Download An assessment of excess carbon dioxide partial pressures in natural

The Science of the Total Environment 210r211 Ž1998. 173]185
An assessment of excess carbon dioxide partial pressures in
natural waters based on pH and alkalinity measurements
Colin Neal a,U , W. Alan House b , Kevin Downa
b
a
Institute of Hydrology, Maclean Building, Crowmarsh Gifford, Wallingford, Oxon, OX10 8BB, UK
Institute of Freshwater Ecology, The Ri¨ers Laboratory, East Stoke, Wareham, Dorset, BH20 6BB, UK
Abstract
Methods of estimating excess partial pressures of carbon dioxide in river waters using pH and Gran alkalinity
measurements are considered using data from several UK lowland rivers covering a spectrum of industrial, urban
and agricultural catchments. Two simple equations are shown to be eminently suitable except for the most
demanding accuracies at pH values greater than 9 when carbonate and hydroxide ions as well as calcium complexes
with bicarbonate, carbonate and hydroxide become larger. The most basic of these equations, which simply allows for
the averaged effects of temperature and ion activity, is
EpCO 2 s Ž Alk Gran in
m Eqrl units q 10
6ypH
. )10 6ypHr6.0.
The second equation, which allows for variation in temperature and average ionic strength, is
EpCO 2 s
Ž 0.95)Alk Gran in m Eqrl units q 10 6 y pH . )10 6 y pH .
Ž 6.46y 0.0636 t8C .
Within this equation, the 0.95 term represents the average factor which converts the chemical concentration of
monovalent ions into chemical activities and t8C is temperature in degrees Celsius. For more demanding situations,
such as at high pHs, the following equation is suggested
EpCO 2 s
Ž 0.95)Alk Gran in m Eqrl units q 10 6 y pH q 10 6qpHqp K water . )10 6 y pH .
Ž 6.46y 0.0636)t8C. ) Ž 1 q 2.38)10 pH y p K 2 .
As in the previous case, the 0.95 term allows for activity concentration relationships for univalent ions. For this
equation, p K water and p K 2 represent minus the logarithm of the equilibrium constants for the respective reactions
U
Corresponding author.
0048-9697r98r$19.00 Q 1998 Elsevier Science B.V. All rights reserved.
PII S0048-9697Ž98.00011-4
174
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
q
2y
H 2 O s Hqq OHy and HCOy
3 s H q CO 3 , where
p K water s y6.0843q 4471.33r Ž 273 q t8C. q 0.017053)Ž 273 q t8C.
and
p K 2 s y6.498q 2902.39r Ž 273 q t8C . q 0.02379)Ž 273 q t8C . .
The Ž1 q 2.38)10 pHyp K 2 . term allows for the effect of the carbonate ion contribution to the alkalinity and it is the
ratio of the carbonate ion to the sum of carbonate and bicarbonate with both the numerator and denominator in
units of equivalent concentration. The 2.38 term converts the ratio of carbonate to bicarbonate from an activity to an
equivalent concentration ratio. Comparisons of measured EpCO 2 for the River Frome agree well with estimates
based on the above equations and this adds to the confidence of the methodologies above pH 6. For pH- 6, other
methods are required owing to interferences from organic acids and aluminium. Q 1998 Elsevier Science B.V.
Keywords: pH; Alkalinity; Carbon dioxide; Partial pressure; Excess carbon dioxide; Respiration; Photosynthesis;
LOIS; Rivers; Tweed; Aire; Calder; Trent; Don; Ouse; Humber; Tweed; Yorkshire; Frome
1. Introduction
Studies of dissolved carbon dioxide in natural
waters provide an important indicator of their
biological productivity and sewage contamination.
This is because dissolved carbon dioxide provides
an indication of the balance between photosynthesis and respiration by biota, both within the
water column and sediments, and carbon dioxide
transfers from the water column to the atmosphere Žas CO 2 gas. and precipitation as, for
example, calcium carbonate minerals ŽHouse,
1989; Maberly, 1996; Hartley et al., 1996.. The
study of such processes are of ecological and
water management importance at the regional
and national level, given Ža. the large range of
carbon dioxide partial pressures observed within
river systems ŽHoward et al., 1984; Hope et al.,
1994; Dawson et al., 1995; Neal et al., 1997a;
Jarvie et al., 1997. and Žb. potential impacts of
changing climate on riverine water quality and
biological status as identified for example within
the UK Land Ocean Interaction Study ŽLOIS;
Leeks and Jarvie, 1998; Marsh and Sanderson,
1997; Neal et al., 1997b..
While there are detailed methodologies available for the measurement of dissolved carbon
dioxide ŽHope et al., 1995., unfortunately they are
not commonly used. However, there is an alternative, much simplified procedure, available based
on the measurement of two water quality measures, pH and alkalinity, which are standard de-
terminands in the water industry and environmental studies ŽNeal, 1988, 1996; Avila and Roda,
1991.. While not as accurate as some direct methods of determination, the advantages of this alternative procedure are Ža. such data are extensively
available for analysis, Žb. these procedures can be
undertaken with ease using standard electrometric and titrimetric laboratory equipment if care is
taken, and Žc. equipment costs and training times
are relatively low.
To calculate carbon dioxide partial pressures
from pH and alkalinity determinations, a simple
algorithm can be used based on equations of the
type
EpCO 2 s Ž Alk Gran q w Hq x. ) w Hq x r pCO2 )K 0,1 4
Ž 1a .
where wx denotes chemical activity and EpCO 2 is
the dissolved carbon dioxide concentration in a
water sample divided by the dissolved carbon
dioxide concentration in pure water in equilibrium with the atmosphere at the same temperature and pressure. For this equation, Alk Gran and
wHqx are, respectively, the Gran alkalinity and the
hydrogen ion concentration in solution Žin m Eqrl
units. and K 0,1 is taken as a constant given by
K 0,1 s K 0 ) K 1 )10 12 .
Ž 1b .
Here, pCO2 is the partial pressure of carbon
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
Table 1
Chemical reactions used for the chemical speciation calculations: wx represents chemical activities
CO2 gas
s CO2 dissolved
CO2 dissolved q H2 O
K0
where wH2 CO3 0 xU
s H2 CO30
s wH2 CO3 0 xU rpCO2
s wCO2 dissolved x q wH2 CO30 x
H2 CO3 0
K1
s Hqq HCO3 y
s wHq x)wHCO3 y xrwH2 CO3 0 xU
HCO3y
K2
s Hqq CO32y
s wHq x)wCO3 2y xrwHCO3 y x
Ca2qq HCO3y
K3
s CaHCO3q
s wCaHCO3q xrŽwCa2q x)wHCO3y x.
