-------
et al. measured the rate constant for
N02-(a) + S(IY)(a) } S(VI) + ? (71)
and observed N02 as a product. Given that (71) does occur in atmospheric
water and some specific environmental conditions, Chang et al. (1981) con-
cluded that significant amounts of sulfate will be produced in cloud water
from an aqueous HONO - S(IV) reaction. However, Martin et al. (1981b) have
concluded that this process in aerosols will not be a major mechanism of
sulfate production. In addition to N02~, Martin et al. (1982b) determined
that NO, N20, and N03~ do not react with aqueous S(IV) under their experi-
mental conditions.
It should be noted as well that the oxides of nitrogen, principally
N02, will oxidize S02 to sulfate upon soot particles (Cofer et al., 1980;
Cofer et al., 1981; Britton and Clarke, 1980); however, Baldwin (1982) did
not observe this reaction. The particulate odd-nitrogen-sulfur dioxide
reactions just described provide an unknown and unquantified link to the
interactions between NOX and SOX in addition to homogeneous HO competi-
tion discussed in Section 1 of this chapter.
It has been speculated that an aqueous atmospheric reaction between
formaldehyde and S(IV) occurs, since ambient measurements have shown the
coexistence of both S(IV) and H202 in precipitation samples (Richards et
al., 1983). H202 is expected to oxidize free S(IV) in solution. H202 does
not, however, react with the formaldehyde bisulfite complex. The analysis
technique used to measure S(IV) cannot distinguish free S(IV) from organi-
cally-complexed S(IV). Consequently, the coexistence of S(IV) and H202 in
rain water may indicate the presence of S(IV) complex. If true, then in
regions of high H2CO concentrations, part or all of the S(IV) available for
aqueous oxidation may be unable to produce sulfate. Key issues in this ar-
gument are the relative rates at which free S(IV) is oxidized or complexed
in droplets, the rates at which H2CO, S02, and oxidants are delivered to
droplets, and the relative atmospheric concentrations of these species in
space and time.
The last research area which bears on the liquid phase oxidation of
S(IY) is the radical - S(IV) reaction; this has been a topic of considera-
tion only since mid-1981. The occurrence of radicals in atmospheric water
was not considered important until Heikes et al. (1982) and Zika and Saltz-
man (1982) found that 03 when bubbled through water produced H202. The
precursors of H202 are thought to be HO, 02~, and H02. These radicals re-
act rapidly with most species in solution, and, in particular, they react
extremely fast with S(IV) (Farhatazis and Ross, 1977). The exact mechanism
of HO and H02 production through aqueous ozone decomposition has not been
established soundly, although unsaturated organic material and hydroxide
ions do appear to be potentially important reactants. The fundamental
question yet to be answered is "where do aqueous HO and H02 and other
radicals come from?"
There are at least seven potentially significant pathways of aqueous
radical production. One of these, aqueous ozone decomposition, has already
been discussed. The others are:
193
-------
(1) The diffusion of gas phase photolysis products (e.g., 0, HO, H02,
R, RO, and R02) to particle surfaces. This has been shown in
theory to be significant during daylight hours (Chameides and
Davis, 1982).
(2) Direct deposition and absorption of energy (e.g., u-v, visible,
and cosmic radiation, on particles). The primary products of
water radiolysis are H, HO, 0, H0~, 0", e--H20, H+, or H20+, and
the secondary products are H02, 02~, or H202. Other species
which could act as sensitizers are N02, N03, 03, HONO, N02",
N03~, transition metals, and organometallics. The relevance of
this mechanism is unknown, but it seems to be low at this writ-
ing.
(3) Deposition of electrons or ions to particles. Cosmic rays pro-
duce -102 ion pairs cm"3 s"1 in the troposphere and are thought
to be one of the principal charging processes leading to light-
.ning (Wagner and Tel ford, 1981). Lightning strokes and cloud
corona provide strong but very localized sources of ions and
radicals, as evidenced by observations of ozone and lightning
spectra. A correlation between cloud electrical activity and
H202 water concentration has been qualitatively noted (Kok,
1982). Also, in aqueous electron beam experiments, primary pro-
ducts are aqueous radicals and radical ions. Electrochemical
reactions in clouds may constitute a significant source of S(IV)
oxidants, but significant research is needed to evaluate this
possibility before any form of this process could be incorporated
into a model .
(4) Organic autoxidation in aqueous solution. Reactions of the form
RH(a) + 02{a) ->- products
are known to occur under certain conditions with products includ-
ing HO, H02, 02~, H202, R, RO, R02, ROOM, and carboxylic acids.
Galloway et al . (1982), Dawson et al . (1980), and Farmer and Daw-
son (1982) have measured gas phase and aqueous formic and acetic
acid in the atmosphere. Lazrus (personal communication, 1982)
has found a non-H202 interference in the measurement of aqueous
H202 and has tentatively attributed this to organic peroxides.
Graedel and Weschler (1981) have also speculated as to the impor-
tance of organic species in aqueous atmospheric chemistry. It
must be concluded, however, that once again there are insuffi-
cient data available to make an assessment of this process.
(5) Organic oxidation by species other than 02, 03, and C^ were
suggested by Heikes et al. (1982) to be H202 precursors. Organic
material may also be oxidized by N02 or N03 in solution and re-
sult in the same products listed in (4) above. Aqueous PAN de-
composition is expected to result in N02~ and other products
(Stephens, 1967). Spicer et al. (1981) have observed nitrate
formation. The difference in products may result from N02~ oxi-
dation by intermediate organic material from PAN decomposition.
194
-------
Again, the relevance of this chemistry to sulfate production is
unknown. Oxidation of S(IV) by a similar reactive species,
H02N02 (peroxynitric acid), is also possible but unevaluated.
(6) Nitrate radical deposition onto particles. The diffusion of N03
to particles is discussed in Section 2.2 and assumed to result in
N03- and radicals (Heikes and Thompson, 1982). The electron af-
finity of N03 is greater than that for Cl~ and other ions common
to atmospheric water, and Daniels (1969) experimentally observes
N03 -»• N03". This process, while important for N03~ production,
may also be very important to radical initiation and significant
to any modeling effort (see reactions in Table 2.9).
c. Comparison of aqueous S(IV) oxidation mechanisms
The myriad solution reactions presented are not all relevant to atmo-
spheric chemistry. The specific mechanisms, rate constants, and oxidant
concentrations will limit the effectiveness of some mechanisms to generate
sulfate with respect to others. This can be demonstrated by assuming con-
ditions appropriate to a cloudy or precipitating atmosphere and calculating
the instantaneous aqueous production rate of sulfate. Then by further as-
suming atmospheric liquid water contents, the aqueous reactions may be com-
pared with the gas-phase rates of sulfate production.
The oxidation of sulfur in aqueous solutions is strongly dependent on
pH and has led to discussions of ammonia "catalysis" (McKay, 1971) and acid
inhibition. Acid inhibition results from (1) the decreased solubility of
SO? with increasing acidity, (2) shifts in S(IV) speciation with changes in
[H*] (most dramatically at pH = pK(20) and pH = pK(2D), and (3) apparent
changes in the oxidation mechanism as evidenced by rate constant dependen-
cies on [H+3. Figure 2.4 illustrates the effect of [H+] on S(IV) solubil-
ity and the partitioning of S(IV) between S02«H20, HS03~, and S03=. Ta- .
bles 2.2 - 2.6 list rate constants for S(IV) reaction with 03, H202, and a
few other possible oxidants which show a marked dependence on [H*].
Figure 2.5 shows the combined effects of the above chemistry on the
aqueous rate of sulfate production. Each line depicts the rate for a given
oxidant under the following assumed conditions:
T = 15 or -5°C, P(S02) = 5xlQ-9 atm, [S02*Aq = P(S02) K(l),
P(S02) K{1) K(20) [H*]-1, [S03=] = P(S02) K(l) K(20) K(21)
P(03) = 5xlO;8 atm, [03] = P(03) K(ll), [soot] = 10'3 g I'1, k(R)
[HO] = 5xlO-3 s -1, P(HONO) = 10-10 atm, [HONO] = P(HONO) K(R3),
[NO,-] = P(HONO) K(3) K(24) [H+]-1, [Fe+++] = 10~5 or 10'7 M,
[Mn*+] = 10-1[Fe+-H']f [H202] = 10"5 M, and [H+] = 10° - 10~7.
The equilibrium constants, K(i), are given in Table 2.7. The oxidation
rate constants are summarized in Tables 2.2 - 2.6, and are taken to be:
k(59) Penkett et al. (1979), k(60) Maahs (1982), k(61) Martin
and Oamschen (1981), k(59') iron catalyzed Martin et al. (1981a),
k(59') soot catalyzed Chang et al . (1981), k(62) Farhataziz and
Ross (1977), and k(79) Oblath et al . (1980) or Martin et al . (1981)
195
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Aqueous Rates of Sulfate Production
sk
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i iii
3 4
pH
6 7
Figure 2.5 Aqueous sulfate production rate as a
function of pH (see figure key on following page).
198
-------
Figure 2.5
Figure Key
Label Mechanism
a SO,' + I 02 + SO,,'
b S(IY) + Q3 « S(¥I) + 02
C SUV) + H202 * S(VI) * H20
[H202] « 10*s N
d S0a« + 1 Oj » SO,."
e S(1V) + Oj » S(VI) + 02
f S(IV) * H202 * S(VI) + H20
[H202] « 10-5 H
[Fe**] « 10-5 M
[Mn**] * 10-6 M
SO," + i 02 Fe**' *** SO,,'
2
[Fe**] « 10-7 M
[Mn**J > 10-8 M
Soot „, ,
Temperature
15*C
15*C
15*C
-5'C
S(I¥)
S(VI) + i M20 + H20
2
SUV) + N(III) -
S(VI) » i
2
SO,,' 15*C
15*C
IS'C
[Soot] » 10-3 9 f1
SUV) + HO(H02) « S(VI) + ? 15*C
k[OH] • k[H02] - SxlO-3 s-1
15'C
1S«C
Rate Constant Reference
Penkett et al. (1979)
Maahs (1982)
Martin and Danschen (1981)
Penkett et al. (1979)
Maahs (1982)
Martin and Danschen (1981)
and activation energy of
Penkett et al. (1979)
for pH » 4.6
Martin et al. (1981a)
Martin et a). (1981a)
Chang et al. (1981)
FarhatazU and Ross (1977)
001ath et al. (1980)
Martin et a). (1981a)
M20
Gas-aqueous equilibrium Is assumed for S02, 02, 03, and HONO. Partial pressures of Oz,
S02, 03, and HONO are assumed to be. respectively, 0.2, 10'9, SxlO"8, and 10'10 atm.
Aqueous concentrations of H202, Fe**, and Mn**, and soot are given under the mechanism
listed above where appropriate.
199
-------
The rate constants chosen reflect most recent measurements and analyses,
and their selection here is not meant to be judgmental with respect to the
accuracy of the other rate constants presented. The Oblath et al. (1980)
expression for k(79) is determined under experimental conditions atypical
of atmospheric water and includes terms which are probably unrealistic at
more normal atmospheric concentrations of S(IV) and N(III). The uncertain
region is shown as a dashed curve in Figure 2.5. .
The assumed reaction conditions are selected to represent typical con-
centrations over eastern North America. The aqueous H202 concentrations
are not calculated from a consideration of vapor-aqueous equilibria since
gas-phase measurements of H202 suffer from sampling errors. H202 measure-
ments in atmospheric water do not exhibit the same errors, are consequently
more reliable, and the [H202] value chosen is representative of the ambient
aqueous measurement in cloud and rain water (Kok, McLaren, and Lind, per-
sonal communication, 1982). Measurements of MONO or N02~ are not available
for the eastern United States, and P(HONO) is taken to be approximately
one-tenth the value measured in Southern California (see Platt et al.,
1980b; Liljestrand and Morgan, 1981). The assumed concentrations of iron,
manganese, and soot are chosen to bracket measurements in precipitation.
The concentration of HO in solution is taken from the steady-state cloud
model results of Chameides and Davis (1982). It should be pointed out
that, aside from the catalytic sulfur oxidation reactions {58'), the other
reactions are all first order with respect to S(IV) and oxidant. Thus, to
examine the effects of different assumed species conditions on the rate of
sulfate production, one need only multiply the rates shown in Figure 2.5 by
an appropriate factor.
It is readily apparent from Figure 2.5 that the rate of sulfate pro-
duction is dominated by H202 at solution pH's < 4.5 (curve c) and by 03 at
pH's > 4.5 (curve b). If the Oblath et al. (1980) rate constants for the
HS03~ - N02~ reaction can be extrapolated to low pH, then sulfate produc-
tion at pH s < 2 will depend on MONO (curve k). This extrapolation does
not seem valid in light of the measurements by Martin et al. (1981b) at
pH's < 3 which predict rates of sulfate production six orders of magnitude
lower at pH=3 and eleven orders of magnitude lower at pH=0 than the Oblath
extrapolated rates. Only when Martin's rates are extrapolated to pH's > 6
do the two N02~ rates come into agreement (curves 1 and k).
The effect of temperature on S(IV) oxidation by H202, 03, and 02 can
be seen in Figure 2.5. At lower temperature, the Henry's Law solubilities
of S02, H202, 03, and 02 all increase. K(20) and K(21) also increase,
which further increases the total S(IV) solubility. On the other hand, the
H202, 03, and 02 rate constants all decrease with decreasing temperature.
The combined effects of temperature on sulfate production rate are shown by
comparing curves a and b for 02, curves b and e for 03, and curves c and f
for H202 rate. The increase in H202 rate is not as large as is possible
theoretically, since Henry's Law solubility did not enter into the calcu-
lation; [H202] in solution was directly assumed. The H202 solubility will
increase by a factor of six in going from 15°C to -5°C. However, the
[H202] may be limited by the rate of H202 generation in the gas phase.
At no time does it appear from Figure 2.5 that an uncatalyzed 02
200
-------
reaction is important. For a soot catalyzed reaction to compete effective-
ly with H202 at pH < 6, the soot concentration must exceed - 0.1 g T ,
and to compete with 03 the soot concentration must exceed 0.1 g 1-1 at pH
- 4.5 and 10 g I'1 at pH - 5.6. Only at high concentrations of iron or
manganese does it appear that an 02-metal-catalyzed oxidation mechanism can
contribute to sulfate production.
Lastly, the hydroxyl radical does appear to contribute to sulfate for-
mation given that the conditions assumed by Chameides and Davis (1982) are
appropriate; namely, HO sticking coefficient > 10, droplet size less than
- 2x10 cm radius, cloud transmissivity > 0.5, midday solar fluxes, and
moderately clean air. Not shown is the contribution from H02 or 02~. Rate
constants for H02 or 02~ reactions with S(IV) are not available, and it is
generally inferred that the rate constant times the radical concentration
for HO and H02 or 02~ are equal, i.e., k[HO] - k[H02] - k[02']. There-
fore, it is assumed that the sulfate production from H02 or Q2~ is equal
to that for HO.
Figure 2.5 in conjunction with Figure 2.6 can be used to assess qual-
itatively the importance of aqueous sulfate production mechanisms in the
atmosphere. Figure 2.6 shows the equivalent gas-phase rate of species
formation (ppbv hr'1) as a function of liquid water mixing ratio,
WjiU-H20/£-air), and aqueous production rate (M s~M at T = 288K and
P = 1 atm. The following relationships between aqueous rates and gas-
phase rates are also useful:
r (molecules cnr3 s-1) = 6.02 x 1020 W. r ,
g x, a
and
r (ppbv hr-1) = 2.95 x 1011 W. T P'1 r ,
g * a
r, (% hr'1) = 2.95 x 10* W0 T P'1 X'1 r = 2.17 x 102k W0 n'1 r,,
9 * a x a
where ra is the aqueous production rate (M s"1), T is temperature (deg
K), P is pressure (atm), W^ is volumetric liquid water mixing ratio of
the air, n is the molecular density of the gas (molecules cm"3), and X is
the total (gas + aqueous) equivalent gas-phase volume mixing ratio of the
reactant species (ppbv). The following three examples will help clarify
the use of Figures 2.5 and 2.6.
Example 1: Haze aerosol, WA = 10~10, pH = 5.6
We would like to know the rate of sulfate formation through an aqueous
0? - S(IV) reaction in a very hazy layer of air such that WA = KT10.
Given that the conditions of Figure 2.5 apply, the air temperature is 15°C
and the aerosol is at pH = 5.6, then the aqueous rate of SO^ production,
ra (SO^3), is - 2x10 M s"1. Going to Figure 2.6, we draw a verti-
cal line through W^ = 1Q-10, and starting from the bottom move upward
along this line until it intercepts the diagonal line corresponding to ra
= 2xlo~6. From this point, we^move horizontally to the left and find that
the gas-phase equivalent rate rg is 1.8xlQ- ppbv hr"1. X can be assumed
201
-------
.0
Q.
a.
cr
o
Q
o
cr
Q-
LU
X
Q.
I
CO
LU
!05
I04
i*P IO3
LU
I-
I02
10'
10°
10
,-3
I io-4
o
IO
10"
10"
IO
rlO
IO
r9
icr8 icr7
LIQUID WATER VOLUME MIXING RATIO
Figure 2.6 Nomogram relating aqueous reation rates
M s~^ , to equivalent gas-phase reaction rates ppbv hr'"*,
and vice-versa for T = 288K, P = 1 atm and given liquid
water volume mixing ratio. Diagonal lines are constant
aqueous reaction rates.
202
-------
equal to 5 ppbv, and the initial rate of S02 conversion to sulfate is 0.36%
hr-T.
Example 2:
Scott (1982) estimates the rate of S02 to sulfate conversion at 10%
hr"1 for storms over the northeastern United States. If the S02 vapor
concentration were 5 ppbv, then the equivalent gas-phase rate is 0.5 ppbv
hr"1. The liquid water volume mixing ratio is typically 10~6 in these
storms. In Figure 2.6, rg = 0.5, and W£ = 10"6 corresponds to ra =
6xlO"9 M s"1. From Figure 2.5, with ra = 6xlO~9 M s'1 and pH from 4 to
5.6, it can be seen that reactions involving 03, H202, HO, and iron-cata-
lyzed 02 are all capable of generating sufficient aqueous sulfate to ra-
tionalize the conversion rates observed by Scott.
Example 3:
What minimum aqueous H202 concentration is needed to account for a 1%
hr"1 conversion of S02 to sulfate when the aerosol pH = 3, liquid water
mixing ratio is 10~u, and the temperature is -5°C? Analogous to Example
2 above, ra is found to be 2x10"^ M s"1. At pH = 3, T = -5°C, [H202] =
lxlO~5 M, and ra = 6xlO~8 M s"1 from Figure 2.5. Because ra is linear
with respect to H202, the required [H202] is 3xlO~2 M. This aqueous H202
concentration corresponds with a gas-phase concentration of 35 ppbv when
Henry's Law equilibrium is assumed.
This analysis illustrates the inability of low liquid water content
aerosols to generate significant amounts of sulfate. Cloud droplets and
hydrometeors, on the other hand, appear able to sustain elevated rates of
sulfate conversion with respect to gas-phase reactions during their life-
times. H202 and 03 are the principal oxidants under the assumed condi-
tions. At no time does the uncatalyzed 02 - S(IV) reaction appear signi-
ficant, and the catalyzed iron and manganese reaction requires atypical
concentrations of these metals. The hydroxy and hydroperoxy radical oxi-
dation of S(IV) may be important. However, substantial research on aque-
ous radical chemistry is needed before a definitive judgment can be made.
If the anomalous rate constant for (79) measured by Oblath et al. (1980) is
correct (e.g., concentrated aerosol solutions), then in low pH solutions
N(III) oxidation of S(IV) may contribute to sulfate production. This seems
unlikely.
2.2 Acid generation from nitrogen-containing species through gas-particle
interactions and aqueous chemistry
a. Features of heterogeneous NOy chemistry: empirical evidence
Depending on season and location, 30-60% of the acidity measured in
precipitation in regions of NOX emissions is due to nitric acid. Since
the gas-phase oxidation of NOX (primarily via OH + N02 " HN03) is a fair-
ly rapid process, approximately ten times faster than its S02 counterpart,
it has generally been assumed that nitric acid in precipitation results
from scavenging of HNOa vapor by falling droplets. Except during times of
precipitation or near the ground, HN03 and the major nitrogen oxides (NO,
203
-------
NO2, NO3, and N^OS) have been assumed to exist in ratios determined by
gas-phase kinetics (see Table 2.9 and Section 1 of this chapter), with HN03
a major contributor to dry acid deposition.
There is growing evidence, however, which suggests that this picture
of tropospheric odd nitrogen chemistry is not complete. For example, Laz-
rus et al. (1982) found as part of APEX that nitric acid appeared to form
continuously over the course of a warm frontal storm and suggested that
in-cloud acidification was partly responsible. Even under dry conditions,
the NOX/HN03 ratio is often much higher than predicted by purely gas-
phase kinetics, and loss to particles is a postulated explanation. This
phenomenon has been observed in both polluted and unpolluted environments
(Kelly et al., 1980; Stedman and West, 1981).
Heterogeneous processes are implicated by measurements of other NOy
species in the troposphere, e.g.: (1) nocturnal N03 levels in virtually all
measurements made to date are lower than can be explained by strictly gas-
phase processes (Noxon et al., 1978; Noxon et al., 1980; Platt and Perner,
1980; Platt et al., 1981); (2) HONO builds up at night at rates much faster
than can be explained by gas-phase mechanisms (Platt et al., 1980).
The species participating in atmospheric nitrogen oxide and oxyacid
chemistry are summarized in Figure 2.7. To the complement of nitrogen
oxides described in Section 1 of this chapter have been added N203 and
N20it, which may figure in NOX gas-to-particle conversion and condensed-
phase chemistry. The arrows designate interconversions among three groups
of NOy compounds: NOX, higher nitrogen oxides, and acids. PAN and
HNO^ nave been grouped with nitric and nitrous acids because they may con-
tribute to acid formation in the condensed phase (Spicer et al., 1981),
although the extent to which this takes place is not certain. This is
partly because PAN and HNO^, like the compound oxides N203, N20tt, and N205,
have varying thermal stability over the range of temperatures typical of .
the boundary layer. The sum of all oxides and acids is referred to as
NOy.
Except for ions which come from acid dissociation in the condensed
phase, Figure 2.7 with different kinetics applies to both gas and condensed
phases, with the latter comprising three particle types: fog or cloud
droplets, small aerosols, and rain or snow (hydrometeors). These are the
same classifications (II-IV) described earlier (Figure 2.2).
The basic features of homogeneous NOX to nitric acid conversion were
discussed in Section 1 of this chapter, where it was pointed out that the
predominant acidification process is OH + N02 ^ HN03; the rate of this
depends critically on [OH], which in turn is largely controlled by atmo-
spheric NOX and hydrocarbon levels (see Section 2.4 of this chapter for a
discussion of heterogeneous effects on hydrocarbons and other oxidants).
In addition, HN03 may be incorporated into particles or may form within
them from oxidation of other NOy species.
The following two sections review heterogeneous NOy chemistry. The
first focuses on aqueous-phase processes, and the second surveys NOy gas-
particle interactions, attempting to describe the key processes as they
204
-------
N0x
NO /
NO 2 - ,
^
higher nitrogen oxides
* N03 £
>> N205
NzO*
N203
C
„ . - ^
<_ —
acids
3 HN03
. .-^ HONO
PAN (?)
HNOj,
N0"2 (condensed
phase only)
NOs
Figure 2.7 Major tropospheric NOy species and schematic inter-
conversion pathways.
205
-------
have been identified by experimental evidence and modeling treatments to
date.
b. Condensed-phase kinetics
A major part of the condensed-phase chemistry of NOy has been tho-
roughly reviewed recently (Schwartz and White, 1981). In terms of nitrogen
acidification in precipitation, cloudwater, or other particles, the crit-
ical equilibria are the ionic dissociations of nitrous and nitric acids:
HN03(a) * H+(a) + M03-(a)
HONO(a) : H+(a) + N02-(a)
The position of the HN03 equilibrium lies strongly to the right {Keq =
15.4; Davis and De Bruin, 1964), and dissociation is expected to be com-
plete in all but the most acidic particles. Nitrous acid is weak (pKa =
3.3) so that if it forms to any degree in particles with pH < 4, a signi-
ficant fraction of it will be present as undissociated HONO.
In addition to the thermodynamic and kinetic characteristics of
aqueous NOy chemistry, Schwartz and White (1981) reviewed the solubility
equilibria of the nitrogen oxides to determine the potential for mixed-
phase N0x-to-acid conversion; i.e., the nitrogen analog to aqueous S(IV)
acidification. The primary contributors,
(H20)
N02(g) + N0(g) £ 2H+(a) + 2N02-
and
(H20)
N20(g) + N02(g) J 2H+(a) + N02'(a) + N03-{a),
have equilibria that lie to the right, but Lee and Schwartz (1981) demon
strated that low NO and N02 solubilities inhibit the oxidations and prob
ably have little effect on aqueous S(IV) oxidation which is highly pH-
dependent. Direct N02 - S(IV) reaction may, however, oxidize the latter.
The kinetics for aqueous NOy chemistry are summarized in Table 2.10
(interactions between NQX and SOX are discussed in Section 2.3 of this
chapter). The list is not exhaustive, but it includes the major inter-
actions among the NOy species and a number of N03 oxidations. The pro-
cesses in Table 2.10 may be supplemented by two other types of reactions.
The first are radical -radical interactions, identical to their gas-phase
counterparts, which can interconvert forms of NOy, e.g.,
R02 + NO + RO + N02
H02 + NO + M02 + OH
The effects of such reactions on condensed-phase acid formation are prob
206
-------
Table 2.10. Liquid-Phase Oxidation of Odd-Nitrogen to Nitrogen Oxyacids
Reaction1'
NO + N02 * 2HONO
w
NO + N02 " M2U3
N203 1 2HONO
N02 + N02 2 MONO + HN03
N02 * M02 + N20^
N20,, » HONO + HN03
N02 + N03 " 2HN03
N20; • 2HNO,
N03 + ? - N03- + ?
N03 + Cl- * N03* + C1
NO, * F." . N03- * Fe-
N03 + N02" » M03~ •*• N02
Rate Constant Comment
7.4xl06 M-1 s"1
IxlO8 M-1 s'1
l.lxio9 M-1 s-1
2xl07 M-1 s-1
S.3xl02 s'1 pH <^ 5
10s M-1 s-1
1.7x10* M-1 s-1
3xl07-9xl08 M-1 s"1
Ixl03-6xl0* s-1
7
> 10s s-1
(7. 59*0.21 )x!03 s-1 add
9.5x10^ add
9.7»102 2.8
8xl03 add
3x10" pH « 7
l.SxlO5 natural
IxlO8 M-1 s-1
(8.0Tl.6)xlOs M-1 s-1 acid
1.2xi09 M-1 s-1 pH » 7
Reference
Gratzel et al.-
(1970)
Treinin and
Hayon (1970)
Ross and Neta
(1979)
Epstein et al.
(1982)
Ross and Neta
(1979)
Lee and Schwartz
( 1981 )
Epstein et al .
(1982)
Ross and Neta
(1979)
Ross and Neta
(1979)
Ross and Neta
(1979)
Ross and Neta
(1979)
Ross and Neta
(1979)
Ross and Neta
(1979)
207
-------
Table 2.10. Liquid-Phase Oxidation of Odd-Nitrogen to Nitrogen Oxyacids
(continued)
Reaction1
N03 i
i- CH3COOH * ?
N03 + HCOOH » ?
H03 i
NO 3 H
M02-
N02-
HONO
HO +
HO +
C03-
Fe"
i- CH3OH » ?
>• CH3CH2OH * 7
+ 03 - M03- + 02
+ H202 « N03- + H20
+ H202 « H+
+ N03- + H20
NO 2 * H02NO
NO * N02- * H*
+ N02 « C02 + M03-
+ N02 l*Fe*** + HOMO
Rate Constant Comwnt
(4.6*0.4)xiO* M-1 s-1
2.06xl05 M-1 s-1
IxlO6 M-1 s-1 acid
2.2xl06-3.9xlOs add
200 [H*]-1 M-1 s-1 pH • 0-3; T - 25»C
4.6»103[H+] M-1 S'1 pH • 0-3; T « 2S'C
2.5xl02 exp(-7650T-M pH * 0.8-3.1;
T « 20-30*C;
x (1 + 7.8 I) M-1 s-1 fonic strength, I
- 0-0.08 M
1.3xl09 M-1 s-1 pH » 9; T » 20-25*C
1010 N-1 s-1 pH » 7; T » 20-2S°C
1x10* M-1 s-1 pH • - 11;
3.1x10* M-1 s-1
Reference
Ross and Neta
(1979)
Ross and Neta
(1979)
Ross and Neta
(1979)
Ross and Neta
(1979)
Martin et al.
