm, and (b) for PBL greater than example of surface ozone concentration plot of obser100 m. vations and 15layer RADM predictions estimated at 10 m (i.e. profile corrected values) for a higher NO, region (the cell containing the West Point Site). The influences the estimation of dry-deposition velocity for plot shows that predicted ozone concentrations at the semi-urban site follow the synoptic trend obtained RADM/6. We compared the cumulative ozone dryfrom the four-dimensional data-assimilated MM-4 deposition fluxes between RADM/6 and RADM/lS simulation (Staufer and Seaman, 1990) quite well over the entire 1988 summer evaluation period (figures not shown here). The difference was less significant for except for a few days when either the daily maxima or minima were off by some significant amount. The the urban New York City cell because nighttime time-series plot for the Salamonie cell having lower ozone concentrations in the model were much lower. NO, (not shown here) shows that predicted ozone For the rural Salamonie cell, the discrepancy was concentrations follow the synoptic trend in the obmuch more significant because nighttime ozone concentrations in the model were relatively high. As servations very well, but the minima and maxima are quite different between model predictions and shown in Fig. 9a and b, the difference can be atobservations. tributed to the differences in the aerodynamic resistTo display the amount of concentration changes ance because the surface resistances for both 6- and due to the profile corrections, we plotted daily minU-layer RADM were the same. The relative amounts imum layer-l and 10 m concentrations for the of ozone removed from the atmosphere through the Salamonie cell in pairs in Fig. 12 as an example. We deposition process were not much different between the 6- and U-layer RADMs during daytime while generated similar scatter diagrams for the twelve there were significant under-estimations of nighttime NDDN sites, representing near source, agricultural, dry deposition in the 6-layer model. and forest cells, respectively. The amount of profile

D. W. BYUN and R. DENNIS

118

Averaged Deposition Velocity: New York City Cell 1

.,.,.,.,.,.,.,.,.,.,.,.,.,.,.,.,.~.,.,.,.,.,.,.~ .

0

RADM/6Vd(Ozone)

(a)

? ?RADM/l5Vd(Ozone)

.

0.8--

0.6--

0.2

0 0

1 2

3

4

5

6

7

8

9 1011 121314151617181920212223

Local Standard Time (HOUR)

Averaged Deposition Velocity: Salamonie Cell 1 ,~1~1’1.1.1.1.1.1.1.~.~.~.~.~.~.~.~~~’~.~”.’.”l 0

RADW6Vd(Ozone)

W

? ?RADWl5Vd(Ozone)

I

0.6--

0.2

0

0

1 2

3

4

5

6

7

8

9 10111213

14151617181920212223

Local Standard Tlme (HOUR) Fig. 9. Averaged diurnal variation of deposition velocities for RADM/6 and RADM/lS: (a) for the New York City cell, and (b) for the Salamonie cell.

correction varies considerably depending on the site, atmospheric stability and concentration gradient at the top of the PBL. For certain conditions, the correction can be as large as 18 ppb. For nighttime hours,

the correction reduces the high bias of model O3 concentrations in the right direction. However, except for the sites close to suburban areas (Ann Arbor, MI; Argonne National Laboratory, IL; and West Point,

Vertical profile correction 0

Correction Factor (day)

=

Correction Factor (night) 1.1

119 o

Correction Factor (day)

x

Correction Factor(night)

r 0 “11!11

v 8 !““‘,

1 8 #““‘,

’ ’ 11’1’1

(b) Salamonie Cell

0.6t

1

10

100

AerodynamicResistance

1000

10000

-f

1

(s/m)

10 Aerodynamic

100 Resistance

1000

10000

(s/m)

Fig. 10. Fractional concentration corrections applied to the first layer ozone concentrations to compare model predictions with NDDN measurements: (a) for the New York City cell, and (b) for the Salamonie cell.

NDDN St0 104 (Woat Paht)

RADY Now York City Cell

”

210

0

420

720

i I

920

aoud-

150r--

” OS0

’

I

1202

I

I

1440

1480

1220

o**rdm

Fig. 11. Model predicted (solid line) and observed (dashed line) hourly ozone time series plots for the NDDN Site 104 and RADM/lS New York City cell. The starting time is 01 GMT, 15 July 1988 and ending time is 23 GMT, 30 September 1988.