Ca2qq CO32y
K4
s CaCO30
s wCaCO30 xrŽwCa2q x)wCO32y x.
Ca2qq OHy
K5
s CaOHq
s wCaOHq xrŽwCa2q x)wOHy x.
Hqq OHy
Kwater
s H2 O
s wHq x)wOHy x
CaCO3 Žsolid.
K7:SOCaCO 3
s Ca2qq CO3 2y
s wCa2q x)wCO3 2y x
dioxide in air at standard temperature and pressure and K 0 and K 1 are, respectively, the equilibrium constants for the solubility of undissociated
carbon dioxide in water and the dissociation of
this component into hydrogen and bicarbonate
ions ŽTable 1.. The 10 12 term in Eq. Ž1b. is a
scaling factor which enables the use of m Eqrl
units for Alk Gran and wHqx .
There are five potential errors contained within
the approach.
K 0 and K 1 vary with temperature and although the variations in part cancel out when
determining K 0,1 , K 0,1 is not completely independent of temperature.
2. K 0,1 is the product of thermodynamic constants defined in terms of chemical activities
and needs to be corrected for the effects of
ionic strength.
3. Eq. Ž1a. does not allow for the effects of
0
complexes such as CO 32y, CaHCOq
3 , CaCO 3
q
and CaOH which can be prevalent in higher
pH waters.
1.
175
4. pCO2 varies with meteorological conditions
and altitude.
5. Other ions such as organic acids and
aluminium contribute to the Gran alkalinity.
In this paper, the influence of temperature,
ionic strength and ion-pairs is examined to assess
the errors involved: Appendix A provides comments on pCO2 corrections for pressure differences, while Neal and Hill Ž1994. cover corrections for aluminium and organic acid interference. The analysis is undertaken by examining
different approximations that might be used, as
applied to a variety of lowland UK rivers covering
a spectrum of environments from pH 6 to over 10
where calcium concentrations can be relatively
high ŽJarvie et al., 1997. and CO 32y, CaHCOq
3,
CaCO 30 and CaOHq are important.
The paper provides a companion to earlier
work focusing on hydrograph splitting methodologies using alkalinity measurements and inorganic
carbon transfers through acidic upland environments ŽNeal et al., 1997c,d.. It also complements
analytical methodologies for acidic waters where
the low alkalinities encountered introduce high
proportionate analytical errors in EpCO 2 estimation ŽNeal, 1988; Neal and Hill, 1994.. A simplified generalized equation is provided for use in
broad based water quality studies and as a basis
for extending and enhancing ongoing LOIS and
associated research ŽNeal et al., 1998a,b,c..
2. Analytical methodology
The primary goal to this paper is to assess to
what degree excess partial pressures of carbon
dioxide can be approximated by simple calculations using only measurements of pH, alkalinity
and temperature. For the calculations, use was
made of about 3 years of LOIS water quality data
collected weekly from 15 sites: 11 for relatively
clean and agricultural environments Žthree sites
on the Tweed, one on the Derwent and seven on
the Yorkshire Ouse and its tributaries . and four
urban and industrial environments Žthe Aire,
Calder, Don and Trent.: some 2052 data points.
Detailed descriptions of the hydrology, water
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
176
Table 2
The temperature dependence of the thermodynamic equilibrium constants given in Table 1 is based on the generalized
equation p K T s ylog 10 K T s aq brTq cT where T is the
temperature in Kelvin
K0
K1
K2
K3
K4
K5
Kwater
K7:SO CaCO3
a
b
c
13.417
y14.8435
y6.498
y2.95
y27.393
1.40
y6.0843
y13.543
y2299.60
3404.71
2902.39
0.00
4114.00
0.00
4471.33
3000.00
y0.01422
0.03279
0.02379
0.01330
0.05617
0.00
0.017053
0.0401
The thermodynamic constants given in this table are taken
from Harned and Davis 1943 Ž K 0 and K 1 ., Harned and
Scholes 1941 Ž K 2 ., Jacobson and Langmuir 1974 Ž K 3 and
K 7:SOCaCO 3 ., Reardon and Langmuir 1974 Ž K 4 ., Gimblett and
Monk 1954 Ž K 5 . and Covington et al. 1977 Ž K water ..
quality and biology of these rivers are given elsewhere ŽScience of the Total Environment, vol
194r195, 1997.; Leeks et al. Ž1997. provide details
of the sampling, storage and analytical chemistry
methodologies used to produce the data presented in this paper.
Five methods are considered, based on chemical reactions and thermodynamic relationships
given in Table 1 and Table 2, to illustrate increasing degrees of thermodynamic complexity with
allowance for
1. Bicarbonate,
2. Bicarbonate, temperature and ionic strength,
3. Bicarbonate, carbonate and hydroxyl ions,
temperature and ionic strength,
4. Bicarbonate, carbonate, hydroxyl, calciumbicarbonate, -carbonate and -hydroxide
species, temperature and ionic strength, assuming a simple relationship between alkalinity and calcium concentration,
5. Bicarbonate, carbonate, hydroxyl and calcium-bicarbonate, -carbonate and -hydroxide
species, temperature and ionic strength
knowing calcium concentration.
2.1. Case 1: the base case
This is the simplest formulation, as described in
Section 1 ŽEq. 1a and Eq. 1b., and presented in
Avila and Roda Ž1991. and Neal et al. Ž1997a.:
EpCO 2 s Ž Alk Gran
in m Eqrl units q 10
6 y pH
.
12
)10 6 y pH % Ž pCO2 ) K 0 ) K 1 )10. Ž 1c .
f Ž Alk Gran
in m Eqrl units )10
6 y pH
. )10 6 y pH r 5.25.
Ž 1d.
For this case, the thermodynamic constants
used to generate the 5.25 term correspond to K 0
and K 1 values set at 208C. For this and all other
cases presented in this paper, pCO2 for the atmosphere has been set to a value of 10y3 .5.
