United States
Environmental Protection
Agency
Environmental Research
Laboratory
Corvallis OR 97330
EPA-600/3-78-053
May 1978
Research and Development
x>EPA
Simulation
of Nutrient Loss
From Soils
Due to Rainfall
Acidity
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EPA 600/3-78-053
May 1978
SIMULATION OF NUTRIENT LOSS FROM
SOILS DUE TO RAINFALL ACIDITY
by
John 0. Reuss
Colorado State University
Fort Collins, Colorado 80523
Project Officer
Donald J. Lewis
Corvallis Environmental Research Laboratory
Corvallis, Oregon 97330
CORVALLIS ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330
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DISCLAIMER
This report has been reviewed by the Corvallis Environmental Laboratory,
U.S. Environmental Protection Agency, and approved for publication. Approval
does not signify that the contents necessarily reflect the views and policies
of the U.S. Environmental Protection Agency, nor does mention of trade names
or commercial products constitute endorsement or recommendation for use.
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FOREWORD
Effective regulatory and enforcement actions by the Environmental Pro-
tection Agency would be virtually impossible without sound scientific data on
pollutants and their impact on environmental stability and human health.
Responsibility for building this data base has been assigned to EPA's Office
of Research and Development and its 15 major field installations, one of
which is the Corvallis Environmental Research Laboratory (CERL).
The primary mission of the Corvallis Laboratory is research on the
effects of environmental pollutants on terrestrial, freshwater, and marine
ecosystems; the behavior, effects and control of pollutants in lake systems;
and the development of predictive models on the movement of pollutants in the
biosphere.
This report describes a simulation model designed to predict the impact
of rainfall acidity on the leaching of cations from non-calcareous soils.
This work was undertaken as a part of a research program at CERL to determine
the effects of acid rain on forest ecosystems.
A. F. Bartsch
Director, CERL
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ABSTRACT
This paper describes a simulation model that provides a quantitative
system utilizing established relationships from soil chemistry to predict the
most likely effect of rainfall acidity on the leaching of cations from non-
c'iicareous soils.
The model utilizes the relationships between lime potential (pH -
'i/2pCa) and base saturation described by Clark and Hill (Soil Sci. Soc.
Arner, Proc. 28:490-492, 1962) and Turner and Clark (Soil $_ci. 99:194-199,
1964), the equilibrium between C02 partial pressure and H and HC03 in
solution, the apparent solubility product of A1(OH)3, the equilibrium of
cations and anions in solution, the Freundlich isotherm description of sul-
fate adsorption, and mass balance considerations, to predict the distribution
of ions between the solution and sorbed or exchangeable phases. Ionic compo-
sition of leachates in response to rainfall c_omposjtion c_an thus be computed.
ions^considered in the present version are H , Ca2 , Al3 , SO^2 , Cl~, and
HC03 .
The model predicts almost exact chemical equivalence between basic
cc'ciuii removed in the leachate and strong acid anions entering the system in
rh- rainfall if pH - l/2pCa is above 3.0, at which point the base saturation
wit! generally not exceed 20|. At lo^er pH - l/2pCa values leaching of
oinohs in association with H and Al3 becomes significant and these cations
predominate when pH - l/2pCa falls below 2.0.
If the soil exhibits sulfate adsorption properties, leaching of bases in
expense to rainfall containing sulfuric acid may be delayed until a sulfate
:i-!:.0!'ption equilibrium is reached, but base removal would continue after the
jiilfuric acid input was stopped.
itjst, of the work reported here was completed while the author was on
ciiignrn^nt as a soil chemist at the Corvallis Environmental Research Labora-
tory , Corval1is, Oregon.
IV
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CONTENTS
Foreword ........... Ill
Abstract ............ iv
Figures .............. vi
Tables viii
Acknowledgement ................ ix
1. Introduction 1
2. Conclusions .............. 2
3. Recommendations ............. 4
4. Model Structure and Theory ....... . . 5
5. Simulation Results ... ........ 17
6. Discussion ................... 35
References
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LIST OF FIGURES
Number Page
1. Generalized diagram of model describing interaction of rainfall
chemistry with soil solution processes 6
2. The pH - l/2p(Ca + Mg) values of soils as a function of base
saturation based on the sum of cations extracted with IN KC1.
(Redrawn from Clark and Hill 1964) 10
3. Flow diagram for model of the rainfall chemistry-soil solution
system 15
4. Model prediction of pH of a 1:1 soil:water extract in a soil with
pH - 1/2 pCa = 3.0 as a function+of [SO^2" + Cl~] concentration in
rainfall. Circles represent Ca2 as rainfall while X's represent
pH 4.0 rain as shown in Table 1. The soil does not adsorb SO^2"
and leachate volume is equal to rainfall 19
5. Model prediction of_concentration of Ca2 in leachate as a func-
tion of [SO^2' + Cl~] concentration in rainfall and pH - l/2pCa
of the soil. The soil does not adsorb SO^2' and leachate
volume is equal to rainfall 21
6. Ratio of Ca2 in leachate per [SOit2" + Cl~] in rainfall (eq/eq),
as a function of anion strength of rainfall and pH - l/2pCa. Soil
does not adsorb sulfate 22
7. Predicted effect of Changing evaporation from 0 to 90% of rainfall
on the amount of Ca2 leached from the soil per equivalent of rain.
pH - l/2pCa was 2.5, rainfall pH 4.0, and there was no adsorption
of S042~ 25
8. Model prediction of concentrations of Ca2 in leachate of a
S042" adsorbing soil as a function of SO^2' + Cl" and pH-
l/2pCa. Leachate volume is equal to rainfall 27
9. Simulated time-based fluctuations in soil pH using pH 4.0 rain-
fall 31
10. Simulated change in total Ca2 (soluble plus exchangeable) in
0.3 meters of soil during a 5-year peiod using pH 4.0 rainfall. . 33
VI
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"11. Simulated total Ca2 found on April 30 in 0.3 meters of soil
stressed with pH 4.0 rainfall over a 10-year period. ... 34
12. Simulated April 30 1:1 soiltwater extract pH values for SO^2"
adsorbing and non-adsorbing soils stressed with pH 4.0 rain-
fall ......... 35
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LIST OF TABLES
Number Page
1. Ion concentrations In rainfall used in similation runs. . . 18
2. Effects of C02 partial pressure on extract pH and on
Ca2 leached using simulated pH 4.0 rainfall 24
3. Initial conditions and soil properties for a 10-year
acid rainfall simulation 29
4. Rainfall and evapotranspiration patterns used for 10-year
simulations 30
vm
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ACKNOWLEDGEMENTS
An undertaking such as that described in this paper requires the contri
butions of many people. I would like to express my appreciation to the
administration and staff of the Corvallis Environmental Research Laboratory
who made my assignment at the laboratory possible, and provided facilities
and encouragement for the completion of the task, particularly Dr. Norman
Glass, Dr. Allen Le Fohn, and Dr. Larry Raniere. Thanks are also due to Fir.
Donald Lewis, who helped in the final stages of the work.
My thanks for their efforts and suggestions are due those who reviewed
the manuscript including Dr. C.V. Ccle (USDA-ARS), Dr. Willard Lindsay, and
Dr. Robert Woodmansee, all from Colorado State University, and Dr. Dale
Johnson, Oak Ridge National Laboratory.
An extra measure of thanks are due to Mr. J. Warren Hart who's efforts
and skills in programming, mathematics, and chemistry contributed substan-
tially to the successful planning of the program.
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SECTION 1
INTRODUCTION
The trend toward increased rainfall acidity over northern and western
Europe and the northeastern United States appears well established. This in
turn is causing concern about the possibility of accelerated losses of miner-
al bases from soils and subsequent losses of productivity (Anon., 1971; Jons-
son and Sundberg, 1972). However, ion exchange properties in soils are com-
plex, and cation losses from soils due to leaching by acid rainfall is modi-
fied by soil properties (Wiklander, 1974; Malmer and Nilsson, 1972).
