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OCR for page 55
3 Theoretical Models of
Regional Air Quality
Analysis of the spatial and temporal behavior of atmc-
spheric parameters and climatological patterns depends on
~ thorough theoretical understanding of the physical and
chemical processes involved. That understanding, in
turn, depends on observations of phenomena in the field
and in the laboratory. One purpose of analyzing the
relationships between emissions of precursor gases and
deposition of acidic or acid-forming substances is to
develop means for assessing the potential effectiveness
of alternative proposals for mitigating the adverse
effects of acid deposition. Uncertainties in the current
understanding of the relevant physical and chemical
processes are reflected in uncertainties in analytical
models of these relationships.
Construction of analytical models is a typical method
by which scientists approach complex problems. For many
years earth scientists have been developing knowledge
about flows of substances in the environment (within and
among the atmosphere, hydrosphere, biosphere, and
lithosphere). All elements cycle naturally through the
environment; sulfur and nitrogen are two prominent
examples. Models have been developed--some conceptual,
some empirical, some theoretical--to organize that
knowledge in ways that allow predictions to be made that
are subject to testing. In recent years, this analytical
approach has taken on considerable practical importance,
because of the need to assess the implications of anthro-
pogenic disturbances on natural ecological processes. So
it is with models of acid deposition.
In this report we are concerned with only part of the
phenomenon of acid deposition: the relationships between
emissions and deposition. Models of the cycling of sub
S5
OCR for page 56
56
stances in the hydrosphere, biosphere, and lithosphere
are beyond the scope of this report.
Models of the distribution of emissions through the
atmosphere and their subsequent deposition can be divided
into two classes: theoretical and empirical. Empirical
models consist of analyses of observations in the field;
Chapter 4 deals with empirical approaches used to manipu-
late data and test hypotheses. In the class of theo-
retical models are both deterministic calculations and
estimates of material balance (or budgets); the current
state of the art in these approaches is described below.
MATERIAL BALANCE
The method of material balance or budgeting involves
assessing the gross flows of a substance into and out of
compartments of the environment. The compartments are
defined for the purposes of analysis; they are generally
large, so that detailed behavior of constituents is not
considered. Leaving out the detail, of course, means
that the results may provide only general guidance and
understanding.
The most straightforward approach to budgets for acid
deposition is to segment processes into one or more
compartments, allowing flow between the compartments
(e.g., Charlson et al. 1978). Budgets for sulfur in the
atmosphere have been constructed for the global atmo-
sphere (Granat 1976) and for regions of Europe and
eastern North America (e.g., Galloway and Whelpdale 1980,
Granat et al. 1976, Shinn and Lynn 1979). A summary of
two budgets for eastern North America is shown in Table
3.-1; these calculations were made for each category by
somewhat different means. They present a qualitatively
similar (but quantitatively different) picture of the
sulfur oxide transport and deposition in the eastern
United States as well as export to the Atlantic Ocean.
Other than giving estimates for the average annual
deposition over large areas, these types of calculations
reveal little about the consequences of changing anthro-
pogenic emissions of sulfur or nitrogen. They also
provide no guidance about the deposition of acid-producing
material on specific regions that are ecologically
sensitive. They do, however, provide a sense of the
scale of exports of atmospheric pollutants from one
region to another.
OCR for page 57
57
TABLE 3.1 Companson of Atmospheric Sulfur Budget
Estimates for the Eastern United Statesa and Northeastern
United Statesb in teragrams (million metric tonnes) per year
Galloway and
Whelpdale (1980)a
Shinn and Lynn
( 1 979)b
Input
Man-made emissions 14 7.5
Natural emissions 0.5 0.6
Inflow from oceans 0.2
Inflow from west 0.4
Transboundary flow 0.7
15.8 8.1
Output
Transboundary flow 2.0 (1.1)
Wet deposition 2.5 1.5
Dry deposition 3.3 2.5
Outflow to oceans 3.9 3.0
11.7 8.1
aArea east of 92° W (Mississippi River).
Connecticut, Delaware, Illinois, Indiana, Kentucky, Maryland,
Massachusetts, Michigan, New Jersey, New York, Ohio, Pennsylvania,
Rhode Island, Virginia, and West Virginia.