(1981a)
Martin et al.
(198U)
Lee and L1nd
(1983, personal
connunl cation)
Farhatazlz
and Ross (1977)
Farhatazlz
and Ross (1977)
Ross and Neta
(1979)
Epstei n et al .
(1982)
208
-------
ably secondary, influencing oxidant levels, S02 conversion, and nitrate
formation. A second group of reactions stimulating acid formation may be
oxidations of N02 and N03 by ions (especially organic) other than those
illustrated:
N02
R0<
A full range of subprocesses must be part of a realistic aqueous-phase ki-
netic scheme.
From Table 2.10, it is apparent that there are a number of routes for
effective conversion of aqueous N03 to N03~. Since N03 appears to be read-
ily scavengeable by particles (see following section), these reactions may
be major contributors to condensed-phase acidification. The contributions
of PAN and HNOt,. to aqueous nitrate formation have not been established.
PAN in particular has been proposed as a mid-troposphere NOX reservoir
(Singh and Hanst, 1981). Both PAN and HNO^ decompose upon dissolution.
PAN may decompose to form N02~ (Mudd, 1966; Nicksic et al., 1967) or N03~
(Spicer et al., 1981); the products are apparently pH-dependent. Nitrite
is in equilibrium with HONO, which because of its relatively low solubility
(Schwartz and White, 1981) could be desorbed from the aqueous phase. The
compound oxides N20H and N203 also form N02~ in solution. Thus, the ox-
ides, PAN, and/or HNOi+ all appear to be potential HONO sources. If so,
the sequence of reactions:
N203
PAN(?)
HNOlf(?)
gas
N02-,
•H
HONO
HONO
gas
aqueous
could represent a heterogeneous source for tropospheric HONO (Heikes and
Thompson, 1982). .
The rates of nitrate and nitrite production through homogeneous so-
lution phase reactions involving NO, N02, and N02~ can be calculated and
qualitatively compared with the rates from gas-phase and heterogeneous
reactions (Section 1 of this chapter). For these calculations, the
following conditions are assumed:
-,.10
T = 25°C, p(HONO) = 10-1(J a tin, [HONO] = K(3) P(HONO),
[N02-] = K(3) K(24) P(HONO) [H+]'1, [Fe++] = 10'5 or 10'7 M,
[H202] = 10- M, P{03) = 5xlO-8 atm, [03] = K(ll) P(03),
[NO] = K(16) P(NO), [N02] = K(17) P(N02), and [HO] = SxlO"13
M.
The partial pressures of NO and N02 are allowed to vary from 10"12 to 10~5
atm and span values found typically in pristine air and moderately dilute
plumes. Solution pH is allowed to range from 0 to 7. r(HONO) and r(HN03)
through reactions 67, 68, 72, 73, 80, 81, and 82 (Table 2.8) are shown in
Figure 2.8. The rate constants used to calculate r(HONO) and r(HN03) are
listed in Table 2.10. It can be seen that N(III) oxidation is dominated by
H202 at pH < 2.7 and by 03 at pH > 2.7. The surprising result in Figure
209
-------
icr6
10
r8
O
-w
io
o
o io-'6
X
IO-I8
10
r20
- Aqueous Rotes of Nitrite or Nitrate Production-
,0
-I2
3 4
pH
i I
,0-l! ,0-IO |0-9 |0-8 |0-7 ,0-6
P(NO),P(N02)OR [p(NO)xP(N02)f,atm
Figure 2.8 Aqueous rate of HONO or HON03 formation as a
function of pH or NO and N02 partial pressure at 25° C
(see figure key on following page).
210
-------
Figure 2.8
Figure Key
Label
Mechani sm
Rate Constant Reference
NO,- + 0, * NO,- + Or
Martin et al. (19815)
b '
N02- + H202 + N03~ + H20
[H202] = ID'5 M
H20
N02 + N02 + MONO + HN03
H20
NO + N02 + 2 HONO
Martin et al. (19815)
Lee and Schwartz (1981)
Lee and Schwartz (1981)
N02 + Fe^ + N02- -»
[Fe**] » 10-5 M
N02 + Fe++ * N02-
[Fe+*] = 10-7 M
NO + HO * HONO
[HO] = 5xlO-i3
N02 •*• HO * HN03
[HO] = 5xlO-13
Epstein et al. (1982)
Epstein et al. (1982)
Farhataziz and Ross (1977)
Farhataziz and Ross (1977)
[03] is calculated assuming Henry's Law and a gas-phase 03 partial pressure of
5x10"8 atra. [NO] and [N02J are also calculated assuming Henry's Law and NO or N02
partial pressures given the lower a5scissa. [N02~] is calculated assuming Henry's
Law and HONO partial pressure of 10-10 atm.
211
-------
2.8 is r(HN03) through 81. The oxidation of N02 by Fe++ exceeds 80 as a
HN03 source up to NO? partial pressures of 4xlQ-9 atm (for [Pe"1"1"] = 10-' M)
and 5xlO-7 atm (for [Fe++] = 10"5 M). The HO, liquid phase oxidation of NO
and N02 does not appear to be a significant source of HONO or HN03.
Figures 2.6 and 2.8 can be used together to compare the aqueous sour-
ces of HONO and HNQ3 with heterogeneous and gas-phase mechanisms. If we
further assume that the rates of HONO and HN03 must exceed 0.1 and 1.0 ppbv
hr , respectively, to be relevant to atmospheric chemistry, then minimum
conditions for the aqueous mechanism can be established. Maximum liquid
water contents for aerosols are near 10_ °. From Figure 2.6, it can be
seen that ra must exceed 105 M s~l for rg > 0.1 ppbv hr"1, and from
Figure 2.8 it is obvious that none of the reactions shown for HONO can
produce the required amount. Similarly, it can be shown that none of the
aqueous HN03 reactions considered is capable of generating 1.0 ppbv hr"1.
Liquid water contents for clouds are near 10" , and _from Figure 2.6 it can
be seen that ra must exceed 10~9 M s"1 in order for rg > 10"1 ppbv
hr"1. Using this value for ra and Figure 2.8, it can be shown that the
partial pressure of N02 must exceed 5x10 atm (• 500 ppbv) or [P(NO)»
P(N02)]~/2 must exceed 6xlO~7 atm before aqueous reactions can be a
significant source of HONO. Such conditions are uncommon for the tropo-
sphere, but might be found within a condensing power plant plume. Again,
in an analogous manner, it can be shown that for r(HN03) >. 1 ppbv hr"1,
then ra >. 10"8 Ms"1. Only the 03 - N02" (67) and the N02 - N02 (81)
aqueous reactions are able to sustain such a rate (Figure 2.8), and even
then the pH must be greater than 5.2 and P(N02) must be greater than 2000
ppbv.
The above analysis suggests that, for the purposes of tropospheric
HONO and HN03 chemistry, homogeneous solution-phase reactions are negli-
gible under all but the most extreme conditions.
c. NOy gas-particle interactions
The partitioning of trace species between the particulate and gas
phases determines the chemical composition of precipitation, and ultimately
the relative amounts of wet and dry deposition. The greater the fraction
of a given species in suspended particles, the smaller is the amount di-
rectly deposited at the Earth's surface. Hence, during periods of low
particle density conditions, nearly all gas deposition is dry.
In principle, nitric acid formation in the atmosphere may occur as a
consequence of either homogeneous or heterogeneous reactions. In the for-
mer case, HN03 is formed in the gas phase. It may be removed by dry depo-
sition or absorbed onto particles. In the latter case, an acid precursor
(NOX or a higher oxide) is adsorbed and then oxidized within or on a par-
ticle surface. Thus, to evaluate HN03 deposition mechanisms, it is ne-
cessary to determine both the gas-particle partitioning of HN03 and the
degree to which HN03 precursors rather than HN03 itself are involved in
deposition processes.
Although ten neutral and two ionic forms of NOy distributed among
four modes (gas phase and three particulate types (Figure 2.2)) would
212
-------
require solution of 46 continuity equations, considerable simplification of
NOy kinetics is usually possible. To begin with, within a given phase
there is usually a rapidly achieved steady state between NO and N02 and
among the compound oxides N204 and N203, NOX, and the acids. Under some
conditions, N03 and N205 can also be assumed to be in a steady-state equi-
librium (Heikes and Thompson, 1982). We have also seen that condensed-
phase conversion of NOX and N02~ to nitrate is negligible under normal
tropospheric conditions. Furthermore, it is usually assumed that, because
of their low solubilities, NO and NQ2 are not absorbed by particles. (This
would not be true if there were significant reaction between N02 and an
organic compound on the particle surface.)
It is convenient to consider two important cases of heterogeneous
NOy chemistry. The first is the small particle which has a pronounced
composition-size dependence at equilibrium and which can be thought of as
starting nuclei for chemical and physical evolution. Although the growth
dynamics of such particles are usually linked to sulfuric acid, the amount
of dissolved HN03 influences pH and the S(IV) - S(VI) chemistry (Chapter V,
Section 2). A second class of heterogeneous processes involves interac-
tions between gases and particles in which the collecting (and evaporation)
properties of the latter are unaffected by gas absorption. In between the
two extremes, particles change composition as they grow or shrink until
they deposit at the surface (see Chapter VI, Section 5) or are scavenged by
cloud droplets or precipitation (Scott, 1982).
Gas-particle interaction coefficients of the type kc(I,J) have been
given for NOy species by a number of investigators (Luther and Peters,
1982; Levine and Schwartz, 1982; Heikes and Thompson, 1982). They follow
Fuchs1 and Sutugin's (1970) formulation of the gas-to-particle diffusion
rate in which the most critical parameter is the sticking coefficient, the
probability that a gas diffusing to a droplet will stick upon encountering
it. Particle removal coefficients corresponding to number densities of ty-
pical aerosol, cloud, and raindrop distributions are given in Table 2.11.
They were calculated for HN03 and other NOy species, but values for most
reactive gases and radicals are similar (Cnameides and Davis (1982); kc
(I,J) for OH and H02). Figure 2.9 shows an approximate altitude dependence
of kc for typical atmospheric conditions, i.e., particle distributions
corresponding to aerosols, fog, and a non-precipitating cloud. For each
entry in Table 2.11, the number in parentheses is k~1=x, the characteristic
removal time for the process. The most rapid removal is calculated for
cloud or fog conditions in which the liquid water content is high.
The particle removal constants for a cloud (.03 -.16 s"1, depending on
the sticking coefficient) are well within the lifetime of a typical cloud
drop (10 min.). Hence, a cloud in contact with a stable air mass will
gradually deplete the air of HN03, and possibly N03 and N205. NO and N02,
because of their low solubilities, will be relatively unaffected (Lee and
Schwartz, 1981). Since HN03, N03, and N205 scavenging are essentially
irreversible (conversion of the latter two species is assumed to form N03~
instantaneously), return of these species to the gas phase occurs only by
particle evaporation. However, scavenged N03 is likely to be returned to
the gas phase as HN03 so that particles have acted as heterogeneous acid
sources. If we assume that a steady-state exists between particle removal,
213
-------
Table 2.11
k(Gas.Part) for HN03, N03, and N205
(in s-1)
Sticking Coefficient k(Gas,Aerosol)
(a)
k(Gas,Cloud k(Gas,Raindrop)
Droplet)
1.0
0.1
0.01
0.001
3.46 x 10-3
(289)
9.58 x 10-"
(1040)
1.21 x 10-*
(8260)
1.26 x 10-5
(79400)
1.65 x 10-1
(6.06)
1.57 x 10-1
(6.37)
1.08 x 10- *
(9.26)
2.99 x 10-2
(33.4)
4.67 x 10-"
(2140)
4.67 x 10-"
(2140)
4.61 x 10-"
(2170)
4.17 x 10-"
(2400)
Heikes and Thompson (1982).
214
-------
10
i «
UJ
Q
r>
0.1
.01
I I I II III| I I I I I INj I I I I I III
i i i i i nil i i i i i nil i i r«j 11 nl i i i i i n
10-4
10-3
10-2
10-1
I
max
part
Figure 2.9 Vertical profiles of normalized first order particle
removal coefficients, kpartApirt -kc (J«J) 1
-------
kc(I,J), and particle breakup, ke(J,I),
/
0 = k (I,J) {[HN03] + [N205] + [N03]} - k (J,I) [N03-],
w tr
the ratio of gas phase acid and precursors to dissolved nitrate is given by
the ratio of the condensation (removal) and evaporation coefficients:
[N03-] k (I,J)
_ v*
JHND3 +1T205 + N037 ke(J,I)
A more detailed steady-state treatment of heterogeneous NOy chemis-
try has been carried out by Heikes and Thompson (1982). Observations of
low nighttime N03 can be accounted for by aerosol removal of the latter,
although olefin scavenging of N03 or a NO + N03 reaction could also explain
the measured levels (Platt et a!., 1980; Platt et al., 1981). Richards
(1982) has discussed the contributions of NQ3 removal to aerosol nitrate
formation in Los Angeles. Heikes and Thompson (1982) have also calculated
the dependence of cloudwater HN03 acidification on kc(I,III), NOX and
03, photolysis rates, and other physical parameters. For example, Figure
2.10 shows the HN03 formation rate, r(HN03), as a function of kc(I,III).
The dotted line represents a gas-phase equivalent rate of 1 ppbv hr"1
(T = 288K, P = 1 atm). At low values of kc(I,J), the primary mechanism
of in-cloud nitrate formation is the reaction OH + N02 •*• HN03, followed by
particle removal of the latter. This pathway would not be operative at
night when OH production ceases. At higher values of kc(I,J), cloud re-
moval of N03 and N20s is fast enough to compete with photolysis and could
produce appreciable HN03 in clouds both day and night. From Figure .2.10,
it can be seen that a 1 ppbv hr"1 HN03 formation rate requires minimum
values: kc(I,J) » 10-3 s"L, NOX = 10 ppbv, and 50-100 ppbv 03. Heikes
and Thompson (1982) have also analyzed the role of NOy and particle/water
vapor interactions in heterogeneous nitric acid formation for fixed levels
of NOX and 03. The results are presented in Figure 2.11.
Other examples of model studies of heterogeneous NOy removal include
one-dimensional calculations of below-cloud HN03 washout (Thompson and
Cicerone, 1982; Turco et al., 1982; Stewart et al., 1982). Durham et al.
(1981) have investigated HN03 scavenging by falling raindrops. Cloud drops
which begin at pH = 5.5 are acidified first by HN03, then by S02 adsorp-
tion; those which start at pH = 4 only add HN03. Although scavenging is
very effective in cleansing the atmosphere of HN03 (Huebert, personal com-
munication, 1981), the implication from the APEX study is that in-cloud
HN03 formation may be an important source of acid precipitation in polluted
environments.
Zero- or one-dimensional model calculations may be able to treat cer-
tain case studies, but they are probably poor representations of long-term
averages since many episodes of varying precipitation intensity and compo-
sition determine mean wet deposition. In places where the composition is
not highly variable, it is important to use properly chosen steady-state
wet removal coefficients Ypart to estimate wet removal (Rodhe and Gran-
dell, 1972). One approach to estimating TTpart is to average episode-
integrated removal over a representative period of time:
216
-------
10s
I08
« I07
o
*
c?
I ,o6
I I
NOX, 03
IC
100, 50
10,10
1.0, 50
0.1,50
ic
5
I0
'4
I0
"3
IO
-2
10'
IOC
Figure 2.10 Effect of NOX and 03 (in ppbv) on HN03 formation
rate, r(HN03), as a function of kpart ['cc(J'1) in text]. Values
for other parameters are: T=288K; P=l atm; OH=106 cm-3.
Photolysis rates used in calculations are for cloudy conditions,
Dashed line reoresents an HN03 production rate of 1.0 ppbv hr-1
(Heikes and Thompson, 1982).
217
-------
10
IOC
Figure 2.11 In-cloud HN03 formation rate r(HN03),
calculated as a function of kpart [kc(I,J) in text]
for various production pathways. Solid curves are
for daylight conditions and dashed curves are for
nocturnal conditions. E's represent total formation
rates. Curve labels refer to the following reactions:
R19, N02 + OH + M -»• HNOs + M; .R29, N205 + N£0 •»• 2HN03;
R37, N03 + wp ->• HNOs; R39, N204 H- wp -*• HONO + HN03;
R40, ^305 + wp -»• 2HN03. Assumed conditions are:
T = 283 K, P =0.9 atm, NOX = 10 ppbv, 03 = 50 ppbv,
100% relative humidity, OH = 106 cm~3 daytime;
OH = 0 niqht. Nocturnal formation rates are not shown
at kpart < 10~2s_i because steady-state model assumptions
are not valid.
218
-------
kpart(z)
cond
k (x,y,z,t)dt
/ dt
where the instantaneous removal coefficient kpart(x,y,z,t) has been writ-
ten to emphasize its spatial dependence (Levine and Schwartz, 1982: Thomp-
son and Cicerone, 1982). Thus, a single value of l(part» e.g., 10 s"1,
may represent a continuous aerosol removal or a few hours per week of fog
or precipitation deposition. Depending on the altitude distribution of
£part» t"6 relative amounts of wet and dry removal may vary by a factor
or two or more (Thompson and Heikes, .1982).
The examples we have described represent simplifications of a four-
phase NQy chemistry, as illustrated in Figure 2.7. Particle evolutions
and transport have been neglected, and heterogeneous processes have in-
cluded primarily irreversible scavenging of HN03 and higher nitrogen ox-
ides. Schematically, interactions of all species between two boxes of the
type shown in Figure 2.7 have been simplified:
Gas: I
NO J higher
oxides
: HMO 3
HONO
Particle: 11,111,1V
ke t
Although this represents a great reduction of complex chemical and micro-
physical processes, it may describe NOy chemistry adequately in many sit-
uations in the troposphere.
2.3 Coupling of NOX - SOX aqueous and particulate chemistries
An issue in the modeling of acid deposition is the question of line-
arity. Linearity usually implies that the amount of sulfate and nitrate
received at the earth is directly proportional to the quantity of sulfur
and odd nitrogen emitted anthropogenically. The relation of deposition to
emission is highly dependent upon the spatial and temporal scales over
which linearity is considered. Clearly, over the globe and on an annual
basis, sulfur or nitrogen deposition is linear. Otherwise there would be
a net accumulation or loss of the oxides of sulfur and nitogen in the atmo-
sphere. However, on a regional scale such as eastern North America, this
question is clouded by the flux of material through the lateral boundaries,
the scales of the deposition phenomena (e.g., precipitation extent and du-
ration), and the chemical mechanisms of acid formation. A point central to
the latter effect is the degree to which the primary acids (HN03 and H2S04)
and their precursors (MOX and SOX) interact.
219
-------
Rodhe et al (1981) demonstrated theoretically that for their highly
simplified chemistry and environmental conditions, the production of sul-
fate in the atmosphere and its deposition are strongly influenced by odd
nitrogen emissions. The link between sulfate and nitrate in their model
is the competition between S02 and NOX for gas-phase oxidant (OH) and
aqueous oxidant (H202). Our discussion of aqueous and heterogeneous SOX
and NOX chemistries has described at least five potentially significant
areas of interaction: gas-phase oxidant competition, aqueous oxidant
competition, acid inhibition, S02 oxidation by NOy, and volatization of
weak and comparatively insoluble acids. We will consider each of these
briefly.
a. Gas-phase oxidant competition
In the gas-phase homogeneous chemistry section (Section 1 of this
chapter), it was shown that the principal acidification reactions were:
N02 + HO + M + HN03 + M (1)
S02 + HO + M + HS03 + M —> H2$Q>*> W
with the reaction (2) being either an HOX radical termination reaction or
more likely an HOX radical chain propagation reaction. In either case,
there remains the competition for OH with the rate constant for (1) being
approximatly one order of magnitude faster than the rate constant for (2).
If one molecule of NOX is emitted with one molecule of S02, as state-wide
emission inventories would suggest, then initially there will be a ten-to-
one production ratio of HN03 to H^O^ in the gas phase. Consequently, on
the basis of HO chemistry, sulfate production and possibly its deposition
will lag significantly behind that of nitrate.
b. Aqueous oxidant competition
In aqueous solutions, the question of oxidant competition is more
clouded. The concentration of S(IY) and its speciation are shown to be
pH-dependent, and the solubility and speciation of N(III) are as well.
The rate constants for S(IV) reaction with 02, 03, H202, N02~ are pH de-
pendent (see Tables 2.2 - 2.6), as are the rate constants for N(III) reac-
tion with 03 and H202 (Table 2.10). The speculated aqueous HOX reactions
leading to S(VI) and N(V) formation compete with each other for HOX and
with almost all other dissolved species as well. The complexities of rate
constants and solution composition do not permit us to conclude on the ba-
sis of oxidant competition whether sulfate oxidation will inhibit nitrate
production or whether nitrate production will inhibit sulfate production.
c. Acid inhibition
It was shown earlier that acidification of aqueous particles will
reduce the S(IV) concentration and, depending upon the oxidant mechanism,
significantly reduce the rate of sulfate production. The production of
S(VI) from S(IV) is in and of itself inhibiting, since one molecule of H+
is released for each molecule of HS03~ which is oxidized at the normal pH'
encountered in cloud and precipitation water. The incorporation of HN03
220
-------
either through gaseous absorption or aqueous production will also acidify
the particle. Therefore, HN03 and/or other acids can influence the atmo-
spheric production rate of sulfate (Durham et al., 1981). Conversely, the
absorption of ammonia will act to neutralize the solution and promote sul-
fate formation (McKay, 1971).
d. S02 oxidation by NOy
Oxides of nitrogen may directly oxidize S(IV) or catalyze other
oxidation mechanisms. Nash (1979) indicates that N02 will oxidize bi-
sulfite to sulfate. However, at his N02 concentrations (80 ppmv), the
reactions
2N02{g) * N204(g)
N02(g) $ N02(a)
2N02(a) * HONO(a) + HN03(a)
* HONO(a) + HN03(a)
can lead to significant MONO formation, and he could have been observing
the reaction
2NUII) + 2S(IV) * N20 + 2S(VI). (3)
Rate constants for (3) are reported by Oblath et al. (1980) and Martin et
al . (1981b). Reaction (3) was shown earlier to be negligible under typical
cloud and rain conditions (Figure 2.5). Another possible way for NOX to
oxidize S(IV) in solution is the diffusion of N03 to particles followed by
a direct N03 - S(IV) reaction or the production of aqueous radicals which
then oxidize S(IV) (as discussed in Section 2.2 of this chapter). It is
premature to assess the significance of this mechanism in sulfate produc-
tion. Lastly, it appears that N02 can catalyze the conversion of S02 to
sulfate on dry soot particles (Cofer et al., 1981), although this would be
of negligible importance under all but the most extreme atmospheric condi-
tions.
e. Volatilization of weak and comparatively insoluble acids
The last interaction between NOX - SOX to be discussed involves
the volatization of weak and relatively insoluble acids. The desorption of
S(IV) as pH decreases has already been discussed as part of the acid inhi-
bition effects. Along with S(IV), there will also be a loss of HONO as the
pH falls. Perhaps most important is the loss of HC1 from NaCl -containing
particles on which HN03 and H2SUi+ are incorporated, and the loss of HN03
from particles upon which ^SO^ has absorbed or been produced. These
effects are all amplified if the wet particle is undergoing evaporation.
The HC1 loss mechanism was proposed by Erickson (1959, 1960) and Yui et
al . (1976) as a source of gaseous chlorine compounds, and has been observed
by Martens et al. (1973), Duce et al . (1965), and Hitchcock et al . (1980).
221
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The volatization of HN03 is thought to be observed in the anticorrelation
between aerosol N03" and SOi^ (Harker et al., 1977) and the fact that in
the northeastern United States little if any aerosol nitrate is observed.
Theoretical studies (e.g., see Tang (1980), Middleton and Kiang (1979), and
Peterson and Seinfeld (1979)) also indicate that the incorporation of sul-
fate on aerosol causes HN03 desorption. The net effect of acid volatiliza-
tion is to reduce aerosol acidity, while at the same time increasing the
concentration of acidic vapors and reducing aqueous rates of SQ^~ and
N03~ formation as the precursors S02 and HONO are lost. In the development
of realistic acid deposition models, the chemical mechanisms employed
should be capable of treating the various interactions.
2.4 The role of hydrocarbons and organic oxidants in heterogeneous
atmospheric processes
a. Introduction
All of the atmospheric organic molecules and radicals participate to
some degree in heterogeneous processes. Many species are found in preci-
pitation (e.g., Galloway et al., 1976; Klippel and Warneck, 1978; Thompson,
1980; Meyers and Kites, 1982), and organic compounds of all classes are
found in aerosols (Grosjean et al., 1976; Hahn, 1980; Ketseridis and Eich-
mann, 1978; Simoneit and Mazurek, 1981).
Organic compounds in particles may be important to acid evolution in
two respects. First, organic acids will partly determine pH, and organic
neutral molecules and radicals will play a counterpart to their gas phase
role in determining dissolved oxidant levels, especially OH and H02. In
addition, a critical uncertainty in acidic particle evolution is the degree
to which organics concentrate on the outer surface of aerosols (Ripperton
et al., 1972; Graedel et al., 1982). A densely-packed organic layer would
inhibit exchange of volatile material between the condensed and vapor
phases (Chang and Hill, 1981).
b. Model treatments and condensed-phase chemistry
Zero-dimensional models which treat organic and inorganic chemistry in
detail (e.g., Calvert and Stockwell, 1982; Atkinson et al., 1982) for the
most part neglect heterogeneous interreactions and condensed-phase chem-
istry. In one-dimensional models which treat a limited number of organic
species (Chameides, 1978; Liu, 1977; Hov, 1982; Thompson and Cicerone,
1982; Turco et al., 1982), it is conventional to include a first-order
removal constant kc(I,J) for the most soluble ones, e.g., peroxides,
aldehydes. Many organic acids, alcohols, and nitrates are probably suffi-
ciently soluble to be removed to particles with rates on the order of kc
(I,part) = (- IQ-^-lQ-1 s'1) for HN03. Like their inorganic analogs OH
and H02, radicals of the type RO, R02 are also probably scavengeable from
the gas phase (Luther and Peters, 1982).
Reviews of aqueous organic chemistry pertaining to atmospheric systems
have been given by Mill (1980) and Graedel and Weschler (1981). In gen-
eral, the reactions proceed as in the gas phase, with the first step con-
sisting of oxidation by OH or 03, followed by 02 addition to form a peroxy
222
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radical R02. Subsequent reactions propagate radical generation and even-
tually form peroxides, alcohols, acids, etc.:
/aldehydes")
OH,03 02 NO,H02 Jketones /
RH > R -»• R02 * (alcohols >
etc. I peroxidesi
vacids /
At all stages of reaction, there is a possibility of material exchange
between gas and condensed phases. For example, particle incorporation of
atmospheric acids and alcohols, lower aldehydes, and peroxides may enhance
significantly the aqueous phase concentrations of these species.
Published aqueous-phase radical kinetics models (Chameides and Davis,
1982; Turco et a!., 1982) do not include the organic molecule contribu-
tions, although these must be included for correct characterization of OH,
H02, RO, R02, and H202. This is an area requiring much additional re-
search. Given the abundance of tropospheric organic species, a reasonable
approach to calculating them in a condensed-phase kinetics model would be
to group them in various ways (as is proposed in the treatment of gas-phase
hydrocarbons) and to determine the effects on aqueous OH, RO, and other
radicals and peroxides. Some of the kinetic information needed to do this,
including numerous organic reactions with OH and H02, is available from NBS
reviews (e.g., Fahrataziz and Ross, 1977; Ross and Neta, 1979). Hoigne and
Bader (1975) have studied ozone reactions in natural waters.
2.5 The possible coupling of chemistry and meteorology
An issue which requires consideration at some point is the decoupling
between a meteorological model and chemical models. It is accepted that
the meteorological process controls species concentrations, reaction, and
deposition. However, the effect of chemistry on the meteorological vari-
ables is less well-known, and is assumed to be negligible by most research-
ers. The latter phenomenon, tentatively called inadvertent weather modifi-
cation, may be important under some as yet unknown conditions. The major
pathway for chemical effects on meteorology is through heterogeneous pro-
cesses. The chemical evolution of aerosol directly influences its growth
characteristics and consequently the number and activity of cloud conden-
sation nuclei (Hung and Liau, 1981) and ice nuclei (Saxena and Hendler,
1982), which in turn determine cloud development (Ochs and Semonin, 1979)
and the onset of precipitation (inferred from Lee et al., 1980). Visibil-
ity degradation in humid and polluted air is one example of aerosol modi-
fication (see Atmospheric Environment, 1981, Vol. 15, 10-12). Cloud forma-
tion and enhancement are observed downwind of Chicago along the Michigan-
Lake Michigan shoreline. Also, power plant plumes are observed to develop
clouds or augment cloudiness in humid air (Koenig, 1981). The St. Louis
urban plume is thought to increase precipitation amounts (through cloud
seeding), but this remains statistically unproven (Chagnon, 1979). The
possibility also exists that pollution may actually decrease precipitation
(over-seeding).