NY), the profile corrections were not enough to explain model high bias of daily minimum 0, concentrations. Other causes must be investigated. We plotted scatter diagrams of the daily oxone minimum, maximum, and mean concentrations between the corrected RADM results and NDDN observations for each group, representing different source AE 29:1-I

or land-use characteristics. In general, the first group can be termed as cells with near-source influence (except for Connecticut Hill, NY), the second group as agricultural cells, and the third as forest cells (except for Bondville, IL). For the near-source group, distributions of daily minimum and mean are little biased compared with observations while there are some low

D. W. BYUN

120 80

t”“l”““““““““’

Daily 03 &

and R. DENNIS anism and emissions input including representation of subgrid-scale reactive plumes and NO, emissions from the soil.

““I ““““j Minimum Correction Site: Salamonie i

NDDN

7. CONCLUDING REMARKS

.

4 I

f

FL,,

111,*1~~11111~1,11~11111111,,~11111

0

0

IO

20 30 40 50 60 NDDN Observation (ppb)

70

80

Fig. 12. Protile corrections to daily minimum ozone concentrations for Salamonie as an example.

bias of model maxima (Fig. 13a). The New York City cell (West Point Site) shows no apparent bias in the model prediction. However, the correlation between the model minimum and observation minimum is not good, indicating the 80 x 80 km2 cell size is too large. The Connecticut Hill cell shows sizable low bias of the model maximum. For the second group, the model shows high bias in the daily minimum, considerable low bias in the daily maximum, and do not show a distinct bias for daily mean concentrations (Fig. 13b). For the third group, the model shows significant high bias for the daily minimum, significant low bias for the daily maximum, and high bias for the daily mean concentrations (Fig. 13~). Both the second and third group show flat model response compared to observations. Several model evaluation studies (e.g. Dennis et al., 1990) have revealed that the results described above display typical characteristics of regional air quality models with coarse vertical and horizontal resolutions. Because the cell size is too large to correctly represent NO, emissions, which have very distinctive subgrid-scale distributions, the result of photochemical reactions with diluted primary species concentrations does not give a similar dynamic range as observed ozone concentrations. We expect that the limited dynamic range in the daily ozone concentrations is related to the over-smoothing of NO, emission rates in the model with coarse horizontal and vertical resolutions. In the companion paper, we will explore the model bias further by considering the vertical and horizontal resolution issues; especially, the effect of emission source distributions. Other model biases that cannot be explained by the vertical and horizontal resolution considerations are probably caused by modeling problems related to the chemical mech-

This study revealed that the 15-layer RADM is much better than the 64ayer RADM in representing the surface dry-deposition processes and surface concentration. We have identified that the 6-layer model is inadequate in estimating the aerodynamic resistance for stable conditions when the boundary-layer height is low because the lowest layer in the u-coordinate can reach the top of the nighttime PBL. The model should have enough resolution in the lower layers to represent the deposition layer correctly throughout the day. As a minimum requirement the deposition layer should be below the height of the maximum eddy diffusivity. Although a PBL profile method was introduced in this study, it does not replace the need for higher resolution which can ensure that the lowest model layer be within lower part of the PBL. In spite of this deficiency, the 6-layer model predicted geographical patterns of the cumulative deposition that are very similar to the 15layer model. However, the ozone deposition amounts differ by about 15% between the two model versions. The difference was caused mainly by errors in the estimation of the drydeposition velocity at night. This paper provided an algorithm to estimate model bias of the dry-deposition velocity caused by the limited vertical resolution of the deposition layer. Also, it presented a method to reduce layer-averaged model predictions of the concentration at the measurement height. The method utilizes the proposed PBL similarity profile for a passive scalar and the drydeposition flux concept. For unstable conditions, the fractional correction is not important because the concentration is well mixed in the boundary layer. At night, the fractional correction is needed since it can be as high as .90% of the layer-mean concentration. Based on a comparison between RADM predictions and NDDN measurements for the agricultural and forested sites, we hypothesize that the model predicted a much narrower dynamic range of ozone concentrations when the NO, emissions are inadequately represented due to the coarse horizontal resolution and uncertainties in NO, emissions, such as NO, emissions from soil. However, RADM prediction does not show apparent bias compared to NDDN measurements for the near-source cells although there are rather wide scatters in the data. This is because there are pervasive NO, emissions in the near-source cells and therefore the emissions strength represents reality even with the coarse horizontal resolution of RADM. In a companion paper, we will explore the model bias further considering the vertical and horizontal resolution issues.

