Environ. Sci. Technol. 1988, 22, 1460-1463
A Method for the Estimation of Historical Sulfate Concentrations in Natural Freshwaters Charles B. Epsteln" Environmental Defense Fund, Inc., 257 Park Avenue South, New York, New York 10010
Studies of the effects of atmospheric sulfur deposition on the chemistry of receiving waters have relied on longterm time series of sulfate concentrations. Such time series are often unavailable for a water body of interest. It is here demonstrated that sulfate concentrations can be calculated in low to moderate ionic strength freshwaters by use of the following equation:
Algebraic M e t h o d
The method relies on two basic chemical principles. First, the equivalence of aggregate cations and anions indicates that the sum of the concentrations of cations will equal the sum of the concentrations of anions on an equivalents basis (ref 7; p 139). Symbolically, we may state that n
[SO?-] = (specific conductance - 0.102[HC03-] 0.134[Cl-] - 0.129[N03-] - 0.292[H+] k)/0.138
+
where specific conductance is expressed in micromhos per centimeter, all concentrations are in microequivalents per liter, and k is a constant reflecting the concentrations of sodium and potassium generally found in the water. The assumptions made in the derivation of this equation, and the limitations to its applicability, are discussed. The equation is then tested against the Regional Integrated Lake Watershed Acidification Study (RILWAS) data set and shown to accurately predict sulfate concentrations in 20 out of 23 water bodies.
1460 Environ. Sci. Technol., Vol. 22, No. 12, 1988
m
c = iCUihi + j=l ccjxj =l
Introduction
*Currentaddress: The Rockefeller University,1230 York Avenue, New York, NY 10021.
(1)
where each ai is the concentration in microequivalentsper liter of one of n anions in the solution, and each cj is the concentration of one of m cations in the solution. The second principle is Kohlrausch's law of the independent mobility of ions, which states that each ion in a dilute aqueous solution makes a discrete contribution to the electrical conductance of the solution; in the limiting case of infinite dilution, this contribution is independent of the other ions present (ref 8; p 97). Symbolically,we may state that n
Long-term time series of sulfate concentrations in surface waters are useful in several fields of environmental and geochemical research (1-5). Studies of the role of anthropogenic sulfur oxide emissions in surface water acidification have been based in part on statistical comparisons of emissions and sulfate concentration time series (e.g., ref 2). Research into the response of aquatic systems to atmospheric deposition has found that sensitivity to acidification is related to the relative rates of temporal change in base cation and sulfate concentrations (6). This ratio can only be directly evaluated from long-term time series of sulfate and base cations. The study of water pollution by atmospheric sulfur would benefit from the availability of surface water sulfate time series extending deeper into the past. Despite the usefulness of surface water sulfate time series data, historical data sets are often fragmentary and lacking in information of interest to contemporary investigators. It would therefore be desirable to develop a method allowing the calculation of sulfate concentrations in historical data sets where sulfate itself was not measured. Such a method is presented here, permitting the calculation of sulfate concentrations from more commonly measured parameters. The method is applicable only to waters in which a sufficient number of chemical species are reliably measured, along with electrical conductivity. It may be particularly applicable to water supply systems, where chemical data are temporally extensive, but limited to relatively few solutes that are conventionally regarded as of interest to water supply managers. In principle, the approach presented below could also be used to derive concentrations of species other than sulfate, under circumstances where sulfate was measured but some other solute of interest was neglected.
m
ccj
cui = j-1 i=l
(2)
where C is the measured specific conductance and hi or hj is the ion equivalent conductance of the ith or j t h ion constituent. Equations 1and 2 constitute a system of two equations in m + n 1variables, which can be solved with the elimination of a variable to yield a single equation in which one unknown (e.g., sulfate) is expressed as a function of m + n - 1 measured quantities. We may apply these equations to natural freshwaters, containing as their major cations Ca2+,Mg2+,Na+, K+, and H+ and as their major anions HCO,, C1-, SO:- and NO,. Other typical components of such waters are excluded because no ion equivalent conductances are available for these substances and/or because they are infrequently measured minor components of the total ionic strength (i.e., organic acids, aluminum, phosphate, fluoride, and ammonium). Consequently, eq 1 becomes [Ca] + [Mg] + [Na] + [K] + [HI = [HC03] + [Cl] + [SO,] + [NO,] (3) Equation 2 becomes C = 0.0595[Ca] 0.05306[Mg] 0.05011[Na] + 0.07352[K] + 0.34982[H] + 0.0448[HC03] + O.O7634[C1] O.O798[SO4] + 0.07144[N03] (4) where all concentrations are measured in microequivalents per liter, and C is in micromhos per centimeter. Limiting ion equivalent conductances were taken from MacInnes (ref 9; p 342). Before solving eq 3 and 4 for sulfate, we note that in many freshwaters, calcium and magnesium bear a roughly constant relation to one another, reflecting their joint determination by the weathering of watershed minerals. If [Ca]/ [Mg] = R is nearly constant in any particular body of water, [Ca] + [Mg] can be approximated as [Mg](R + 1)while the contributions of calcium and magnesium to the overall specific conductance can be approximated as [Mg](hM,4- RhMg). Substituting these terms for ([Ca]
+
+
+
+
0013-936X/88/0922-1460$01.50/0
0 1988 American Chemical Society
Table I. Partial Derivatives of Sulfate from eq 5 and the Error in Calculated Sulfate Resulting from a 1% Error in Measurement of an Independent (i.e,, Input) Variable (Concentrations of Other Major Solutes in These Waters Are Also Shown) variable
(X)
cond, pmhos/cm chloride, pequiv/L nitrate pequiv/L bicarbonate pequiv/L hydrogen pequiv/L sodium pequiv/l potassium pequivll PH sulfate, pequiv/L calcium, pequiv/L magnesium, pequiv/L
d[SOl]/d(X)
typical value (Clear Pond)"
error term,b pequiv/L SO4
typical value (Squash Lake)"
error term,b pequiv/L SO4
30.0 7.3 3.8 80.3 0.2 39.1 3.9 6.7 126.0 164.9 33.3
2.18 0.07 0.04 0.59
34.0 7.7 23.7 7.7 40.0 21.9 10.0 4.4 131.0 61.6 16.9
2.47 0.07 0.22 0.06 0.85 0.01 0.01
7.26 0.97 0.94 0.74 2.12 -0.06 0.11
0.00 -0.02
0.00
*
ORILWAS. 1% of typical value times partial derivative.