This paper describes a model that calculates ion loss from soils as a
function of soil properties and of the composition and distribution of rain-
fall. The objective of the model is to provide a quantitative system that
utilizes established principles of soil chemistry to predict the most likely
effect of rainfall acidity on leaching of basic cations from non-calcareous
soils. It must be regarded as preliminary due to the limited number of ions
considered and numerous simplifying assumptions. Nonetheless, in my opinion,
the model provides the most reliable method presently available for estima-
ting the effect of rainfall composition on losses of bases from soils. It
also provides the basic structure that can be used in subsequent models inco,
porating additional ions and processes.
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SECTION 2
CONCLUSIONS
It is entirely feasible to simulate the ion exchange and removal pro-
cesses that are likely to occur in soils as a consequence of rainfall acidity.
Known physical-chemical relationships coupled with simulation techniques com-
bine to give the best prediction presently possible of long term effects that
are not amenable to experimental measurements within a reasonable length of
time. The following specific conclusions were arrived at by a first generation
model of this type that applies only to non-calcareous soils.
The initial results of these investigations indicate that significant
acidification and depletion of bases could occur over a period of a few de-
cades if rainfall inputs are consistently acidified to pH 4.0 with sulfuric
acid.
He can expect almost an exact chemical equivalency between strong acid an-
ion content of rainfall and leaching of bases from soils with base saturation
levels above about 20%. As base saturation becomes lower the leaching will
diminish and then cease but the exact nature of this relationship must await
further investigation.
Leachate composition will initially be controlled largely by the anion
concentration of the rainfall, and will be independent of whether the* rainfall
cations are mineral bases or H . The long term base status of the soils will,
however, respond to the cation composition of the rainfall.
Soils with a significant capacity to adsorb sulfates will tend to dampen
the effect of sulfuric acid induced leaching of basic cations. The leaching
of bases will respond more slowly to acidic imputs than on non-sulfate adsorb-
ing soils but will reach a similar equilibrium rate of leaching as the sulfate
adsorption capacity reaches equilibrium with the rainfall sulfate. On these
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soils high rates of leaching induced by rainfall containing sulfuric acid
eoiild be expected to persist for some time after acid rainfall input ceased.
Soil pH as measured by soil water suspensions may be markedly lowered by
increased rainfall ion concentrations. This rapid change is a result of rain-
fall anion concentration and would occur in a similar manner in response to
rainfall containing either strong acids or neutral salt.
Soil pH as measured by soil water suspension is well known to vary with
time. However, the predictions given by the model show clearly the effect of
seasonal precipitation-evaporation relationships of a magnitude of about 2.5
times the overall change that would be expected to occur in a decade in res-
ponse to pH 4.0 rainfall. Experiments that depend on soil water extract or
suspension pH measurements to evaluate the effect of acid rainfall inputs
would be subject to serious errors due to these fluctuations.
The long term leaching of cations in response to rainfall acidity will be
largely independent of the precipitation/evaporation ratio as long as periodic
leaching occurs.
Cation removal in response to rainfall mineral composition will be largely
independent of CQ? partial pressure.
The initial model results indicate that base removal due to rainfall acid-
ity from actual soil systems can validly be investigated on an experimental
basis by increasing the acidity of applied water to levels in excess of that
normally found in rain. This would shorten the time necessary to investigate
base removal. Measurement of pH on soil water suspensions from such experi-
ments would not be valid as much lower values would be expected than would oc-
cur if the weaker acid were applied for the longer time periods.
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SECTION 3
RECOMMENDATIONS
Simulation modelling based on known physical-chemical relationships in
soil offers the most feasible method of evaluating long term effects of acid
rainfall on the base status of soils. The model reported here is useful in
this regard but is limited by the inclusion of only part of the important ions
and by simplifying assumptions concerning water movement in soils. The rela-
tionships are sufficiently understood to develop a more complete model inclu-
ding additional ions and more sophisticated water movement relationships.
Such a model should be developed immediately.
At the same time laboratory work with soil suspensions and soil columns
should be undertaken for experimental verification of the model. If results
coincide with model predictions it will add confidence to model prediction of
long term effects not easily amenable to direct experimentation. If predic-
tions of laboratory systems do not give acceptable precision, hopefully the
reason can be discerned and the model modified accordingly.
The model should also be used to simulate on-going field experimentation,
both to validate the model, and to determine if the procedure used in the
field trials can reasonably be expected to give reliable and useful results.
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SECTION 4
MODEL STRUCTURE AND THEORY
GENERAL DESCRIPTION
A general schematic representation'of the model is shown in Fig. 1. The
model was developed using a daily time step. Data supplied on a daily basis
from external sources include rainfall and evapotranspiration in millimeters,
2+ + - 2-
and the concentration of Ca , H , Cl , and SO. ions (moles/liter) in the
rain. The present form of the model has been restricted to these ions plus
HC03 , and Al . Various initial conditions must be specified at the start of
each run and these will be pointed out in the discussion of the soil process-
es.
After the rain has entered the soil composition of the soil water is recal-
culated based on previous water content, constituents added, and evapotranspir-
ation. The ionic equilibria are then calculated and a new solution concentra-
tion is established for each ion. If the new water content is greater than
field capacity, the excess is removed as leachate, which is assumed to have
2+ 2-
the same composition as the soil solution. The total amounts of Ca , SO. ,
and Cl" ions in the system are specified initially. The amount entering in
the rain is known from the input data and the amount lost in the leachate at
each time step are calculated within the model, so the total sorbed plus sol-
ution amount of each ion is known at all times.
EQUILIBRIUM PROCESSES
The equilibrium between solution ions and sorbed ions is the principle fo-
cus of the model. In the initial stages it was assumed that the soil-solution
and atmosphere-solution equilibria were uniform to the depth being considered
and all results reported are from this version. Later revisions include the
capabilities of considering various depth layers with different soil properties
separately.
5
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Soil Surface
Evapotranspi ration
A
Rain FLO
Ca2+, H+
HCO ~ Cl~, SO
2-
C02<:
Soil Solution
=> A13+, Ca2+, H+
HCO,
Bottom of Rooting Zone
, S0
2-
Sorption
Processes
Sorbed
Ions
Ca
++
-, SO
2-
Leachate
Figure 1. Generalized diagram of model describing the interaction of rainfall
chemistry with soil solution processes.
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Sulfate Adsorption
Soils exhibit the phenomenon known as sulfate adsorption to varying de-
grees. Sulfate adsorption is commonly encountered in acid soils, particularly
those that are highly weathered and contain iron and aluminum sesquioxides.
Haward and Reisenauer (1965) discuss possible mechanisms of sulfate adsorption
processes. Whatever the mechanism, soils that adsorb sulfate tend to maintain
2_
an equilibrium between SO. in solution and that sorbed onto soil surfaces.
0 O
S04 (solution) < > S04 (sorbed)
Various expressions have been used to describe this equilibrium, including the
Freundlich and Langmuir adsorption isotherms (Chao e_t aj_. , 1962; Hasan et al . ,
1970)
2_
I have chosen to describe the SO. adsorption process in the model with
the Langmuir equation which is used in the form:
, K [SO.2"]
SO/' (sorbed) = -* - 1 (1)
2_
Where [SO. ] is the equilibrium sulfate concentration in moles/liter, K
M- o IMaX
is the adsorption maximum, i.e., moles SO. ~ adsorbed per unit of soil at in-
2- 2-
finite [SO. ], and k: is related to the bonding energy and is the [SO ] at
2 ^ 2-4
which SO. adsorbed is equal to one-half K . Total S04 is always known
and consists of the sum of the sorbed and solution components so that:
S042" (total) = S042" (sorbed) + SO/' 0 D (2)
Where 0 is the volumetric moisture content (liters water/liter soil) and D is
2_
the depth in millimeters of the soil profile simulated. The units of SO.