2.2. Case 2: the base case with correction for the
temperature dependence of K 0 and K 1 and a¨erage
ionic strength
To allow for the effects of temperature on
EpCO 2 estimation, the 5.25 term in Eq. Ž1d.
needs to be replaced by a temperature related
variable Ž f Ž t ...
Using the thermodynamic constants given in
Table 2, f Ž t . is shown to vary in the range 6.44 at
08C to 5.17 at 208C, a range of "11% about the
mean of 5.84 at 108C. The relationship between
f Ž t . and temperature is only slightly curvilinear in
this temperature range. Consequently, linear regression of f Ž t . against t, in 8C, provides an
excellent approximation
f Ž t . s 6.46y Ž 0.0636) t8C. .
Ž 2a .
r 2 s 0.9993 and n s 21 Žtemperatures used for
the calculation 0, 1, . . . , 208C.. Applying this regression relationship within Eq. Ž1c. gives
EpCO 2 s
Ž Alk Gran in m Eqrl units q 10 6 y pH . )10 6 y pH .
Ž 6.46y Ž 0.0636)t8C..
Ž 2b .
To allow for the effects of ion activity Žg . on
EpCO 2 estimation, the right hand side of Eq. Ž2b.
needs to be modified to allow for the relationship
between the concentration and the activity of
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
bicarbonate and hydrogen ions. For charge
balance purposes, bicarbonate needs to be computed from alkalinity and pH in concentration
units in the ŽAlk Gran in m Eqrl units q 10 6y pH . term
of Eq. Ž2b. that approximates the bicarbonate
concentration. In practice, this means that the
10 6y pH term in the bracket must be divided by
the appropriate univalent ion activity coefficient
Žg 1 .. However, to use the full equation, the resultant estimate of bicarbonate concentration must
be converted to chemical activity by multiplying it
by the same ion activity coefficient i.e. the modified term becomes
w HCOy
x
3 f g 1 ) Ž Alk Gran
in m Eqrl units
q10 6 y pH . rg 1
Ž 2c .
which is equivalent to
x
w HCOy
3 f Ž g 1 ) Alk Gran
6 y pH
..
in m Eqrl units q 10
Ž 2d.
The ion activity coefficient varies as a function
of the salt content of the solution and this needs
to be allowed for. For the calculation a typical
background ‘sea salt’ concentration of 10 mgrl of
chloride is used, the charge balance being
matched by monovalent ions. Within the calculation, an allowance is also made for the effect of
alkalinity where it is assumed that the alkalinity is
primarily as bicarbonate ions and that the counterbalancing cation is a divalent one Ži.e. the
alkalinity is taken to be derived from base cation
weathering.. Using the Davies equation ŽAppelo
and Postma, 1993. to calculate g 1 gives values of
0.99 to 0.90 within the alkalinity range considered
in this paper. This variation leads to a reduction
in the EpCO 2 estimate from Eqs. Ž1c. and Ž1d. of
between 0 and 10% depending upon the alkalinity
value. Since the activity correction is rather small,
only the average uni-charged ion activity coefficient Ž0.95. is used to simplify matters. Allowing
for the activity by modifying Eq. Ž2b. and Eq. Ž2d.
gives
EpCO 2 s
177
Ž 0.95)Alk Gran in m Eqrl units q 10 6 y pH . )10 6 y pH .
Ž 6.46y 0.0636)t8C .
Ž 2e .
2.3. Case 3: the base case with additional allowance
for temperature, a¨erage ionic strength, [OH y], and
[CO32 y ]
In this case, allowance is made for the contributions that carbonate and hydroxide ions make
to the total alkalinity by modifying Eq. Ž2b. in two
ways.
Firstly, a hydroxide component is added to the
Ž0.95)Alk Gran in m Eqrl units q 10 6y pH . term. This
component is the hydroxide concentration in
m Eqrl and is given by 10 pHyp K waterq6rg 1. Thus
Eq. Ž2d. becomes
w HCOy3 x f g 1 ) Ž Alk Gran
in m Eqrl units q 10
q10 pH y p K waterq6rg 1 .
6 y pH
rg 1
Ž 3a .
which is equivalent to
w HCO 3y x f Ž g 1 )Alk Gran
in m Eqrl units
q10 6 y pH q 10 pH y p K waterq6 . .
Ž 3b .
Secondly, there is a term for CO 32y and this
equals 1rŽ1 q 2)Žg 1rg 2 .)10 pHyp K 2 ., the ratio
of the bicarbonate to the bicarbonate plus carbonate in equivalent concentration units and g 2 is
the ion activity coefficient for CO 32y. The resultant equation is
EpCO 2 s
Ž 0.95)Alk Gran in m Eqrl units q 10 6 y pH
y10 pHq6 y p K water . )10 6 y pH
= Ž 6.46y 0.0636)t8C .
= Ž 1 q 2.38)10 pHyp K 2 . .
Ž 3c .
2.4. Case 4: allowance is made for temperature,
ionic strength, [CO32 y ], [CaHCO3q], [CaCO30 ] and
[CaOH q] using an approximation linking alkalinity
with calcium concentration
178
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
For this case, calcium complexes with bicarbonate, carbonate and hydroxide are allowed for
under the circumstances where no direct measurement of calcium has been made. To provide a
methodology using the equations presented in
Table 1, an estimate of the total calcium concentration in solution, Ca T 4 , Ca2qq CaHCOq
3q
CaCO 30 q CaOHq, is required. To do this, Ca T 4
is taken to equal the number of equivalents of
bicarbonate and carbonate charge, i.e.
Ca T 4 Ž in m M r l units . s Alk Gran in
m Eqrl units r 2.
Ž 4a .
This is equivalent to defining the alkalinity
generated within the catchments as being
counter-balanced by the production of calcium by
weathering. The approach is reasonable at moderate to high alkalinities for UK rivers as Ž1.
there is a very strong linear link between calcium
and alkalinity ŽJarvie et al., 1997., Ž2. within
catchment weathering is associated with calcium
aluminosilicate and carbonate weathering and Ž3.
calcium is the dominant non-atmospherically-derived base cation in the rivers. For the calculation, the charge balance is given by
2 y4
4
4
Alk Gran s HCOy
q CaHCOy
3 q 2) CO 3
3
q2) CaCO 30 4 q CaOHq 4 q OHy 4 y Hq 4
Ž 4b .
where all the terms in the 4 brackets are as
concentrations and not as activities.