Changes in aerosol characteristics and cloudiness directly affect the
223
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short- and long-wave radiative properties of the air and, indirectly, the
heating and cooling of the earth's surface—or, in other words, the driving
forces of the atmospheric motions. The extent of this is unknown, and is
probably of negligible importance to current modeling. It is, however, at
the heart of aerosol-climate studies.
2.6 Summary of the chemical reactions important for acid generation
in the troposphere
In the preceding discussions in Sections 1 and 2 of the current chap-
ter of this review, we have learned that there is a great diversity and
seeming complexity of the reaction channels in the troposphere which con-
vert S02 and NOX into H^Oi, and HN03, respectively. Obviously, all of
these many reactions are not required in any acid generation and preci-
pitation model to insure some reasonable accuracy for the chemical trans-
formations leading to acids. Sensitivity studies allow one to arrive at
some minimum set of reactions for use with any given model which will
provide the desired level of accuracy. Our current review and evaluation
gives some guidance in this choice. The following reactions are judged to
be of primary importance for acid generation for tropospheric conditions
which are commonly encountered:
Gas Phase: HO + S02 (+M) + HOS02 (+M) •»• H2SO^ (1)
HO + N02 (+M) -» HN03 (+M) (6)
Liquid Phase: S(IV) + H202 * H2S04 + ... (61)
S(IV) + 03 •»• H2S04 + ... (60)
S(IV) + HO •*• H2S04 + ... (62)
S(IV + H02(02") + H^... (63,64)
S(IV) + N03 + H2S04... (65)
N205 + H20 > 2HN03 (78)
The gas phase reactions (1) and (6) appear to be major acid forming
steps in the troposphere. Thus, for a moderately polluted troposphere
during relatively cloud-free daylight hours, the theoretical rates of S02
and N02 transformation through (1) and (6) in summertime amount to about
16% and 150%, respectively, per 24 hr period. In wintertime, significantly
lower rates are expected: about 3 and 25% per 24-hr period, respectively.
Reactions of S02 with 0(3P), CH202 (and other Criegee intermediates),
CH302, etc., may also contribute to the acid generation, but the conditions
necessary for their significant occurrence are probably rare.
When gaseous S02 encounters cloud water, fog, or rain water, it dis-
solves in part to form S(1V) species (S02-H20, HS03-, SOH=, and H?0+).
The reactions of these species with various water soluble, oxidizing
impurities in the water can occur and lead to acids. Thus, reactions (61)
and (60) of the S(IV) with H202 and 03 are expected to be very important
224
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acid-forming processes in the liquid water-containing air masses. Rates of
these can be as high as several hundred percent per hour for pH and reac-
tant concentrations which are not uncommon in the troposphere (see Figures
2.5 and 2.6). The reactions (62)-(65) and (78) involve gas-phase-gener-
ated, transient species which are transported to and captured by the water
particles. If the fraction of the species captured per collision is suf-
ficiently high (greater than about Ixio ) and their competitive reactions
with other impurities are unimportant, then these reactions appear in the-
ory to be very significant to acid generation in clouds; state-of-the-art
models of acid generation and transport should include them. Further work
on the experimental evaluation of the capture coefficients will be neces-
sary to quantify the estimates of the rates of these processes within the
troposphere. In addition, the reactions of other oxidizing agents such as
PAN (peroxyacetylnitrate), H02N02 (peroxynitric acid), CH302H (methyl hy-
droperoxide), etc. may be important, although further experimental work
will be necessary to define better these possibilities. State-of-the-art
models should include these reactions if and when they are shown to be
important. For certain relatively uncommon conditions encountered in
highly-polluted atmospheres (e.g., urban fogs), the Fe3"1", Mn2+, and the
graphitic carbon-catalyzed reactions of S(IV) with 02 can be significant
sources of acid in theory; provision for their inclusion for these cases
should be made.
The homogeneous gas-phase chemistry typical of the reactions in smog
must be included in model development to generate in a realistic fashion
the concentration-time profiles for the reactive species (HO, 03, H202,
N03, N205, H02, etc.) which are responsible for the acid production in the
above reactions. Two somewhat sophisticated "smog" models developed and
tested by Atkinson et al. (1982b) and Whitten et al. (1982) are available
to modelers today. These mechanisms contain relatively large numbers of
reactions (80 and 75, respectively) and chemical species (about 53 and 39,
respectively). Some simplification of these schemes appears to be possible
with sacrifice of chemical detail. However, it is clear that a state-of-
the-art description of the chemistry of acid development is not a trivial
exercise; a very large number of reactions and equilibria must be employed
to achieve an accuracy comparable to those obtainable in the transport and
dry deposition portions of sophisticated regional transport models. A mod-
ular approach to the treatment of chemistry is recommended to those who
plan to develop future models; this will allow a suitable updating of the
mechanism as knowledge of acid-forming processes grows without serious
perturbation of the transport and other computer packages in the model.
3. PHOTODISSOCIATIVE PROCESSES IN CHEMICAL MODELING
3.1 Introduction
Accurate modeling of tropospheric photochemistry requires photolysis
rates based on a radiation field which includes ozone absorption and mo-
lecular scattering. Photolysis rates also depend on cloud cover, aerosol
loading, and surface reflection, so that a close connection exists between
meteorological conditions and trace gas distributions. Since clouds and
aerosols may change over a short period of time and surface reflection
225
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varies with location and solar angle, it is necessary to have a rapid means
of calculating radiation in a regional-scale model.
The photolysis rate of a molecule A by fragmentation pathway I,
js"1), is an integrated product of three wavelength-dependent terms:
f
dxFtotal(x)oA{x'THA(x'T)
(1)
where a.(x,T)) = the absorption cross-section (cm2) of molecule A at wave-
length X and temperature T,
$A(x,T) = quantum yield or probability that molecule A decomposes
by pathway I on absorbing radiation of wavelength X, and
Ft . -,(x) = the solar flux (cnr2), wavelength x, at x,y,z.
For tropospheric J^'s, it is appropriate to integrate in the wave-
length range Xx, X2 - 280, 730 nm, because stratospheric 02 and 03 block
out most of the uv radiation and because no photochemistry of interest
takes place beyond the Chappuis band of ozone. In practice, the inte-
gration is carried out by summing over wavelength intervals of 10-20 nm:
,1
AX. F(x.
total
(xi,T)
(2)
In
the
the near uv (295-325 nm), refined resolution is required for calculating
rate of the photolysis of ozone: 03 n¥ 0(1D) + 0?.
For many of the species which photodecompose in the troposphere, ab-
sorption cross-sections and quantum yields have been measured in the lab-
oratory; some have been determined over the appropriate temperature range
(220-300 K). Tabulations of these quantities and the extraterrestrial
solar flux are available in a convenient form for use in model calculations
(NASA, 1982; WMO, 1981). Hence, the problem of calculating photolysis
rates in a photochemical transport model reduces to calculation of the near
uv-visible solar flux under a variety of atmospheric conditions.
There is an enormous body of radiation literature (see, for example,
the review by Coulson and Fraser (1975)), most of it dealing with highly
accurate methods of solving the radiative transfer equation. They are
prohibitively costly, even in a one-dimensional model, and they would not
guarantee highly accurate photolysis rates since absorption cross-sections
and quantum yields are rarely determined to better than 20% (NASA, 1982).
Thus, a few percent accuracy in calculating the solar flux is probably
sufficient for computing JA* (This can be compared to gas-phase bimo-
lecular rate constants which can be uncertain to factors of 2 or 3 for
certain complex reactions.)
226
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3.2 Flux calculations and photolysis rates
a. Clear sky values: effects of multiple scattering and surface reflec-
tion
The total solar flux (cnr2) can be expressed as a sum of direct and
diffuse radiation:
Ftotal = Fdirect + Fdiffuse
Calculation of direct flux at a point in the atmosphere is straightforward.
In the wavelength range A = 280-730 nm, the extraterrestrial solar flux
F0U) is absorbed somewhat by ozone in its Muggins band and to a lesser
extent in the Chappuis band. (In very polluted situations, absorption by
N02 can also attenuate Fg(x) near the surface, and an additional term,
a N02^°2^k,k+l» is required in the equations which follow. See Figure
3.1). In a'plane-parallel atmosphere between grid points k and k+1 (Fig-
ure 3.2), the direct beam (solar zenith angle 60) is attenuated by 03 ab-
sorption along the path it traverses:
FdirectU) ' Fdirect'x)
i.e., [03]u fc+i = sec SotOslkfk+l' where [03]fce£+i is the column
depth (cm ) along the normal"between k and k+I. The direct flux at k
in turn is given by
FdirectU) = Fo(A) exp <>sec 9° °03(X'T)
where [O^0 a represents the entire overhead 03 column (top of the
atmosphere along a normal to level k). The direct flux at 0 and 15 km,
calculated assuming a typical midlatitude 03 profile (0.36 cm-atm overhead
column), appears in Figure 3.3. 03 absorption is strongest in the near-uv,
and there is attenuation between 15 and 0 km only at X < 330 nm.
The diffuse flux includes contributions from molecular and aerosol
scattering and radiation reflected from the surface and clouds. Since
radiation is scattered out of the level between k and k+1 and is also
received from the surroundings,
Fk+l _ pk+1 Fk+l {6)
diffuse scattered in scattered out '
^diffuse ls positive or negative depending on the balance between in-
coming and outgoing scattered fluxes. Since molecules and aerosols are
concentrated near the surface and^cloud depths and levels are variable,
the degree of scattering, hence Fdiffuse, is strongly altitude-dependent.
In molecular or Rayleigh scattering, all molecules absorb and scatter
radiation with a cross-section which is strongly wavelength-dependent,
227
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lO'16
CVJ
E
o 10"
I
17
z ift
g I0"18
o
LJ ,Q
CO 10"l9
CO
CO
O in-20
tr iu
o
o io-21
| icr22
CO
CD
IO'23
NO-
I
I
I
200 300 400 500 600
WAVELENGTH -nm
700
Figure 3.1 Absorption cross-sections for 03 and N0£ in the
uv and visible regions of the spectrum (Luther and Gelinas,
228
-------
Direct Solar Beam
Figure 3.2
angle 0
0
Transmission of direct solar beam, incident
between two levels of plane-parallel atmosphere
229
-------
10
16
CJ
I
E
o
c
o
2. I015 i
o
OL
a:
o
CO
o
LJ
CE
O
I014
10
13
300
700
Figure 3.3 Direct solar flux at 0 and 15 km as a function
of wavelength, X; 0.36 cm-atm total overhead ozone column.
Calculations based on extra-terrestrial solar flux from
WHO (1981).
230
-------
« X'1*, and is significant only at \ < 450 nm. Figure 3.4 shows
the Rayleigh scattering optical depth or extinction
for 1 and 15 km thicknesses and at ground (Valley, 1965). [M]+i is
the normal molecular depth (cm~2) between k and k+1. Also given are the
03 optical density at 15 km and ground and a typical aerosol attenuation
near ground.
In molecular scattering, half of the scattered radiation goes in the
forward direction; half goes backward. Since TRay per km is greatest
near the surface, Rayleigh scattering gives a net loss of flux near the
ground relative to the flux calculated assuming only 03 absorption
(^direct)' Away ^rom the surface, backscattered radiation enhances the
flux beyond the pure absorption value. This can be seen in Figure 3.5,
which shows fluxes calculated with multiple scattering and 03 absorption.
Results are given for 60° solar angle and are qualitatively similar for
other angles. Ground albedo is assumed to be zero in these examples for
all wavelengths so that the flux shows the effect of molecular scattering
alone. Although only altitudes to 15 km are shown in Figure 3.5a, the
diffuse radiation from Rayleigh scattering reaches a maximum at 20-30 km
and decreases with increasing altitude (Luther and Gelinas, 1976). When
surface albedo is greater than zero, the diffuse flux includes a substan-
tial contribution from reflection of both scattered and direct radiation,
An example appears in Figure 3.5b, where the flux at 15 km is shown as
calculated with molecular scattering and three values of albedo.
Table 3.1 lists some of the major photodissociating species in the
urban atmosphere. Photolysis rates calculated from Eg. (2) (solar angle
= 60°) are illustrated for two photolyses of ozone, Jo3, which produces
O^D), and JQ , which. gives 0(3P) (Figure 3.6). Surface and scattering
effects on JQ and JQ illustrate different sensitivities of a uv and
visible absorber since the absorption maximum to produce O^D) is at 290 nm
and that of 03 •»• 0( P) is at 600 nm (Figure 3.3). For example, looking at
the zero-albedo curves in Figure 3.6, it is clear that ozone absorption and
molecular scattering in the near uv produces a stronger altitude gradient
in Jo3 relative to JQ (cf. the altitude pattern of the direct flux in
Figure 3.3). The effect of surface reflection is also different for J(j3
and jQ3, and is consistent with the flux pattern of Figure 3.5a. Surface
albedo is much more effective for Jg^ than for JQ , because the Chap-
puis absorption is located where the atmosphere il nearly transparent
(A > 400 nm, Figure 3.1), and the reflected flux is transmitted upward with
little loss of intensity. The choice of Luther and Gelinas1 (1976) calcu-
lation of Jg3 to illustrate the sensitivities of a uv absorber has been
made for convenience. In fact, a temperature-dependent quantum yield for
the 03 -»• Ql1^) photolysis (NASA, 1981) increases JQ at the ground rela-
tive to Jg3 at 15 km. Molecular scattering is discussed more fully by
Luther and Gelinas (1976)," and its effects on trace gas chemistry are
described by Luther et al. (1978). The latter paper emphasizes strato-
spheric chemistry. Two recent studies of chemical effects of multiple
scattering and surface albedo discuss tropospheric chemistry more ex-
231
-------
a.
UJ
o
o
h-
Q.
O
14,15 km
0, I km
300
350
400
450
X(nm)
Figure 3.4 Optical depth (per km) versus wave-
length, X, due to 63 absorption and Rayleigh
extinction in the upper troposphere (14-15 km)
and in the lowest km. Also shown is the optical
density due to aerosols near the ground, Optical
depths taken from Valley (1965).
232
-------
o
o.
V)
X
ID
-I
U_
300 400 500 600
X(nm)
700 400 500 600 700
X(nm)
Figures 3.5a and 3.5b Effects of molecular scattering and surface
albedo on fluxes calculated for solar zenith angle 60° and wavelength
A. Fluxes are presented as a ratio of fluxes calculated with scattering,
surface reflectance and 03 absorption flux (ms) relative to fluxes
calculated with 03 absorption flux (pa) only:
(a) Flux at four levels in the troposphere with ground albedo equal
to zero shows the effect of scattering only;
(b) Flux at 15 km for three values of surface albedo (alb) shows
the effect of surface reflectance (Thompson, 198Qb).
233
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Table 3.1
Major Photodissociating Species
in the Urban Atmosphere
03 + hv * 0(1D) + 02
03 + hv > 0(3P) + 02
N02 + hv •»• NO + 0
HN03 + hv * N02 + OH
H202 + hv -»• 2 OH
N03 + hv ->• NO + 02
N03 + hv -»• N02 + 0
H2CO + hv -»- H + CHO
H2CO + hv * H2 + CO
HONO + hv -»• NO + OH
CH3CHO + hv -»• CH3 + HCO
HNOi+ + hv ->• products
(CH3)2CO + hv * CH3 -H CH3CO
CH3OOH + hv * CH30 + OH
N205 + hv •»• NO2 + NO3
234
------- An error occurred while trying to OCR this image.
-------
tensively (Demerjian et al., 1980; Augustsson and Levine, 1982).
Uv-visible differences are also apparent in the diurnal variation of
photolysis rates. Figure 3.7a,b (from Demerjian et al., 1980) shows JMQ?
and Jg3 calculated as a function of local .solar time. Because 03 extinc-
tion increases rapidly with solar angle, OQ is more sharply peaked about
the noontime maximum than is JNQ..
b. Aerosol and cloud effects
Aerosol s
Flux calculations which include aerosol scattering are more compli-
cated than Rayleigh scattering because the flux from aerosol scattering
(i.e., the phase angle distribution of scattered radiation and the inten-
sity integrated over all angles) depends on the shape and size of the
aerosols. If the scattering is mostly peaked forward, then the principal
effect of an aerosol layer close to the surface is absorption (i.e., simple
attenuation of incident radiation and not much backscattering). This be-
havior characterizes background tropospheric aerosols (Logan et al., 1981).
For a moderately to highly polluted aerosol situation, however, Demer-
jian et al. (1980) find that approximately 9Q% of the total extinction is
due to scattering. The Demerjian et al. (1980) calculations also show that
when aerosols are present at concentrations typical of high pollution sit-
uations, 3-5% less visible radiation and 15-20% less uv radiation reaches
the surface than when no aerosols are present.
Clouds
Clouds represent the major cause of perturbation to the tropospheric
radiation field, and their effects must be included in the calculation of
photolysis rates. These effects are highly variable, depending on cloud
height, thickness, type, number of layers, and zenith angle. This can be
seen in Figure 3.8, which shows cloud reflectance as a function of h/L for
a cloud of thickness h, where L is the mean free path of a light ray, i.e.,
a measure of cloud density.
It is convenient to think of cloud effects in three categories: (1)
above cloud, (2) below cloud, and (3) within cloud. Above a dense cloud
layer, radiation can be calculated as in a clear sky with the cloud as a
reflecting surface instead of the earth.
Below-cloud radiation can be approximated (Demerjian et al., 1980) by
multiplying the clear-sky flux by a semi-empirical correction factor. At-
water and Brown's (1974) formulation can be used:
n [1 - f, (1 - T.)] (8)
1 =1 1 ]
where n = the number of cloud layers, f^ = the amount (coverage) in the
ith layer, and T-j = transmission of the layer, a function of cloud type.
236
-------
10.0
10 12 14
TIME, hrs L.S.T.
16
18
20
Figure 3.7a Diurnal variation of the photolytic rate constant
for the formation of 0(^0) for 63 in Los Angeles on 21 June at
the earth's surface and at three levels above the surface
(Demerjian et al., 1980).
237
-------
14.0
= 12.0
o
4-
O
o
CJ
cc
10.0
~ 8.0
o
6.0
4.0
2.0
0.0
10 12 14
TIME, hrs L.S.T.
16
13
20
Figure 3.7b Diurnal variation of the photolytic rate constant
for the formation of 0(3p) from N0£ in Los Angeles on 21 June
at the earth's surface and at three levels above the surface
(Demerjian et al.5 1980).
238
-------
-------
Haurwitz's (1948) transmission functions are usually used for T-j. At-
water and Brown (1974) have demonstrated consistency of their calculations
with both measurements and more exact calculations of surface radiation,
although Demerjian et al. (1980) point out potential inaccuracies in apply-
ing Eq. (8). One problem is lack of wavelength discrimination in Haur-
witz's (1948) functions. Calculations of surface radiation by Spinhirne
and Green (1978) as well as field measurements of solar fluxes and photo-
lysis rates (Dickerson et al., 1980) reveal that clouds block out uv 20-30%
less effectively than visible radiation. Thompson (1980) has incorporated
this distinction into a simplified cloud radiation calculation. Thompson's
treatment also accounts for cloud reduction of surface albedo to a very low
value independent of surface type and zenith angle.
Examples of above- and below-cloud radiation effects are shown in
Figure 3.9. Fluxes (actually the ratio Fluxcloud/Fluxno cloud) nave been
calculated assuming that a single dense cloud layer exists in the mid-tro-
posphere. As in the case of molecular scattering and surface reflection
calculations (Figure 3.6), above-cloud flux enhancement is greater in the
visible than in the uv. This alters the mid-to-upper troposphere ratio,
JNQ/JQO (Figure 3.10), and may have an appreciable effect on above-
cloud chemistry (Thompson and Cicerone, 1982).
The simplest treatment of fluxes within a cloud or among cloud layers
is to interpolate between cloud-top and cloud-base values, although in some
cases internal reflections can actually enhance uv radiation above the
cloud-top values (Schmetz et al., 1981; Twomey, 1972). To a first approx-
imation, these fluxes could serve to calculate photolysis rates for gases
dissolved in cloud droplets. Graedel and Weschler (1981) have reviewed
aqueous-phase absorption spectra and quantum yields for a number of species
of atmospheric interest. In general, aqueous absorption spectra are simi-
lar to the gas-phase, but solvent cage effects typically cause dissociation
quantum yields to be only 10~3 to 10 of their gas-phase counterparts.
3.3 Photodissociation calculations in a regional-scale model
A regional-scale model must supply photolysis rates for chemical kine-
tics calculations at all daylight times and at every point in the spatial
domain. All the basic components of radiation vary in a regular way with
solar zenith angle, while 03, aerosol, and cloud attenuation vary irregu-
larly in space and time as meteorology changes. For some species, the ab-
sorption cross-section and/or quantum yields are temperature-dependent.
Thus, the potential computational problem is enormous; e.g., a 50 x 50 x 10
grid requires calculation of 2500 photolysis rates for each species. For-
tunately, some simplifications immediately suggest themselves, and others
can be investigated fairly easily with existing models.
The first simplification is that a fixed ozone and N02 pattern can be
assumed over the entire region. Even in photochemical smog situations, the
principal local perturbation to radiation is likely to come from aerosols
or clouds rather than from tropospherically-produced 03 which is only a
small part of the total overhead ozone column. (Exceptions to this would
present a subgrid-scale problem and could be studied with a one-dimensional
photochemical model.) This means that chemical feedback on the uv-visible
240
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TJ
I 2.0
x 1 5
ID ]'D
-J
LL
>^
"g 1.0
u
§ 0.5
u_
0.0
SZA=30° . .
Cloud Reflectance{oejuvj
Ground Albedo-0.0
ble)
'Above Cloud (10 km)
Below Cloud (Okm)
300
350 400
X (nm)
450
Figure 3.9 Flux above and below cloud (as a function of wave-
length X) expressed relative to no-cloud conditions with zero
surface albedo in both cases. Cloud is represented as a single
dense layer between 5 and 6 km with reflectance 0.8 in the
visible and 0.6 in the uv. Solar zenith angle is 30° (Thompson,
1980b).
241
-------
e
J£
o
10
O
CVJ
O
0 Ground
albedo'
— No cloud
— 0.8 Cloud albedo
~ Ql(UV)}Cloudalbedo
1
20° 40°
SOLAR ZENITH ANGLE
60*
Figure 3.10 The effect of cloud reflectance on above-cloud ratio
of photolysis rates: JNQ9/ jjjv at 10 km. Two cloud cases are shown.
One assumes uniform reflectance (0.8) for all wavelengths; the other
assumes 0.8 reflectance in the visible and 0.6 in the uv. Surface
albedo is zero in both cases. Cloud is assumed to be dense layer
between 5 and 6 km, but result is similar if it is assumed to be
located anywhere in the lower troposphere (Thompson, 1980b).
242
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radiation field can be neglected, and meteorological variables alone can be
used to compute fluxes. The meteorology of a given synoptic situation (in
terms that can be used to specify aerosol distribution and clouds) can be
used to calculate photolysis rates once and for all. Thus, photochemical
processes can be driven with stored photolysis rates.
Depending on the time resolution employed in the regional dynamic
model, another reduction in computation could come from interpolation of
photolysis rates at various times of day as is common practice in general
circulation models. The interpolation might employ a functional relation
derived from more exact temporally-resolved calculations (e.g., Luther and
Gelinas, 1976, or Demerjian et a!., 1980).
Interpolation is only practical for clear sky conditions. Even then,
molecular scattering and surface reflection must be included in those flux-
es which are actually calculated. Highly accurate methods (e.g., Luther
and Gelinas, 1976; Anderson and Meier, 1979; Demerjian et al., 1980) are
too costly to use, but two rapid approximation methods (Isaksen et al.,
1977; Luther, 1980) are available.
The inclusion of clouds and aerosols on a large scale is more prob-
lematic because these phenomena can produce intense, rapid, and widespread
changes in the radiation field. One approach would be to develop a parame-
terization based on Coakley et al.'s (1983) treatment of tropospheric aero-
sols. An extension of Coakley's method (Charlock and Ramanathan, 1983)
could be used to treat clouds. The only required meteorological input
would be total liquid water content. Coakley's technique, which is based
on direct and diffuse adding with the 6-Eddington approximation (Joseph et
al., 1976), would give sufficiently accurate radiation fluxes for photodis-
sociation rates. However, we expect that the parameterization adopted for
use in a regional-scale model could be developed from calculations made at
a few key wavelengths, and the final choice of technique would strike a
good balance between accuracy and computational economy.
Clouds and aerosols also raise the question of subgrid-scale radiation
effects. Fog, haze, and low clouds which form over a limited region can
give rise to a rapid oxidation of S02 and N02 through solution phase chem-
istry. There is a concomitant effect on radiation which is important to
calculate correctly.
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CHAPTER SIX
DEVELOPMENT OF ACID DEPOSITION MODELS
In this chapter, we take a more forward-looking view toward develop-
ment of a new generation of acid deposition models. Based largely on the
topics reviewed in earlier chapters, we focus on essential components and
practical issues involved in developing a comprehensive model, with extra
emphasis on topics needing great improvement or omitted in present models.
Specifically, this chapter discusses needed emissions data; salient fea-
tures of long-range transport of pollutants; features and mechanisms of
acid rain chemistry that are necessary to embody in a credible, compre-
hensive model; cloud types, processes, and scales involved in pollutant
transfer and chemical transformations; and the mechanics and overall phe-
nomenology of dry deposition. Further, we enumerate key issues and guiding
principles on model resolution, pertinent numerical methods, and strategies
for model validation and sensftivity analysis.
1. EMISSIONS
1.1 Introduction
Before defining specifically which emissions are central to the acid
rain problem and what kind of data are needed, let us recognize the need
for specific and detailed information. Regardless of whether one sees the
acid deposition model as an assessment tool for regulatory policy or as a
purely scientific construction without intended practical utility, it is
clear that the acid rain phenomenon originates with ground-level (or near)
emissions. While it is true that there are upper atmosphere sources of
acidic gases, e.g., NOX produced by lightning, we know that these are not
often significant compared to other more obvious sources, e.g., S02 from
coal burning and NOX from internal-combustion engines.
For modeling purposes, very detailed information is required for a
number of chemical species. An inventory of emissions with suitably re-
fined spatial and temporal resolution is required as input to a regional
acid deposition model before any serious investigation of the principal
sources of deposited acids can be mounted. At present, major unresolved
scientific questions include the relative importance of local and distant
sources, the contributions of mobile and stationary sources, the influence
of natural emissions, and the significance of other directly emitted pol-
lutants which affect the conversion of acid precursors to acids. In this
section, the type of information required to address these questions is
discussed and the adequacy of existing data bases to meet these require-
ments is reviewed.
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1.2 Needed data for an emissions inventory
a. Chemical species
Because the principal acids in North American precipitation are sul-
furic and nitric, it is quite clear that accurate estimates of regional S02
and NOX influxes into the atmosphere are required. Although S02 and NOX
are the major acid precursors, a spectrum of other species significantly
influences or contributes directly to acid formation. These include the
volatile organic carbons (VOC) and carbon monoxide, because of their role
in the oxidation process; ammonia (NH3), because of its role as a buffering
agent in cloud chemistry processes; and several reduced sulfur species, be-
cause of their potential importance as naturally emitted precursors to acid
rain. In addition, sulfate aerosols are thought to contribute significant-
ly to the overall sulfuric acid budget.
Other direct sources of acidity must also be considered. In certain
regions, hydrochloric acid and occasionally hydrofluoric acid vapors can be
incorporated into clouds and precipitation in non-negligible amounts. Di-
rect contributions to acidity from organic acids are possible, although
some data from Los Angeles suggest a minor role (Lil jestrand, 1980). By
contrast, Keene et al. (1983) and Galloway et al. (1982) have found direct
and indirect evidence of major contributions to total precipitation acidity
from weak organic acids. Their data are from remote sites (Australia and
Venezuela); the organic acids might arise from biomass burning. While not
likely to be ubiquitous or regular in North American precipitation, the or-
ganic acid possibility needs attention. Finally, in some localized areas,
sea-salt particles or coarse aerosols (those with diameters greater than
2.5 jjm) can be important to acid production.