2 ^
sorbed and S04 total as used in the model are moles per square meter to
depth D. Equations (1) and (2) are sufficient to define the distribution of
total sulfate between the solution and sorbed phases, and this distribution is
calculated in the model at each time step prior to calculating the concentra-
tion of the remaining ions as described below.
These calculations depend on the availability of values of K and kj for
max -^
any soils to be simulated. Many soils adsorb very little sulfate and can be
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simulated by simply inserting very low values for K . Literature values are
max
available for a number of typical sulfate adsorbing soils (Chao et_ al_., 1962;
Hasan et al_., 1970).
Chao e^t a]_. (1962) point out the limitations of the Langmuir isotherm.
The soils they studied did not exhibit appropriate adsorption maximas, even
though they did follow the relationship over a substantial range from which an
"adsorption maxima" could be predicted. Hasan ert a]_. (1970) refer to this as
a "first phase adsorption maxima." Thus for any particular soil simulated, the
relationships in the model are only valid for the range of sulfate adsorption
within which the Langmuir relationship is valid. In addition it should be un-
2_
derstood that the SO. concentration in (1) might better be expressed in
terms of activity. However, the literature values available are generally in
2_
terms of concentration so no activity coefficients are applied to SO. in
the model.
Ca - H Equilibria
+ 2+
In order to define the H and Ca exchange equilibria, I chose to util-
ize the concept of "Lime Potential" of Schofield and Taylor (1955). Soil pH
measurements are highly sensitive to factors such as dilution and salt effects,
but these authors demonstrated that the Lime Potential, defined as
pH - %p(Ca + Mg), is remarkably constant for a given soil even though soil wa-
ter content may vary widely. With changes in water content the shifts between
2+ +
exchangeable and solution Ca and H are such that K. remains constant. In
our system where Mg is not presently considered we can write:
pH - %pCa = KL (3)
K, , the Lime Potential, can easily be determined for any given soil by measur-
2+
ing the pH and the activity of the Ca ion in a suspension of soil. pH and
+ 2+
pCa are defined as the negative logarithms to the base 10 of the H and Ca
activities respectively.
The relationship in (3) is sufficient for our purposes if only short term
simulations are used. However, if losses or gains of calcium are significant
2+
the fraction of exchange sites occupied by Ca (base saturation) changes so
that KL changes also. It appears, however, that K, can be satisfactorily rel-
-------
ated to base saturation as shown by Clark and Hill (1964). In our system, the
only base considered is calcium, so base saturation V is defined by
V = 2CaX
CEC
Where CaX is the moles of exchangeable Ca per unit of soil and CEC is the
cation exchange capacity in equivalents. If we accept the relationships found
by Clark and Hill (1964), (Fig. 2) one for montmorillonitic soils, and the
other for more weathered soils, we can write:
PH - hpCa = f() (5)
CaX
Where ^FFK) is the function shown in Fig. 2 for the soil we wish to simulate.
In the program coordinates of the points on the appropriate curves are fur-
nished as data and intermediate points are calculated by linear interpolation
as required.
Some care is required in the interpretation of Fig. 2 due to the manner
in which CEC is defined. Clark and Hill refer to this as "permanent", i.e.
non-pH dependent, charge. In reality in highly base saturated soils, some pH
dependent charge would be included. Thus, if a highly base saturated soil is
acidified, CEC may decrease. Simulations resulting in large changes in base
saturation could be subject to error from this effect.
2+
In addition to the relationships shown in (5), the total Ca in the simu-
lated system is always known, so that:
Catotal = CaX + [Ca2+] G D (6)
2+
Where Ca is the solution concentration in moles/liter, and CaX is the ex-
2
changeable Ca in moles/in to whatever depth is considered, and D is expressed
in millimeters.
Chemical Equilibria
In addition to the above, certain chemical conditions must be satisfied.
In soils above pH 5.0 the HCO ~ ion may be an important constituent. The con-
O
centration of this ion is controlled by C02 partial pressure such that:
-------
6.0
5.0
4.0
3.0
2.0
Montmorillonitic
o Others
20 40 60 80
% Base Saturation
100
Figure 2. The pH - ^plCa + Mg) values of soils as a
function of base saturation based on the
sum of cations extracted with IN KC1.
(Redrawn from Clark and Hill, 1964).
10
-------
(H+) (HCO ") = (COJ lO"7'81 (7)
O C-
Where (C02) is the partial pressure of CCL in atmospheres, and (H ) and (HC03~)
are the activities of the two ions in moles/liter. In the model the CCL par-
tial pressure must be specified initially.
In acid soils Al may be one of the major cations in the system, and neg-
+ 2+
lecting this ion results in unacceptable errors in the predicted H and Ca
solution concentrations. From the solubility product of A1(OH)3 we can write:
(A13+) (OH")3 = KA1
10-14
and substituting - r- for (OH) we obtain eq. (8).
(H+)
-14 3
(A13+) (-^-f-) = Kfl1 (8)
(H+) A1
In soils the K», would represent the apparent solubility product for
Al(OH)o which may vary depending on the degree of weathering. For the system
_oo /i -T3 R
simulated here, values of 10" ' to 10" ' were used (Turner and Clark, 1964;
Turner, Nichol and Brydon, 1963).
In order to maintain electrical neutrality in the system the total equiva-
lents of anions and cations in the solution must be equal, so that:
[H+] + 2[Ca2+] + 3[A13+] = 2[S02"] + [HC0~] + [CM (9)
The brackets again indicate molar concentrations. In this system Cl is pre-
sumed to exist only in solution, so that when the initial amount is specified
and the gain in rainfall and losses in leachate are all known, the amount pre-
sent at each time step can be calculated.
If we examine eqs. (5) through (9), we find the following parameters are
either known or specified; CEC, f (-) , Catotal ' 03 D' ^Vg' tS042"] and
[Cl"]. The unknowns are (Ca2+), (H+), [Ca2+] , CaX, (HCO "), [HCO ~] , [H+]
3+ <5 3
and (Al ). If for the moment we consider activities ( ) to be equal to con-
centrations [ ] , we have only [Ca ] , [Al +] , [H+] , [HC03~] , and CaX as
11
-------
unknowns.
The five equations in five unknowns define the system, so by solving this
set we could calculate the solution concentrations of Ca , H , Al , HCCL ,
2+
and the exchangeable Ca .
An assumption that activities and concentrations are equal is not accept-
3+
able, particularly in relation to the tri-valent Al ion. It is necessary,
therefore, to calculate the activity coefficients y., Y2> Y3» where:
Y, [Concentration] = (activity) (10)
The Debye-Huckel Theory is used to calculate these coefficients in a manner
similar to that utilized by Dutt et al_., (1972).
-.509Z.V5
log Y, = V~ (ID
1 1 + y'5
Where Z is the valence and:
n 0
y = h I , C.r. (12)
i=l i i
Where n is the total number of ion species present, and C. is the concentra-
tion of each ion.
Equations (1) through (12) are sufficient to define the solution concen-
trations of the ions considered as well as the amounts sorbed provided the to-
tal amounts of input and output are known. Thus by devising a solution to
this set of relationships it is possible to predict the changes that will take
place as a result of any rainfall composition, provided the amount and distri-
bution of rainfall and the evapotranspirations are known.
Some cautiqn is necessary in interpreting ion concentration or activities
as calculated from these equations, particularly in terms of (H ) or ph'. The
ion activities reported here as calculated from the above equations should
represent those found in the solution phase, commonly referred to as the "outer
solution." The boundary between "inner solution" or sorbed phase and "outer
solution!!may not be well defined and pH measurements made on soil suspensions
or pastes are generally lower than those of the extract or supernatant solu-
tion due to the influence of this "inner" phase. Probably the best interpre-
12
-------
tation of the pH values calculated by the program would be those of an extract
from a paste or suspension prepared from the indicated soi1:water ratio.