Allowance is made for chemical activities using
the Davies equation as in case 3 except for the
ion activity coefficients being allowed to vary as a
function of ionic strength rather than being set at
average values.
Using Eqs. Ž4a. and Ž4b., the Davies equation
and the expressions given in Table 1 and Table 2,
the excess carbon dioxide pressure is solved iteratively within a simple spreadsheet programme as
outlined in Appendix B. Within the iterative solution, an initial EpCO 2 value has to be set and this
value is given by the solution given with Eq. Ž2e..
A solution is obtained to these equations when
the Gran alkalinity matches the estimate for the
right hand side of Eq. Ž4b..
2.5. Case 5: allowance is made for temperature,
ionic strength, [CO32 y ], [CaHCO3q], [CaCO30 ] and
[CaOH q] using measured ¨alues of calcium
concentration in solution
For this case, directly measured calcium concentrations are used with the iterative scheme
provided in case 4 to determine more precisely
the calcium complexes with bicarbonate, carbonate and hydroxide. To do so, Eq. Ž4a. is replaced
by the constraint that
Ca T 4 s Ca2q 4 q CaHCO 3q 4 q CaCO 30 4
q CaOH q 4 .
Ž 5a .
As with case 4, allowance is made for the
chemical activity-concentration difference using
the Davies equation within the calculations and
the methodology is presented in Appendix B.
2.6. Comparisons between direct measurements and
case 1 to case 5 methodologies
In order to provide a validation of the theoretical methods developed in this paper, the formulations derived have been ‘blind’ tested against
experimental measurements of EpCO 2 using unpublished data originally collected during 1982.
The methods used for the determination of pH,
alkalinity, temperature and calcium concentration
were similar to those used during the LOIS study.
The pH electrode was calibrated in the field at
the field temperature using two buffers
ŽKH 2 PO4-Na 2 HPO4 ; 1:1 ; pHs 7.472 and 0.01
M Na 2 B 4O 7 ? 10H 2 O; ; pH s 9.332, both at
108C.. The cell constant of the conductance cell
was determined over a range of conductances
Ž60]390 m S. using KCl solution and the concentration-conductance data from the LindZwolenik-Fuoss equation ŽLind et al., 1959.. Total alkalinity was measured by Gran titration with
0.1 M HCl and a total of five points in the pH
range of 4 to 3 ŽMackereth et al., 1978..
The field site was at the river gauging station
on the R. Frome in Dorset, England ŽNGR
SY868868.. This site has been used in many previous studies of long-term changes in water quality and investigations of nutrient loads Že.g. Casey,
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
1975; Casey and Clarke, 1979; Talbot et al., 1990;
Casey et al., 1993.. Ten measurements were made
between April and September. The procedure
consisted of making field measurements between
09:00 and 10:00 h of temperature, conductivity
and pH with the calibration of all instruments in
the field prior to the measurements. A 1-l sample
of water from a depth of ; 0.5 m below the water
surface was collected from a well-mixed zone of
the river. This was immediately returned to the
laboratory and filtered through a 0.45 mm cellulose nitrate membrane prior to total alkalinity
and major ion analysis. A separate sample of 250
ml was immediately placed into a glass vessel in a
water thermostat regulated to the temperature of
the river. A humidified gas stream of CO 2 Ž- 10
ml miny1 . and nitrogen Ž; 1 l miny1 ., at the
temperature of the river, was then purged through
the water via a sintered-glass frit. The solution
was then allowed to equilibrate with the gas mixture } taking ; 20 min when pH- 8 and ; 50
min between pH 8 and 8.5. The procedure was
repeated with at least another three different gas
mixtures to give gas compositions with partial
pressures of CO 2 in the range of 0.5]4.3, i.e.
EpCO 2 s 1.5]12.6.
The partial pressure of CO 2 in the gas mixture,
pCO2 , was calculated from the CO 2 flow rate and
saturated water vapour pressure at the river water
temperature with corrections for deviations of the
atmospheric pressure from 760 mmHg. The low
flow rates of CO 2 were calculated from measurements of the pressure difference across a stainless
steel capillary using a dibutyl phthalate manometer. Both the nitrogen and CO 2 gas lines were
calibrated using bubble meters. The pH values
179
obtained at equilibrium for the different CO 2rN2
mixtures are related by the equation:
1 r pCO2 s Ka1 K 0r Ž Alk Gran
ž
in m Eqrl q 10
6 y pH
.
)10 6 y pH q 2 Ka1 Ka2 K 0
/
% Ž Alk Gran
ž
in m Eqrl q 10
6 y pH
. 10 y 2pH /
which is:
1 r pCO2 s R1r10ypH q R 2r10y2 pH
where R1 and R 2 are regression coefficients and
the Ka terms refer to an apparent dissociation
constant. Hence the calibration involved the determination of the regression coefficients from
the laboratory data and using the relationship to
interpolate the pCO2 from the field pH measurement of the same river water.
3. Results
The LOIS rivers show a pH variation in the
range of about 6.6 to 10.4 while the alkalinities
vary between 65 and 4425 m Eqrl. As pH increases, EpCO 2 decreases dramatically from
around 48 at pH- 7 to around a fiftieth of the
atmospheric value at pH 10 to 10.4, as conditions
change from those controlled by predominantly
respiration at low pH to predominantly photosynthesis at high pH in the cleaner rivers ŽTable 3..
Thus, the pH range across the LOIS rivers is
largely determined by the biological activity and
CO 2 transfer to the atmosphere Žsee also Neal et
al., 1998a,b,c..
Table 3
Summary pH, alkalinity and EpCO 2 and methodology error statistics
pH
AlkGr an
Ž m Eqrl.
EpCO2
case 5
% Error
case 1
% Error
case 2
% Error
case 3
% Error
case 4
6.85
7.55
8.34
9.36
10.31
1812
2318
2444
1383
1662
42.65
11.48
2.38
0.12
0.06
18.0
14.3
15.6
35.6
214.8
y1.5
y0.7
0.7
19.1
197.4
y1.6
y1.1
y1.1
y1.9
11.2
1.5
1.6
1.5
0.9
1.8
The percentage errors relate to a comparison of EpCO 2 data for cases 1 to 4 with case 5 estimates. The table presents averages for
pH ranges 6 to 7, 7 to 8, 8 to 9, 9 to 10 and ) 10.