Less directly, but important in chemical transformation pathways, are
those substances that affect oxidant production. As discussed in Chapter
V, oxidants like 03) H202, and organic peroxides play key roles in acid
production. Thus, emissions of species like reactive hydrocarbons and
nitrogen oxides are important as sources of oxidants.
The buffering aerosol species (the alkaline dusts) and the aerosol
components important to catalytic conversions in aqueous reactions (e.g.,
soot, iron, and manganese) are also important in determining precipitation
acidity; their emissions are difficult to quantify, as an important com-
ponent is wind-driven and natural.
Ammonia emissions deserve special note. As a potentially important
buffering gas, emissions inventories are needed. Though often thought to
be naturally produced by microbes in soils and waters, one must also real-
ize that much NH3 emission is stimulated by man's activities in localized
areas— although biogenic, ammonia release to the atmosphere is not wholly
natural. The localization of fixed-nitrogen application (fertilized
fields) and waste collection (cattle feedlots and municipal waste plants)
makes it possible to estimate regional ammonia emissions.
245
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b. Classification of sources
The total emissions of many of these pollutants are dominated by man-
made sources. For VOC's, NH3, and the reduced sulfur species, as well as
some of the aerosol components, and possibly NOX, natural source inven-
tories are needed for a complete emissions inventory.
Man-made sources are comprised of point and area sources. Point and
stationary area sources can be classified as industrial, commercial, insti-
tutional, and residential sources. Associated with each source is a dif-
ferent mix of pollutants. Because of these different mixes, it is impor-
tant to subdivide the mobile source into light and heavy-duty vehicles,
using either gasoline or diesel fuels.
Natural emissions result mostly from soils, vegetation and animal
wastes, inland water such as marshlands, and, for NOX, from lightning.
c. Spatial scales
Significant sections of the United States and Canada must be included
in any acid deposition study. Thus, comparable emissions data are required
for both countries. The appropriate subdivision of such a large region is
still a matter of debate. It is currently thought that area sources can be
averaged over grids that are on the order of 20 x 20 km. Large point sour-
ces, however, need to be considered individually because of their impact on
chemical and physical phenomena on a smaller scale (Lamb, 1982). In addi-
tion, the impact of a specific power plant cannot be addressed unless each
major plant is considered individually in an inventory.
d. Temporal scales
For many stationary sources, seasonal averages or even annual averages
are an adequate representation of the temporal variations of the sources.
For some stationary sources such as home heating and for mobile sources,
diurnal patterns are required for sufficient description of the temporal
variations of the emissions. For these sources, a representative week/
weekend day diurnal pattern (hour by hour) for each season is adequate.
Some natural sources such as those controlled by sunlight are also defined
on seasonal and representative diurnal scales.
e. Number of inventories
Typically, emissions inventories are created for a base year. To ob-
tain an assessment of the effect of emissions changes on acid deposition,
it would be very useful to have emissions inventories for two different
years for which quantitative differences in emissions exist for at least
part of the model region. The availability of two emissions inventories
would provide an opportunity to test a model's ability to predict the ef-
fect of emissions changes {see model validation section in Section 8 of
this chapter for discussion).
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1.3 Adequacy of existing data
The major man-made emissions data bases are described in Table 1.1.
Some sources of additional data for the development of a natural source
inventory are listed in Table 1.2. Since the available man-made data bases
are reasonably comprehensive for at least the major acid precursors S02 and
NOX, more attention is given to a critique of the less well-documented
natural sources.
It has been concluded (Galloway and Whelpdale, 1980) that anthropo-
genic emissions of S02 exceed natural emissions of gaseous sulfur compounds
by at least a factor of ten in eastern North America, and a similar conclu-
sion has been reached for Europe (Semb, 1978). This strong regional domi-
nance of man-made sulfur sources over natural ones is probably correct, but
the array of uncertainties that appears when one attempts a critical review
of the actual data does not inspire great confidence. In the case of sul-
fur, there has been one systematic and high-quality field survey of natural
gaseous sulfur sources (Adams et al., 1980). Because of the remaining
problems cited below, estimates of the natural S emission rates for eastern
North America can be improved only at appreciable cost. Quantitative com-
parisons of anthropogenic and natural sources of NH3, hydrocarbons, NOX,
and CO must await field measurements of natural sources. Presently, only
gross estimates or spot measurements of actual field emissions are avail-
able.
Natural sulfur sources are known to be very patchy spatially and var-
iable with season; less well-known is the fact that the release of S-con-
taining gases from shallow coastal and inland waters is strongly dependent
on sunlight and pH, details of the microbial ecology, and, of course, time
of day (Jorgensen et al., 1979; Hansen et al., 1978). Further, the iden-
tity of the principal S-bearing compound, usually a reduced-sulfur species,
that escapes these important environments into the air also varies with
time of day, largely because these shallow-water sites can change from an-
oxic to oxygenated with time of day. The only serious attempt to consider
most or all of these factors in a multi-site field measurement program fo-
cused on natural sulfur sources (that of Adams et al.), measured H2S, COS,
CH3SH, (CH3)2S, CS2, and (CH3)2S2 emissions at about twenty sites, and
documented the soil types and related variables at each site. Carefully-
controlled analytical methods also appear to have been used. Extension of
the Adams et al. research with emphasis on more detailed diurnal and sea-
sonal variations and extension to Gulf Coast locations seems advisable.
Also, as is common in all such work, improvements to flux-measurement
methods are needed (see below).
Similar comments can be made about the effort at measuring natural hy-
drocarbon emission rates that was mounted by Zimmerman in 1977 (see Table
1.2). The number of distinct hydrocarbons that were analyzed and the anal-
ytical methodology are impressive. Further, the vegetation and soil-typing
were performed systematically. Extension of this kind of field program to
much larger areas and to longer periods of observation seems necessary. To
be able to compare properly the natural hydrocarbon and anthropogenic emis-
sions, the full range of variation of the latter needs better documenta-
tion. For example, the temperature dependence of the evaporative loss from
247
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Table 1.1 Major Currently Available Man-Made Emissions Data Bases
(EPA, 1982).
1. National Emissions Data System (OAQPS)
Pollutants: SOX, NOX, HC, CO, particulates
Geography: National, coordinate location for significant point -
sources country level aggregation of all remaining sources
Sources: All area and point-source categories
Time Frame: 1972-1980
2. Eastern U.S. SOX Emissions Inventory (ORD-MITRE)
Pollutants: SOX
Geography: Eastern 32 states, state level totals
Sources: All except electric utilities aggregated into nine source
categories
Time Frame: 1980
3. Electric Utility Emissions (ORD-E.H.P.A.)
Pollutants: SOX and NOX
Geography: National, coordinates for all point-sources
Sources: All electric utility plants
Time Frame: 1976-1980
4. MAP3S (ORD-BNL)
Pollutants: SOX, NOX, HC, CO, particulates
Geography: National, with Canadian sources. Coordinates for
point-sources and county level area sources
Sources: All area and point-source categories
Time Frame: 1979-1980
(This data base is the NEDS data base with some additions and modifica-
tions. )
248
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Table 1.1 (continued)
5. U.S.-Canadian Work Group 3B Data Bases
a. 1978 Data Base
Pollutants: SOX only
Geography: National, U.S. and Canada--U.S.—major point-sources,
county level area sources in the East, State areas sources
for Western States. Canada—major point-sources and area
sources in 127 km grids.
Sources: All sources aggregated to 10 categories
Time Frame: 1978
(The U.S. portion of this data base was constructed from parts of 1 through
4 above to meet immediate needs for atmospheric modeling.)
b. 1980 Data Base
Pollutants: SOX and NOX
Geography: National—U.S. and Canada—U.S.—State level totals.
Canada—major point-sources and area sources in 127 km
grids.
Sources: All sources aggregated into six categories.
Time Frame: 1980
c. Preliminary Estimates
Pollutants: Primary Sulfates, VOC, Trace Metals
Geography: U.S. and Canada—U.S.— State level. Canada—province
level.
Sources: All sources aggregated into major categories
Time Frame: 1980
6. Northeast Corridor Regional Modeling Project (NECRMP) Inventory
(OAQPS)
Pollutants: NOX, VOC, CO
Geography: 14 Northeastern States plus D.C. All sources allocated to
20 x 20 km grid squares.
Sources: All area and point-sources
Time Frame: 1979, 1980 allocated to hourly emissions
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Table 1.2 Some Currently Available Natural Emissions Data Bases
1. EPRI-^Washington State University "Biogenic Sulfur Emissions in the SURE
Region"
a. 1980 Data Base
Species: Gaseous H2S, COS, CH3SH, (CH3)2S, CS2, CH3SSCH3
Geography: Eastern U.S. excluding deep South
Sources: Inland waters and soils (various types)
Time Frame: 9/77-9/79
b. 1982 Data Base (not yet available)
All categories as above, except that geographical area was to be
Gulf Coast and field studies were to begin after those listed above
were completed.
2. EPA-Washington State University "Determination of Emission Rates of
Hydrocarbons from Indigenous Species of Vegetation in the Tampa-St.
Petersburg, Florida, Area"
Species: CH^, total nonmethane hydrocarbons, parafins, olefins,
aromatics, plus several other species
Geography: Tampa-St. Petersburg, Florida, area
Sources: Most indigenous plant species
Time Frame: 6/77-8/77
250
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liquid reservoirs is potentially important (Zimmerman, private communica-
tion). Changing emissions-control strategies also mandates that the com-
bustion source of man-made hydrocarbons be reviewed regularly.
Key gaps in the available data on natural sources are in NH3 emis-
sions, NOX sources and possibly CO emissions, and in the effects of dis-
tant natural surfur sources (Galloway and Whelpdale, 1980; Granat, 1978).
There is no NH3 emissions inventory at all for the midwestern or eastern
United States or for Canada, although a state-by-state survey is now being
prepared (R. C. Harriss, private communication). Also, R. Husar (private
communication) is preparing NH3-source, NH^"*" deposition surveys for Morth
America, and G. Cass (private communication from J. Seinfeld) has recently
expanded NH3 sources for the Los Angeles area. Reliable field measurements
of NH3 losses from fertilized fields, animal pastures, and cattle feedlots
are extremely rare, even though nitrogen-balance studies imply that NH3
losses can account for 20-50% of all deposited fixed nitrogen (Liu et al.,
1977). The midwestern U.S. should be a major source of gaseous NH3 to the
atmosphere because of the intensive use of fixed-M fertilizers there. Hut-
chinson et al. (1982) very competently measured NH3 and amine losses from a
Colorado feedlot in 1982, and one or two Australian publications exist to
guide our estimates of NH3 sources.
For NO and N0£, there are tantalizing indications in the literature c-f
soil science and atmospheric chemistry of soil sources of NO and possibly
of N02, but little if any quantification. Not to be confused with dry de-
position to soils and other surfaces as a loss process for atmospheric N02,
these potential soil sources are microbial nitrification and denitrifica-
tion, as for N20. The production of NO and N02 in lightning events is cer-
tain; the actual amounts produced per event and/or annually are uncertain.
A recent review (Bauer, 1982) estimates that about 1.5 million metric tons
(N) are produced annually in the latitude belt 30-50°N, mostly over conti-
nents. Electrical storm activity is sporadic. Accordingly, there could be
important NOX contributions from individual events. Sporadic intrusions
of stratospheric ozone to near ground level have occasionally led to 03
concentrations above air-quality standards; on an event basis, lightning-
produced NOX and 03 from distant sources might be analogous.
Finally, a number of endemic weaknesses in all natural source assess-
ments appear when one attempts a critical review. These include inadequate
flux-measurement methods, overreliance on deposition data and assumed re-
gional or global steady-state elemental cycles in the deduction of source
strengths, too fe* empirical data on diurnal and seasonal variations, and
almost no basic understanding of the mechanisms that drive the release of
gaseous sulfur (or gaseous hydrocarbons or NOX or NH3). For example, in
many field measurements of fluxes, it has been necessary to use closed
chambers that can perturb the system under study in many ways. Micro-
meteorological ly- and biologically-acceptable methods are not generally
available, often because of a lack of appropriate analytical chemistry
technology for the species at hand. Similarly, when deposition data are
used (e.g., for SOt^, N03~, or NH.,4"} tc deduce source strengths, one must
carefully include the potential effects of long-range transport and of dry
deposition (usually characterized poorly), and proper spatial coverage and
temporal averaging must be used. It also appears that assessment of
251
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ral sources has been performed better by Europeans than by Americans, and
often with a global point of view rather than regional.
Assuming that natural S sources are negligible compared to regional
man-made inputs (Whelpdale and Galloway, 1980; Adams et a!., 1980), then
for an adequate regional acid deposition model we must still include spa-
tially-resolved man-made sources (see below) and natural sources for NH3
and possibly NOX (at least the lightning-produced NOX). Creating
model-compatible source grids and assessing model sensitivities to the
adopted N03 and MOX emissions remains to be done.
Source inventories for HC1, HF, and the various aerosol species are
also inadequate at. this time. Local measurements exist, but these have yet
to be assembled into an appropriate regional inventory (NAS, 1979). Al-
though total suspended particulate inventories are available, these are
bulk estimates of total aerosol mass and thus do not provide the detailed
information required in the model.
A brief summary of pollutants and the status of their inventories is
given in Table 1.3. Major research efforts are required for NH3 and the
aerosols. Careful and appropriate spatial and temporal discrimination is
needed for the point and area sources of all of the pollutants. Some tech-
niques (e.g., EPA, 1982) for obtaining these discriminations, such as the
diurnal patterns of mobile sources, are available.
A major concern regarding all of the existing data is the lack of un-
certainty estimates. Such information is crucial to a proper use and eval-
uation of any model.
The list of species and sources presented here should not be consi-
dered to be complete. Future research may identify other important pollu-
tants. Thus, flexibility in the emissions data input design is of primary
importance in the development of an acid deposition emissions inventory.
1.4 Subgrid issues
Emissions, whether at the surface or from elevated sources, tend to be
subgrid-scale phenomena; that is, the source is inevitably smaller than the
grid volume of the numerical model. Thus, for the reasons discussed later
in this chapter, the model necessarily deals only approximately with the
emissions. Furthermore, the initial dispersion of emitted material from
both surface and elevated sources depends strongly on the state of the
PBL. During the day, when the PBL is convective, both vertical and lateral
dispersion are much larger than at night when the PBL is stably stratified.
Thus, the same source can give radically different concentration distribu-
tions in the first grid volume, depending on the time of day.
The subgrid problems which this creates have not yet been completely
solved. However, we do know a good deal about dispersion from both surface
ana elevated sources in the PBL; this would seem a necessary ingredient for
the ultimate solution to the subgrid emissions problem. Some new effort
here seems appropriate during the development of a regional acid deposition
model.
252
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Table 1.3 Summary of Emissions Status
GASES
Sulfur
SO 2
H2S
Nitrogen
NOX
Carbon
VOC
CO
Other
HC1
HF
MAJOR MISSING FEATURES
20 x 20 km
20 x 20 km, some categories
20 x 20 km beyond 14 eastern states
20 x 20 km, some categories
20 x 20 km beyond 14 eastern states
20 x 20 km beyond 14 eastern states
20 x 20 km, some categories
20 x 20 km, some categories
AEROSOLS
Sulfate
Alkaline dust
Catalysts
20 x 20 km, some categories
20 x 20 km, some categories
20 x 20 km, some categories
253
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2. LONG-RANGE TRANSPORT OF POLLUTANTS
It is well known that pollution affects not only people in the immedi-
ate vicinity of the source, but also those people hundreds to thousands of
kilometers downstream. For example, sulfur dioxide emitted in one country
may lower the pH of rain to a value of 4 or less in other countries (Li-
kens, 1976).
When regional air quality is considered, the temporal and spatial var-
iation of the meteorological parameters (the three-dimensional wind compo-
nents, the vertical temperature structure, the humidity, and the precipita-
tion) become more important than in localized air quality problems. On the
time scales of many pollutants that affect regional air quality (6 to 48
h), the horizontal winds vary in speed and direction, the vertical trans-
port by the mean vertical motions becomes important, and the height of the
mixed layer may vary considerably. Furthermore, many of the pollutants may
react with other pollutants or be removed through processes which depend on
the meteorology—particularly the humidity and precipitation.
The general goal of an air quality model is to forecast the concentra-
tion of a contaminant, Q (in dimensions of mass per volume), over space and
time, given the initial conditions on the atmospheric structure and on the
distribution of Q, and given the boundary conditions. For limited domains,
the boundary conditions generally consist of the meteorological and concen-
tration variables on the upwind side of the domain (lateral boundary condi-
tions); the conditions at the surface, including surface heat, moisture,
and momentum fluxes; the emission rates in space and time over the domain;
and appropriate upper boundary conditions. We then solve the equation for
the time rate of change of Q(x,y,z,t)
=-Vu.vQ-w-_ QV-V - Vu • V' Q1 - -Ir- + sources + sinks, (1)
3t ~H 3Z - n ~n 9Z
given Q(x,y,z,t0), the time-dependent mean1 horizontal and vertical ve-
locities (YH and WK tne horizontal and vertical eddy fluxes represented
by VH*VH'Q anc* 3w'Q'/3z, and the volume sources (emission rates) and
sinks fe.g., deposition, rainout, reactions).
It is obvious from Eq. (1) that the mean wind and the turbulent fluxes
play a major role in determining the behavior of the concentrations. Gen-
eral, predictive meteorological models (discussed in Section 4 of Chapter
III) contain forecast equations for these meteorological processes. To
understand the acid deposition problem fully, it is necessary to account
for complex, three-dimensional mesoscale (horizontal scales of 2.5 km to
2500 km) processes such as cumulus convection. For example, if strong
cumulus convection is present, pollution in the mixed layer may be trans-
:Here the mean refers to averages over appropriate space and time
scales. In a grid-point numerical model, for example, the spatial average
is the average over a single mesh volume; the time average is over one time
step.
254
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ported to the upper troposphere (height ~ 8 km) in a matter of minutes;
ordinarily, mixing through this depth .night require days. Furthermore, the
precipitation associated with the convection may act as a very efficient
removal mechanism; approximately 86 percent of the sulfates in the atmo-
sphere are removed by precipitation (Kellogg et al., 1972).
When considering a general acid deposition model, it is convenient to
break the total model into two major components—a meteorological model (of
the type reviewed in Section 4, Chapter III) and a chemistry model. The
meteorological model provides the meteorological variables that affect the
transport, diffusion, and reaction of Q. These variables are then utilized
in the pollutant model to forecast the advection and diffusion of Q. If Q
is passive--that is, its behavior does not appreciably affect the meteor-
ology—the meteorological and pollutant models may be run in series. The
meteorological model is run first; the appropriate data are stored and then
used in the subsequent air quality model.
The importance of utilizing three-dimensional, time-dependent meteoro-
logical models that contain the relevant physics on regional-scale air
quality modeling can be seen by considering the variability of trajectories
on the appropriate time scale of 0-2 days. Because of the importance of
vertical motions on the movement of air over periods of a day or more, cal-
culation of trajectories on these time scales must consider the three-di-
mensional atmospheric motions unless the pollutants are trapped in a well-
defined mixed layer. The combination of typical synoptic-scale vertical
motions (5 cm/s) and moderate vertical wind shear can lead to significant
differences between horizontal and three-dimensional trajectories over
24 h, especially when the wind changes direction with height. For example,
let the wind change linearly from west at 10 m/s at a height of 1 km to
east at 10 m/s at a height of 3 km. If the vertical velocity were constant
at 2.3 cm/s during the 24 h period, the parcel would rise from 1 km to 3 km
in 24 h. Its average east/west velocity during this period would be zero,,
and so its true horizontal displacement would be zero. A constant-level
trajectory, however, would erroneously place the parcel 864 km downwind!
Utilizing real data, Danielsen (1961) has found similar errors.
Figure 2.1 illustrates a 24 h trajectory computed from the three-
dimensional forecast wind field in a regional numerical weather prediction
model (Anthes et al., 1982a). The parcel originated at 850 mb over the
Texas-Oklahoma border, flowed horizontally northward in a low-level jet,
and then rose rapidly in a frontal zone over Iowa to a pressure of 300 mb.
Such trajectories are not unusual in regions of precipitation.
General meteorological models capable (with some modifications) of
providing the necessary meteorological variables to an air quality model of
acid deposition are reviewed in detail in Section 4 of Chapter III. The
operations in these models consist of: (1) measuring initial values of the
dependent variables, such as winds, surface pressure, temperature and mois-
ture; (2) analyzing these data to produce consistent three-dimensional ini-
tial fields; (3) applying boundary conditions on the edges of the domain;
(4) modeling important physical processes such as advection; turbulent
fluxes of heat, moisture, and TOmentum; radiation; and condensation; and
(5) solving numerically the finite difference equations that represent the
255
-------
100
500
1000
Figure 2 } 24 h trajectory of air parcel originating at
850 mb at 0000 GMT, 25 April 1979 (Anthes et al ., 1982a)
256
-------
processes in (4). Each of these complex component operations is discussed
in Chapter V. As discussed in these sections, considerable progress has
been made in developing accurate techniques and realistic physical param-
eterizations for modeling regional atmospheric flows. It is therefore
feasible to develop and test fully such models on the regional acid
deposition problem.
3. ACID RAIN CHEMISTRY
In the discussions in Sections 1 through 3 of Chapter V of this re-
view, we have learned that there is a great diversity and seeming complex-
ity of the reaction channels in the troposphere which convert S02 and NOX
into H2S04 and HN03, respectively. Obviously, all of these many reactions
are not required in an operative acid generation and precipitation model.
Some reasonable accuracy for the chemical transformations leading to acids
can be maintained with a much simplified reaction scheme. Sensitivity
studies allow one to arrive at some minimum set of reactions for use with
any given model which will provide the desired level of accuracy. Our cur-
rent review and evaluation gives some guidance in this choice. The follow-
ing reactions are judged to be of primary importance for acid generation
for tropospheric conditions which are commonly encountered:
Gas Phase: HO + S02 (+M) + HOS02 (+M) - - - * H^ (1)
HO + N02 (+M) -»• HN03 (+M) (6)
Liquid Phase: S(IV) + H202 * H^O,, + ... (60)
S(IV) + 03 * H2SOk + ... (59)
S(IV) + HO •»• H^Oi, + ... (61)
S(IY) + H02(02") + ti2SQ* ••• (62,63)
S(IY) + N03 + H^ ,.. (64)
N205 + H20 •»• 2HN03 (77)
The gas reactions (1) and (5) appear to be major acid forming steps in
the troposphere. Reactions of S02 with 0(3P), CH202 (and other Criegee in-
termediates), CH302, etc., may also contribute to the acid generation, but
the conditions necessary for their significant occurrence are probably
rare.
When gaseous S02 encounters cloud water, fog, or rain water, it dis-
solves in part to form S(IV) species (S02-H20, HS03~, SO,+=, and H30+),
The reactions of these species with various water-soluble, oxidizing impur-
ities in the water can occur and lead to acids. Thus, reactions 60 and 59
of the S(IV) with H202 and 03 are expected to be very important acid-form-
ing processes in the liquid water-containing air masses. The reactions
61-64 and 77 involve gas-phase-generated, transient species wnich are
transported to and captured by the water particles. If the fraction of
257
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the species captured per collision is sufficiently high (greater than about
1 x 10~3), then these reactions appear in theory to be very important in
clouds; state-of-the-art models of acid generation and transport should
include them, Further work on the experimental evaluation of the capture
coefficients will be necessary to quantify the estimates of the rates of
these processes within the troposphere. In addition, the reactions of
other oxidizing agents such as PAN (peroxyacetylnitrate), H02N02 (peroxy-
nitric acid), and CH302H (methyl hydroperoxide), etc., may be important,
although further experimental work will be necessary to define these possi-
bilities better. State-of-the-art models should include these reactions if
and when they are shown to be important. For certain relatively uncommon
conditions encountered in highly polluted atmospheres (e.g., urban fogs),
the Fe3+, Mn2"1", and the graphic carbon-catalyzed reactions of S(IV) with 02
can be significant sources of acid; provision for their inclusion for these
cases should be made.
The homogeneous gas phase chemistry typical of the reactions in smog
must be included to generate in a realistic fashion the concentration-time
profiles for the reactive species (HO, 03, H202, N03, N205, H02> etc.)
which are responsible for the acid production in the above reactions. Two
somewhat sophisticated models developed and tested by Atkinson et al.
(1982b) and Whitten et al. (1982) are available to modelers today. Both
the reaction scheme of Atkinson et al. (1982b) and that of Killus and Whit-
ten have relatively large numbers of reactions (80 and 75, respectively,
excluding S02 chemistry) which are required to explain the hydrocarbon-
NOX chemistry in the troposphere. We feel that the formulation of the
chemical module of an acid deposition model with either of these rather
extensive reaction schemes, together with the very extensive meteorology,
cloud chemistry, etc. in the other modules, would lead to a rather restric-
ted use of the model as a result of its large demand for running time. As
a consequence, we feel that one should develop a somewhat simpler operating
chemical package, hopefully of near equal accuracy, to simulate the gas
phase oxidation of S02 and N02. There are two approaches which could be
used in this development.
The first approach involves an extension of the method employed pre-
viously by Lavery et al. (1978, 1980). Isopleths are prepared for the
maximum 03 and HO-radical concentrations as a function of the hydrocarbon-
MOX ratio using both the Atkinson et al. (1982b) and the Whitten et al.
(1982) models, updated and expanded to include the S02 chemistry as out-
lined previously as a basis for the estimates. These isopleths are made
for several seasons [summer, fall (or spring), and winter] at 40°N lati-
tude. These are keyed into a program which for a given RH-NOX simulation
mixture at a given time selects the proper HO-max levels. This is atten-
uated by the appropriate sunlight intensity function to provide an HO-radi-
cal estimate for the given conditions. Then the products of [HO][S02]k1
and [HQ][N02]k7 are used to derive the rate of H2SOlf and HN03 generation in
the reactions 1 and 7, respectively. Tne sutf of the products of the [HO]
[RHl-jk-j terms, where RH-j includes all hydrocarbons and aldehydes, is
used to develop the rate of H02 and R02 radical formation. This is to be
used to drive the NO to M02 conversion through reactions 50, 53, and 10,
and H202 formation through reaction 58:
253
-------
H02 + H02 * H202 ' (58)
The rate constant for 58 is [H20] dependent and is adjusted for this in the
simulation. The ozone concentration is estimated from the [N02]/[NO] ra-
tio, and the relation 47 from Section 1, Chapter V is corrected for expect-
ed deviations for conditions of low [NO]. The ozone so evaluated is used
to derive the rate of Criegee intermediate formation and alkene loss
through the 03-alkene reactions. The concentration of hydrocarbons, NO,
N02, 03, S02, H202, and aldehydes is updated continuously as emission and
loss from chemistry or deposition occur. This method should allow an ef-
ficient use of the computer time, since extensive integrations are not re-
quired. At every stage of the development of this system, a check on the
errors of the approximate methods is made, using the more complete reaction
schemes of Atkinson et al. (1982b) and Whitten et al. (1982), together with
the extensive experimental data of Jeffries et al. (1982) derived from the
outdoor smog chamber experiments.
In the second approach, one attempts to use a simplified reaction
scheme which parameterizes the hydrocarbon chemistry. Three hypothetical
hydrocarbons of different reactivity are used, which represent the alkanes,
alkenes, and aromatic species. The rate constants for the reactions of
these species with HO and 03 are calculated as a concentration-weighted
average of the species in the mixture within a given structural class at a
given time. The reaction of HO-radicals and 03 with these species is par-
titioned between the various species according to their relative reactivi-
ties, and the composition of the mixture is regularly recalculated. This
is used to redetermine the new average rate constant, etc.
The yield of products of the reactions, namely H02, R02, CH20, CH3CHO,
etc., is a function of the composition of the mixture at any time, and is
updated regularly from the prepared stoichiometry tables. Through such an
approach, one can save considerably on the integration time required for
the large number of reactions in most detailed mechanisms. The bookkeeping
job of establishing the average rate constants for the hydrocarbons and the
product distribution in the reaction mixture can be handled efficiently
through the computer. A similar simplification is envisaged for the alde-
hyde and ketone product chemistry. The average rate of photochemical gen-
eration of reactive species from the carbonyl compounds (H02, CH302) etc.)
and the distribution of these products can be adjusted through the use of
the averaging techniques, tables of product distributions, and the book-
keeping procedures of the computer.