MODEL STRUCTURE
Numerical Solutions
The heart of the model is the numerical solution of sets of equations des-
cribing sorption and chemical equilibria. The system utilized evolved during
development of the model and is probably not the most efficient that could be
devised. However, it works well and the processor time required is moderate,
even for long term simulations. A brief description of the approach seems
appropriate.
First the activity of Al is calculated from eq. (8) and the value of
(H ) is taken from the previous time step or iteration. If no previous value
+ 2-
of (H ) is available, a value is assumed. The solution and sorbed SO. are
then calculated using eq. (1) and (2). Activity coefficients are calculated
using eq. (11) and (12) and previous concentrations or if none are available
activity coefficients are assumed for the first iteration.
Next, an iterative method is used for solving equations (5), (6), (7), and
(9). This solution is the most complicated in the model. Equations were suc-
cessively eliminated by substitution and rearranged until one complicated ex-
pression of the form f(H ) =0 was obtained. This is solved by an adapta-
tion of Newton's method. The value of f(H ) for an assumed value of (H ) is
calculated and the derivative of f(H ) is evaluated. A new estimate of (H )
is obtained by projecting the tangent to the abcissa. The processes are re-
peated until the change in the value of (H ) is within limits prescribed by
the operator. In our simulation this change must be <10 times the new value
of H . In the initial equilibration, the program assumes a trial value of
(H ), but in subsequent equilibrations the value from the previous time step
is used. Special precautions are taken to avoid estimates for which f(H) is
nonexistent and to avoid divergence. When convergence is satisfactory, new
2+
values are calculated for CaX and the concentration and activities of Ca and
3+2
HC03 . The program then returns to the calculation of (Al ), [SO. ~] and
activity coefficients. The process is repeated until the changes in the acti-
vity coefficients between successive iterations are within prescribed limits.
13
-------
General Structure
A generalized flow diagram is shown in Fig. 3. Some of the steps shown in
this diagram, particularly the equilibrium calculations discussed above, are
quite complex and have their own internal flow patterns.
First the initial conditions are read. These include; constants for
o
SO. adsorption, Kfll , depth, CEC, initial water content, field capacity,
H ML 2+ -
permanent wilting points, total SO., total Ca , and total Cl in the soil,
and C0? partial pressure. Coordinates of points for the pH - ^pCa as a func-
tion of base saturation relationship are also read as data, as are the limits
allowed for the checks of convergence.
The initial equilibria are then calculated for any five specified water
contents, and the ion concentrations printed. The initial ion concentration
at field capacity defines the initial concentration in the leachate.
If actual rainfall simulations are desired, rainfall is added. Rainfall
of any selected composition is presently added in a preset pattern but actual
rainfall and evaporation could be read from a data file. After daily rain-
fall is added, evapotranspiration is subracted unless this would reduce soil
water content below the permanent wilting point in which case soil water con-
tent is set at the permanent wilting point.
The program provides for printed output at preset intervals. If the date
is one for which printed output is required, the procedure is as follows:
First, a check is performed to determine whether total water is above field
capacity, and if not, no leaching will occur and the program skips directly
to the output section. If leaching will occur, the ion equilibration routines
are utilized to determine solution concentration. Water in excess ofc field
capacity is removed, and the amounts of ions removed are accumulated. The
program then moves to the output routines in which the equilibration routines
are called for the preset output water contents; and the concentrations, the
accumulated amounts of ions added and leached, and the present amounts of sor-
bed ions are printed. The program then updates base saturation, checks for
end of run and returns to add the next day's rain.
On days when no print is required, the system is simpler; if water content
is below field capacity, no further calculation is required and the program
14
-------
f START J
/READ
INITIAL
CONDITIONS/
Figure 3. Flow diagram for model of the rainfall chemistry-soil solu-
tion system.
15
-------
returns to check for end of run and rainfall addition. If field capacity is
exceeded, new ion equilibria are calculated, the solution in excess of field
capacity is removed, and the amounts of water and ions lost are accumulated.
Base saturation is updated, end of run is checked and the next days rain is
added.
Output
As mentioned previously, output is printed at pre-selected intervals. For
the output to be comparable from one time to the next, it is necessary for the
output equilibria to be calculated for the same water content each time. Also,
water contents at which laboratory measurements of pH or solution ion concen-
tration are made may vary. For this reason, provison is made for output of
ion concentrations and sorbed ions at five specified water contents. The vol-
umetric moisture contents (9) desired are entered. In these runs, I have used
field capacity, approximate saturation (2 x field capacity); and 1:1, 1:5 and
1:10 soil:water ratios. The latter was obtained by setting 0 such that bulk
density/0 is equal to the desired ratio.
In addition to the ion concentrations and sorbed ions, the accumulated
water and the ions added and leached since the start of the run and during the
preceding interval are printed.
Coding
The model is coded in the standard FORTRAN IV computer language. For the
version used in the runs reported here, core memory requirement was about
70000 (octal). Execution time is minimal and by placing a compiled version on
a system file, processor charges on the system utilized were less than $2 for
a ten year simulation run.
16
-------
SECTION 5
SIMULATION RESULTS
SHORT-TERM SIMULATIONS
One of the most important applications of the model is for short-term
runs in which the ion input-output relationships can be examined as a fun-
ction of soil and rainfall characteristics. These simulations provide a ba-
sis for understanding how cation loss due to acid rainfall is influenced by
soil properties.
Non-Sulfate Adsorbing Systems
First, we shall examine results of short-term simulations of a soil sys-
tem with very low sulfate adsorbing capacity. These runs were made simulating
-4
rainfall varying in pH from 3.00 to 6.35 with C0? at 3 x 10 atmospheres.
The ionic composition of the rain is shown in Table 1. The pH - %pCa values
of the soil were varied from 1.5 to 4.0, corresponding to soils that are near-
ly base saturated (4.0) and extending below the levels normally expected in
soils. The pH - ^pCa values were not allowed to change during a run. No ev-
aporation was allowed and steady state conditions were required, i.e., the
2-
SO. and Cl concentrations were in equilibrium with those of the rainfall
and did not change during the run.
Under these conditions, soil solution pH was markedly affected by chang-
ing composition of the rain. The results for pH - %pCa = 3.0 are shown in
Fig. 4. This should not be interpreted as due to rainfall acidity but rather
to a "salt effect". This can easily be demonstrated with the model by repla-
2+
cing the "acid rainfall" with a CaSO. rainfall in which the Ca concentra-
2-
tion is adjusted to equal the sum of the SO. plus Cl (in equivalents per
liter). Such rainfall would be essentially neutral but the effect on soil pH
is almost identical to that of acid rainfall of the same anion concentration,,
A conceptual model of this effect is that an increase in anion concentration
17
-------
TABLE 1. Ion concentrations in rainfall used in simulation runs.
No.
1.
2.
3.
4.
5.
6.
7.
*
pH
3.00
3.50
4.00
4.49
4.98
5.67
6.35
Ca2*
micro
30
30
30
30
30
30
30
<
equivalents/liter
1010
330
110
42
20
10
0
Cl
40
40
40
40
40
40
40
log [SO/' + Cl"]
-log (eq/ liter)
2.99
3.46
3.89
4.21
4.40
4.52
4.70
_
pH at 3 x 10 atm (XL
-------
6.0
Q>
5
I 5.0
w
4.0
5-0
^ Acid Rain (pH 4.0)
0 Co S04 Rain
4.5 4.0 3.5 3.0
log [SO^'+Cf] in Roinfdl.eq /liter
Figure 4. Model prediction of pH of a 1:1 soil: water extract
in a soil with pH - %pCa = 3.0 as a function of
2-
[SO. + Cl J concentration in rainfall. Circles
2+
represent Ca as rainfall while X's represent pH
4.0 rain as shown in Table 1. The soil does not
2_
adsorb SOZ
fall.
and leachate volume is equal to rain-
19
-------
in solution requires a corresponding increase in cation concentration, inclu-
ding H . A soil solution with very low anion concentration could not be high-
ly acidic.