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
180
Table 4
Linear regression analysis of EpCO2 estimates from cases 1 to
3 with case 5
Case
Constant
Gradient
r2
1
y0.13
Ž"2.04.
0.00
Ž"0.28.
y0.03
Ž"0.27.
0.0023
Ž"0.060.
1.155
Ž"0.004.
0.993
Ž"0.000.
0.993
Ž"0.000.
1.018
Ž"0.000.
0.9930
2
3
4
However, if percentage errors are considered,
then, for the cases without allowance for carbonate and calcium complexation, the magnitude of
these errors increase with increasing pH ŽTable
3.. Thus, in the pH range 9]10 there are errors of
up to about 35% and above pH 10 there are
errors of the order of 200% for cases 1 and 2. For
cases 3 and 4, where a simple approximation is
made for calcium concentration and calcium complexation is allowed for, the errors become much
reduced throughout the pH range when estimates
are compared with the most accurate assessment
Žcase 5.. The similarity of these cases illustrates
that the main reason for the discrepancy between
cases 1 and 2 and 3 and 4 is related to the
changing importance of carbonate ions through
the pH range: calcium complexation is of much
lower significance.
With regards to a comparison of more direct
and estimated EpCO 2 values based on data from
the River Frome, measured EpCO 2 values are in
the range 2]7 times the atmospheric value ŽTable
5.. Calculated values of EpCO 2 based on the case
2]5 equations give slightly higher values than
those measured Žby about 11%.: the case 1
methodology gives a positive error of about twice
this value. In comparison, thermodynamic estimation of EpCO 2 based on a full chemical analysis
where all the major inorganic carbon complexes
are allowed for ŽWateq: Truesdell and Jones,
1974; Nordstrom et al., 1984., give values typically
about 8% too low. Elimination of one outlier
point Ža q34% and q9% error for method three
0.9998
0.9998
0.9999
The terms in brackets correspond to twice the standard error:
N s 2052.
Comparison of calculation methodologies show
remarkably consistent patterns with very strong
linear inter-relationships between computed
EpCO 2 values when compared with the most
accurate case 5 assessment ŽTable 4.. The poorest
relationship occurs for the simplest estimate
where EpCO 2 is typically overestimated by about
15]20% and data scatter is higher. However, even
in this case, the variation is small compared to
the wide range of EpCO 2 values determined Ž0.1 to ) 100 times the atmospheric value.. Furthermore, a change in K 0,1 within Eq. Ž1d. from
5.25 to about 6 based on a value more appropriate to an average temperature for the UK rivers
and a typical ionic strength, would cancel out the
average deviation Žbut not the scatter .. For the
remaining cases, the correspondences are higher
and there seems little to choose between the
approaches ŽTable 4..
Table 5
A comparison of measured and calculated EpCO 2 for the river Frome
pH
Alk Ž m Eqrl.
Temp Ž8C.
Method 1
Method 2
Method 3
Method 4
Method 5
Method Wateq
Measured
8.29
8.38
8.21
8.31
8.24
8.42
8.32
8.17
8.01
8.20
3930
3880
3970
4010
3850
3890
3940
3930
3680
3970
12.2
10.6
13.6
18.0
16.6
15.2
17.0
17.8
16.6
15.3
3.8
3.1
4.6
3.7
4.2
2.8
3.6
5.1
6.8
4.8
3.4
2.7
4.1
3.5
3.9
2.6
3.3
4.8
6.3
4.4
3.3
2.6
4.1
3.4
3.8
2.5
3.3
4.7
6.3
4.3
3.4
2.6
4.1
3.5
3.9
2.5
3.3
4.8
6.4
4.3
3.4
2.7
4.2
3.5
3.9
2.6
3.3
4.8
6.4
4.4
2.8
2.2
3.5
2.9
3.2
2.1
2.7
3.9
5.3
3.6
2.6
3.9
3.3
3.4
2.3
2.5
4.5
5.7
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
and Wateq estimation, respectively. reduces the
case 2]5 errors to about q7% and increases the
Wateq error to about y10%. From this, it is
clear that Ž1. the alkalinity-pH estimated values
of EpCO 2 agree well with observation with typical errors of less than 15% and Ž2. detailed thermodynamic assessment of EpCO 2 based on an
elaborate full set of major ion chemistries does
not significantly improve on the accuracy of prediction. Thus, the field measurements add support to the validity of the methodologies developed within this paper ŽTable 6..
4. Discussion
For all the waters studied, a simplified approach to EpCO 2 assessment based on pH and
alkalinity measurements is shown to be adequate
from a theoretical standpoint and all the calculations needed can be made using standard spreadsheet packages ŽLOTUS 123 version 5 in this
case.. For many applications, there is little need
to use more elaborate formulation than either
Eq. Ž1d. Žwith the 5.25 term replaced by 6. or Eq.
Ž2e. and the latter approach is recommended
when information on water temperature is available. However, for more rigorous applications,
particularly at pH) 9, then Eq. Ž3c. is recommended.
4.1. Other analytical uncertainties
Within the paper comment has not been made
on Ža. waters which are more acidic ŽpH- 6. and
Žb. analytical chemistry errors. In the former case,
Table 6
A comparison of measured and estimated excess partial
pressures of carbon dioxide for eight Frome river samples:
percentage errors, minimum and maximum percentage errors
and standard deviation to errors
Method 1
Method 2
Method 3
Method 4
Method 5
Wateq
Average
Minimum
Maximum
S.D.
21.8
11.3
9.5
11.2
12.1
y7.8
12.8
2.1
0.3
1.6
2.5
y16.5
44.5
34.0
31.5
33.5
34.7
9.2
9.2
9.3
9.0
9.2
9.3
7.1
181
such acidic waters pose a more difficult challenge
as alkalinities are much lower Žnegative in some
cases. and there are strong interferences from
aluminium and organic acids which are enriched
in such waters. However, there are more appropriate analytical titrimetric procedures available ŽNeal, 1988.. In the latter case, the main
error is probably associated with the measurement of pH where discrepancies of 0.1 pH or
more can occur in the field and laboratory without the most rigorous degree of analytical care.