4. CLOUDS
4.1 The roles of clouds in acid rain
Clouds have diverse roles in the acid rain process, as Figure 4.1
shows. While several of these processes have been described in previous
sections, it is worthwhile to consider them once again as a whole. The
most important processes associated with clouds appear to be these:
259
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EFFECT ON
J's AND OH
TRANSPORT TO
UPPER TROPOSPHERE
CHEMICAL^
REACT!ON(
IN DROPLETSy
AND RAIN f
ORGANIZATION OF SURROUNDING
MESOSCALE MOTIONS
TRANSPORT TO
LOWER TROPOSPHERE
INJECTION OF
CLEAN AIR
RAINOUT AND WASHOUT
OF GASES, PARTICLES
DILUTION OF EFFECTS ON VEGETATION
RAIN ACIDITY POLLUTION UPTAKE?
(RAINFALL AMOUNT)
Figure 4.1 Principal effects of clouds on the atmospheric
chemistry and physics of acid rain deposition.
260
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(a) rainfall production—Intensity and duration, a major determinant
of rain pH and total [H"1"] burden
(b) effects on large-scale meteorology—through latent heat release
to the air and transport of momentum
(c) effects on photolysis rates and gas phase OH oxidation rate
(d) transport of sulfur and nitrogen species out of the polluted
boundary layer to:
• the lower free troposphere—away from surface deposition,
allowing longer-distance transport and deposition
• the upper troposphere—likely into a global circulation,
with deposition beyond North America
• the boundary layer once more—possibly chemically-modified
(e) chemical reactions (oxidation) within clouds and rain
(f) removal—rainout and washout of gases and particles
(g) organization of small mesoscale convergent motions in the
polluted boundary layer, thus bringing polluted material to
cloud base
The first two processes were discussed in Section 2 of Chapter III, and are
clearly quite important factors in determining acid rain. This section
assesses the transport processes, and suggests that each process should be
treated simply but in a manner consistent with the others. (Since the de-
tailed motions of cloud are extremely complex, semi-empirical descriptions
are frequently appropriate, and, consequently, overall consistency may need
to be sacrificed.)
4.2 Boundary-layer venting and clouds
Perhaps the least well-simulated process occurring in the acid rain
problem is the process of vertical transport between the boundary layer and
the rest of the atmosphere. It appears that this process may play a funda-
mental role in transporting acidic material long distances to remote but
environmentally sensitive areas, and perhaps also in transporting the pol-
lution far away to the clean atmosphere. In this section, we will examine
the little available evidence that allows a preliminary evaluation of these
transport effects, and also some possible methods of simulating them.
a. Observational evidence that cloud transport is important
Observations show that a large fraction of the sulfur transported out
of the Midwest has passed through clouds. Data from the four hundred air-
craft spirals made by Meteorology Research Institute and Research Triangle
Institute during the SURE program give a good climatological view of the
vertical distribution of S02, NOX, bscat (a measure of light scattering
261
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by aerosols), and CN in the Midwest. The latter two serve, in combination,
as a reasonable indicator of the concentration of sulfate aerosol and its
age. Figures 4.2 and 4.3 show vertical profiles of median values of these
variables and an indication of typical high and low values. Midday mixed-
layer (interpreted as subcloud-layer) heights ranged from 1000 m to 1500 m
in the summer; these are climatologically typical values. Substantial
vertical transport of material beyond these heights must be accompanied by
condensation over eastern North America. Further west, deeper mixing can
occur without condensation, due to the typically lower relative humidi-
ties. However, these regions have much lower S02 emissions.
Notice that the behavior of S02 and N02 is different from that of the
particle measurements. S02 and N02 drop strongly in concentration above
the 1000 to 1500 meter level, while bscat and CN fall away at higher al-
titudes, around 2500 m. Many low clouds have tops extending up to this
level. A reasonable explanation of the different pollutant distributions
is that sulfur has been carried through low clouds to produce the aerosol.
Do the clouds transform S02 to SOi^? It is not clear. It could be
that these cloud promote S02 reaction to sulfate strongly, or possibly that
S02 simply exhibits a shorter lifetime against transformation-removal, and
only its product remains in significant concentration above cloud base.
Other data from the SURE airplane flights indicates that around 30%
of the sulfur column present at any time is above 1500 m, the height of the
summertime mixed layer (see Figure 4.4). The percentage varies from 15%
to 70% (Bornstein and Thompson, 1981), indicating that a very substantial
amount of the sulfur loading present at any time over industrialized east-
ern North America has passed through cloud. Since the region above cloud
base is "better ventilated" with higher winds, an estimate of the flux of
sulfur towards an acid deposition region above clouds is perhaps nearer
40-50% of the total. Ferek's (1982) analysis of aerosols during wintertime
(APEX) conditions and in summmertime conditions suggests also a large
amount of sulfate above cloud base; Ferek suggests that his data support
a large role for cloud-droplet oxidation processes, both in storm and in
fair-weather low clouds.
b. Previous simulations
Several authors have made significant contributions to the interaction
of cloud transport to air chemistry on the synoptic scale. Ching (1982)
has shown the potentially great sensitivity of the regional oxidant buildup
process to cloud venting (net removal of ozone from the mixed layer).
Greenhut et al. (1982) have shown a case study of this venting process, and
find a large effect in the neighborhood of the cloud system studied. The
extension of this study to broader effects of cloud on pollutants is diffi-
cult. Lamb (1982) has shown how to include the effects of low clouds, es-
sentially those forced by boundary layer dry convection, into a mesoscale
air pollution model, using information derived from thermodynamic proper-
ties like local surface heat flux. Scott (1982) has presented two cloud
microphysical models, in which individual systems interact with an environ-
ment that is characterized by observed clirnatological pollutant concentra-
tions and meteorological variables. He presents simulations of summertime
262
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3000
v
U
o
D
zooo
1000
Night
and
Early
Morning
Midday
ZO
40
ZO
40
CONCENTRATION SO2 (ppb)
3000
ZOOO
U
Q
H
1000
Night
and
Early
Morning
20 40 0 20
CONCENTRATION NOX (ppb)
40
Figure 4.2 Concentrations of the primary acid rain pollutants, S02 and
nitrogen oxides, [NO] + [N02], (below) as a function of altitude during
189 aircraft spirals above the Midwest made by MRI during the SURE program.
(Figure from Blumenthal et al., 1981). There is a drop-off in NOx and S02
above 800 m in the morning and '!200 m in the afternoon in most instances.
This level reflects the top of the region typically mixed by dry convection.
263
-------
3000
Night and
Early
Morning
CONDENSATION NUCLEI (103cm"3)
3000 »"
2000
u
Q
H
1000
scat
Figure 4.3 Concentrations of condensation nuclei (above) and bscat (below),
aerosol measurements which serve as a proxy for a continuous measurement of
sulfate particles (see Blumenthal et al., 1981), Notice that there are high
values of these extending up to 2000-2500 m suggesting that transport from
below through the mechanism of low clouds has distributed sulfate through a
deeper layer. Condensation nuclei counts provide a measure of newly-formed
small aerosol; bscat is a measure of the light scattering properties of
submicron size-aerosol.
264
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S6 -
22
28
3 20
'9
II
Su F W Sp So
Su F w Sp Su
J— 1977— +— 1978 — j
F w S» Su
f—1978—j
SMU*
1978— (
Figure 4
sulfate
in milli
bar indi
1500 m 1
sampled
base is
to 1000
day.
.4 Column-integrated concentrations of total
over Philo, Ohio (left) and the entire SURE region,
grams per square meter. The shaded portion of the
cates the integrated amount of sulfur found above
n aircraft sampling. The remaining portion was
below 1500 m. Mean mid-afternoon summertime cloud
around 1.5 km in this region. Cloud bases from 500
m are characteristic of other seasons and times of
m
265
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(convective) and wintertime (stable cyclonic) storms with simple models of
updraft and downdraft structure. Scott's models include many processes,
but the implications and sensitivities remain to be more fully understood.
Fisher (1982) has shown how some of the essential motions of a wintertime
warm-front warm-sector storm can be parameterized in a manner simple enough
to allow detailed study of scavenging and chemistry. Hong and Carmichael
(1982) have begun work describing the interaction of a small cloud's water
phase chemistry with a predefined advective transport through cloud.
Gidel (1982) has considered the effects of cloud transport on meteor-
ological tracers with prescribed first-order decay rates, and finds their
inclusion to be of very great importance in the tropospheric nitrogen and
ozone budgets. Chatfield (1982) has constructed a model of the tropo-
spheric transport and photochemistry of S02 and other reactive reduced
sulfur species, and finds vertical distributions of S02 completely differ-
ent from those of diffusion models cited in his work. He also includes a
highly parameterized trajectory model for washout of S02, and finds that
the treatment of the washout and reaction processes below and just above
cloud base is crucial to the transport of S02 through cloud.
4.3 Vertical transport of pollutants—a mathematical framework
Above the boundary layer, the most important vertical transport mech-
anism is involved with the action of clouds, either on the synoptic scale
of cyclonic cloud systems or on the smaller mesoscales of other clouds
(CIAP, 1975; Wallace and Hobbs, 1977). Indeed, the boundary-layer top is
frequently taken to be at or near cloud base for the relatively humid situ-
ations characteristic of Europe and eastern North America. Many cloud sys-
tems create temperature inversions at their bases. Other mixing processes
such as intermittent clear air turbulence {CIAP, 1975) do occur. The
thickness of such cloud-free mixing is limited, however; upward motion over
distances over 1 km is typically accompanied by condensation—cloud—for
relative humidities usually enountered over the region (Ludlam, 1980;
Wallace and Hobbs, 1977).
The description of transports due to clouds usually involves time and
spatial scales that are smaller than usually handled by air pollution or
meteorological models. For this reason, the mathematical treatment needs
to smooth greatly the effects of cloud without, however, missing basic
transport processes. The transport processes combine
(a) direct advective transport of the organized cloud updrafts and
downdraft—hundreds of meters wide and hundreds to many thousands
of meters deep, and
(b) turbulent motions, tending to produce more local mixing at all
scales down to the molecular scale.
These transport processes may have very different character. Acid rain
simulations and most other air chemistry simulations to date have used eddy
diffusion parameterizations, which are demonstrably effective for the smal-
ler scales.
266
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It is not difficult to provide a mathematical framework for these
transports. For example, we can provide a description using the notation
of Eq. (2) in Section 6 of this chapter. In this notation, the ensemble
and spatial mean transport of species due to cloud and associated small -
mesoscale motions is
9n,
-~ due to cloud transport =
0 t
Ta (x,z) = / dx'Q/z toP{f(x,z|x',z') na(x',z')}
where the function f describes the probability of subgrid-scale transport
of the concentration of a species a, vertically and horizontally (per unit
time and unit volume). Generally such horizontal transport will be re-
stricted to neighboring grid elements since larger-scale transport can be
explicitly resolved, but the vertical transport may span the depth of the
troposphere. Such probabilities can be evaluated in several ways:
(a) From diagnostic case studies of cloud motions in different
synoptic situations. While most of these diagnostics describe
tropical situations (e.g., references in Houze and Betts (1981),
Chatfield, (1982)), there are descriptions of mid-latitude
motions (Johnson, 1976; references in UCAR, 1983).
(b) From summary statistics derived from models of individual cloud
or cloud systems (e.g, trajectory studies like those of Miller
and Betts (1976)).
(c) From convective parameter!zations that frequently form part of
a meteorological model.
Both diagnostics and parameter!zations, however, give information about on-
ly the averaged transports due to clouds. Spatial averaging over (50 km)
is commonly used, and temporal averages of 1 to 12 hours are typically im-
plicit. Furthermore, parameterizations can describe only the most likely
(i.e., ensemble-average) behavior.
Other mathematical descriptions of cloud transport are possible. This
one was based on the work of Chatfield (1982). Lamb's (1982) analysis of
low cloud is more detailed.
4.4 Four time scales associated with cloud
For an assessment of the effect of cloud transports, both on subcloud
polluted layers and on the material source for upper layers, a few time
scales are useful.
a. Residence time below cloud base, TSut> Cld
One very basic time estimate can be defined for removal of pollutants
from the whole boundary layer:
267
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_ (typical boundary layer concentration)(subcloud layer depth)
sub eld (cloud base flux)
We assume that this time scale is approximately constant for all levels
below cloud base. This can be thought of as the time for depleting the
mass in the boundary layer by exporting out through cloud bases. It is
thus a residence time (against this cloud-base transport) for any molecule
within the mixed layer. It must be remembered, however, that other proces-
ses, such as reaction or absorption into rainfall or onto the ground, are
competing with this transport. A different residence time must be quoted
for each general type of cloud, since clouds display widely different-
cloud-base vertical velocities and mass fluxes. To interpret this time
scale as a residence time, we must also assume that the cloud field remains
almost unchanged in character for times longer than tsub eld- Tnis t1me
scale can be used in analyses of air pollution venting from the boundary
layer. Such time scales could also be used in parameterizations in large-
scale acid rain models where explicit vertical transport due to cloud is
not included.
b. Transport-to-cloud time scale, t-^rans
A related time scale is harder to estimate. Suppose we wish to con-
sider a molecule anywhere in a polluted boundary layer, under either clear
or cloudy skies. What is the average time until the particle reaches cloud
base? This involves knowledge of the transport to that variety of cloud
field. This is the definition of T^rans, and naturally only a very crude
estimate can be made without reference to complex models.
This time scale is useful mainly in general analyses; the estimated
time scales shown in Table 4.1 suggest that cloud removal of sulfur is
important in the sulfur budget of eastern North America, and approaches
the importance of dry deposition and wet removal.
c. Transport times through clouds, Tjnsoi and TSO]
Two other time scales provide information about transport through
clouds. It is frequently useful to have a rough estimate of the expected
time a molecule spends within cloud, so as to estimate the relevance of
possible aqueous or gaseous phase reactions. A nearly insoluble gas will
have a transport time through cloud like that of the air between droplets,
and this time we call Tjnso-j. Highly soluble gases (those that apportion
predominantly into the liquid phase) will frequently have a rather differ-
ent lifetime, since most cloud droplets have an appreciable fall velocity
with respect to the moving air. Time scales for the residence of soluble
species in cloud must be calculated with such considerations taken into
account, using information from textbooks of cloud physics (Ludlam, 1980;
Pruppacher and Klett, 1978).
Time scales like these are necessary for estimating the extent to
which "slow" reactions can proceed within cloud droplets. Estimates of
these time scales for a variety of cloud types can be found in Table 4.1.
These cloud types will be described in Section 6 of this chapter. Many of
the estimates are based on a simple technique that we may call the "kine-
268
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Table 4.1
Comparison of Cloud Time Scales
T T T T
Cloud type insol sol sub cld transport
C
0 .
N Cumulus1 5-20 min 5-25 min 10-30 min -14 hr
E (humulis mediocris)
C
T Cumulonimbus2 15-40 min 15-60 min 15-30 min -46 hr
I
V
E
S
T Stratocumulus 3-12 hr 3-9 hr 2-7 hr >30-120 hr
A -stratus3
3
L Nimbostratus"'5 5-48 hr 3-48 hr 1-3 hr 35-120 hr
E
LeMone (1976, 1980), Betts (1973), Houze and Betts (1981), Ludlam
(1980), and Stull (1982) and references therein.
2See Johnson (1976), Anthes et al . (1983), Ogura and Liu (1980), and
Herzech and Hobbs (1981) and references therein.
3See Hales et al . (1982), Ludlam (1980), and LeMone (1980) and
references therein.
See Houze et al . (1981), Ludlam (1980), Hobbs (1978) and references
therein.
5
5See also Telegadas and London (1954) for a general reference on cloud
amount.
269
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matic method," which assumes that the subcloud layer is sufficiently mixed
that all molecules have the same probability of incorporation into a cloud
updraft. For example, an estimate of rsub eld ^ given by:
_ (height of cloud base)
Tsub eld (typical updraft(local fraction of cloud-base '
velocity) surface with updrafts)
whereas a simple description appropriate when cloud updrafts are widely
dispersed (e.g., cumulonimbus, cumulus, and some stratocumulus clouds)
would be:
Tsub eld
transport ~ (fraction of continental area with cloud and amount) "
Some data is available from Telegadas and London (1954). More sophis-
ticated techniques are possible. For example, Lamb (1982) estimates
Tsub eld f°r shallow cumulii using thermodynamic analyses. Such tech-
niques are likely superior for this type of cloud; other specialized
diagnostic techniques should be developed for other types.
4.5 Four representative cloud types
Four types of clouds, illustrated and described in Figures 4.5
through 4.8, demonstrate the range of cloud effects. These are:
t Cumulus clouds, typically the fair-weather cloud cumulus humilis and
cumulus mediocris, but including also scattered, relatively active
stratocumulus (see Figure 4.5). The main transport effect of these
clouds appears to be to remove sulfur (S02 and sulfate) from the sub-
cloud boundary layer, and thereby to reduce greatly the possibility
of deposition onto the ground. (Recall that dry deposition is thought
to be as important a sink of S02 as any.) There is also the possi-
bility of reaction within water droplets, as described in Chapter V.
This is a predominant summertime cloud, and may contribute greatly to
the sulfur loading above 1000 meters altitude.
• Deep convective storms like cumulus congestus and cumulonimbus (Fig-
ure 4.6). Such convection is important both in air-mass thunderstorms
of summertime and in cold-frontal convection of winter storms (Herzegh
and Hobbs, 1981, and references therein). These may require the most
sophisticated treatment, since they allow large deposition of sulfur
as acid rain, and also removal of sulfur to the upper troposphere,
where it may be input to the global troposphere, and lost from the
continental sulfur supply. This sink may or may not account for the
apparent imbalance of sulfur sources and sinks, with wet deposition
accounting for only about one-fourth of industrial sulfur emissions
(see, e.g., Golomb, 1982). The sulfur that is transported rather than
scavenged into rain is likely distributed throughout the troposphere,
with greatest detrainment in the upper troposphere. In particular,
one does not expect the dropoff with altitude such as found in many
eddy-diffusion calculations (e.g., Rodhe and Isaksen, 1980; Graven-
270
-------
Figure 4.5 Cumulus mediocris circulation patterns shown for a
marine environment (Lemone, 1976). Note several important features
of these clouds that should be incorporated into an acid rain model :
(a) Transport of material at cloud base is downward between clouds
and upward transport is almost exclusively through clouds, implying
different effective transport for species with little reaction in
water phase (i.e., ozone, sulfate) and those with potentially great
reaction (i.e., SO?, HOOH).
(b) Material above cloud base is removed from frequent contact
with the surface, greatly reducing dry deposition for materials like
sulfate aerosol.
(c) A substantial portion of the material passing through these
clouds originates from near the surface, at least during the early
part of of the life cycle of each cloud.
271
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Figure 4.6 A particularly active cumulonimbus cloud (Ludlam, 1980).
Clouds of this variety cause great deposition of [H*] ion in a few
events over summertime in Eastern North America (Niemann, 1982), but
may also allow substantial removal of sulfur from the region, as sub-
stantial amounts of water are detrained above five kilometers, so that
very-long distance transport is more likely than reentrainment into a
precipitating system. The cloud portrayed is a severe storm, much more
active than climatologically more typical cumulonimbus clouds, but a
variety which has been better characterized due to its
effects. Most cumulonimbi
times in their life cycle;
destructive
show the features portrayed at various
usually, only the severe storms maintain
Other features important in the simulation
a quasi-steady structure.
of acid rain are:
(a) Boundary layer air is spread through rather broad regions in
the upper troposphere, so that mean concentrations of S02 of 0.3 to
0.5 ppb may represent a substantial removal flux from the 1 km boundary
layer.
(b) Air ventilating the boundary layer in the downdraft may be a
combination of relatively clean air from above three kilometers and
somewhat polluted air from one to three kilometers from one to three
kilometers. For an examp-le of such ventilation, see the unusually
low CFC13 concentrations observed on August 1 in sampling shown in
Figure 6.6 of Chapter VI.
272
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i— C
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O ••— QJ r—
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O 4J -t-2 TD
X C
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at o
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r-
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4-1 -O
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to i—
'NOI1VA313
273
-------
«'CM UOUIQ KKftTES CONTENT
MICH ICE PARTICLE CONCENTRATIONS ^
Figure 4.8 Nlmbostratus and altostratus characteristic of
cyclonic warm fronts. These are most frequent in wintertime
and their large horizontal extent and uniformity allows material
transport to be relatively well described. Note also that
(a) much of the upward motion in these storms occurs in limited
regions with vertical velocities of 10 to 50 cm/sec, so that
material may be lifted from near the surface to two to five
kilometers over times as short as three to ten hours, and
(b) small-scale transport of reacting chemical species: soluble
species like HOOH, may cross the frontal surface under common
conditions, borne within cloud and rain droplets. Hydrogen
peroxide may be transported within tne warm sector, originating
in sunlit, moist, maritime, tropical air. Sulfur dioxide may
accumulate to the more northern, stable air ahead of the warm
front in these circumstances. In summary, even large-scale
cloud systems may exhibit transport effects taking place on the
scale of kilometers.
274
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horst et al., 1978). Figure 4.2 suggests that such concentrations
are less than about 1 or 2 parts per billion above 3 km. Data taken
over relatively unpolluted regions of western North America suggest
that these concentrations are around 0.2 to 0.3 ppb even at 5 km
altitude (Maroulis et al., 1980). Much lower concentrations, one
third as high, are found over ocean regions, Chatfield (1980) has
suggested that such low but non-negligible concentrations may ori-
ginate from ground-level sources in midlatitudes and tropics, with
reduced sulfur redistributed in deep convective updrafts.
• Stratus and stratocumulus characteristic of cyclonic warm fronts .and
orographic clouds. These form large-scale cloud systems and so might
seem to present the fewest subgrid-scale problems. Perhaps the best
estimate of transport 1S the synoptic time scale of five days (win-
ter) to perhaps twice that (summer). However, in most synoptic situ-
ations with flow across the Appalachians, orographic stratiform cloud
is quite likely to affect the sulfur transport and chemistry, giving
Ttransport mucn smaller than that shown in Table 4.1.
• Nimbostratus of warm-frontal systems. Again, these form broad-scale
cloud systems, but, as Figure 4.8 shows, there may be significant
small-scale effects, including vertical motions on the order 20 cm/
sec, so that there may be fairly rapid transport to the low and middle
troposphere on a sporadic basis. These systems may also contribute to
removal of sulfur from the continental sulfur budget and into the hem-
ispheric budget, as previously described. Although the large-scale
features of these cloud systems are well simulated by regional models,
a significant amount of vertical transport, precipitation, and .chemi-
cal interchange between air masses may occur in small (30-km wide)
bands (Houze et al., 1981, and references therein).
4.6 Cloud transport as described by large-scale meteorological models
We have seen that cloud transports of material can both
• help preserve sulfur species from ground-level uptake by carry-
ing a third to a half of sulfur out of the boundary layer and
towards regions of rainout, and
• help remove sulfur and nitrogen from the subcontinental lower
tropospheric reservoir that produces acid rain, perhaps account-
ing for a portion of the "missing sulfur" that is emitted but not
deposited.
Let us describe the present state of meteorological parameterizations in
terms of the general cloud types given above:
• Low clouds, such as fair-weather cumulus and stratocumulus, are es-
sentially not diagnosed in weather forecast models (see following
section on cloud modeling and Chapter IV, Section 6), but have been
considered in more specialized diagnostics like those of Miller and
Betts (1975) and Stull (1983). Stull (1983) has given a review.
275
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• Cumulonimbus and related types make sufficient impact on the energy
and momentum fields that their effects are usually diagnosed {see
following section and Chapter IV, Section 6). Only a few parame-
terizations, such as that of Arakawa and Schubert (1974) and its
successors, can be interpreted explicitly as describing from which
level sulfur molecules are removed and to which levels they are trans-
ported. However, such models may or may not give a good description
of the effects on energy, moisture, and momentum fields within a me-
teorological model (see comparison studies listed in Chapter IV,
Section 6). Many parameterizations are based on considering a single
cloud which detrains material only in the top ten percent of the-cal-
culated cloud depth, and so simulate very high removal of sulfur com-
pounds from the lower atmosphere.
t Large cloud systems, including warm-frontal and orographic nimbo-
stratus and stratocumulus, are not so complex. However, it may be
necessary to account for their own slow convective circulations,
as shown in Figure 4.8. The larger vertical velocities here
(- 30 cm/s) may allow escape of material to the upper troposphere,
while the enhanced rainfall may allow introduction of soluble species
like HOOH with a warm-sector origin.
Some concluding remarks provide an overview of the roles of clouds:
(a) Clouds have several different important effects in acid rain
models, especially in removing sulfur from the mixed layer.
(b) Descriptions of vertical transport superior to eddy diffusion
parameterizations are emerging, but they require a climato-
logical data base.
(c) Parameterizations of the effects of clouds on horizontal winds,
vertical transport, and photolytic radiation are separate, and
closely consistent, descriptions.
4.7 Cloud Modeling
The preceding sections have indicated the complexity of cloud proces-
ses and the variety of parameterization procedures, some rather ad hoc,
that have been employed. More concrete descriptions of these processes are
contained in cloud-scale models, and this section will describe what we can
learn from them for acid deposition modeling.
The nonhydrostatic meso-y scale model (i.e., the cloud-scale model)
can be extremely useful in the following two major aspects of developing a
regional-scale Eulerian acid deposition model:
(1) understanding the relationship between cloud/precipitation
processes and chemical/physical processes of pollutants, and
developing and testing parameterization schemes of cloud chem-
istry for regional-scale models; and
(2) revealing mutual interactions between regional-scale phenomena
276
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(which have the potential to carry pollutants over a long
distance) and associated clouds, i.e., the interactions between
the regional scale (hydrostatic) and the cloud scale (nonhydro-
static), and parameterizing and testing the collective effects
of clouds for regional-scale models.
Clouds are the obvious agency for producing wet acid deposition, after
chemical species are mixed with water in the clouds. The relationships be-
tween cloud/precipitation processes and the chemical/physical processes of
pollutants are not clear. The state of the art at present allows detailed
numerical simulations of clouds. With such a model, chemical/physical pro-
cesses of pollutants may be included at least in a parameterized fashion.
Thus, investigation of the evolution of pollutants in the cloud and the
surrounding environment becomes possible. Since the actual effect of
cloud/precipitation processes on chemical/physical processes of pollutants
(or vice versa) occurs via cloud microphysics, a cloud model must treat
microphysics in as much detail as possible in order to study cloud chem-
istry. The microphysical processes may include nucleation, condensation,
evaporation, deposition, sublimation, stochastic collection and breakup,
and sedimentation, and they may be complicated further by cloud electri-
fication and radiation processes.
On the regional scale, cloud and precipitation processes can affect
the transport and deposition of pollutants. A more accurate representation
of the collective effect of cloud and precipitation processes in a region-
al-scale model is undoubtedly needed. Obviously, comparing observed data
with the results from a regional-scale model which includes parameterized
cloud and precipitation processes can show the merit of the parameteriza-
tion schemes. However, if we can learn more about the mutual interactions
between the regional and cloud scales, new parameterization schemes may
provide more accurate prediction of cloud precipitation. To gain some
basic knowledge of (1) how convective clouds and precipitation will be
initiated and maintained under different regional-scale settings, and (2)
how the convective clouds and precipitation will feed back on the regional
scale, the ideal method is to develop a time-dependent, three-dimensional
system with a cloud-scale model nested within a regional-scale model with
two-way interactions between the scales. A cloud-scale model with complete
dynamics (i.e., nonhydrostatic, three-dimensional, time-dependent) is re-
quired for this nested system.
Various cloud-scale models, either steady-state or time-dependent and
in one, two, or three space dimensions, are being used in a number of as-
pects of cloud microphysics/dynamics research. The complexity of micro-
physics or dynamics depends on the nature of the research topic and indi-
vidual interest. For studies of cloud microphysics with a relaxed dyna-
mical structure, the cloud model can perform detailed calculations of the
evolution of particle spectra, including perhaps radiation and electrical
effects on the spectra. On the other hand, for cloud dynamics research, a
three-dimensional and time-dependent model is necessary to reveal the de-
tailed circulation of the cloud and its environment, and only a highly
parameterized procedure for the micro-physical processes may be afford-
able with present computer resources.
277
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Excellent reviews of cloud microphysical and dynamical processes have
been made by Cotton (1975a, 1979) and Schlesinger (1982); the complexities
of cloud microphysics and dynamics have been well described. The emphasis
of this section is on the parameterization of microphysical processes for a
three-dimensional cloud-scale model, and on the parameterization of convec-
tive clouds and precipitation for a three-dimensional regional-scale model.
To consider a complete set of microphysical processes, the range of
particles may span from 10~2 urn in radius for aerosol particles to 105 pro
for hail. The conventional method for calculating the evolution of a par-
ticle spectrum is to increment the particle radius logarithmically. In
order to represent such a broad range of particle sizes precisely, a large
number of increments is needed, giving a large number of field equations
for the size classes. As shown by Silverman and Glass (1973), 45 mass
classes for hydrometeors ranging from 2 to 4040 pm in radius may be neces-
sary for satisfactory spectral resolution just for the warm-rain cloud.