One application of the method has been to assess the
transport of pollutants across international boundaries.
Because certain pollutants, particularly sulfates and
nitrates, may be transported large distances from the
sources of their precursor gases, air pollution is an
interstate and even an international issue. Not all the
sulfur and nitrogen emitted from sources in the United
States comes to the ground in the United States, and not
all the sulfur and nitrogen that comes to the ground in
the United States is emitted from sources in the United
States. The same, of course, can be said for states and
regions within the United States.
It has been estimated that, of the total sulfur
emitted to the atmosphere in the eastern part of the
United States, about one third is transported to the
western Atlantic Ocean and beyond, while roughly one
sixth is exported to Canada. The remainder, about one
half, falls in the United States (Galloway and whelpdale
1980).
The fraction of the exports of atmospheric sulfur from
the United States to Canada that is deposited in Canada
is unknown. It has been hypothesized that the fraction
of Canadian emissions of sulfur that falls in Canada is
larger than the fraction of U.S. exports to Canada that
OCR for page 58
58
falls in Canada. This supposition can be explained by
the differences in the deposition processes for SO2 and
sulfates and the fact that U.S. exports of atmospheric
sulfur to Canada are likely to be richer in sulfates than
Canadian emissions. Nevertheless, more sulfur is
deposited than emitted in eastern Canada (Galloway and
Whelpdale 1980), so U.S. exports can account for
substantial quantities of the sulfur deposited there.
DETERMINI STIC MODELS
Most of the effort to develop models of acid deposition
during the past decade has been devoted to deterministic
descriptions of the distribution of sulfur oxides in
plumes. The work has grown from efforts to develop plume
models for studying effects of emissions on ambient
concentrations of pollutants at relatively small distances
from sources. Current models used to analyze regional
pollution problems such as acid deposition apply to areas
of the order of 106 km2 and focus on long-term
"annual) average behavior, taking into account emissions,
airflow, mixing, chemical transformations, and both wet
and dry deposition. Generally, chemical transformations
and deposition processes are treated parametrically,
whereas transport is calculated using available data on
wind fields, for example. The models are based on sets
of continuity equations for concentrations of the species
of interest; the continuity equations are coupled through
terms representing the production and destruction of
species in chemical reactions. The equations are solved
using computers.
In effect, deterministic models represent detailed
material balance calculations analogous to the compart-
mentalization approach mentioned earlier, but in this
case the compartments in the atmosphere are much smaller,
so detailed behavior must be included.
Once confidence in deterministic models has been
achieved, through testing and verifying, it should be
possible to use them to assess the potential consequences
of alternative proposals for mitigating acid deposition,
since sensitivity tests would be feasible with this type
of model.
There is a variety of regional models for average
deposition rates of sulfur oxides over eastern North
America (e.g., U.S./Canada Work Group #2 1982). The
models use different approximations to characterize
OCR for page 59
so
atmospheric processes (Table 3.2). They have not been
verified systematically because of a lack of observa-
tional data. However, testing and initial comparisons of
several models for annual averages indicate that their
accuracy in estimating either ambient SOx concentrations
or wet-deposition rates is inadequate for quantitative
assessment of the effects of emissions from specific
sources (U.S./Canada Work Group #2 1982). Initial
comparisons show no preference by performance for a
specific model for application to the situation in
eastern North America, although from the limited number
of comparisons currently available, it appears as if
models that treat meteorological parameters in a gross
statistical sense appear to perform as well as the more
sophisticated models (U.S./Canada Work Group #2 1982).
At least three models (SURADS, ATM-II, and STEM) are
capable of simulating regional sulfate pollution episodes
over eastern North America (Table 3.2). These models use
added sophistication in treating atmospheric processes,
including incorporating multilevel winds and mixing,
diurnally varying chemistry according to photochemical
modeling, and variable dry-deposition rates. However,
the SURADS model has not incorporated cloud processes and
wet deposition in published applications. Tests of the
SURADS model against the data from the Sulfate Regional
Experiment yielded promising results for ambient sulfate
conditions but less satisfactory results for sulfur
dioxide concentrations "Mueller and Hidy 1982a). The
other two models, RTM-II and STEM, incorporate cloud
processes and other aspects of precipitation chemistry,
but their performance in comparison with observations has
not been reported.