Vertical profile correction

MlNlom

x

MAXlOm

+

MEAN1 Om

??

x

121

MHlom

MAXlOm

+

Ann Arbor

??

Argonne

MEAN1 Om

NL

120tn

‘*v----

??

0

20

40

60

60

100

120’

0

20

40

Obrenntionrt lom x

+

MHlOm

MAXlOm

Connecticut

0-d 0 (a)

’ ’ ’ ’ ’’ 20

40

60

MEAN1 Om

??

x

MHlOm

+

Hill

60

100

120

MAXlUm

??

MEANlOm

West Point

’ ’’ ’ ’ 80

60

cklssndon al 1Om

’’ ’ ’ ’

100

120

0

Obswatbn ti 10m

20

40

60

60

100

Obrenatbn at 1Ot-n

Fig. 13a.

120

140

122

D. W. BYUN and R. DENNIS

x

MHlOm

MAXlOm

+

??

MEAN1 Om

x

MlNlOm

20

40

60

80

100

120

0

20

40

MlNlOm

MAXlOm

+

e

x

MEAN1 Om

MlNlOm

+

Salamonie 120-

MEAN1 Om

60

80

100

120

otnmtion a! 10m

obselvrtionat 1Om x

??

Atdentsville

Alhambra

0

MAXlOm

+

MAXlOm

??

MEAN1 Om

Vincennes /

L

::j--yq

i

Ov...“‘.““‘.‘.‘.,.‘.“’ 0 (b)

20

40

60

80

100

120

0

20

40

60

80

Otsmvational 1Om

c4mwliin at 1Om Fig. 13b.

100

120

Vertical profile correction

x

+

MlNlCtn

MAXlOm

9

MEAN1 Om

123

+

MlNlOm

x

MAXlOm

Cedar

Bondvllle

??

MEAN1 Om

Creek

,,,,..,...,.-.-

OI/(“““““““““““’ 0 x

20

MHlOm

40 60 80 clbs~lvdionat lcm +

MAXlOm

100

??

0

120

MEANlOm

x

20

40 60 80 ob%w*sn al lOIn +

MHlOm

Laurel Hill

MAXlOm

100

??

120

MEAN1 Om

Lilley Cornett

:::J---

0

(c)

20

40

60 80 100 Obswv~iDlla 1Om

120

140

0

20

40 60 80 Ohservat’ion al 10m

100

120

Fig. 13. Scatter pbots of the RADM predicted daily ozone minimum, maximum and mean concentrations vs NDDN measurements: (a) Ann Arbor, Argonne National Laboratory, Connecticut Hill, and West Point cells, (b) Alhambra, Ardentsville, Salamonie, and Vincennes cells, and (c) Bondville, Cedar Creek, Laurel Hill, and Lilley Comett cells.

D. W. BYUN and R. DENNIS

124

Acknowledgements-The authors express their appreciation to MS Evelyn Poole-Kober for providing editorial assistance. The authors are indebted to the two anonymous reviewers who helped improve the quality of this paper. Disclaimer-The information in this document has been funded wholly or in part by the United States Environmental Protection Agency. It has been subjected to Agency review and approved for publication. Mention of trade names or commercial products does not constitute endorsement or recommendation for use.