(The microphysical processes involved are only condensation/evaporation,
stochastic coalescence, and breakup.) Gillespie (1975) has suggested a
Monte Carlo computational algorithm for simulating the evolution of the
spectrum by stochastic coalescence. Although the statistical algorithm is
generally satisfactory, it is quite demanding computationally. To minimize
the artificial spreading of particle distribution, Ochs and Yao (1978) and
Ochs (1978) have developed a moment-conserving technique to calculate par-
ticle-spectrum evolution. As Ochs (1978) indicates, the increase in accu-
racy obtained with this technique comes with considerable computational
cost. A distribution function approach put forth by Clark (1974, 1976) and
Clark and Hall (1982) to simulate the evolution of the particle spectrum
has shown a very accurate and computationally efficient solution, compared
with the solution of the standard finite-difference approach. There is a
very high potential for applying this new approach to multidimensional
cloud models.
One-dimensional time-dependent cloud models cannot provide the com-
plete cloud circulation, but are efficient and effective tools for develop-
ing and testing complex microphysical processes. The dynamical framework
formulated by Asai and Kasahara (1967) embraced significant cloud dynamics;
they averaged the fundamental equations about the central axis over a fixed
radius by assuming axial symmetry in a cylindrical coordinate, taking into
consideration both updraft and downdraft areas. Later this system was sup-
plemented by Holton (1973) to include dynamic pressure calculations, and by
Cotton (1975) to upgrade the formulations of turbulent transport. The de-
tailed interactions of cloud microphysical and chemical processes may be
simulated by using such dynamically simple models.
Schlesinger (1982) gave an excellent review of the three-dimensional
numerical modeling of convective storms. First, he established arguments
for the third dimension in cloud models, and showed how complicated a cloud
model could be. Explicit calculations of the evolution of the particle
spectrum by the conventional finite-difference method become impossible
with present computer resources. Based in part on a Marshall-Palmer dis-
tribution, the Kessler (1969) parameterization, with some variations, has
been adapted most widely for the microphysical processes in three-dimen-
sional cloud models. Such parameterizations usually divide liquid parti-
278
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cles into two categories: cloud droplets, which do not have falling velo-
cities, and raindrops, which do. A similar approach could be applied to
the ice particles (Koenig and Murray, 1976; Koenig, 1977). Schlesinger
(1982) then identified some difficulties in the three-dimensional modeling
study; namely, model initializations, boundary conditions, numerical meth-
ods, and verifications.
Past models have been quite complex, and often are the focus of large,
autonomous research efforts. However, the preceding review suggests that
enough has been learned to merit the adaptation of cloud models to simulate
several processes required by acid deposition research.
A list of cloud models, including distinguishing characteristics, can
be found in Table 4.2. The development of a three-dimensional model is it-
self a challenging and time-consuming effort. The most reasonable approach
appears to be a nested-grid technique allowing a large regional model to
supply boundary conditions for individual cloud simulations. Such a de-
tailed nested-grid model would be ideal for the comparison of model results
with specific air-chemistry observations. However, for studying cloud
chemistry and the interactions between cloud and regional scales, one can
use an existing cloud model rather than developing a new one. Accurate
representation of chemical/physical processes of pollutants in clouds and
the cloud/precipitation processes is the primary emphasis in regional-scale
acid deposition applications.
The treatment of cloud microphysics in a cloud model is extremely
important, and one of the best in this regard is the three-dimensional non-
hydrostatic model developed by Clark (1977). This model uses terrain-fol-
lowing coordinates and excellent cloud microphysical parameterizations
(Clark, 1979; Clark and Hall, 1979).
In summary, the utility of nonhydrostatic cloud-scale models for re-
gional acid deposition studies has been stressed. To investigate and par-
ameterize the microphysical processes of clouds, the chemical processes of
pollutants, and their interactions, a simplified cloud model can be very
useful. The dynamical framework of Asai and Kasahara (1967) with supple-
mentations is recommended. Furthermore, to reveal the mutual interactions
between cloud and regional scales and to parameterize the collective ef-
fects of convective clouds on the regional scale, a complete cloud model
with sound microphysics is required. For this purpose, the three-dimen-
sional cloud model of Clark (1979) is appropriate.
5. DRY DEPOSITION
5.1 Introduction
The role of dry deposition in the regional acid deposition problem is
important. However, the fact that this deposition of atmospheric acidity
is commonly referred to as "acid rain" indicates that dry deposition has in
the past been overlooked or considered as playing only a minor role. Per-
haps this is because precipitation would seem to be the most obvious source
of acid deposition. Another reason is the difficulty in actually measuring
279
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Table 4.2
Three-Dimensional Time-Dependent Numerical Cloud Models
Model
Blechman (1981)
Clark (1979)
Clark and Hall (1979)
Cotton and Tripoli
Klemp and Wilhelmson
(1978a, b)
Lipps (1977)
Miller (1978)
Miller and Pearce
Moncrieff and Miller
(1976)
Pastushkov (1975)
Schlesinger (1975)
Schlesinger (1978,
1980)
Simpson and van Helvoirt
(1980)
Simpson, van Helvoirt,
and McCumber (1982)
Distinguishing Characteristics
Applied model of Schlesinger (1978); nested
grid (two-way)
Terrain-foil owing coordinate; anelastic;
Coriolis parameter included; precipitation
parameterization of Kessler (1969)
Applied model of Clark (1979); shallow; log-
normal distribution function parameterization
for cloud microphysics
Height coordinate; elastic; Coriolis parameter
included; moist but no precipitation
Height coordinate; elastic; Coriolis parameter
included; precipitation parameterization of
Kessler (1969)
Height coordinate; incompressible; shallow;
moist but no precipitation
Applied model of Miller and Pearce (1974)
Pressure coordinate; anelastic; Coriolis
parameter included; precipitation parameter-
ization of Kessler (1969)
Applied model of Miller and Pearce (1974)
Height coordinate; anelastic; precipitation
parameterization of Takeda (1966)
Height coordinate; anelastic; moist but no
precipitation; no turbulence
Applied model of Schlesinger (1975); preci-
pitation parameterization of Takeda (1966)
Applied model of Schlesinger (1978)
Applied model of Schlesinger (1978)
280
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Table 4.2
Three-Dimensional Time-Dependent Numerical Cloud Models
(continued)
Model
Sommeria (1976)
Steiner (1973)
Tag and Rosmond
(1980)
Thorpe and Miller
(1978)
Tripoli and Cotton
(1980)
Turpeinen and Yau
(1981)
Wilhelmson (1974)
Wilhelmson and Klemp
(1978, 1981)
Yau (1980)
Yau and Michand
(1982)
Pistinguishing Character!'stics
Height coordinate; anelastic; shallow; Coriolis
parameter included; moist but no precipitation
Height coordinate; incompressible; shallow;
moist but no precipitation
Height coordinate; anelastic; moist but no
precipitation; no turbulence
Applied model of Miller (1978)
Applied model of Cotton and Tripoli (1978);
no Coriolis parameter; precipitation para-
meterization of Kessler (1969)
Applied model of Yau (1980)
Height coordinate; anelastic; precipitation
parameterization of Kessler (1969)
Applied model of Klemp and Wilhelmson (1978a)
Applied model of Steiner (1973); anelastic;
precipitation parameterization of Kessler (1969)
Applied model of Yau (1980)
281
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and defining the dry deposition contribution {Hicks et al., 1980).
Indications now are that nonprecipitation-related deposition of acidic
or potentially-acidic species is approximately equivalent to that directly
related to rain and snowfall (Record et al., 1980).
Dry deposition refers to the direct transfer of material from the free
atmosphere to the vegetation, soil, or water surface where it is taken up.
In the Eastern United States and Canada, most of the surfaces exposed to
the atmosphere are not bare soils, rock, or concrete, but are the leaves of
growing plants. In general, dry deposition may be conveniently separated
into two reasonably distinct aspects.
The first part involves the transport through the surface layer to a
laminar surface sublayer. This is due to the turbulent processes in the
atmosphere and is the aerodynamic component of the transport. It governs
the rate at which atmospheric species are carried into the immediate vicin-
ity of the surface.
The second part involves the transport by diffusion through the lami-
nar surface sublayer to the ultimate absorbing/reacting substrate, and is
the surface component of the transport. Although the laminar surface sub-
layer is typically only - 100 ym in thickness, the processes operative
within this layer are critically important in establishing the deposition.
The reactivity/solubility/adhesion of atmospheric species at the surface
governs the ultimate rate at which atmospheric species are removed, as
nonreactive species such as Ar and He have deposition velocities of zero.
Although the mechanism of transport is complex, involving different
scales of turbulence, the overall result can be described simply. At any
height, the concentration of a species, C, and the dry deposition flux, F
(C-velocity), define a deposition velocity:
Vd - F/C
A useful model which has been developed to handle the mathematical
treatment of deposition is based on the analogy to electrical flow through
resistances. In this convention, the overall deposition velocity (or con-
ductance) of any atmospheric species is defined as the sum of the various
resistances to the uptake by the surface.
In a complicated system such as a forest, the resistances to deposi-
tion are complex. The ultimate uptake/reaction can take place at the soil,
at the leaf cuticle, at the plant tissue in the interior of the leaf via
the stomata, or at the leaf hairs. Turbulent transport must be considered
to canopy top leaves, to the understory, and to the soil. In order to de-
fine the total conductance of a trace constituent, all these resistances
must be considered.
The analysis of such a resistance network where seme are in series and
some in parallel yields a single equivalent resistance. However, for dry
deposition, it is most profitable to separate the total resistance into
an aerodynamic (turbulent flow) resistance, ra, and a surface (diffusion
282
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flow) resistance, rs. Then, the total conductance (or deposition velo-
city) may be expressed as
The aerodynamic resistance, ra, is an expression of the turbulent
transport from the free atmosphere to the surface laminar sublayer. The
value of ra is dependent upon atmospheric stability and upon surface
roughness. Micrometeorological research has as its concern the prediction
and definition of this resistance term for the boundary layer transport of
heat and momentum. The additional input required for the calculation of
ra within an advanced acid deposition model is a parameterized grid of
surface cover/land use. Such information is available and must also be
utilized in defining rs.
The surface resistance component, rs, is more difficult to treat.
Because of the difficulties involved in measuring chemical deposition
rates, there is not a lot of data available, much of what is available is
unreliable, and even the reliable data is mostly for ideal conditions of
surface cover and weather.
Various experimental techniques are used to measure deposition velo-
city. These include:
(1) Box methods
(2) Profile or gradient analysis
(3) Eddy correlation measurements
A fourth method, budget analysis, can also be applied to either or both wet
and dry removal.
The box method basically consists of placing an enclosure over a
surface to be tested and measuring the rate of decay of the concentration
within the enclosure, which is presumed to be related to removal at the
surface. Although the method is simple in concept and requires only the
measurement of the mean concentration as a function of time, there are many
assumptions involved in its application. First, it is assumed that the
enclosure does not affect the removal rate and that the results can be cor-
rected for the effects of the enclosure. These effects include adsorption
on the enclosure walls, lack of natural ventilation, and changes in the
solar and infrared radiation balance which also affect the heat and water
vapor budgets within the enclosure. Over water, an enclosure will also
modify the waves. Over forests, an enclosure covering a significant area
would be unwieldy, and enclosures covering a branch may not be representa-
tive. For these reasons, box or enclosure methods will probably never be
entirely satisfactory.
Measurement of the mean concentration profile has the advantage of a
minimal disturbance of the surface and the overlying atmosphere. However,
283
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accurate concentration differences must be measured (on the order of 1% of
the mean concentration or better). Furthermore, the stability of the lower
atmosphere and a flux-profile relationship must be known. These require
additional micrometeorological measurements.
The eddy correlation technique is a direct measurement of the turbu-
lent flux at a particular level. Within the surface layer, which is typi-
cally of order 10 m deep, the flux of species with lifetimes greater than a
few minutes is sensibly constant. Therefore, the downward flux within the
surface layer is a measure of removal at the surface. The vertical flux of
a species is obtained by averaging the instantaneous product of the species
and the vertical velocity after removing the mean from each of them. The
average must be taken over a time long enough so that fluctuations in the
average are not significant. The sensor time response must be short enough
to resolve all the significant contributions to the turbulent flux. For a
fixed site within the surface layer, this requires an instrument of at
least 1 Hz bandwidth; for an aircraft, several Hz bandwidth are required.
Although accurate absolute measurements are not necessary, small-scale
fluctuations need to be resolved.
With current technique improvement, it is likely that within the next
years much better and more comprehensive estimates of surface resistance,
rs, will become available for different surfaces under different condi-
tions.
A regional acid deposition model should have ra and rs for each
grid square. There is a conceptual problem of establishing mean values
of ra and rs for 50 km x 50 km grid squares. For areas of monoculture
such as the western wheat lands and the midwestern corn lands, this is pos-
sible, but for eastern mixed land use, it is doubtful. A redeeming factor
is that in the daytime a deposition regime may be established within dis-
tances comparable to the height of the boundary layer. Thus, even for grid
squares with inhomogeneous surface cover, an average of the different depo-
sition regimes is valid if the individual elements of surface cover have
linear dimensions of several kilometers. The greatest difficulty is in-
volved where the scale of the mix of land use is less than one kilometer.
5.2 Available model input
a. Aerodynamic resistance
The aerodynamic resistance, ra, is a function of wind velocity, at-
mospheric stability, and surface roughness. These are variable, although
surface roughness normally is associated with vegetative cover and only
seasonal variations need normally be considered. Figure 5.1 indicates the
range of Vj max = l/ra for different natural surfaces normalized for a
constant friction velocity. Water surfaces represent an interesting var-
iation as increased wind speed is marked by increased wave activity and
changed surface roughness.
b. Surface resistance
Deposition velocity measurements for a number of species have been
284
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1000 =•
- 1000
100 =•
£
a
X
r-
UJ
Displacement
Height
(required to generate v
this
Friction
Velocity
Max Deposition
Velocity = -
Roughness
Length
-J .£ •* .£ •* CD Q. _
— -c---c---'Oo<2
i±| QJ J X
Figure 5.1 Maximum deposition velocity for
different surfaces normalized to a constant
friction velocity.
285
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carried out over the past decade or so. Several recent critical reviews of
this data have attempted to establish reliability and to link the observa-
tions to a theoretical basis (Hosker and Lindberg, 1982; McMahon and Deni-
son, 1979).
For trace gases, the surface resistance is correlated with their solu-
bility/reactivity. Figure 5.2 represents an attempt to correlate the solu-
bility/reactivity of different trace gases with their experimentally-deter-
mined deposition velocities. By arranging the chemical species in this
manner, a generally well-ordered relationship can be obtained. However,
such arguments can only be used in a general fashion, as certain specific
effects may sometimes dominate. For example, the specific takeup mechan-
isms for 03 and for S02 are different. Ozone is an oxidant which reacts
with vegetative tissue primarily via the stomatal openings; thus, rs(03)
variation is dependent not only upon vegetation type but also upon plant
maturity, photosynthetic activity, moisture stress, and insolation. Sulfur
dioxide, on the other hand, is an acid anhydride which is taken up by moist
surfaces. As the pH decreases, a point is reached when no more S02 will be
dissolved. Thus, the variation of rs(S02) is dependent upon a different
set of factors.
For particles, the situation is much more complex. Different physical
processes, including gravitational settling, inertial impaction, diffusion
and thermophoresis, molecular diffusion, surface adhesion, and other fac-
tors, dominate in different particle size regions, and so the surface re-
sistance of an aerosol is a strong function of its size distribution even
for ideal particles and uptake surfaces. For real aerosols and surfaces,
many more factors come into play. Figure 5.3 indicates some of the phys-
ical processes involved in defining the deposition velocities to smooth
surfaces and compares an assemblage of laboratory and field measurements
taken from a review of experimental data.
Although surface resistances for different gases and aerosols are very
difficult to assign precisely, enough is now known to allow reasonable val-
ues to be set for modeling purposes. As better, more comprehensive mea-
surements are made, the newer values of rs may be incorporated.
5.3 Suitable models
The model of Sheih et al. (1979) may be taken as representative of the
style of dry deposition treatment which may be used to generate a submodel
for a regional acid deposition model. Although Sheih et al. dealt only
with S02 and so£~, other gases and aerosols may be treated similarly.
In this model, surface cover categories were defined for a 0.5° grid,
using data from USDA land use maps. The surface cover field shown in Fig-
ure 5.4 was then used, together with the model-generated stability class
field, to produce values of ra for each grid square. Thus, for the cal-
culation of deposition velocities, the surface cover map is used both to
define ra by means of surface roughness and to define rs.
286
-------
10
vd
cm sec"
0.01
-
^
~x
-X
X
-
^
_
—
-
—
—
— „
—
II!!!
x H
x H
x J^ H
X sK y H
x *i H G
| |- ' 'Mr»_ ' rt 1 Mrt 1 DAM' u e'lu o' r>/->
OSNOPAN
HNO,
DMS
Figure 5.2 An assemblage of the available deposition
velocity data for trace gases ranked approximately in
terms of reactivity.
287
-------
I02
10'
10°
o
at 'O
e
o
~ io-2
io-3
!0-4
io-5
I I i I
"DRY DEPOSITION TO SMOOTH SURFACE
(derived from Slinn,l976)
psIatmos
72.6cms"1, evap/cond = lcm/hr"
D(c)
NET Vd
(for no evap./cond.)
G.S./
EXPERIMENTAL DATA FOR VARIOUS SURFACES
C3 Laboratory
o F' Id
McMahon ft Denison (1979)
J_
"3
IO" IO"2 IO"1 10° 10' IO2
PARTICLE RADIUS (/j.m)
Figure 5.3 Experimental data plotted over a format showing the
physical processes involved in the dry deposition of particles
(G.S. = gravitational settling; II = inertia! impaction;
M.D. = molecular diffusion; D(e) = diffusiophoresis, 1 cmhr"^
evaporation; D(c) = diffusiophoresis, 1 crnhr-1 condensation.)
288
-------
0 Cropland and Potturt
1 Crop*ondt Woodland end Grazing Land
2 Irrigattd Crop
3 Grazed Fortst and Woodland
4 Ungraztd Fomt and Woodland
5 SubJiurmd Grassland and Stmiarid
Grazing Land
6 Op«n Woodland Grawd
7 Dtstrl Shrubland
A Swomp
B Mainland
C Metropolitan City
F Lake or Octan
SURFACE COVER
VEGETATION TYPE
Figure 5.4 Example of a land use map (from Sheih et al.,
1979) and the conceptual relationship leading to the definition
of a deposition velocity field.
289
-------
5.4 Phases of complexity
(1) Use available surface cover/land use maps to define a deposition
velocity field for each species of interest.
(2) Use available surface cover/land use maps to allow the model to
. define its own micrometeorology and to generate ra fields which
change with time. Define rs for each grid and allow a deposi-
tion velocity field to be generated internally.
(3) Use (2) for ra, but by parameterizing the effect of seasonal,
and diurnal cycles, available moisture, insolation, and other
factors on rs, establish a realistic variation of rs, and
again internally generate a deposition velocity field for each
species of interest.
(4) Improve surface cover/land use maps (treat subgrid scales) and
improve the parameterization of ra and rs.
6. MODEL RESOLUTION
6.1 Introduction
a. The disparity of spatial scales
To understand quantitatively the production of acid rain, we must
consider processes occurring at very different time and space scales. The
deposition of sulfate and nitrate takes place primarily over the eastern
third of the North American subcontinent, controlled by the synoptic mete-
orology of a one-to-two-thousand-kilometer-wide region. Let us call this
large area the deposition region. However, the acid material is derived
from the oxidation of SO 2 and NOX, which are emitted largely from concen-
trated sources that form plumes hundreds of kilometers long but only 1-30
km wide (see Figure 6.1). Within these plumes, there is frequently a pat-
tern of suppressed and then enhanced photochemical activity which modulates
the transformation of the emissions to the oxidized, acidic forms. How-
ever, a competitive process, uptake by the ground, is also rapid, and this
makes the details and timing of conversion important. We may call this the
primary reaction region, bearing in mind that continued reaction occurs to
the diluted and partially reacted material in the broader regions between
plumes. An estimate of the ratio of the areas of these regions is
Area of Deposition Region _ >(inn\2 = in4
Area of Primary Reaction Region
based on data presented in this chapter. This ratio partially explains why
there have net been large-scale acid rain models that include a description
of chemistry on other than an extremely empirical basis. At least one grid
point needs to be devoted-to each primary reaction region, and the result-
ing requirement of 1Q1* grid points per horizontal plane begins to strain
the resources of the largest computers used to date if many field variables
are carried.
290
-------
100 km-
100 km True Reaction « 0
Computer Simulation
of Reaction
OH, 0,
True Reaction ^
Simulated Reaction
Figure 6.1 Resolution cf reaction between chemical species. Power
plant plumes are strong sources of S02 and city plumes frequently
contain particularly high concentrations of oxidants such as QS and
HO. The middle sketch shows how a regional model with a large grid
spacing must simulate these plumes -- just as if they were completely
dispersed in a grid volume. Clearly, if the true geometry of the
plumes is like the top sketch, the regional simulation will give a
great over-estimate of the reaction rate. We will see that if the
source geometry is more like the bottom sketch, the computer simu-
lation will give a great under-estimate.
291
-------
Eulerian models to date have been restricted to grid meshes of 50 by
50 or smaller, with only one or two levels in the vertical. For an area of
2000 km in horizontal dimensions, this corresponds to a 40 km grid spacing,
about five to ten times coarser than needed to describe power plant plumes
during the daytime. These models have furthermore carried only two or
three chemical species and a very simply parameterized oxidation. Regional
air quality models describing oxidant production have been limited to smal-
ler regions with dimensions of up to 800 km, allowing finer grid resolution
(e.g., Burton and Liu's (1981) work referenced in Hayes (1981)). Yet reso-
lution down to the spatial scales appropriate for the first four daylight
hours after emission appears necessary; otherwise, it will not be possible
to understand the interaction of NOX with S02 and their interactions with
other pollutants. These interactions determine if the species will oxidize
or undergo dry deposition near the sources.
b. The need for fine resolution
There are two important reasons for computer simulations of air chem-
istry to have fine spatial resolution:
• Comparison with data: concentration measurements, made with
point resolution in time and space, are more easily compared
with simulations with fine spatial resolution. The problems
of relating the results of simple models to observations have
been noted by those who compare them (e.g., Niemann, 1982).
• Averaging of nonlinear chemistry: if the same photochemical
and cloud chemistry are simulated with otherwise identical.
models differing only in spatial resolution, the computed S02
and NOX oxidation rates may vary significantly. This is be-
cause grid-point modeling implicitly involves spatial averag-
ing, and the product of averages can be much different from the
average of products. Figure 6.1 shows cases where overestimates
and underestimates can occur. We believe that the latter is more
prevalent, and will describe it more fully later in this section.
c. The advantages of limited-resolution models
There are also advantages to models with less spatial resolution:
e Interpretability: smaller and simpler models are generally
easier to examine and interpret than larger, more complex
models. It can also be argued that acid rain effects are
averaged over many events, perhaps many years, so that
spatially-averaged concentrations are useful.
t Computer storage: the CRAY-1 computer, the largest currently
available for this problem, can provide for arrays of one-half
million variables (with 64-bit precision), a number that would be
required for the following resolution:
50 x 50 x 8 25 = 500,000
latitude x longitude x vertical x chemical species " variables
292
-------
Perhaps two or three times as many array elements may be required
if the integration program is more complex.
t Computer time: The integration time required for a species will
vary roughly as the inverse square of the separation of grid
points. There are perhaps better uses for computer time than
increasing the resolution of the model, e.g., validation runs
for components of the model, more case studies of transport, and
tests of the sensitivity of the chemical and physical mechanisms
used.
6.2 Observations of the variability of S02 and NOX concentrations
Observations made over the past decade indicate considerable variabil-
ity of pollutant concentrations over tens of kilometers. Two sorts of ob-
servations have proved particularly useful: simultaneous observations of
many compounds made at fixed surface sites, producing a time series; and
airborne observations of a smaller subset of compounds, presenting a spa-
tial sampling. Each strategy has particular advantages, so we present a
glimpse of each.
a. Aircraft observations of variability
Figure 6.2 is a portrait of the variability in S02 concentrations
produced in the midwestern United States by the Labadie and Kincaid power
plant plumes. These plumes retain their identity for up to 400 km down-
wind, and during daytime they spread to widths (half-widths) of 10 to 40
km; at night their spread is restricted to 5 km or so, although wind shear
is apt to separate laminae (Gilliani et al., 1978, Smith et a!., 1978).
Sometimes these plumes are embedded in an urban plume; the latter are the
most significant sources of reactive hydrocarbons, and therefore a source
of extra photochemical activity in many circumstances. Beyond the plume
boundary, S02 becomes undetectable.
How common are plumes? Figure 6.3 shows observations made on a
cross-country flight during the SURE program (Blumenthal et al., 1982).
Figure 6.3a shows a region of the Midwest with many sources during an epi-
sode of regional pollutant buildup. S02 and other compounds show signifi-
cant variability over distances of 25 km or so. Backgound concentrations
of S02 between the plumes are quite high at this time, at apparently 6-8
ppb. Figure 6.3b shows a region with fewer sources during this same epi-
sode. Background S02 concentrations in this case are typically a few ppb,
a level at which S02 measurements may become unreliable.
A broader "climatology" of air pollution variability is shown in the
cumulative frequency distributions of pollutants sampled by aircraft during
the SURE program. Figure 6.4. These cumulative distribution functions of
Figure 6.4 describe the magnitude of pollutant variations. The shaded
areas in each cumulative distribution function curve indicate integrals
that sum to the mean concentration of the species. In the S02 graph, the
horizontal lines indicate that approximately half of the area lies in a
thin upper portion of the graph, corresponding to samples with more than 14
ppb mean S02 in the boundary layer. That is, one half of the S02 monitored
293
-------
Figure 6.2 Horizontal profiles of 863 during selected
constant-altitude aircraft traverses on July 9 and July
18, 1976. July 9 traverses are at about 450 m AGL, arid
July 18 traverses are at about 750 m AGL. The Labadie
plume sections are shaded. Also shown are backward
trajectories for the Labadie plume (Gillani et al ., 1978).
294
-------
2
8
i*s
o
40
35
30
25
20
IS
10
5
0
0.15
0.12
0.09
0.06
0.03
0
r'-vv- *._.-•
huTMoa Caurtluid
CoT~At
Flight Pith
8 ~~
6 ^
4 2
2 1
0 -0"
u _
Q -
4000 ? g
3000 t
2000 <- -*
1000 -J -
30 60 90 120 150 180 210 240 270 300
DISTANCE (kilometers)
200
3
& 125
m
O
so
100
75
so
25
...... "
.cat
100 -
- 75 -
8
50 -
25 -.'
Ozone
-.-. NO
1
Direction of Flight
->•
---- 30
J\A
=
150
75
100
ROCKPORT
200
LOUISVILLE
300
400 500
DUNCAN FALLS
DISTANCE (Ian)
Figure 6.3 Spatial variations of ozone, nitrogen oxides and participate
scattering within the boundary layer as sampled by two instrumented aircraft
on flights across portions of the Midwest. Both flights were made during a
regional pollutant build-up episode, 20 July 1978. The upper figure shows
sharp peaks revealing plumes with widths of 10 km to 100 km rising from back-
ground levels elevated above normal. The lower figure shows even greater
spatial variability in a region with lower background concentrations (figures
from Blumenthal et al., 1981).
295
-------
ti:-:-:-:-:-:-!-:
u
V
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<*- <4_ E
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C
at
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NVHX SS3T %
296
-------
was found in only 10 to 15% of the samples, those with concentrations over
- 14 ppb. This data and the data time series of Figures 6.3 and 6.5 show
the degree to which S02 is found in intermittent plumes of high concentra-
tion. The oxidant chemistry and dry deposition properties of the restrict-
ed regions containing this sulfur are clearly quite important in evaluating
the total S02 transformation of the Midwest.