Another characteristic observed in these short-term simulations was that
2+
the concentration of Ca in the leachate was strictly dependent on the
2-
SCL + Cl concentration of the rainfall regardless of whether the rainfall
4 2+ + 2+
cation was Ca or H . The net change in Ca in the soil, of course, was
2+ +
markedly affected by the balance of Ca and H in the rain.
2+
Fig. 5 shows a plot of the log of the Ca concentration in the leachate
as a function of the log of the anion concentration of the rainfall. Note that
2+
at pH - igpCa = 3.0, the Ca concentration of the leachate is almost identi-
cal to the rainfall anion concentration over the range of 10" ' to 10
equivalents per liter. At pH %pCa above 3.0 and rainfall concentrations be-
-4 0 2++
low 10 ' equivalents per liter the leachate Ca concentration is greater
2-
than the sum of the SO. + Cl due to significant amounts of HCCL . As
2+
pH - ^pCa drops to 2.0, the leachate Ca is substantially lower than the rain-
fall anion concentration, indicating that H and Al are significant compo-
nents of the leachate.
2+
The actual ratio of Ca leached per strong acid anion input in the rain
(eq/eq) is shown in Fig. 6. Here, values greater than 1.0 indicate leaching
in association with HCO- while values less than 1.0 indicate strong acid
+ 3+
anions leached in association with H and Al . Note that the basic cations
removed are approximately equal to anion input at pH - ^pCa =3.0. At rain-
fall ion concentrations relevant to the acid rain system (greater than about
10 eq. /liter) even at pH - J^pCa = 2.5 the Ca leached amounts to about
2+
80% of the anion input, but Ca leaching drops off very rapidly as pH - %pCa
is lowered to 2.0. A comparison of these values with the curves in Fig. 2 in-
dicates that we would expect almost a stochiometric 1:1 removal of bases
except on soils of very low base saturation, perhaps less than 20% of perma-
2+
nent charge. However, as base saturation is further depleted, the Ca remov-
al would decrease rapidly and for the pH 4.00 rainfall shown in Table 1, the
?+
Ca input would equal the amount leached at about pH %pCa = 1.9.
An important consideration is the effect of evapotranspiration. If evapo-
20
-------
£4
o
o
Q» 5
O
O 6
O>
O
pH-l/2pCo
5.0
4.5
4.0 3.5 3.0
-log [so 4 Cl ] in Rainfoll, eq/liter
2+
in leachate
Figure 5. Model prediction of concentration of Ca
2-
as a function of [SO, + Cl ] concentration in
rainfall and pH - %pCa of the soil. The soil does
2_
not adsorb SO and leachate volume is. equal to
rainfal1.
21
-------
CT
0)
CT
0>
c
o
2.0
= I 5
o
c
o
Q:
0.5J
o
o
0-0
2.5
2.0
1.9
2.0
1.0
Figure 6.
5.0 4.5 4.0 55 3.0
-log [804" Cl~] in Roin,eq/liter
2+ 2-
Ratio of Ca in leachate per [SO. + Cl ] in rain-
fall (eq/eq), as a function of anion strength of
rainfall and pH - ^pCa. Soil does not adsorb sulfate
22
-------
transpiration is always greater than rainfall, removal is zero and the system
accumulates ions from the rainfall. In the previous simulation, evapotrans-
piration was assumed to be zero. When evaporation occurs the effect is to
concentrate the soil solution and decrease the amount of leachate. The impli-
cations of this concentrating effect on base leaching were demonstrated by
2
simulating systems in which 10 liters/m of rainfall per day were applied
with no evaporation. After equilibrium the evaporation was changed to 9 lit-
ers per day; resulting in leaching dropping from 10 to 1 liters per day- In
these runs base saturation was held constant to avoid confounding the effect
2+
of evaporation. When evaporation was started, the Ca leached per unit of
rain immediately decreased due to the decrease in amount of leachate (Fig. 7).
The soil leachate than started to become more concentrated until a new equil-
ibrium with soil solution was established. In the case shown (pH - %pCa =
2.5), field capacity = 0.30 and depth = 300 millimeters. This new equili-
2+
brium was reached in about 1000 days, at which time the Ca leached per unit
of rain was only very slightly higher (10.34 x 10" vs. 10.22 x 10" eq/liter)
than in the system where no evaporation was allowed. If evaporation was de-
creased instead of increased, a period of increased base loss per unit of
rainfall was obtained, and the resultant plot is virtually the inverse of that
shown in Fig. 7.
Only a few experiments were conducted with the model in which partial
pressure of C09 was a variable. Results of one of these (Table 2) show that
-4 -3
at pH - %pCa = 3.0 changing C09 from 3 x 10 to 3 x 10 atmospheres had
2+
very little effect on soil pH or on leaching of Ca" . However, at pH - ^pCa
2+
=4.0 and 4.5 leaching of Ca increased by 33 and 78%, respectively, with
2+
the increase in C09. Increased leaching of Ca leached due to C09 was ac-
companied by an equivalent increase in HCO ~ in the leachate. Apparently
2+
changes in Ca leaching due to the strong acid anions in the rainfall are
virtually independent of CO- partial pressure. Leaching of cations in asso-
ciation with HCOZ seems to be relatively unimportant when pH - %pCa is 3.5 or
less but at pH - J^pCa levels above 4.0 it becomes the major factor, particu-
larly if the rainfall is non-acidic.
Sulfate Adsorbing System
The effects of sulfate adsorption on base removal by acid rainfall as pre-
23
-------
2+
Table 2. Effect of CCL partial pressure on extract pH and on Ca leached
using simulated pH 4.0 rainfall.
C02 _ Ca leached
o
pH - %pCa (atm) pH, 1:1 meq/m % change
~ n 3 x 10": 5.41 12.28
<3'u 3 x TO'3 5.36 12.80
. , 3 x 10"J 5.88 12.94
3 x 10"° 5.77 14.50
, n 3 x 10"^ 6.34 13.48
^'U 3 x TO"3 6.16 17.94
45 3 x 10-^ 6.77 14.72
3 x 10-3 6.52 26.20
24
-------
12
in
O
x 10
0!
cr 8
cr
-------
dieted by the model are interesting and important. I know of no experimental
results that either support or refute these predictions. Therefore the pre-
dictions should be considered as testable hypotheses.
For these short-term simulations involving a soil with significant sulfate
_2
adsorption capacity an adsorption maxima (1C,..) of 3.6 x 10 moles/kg and a
/L
one-half maximum concentration (kj) of 1.8 x 10" moles/liter were used.
-s
These values were calculated from the results of Chao ejt al_. (1962) and app-
2-
roximate their values for an Astoria soil. Total SO. initially present in
-4
the soil was assumed to be 3.15 x 10 moles/kg.
When short-term simulations were conducted with this system using various
characteristics and values of pH - hpCa ranging from 1.5 to 4.0 (Fig. 8), the
results were quite different from those of the non-adsorbing soil (Fig. 5).
2+
In the adsorbing system the Ca ions in the leachate were nearly independent
of the sulfate ion concentration in the rainfall, i.e. independent of sulfuric
acid induced rainfall acidity. The reason for this independence is that the
solution concentration was largely controlled by the sulfate adsorption pro-
perties rather than rainfall.
2-
This independence was temporary, when the input SO, concentration was in-
2-
creased, the adsorbed SO, tended to increase until eventually a new equili-
brium was established with a higher solution concentration, and base removal
then proceeded at the higher rate.