Treatment of Transport and Mixing
Because long-range transport is at the heart of the
controversies surrounding acid deposition, we review here
the ways in which regional-scale models typically treat
trajectory analysis.
Meteorologists have approached the transport problem
in a number of ways. The simplest method is to use
observed values of horizontal winds at specified altitudes
to calculate by interpolation where the winds would carry
a given air parcel containing the material of interest
(i.e., Lagrangian or trajectory model). This type of
trajectory model has been widely used and is referred to
OCR for page 60
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OCR for page 76
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Nonlinearity in the SO2 transformation of the Rodhe
et al. model was also observed in subsequent studies by
Sampson (1982). He employed a somewhat improved hydro-
carbon reaction scheme, but in other respects the
mechanism was identical to that employed by Rodhe and his
co-workers. Some of Sampson's results are reproduced in
The solid lines in the figure Rive Samoson's
Figure 3.1. _ _
results for the percentage change in ambient sulfate
concentration after 24, 48, and 96 hours of transport
from the source region as a function of changes in SO2
emissions. The results of the model suggest that a
relatively small reduction in sulfate levels (roughly 15
percent) may result for long transport times (96 hours)
from a 50 percent reduction in SO2 emissions.
The results of Rodhe et al. and Sampson should be
treated with caution. The so-called Rodhe-Crutzen-
Vanderpol model used in both studies employed specific
sequences of chemical reactions and assumed uniform
additions of polluted background air throughout the
period of transport and transformation. Different
choices of oxidation pathways and changes in the strong
background source may alter the results significantly.
For example, the dashed lines of Figure 3.1 are the
result of running Sampson's computer program without
continuous dilution of the product mixture with
background air containing sulfate (P.J. Sampson,
University of Michigan, personal communication, 1982).
The shift toward the linear curve (from the solid to the
dashed curves in Figure 3.1) is the result of eliminating
the trivial source of nonlinearity arising from the
background source, term B in the equation, c = kS + B.
considered earlier. The dashed lines of Figure 3.2 are
the result of both deleting the background source of
sulfate and selecting an alternative pathway for the
homogeneous gas phase oxidation of SO2. Note that the
alternative assumptions give a result that is essentially
linear (with proportionality constants less than unity).
The original Rodhe-Crutzen-Vanderpol model employed
reaction (3.1) for oxidation of S02,
HO + SO2 ~ H2SO4,
(3.1)
whereas the modification that produced the dashed curves
of Figure 3.2 used
HO + SO2 (+ O2, H2O) ~ H2SO4 ~ HO2.
(3.2)
OCR for page 77
77
Reaction (3.1) is a single, simplified reaction in which
an attempt is made to condense the chemistry that occurs
in and following the primary hydroxy radical attack on
so2
HO + SO2(+M) ~ HOS02(+M)
[Equation (A.56) in Appendix A]. See Appendix A for a
more complete discussion of the reaction.
The use of reaction (3.1) is equivalent to assuming
that the addition of the hydroxy radical to SO2 ter-
minates the chain reactions of the HO radical, and by
some undefined process the initial product of reaction
(3.3) leads to H2SO4 without regenerating a chain-
carrying species. The assumption of reaction (3.1)
perturbs the atmospheric reaction cycles involving HO2
and HO radicals, which result in the oxidation of
hydrocarbons, aldehydes, CO, SO2, NO, NC2, and other
impurity species. For example, the oxidation of CO
occurs in reactions (3.4) through (3.6) by way of
HO-radical attack on CO:
HO + CO ~ H + CO2'
H + O2(+M) ~ HO2(+M),
HO2 + NO ~ HO + NO2.
(3.3)
(3.4)
(3.5)
(3.6)
Note that although an HO radical is lost in reaction
(3.4), another is regenerated in reaction (3.6). Similar
cycles occur involving CH2O and the hydrocarbons, for
example. Now if a reaction such as (3.1) occurs, an HO
radical is removed; no further regeneration of the HO
radical occurs.