By contrast, one half of the ozone is contained in a minimum of 35-40%
of the samples. The behavior of nitrogen oxides is intermediate between
sulfur dioxide and ozone, indicating locally great concentrations and also
a continuous background. The aerosol parameters, CN and bscat, are not
precise measures of sulfate, but the distribution function for bscat does
indicate the pervasive distribution of sulfate in space and time.
b. Ground-level measurements of pollutant variability
Figure 6.5 shows pollutant variability from another viewpoint, namely
the time series of concentration at a surface site. These measurements
were made near the small town of Glasgow in southern Illinois, about 100 km
north of Saint Louis (Ellestad, 1980). The striking attribute of the many
pollutants displayed is their variability in time, as the instruments sense
plumes from a variety of sources, such as cities, industries, and power
plants. While some pairs of species are correlated, others are not at all:
clearly the photochemistry of the situation is changing rapidly on a scale
of three hours or so. Once again, background S02 concentrations frequently
fall below a 1-2 ppb apparent detection limit. A longer time series of se-
lected pollutants is shown in Figure 6.6. During this summertime period,
the Midwest undergoes cycles of regional accumulation of long-lived pollu-
tants; summertime cold fronts and possibly associated thunderstorm activity
intermittently sweep into the area, introducing cleaner air (Chatfield and
Rasmussen, 1977). The well defined nature of urban plumes is apparent in
the variation of CFC13, which serves as an urban tracer. This accumulation
and cleansing behavior takes place over large regions, and it must also be
captured in a regional model.
6.3 Physical laws, averaging, and computer solutions; the mathematics of
subgrid-scale averaging
The mathematical description of air chemistry reduces to a simple
equation describing the sources, conservation, and reactions of chemical
species. For each species there is an equation of the following type:
9n
— = - v-(un_) + KvV + Q + H. (1)
at - " a a a a
Va
297
-------
CARBON MONOXIDE, ppm NITROGEN OXIDES, ppm
8 in
- £
"rid'3NOZO
NUCLEI
SULFUR DIOXIDE, ppb CONCENTRATION, lOOO/cm3
m
^—
01
c
O 01
s-
U O
c 2:
o
o
•M 01
C •!-
00 C
03 CU
00 00
cu ro .n
•a cu
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O CU -(->
r— +J
CU (O >>
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S- i—
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t— C
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cu
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cu
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i- 4-> i. -i-
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298
------- An error occurred while trying to OCR this image.
-------
nsp "SP
+r=l s=l k'
where
n = number density of species a
nr,ng = number density of other species (molecules/cm3)
u = velocity of air at each point
K = molecular diffusivity of air
k = reaction rate coefficient for species a and b to
' react and product species s
sa = stoichoimetric coefficient related to k (e.g.,
a'a~"r 2 for the reaction HOO + HOO ->- HOOH + 02 when
a = HOO)
Q = physical sources and sinks of material (e.g.,
pollutant emissions, dry deposition, etc.)
H = cloud and aerosol interactions (likely a complex
function of many reactive species)
The character of these equations differs for each constituent. For very
unreactive species, the equation is essentially a simple partial differ-
ential equation of transport with small sources and sinks (which may be,
however, locally concentrated). For reactive species, it has more the
character of a highly nonlinear set of ordinary differential equations.
These equations are several steps removed from those equations that
can be solved numerically on a computer. Lamb (1975, 1982) has pointed out
some of these differences, and much of this section follows his analysis
technique as applied to the problems of mesoscale air chemistry.
a. Averaging and computer simulation
When we wish to understand the processes of air pollution chemistry
using Equation (1), we are faced with two related facts. First, the air
motion fields that are shown in (1) include, in principle, every wind gust
and eddy down to the viscous distance and timescales. Such detailed infor-
mation is, of course, not available. Typically, what is actually available
is one of two data sets:
(a) Surface winds recorded by the National Weather Service stations, typi-
cally every three hours (at best) for stations separated by distances
of 40-200 km, and upper-level winds recorded every 12 hours from ra-
windsonde stations separated by distances of around 500 km. Local
wind gusts not representative of the whole area around the station
300
-------
are registered in these records.
f
(b) Wind vectors provided by weather forecast models with grid resolutions
of approximately 180 km, or similar winds from large mesoscale models
with grid spacing of 40-100 km. These are available every 10 to 60
minutes of simulated time. These models must smooth out or ignore any
wind gusts with wavelengths smaller than twice the grid spacing.
This discrepancy in spatial resolution must be addressed before we can
solve the transport equations.
Nonetheless, the equations of air chemistry as stated so far are valid
at all points in space. These equations cannot be solved, however, until
they are transformed into a system of difference equations through finite-
difference approximations. As they are most commonly stated (e.g., Lapidus
and Finder, 1982), these approximations require that grid points be located
closely enough together so as to capture most of the variation of chemical
concentrations; for example, that the concentrations can be reasonably re-
presented by low-order polynomials (regarded as truncated Taylor series).
This requirement is probably not met for most photochemical models, whether
describing industrial plumes, cities, or mesoscale regions. Figures 6.2
through 6.6 suggest that 5 or 10 km resolution would be required to capture
typical variations, and even finer resolution would in fact be necessary in
practice.
An alternative viewpoint is that the finite-difference equations de-
scribe grid-volume averages of species concentrations. This viewpoint ap-
pears, usually implicitly, in the construction of virtually all acid rain
and photochemical models, whether Eulerian or Lagrangian in concept. We
may define the volume average, represented by a tilde, like this:
"a ' { dv "a '
where V represents the grid volume. The continuous concentration field may
be represented in terms of means and deviations,
na = "a + na '
We can make this averaging explicit. By averaging Equation (1) over the
grid volume, we can produce an equation which may be treated by finite-
difference techniques:
a
—1 = - V.(un) + T + Q + H (2)
3t - a a a a
301
-------
Here the latter terms represent the interplay of subgrid-scale variations
(i.e., sub-grid terms). We will see that in some cases they are as impor-
tant as any other terms in the equation (refer again to Figure 6.1). The
equation is rather removed from the physical and chemical laws described in
Equation (1), but it is solvable on current computers if the subgrid terms
are known.
This alternative viewpoint emerges naturally from the finite-element
approach to the solution of partial differential equations, which is not
based on assumptions of Taylor series approximation to smooth functions.
By using the method of weighted residuals, and the "subdomain"-method ele-
ments and weighting functions, it appears possible to derive difference
equations that are like the finite-difference equations, but with volume-
averaging made explicit (Lapidus and Pinder, 1982).
b. Why are grid-point simulations often satisfactory?
For many species in many situations, the right-hand side of Equation
(2) is dominated by terms other than those describing subgrid-scale ef-
fects. Some reasons for this include:
(a) Transport may dominate. Species like sulfate aerosol have
sufficiently slow reaction and deposition processes that
concentrations are determined mainly by transport. In the
relatively clean air of the unpopulated, non-industrial western
North America or northern Canada, ozone, carbon monoxide, and
nitrogen oxides may also be primarily determined by transport
over hundreds and thousands of kilometers, except within ten
meters of the surface.
(b) Chemical sources and sinks may be uniform. In the clean
atmosphere just described, even hydroxyl radical (HO) may have
a relatively uniform distribution, even though its one-tenth-
second chemical lifetime is very short. In this case, HO
production and removal is determined by products of concen-
trations of ozone, carbon monoxide, nitric oxide, and less
reactive alkanes that are themselves smooth functions of
position. Species with chemical lifetimes longer than HO,
like formaldehyde and hydrogen peroxide, with chemical
302
-------
timescales of hours, will not so quickly reach steady states,
and can be more affected by horizontal and vertical transports.
(c) Intracell transport may be rapid compared to chemical reaction.
Lamb (1975) has shown that, under certain circumstances where
the source term Qa and chemical reactions are dominant, a
long chemical reaction timescale allows complete mixing.
(d) No branching of reactions. There may be subgrid-scale terms that
do not significantly affect those chemical species of most impor-
tance. The only reaction explicitly studied in this context is
NO + 03 * N02 + 02
(Lamb, 1975, 1980; Lamb and Shu, 1978; Shu et al., 1978). In
many circumstances, fresh emissions of NO may produce substantial
subgrid effects on small scales; for example, a substantial delay
in the conversion compared to calculations based on volume aver-
ages. Luckily, for many questions these effects are of secondary
importance: NO will react with ozone later, there being no other
competing reaction producing another fate. A delay of 10-20
minutes in the conversion of NO to N02 has apparently little
consequence for a subsequent reaction, the conversion of N02 to
HN03, which characteristically takes from 4 to 24 hours. N02
does have alternative fates: deposition on the ground or con-
version to nitric acid, so that subgrid processes affecting one
rate have important consequences on the production of acid aero-
sol and acid rain. Similar considerations hold for S02. .
c. Limits on the magnitude of subgrid-scale effects
Consider the simplest example of chemical reaction
a + b * c (products)
where the bimolecular rate coefficient is given by k. Let us compare the
magnitude of mean and subgrid-scale contributions to the single reaction
term
ka,b+c Vb = ka,b+c Vb
Since na and n& are positive definite, /n^> = a nanb for some
factor a between zero and infinity. The extreme cases are:
(a) a = 0 when na and n^ are non-zero only in different places.
(For example, each may undergo rapid chemical decay or be
transported out of the model volume.) See Figure 6.1.
(b) a = « when, for example, na = xnb (they have similar sources
and sinks), and they are very concentrated within the model
volumes (e.g., in very narrow plumes). Then:
303
-------
- x(nj) >> MS,,)* . n^.
We can get a rough idea of the way error depends on the degree of concen-
tration: if the chemical species are uniformly distributed over a small
volume v, much less than the grid volume V,
v = eV, E « 1,
and zero elsewhere, then it is easy to show that:
ka,b+c Vb = 1/e ka,b-H: "aV
If a single power plant plume occupies one-tenth of a 100 x 100 km grid,
and species a and b have^negligible concentrations outside the plume, then
the error in estimating nant, by nan"b is a factor of tenl
6.4 Situations in which subgrid effects are important
How can we reach some practical assessment regarding the representa-
tion of subgrid effects in the simulation of localized intense emissions
within large grid volumes? What happens when many nonlinear reactions
interact in time? Let us focus on one important simulation problem, the
emission of power-plant S02 into a relatively clean Midwestern rural area.
What are the difficulties in simulating the photochemical reaction of HO
with SO2?
A useful general guide can be found in the summaries of photochemical
smog reaction provided by the isopleth description used in the Empirical
Kinetic Modeling Approach (EKMA) to urban ozone chemistry. Isopleth plots
of 03, HO, HOOH, and HN03 are shown in Figures 6.7 and 6.8. These species
are portrayed as functions of hydrocarbon and NOX concentration, but only
the lower left corner of the diagrams presented are applicable to the situ-
ation of urban and power-plant plumes diluting into a regional atmosphere.
These figures, from Bergstrom (1981), are based on the SAI Carbon Bond
Mechanism of Whitten and Hogo (1978, 1979). The calculation algorithm
constituting this isopleth method and the further assumptions in the EKMA
process are reviewed in Hayes (1981) and references therein.
In brief, the two-dimensional isopleth plots show lines of equal con-
centration of various secondary pollutants as a function of only two vari-
ables, assumed initial hydrocarbons and nitrogen oxides, the primary emis-
sions. The EKMA analysis technique, essentially an extension of early
city-smog analyses, produces predicted secondary pollutant maxima that oc-
cur during the course of a day as a function of primary, completely unre-
acted emissions whose concentrations are taken to be early-morning values.
Therefore, this technique crudely calculates the history of the photochem-
istry for at least one day. However, other parameters, such as dilution of
material and photolysis rates, are important, and are crudely parameterized
in EKMA. Furthermore, other situations besides the morning-through-after-
noon period simulated in EKMA are important to large-scale transformation
rates. Nevertheless, the general shapes of the contour plots are generally
304
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0.1
0.1
0.0
0.8
i.o
1.2
1.4
1.6
i.a
0.8 1.0 1.2 1.4 1.6 l.f
NMHC.PPHC
0.4 0.6 0.8 1.0 1.2 1.1 1.6 1.9
o.z
"
0.2
0.4
0.6
0.8
1.0
NMMC.PfHC
1.2
1.4
1.8
2.0
Figure 6.7 Contour plots of hydroxyl radical and ozone concentrations
that are simulated as resulting from initial hydrocarbon and NOX concen-
trations. Point R depicts conditions representative of a relatively
unpolluted, rural Midwest atmosphere. Point Pa indicates conditions
generally representative of a power-plant plume dispersed through the
mixed layer. Point Pm represents concentrations that would be simulated
by a computer model with large (roughly 100 km) grid resolution, con-
taining pollutant concentrations from Pa and R. Above: HO radical con-
centration, contours in multiples of 10-6 ppm (roughly 2.3 x 10? molecules
per cm3). Below: ozone concentrations, contoured in ppm.
305
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1.8
1,8
2.0
Figure 6.8 Concentrations of hydrogen peroxide and nitric acid simulated
as resulting from the primary pollutant emissions of hydrocarbons and NOx-
Contours in parts per million. This figure and Figure 6.7 are taken from
Bergstrom et al. (1981). If these contours were equally spaced parallel
straight lines, secondary pollutants would be linear functions of primary
pollutants, and sub-grid processes would average out appropriately. They
are not,
306
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similar among a variety of simulations with varying asumptions (Hayes,
1981) and are complex enough to demonstrate the pervasive nature of model -
resolution effects.
What do these contour plots suggest about resolution problems in the
case of the HO + S02 reaction? A crude estimate of subgrid effects in the
simulation of a power plant plume may be made from Figure 6.7. Point R
represents a rural atmosphere with 70 ppbC of hydrocarbons and 6 ppb of
NOX. Point Pa represents the actual concentrations of hydrocarbons (70
ppbC) and NOX (50 ppb) in a power plant plume. Virtually all of the
NOX and S02 in such a plume comes from the power plant; virtually all of
the hydrocarbons come from the environment. Assume our regional model has
100-km grid resolution, and assume that this power-plant plume actually
occupies 10% of a given grid square, which is consistent with Figures 6.4
through 6.6. Mass conservation then requires that the grid-square-averaged
NOX concentration be 0.10 (plume concentration) + 0.9 (rural air concen-
tration), or, in this case, somewhat more than 0.10 of the plume concen-
tration. This is represented by point Pm in Figure 6.7.
Now let us do a calculation of the S02 conversion rate in two ways:
first, using the actual information on plume geometry and concentration;
and second, using grid-square-averaged concentrations and ignoring sub-
grid-scale effects.
The first calculation proceeds as follows. In the plume, which oc-
cupies 10% of the grid square, NMHC is 70 ppbC; NOX is 50 ppb; S02 is 50
ppb; and HO, from Figure 6.7, is 4xl08 ppm. From the expression conversion
rate = k[HO] [S02], the conversion of S02 in the plume is 3.2xlO~6 ppm min-
ute'1. In the rural, non-plume air, which occupies 90% of the grid square,
NMHC is 70 ppbC; NOX is 5 ppb; S02 is 2.7 ppb; and HO, from Figure 6.7,
is IxlQ- ppm. Thus, the non-plume conversion rate is 4.3x10 ppm min-
ute . Finally, accounting for the S02 masses in the plume and in the
rural air gives a total conversion rate over the grid square of 7.1xlO~7
ppm minute , which is equivalent to 0.57% hr"1.
The second calculation, which ignores subgrid effects, proceeds as
follows, where each figure given is a grid-square average. NMHC is 0.1
(70) + 0.9 (70) = 70 ppbC; NOX is 0.1 (50) + 0.9 (5) = 9.5 ppb; S02 is
0.1 (50) + 0.9 (2.7) = 7.4 ppb: and HO, from Figure 6.7, is 1.4xlQ-7 ppm.
The conversion rate is 1.6xlO~6 ppm minute"1, or 1.34% hr .
Clearly, very different rates of reaction may be calculated for S02
oxidation, depending on the degree to which spatial variations of pollutant
concentrations are recognized and simulated. In this case, the simulated
segregation of most of the S02 from a relatively highly-oxidizing rural air
lowered the simulated reaction rate of S02 by a factor of 2.6. Further-
more, the coarse-grid simulation would suggest that most sulfate production
was due to a local S02 source, while in fact most sulfate production was
outside of the plurne.
The numbers here are not particularly significant, but the sample
calculation could be applied to other isopleth diagrams and other situa-
tions; the shapes of the contour plots (in particular, their nonlinearity,
307
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a near-universal feature) suggest that large grid spacing will give sub-
stantial inaccuracies (see Figures 6.7 and 6.8). It is difficult to see
how such inaccuracies will simply "average out" due to the complexity of
the chemistry and meteorology; they will more likely compound in a confus-
ing way. (In this case, the cruder model gave a first-order reaction rate
for S02 nearer the currently accepted large-scale average, about 1% hr ,
but for the wrong reasons. It does not accurately reflect the chemistry of
the model.)
6.5 Approximate treatments of subgrid processes
It appears that a naive direct attempt to model the photochemistry of
the oxidants ozone, hydroxyl radical, and hydrogen peroxide as they affect
the transformation of sulfur dioxide and nitric oxide to acids would give
results somewhat worse than current "tuned" or empirical models. Such a
simulation would be reminiscent of the first numerical weather forecast by
L. F. Richardson (1922)--disastrous results, but very instructive. (Inci-
dentally, this forecast eventually led to techniques for treating small-
scale phenomena.)
There are several ways to treat small-scale processes in a large meso-
scale model:
(a) Fine-mesh calculations within the mixed layer. Under certain
conditions, mesh distances of 20 km or less could be used in a
computer the size of the CRAY-1 (750,000 64-bit words for storage
and user program). Such a mesh could be used to simulate two or
three lower layers which contain urban and industrial plumes.
Other layers would require much less resolution. There would be
more programming overhead, possibly including word-packing, less
accurate numerical techniques, and a simpler photochemical reac-
tion set. Calculations made using a smaller geographical domain
could show the magnitude of any remaining subgrid processes.
There are problems obtaining geographical data on emissions down
to this fine resolution, but the major NOX and S02 sources have
been identified (OTA, 1982), and an assumption that many hydro-
carbon emissions are primarily a function of local population
density appears justified.
(b) Adjustment of emissions or concentrations. This apparently has
been the past procedure. Hydrocarbon concentrations have been
estimated on the basis of nitrogen oxide concentrations and
emissions estimates (Lavery et al., 1980). Similar approaches
could be used to estimate net export of NOX and S02 based on
field studies,
(c) Lagrangian modeling of plumes can give estimates of the export of
material from cities and power plant plumes (Liu et al., 1981;
Durran et al., 1979; Graedel et al., 1981). Simulations would
be required for a variety of parameters (time of day, size of
city or power plant, combined city and industrial plant).
(d) "Two-fluid" or "three-fluid" modeling of plumes. It is possible
308
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to construct consistent descriptions of power plant plumes, city
plumes, and rural air on duplicate arrays for each species. The
same general description of dilution and dispersion plumes used
for Lagrangian models can be used to specify transfers of ma-
terial between plume and non-plume arrays. There are potential
difficulties when plume materials cross grid-volume boundaries,
and in treating the aging of plumes. The simplest technique is
to use separate arrays for fresh and old plumes, and transfer
from the first to the second that portion of material calculated
to cross a grid boundary. Old-plume air is similarly "trans-
ported" and diluted back into rural air. This sort of subgrid
modeling is most advantageous for larger grid meshes {- 100 km),
since the savings in computer storage and run time are propor-
tional to the inverse square of the grid mesh. Much storage is
freed for the extra arrays required. Certain processes very
difficult to model such as the transport of unreacted S02 and MO
at night, are better treated with the larger mesh size. The
method is most appropriate in simulating the general level of
concentration of plume material for non-linear chemistry, and may
introduce small errors in the location of pollutant material in
the cross-stream direction. Such errors appear unimportant.
Emissions inventories are also more suited for this sort of
analysis than for fine-grid models, since they are reported by
county or large area. All power-plant emissions in a single
model volume need to be lumped into a single collective plume
with an appropriate dilution rate, but this should capture the
basic features of subgrid chemistry and physics.
6.6 Boundary-layer transport and the need for fine vertical resolution
In the preceding sections, we have demonstrated the importance of
horizontal grid resolution in the numerical modeling of chemical reactions,
sources and sinks. Here we illustrate briefly the need for good vertical
resolution in describing near-surface chemistry in a coupled transport-
kinetics model.
There are two main reasons why fine vertical resolution is desirable:
(1) the Earth's surface and inversion base allow sinks for important com-
pounds, and (2) sources of pollutants often are concentrated initially into
plumes, and their plume chemistry is affected by their degree of concentra-
tion as seen in Section 6.4. The effect of concentrated sources is clear
in recent aircraft data. Data from the SURE program suggests that vertical
variations in S02, NOX, and presumably OH can be substantial.
Figure 6.9 shows two closely-spaced aircraft spirals in the Midwest.
One spiral shows little variation below the top of the inversion layer.
The other spiral shows dramatic fluctuations due to several plumes. Smith
et al. (1978) have also shown complex cross-sections of such plumes, and
Lenschow (1982) has observed the interaction of plumes and an inversion
layer in ozone profiles.
Numerous models exist which solve the species continuity equation (2)
with vertical transport only. Most of these have been used to study bud-
309
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3000
2500
2000
•=• 1500
W
Q
D
H
H
•<
1000
500
— Spiral 1 - Upwind
Spiral 2 - Over Station
Spiral 3 - Downwind
100
CONCENTRATION SO (ppb)
Figure 6.9 SOg profiles in the Midwest (reported by Blumenthal
et al., 1981) illustrate the great vertical variation of pol-
lutants that can be produced by intense sources. The profiles
with lower concentrations show air well-mixed in S02 upwind of
a source. The profiles marked with X's show the effect of a
complex source or complex striations produced by incomplete
mixing. Few models can afford the expense of simulating such
complexity: at least 12 levels below 200m would be required
in order to resolve all pollutant spikes.
310
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gets of longer-lived trace gases In unpolluted situations. The flux di-
vergence in those cases is represented by edciy diffusion:
o*. Z dZ
In this equation, N(z) is the molecular density at altitude z, and
x-(z,t) is the mixing ratio of species i. An eddy diffusivity, Kz,
typical of those used in one-dimensional simulations, appears in Figure
6.10. Note that a large diffusivity is assumed to extend to the ground.
In steady-state calculations appropriate for chemical budget estimates,
Kz(z) is time-invariant and the time rate of change of species concentra-
tion is set equal to zero.
There can be problems in using a transport formulation such as that
given in Figure 6.10 even in budget calculations of background-level chem-
istry. For example, Thompson and Cicerone (1982) have shown that, when a
rapidly-mixing boundary layer (Kz(z) > 106 cm2 s"1 at the surface) is
replaced by a transport-resistant boundary layer, dry deposition of meta-
stable trace gases, e.g., HN03, aldehydes, peroxides, is reduced and these
species can accumulate above the resistant layer.
More detailed studies (Carney and Fishman, 1982; Hov, 1982; Graedel
and Schiavone, 1981) also show the importance of surface layer resistance,
although the limited applicability of one-dimensional eddy transport to
most meteorological situations must be kept in mind when interpreting those
model results. These simulations indicate the need for several model
levels below 100 m when chemical reactions are rapid, as they are near a
source region. In some cases, however, diffusion in the surface layer may
be treated with an analytic approximation (Chapter IV, Section 5). Region-
al models of urban air pollution have also suggested the need for multiple
levels for the wind field in the boundary layer and the importance of sur-
face sinks for N02, S02, and HN03 even in a small distance scale_(Killus et
al., 1977).
An example of a source effect on boundary-layer chemistry can be seen
in Hov's (1982) simulation of the moderately polluted lower troposphere.
Hov's model uses 20 grid points log-linearly distributed from 0-2 km and
a time-dependent K2 (Figure 6.11) based on the diffusion of heat. The
depth of the convective boundary layer increases with heating, reaching a
maximum height, > 1200 m, by midafternoon and decreasing to 100 m by sun-
set. Dry deposition is also reduced at night. Thus, Hov finds that, with
boundary conditions appropriate for a moderately polluted atmosphere, ozone
above the boundary layer is nearly unchanged at night, even though its pho-
tochemical formation has ceased. Within the thin boundary layer, both de-
position and destruction by reaction with emitted NO cause ozone to de-
crease. In the early morning, increased convection mixes 03-rich air from
above toward the ground just as 03 is starting to be produced photochemi-
cally. The result is an increase in 03 throughout the boundary layer.
Surface deposition slowdown caused by a diurnally varying boundary layer
causes other longer-lived gases to accumulate in the lower troposphere,
e.g., HN03, PAN, S02. Some of these effects can be seen in Figure 6.12.
311
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10
LU
Q
Ql
0.01
I I I I I I I 11 I I
1 T^tn |
II1 I Mil
SBLX
x
NoSBL
j I _l_l_LLU I I I I I I I I I II II I 1 j
I02
!0
I05
Figure 6.10 Eddy diffusion coefficients with rapid
mixing extending to surface (no surface boundary
layer^ Ho SBL) and with surface boundary layer (SBL)
below 100 m (Thompson and Cicerone, 1932).
312
-------
15
13
.2 M
V)
c
I 9
i5
UJ 5
X
I
O.I 1.0 10 100
EDDY DIFFUSION COEFFICIENT K
1435
1295
1157
1021
886
754
624
499
380
268
170
90.6
38.2
12.8
3.68
1.00
m
o
x
H
1000
Figure 6.11 Calculated profiles of eddy diffusion
coefficient K(z,t) for chemical transport at various
times of day (Hov, 1982).
313
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l\W/f OH
1 , ^ I I (x 10*)
//
ii-n-ii-ii irii'irirH'irn ii-ii-n7ij-n'
•q.Braa \mffm;
^ii'ii'ii'ii'iru irii ii'irii'ii'!i-irii
1E5B-
UJ
o
HNO,(ppb)
• 11 • fI•11•if•11•u • i i • 11 • II • 11 • i I • 11 • n' 11' 11 ii
NMHC (ppbC)
TIME OF DAY
Figure 6.12 Time development of species in a moderately
polluted boundary layer calculated in a one-dimensional
model with the time-dependent eddy diffusion profiles of
Figure 6.11 . Note the build-up of material in the mid-
boundary layer region during the second day of simulation.
Emissions near the lower boundary are distributed over the
lowest three grid points: NCL, : 2 x 10" cnr2 s"1; S02,
NMHC (nonmethane hydrocarbons) and CO fluxes are 1.5,
1.5 and 10 times the NOX flux (Hov, 1982).
314
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The variable boundary layer also results in a large positive deviation from
the photostat!onary state (Calvert and Stockwell, 1982) within the convec-
tive boundary layer and a negative deviation at the surface.
The implications of these vertical gradients for longer-term and
longer-range transport are not clear. Some indication is given in a recent
study (Carney and Fishman, 1982) which focuses on chemical exchange between
the boundary layer and the free troposphere. In this calculation, a
"burst" of convective transport is simulated with a brief period of intense
upward vertical motion {i.e., high eddy viscosity). Greenhut et al. (1981)
have observed and others have modeled an important role for such mixed-
layer venting due to clouds (see Chapter V, Section 4.2). Hence, oxidants,
oxidant precursors, and acids may accumulate above the boundary layer, and
the ratio of hydrocarbons to NOX may have pronounced vertical structure
extending into the free troposphere.
Vertical gradients may be partially offset by advection. Graedel and
Schiavone (1981) and Schiavone and Graedel (1981) simulate urban chemistry
in two dimensions for both stagnant and convective conditions. Vertical
transport is limited to a three-element vertical mesh, but in the convec-
tive case a simple advection scheme is used to study horizontal transport
over a 140-km-wide region which includes a segment of intense pollutant
emission. Graedel and Schiavone (1981) predict that OH and H02 (as well as
03) are small near the source of intense hydrocarbon and NOX emissions
and increase with altitude. Graedel and Schiavone argue that, as a conse-
quence of the OH minimum, only air upwind and downwind of the emissions
center will be rich in oxidants and more stable products such as HN03 and
S02. Thus, unless they are efficiently scavenged or removed rapidly
through OH attack or photolysis, these species are available for transport
into the free troposphere and can travel far from a source region. For
example, Graedel and Schiavone (1981) predict that significant fractions of
anthropogenically-emitted C, S, and N compounds (74% C, 12% N, and 10% S)
will be transported beyond 100 km of the source region even with dry depo-
sition and aerosol scavenging of these species. Since scavenging is the
major loss mechanism, these fractions are very sensitive to the treatment
of heterogeneous removal. It should be pointed out that Graedel and Schia-
vone's prediction of minimum OH near the emissions source is in disagree-
ment with Hov's (1982). The reason is that oxidant levels are highly sen-
sitive to the assumed hydrocarbon/NOx ratio (Chapter V, Section 1), which
differs in the two studies.
From this brief summary of model and experimental studies, it appears
that three or four concentration values in the vertical might reproduce
observed pollutant variation. A larger number would be required to show
detailed features of the vertical distribution. Obviously, in formulating
a regional-scale model, the need for vertical resolution must be weighed
against the demands for horizontal accuracy and the number of chemical and
meteorological variables.