Conversely, when the solution rainfall input was again lowered, base re-
moval preceeded at a higher rate while sulfate desorption occured. When the
2
evaporation experiment shown in Fig. 7 was conducted using a simulated SO,
adsorbing soil, the time required to reach a new equilibrium was increased by
several -fold. The actual time, of course, was a function of the specific
K and k: of the soil. These effects point out the possibility that with
max '2
sulfate adsorbing soils, increased base removal may not occur in detectable
amounts until stressed with acid rain for long periods, but if the stress is
2_
removed, base removal would continue until the adsorbed SO. decreased to
equilibrium with the new input level. It should be recognized that these sim-
ulations were based on the assumption of complete reversibility of sulfate
adsorption. If a portion of the adsorption sites were irreversible the leach-
ing of basic cations after sulfuric acid stress was removed would be less than
26
-------
3.0 .
0>
0)
£4.0
o
o
o>
5.0
' o
,O
o>
O
i
6.0 .
pH-l/2Pco
4.0
3 O
20-
I -5
5.0
45
4.O
3.5
3.0
F 2- .1
-log I SO, + CM in
Rainfall, eq / littr
Figure 8. Model prediction of concentrations of Ca
2-
2+
in leachate
2-
of a S04 adsorbing soil as a function of [SO. + Cl~]
and pH - %pCa. Leachate volume is equal to rainfall.
27
-------
the equivalent amount of sulfate adsorbed.
LONG-TERM SIMULATIONS
Several longer-term simulations were run with the model. In contrast to
the results reported above, in these cases base saturation and pH - %pCa were
2+
.allowed to respond to gains or losses in Ca . Results are reported for two
runs, one assuming sulfate adsorption properties similar to those of the As-
toria soil (Chao et_ aj_., 1962), and the other assuming very low sulfate ad-
sorption. The initial base saturation was low (20% of permanent change), and
the relationship of pH - JgpCa to base saturation was that shown by the lower
line (montmorillonitic soils) of Fig. 2. Initial conditions and soil proper-
ties used in these simulations are shown in Table 3.
The rainfall used was the pH 4.0 rain shown in Table 1. A total of 1100
mm rain per year was simulated, one-twelfth of which was applied each month.
The pattern within months included 13 days per month in which rain occured in
amounts varying from 1.1 to 22 mm/day (Table 4). Potential evapotranspiration
rates were changed each month and are typical of those in the northeastern
United States. Potential evaporation exceeded rainfall for the May - Sept.
period.
The predicted solution pH values of a 1:1 soil-water system for a five-
year period are shown in Fig. 9. The seasonal fluctuations predicted are of
the order of .25 pH units for the non-adsorbing soil. This results from changes
in solute concentration due to the lack of leaching during the summer period
when evapotranspiration exceeds rainfall. The increased solute concentration
o
decreases pH due to the "salt effect" discussed previously. In the SO, ad-
sorbing soil these fluctuations are much smaller. This damping effect is due
2_
to the control the SO. adsorption exerts on solution anion concentration.
Measurements of pH in soil water suspensions or leachates often vary mark-
edly with time (Russel, 1961 p 105; Cole and Ballard, 1970). Smooth seasonal
fluctuations such as are observed in the model output are rare, but actual
rainfall and leaching patterns are also highly variable between seasons. The
effects demonstrated by the model are undoubtedly a major factor in inducing
fluctuations. Effects of this magnitude are probably realistic and could con-
stitute a major source of error in experiments attempting to measure field pH
changes due to acid rainfall inputs.
28
-------
Table 3. Initial conditions and soil properties for a 10-year acid rain-
fall simulation
2_
SO. Adsorbing Non-adsorbing
Soil Soil
Cation Exchange Capacity
(eq/kg)
Initial Base Saturation
(«)
Depth (meters)
0.10
20.00
0.30
0.10
20.00
0.30
Field Capacity
(% volume) 30.00 30.00
Permanent Wilting Point;
(% volume) 12.50 12.50
Bulk Density
(kg/liter) 1.25 1.25
C02 Partial Pressure (atm) 3 x 10~4 3 x 10~4
2_
SO, Adsorption
K (moles/kg) 3.6 x 10"3 3.6 x 10"5
rriuX
\ (moles/liter) 1.8 x 10"4 1.8 x 10"3
Initial S (moles/kg) 8.56 x 10"5 1.42 x 10"5
K - A1(OHK 10-33.8 lo'33'8
5 p -3
29
-------
Table 4. Rainfall and evapotranspiration patterns used for 10-year simula-
tions
Month
Jan.
Feb.
March
April
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
Potential
Evapotranspiration
mm/ day
.033
.067
.533
1.533
3.067
4.367
5.133
4.533
3.323
1.767
.633
.100
mm/month
1.0
2.0
16.0
46.0
92.0
131.0
154.0
136.0
100.0
53.0
19.0
3.0
Rainfall
mm/month
91.7
91.7
91.7
91.7
91.7
91.7
91.7
91.7
91.7
91.7
91.7
91.7
1100.4
30
-------
58r
«- 5.6
^
5.01-
Non-Adsorbing So
, 2-
SO4 Adsorbing Soil
MAY OCT MAY OCT MAY OCT MAY OCT MAY OCT MAY
Time
Figure 9. Simulated time-based fluctuations in soil pH using pH
4.0 rainfal1.
31
-------
The total (exchangeable plus solution) Ca2+ in the system dropped in a
stepwise pattern (Fig. 10). A small gain occured during the summer due to
rainfall inputs with no leaching. This was followed by a sharp drop in the
fall. In this case the loss was lower for the sulfate adsorbing soil than for
the non-adsorbing soil, but in the adsorbing soil the loss increased slightly
each year. This increase is more apparent in Figure 11 where only the April
30 values are shown. By the end of the 10-year period the loss rate approach-
ed that of the non-adsorbing soil. This occured because sulfate was adsorbed
from the rainfall, resulting in higher equilibrium solution concentrations.
While these effects may be of considerable importance, the graphs must be
interpreted with caution as the base loss pattern of sulfate adsorbing soils
depends on the initial sulfate level. It appears, however, that adsorption
dampens the seasonal oscillations.
An interesting effect is observed in the plot of solution pH values on
2+ 2-
April 30 (Fig. 12). Even though less Ca was lost from the SO. adsorbing
soil than the non-adsorbing soil, the pH of the soil-water suspension dropped
at a slightly faster rate. The reason for this is not clear.
2+
The net change in soil Ca per equivalent of excess acidity in the rain-
fall is about 98% at the start and 96% at the end of the ten-year period for
the non-adsorbing soil. Base saturation decreased from 20% to 17.12%. Fur-
2+
ther declines in base saturation would rapidly decrease the Ca loss per unit
of H added. More precise information on the nature of the functional relation-
ship between base saturation and pH - %pCa is required to simulate more accur-
ately the effects in this region.
32
-------
3.8
CO
QJ
O
3.7
CM
OJ
U
3.6
o
3.5
Non-Adsorbing Soil
2-
SO4 Adsorbing Soil
OCT MAY
OCT
MAY OCT
Time
2+
MAY
OCT
MAY
OCT
Figure 10. Simulated change in total Ca (soluble plus exchange-
able) in 0.3 meters of soil during a 5-year period
using pH 4.0 rainfall.
33
-------
3.8
CM 3.6
E
l/l
"o
CM
0)
u
To
+->
o
3.4
3.2
3.0
S2-
-SO4 Adsorbing Soil
o- Non-Adsorbing Soil
0
4 6
Years
8
10
Figure 11.
2+
Simulated total Ca found on April 30 in 0.3 meters
of soil stresses with pH 4.0 rainfall over a 10-year
period.
34
-------
-------
SECTION 6
DISCUSSION
LIMITATIONS
The major limitation of the model is the exclusion of all basic cations
except calcium. The system is complex and it appeared desireable to success-
fully complete and test the model in the present form before attempting to
include additional ions. The time and resources alloted to the initial pro-
gram were fully utilized in completing the version reported here. Fortunately
the model has been useful in providing a basic insight into the effect of soil
properties on leaching of cations due to acid rainfall.