In writing reaction (3.2), we assume in accordance
with experience in other atmospheric reaction cycles that
a chain-carrying radical (HO2) is developed following
the occurrence of reaction (3.3). For example, reaction
(3.2) summarizes the net result of the sequence (3.3),
(3.7), and (3.8):
HO + SO2(+M) ~ HOSO2(+M),
HOSO2 + O2 ~ HO2 + SO3,
SO3 + H2O ~ H2SO4.
(3.3)
(3.7)
(3.8)
Presumably, reaction (3.7) would often be followed by
regeneration of the HO radical through reaction (3.6), at
least in NO-rich polluted atmospheres.
OCR for page 78
78
-50 -30 -10
24h
24h' ~/
48h ~/
+50- _ ~
t 1 0 ~ :48h
~1 1 1 1~
+50
96h,
~ ~I
+10 +30
_
_ _
-50 - _
-30
ASO2(percent)
with reaction (3.1 ) and sulfate background
with reaction (3.1 ) but without su If ate backgrou nd
FIGURE 3.1 Effect of the assumption of background sulfate on the Rodhe-Crutzen-
Vanderpol model for chemical transformation. SOURCE: Sampson (1982) and P.J.
Sampson, University of Michigan, personal communication (19823.
The participation of reaction (3.1) results in a
direct nonlinear feedback into the SC2 oxidation
mechanism, while reaction (3.2) does not seriously
perturb the concentration of the hydroxy radical. The
best available experimental evidence today supports the
contention that the HO level in reacting mixtures of
hydrocarbons, NOx' and SO2 is relatively insensitive
to SO2 concentrations and that the sequence (3.3),
(3.7), (3.8), or some similar chain-propagating reactions,
is important (Stockwell and Calvert 1983). In the
experiment, Stockwell and Calvert varied the amount of
OCR for page 79
79
+50 ~
-
a,
Q +30~
11 ~
o
u'
a
+10
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/~'
/~'
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96h
A' ~ 48h
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48h ~ /
96h ~
i\SO2 (percent)
,~,7
-30~
-50 ~
with reaction (3.1 ) and sulfate background
with reaction (3.2) but without sulfate background
FIGURE 3.2 Effect of the assumptions of background sulfate and chain termination
on the Rodhe-Crutzen-Vanderpol model for chemical transformation. SOURCE:
Sampson (1982) and P.J. Sampson, University of Michigan, personal communication
(1 982).
SO2 in dilute, irradiated mixtures of CO, MONO, and
NOx in air (at 1 atm), monitored the concentration of
HO radicals by measuring the rate of formation of CO2,
and observed the ultimate formation of H2SO4 aerosol
as identified by its infrared spectrum. Within the
limits of experimental error, the concentration of HO
radical was found to be insensitive to the concentration
of SO2 even when as much as one half of the HO radicals
in the system reacted with SC2 leading ultimately to
OCR for page 80
80
the formation of sulfuric acid aerosol. Chain termina-
tion as implied in reaction (3.1) was found not to be
important.
The main point to recognize from this discussion is
that either an apparent near linearity or a nonlinearity
in the model may result from different, rather subtle,
simplifying assumptions related to the choice of chemical
mechanism. We conclude from these results that deviations
of SO2 conversion rates from linearity with respect to
SO2 concentration may be much smaller than has been
implied recently from the results of simulations employing
the seemingly realistic yet simplified reaction schemes.
Generation of nitric acid in gas-phase reactions does
involve termination of an HO-radical chain directly via
HO + NO2(+M) ~ HNO3(+M),
(3.9)
and in this case we must expect the concentration of the
reactant HO to be a function of the NO2 concentration.
The concentration of the HO radical in an air mass is
determined by the rates of reaction that generate it and
those that destroy it. That is, at any time t the
steady-state concentration of HO is given by
[HO] = 7(Ri)t/£ki[Ai]t,
where [(Ri)t is the sum of the rates of all HO-
radical generating reactions at time t, ki is the rate
constant for the ith removal reaction of HO with reactant
Al, and the summation [ki[Ai]t extends over all HO-loss
reactions. It should be noted that reaction (3.9) is
only one of several HO-HC2-radical chain termination
reactions that occur in the troposphere. Thus in theory
the effect of small changes in the concentration of NO2
on the concentration of HO is not expected to be dramatic.