Accurate measurement of pH is particularly problematical in acidic waters due to the low ionic
strengths involved ŽNeal and Thomas, 1985.. Correspondingly, for less acidic and more basic waters, degassing of carbon dioxide during sampling,
storing and subsequent pH measurement can lead
to anomalous increases in pH. Even with reasonable care, the introduction of such errors can
result in an EpCO 2 measurement uncertainty of
plus or minus 25% in terms of accuracy although
precision may be much better Ži.e. the electrode
response and degassing effects are consistent ..
While there is considerable merit in undertaking
pH measurement in the field to minimize degassing and other sample storage effects, it must
be remembered that electrode drift due to differences in temperature between sample, electrodes and buffers as well as electrode storage
prior to analysis can be important. No standard
procedure is recommended here, but it is strongly
urged that good protocols be established which
take into account these potential errors.
With regards to allowances for the actual ionic
strength of water samples, a method analogous to
the case 3 situation ŽHoward et al., 1984; House
et al., 1988. estimates the ionic strength from a
conductivity measurement of the sample ŽTalbot
et al., 1990. and then applies the Davies equation
to determine individual ion activity coefficients.
While, this change is of second order importance,
where conductivity measurements are available, a
correction can be made using a linear relationship between ionic strength Ž I . and conductivity:
regression analysis of all the LOIS core data gives
I Ž molr l . s 13.1)10 y 6 )conductivitym Srcm
at 258C
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
182
q 0.7051)10 y 3
where R 2 s 0.573 and N s 1000.
Given all these factors, then for situations Ža.
where highly accurate EpCO 2 determinations and
Žb. where alkalinity becomes especially high and
calcium carbonate solubility controls and complex
speciation interactions become more dominant,
then detailed chemical and thermodynamic analysis may well be required. However, at this level of
sophistication, direct measurements of EpCO 2
such as those described by Hope et al. Ž1995.
become appropriate.
For the lowland waters with positive alkalinities
studied in this paper, the difference between
measured and calculated values of EpCO 2 of
- 40% is adequate and surprisingly good for the
level of analytical sophistication and simplicity of
methodology.
5. Conclusions
Measurement of pH and alkalinity in the field
is relatively quick and easy to undertake provided
reasonable care is taken over pH measurement
and samples of river water are not allowed to lose
carbon dioxide prior to pH measurement. Given a
good analytical procedure and the merit of simple
algorithms for assessing EpCO 2 , then campaigns
can easily be undertaken to examine at a semiquantitative to quantitative level the dynamics of
CO 2 transfers within river systems.
The measurement of EpCO 2 using pH and
alkalinity analysis needs to be considered an integral part of riverine environmental water quality
and biological studies. Such studies take on a
special importance within areas such as lowland
UK waterways where the effects of climate variability and drought conditions are most apparent.
Appendix 1
Air pressure dependence upon EpCO 2Within
the calculations of EpCO 2 described in the text,
the partial pressure of carbon dioxide in the air
has been taken as 10y3 .5, the standard value for
sea level, at an atmospheric pressure of 760 mmHg
Ž1013.25 mb.. However, with altitude and changing weather conditions, atmospheric pressure
varies about this value. For more accurate EpCO 2
assessment, allowance for this difference is required. If the actual pressure is not known, then
it may be calculated from the expression
PsrP0 s ŽŽ 288 y 0.0065) s . r288.
5.256
Ž A-1a.
where P is pressure, s is the altitude in metres
and P0 is the standard atmospheric pressure at
sea level ŽSmithsonian Institute, 1966.. Alternatively if the pressure is known then
PsrP0 s mmHgr760s mbr1013.25
Ž A-1b.
To compensate for the pressure change,
EpCO 2 s EpCO 2
calculated ) PsrP0
Ž A1-c.
Thus, for example, based on Eqs. ŽA-1a. and
ŽA-1c., at an altitude of 1000 m, PsrP0 s 0.887, a
change in EpCO 2 of about 11%.
Appendix 2
EpCO 2 estimation using methods 1]5 presented in this paper, using a LOTUS 123 spreadsheet programme
Here two tables are provided. The first gives
the spreadsheet formulations to use and the second provides an automated means of undertaking
the iterative calculations for a matrix of values
rather than a single solution.
Table 1a shows a spreadsheet formulation for
EpCO 2 estimation. To determine a solution to
the equations presented in cases 4 and 5, the
spreadsheet routine backsolver is employed. To
use backsolver, where the equation cell is the
charge equation Žcolumn i., the adjustable variable is the case 4r5 EpCO 2 estimate cell Žcolumn
h. for a target value is 0. The calculation is based
on information in row 17 Žhence the terms a17,
b17, c17 . . . ab17.. For the case where no calcium
data is available, then either zero or negative
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
values need to be given in the calcium cell Žd17.:
cell j17 provides an algorithm for distinguishing
the case 4 and case 5 situations. Within the table,
concentrations are provided as activities unless
stated; rootŽI. is the square root of the ionic
183
strength and gamma1 and gamma2 correspond to
g 1 and g 2 , respectively. The wording highlighted
in bold in the value column of the table corresponds to positions where data values need to be
inserted.
Row
Header row
Value row
a
b
c
d
e
f
g
pH
Alkalinity Ž m Eqrl.
Temperature Ž8C.
Ca Žmgrl.
EpCO2 Case 1
EpCO2 Case 2
EpCO2 Case 3
h
EpCO2 Case 4r5
i
Charge
j
k
l
m
n
o
p
q
r
s
t
u
v
w
x
y
z
aa
ab
ac
ad
CaŽtot.
CaCO3 sat
k0
k1
k2
k3
k4
k5
kwater
k7
OH
H2CO3
HCO3
CO3
Ca2 q
CaHCO3
CaCO3
CaOH
rootŽI.
gamma1
gamma2
Insert value
Insert value
Insert value
Insert value
ŽB17 q Ž10H y A17..) Ž10H Ž6 y A17..r5.25
ŽŽ0.95) B17. q Ž10H y A17..) Ž10H Ž6 y A17..rŽ6.46y Ž0.0636) C17..
ŽŽ0.95) B17. q ŽŽ10H y A17.r0.95. q ŽŽ10H ŽA17q 6 q @LOGŽR17...r0.95..) Ž10H Ž6 y A17..
rŽŽ6.46y Ž0.0636) C17..) Ž1 q Ž2) Ž0.95r0.8.) 10H ŽA17q @LOGŽN17.....