REFERENCES

Eulerian Model Evaluation and Field Study. The Electric

Power Research Institute, Palo Alto, CA. Hicks B. B., Hosker R. P. Jr, Meyers T. P. and Womack J. D. (1991) Dry deposition inferential measurement techniques-1. Design and tests of a prototype meteorological and chemical system for determining dry deposition. Atmospheric Environment 25A, 2345-2359.

Lenchow D. H. and Delany A. C. (1987) An analytic formulation for NO and NO, flux profiles in the atmospheric surface layer. J. atmos. Chem. 5, 301-309. Louis J. F. (1979) A parametric model of vertical eddy fluxes in the atmosphere. Boundary Layer Met. 17, 187-207. Mevers T. P.. Hicks B. B.. Hosker R. P. Jr. Womack J. D. and Sgtterfield’L. C. (1991)Dry deposition inferential measurement techniques-II. Seasonal and annual deposition rates of sulfur and nitrate. Atmospheric Environment 25A, 2361-2370.

Anthes R. A., Hsie E. Y. and Kuo Y. H. (1987) Description of the Penn State/NCAR Mesoscale Model version 4 (MM4). NCAR Technical Note, NCAR/TN-282 + STR, National Center for Atmospheric Research, Boulder, CO. Blackadar A. K. (1976) Modeling the nocturnal boundary layer. In Proc. of the Third Symposium on Atmospheric Turbulence, Diffusion and Air Quality, pp. 46-49. American Meteorological Society, Boston, MA. Brost R. A. and Wyngaard J. C. (1978) A model study of the stably stratified planetary boundary layer. J. atmos. Sci. 35, 1427-1440.

Businger J. A., Wyngaard J. C., Izumi Y. and Bradley E. F. (1971) Flux profile relationships in the atmospheric surface layer. J. atmos. Sci. 28, 181-189. Byun D. W. (1990) On the analytical solutions of flux-profile relationships for the atmospheric surface layer. J. appl.

Padro J., den Hartog G. and Neumann H. H. (1991) An investigation of the ADOM dry deposition module using summertime 0, measurements above a deciduous forest. Atmospheric Environment 25A, 1689-1704.

Staufer D. R. and Seaman N. L. (1990) Use of four-dimensional data assimilation in a limited-area mesoscale model. Part I: experiments with synoptic-scale data. Mon. Wea. Rev. 118, 1250-1277. Thompson A. M. and Lenschow D. H. (1984) Mean profiles of trace reactive species in the unpolluted marine surface layer. J. geophys. Res. 89(D3), 4788-4796. Zilitinkevich S. S. (1989) Velocity profiles, the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer. Boundary Layer Met. 46, 367-387.

Met. 29, 652-657.

Byun D. W. (1991) Determination of similarity functions of resistance laws for the planetary boundary layer using surface-layer similarity functions. Boundary Layer Met. 57, 17-48.

Chang J. S., Binkowski F. S., Seaman N. L., Stockwell W. R., Walcek C. J., Madronich S., Middleton P., Pleim J. E. and Lansford H. H. (1990) The regional acid deposition model and engineering model. State of Science/Technology Report 4, National Acid Precipitation Assessment Program, 722 Jackson Place, NW, Washington D.C. 20503. Chang J. S., Brost R. A., Isakson I. S. A., Madronich S., Middleton P., Stockwell W. R. and Walcek C. J. (1987) A three-dimensional Eulerian acid deposition model: physical concepts and formulations. J. geophys. Res. 92(D12), 14,681-14,700. Clarke J. F. and Edgerton E. S. (1993) Dry deposition flux calculation for the national dry deposition network. EPA/&IO/R-93/065, Atmospheric Research and Exposure Assessment Laboratory, Research Triangle Park, NC. Dennis R. L., Binkowski F. S., Clark T. L., Reynolds S. J. and Seilkop S. K. (1990) Evaluation of regional acidic deposition models (part I) and selected applications of RADM (part II). State of Science/Technology Report 5, National Acid Precipitation Assessment Program, 722 Jackson Place, NW, Washington DC. 20503. Edgerton E. S. and Lavery T. F. (1990) National dry deposition network fourth annual progress report. Prepared for the U.S. EPA. Contract No. 88-02-4551, Environmental Science and Engineering, Inc., Gainsville, FL. EMEFS (1991) The Eulerian model evaluation field study: an interim report. PNL-7914, prepared by Pacific Northwest Laboratory for the U.S. EPA, Research Triangle Park, NC. IAG DW89933040-01-07. Gao W. and Wesely M. L. (1993) Numerical modeling of the turbulent fluxes of chemically reactive trace gases in the atmospheric boundary layer. In Proc. Conf: on Atmospheric Chemistry, Anaheim, 17-22 January, American Meteorological Society, Boston, MA. Hansen D. A. (1989) Project Plan for the Acid Deposition