For example, computer simulations of the chemistry of the
polluted atmosphere (see the mechanisms of Calvert and
Stockwell 1983) show that only about 10 percent of the
HO-HO2-radical termination occurs through the HO-NO2
reaction (3.9) for a tropospheric air mass typical of an
urban, polluted area with an ambient concentration of
NOX of 100 pph at sunrise. Air masses containing one
tenth and one one-hundredth of this concentration of
NOX at sunrise, but the same levels of other pollutants
as before, give about 0.1 and 0.01 percent of the total
HO-HO2-radical chain termination through reaction
(3.9). The time dependence of the concentrations of
OCR for page 81
81
reactants that form HO or react to destroy it are complex
functions of the initial pollutant concentrations, so
that the quantitative effect of the concentration of HO
on NOX initial concentration can be obtained only
through detailed calculations. However, the net effect
of lowering the initial NOX concentration by a factor
of 10 (from 100 to 10 ppb) while keeping all other
impurities at the same fixed level of the highly polluted
air mass is to lower the maximum HO concentration from
1.6 x 10 7 to 0.96 x 10-7 ppm, only a factor of about
1.7. Clearly the dependence of HO concentration is not
so sensitive to NCX concentration as one might have
expected at first consideration. Thus a more detailed
analysis of the complex homogeneous chemistry of the
troposphere predicts that the relationship between
changes in ambient concentrations of SO2 and changes in
gas-phase formation of sulfate should exhibit only small
deviations from linearity. The simple theoretical
considerations of Oppenheimer (1983) lead to the same
conclusion.
Nonlinear conversion of SO2 to sulfate can in theory
result from the liquid-phase oxidation of SO2
(HSOi) by hydrogen peroxide (H2O2). For certain
atmospheric conditions a limited supply of H2C2 may
exist in the atmosphere through gas-phase reactions
(3.10) to (3.12):
2HO2 ~ H2O2 + O2,
HO2 ~ H2O ~ HO2eH2O'
HO2. H2O + H2O ~ H2O2 + H2O + O2.
The rate of hydrogen peroxide generation in reactions
(3.10) and (3.12) depends on the square of the HO2
radical concentration.
In NO-rich polluted atmospheres, however, reaction
(3.6), the rate of which is proportional to the first
power of the HC: concentration, competes favorably for
HO2 radicals. Reaction (3.6) is very fast in NO-rich
atmospheres, with the result that the generation of H2O2
in reactions (3.10) and (3.12) is suppressed. Although
the uptake of the limited H2°k into cloud water and
rain will take place efficiently, for these circumstances
the amounts of H2O2 may be significantly less than
those of HSo] in the water. Obviously, the oxidation of
only a fraction of the HSO3 can occur for these con-
ditions, and the reaction becomes oxidant limited. SO2
in cloud water cannot be oxidized faster than the oxidant
is provided to the droplet.
(3.10)
(3.11)
(3.12)
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82
Note that for the case of an oxidant-limited reaction,
a nonlinear response in sulfuric acid deposition will
result from emission reductions. Only when Sal emissions
are reduced so that ambient concentrations of SO2 approach
the level of the oxidant present in cloud water will a
decrease in the sulfuric acid formation and deposition
result. For example, if the H2O2 available in cloud water
were consistently only 40 percent of the SO2 that is
dissolved in the cloud water at a given location, and if
oxidation occurred largely through the H2Oz-HSO3 reac-
tion, then a 60 percent reduction of the SON would result
in no reduction in the sulfuric acid in cloud water at
this location, but subsequent reductions would lead to
proportionally lower acid formation and deposition. It
is also possible that even with sufficient oxidant in
cloud water, other substances that may also be present,
such as formaldehyde, may inhibit the H2O2-HSO3 reaction.
Existing analytical data for H2O2 in clouds do not allow
an unambiguous conclusion to be reached today on the
possible importance of these nonlinear effects.
Limitation of oxidant for HSO3 or SO2 may arise
because of physical processes as well as the chemical
influence described.
For example, we have noted pre-
viously that it is likely that H2O2 vapor present in dry
air dissolves in cloud droplets to provide oxidant for the
conversion of SO2. Hydrogen peroxide is a very soluble
gas and may be rained out early in some storm systems,
leaving a significant fraction of SO2 vapor unreacted.
Several types of nonlinear effects may be expected
from factors not immediately related to oxidant levels.