315
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7. NUMERICAL METHODS
7.1 Introduction
Long-range transport of air pollutants has received increasing atten-
tion during the last decade. Numerical models have been utilized to study
the dispersion, transport, and deposition of pollutants and to regulate the
emission of pollutants from various sources. Such models employ two funda-
mental but different approaches, the Lagrangian and Eulerian, which have
been reviewed by Anthes (1979) and Eliassen (1980) in detail. In order to
include necessary physical and chemical processes which may be highly.non-
linear, the Eulerian approach is considered better for regional-scale phe-
nomena. Detailed justification for this choice is given in Section 1 of
Chapter III.
In general, models for atmospheric dispersion and transport of pollu-
tants are "kinematic" models. In such models, the atmospheric circulation
itself is not calculated, but the limited information on the motion that is
known from observation is used as a model input. However, more general
systems can be developed in which the regional-scale dispersion and trans-
port model of pollutants is driven by a regional meteorological model which
will be capable of simulating real meteorological events.
For Eulerian grid computations, the concentrations of pollutants have
to be nonnegative, and when the concentrations have no sources or sinks
they must be conserved. Molenkamp (1968), Crowley (1968), Mahlman and
Sinclair (1977), Long and Pepper (1981), and McRae et al (1982) have pre-
pared excellent reviews on different numerical schemes applicable to a sca-
lar quantity, and comparisons among them also have been made. Those which
have shown potential for use in a multidimensional transport model are sum-
marized as follows:
7.2 Particle-in-cell scheme
In this scheme, pollutant concentrations are represented by Lagrangi-
an-marker particles inside a fixed Eulerian grid. The transports of pollu-
tants are obtained from the trajectories of the particles. The scheme has
been applied to a photochemical smog model by Sklarew et al. (1972), and to
a tracer model by Lange (1976). Later it was coupled with a two-dimension-
al mixed-layer model to study the transport of S02 in a boundary layer
(Anthes, 1979). The moment scheme devised by Egan and Mahoney (1972) may
be regarded as an extension of the original particle-in-cell concept. It
is a material-conserving computational procedure involving the zeroth,
first, and second moments of the concentration distribution within each
Eulerian grid element. The accuracy of the moment scheme has been further
improved by readjusting the second-moment of the distribution with a
width-correction technique (Pedersen and Prahm, 1974; Prahm and Pedersen,
1978).
7.3 Pseudo-spectral scheme
Using globally continuous and orthogonal functions, the spectral and
pseudo-spectral schemes can produce highly accurate numerical solutions to
316
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the nonlinear advective-diffusive-type equation. In applying these
schemes, periodic boundary conditions are necessary. This is recognized by
Christensen and Prahm (1976), who employed the pseudo-spectral scheme in
their pollution model. In order to expand the pollutant concentration into
Fourier functions, they have assumed that the concentration decays exponen-
tially in the two outmost row and column grid points, and that the time-
tendency of concentration vanishes at the boundary. Such unrealistic as-
sumptions may quite possibly cause steep gradients of concentration along
the boundary of a limited-area model. Other applications of the pseudo-
spectral scheme to atmospheric advective and diffusion models are reported
by Prahm and Christensen (1977), Berkowicz and Prahm (1978), and Wengle and
Seinfeld (1978).
7.4 Finite-element scheme
A linear combination of locally-continuous basis functions can be cho-
sen to approximate the advective-diffusive equation. The scheme requires
that the error between the differential equation and the approximate equa-
tion be orthogonal to all the basis functions. Then the coefficients in
the linear combination of basis functions can be obtained by solving an
algebraic matrix equation. Basic principles of the finite element scheme
can be found in Strang and Fix (1973). The scheme with simple chapeau
function has been applied to the pollution model with even grid spacing by
Pepper and Baker (1974). The use of the scheme on variable grid spacing is
discussed by Raymond and Gardner (1976) and Pepper et al. (1979). Recent-
ly, a substantial effort to apply finite-element schemes with high-order
basis functions to air pollution models has been undertaken by a research
group at the Lawrence Livermore National Laboratory (Lee et al., 1976; Lee
and Gresho, 1977; Gresho et al. 1979). Other groups have also been heavily
engaged in research in this area. The computational algorithm is quite in-
volved and complex.
7.5 Upstream-correcting scheme
To solve the advection equation for a nonnegative scalar, the simplest
numerical scheme is the upstream scheme, which does not generate numerical
dispersion but suffers from very strong numerical diffusion (Molenkamp,
1968). The deficiency of the upstream scheme has been corrected by hybrid-
izing with other mass-conserving schemes. The flux-corrected transport
scheme (Boris and Book, 1973, 1976; Book et al., 1975; Zalesak, 1979) and
the self-adjusting hybrid scheme (Harten, 1978; Marten and Zwas, 1972) are
based on a hybrid scheme in which the advective flux is given as a weighted
average of the first-order positive definite scheme's flux and the high-
order mass-conserving scheme's flux. These methods are used to study
shocks and contact discontinuities, and results are very accurate. How-
ever, the usage of these schemes is rather limited for atmospheric models
of pollutant transport because of the excessive computational time re-
quired. Purnell (1976) has introduced the upstream-interpolation scheme.
The advection term in the original upstream scheme is approximated by a
cubic spline instead of a truncated Taylor series with first-order accu-
racy. This scheme has been applied by Mahrer and Pielke (1978) in their
studies of air flow over a mountain and sea and land breezes. In their
study of stochastic condensation theory, Clark and Hall (1979) have sug-
317
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gested a nonlinear switch in their hybrid numerical scheme of the upstream
scheme as a low-order approximation and Crowley's (1968) scheme as a high-
order approximation, in order to assure positive definiteness of several
field variables. This approach is adapted from a concept by Mahlman and
Moxim (1978). The nonlinear switch does not satisfy the sufficient condi-
tions to be a monotone operator which guarantees positive definiteness, as
described by Marten (1978), but the switch does prove to be adequate for
their numerical experiments. Smolarkiewicz (1982) has improved Crowley's
original (1968) scheme by retaining the cross-differential terms (Leith,
1965) of the numerical approximations in the multidimensional flux-form
advection equation. Smolarkiewicz (1983) has also proposed a new posi-
tive-definite advection scheme which has a simple form, small implicit
diffision, and a low computational cost compared with the previously
mentioned variations of the upstream-correcting scheme. The implicit
diffusion is first identified in an analytic form, and then a simple anti-
diffusion procedure is developed to restore the artificial diffusion with-
out inducing numerical dispersion, which could generate the negative scalar
concentration values.
7.6 Numerical schemes for chemical systems
From the previous discussions, it is clear that almost none of the
existing acid deposition models in the literature has included a detailed
description of chemical interactions and transformations of acid precursors
(Rodhe et a!., 1981). The previous chapter (Chapter V) has described in
detail the wealth of knowledge that is being ignored by the simple "percent
per hour" sulfate loss rates that are in common usage. One virtue of such
a simple chemical model is the avoidance of sophisticated numerical.analy-
ses necessary for dealing with the complex system. However, if we are to
understand the chemistry of acid deposition, then we must face the full
complexity as outlined in Chapter V.
It is well known that differential equations arising from chemical
kinetics interactions are often difficult to solve numerically (Curtiss and
Hirshfelder, 1952; Chang et al., 1974). This difficulty is generally de-
scribed as the problem of "stiffness." A complex chemical system often
includes many interactions with greatly differing reaction rates or time
constants. This results in a unique computational dilemma for the mathe-
matical system: when the desired solution contains closely-coupled com-
ponents with greatly differing time constants, in order to obtain the solu-
tion at late times (or great distances), one must compute accurately at all
times the evolution of the already-equilibriated components, which in fact
may contribute very little to the components of interest. Many powerful
and highly-accurate numerical techniques have been developed and used for
stiff ordinary differential equations (Gear, 1971; Lapidus and Seinfeld,
1971). However, there are only limited applications to coupled transport
and chemical kinetics equationss e.g., systems of coupled partial differ-
ential equations (Chang et al., 1974; Edelson and Schryer, 1978; McRae et
al., 1982). In general, there are three approaches: the method of frac-
tional steps, the method of lines, and family grouping.
The method of fractional steps (Yanenko, 1971), or the operator split-
ting technique, at first may appear to be a natural method for this type of
318
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system of equations. By splitting the transport operator and the chemical
operator and treating each- with the most accurate numerical scheme, this
method conceivably can deal with all the intrinsic difficulties of this
system. However, it quickly becomes evident that every time the transport
operator is applied, the chemical system is rudely perturbed and a signi-
ficant amount of computing is then required to smooth the total system
again. This is very similar to the basic difficulty in computing nonlinear
chemical interactions in a Lagrangian Gaussian plume model. The Lagrangian
transport of Gaussian plume is but a special case of the split transport
operator for the whole system. The recent review by McRae et al. (1982)
provides an excellent detailed summary of recent findings.
In the method-of-lines technique, the transport operator is first
discretized over an Eulerian grid, perhaps with one of the previously men-
tioned schemes. The resulting system of ordinary differential equations
can then be solved with an appropriate stiff solver. This approach is both
accurate and flexible for one-dimensional models, but already for two-di-
mensional models it is found to require an inordinate amount of computer
memory and execution time. For example, a 50 by 50 two-dimensional grid
with 30 chemical species would result in a system of 75,000 coupled ordi-
nary differential equations. Clearly, this approach is impossible for
three-dimensional models.
The final alternative, family grouping, is less mathematical and de-
pends heavily on our understanding of the whole chemical system. Although
it has seen broad applications both for stratospheric models and air qual-
ity models, there exists no detailed analysis from the computational (nu-
merical) viewpoint. In this approach, subsets of closely-coupled chemical
species are first identified, which then provide a reduced set of equations
to be solved. At each time step, the families are then partitioned into
their components, which in turn determine the various rates of chemical
interactions. This final partitioning can only be achieved with a heavy
dose of physical insight and intuition. Without these physically-based
constraints, usually in the form of algebraic relations, the system of
mathematical equations representing the partitioning operation is underde-
termined. The choice of family groupings is non-unique and often changes
as the initial conditions and physical problems change. In contrast to the
other two approaches, this tends to limit the generality of the solution
scheme. Much research is still needed in this area, especially since this
may be the only viable approach suitable for the detailed chemistry in acid
deposition models.
8. MODEL VALIDATION AND SENSITIVITY ANALYSIS
Hypothesis: The long-term-average distribution of wet and dry deposi-
tion is determined by highly-variable deposition patterns that can be re-
lated to distinct synoptic types. The deposition associated with these
types is a function of ambient concentration, wind speed, temperature, and
solar intensity and cloud and precipitation type and amount. Both the am-
bient concentrations and the meteorological components have predictable and
stochastic components. Therefore, to understand the long-term distribution
of total acid deposition, it is necessary to study and understand both the
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predictable and stochastic components of the deposition patterns associated
with each synoptic type.
8.1 Introduction
Current models of long-range transport and acid deposition are highly
parameterized models of the complex meteorological and chemical processes
that determine acid deposition. Deterministic (as opposed to statistical)
models, incorporating all relevant meteorological and chemical processes,
are necessary for an understanding of the entire process of acid deposi-
tion, from sources to receptor, an understanding of the relative contribu-
tions to the total process by individual components, and a proper design of
control strategies.
The current status of acid precipitation models is summarized well by
Dittenhoefer (1982):
"Considerable improvements in the accuracy of LRT/acid precipitation
models are needed before they can be applied in the evaluation of al-
ternative emission control strategies and in policy and planning
studies. The predictive success of LRT models is limited by a lack of
detailed understanding of the temporally-and spatially-varying proces-
ses of emission, transport, chemical transformation, and deposition;
by the constraint of treating these processes in a computationally
efficient manner; and by the adequacy of input data bases.
Little consensus of opinion exists among modelers concerning the
specification of the wind field, and the methods employed all suffer
from various shortcomings. These transport mechanisms generally ig-
nore vertical motions, wind shears, diurnal mixing depth variations,
vertical pollutant profiles, atmospheric thermal structure, precipi-
tating cloud type, and major scavenging mechanisms. Although these
factors are important for short-term, episodic analyses, it remains to
be seen if these limitations seriously affect long-term impact assess-
ments.
Most LRT models treat sulfur chemistry only as a highly parameterized,
linear process, ignoring total acid formation and precipitation neu-
tralization processes. Models fail to treat aqueous phase chemistry,
which may be less than first order with respect to emissions, and
ambient air quality (i.e., photochemical oxidants), which may limit
sulfuric and nitric acid formation. Until a nonlinear, multi-species
approach is incorporated into these models, accurate estimates of the
Tmpact on acid deposition resulting from incremental changes in emis-
sion are not possible."
Even when a deterministic model combining meteorology and chemistry
with state-of-the-art components is developed, its use in identifying and
isolating physical processes, improving understanding, and evaluating al-
ternative control strategies is not straightforward. This is because even
the best deterministic model will always have an uncertainty (random or
stochastic) component associated with any given prediction or realization
because of inherent uncertainties in the model input data as well as the
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model parameter!'zations and numerical approximations. While a model may be
"perfect" in the sense that a large number of realizations with slightly
perturbed initial conditions, physical parameter!'zations, etc. will cluster
around the true solution, any single realization cannot be expected to co-
incide perfectly with the particular atmospheric evolution. This stochas-
tic component undoubtedly varies greatly under different weather regimes
and seasons. Thus, a careful design of a scheme for evaluating determin-
istic models is necessary, and this design must explicitly recognize the
stochastic nature of the problem. A similar strategy must be worked out
for application of the model by policy-makers--for example, to test the
impact of reduced emissions in certain areas of regional acidification.
Without a recognition of the stochastic component, misleading conclusions
regarding the effectiveness of proposed regulatory options could easily
result.
This fundamental uncertainty problem is schematically illustrated in
Figure 8.1. Uncertainties and errors (represented by volumes in n-dimen-
sional space) associated with meteorological data and the numerical and
physical approximations in the numerical model lead to uncertainties in
meteorological solution space. These uncertainties, together with addi-
tional uncertainties introduced by the emissions inventories, initial chem-
istry data, and the chemistry parameterizations, lead to a final uncertain-
ty in the concentration (or deposition) space. The problem is to quantify
how these uncertainties propagate through the entire system, amplifying or
damping in the process.
This section on validation assumes that a complete deterministic model
with all relevant physical and chemical processes can be developed,.and
that this model is "perfect" in the sense described above. It outlines a
strategy for testing the hypothesis that the acid deposition model is a
perfect model and for assessing the uncertain, or stochastic, component of
its simulations or predictions under various meteorological conditions.
An outline of a strategy for validating a complete model is as fol-
1 ows:
1. Validation of individual components and assessment of uncertainties
1.1 Meteorological components
a. Testing of physical parameterizations, such as PBL processes,
in one-dimensional models under simplified atmospheric condi-
tions (e.g., homogeneous, steady state) against observations
for special field programs (e.g., SESAME).
b. Verification of complete meteorological model using opera-
tional and special data sets with various objective measures
of skill.
1.2 Chemistry components
a. Testing of chemical parameterizations, such as the aqueous
phase reaction scheme, in zero-dimensional (box) models using
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SOURCES OF UNCERTAINTY IN THE
REGIONAL ACID DEPOSITION MODEL
MET
DATA
MET MODEL
•PHYSICS
•NUMERICS
MET
-** SOLUTION
CHEM
INITIAL
DATA
EMISSIONS
AQM
TRANSPORT
DIFFUSION
TRANSFORMATION
REMOVAL
CONCENTRATION
SPACE
Figure 8.1 Sources of uncertainty in the regional
acid deposition model.
-------
laboratory data.
b. Verification of complete chemical model components (such as
the gas phase chemistry submodel) against results of more
complex models (e.g., Whitten et al., 1980; Atkinson et al.,
1982), validated against smog chamber studies (Jefferies et
al., 1982).
c. Review of existing field data to determine possible assess-
ments of chemical components under simplified meteorological
conditions.
2. Validation of complete acid deposition model
2.1 Analysis of deposition associated with each synoptic type, sensi-
tivity tests, Monte Carlo simulations, tests against special data
sets, verification of "structure" or "climatology" of model.
2.2 Preparation of climatology of synoptic types and integration over
expected frequency to obtain monthly, seasonal, or annual aver-
ages. Comparison against long-term average data.
8.2 Discussion of validation strategy
There are two phases to the validation strategy. The first phase is
to validate each component separately, under simplified conditions, to es-
timate the error (uncertainty) associated with that component. The uncer-
tainty of a particular component is evaluated by performing a set of com-
puter experiments in which input data are varied, and then comparing the
results of each experiment to observations. The variations in input data
are determined by the uncertainty in the data. From the set of compari-
sons, statistical measures such as variance and bias are calculated, and
significance tests are performed for each model component evaluation. This
information comprises the estimate of error associated with each component.
An example is the testing of the physical components of the meteoro-
logical model, such as radiation or boundary layer physics, against special
data sets. For example, Driedonks (1982) describes the performance of a
slab model for the evolution of the mixed layer during the day. Zhang and
Anthes (1982) tested Blackadar's PBL model under both day and night condi-
tions using the SESAME 1979 data set.
Similar tests must be done for all components, including the chemistry
modules. The data to be used in these tests can be obtained from field
studies, laboratory experiments, and more complicated models that have al-
ready been validated. For example, assume the gas phase chemistry model is
based on existing, more complicated models (e.g., Whitten et al., 1980)
which are verified with smog chamber data (Jefferies et al., 1982). In
this case, the model component is tested against existing model results.
For the component evaluations, a wide range of possible conditions can
be tested. When it is determined that critical data are inadequate, addi-
tional field or laboratory studies will be needed, and the model components
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can be used to help design the necessary measurements. However, we anti-
cipate that sufficient data already exist for a preliminary evaluation of
each component.
In addition to evaluation of the individual components, similar eval-
uations can be made with various combinations of components. For example,
the radiation and turbulent mixing parameter!' zations can be combined and
tested in a one-dimensional model. Similarly, gas and aqueous phase chem-
istry can be combined and evaluated in a zero-dimensional model. The com-
plete meteorological model can be evaluated separately from the chemistry
component, using the various measures of skill discussed in Chapter HI.
Likewise, the chemistry model can be exercised under simplified meteorolo-
gical conditions such as discussed by Lamb (1982) regarding the evaluation
of regional oxidant models.
The testing of a complete acid deposition model also must recognize
the stochastic component of the problem. Since the uncertainties in many
variables must be considered, it is necessary to use variations of the Mon-
te-Carlo method to estimate the uncertainties associated with predictions
under various meteorological situations. A complete Monte Carlo treatment
--the random varying of all of the sources of model uncertainty — is not
feasible or required. Many of the variable uncertainties can be inves-
tigated using sensitivity studies and/or by grouping dependent variables
together into a single examination. Some aspects of this approach have
been used in the evaluation of global climate models (Katz, 1982).
The first step in the validation of an entire model is the identifi-
cation of weather types (Figure 8.2) that contribute to the annual depo-
sition. For example, Niemann et al . (1979) identify ten synoptic weather
types that contribute to regional sulfate episodes. Ladd and Driscoll
(1980) present objective and subjective methods of identifying weather
types. The types must be chosen carefully to include dry and wet deposi-
tion patterns associated with nitrogen as well as sulfur compounds. Those
types that produce the greatest contribution to the total annual deposition
should receive the greatest attention. These types can be identified from
previous observational studies (e.g., Niemann, 1982) as well as preliminary
exercises of the complete model.
Having stratified the meteorology into a reasonable number (M « 10-20)
of types, where the expected annual frequency f^ of each type is known, a
number (N) of modified (as defined above) Monte-Carlo runs can be made for
each type. The number of runs is determined by the number of model uncer-
tainties that need to be considered. From these runs, the mean deposition
DJ and the variance Vj of the deposition can be computed for each i'th
type (Figure 8.3). The annual estimate of mean and variance can be com-
puted from
, M
U - £ ^i S
and
324
f. (1)
-------
All
Others
(13)
Figure 8.2 Example of synoptic types con-
tributing to annual deposition in a given
region.
325
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CANADA
UNITED
STATES
Figure 8.3 Illustration of the average (solid line)
and standard deviation (dashed line) of deposition
obtained from N Monte Carlo runs under synoptic type M,
326
-------
M
The standard deviation, a, is simply /V.
The model can now be verified in the climatological sense by comparing
paring Uwith the observed U. The standard deviation gives an estimate of
the uncertainty associated with IT. The smaller V, the greater the predict-
ability. Verification is done by testing the probability that the differ-
ence between the observed and predicted values of D" is significant. The
estimation of variance, bias, noise, and gross error (Fox, 1981) is also
important for assessing the significance of changes produced by variations
in the emissions. The statistical significance of such changes can be es-
timated by standard tests (e.g., F-Tests and T-Tests).
8.3 Synergistic relation of modeling and measurement programs
Complete validation of a total model is an evolutionary process.
Appropriate data bases for testing the model under some of the important
conditions exist, but it is likely that these bases are incomplete. Model
simulations and tests can be helpful in identifying the weaknesses in the
data bases, and can be used in the design of future measurements programs.
A synergistic interaction between modeling and field experiments can lead
to improvements in both modeling and measurement programs.
Ideally, one would test a model under different emissions, since the
ultimate practical use of a model is to assess the impact of changes in
emissions. However, it is unlikely that in such experiments varying real
emissions will be possible. Therefore, a model must be used in much the
same way that climate models are used to assess the effects of C02 in-
creases or changes in sea-surface temperature. First the model is vali-
dated in a climatological sense, using current emissions; then the assump-
tion is made that the changes in deposition associated with hypothetical
changes in emissions would be a good estimate of the actual changes that
would occur if emissions were changed.
8.4 Sensitivity analysis
Every model is an approximation of the existing state of knowledge.
Even if it is validated to the fullest extent possible with existing data,
its prognostic application, by definition, means projection into the un-
known. The correctness of its fundamental physical principles and the
demonstrated validity of its theoretical equations lend a significant level
of credibility to model predictions (assessments). Nevertheless, it is
perfectly reasonable and often necessary to ask "How certain are the pre-
dictions?" Sensitivity analysis is a technique for providing some quan-
tifiable answers to this often-posed question.
All input information to a model contains inherent uncertainties.
These data must then be organized into forms usable by a model. Whenever
data are manipulated, additional errors may creep in. Given an estimate of
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the range of uncertainty in the data set, it is possible to derive the
corresponding range of predictions and some estimate of the most likely
results. Strictly speaking, the initialization procedure for a meteoro-
logical model (Chapter IV, Section 2) is a well-studied special case of
model sensitivity analysis. The need also exists for a parallel procedure
for chemical species. Unfortunately, no such work has been done except for
a preliminary report by Dennis et al. (1982). The available sensitivity
analysis on uncertainties in source functions with Lagrangian Gaussian
plume models sheds very little light on Eulerian grid models due to the
intrinsic linearity of the former type of model. The detailed consider-
ation of nonlinear processes presents the most interesting possibilities.
Sensitivity analyses on model input parameters such as chemical kine-
tics rate coefficients, hydrological submodel parameterizations, radiative
processes, or even model grid resolutions have only been done in a limited
sense in stratospheric chemical models and air quality models (Duewer et
al., 1977; Stolarski et al., 1978; Cukier et al., 1973; Schaibly and Schu-
ler, 1973; Til den and Seinfeld, 1982). The techniques range from simple
parametric analysis to full Monte-Carlo simulations. Although these tech-
niques are all well established, their pragmatic implementation in acid
deposition modeling is yet to be studied.
328
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CHAPTER SEVEN
SUMMARY AND CONCLUSIONS
In this report, we have reviewed the existing numerical models for
acid deposition, air quality, and mesoscale meteorology. We have not at-
tempted an exhaustive review, but rather a critical review based on analy-
sis of the fundamental physical processes. After having examined much of
the relevant, published literature, we have concluded that a comprehensive
acid deposition modeling system on an Eulerian grid can be developed in a
few years by a sufficiently broadly based and closely coupled research and
development team.
While most, if not all, past and present models have contributed to
our understanding of acid deposition phenomena, there are important fun-
damental weaknesses in existing models of regional acid deposition. The
crude, empirical parameter!zations of major physical processes in these
models severely limits their predictive capability. The lack of proper
upper-air transport and dispersion, omission of detailed chemical reac-
tions, lack of cloud physics, and the absence of terrain and surface ef-
fects in existing models are particularly critical. Chapter III has sum-
marized the current status of existing models with emphasis on the extent
to which they deal with these key physical processes.
Recent advances in understanding these key processes, as discussed in
Chapters IV and V, suggest that major improvements in modeling both the
meteorological and chemical aspects of acid deposition processes can be
made. Our reviews of these advances are quite detailed, and motivated by
our desire to highlight the vast untapped scientific resources for acid
deposition modeling. We devoted considerable space to the procedures for
assessing the so-called "goodness" of mesoscale numerical models. There is
an urgent need to extend these concepts to regional acid deposition models.
This is particularly important in view of the potential role of acid depo-
sition models in regulatory considerations.
As is well recognized, there is an embarrassing absence of chemical
details in existing acid deposition models. Although there are many rea-
sons for this, the lack of understanding of the fundamental chemistry is
certainly not one of them. The wealth of information noted in Chapter V
clearly supports the cry for action now. Although there are gaps in our
understanding of all the transformation and deposition mechanisms in the
acid rain process, without a comprehensive model we cannot utilize the
available scientific knowledge properly and cannot even reliably evaluate
the remaining uncertainties. The chemical system is so complex that, with-
out the proper accounting of the full set of interactions, it is difficult
to assess the need for better information on solution phase chemistry and
329
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heterogeneous processes, for example.
However, these advances cannot be achieved without research and de-
velopment efforts on all components within the idealized modeling system
concept discussed in Chapter VI. The essential areas of model validation,
initialization, and sensitivity analysis, all critical factors in the de-
cision-making process, need particular attention. The development of such
a comprehensive model system requires a clearly focused, multidisciplinary
group effort under strong scientific leadership. Much potentially useful
work relevant to the design of a comprehensive acid deposition model has
already been done, and this work should be used whenever feasible in the
development of the model system. Nevertheless, critical reexamination of
available results in the context of the structural requirements of the com-
prehensive model system is still required. Because of the desire for mod-
ular structure, for ease in incorporating new concepts and ease of physical
interpretation of modeling results, we judge the Eulerian framework as most
suitable for representing the essential physical and chemical processes in
regional acid deposition.
In our companion report, Regional Acid Deposition: Design and Manage-
ment Plan for a Comprehensive Modeling System, we present a framework for a
model system incorporating our findings.This companion document also out-
lines the implementation of this modeling project and some details on model
components and system integration, keeping in mind the broad spectrum of
potential users ranging from research students to regulators.
330
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CHAPTER EIGHT
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
. REPORT NO.
2.
3. RECIPIENT'S ACCESSIOWNO.
TITLE AND SUBTITLE
REGIONAL ACID DEPOSITION:
PROCESSES
5. REPORT DATE
MODELS AND PHYSICAL
6. PERFORMING ORGANIZATION CODE
. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
The NCAR Acid Deposition Modeling Project
. PERFORMING ORGANIZATION NAME AND ADDRESS
National Center for Atmospheric Research
P. 0. Box 3000
Boulder, Colorado 80307
10. PROGRAM ELEMENT NO.
CCVNIA/01 Task 2295 (FY-84)
11. CONTRACT/GRANT NO.
Interagency Agreement No.
AD49F2A203
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory - RTP, NC
Office of Research and Development
U. S. Environmental Protection Agency
Research Triangle Park, NC
13. TYPE OF REPORT AND PERIOD COVERED
Final - 7/1/82-5/31/83
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This report represents the results of a ten-month study on the current status of
research on fundamental concepts and physical processes relevant to regional acid
deposition modeling. The role of models in environmental assessment is first de-
scribed. This is followed by a review of existing models in a chapter designed more
to establish a reference framework for the bulk of the report than to provide a
comprehensive review. Most, if not all, of the principal concepts in model con-
struction and evaluation are discussed. Extensive discussions of state-of-the-art
regional meteorological modeling and the chemistry of acid generation in the tropo-
sphere are presented in Chapters IV and V. Chapter VI then focuses on the develop-
ment of a new generation of acid deposition models. Based largely on the topics
reviewed in earlier chapters, the desirable features of a comprehensible model are
described, with emphasis on topics needing great improvement or omitted in present
models. These include emissions data, detailed acid rain chemistry, cloud proces-
ses, dry deposition, model validation, and sensitivity analysis.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b-IDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Group
13. r,.5Ta.iaunc\ STATEMENT
RELEASE TO PUBLIC
EPA . arm 2220 ' (9-73)
19. SECURITY CL.ASS / fins Report)
UNCLASSIFIED
21. .MO. OP PAGES
120. SECURITY CLASS /This page I
UNCLASSIFIED
22. PRICE
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