APPENDIX A: BOUNDARY LAYER PARAMETERIZATIONS IN RADM 2.6 A meteorological preprocessor (hereafter, referred to as the preprocessor) provides the required meteorological inputs to RADM using a mesoscale meteorological model, MM4 (Anthes et al., 1987; Staufer and Seaman, 1990). It includes mean meteorological fields for temperature, horizontal wind components, humidity, pressure, planetary boundary layer (PBL) parameters, precipitation rate, cloud fraction, and cloud bottom and top heights. The preprocessor also provides estimated dry-deposition velocities for various chemical species in RADM. The Eulerian Model Evaluation Field Study (EMEFS, 1991; Hansen, 1989), a binational (U.S. and Canada) discovered an overprediction of the minimum concentrations of certain species during nighttime by an earlier RADM version. In discussions by the Model Evaluation Team (MET), it was speculated that the estimated nighttime dry deposition velocities were too small. A further study showed that the nighttime friction velocity was predicted to be much less than 1 mm s-l over a large area of the modeling domain as a result of using Louis’s (1979) formulation (Padro et al., 1991). New PBL profile functions (Byun, 1991) provide estimations of PBL parameters from the mean wind and temperature, predicted by a grid model such as MM4, that extend into the entire PBL, whereas that of the Louis(1979) is limited to the surface layer, the lowest one-tenth of the PBL. The new approach has the following features. A.l. Estimation of surfacejluxesfrom output

MM-4 grid model

The wind and temperature predicted by a meteorological grid model represent layer averaged values. In order to simplify computation of the surface fluxes, we apply the assumption that the predicted wind for the lowest model layer has the same direction as the surface stress (i.e. til +fizu 2 where li, and I?, are latitudinal and longitudinal m_ u,,

125

Vertical profile correction components of the first layer mean wind and u, is the layer mean wind speed in the direction of surface stress). Applying the PBL momentum profile functions of Byun (1991) and integrating them vertically from ze (roughness length) to the top of the lowest RAJJM layer (zrr d h), we get the following result:

as (Brost and Wyngaard, 1978), Stable ku,z(l - z/h)“‘2 K, =

forz/L>O, &(z/L)

Unstable

u* Um=KZ

K,=kw,z(l-z/k)

x{(rl~-tlo)C-lntlo+~~(~tl~)l

‘[rmhF)

-

for z/L<0

r_

rmhO)l

(A7)

where

+(~F1ntlF-~O1n’lO)-_(lF-‘tO)

-

w4

-II/J

+$(%-40)p+1)

P

=

+4

h,

641)

VF)>

where qo=zo/h,

and

qF=zF,/h

p=h/L.

For the detailed description of the notations used, refer to Byun (1991) and the Nomenclature. Similarly, we can compute layer mean potential temperature as Pr, 19,

0,-e,=--

k(w-tlo) x

((rll~-tlo)C-lntlo+~~61~0)l

+hF

-

ln%-vO

~m’Id

lntlO)-_(‘lF-‘lO)

-

T&‘lo)]

+$;(9F-‘lo)‘tlj

Pr,e, =k

P0h

(0

VO? a).