For example, as described in Chapter 2 and Appendix A,
there is some evidence that SC2 is oxidized more
readily in the aqueous phase than in the gas phase.
Also, increased concentrations of alkaline soil dust in
the air due to drought or changing wind patterns can
result in the neutralization of precipitation acidity.
In the absence of extensive measurements, we judge
that nonlinear effects of SO2 emission control on acid
deposition that arise from chemical conversion mechanisms
are probably small for the gas-phase conversion steps,
but significant nonlinearity is anticipated for certain
special conditions such as an oxidant-limited H2O2-HSO3
reaction in cloud water. However, these conditions
cannot be tested from the existing data base.
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83
FINDINGS AND CONCLUSION S
Application of current air-quality models to regional-
scale processes has provided guidance on the significance
of dynamic processes influencing sulfur deposition.
Theoretical models have provided results that are
qualitatively consistent with empirical observations,
thus demonstrating important temporal and spatial scales
of source-receptor relationships. Qualitatively the
models have pointed to the importance of certain geo-
graphical groupings of SCAN sources and the potential
influence of the sources on certain receptor areas.
However, current models have not provided results that
give confidence in their ability to translate SO2
emissions from specific sources or localized groupings of
sources to specific sensitive receptors. Little has been
done in models to translate NOx emissions into nitrate
deposition or to link sulfate and nitrate to acid (H+)
deposition. These capabilitities are considered assent
tial for models to be used to study the consequences of
alternative control strategies in circumstances in which
long-range transport processes are involved.
Because of the simplifying assumptions that are made
in order to develop practical, economical regional-scale
models of air quality and because data are not available
to validate or verify them, researchers in the field gent
orally have only limited confidence in current results.
The models and their results are useful research tools.
However, because of deficiencies in the base of meteoro-
logical data required as input and because of the sen-
sitivity of their output to simplifying assumptions
regarding both the physical and chemical processes, we do
not regard currently available models as sufficiently
developed to be used with confidence in predicting
responses of the atmospheric system to alternative
control strategies.
Despite these limitations, theoretical models are and
probably will continue to be used in industrial and urban
planning, for which spatial scales are smaller than those
of interest in acid deposition. Given the state of
knowledge of the physics and chemistry of the atmosphere
in the context of long-range transport of air pollution,
and given the state of the art of techniques for making
quantitative estimates, we advise caution in projecting
changes in deposition patterns that result from changes
in emissions of precursor gases.
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84
On the basis of laboratory evidence, we conclude that
an alternative to the model of Rodhe et al. (1981), which
has been widely used to represent the chemical processes
involved in acid deposition, more correctly employs gas-
phase reactions leading to oxidation of SO2 that results
in HO-HO2-radical chain propagation. Laboratory evidence
suggests that chain-terminating reactions involving SO2
probably play only a minor role in atmospheres polluted
with SCt. When the Rodhe-Crutzen-Vanderpol model is
modified so that SC2 oxidation does not terminate
chains, the nonlinearity in the relationship between
changes in ambient SO2 concentrations and changes in
ambient sulfate concentrations (i.e., the commonly
reported result of the Rodhe model) is greatly reduced.
Laboratory and field studies as well as theory suggest
that oxidation of SO2 in cloud water is rapid and come
plete, provided that concentrations of oxidants (H2O2,
O3) are sufficient (see Chapter 2). Measurements of
oxidant concentrations in cloud water, although limited,
suggest that concentrations may be sufficient in eastern
North America for complete oxidation of SC2, except
perhaps in winter. If this is the case, then strong
deviations from linearity in the relationship between
changes in annual average ambient SO2 concentrations
and changes in the net production of sulfate in clouds
would not be expected.
The relationships between emissions of so2 and NOX
and the deposition of sulfuric and nitric acids are
complex. Models to predict patterns of the deposition of
hydrogen ion will have to account for neutralizing
substances as well as sulfuric and nitric acids.
Assuming that the ambient molar concentrations of NOx
and basic substances (such as ammonia and calcium
carbonate) remain unchanged, we conclude that a reduction
in sulfate deposition will result in at least as great a
reduction in the deposition of hydrogen ion.
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Representative terms from entire chapter:
cloud water