Insert estimate
ŽThe value of the case 3 estimate of EpCO2 , g17.
ŽB17)Ž10H y 6.. q ŽŽ10H y A17.rAC17. y ŽV17rAC17. y Ž2) W17rAD17.
yŽY17rAC17. y Ž2) Z17r1. y ŽT17rAC17. y ŽAA17rAC17.
@IFŽD17-s 0,B17r2000000,D17r40000.
@LOGŽW17) X17. y @LOGŽS17.
10H y Ž13.417y Ž2299.6rŽ273 q C17.. y Ž0.01422) Ž273 q C17...
10H ŽyŽy14.8345q Ž3404.71rŽ273 q C17.. q Ž0.03279) Ž273 q C17....
10H ŽyŽy6.498q Ž2902.39rŽ273 q C17.. q Ž0.02379) Ž273 q C17....
10 H y Žy2.95q Ž0.0133) Ž273 q C17...
10H ŽyŽy27.393q Ž4114rŽ273 q C17.. q Ž0.0561) Ž273 q C17....
10H y 1.4
10H y Žy6.0846q Ž4471.33rŽ273 q C17. q Ž0.017053) Ž273 q C17....
10H y Žy13.543q Ž3000rŽ273 q C17. q 0.0401) Ž273 q C17...
qR17r10H y A17
qL17) Ž10H y 3.5.) H17
qM17) U17rŽ10H y A17.
qN17) V17rŽ10H y A17.
qJ17)AD17rŽŽ1rAD17. q ŽV17) O17rAC17. q ŽW17) P17rAC17. q ŽQ17) T17rAC17..
qO17) X17) V17
qP17) X17) W17
qQ17) T17) X17
ŽŽŽ20r35450. q T17q V17q Ž10H y A17. q Ž4) ŽW17q J17...r2.H 0.5
10H y Ž0.5) ŽŽAB17rŽ1 q AB17.. y Ž0.3)AB17...
10H y Ž0.5) 4) ŽŽAB17rŽ1 q AB17.. y Ž0.3)AB17...
Table 1b shows a macro scheme to use with the
spreadsheet formulation given in Appendix B,
Table 1a. Within the table, cell c10 and cells d3 to
d7 require user-specified values. In the case of
cells c10 and d3 to d5, fixed values of 1, 0, 9 and 8
are respectively used. The start and end rows are
given as 17 and 56 in cells d6 and d7 to provide
an example of calculations for data provided in
rows 17 to 56 inclusive, but these are changed
according to individual needs. To use this scheme
it is recommended that
Row Column a
1
2
3
4
5
6
7
8
9
10
Column c Column d
for $c$10;$d$6;$d$7;1;$a$84
Target value s
Equation cell Žcolumn. s
Adjustable variable Žcolumn. s
Start rows
End rows
backsolve @coordŽ1;$d$4;$c$10;1.;
$d$3;@coordŽ1;$d$5;$c$10;1.4
Counter s
0
9
8
17
56
1
184
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
1. The information given in Appendix B, Table
1b be typed into the spreadsheet beginning in
cell a1;
2. The header row presented in Appendix B,
Table 1a be typed into the spreadsheet row
15 and the equations given in the table be
typed into row 17;
3. Data for pH, alkalinity, temperature and calcium be typed into rows a17, b17, c17 and
d17; a18, b18, c18, d18 etc. and the formulas
Že17 to ad17. be copied to all the rows with
data. If calcium concentrations are not determined then insert zeros or negative values
in the appropriate row of the d column. If
temperature is not known then insert an average estimate Že.g. 108C.;
4. The spreadsheet be saved for safety;
5. Provide an estimate of EpCO 2 in column h
using values from the corresponding case 3
estimate Žcolumn g. using the range-value
keys;
6. Apply the tools-macro-run facility, starting in
cell a1.
References
Appelo, C.A.J, Postma, D., 1993. Geochemistry of groundwater and pollution. Balkema, Rotterdam, p. 536.
Avila, A., Roda, F., 1991. Red rains as major contributors of
nutrients and alkalinity to terrestrial ecosystems at Montseny ŽNE Spain.. Orsis 6, 215]229.
Casey, H., 1975. Variation in the chemical composition of the
R. Frome from 1965]1972. Freshwater Biol. 5, 507]514.
Casey, H., Clarke, R.T., 1979. Statistical analysis of nitrate
concentrations from the River Frome ŽDorset. for the
period 1965]76. Freshwater Biol. 9, 91]97.
Casey, H., Clarke, R.T., Smith, S.M., 1993. Increases in nitrate
concentrations in the River Frome ŽDorset. catchment
related to changes in land-use, fertilizer applications and
sewage inputs. Chem. Ecol. 8, 105]117.
Covington, A.K., Ferra, M.A., Robinson, R.A., 1977. Ionic
product and enthalpy of ionization of water from electromotive force measurements. J. Chem. Soc. Faraday Trans.
1, 1721]1730.
Dawson, J.J.C., Hope, D., Cresser, M.S., Billett, M.F., 1995.
Downstream changes in free CO 2 in an upland catchment
in NE Scotland. J. Environ. Qual. 24, 699]706.
Gimblett, F.G.R., Monk, C.B., 1954. E.M.F. studies of electrolytic dissociation, part 7. Some alkali and alkaline earth
metal hydroxides in water. Trans. Faraday Soc. 76, 964]972.
Hartley, A.M., House, W.A., Leadbeater, B.S.C., Callow, M.E.,
1996. The use of micro-electrodes to study the precipitation
of calcite upon algal biofilms. J. Colloid Interface Sci. 183,
498]505.
Harned, H.S., Davis, R., Jr, 1943. The ionization constant of
carbonic acid in water and the solubility of carbon dioxide
in water and aqueous salt solutions from 0]508C. J. Am.
Chem. Soc. 65, 2030]2037.
Harned, H.S., Scholes, S.R., 1941. The ionization constant of
HCOy
3 from 0]508C. J. Am. Chem. Soc. 63, 1706]1709.
Hope, D., Billett, M.F., Cresser, M.S., 1994. A review of the
export of carbon dioxide in river water, fluxes and processes.
Environ. Pollut. 84, 301]324.