Inclusion of additional cations should not present any serious difficul-
ties. They can probably bast be handled by the use of the well known Gapon
type relationship as shown in eq. (13) - (15) for two component systems.
= C
CaX Cl
= C
= c
(Na+)
.
PaY ^ 9+ 94- 'a
CaX 3 (Ca2+ + Mg2+)
Where [MgX]/[CaX], [KX]/[CaX], and [NaX]/[CaX] denote the ratios of these ions
on the exchange complex, the ( )'s denote solution activities in moles per li
ter, and C,, C?, and C~ are constants for which approximations are available
in the literature. These relationships plus the concept that the total ex-
changeable plus soluble amounts of these ions are always known in the model,
and the equivalence of soluble anions and cations allow the inclusion of any
36
-------
or all of these ions. The exchange relationships are the same as those used
by Dutt et_
-------
2+
would expect to have a leachate with log [Ca ] of -4.52 with no evaporation
(fig. 5). Actually the K comprises a significant portion of the cation in
the leachate so that log [Ca2+ + K+] = -4.52 or [Ca2+] = 3.16 x 10"5 - K. For
this semiquantitative calculation we can assume activities equal to concen-
trations and substitute into (16) so that:
0.025 - 0.008 + 6(K+)/(3.16 x 10"5 - (K+)) (17)
Solving (17) we find [K+] = 9.4 x 10"6 and [Ca2+] = 2.2 x 10"5.
The ratio of dissolved K/Ca is 0.42, or more than 16 fold the ratio of the
exchangeable ions. Surprisingly if this same calculation is carried through
for the pH 3.0 rainfall (Table 2), where log K+ + Ca2+ from Fig. 5 is -3.0,
the predicted ratio of dissolved K/Ca is 0.067 or only about 2% times the
ratio of the exchangeable ions. Thus K appears to be selectively leached in
this system, but the selective removal of K is diminished by the higher ion
concentration in the more acid rainfall. Similarly the selectivity of K leach-
ing would be depressed by the concentration effect of evapotranspiration.
As the ratio of exchangeable K/Ca decreases, the selectivity of K leach-
ing also decreases. For rainfall pH 4.0 from Table 2 and assuming no concen-
tration by evapotranspiration we find that at an exchangeable K/Ca ratio of
0.0087, K/Ca ratios would be equal for the solution and exchangeable compo-
nents. If exchangeable K is depleted below this level, Ca would be selective-
ly leached. It should, however, be noted that equation (16) predicts a zero
level of soluble K at an exchangeable K/Ca ratio of 0.008. This apparent
intercept is an artifact due to sites that exhibit specificity for K and at
very low exchangeable K/Ca levels (16) becomes invalid (Beckett et_ al_., 1966).
+ ?+
However, the concept that selective leaching of K in preference to a
ceases and even reverses at very low exchangeable K/Ca ratios remains valid.
The assumption of uniform equilibration throughout the depth of soil con-
sidered also imposes limitations. The results of the model in the form used
for this report should have general validity but will suffer in applicability
to specific situations where various profile depths have widely varying pro-
perties. Depth effects can be included by dividing the soil into discrete
layers for which successive equilibrations are calculated in the model.
Initial conditions must then be supplied for each depth. Precision may also
38
-------
be added by coupling a soil water model to the exchange equilibrium model in
the manner used by Dutt et_ aj_. (1972) rather than simply assuming leaching of
the soil solution in excess of field capacity.
The relationship of base saturation to Lime Potential utilized here (Clark
and Hill, 1964) is highly empirical. Similar curves can be derived on a much
more theoretical basis. Turner and Clark (1964) show that the relationship
can be described by (18).
K 3
PH - h p(Ca + Mg) = 1/6 log -^L + 1/6 log [CaX %M9X] (18)
KjK [A1X] CEC
Where [CaX] , [MgX] and [A1X] refer to the exchangeable ions in moles and CEC
is the cation exchange capacity in equivalents taken as the sum of the ex-
-14 o
changeable Ca, Mg, and Al ; the K is the ion product of water of 10 at 25 C,
-1 5
K1 is an ion exchange constant for this system determined to be 10 ' , and
3
KAI is the solution product (A1)(OH) . If Mg is not included:
CaX = (CEC)
Where V is the base saturation.
Eq. (18) can then be written as
K 3
pH - %pCa = 1/6 log A1RC- -r + 1/6 log 9/8 (V ^ ~ (19)
10"bb-b (1 - V)
Thus eq. (19) shows a theoretical functional relationship between base sat
uration and pH - %pCa, dependent only on the value of K. -, . The functional re-
lationships assumed from Fig. 2 and used in the model as eq. (5) could be re-
placed directly by eq. (19). A more straightforward approach would be to drop
MgX and use eq. (18) directly along with (20) which simply states that the eq-
uivalents of CaX and A1X add up to the cation exchange capacity.
CEC = 3A1X + 2CaX (20)
The eight equations (1), (2), (6), (7), (8), (9), (18), and (20) now form
a set in which, (considering activities to be equal to concentrations), the
39
-------
unknowns are; S04(sorbed)> tS04], [H+], [Ca2+], [A13+], [HC03"l, CaX and ATX.
The use of the Lime Potential K, as a constant or as an empirical function of
the base saturation is actually unecessary and the validity of the system is
not actually dependent on the "constancy" of the Lime Potential.
Unfortunately, I did not recognize the potential of this approach until its
inclusion would have required a major restructuring of the equilibration sec-
tion of the model so it has not been included in the version reported here.
3+
Controlling solution Al in the model by means of an "apparent solubility
product" of A1(OH)0 is a vast oversimplification of this equilibrium involving
3+ - 3
Al. Apparently the two lines in Fig. 2 arise from different (Al )(OH ) ion
products with the values for the montmorillonitic soils generally ranging
or r o/i -j
between io~°°'° and 10 while most of the non-montmorillonitic soils are
-34 1 -3? R
in the range of 10 to 10 . This difference rather than any direct
effect of the clay type appears to account for the different lines on Fig. 2
(Turner and Clark, 1964). I assume that the lower equilibrium levels of Al
in the montmorillonitic soils is related to the fact that this clay mineral is
generally found in soils that are not highly weathered. For broad scale appli-
cation of the model it would seem appropriate to investigate whether this ion
product can reasonably be predicted by any of the common soil classification
schemes.
The model does not take into account the possible release of cations from
soil minerals to the exchange complex as a result of weathering processes.
In the present form it is not feasible to include this process, but one can
imagine a more sophisticated system including equilibria for various Al, Fe,
and Si species that would predict rate of weathering and cation release from
soils of known mineral composition.
USEFULNESS
Even though several deficiencies of the model are recognized, it is never-
theless extremely useful. The predictions relating to the buffering or dam-
2_
pening effect of soil SO. adsorbing properties are important. Acidity ef-
fects such as pH changes or cation leaching could lag well behind the acid
inputs of the rainfall due to this mechanism, but increased base removal
would continue after the acidity inputs ceased.
40
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It is often assumed that soils with low pH and low basic cation contents
would be highly susceptible to atmospheric chemical influence (Jonsson and
Sundberg 1972). The fallacy of this viewpoint has been previously pointed out
(Wiklander 1973; Wiklander 1974; Malmer and Nilsson 1972). The output of this
model confirms that soils well supplied with bases are most susceptible to base
loss and that as base saturation and lime potential fall to low levels acid
precipitation causes leaching of K+ and Al + ions rather than bases. Unfor-
tunately this transition takes place at very low base saturation levels, as
base removal is almost equivalent to rainfall acidity inputs at 20% base sat-
uration or above.