Initially, the atmospheric stability p is approximated by the analytical solutions of flux-profile relationships proposed by Byun (1990) from the bulk Richardson number estimated by u,,,, 8,, and 0, (surface temperature). Then, we compute atmospheric stability t.~),u,,, and 6, using equations (Al) and (A2), with Newton-Raphson iteration. A.2. Eddy-diffisiuity

formulations

in RADM

These parameterixations for K, are very sensitive to the boundary-layer height(h) and the surface-layer height. However, the vertical resolution of the 6-layer RADM is too coarse to use these eddy-diffusivity profiles directly for the estimation of diffusive fluxes across layer interfaces. If, for example, the estimated PBL height is just below the bottom of the third layer, very little diffusive flux into the third layer is predicted. However, if the estimated PBL height is just above the third layer, there will be significant diffusive flux across the interface. Our estimation of PBL height, based on the potential temperature profile and a length scale determined by u* and the Coriolis factorf, is not precise and may easily have error of &SO m or more. Furthermore, the resolution of the pollutant concentration profiles, which represent the layer mean, is limited to the vertical resolution of the model itself. Given these limitations, use of a “representative” eddy digusivity together with the mean-concentration gradient at the layer interface seems to be more appropriate for the estimation of the diffusive flux. In fact, the diffusive flux across the interface can be estimated more accurately with mean diffusivity and mean concentration gradient than with local diffusivity and mean concentration gradient; the former has an error of G(s*) while the latter has an error of G(s). To estimate the “representative” eddy diffusivity at the layer interface, integrated eddy ditfusivity formulas are used in RADM. They are summarized in the following equations: A.2.1. Surface layer. Stable conditions ku z 1 K, = zz - z, i :: 0.74 + 4*17(z/L) dz ku, = 0.74(2, - ZJ

1 In jq

2.6

We use the following eddy diffusivity for the surface layer: ku,z K,=-.

(A3)

4.7 j1 = 0.74 L’

Unstable conditions

&(z/L)

The profile functions used are (Businger et al., 1971) Stable ku, = 0.74(2, - z,) &(Z/L)

= 0.74 + 4.7;

forz/L>O,

644) X

Unstable &(z/L) = 0.74[1 - 9z/L]-“*

for z/L c 0.

(AS)

Eddy diffusivity in the PBL (above the surface layer) is given

-

1 II

2(3az, - 2)(1 + azz)3/2 15az

[

2(3az, - 2)(1 + az1)3’z 15a2

where a = - 9/L.

649)

D. W. BYUN and R. DENNIS

126

A.3. Aerodynamic resistance formulations in RADM 2.6

A.2.2. Planetary boundary layer. Stable conditions =I z(l - z/h)3’2

ku

R, = * z2 - z1 I z, 0.74 + 4.7(2/L)

General formulation for the aerodynamic resistance is divided into two components; resistance in the surface layer and resistance in the PBL above the surface layer;

dz

ra=J,,K,(z)= J

z.

= 0.74 /?(z2 - 21) X

1 r: 1 [ 1 (a+r2)la--r,l ’ 11 [ 4

--

{ -

[

s+

-+ 5

a2 -

-

1

3

r: + (a4 - a2)rz

+

--In 2a

Ja-r21(a+rI)

(Al3) 0.74

4.7 h 0.74 L

+ln

’

rl = (1 - z,/h)“‘,

a2= (1 + B)/B.

r~ = Eln

=kw,

-[

2

k

dz

Zl u II

> z:

+ Z2Zl

3h

+ z:

1

2(8+1) - E

(-1+JGJcl+J=ia [I(l+J=ig(-l+&TL)

Ill

.

Unstable conditions

Unstable conditions =’ z-f

2(8 + 1) I Jr-,,,

(Al4)

r2 = (1 - z2/h)‘12,

z2 +21

(A13

+ (a* - a2)rl

fj=-

22 -

2 dz = rsSL+ rapBL. ISI.K,(z)

5

rapnL= ig

R,=kwf

dz

K,(z)

Stable conditions

a2 - 1 -r: 3

+(a6-a4)

p,

fz dz

2ku,h2

(Al 1)

1’ W)

(J_)

- l)(J=%Zi)

+ 1)

(JiT$Zi)

+ l)(J/KKZi)

- 1)

(Al@