Hope, D., Dawson, J.J.C., Cresser, M.S., Billett, M.F., 1995. A
method for measuring free CO 2 in upland streamwater
using headspace analysis. J. Hydrol. 166, 1]14.
House, W.A., 1989. Kinetics of crystallisation of solids from
aqueous solutions. In: Comprehensive chemical kinetics
reactions at the liquid-solid interface, vol. 28, chapter 3.
Elsevier, Amsterdam.
House, W.A., Shelley, N., Fox, A.M., 1988. Chemical modelling applications to experimental streams. Hydrobiologia
178, 93]112.
Howard, J.R., Skirrow, G., House, W.A., 1984. Major ion and
carbonate chemistry of a navigable freshwater canal. Freshwater Biol. 14, 515]532.
Jacobson, R.L., Langmuir, D., 1974. Dissociation constants of
calcite and CaHCOq
3 from 0]508C. Geochim. Cosmochim.
Acta. 38, 301]318.
Jarvie, H.P., Neal, C., Leach, D.V., Ryland, G.P., House,
W.A., Robson, A.J., 1997. Major ion concentrations and the
inorganic carbon chemistry of the Humber rivers. Sci. Total
Environ. 194r195, 285]302.
Leeks, G.J.L., Jarvie, H.P., 1998. Introduction to the Land
Ocean Interaction Study ŽLOIS.: rationale and international context. Sci. Total Environ. 210r211, 5]20.
Leeks, G.J.L., Neal, C., Jarvie, H.P., Casey, H., Leach, D.V.,
1997. The LOIS river monitoring network: strategy and
implementation. Sci. Total Environ. 194r195, 101]110.
Lind, J.F., Zwolenik, J.J., Fuoss, R.M., 1959. Calibration of
conductance cells at 258C with aqueous solutions of potassium chloride. J. Am. Chem. Soc. 81, 1557]1559.
Maberly, S.C., 1996. Diel, episodic and seasonal changes in pH
and concentrations of inorganic carbon in a productive
lake. Freshwater Biol. 35, 579]595.
Mackereth, F.J.H., Heron, J., Talling, J.F., 1978. Water analysis: some revised methods for limnologists. Scientific publication no. 36. Freshwater Biological Association 120, 35]42.
Marsh, T.J., Sanderson, F.J., 1997. A review of hydrological
conditions throughout the period of the LOIS monitoring
programme } considered within the context of the recent
UK climatic volatility. Sci. Total Environ. 194r195, 59]70.
Neal, C., 1988. pCO2 variations in stream waters draining an
acidic and acid sensitive spruce forested catchment in midWales. Sci. Total Environ. 76, 279]283.
C. Neal et al. r The Science of the Total En¨ironment 210 r 211 (1998) 173]185
Neal, C., 1996. Towards lumped integrated models of complex
heterogeneous environmental systems. Sci. Total Environ.
183, 115]124.
Neal, C., Thomas, A.G., 1985. Field and laboratory measurement of pH in low-conductivity natural waters. J. Hydrol.
79, 319]322.
Neal, C., Hill, S., 1994. Dissolved inorganic and organic carbon in moorland and forest streams: Plynlimon, mid-Wales.
J. Hydrol. 153, 231]243.
Neal, C., Robson, A.J., Harrow, M., Hill, L., Wickham, H.,
Bhardwaj, C.L., Tindall, C.I., Ryland, G.P., Leach, D.V.,
Johnson, R.C., Bronsdon, R.K., Cranston, M., 1997a. Major, minor, trace element and suspended sediment variations in the River Tweed: results from the LOIS core
monitoring programme. Sci. Total Environ. 194r195,
193]206.
Neal, C., House, W.A., Jarvie, H.P., Leeks, G.J.L., Marker,
A.H., 1997b. Conclusions to the special volume of Science
of the Total Environment concerning UK fluxes to the
North Sea, Land Ocean Interaction Study: river basins
research, the first two years. Sci. Total Environ. 194r195,
467]478.
Neal, C., Robson, A.J., Shand, P., Edmunds, W.M., Dixon,
A.J., Buckley, D.K., Hill, S., Harrow, M., Neal, M., Reynolds,
B., 1997c. The occurrence of groundwater in the lower
Palaeozoic rocks of upland Central Wales. Hydrol. Earth
System Sci. 1, 3]18.
Neal, C., Hill, T., Alexander, S., Reynolds, B., Hill, S., Dixon,
A.J., Harrow, M., Neal, M., Smith, C.J., 1997d. Stream
water quality in acid sensitive UK upland areas, an example
185
of potential water quality remediation based on groundwater manipulation. Hydrol. Earth System Sci. 1, 185]196.
Neal, C., House, W.A., Jarvie, H.P., Eatherall, A., 1998a. The
significance of dissolved carbon dioxide in major lowland
rivers entering the North Sea. Sci. Total Environ. 210r211,
187]203.
Neal, C., Harrow, M., Williams, R.J., 1998b. Dissolved carbon
dioxide and oxygen in the River Thames: spring and summer
1997. Sci. Total Environ. 210r211, 205]217.
Neal, C., House, W.A., Whitton, B.A., Leeks, G.J.L., 1998c.
Conclusions to special issue: water quality and biology of
UK rivers entering the North Sea: the Land Ocean Interaction Study ŽLOIS. and associated work. Sci. Total Environ.
210r211, 585]594.
Nordstrom, D.K., Valentine, S.D., Ball, J.W., Plummer, L.N.,
Jones, B.F., 1984. Partial compilation and revision of basic
data in the WATEQ programmes. United States Geological Survey, Water Resources Investigation Report 84-4186.
Reardon, E.J., Langmuir, D., 1974. Thermodynamic properties
of the ion pairs MgCO30 and CaCO 30 from 10 to 508C. Am.
J. Sci. 274, 599]612.
Smithsonian Institute, 1966. Smithsonian miscellaneous collections, 114, 6th ed. Smithsonian Institution Press, Washington, p. 268.
Talbot, J.D.R., House, W.A., Pethybridge, A.D., 1990. Prediction of the temperature dependence of electrical conductance for river waters. Water Res. 24, 1295]1304.
Truesdell, A.H., Jones, B.F., 1974. WATEQ, a computer programme for calculating chemical equilibrium of natural
waters. US Geol. Survey J. Res. 2, 233]248.