The obvious method of evaluating rainfall acidity effects in the field is
to measure pH changes. Several of the problems with this approach are appar-
ent from the output of this model. For instance the imposition of acid rain-
fall may immediately lower the measured pH value simply due to higher anion
content, even though a similar effect would occur due to addition of rainfall
containing a neutral salt, or as a result of concentration of salts found in
rainfall by evapotranspiration effects. The seasonal effects on pH shown in
the model are striking. Unfortunately, in nature these are not smooth annual
cycles but are highly irregular. Cole and Ballard (1968) show a variation of
0.3 pH units in drainage water through the forest flow over a period of about
4 hours, the pH decreased as conductivity increased as would be expected
from the present model. The acidic characteristics are further complicated by
biotic uptake and release of both anions and cations. These processes affect
the acid base status of the soils (Reuss 1977). Changes in more fundamental
soil properties such as pH - JgpCa or pH - l/3pAl are much more likely to give
meaningful measures of the effect of external acidity imposed on soils than
are pH measurements.
The initial output from the model indicates that loss of bases from the
system in response to rainfall acidity could be significant when considered
on a time scale of several decades. The system simulated would have lost a-
2+
bout 0.5 moles Ca per square meter over a decade when subjected to pH 4.0
rainfall at a rate of 1100 millimeters per year. While subject to wide annual
variation the downward trend in solution pH of a 1:1 soil water system was
proceeding at a rate in excess of 0.1 units per decade for a soil with the
41
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properties chosen for simulation.
One method of shortening the time necessary for field investigations of
the effect of rainfall acidity is to apply highly acid artificial rainfall.
The model output indicates a reasonable prediction of base removal due to ion
exchange effects, at least to the extent of inputs at pH 3.0 which was the lo-
wer limit of the test run. This can be discerned from the fact that the lines
on Fig. 6 are nearly horizontal in the region where rainfall pH values are be-
low about 4.0. Caution should be observed in interpreting pH values from such
investigations, as highly acid artificial rainfall would increase the solution
ion concentration and pH measurements on the common water suspensions would be
unrealistically depressed.
The model is strictly abiotic and does not take into account biological
processes of any type. It could be very logically used, however, as a module
in a more comprehensive ecosystem nutrient cycling model.
42
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REFERENCES
Anon. 1971. Sweden's case study for the U.N. conference on the human envir-
onment. Air pollution across national boundaries. The impact on the en-
vironment of sulfur in air and precipitation. Stockholm, 1971.
Beckett, P.H.T. 1965. Cation exchange equilibria of calcium and magnesium.
Soil Science 100:118-123.
Beckett, P.H.T., J.B. Craig, M.H.H. Nafady, and J.R. Watson. 1966. Studies
in soil potassium V: The stability of Q/I relationships. Plant and Soil
XXV:435:455.
Chao, T.T., M.E. Harward, and S.C. Fang. 1962 Adsorption and desorption
phenomena of sulfate ions in soils. Soil Sci. Soc. Proc. 26:234-237.
Clark, J.S. and R.G. Hill. 1960. The pH-percent base saturation relation-
ships of soils. Soil Sci. Soc. Amer. Proc. 28:490-492.
Cole, E.W. and T.M. Ballard. 1970. Mineral and gas transfer in a forest
floor - a phase model approach. In: Tree growth and forest soils. (C.T.
Youngberg and C.B. Davey) Oregon State Univ. Press. Corvallis Ore. p.
347-357.
Dutt, G.R., M.J. Shaffer, and W.J. Moore. 1972. Computer model of dynamic
bio-physiochemical processes in soils. Univ. of Ariz. Agric. Expt. Sta.
Tech. Bull. No. 196.
Harward, M.E. and H.M. Reisenauer. 1965. Reactions and movement of inorganic
soil sulfer. Soil Science 101:326-225.
Hasan, S.M., R.L. Fox, and C.C. Boyd. 1970. Solubility and availability of
sorbed sulfate in Hawaiian soils. Soil Sci. Amer. Proc. 34:897-901.
Jonsson, B., and R. Sundberg. 1970. Has the acidification by atmospheric
pollution caused a growth reduction in Swedish forests? Institutionen
for Skogsproduktion (Department of forest yield research) Rapporter och
Uppsater (Research Notes), Skogshogskolan (Royal College of Forestry),
Stockholm 48 p.
Malmer, Nils, and Ingvar Nilsson. On the effects of water, soil, and vegeta-
tion of an increasing supply of atmospheric sulfur SNV PM 402E. Depart-
ment of Plant Ecology. Univ. of Lund. Lund, Sweden.
43
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Reuss, J.O. 1972. Chemical and biological relationships relevant to the ef-
fect of acid rainfall on the soil-plant system. Water, Air, and Soil
Pollution, 7:461-478.
Russel, E.W. 1961. Soil condition and plant growth. 9th edition. Longmans,
London.
Schofield, R.K., and A.M. Taylor. 1955. The measurement of soil pH. Soil
Sci. Soc. Amer. Proc. 19;186-191.
Turner, R.C., and J.S. Clark. 1964. Lime potential and degree of base satu-
ration of soils. Soil Sci. 99:194-199.
Turner, R.C., W.E. Nichol, and S.E. Brydon. 1963. A study of the lime poten-
tial^. Soil Sci. 95:186-191.
Wiklander, L. 1973. The acidification of soil by acid precipitation. Grund-
forbattring 26:155-164.
Wiklander, L. 1974. Leaching of plant nutrients in soils. 1. General Prin-
ciples. Acto Agriculturae Scandinavica 24:349-356.
44
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing}
REPORT NO.
EPA 600/3-78-053
3. RECIPIENT'S ACCESSION NO.
4.TITLE ANDSUBTITLE
SIMULATION OF NUTRIENT LOSS FROM SOILS
DUE TO RAINFALL ACIDITY
5. REPORT DATE
May 1978
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
John 0. Reuss
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Research Laboratory-Corvallis
Office of Research and Development
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
10. PROGRAM ELEMENT NO.
1AA602
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
same
13. TYPE OF REPORT AND PERIOD COVERED
inhousp
14. SPONSORING AGENCY CODE
EPA/600/02
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This paper describes a simulation model that provides a quantitative system utilizing
established relationships from soil chemistry to predict the most likely effect of
rainfall acidity on the leaching of cations from noncalcareous soils.
The model utilizes the relationships between lime
saturation described by Clark and Hill (Soil Sci.
and Turner and Clark (Soil Sci. 99:194-199, 1964).
potential (pH - l/2pCa) and base
Soc. Amer. Proc. 28:490-492, 1962)
-.-.... v-_ . . --.. --.... . __, .-.-.,, the equil ibrium between C0? partial
pressure and H and HC03- in solution, the apparent solubility product of AL(OH)3, the
equilibrium of cations and anions in solution, the Freundlich isotherm description of
sulfate adsorption, and mass balance considerations, to predict the distribution of
ions between the solution and sorbed or exchangeable phases. Ionic composition of leach
ates in response to rainfall composition can thus be computed. Ions considered in the
present version are H+, Ca2+, Al3+,SO/i2~ CL", and
The model
leachate and
,S04d~, CL", and HC03
predicts almost exact chemical equivalence between basic cation removed in
strong acid anions entering the system in the rainfall if pH - l/2pCa
th
above 3.0, at which point the base saturation will generally not exceed
pH - l/2pCa values leaching of anions in association with hT and Al3 b
and these cations predominate when pH l/2pCa falls below 2.0.
is
20%.
becomes
At lower
significar
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS C. COSATI F;ield/GrOUp
Rainfall
Water analysis
Water chemistry
Soil science
Soil chemistry
Plant nutrition
Ecology
Rainfall chemistry
Precipitation
(meteorology) chemistry
Acid rainfall
Soil acidification
04/E
06/F
8. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (This Report,
unclassified
21. NO. OF PAGES
56
20. SECURITY CLASS (This page)
unclassified
22. PRICE
EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION is OBSOLETE
45
U. 5. GOVERNHENI PKINIIFrcTDFKcE. 1976-797-234/194 REGION 10
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