+
[Mg]) and ([Calka [Mg]XMg)in eq 3 and 4, respectively, and then solving for [SO,] with the elimination of the variable [Mg] yields [SO,] = (C - 0.102[HC03] - 0.134[C1] - 0.129[N03] 0.292[H] 0.008[Na] - 0.016[K])/0.138 (5)
+
Each coefficient in eq 5 represents the sum (cations) or difference (anions) of -1 times the limiting ion equivalent conductance of the corresponding ion and a term equal to (R& AM ) / ( R 1)or 0.058 for R in the range 2.15-5.15, as is typica\ly found. The denominator on the right side of eq 5 represents this term added to the limiting ion equivalent conductance for sulfate. Thus, the ion coefficients in eq 5 depend on R, but they are virtually constant; while the coefficients shown here are correct to 3 significant digits for R in the range 2.15-5.15, they are off by only 1 part per thousand for R in the ranges 1.12-2.14 and 5.16-140.6. For comparison, the surface waters of the Regional Integrated Lake Watershed Acidification Study (RILWAS)data set discussed below have average R values of 2.60-5.24 (IO). The seven measured variables receive very different weights in the determination of the unknown, sulfate. Table I shows the partial derivatives of sulfate with respect to each of the seven measured quantities. These terms are then multiplied by 0.01 times the value of the corresponding variable in a representative freshwater, with and without appreciable [H+], to show the effect of a 1% measurement error in each variable on the calculated value of sulfate. By inspection of Table I, for eq 5 to predict sulfate accurately [H+]must be reliably measured in acidic waters, bicarbonate must be reliably measured in circumneutral waters, and specific conductance must be reliably measured in all waters. Sodium and potassium are relatively unimportant in the calculation of sulfate. Omission of both in evaluating eq 5 leads to a small (under 2 pequiv/L) systematic underestimation of sulfate for both waters shown in Table I. A more widely applicable equation of nearly the same accuracy would be [SO,] = (C- 0.102[HCO3] - 0.134[Cl] - 0.129[NOs] 0.292[H] + k)/0.138 (6)
+
+
where k is a constant reflecting the concentrations of sodium and potassium generally found in the water. Omission of the [H+] term leads to under 1 pequiv/L error in calculated sulfate in waters having a pH over 6.3. R e s u l t s a n d Discussion: T e s t i n g t h e M e t h o d
The accuracy of the predictions made by eq 5 was evaluated by using the RILWAS data set from Adirondack lakes (10). In this data set, which is based on monthly
CALCULATED AND MEASURED SULFATE 320
n.27
-
I
\
g
-
i
280 240 200
W
c
z ~
160 120
W +
; 80
U -
40 0 -20
I
I
50
70
I
n.75
n:127
I
1
I
90
110
130
I
150
n.39 I
170
Measured Sulfate (peq/l)
Figure 1. Calculated sulfate, averaged in each quantile, plotted against the mid value of the quantile.
samples of 23 Adirondack lakes over the period July 1983 to July 1985, all of the solutes in eq 3 are measured, as are specific conductance, dissolved organic carbon (DOC), monomeric aluminum, and dissolved inorganic carbon (DIC). Bicarbonate was calculated from DIC (assumed equal to total dissolved inorganic carbon or C,) by use of eq 2.22 from Butler (1.2). Equilibrium constants corresponding to 10 OC and infinite dilution (ref 11; Table 2.2) were used throughout. For each observation date at each site, eq 5 was used to calculate sulfate, allowing 545 separate comparisons of measured and calculated sulfate. On an additional 28 site-dates, no calculation was possible, usually because conductance or DIC was not reported. All but five of the measured values fell between 40 and 180 pequiv/L sulfate. These were grouped into seven quantiles, each spanning a 20 pequiv/L range, as 40-59.9 pequiv/L, 60-79.9 pequivlL, etc., and the mean and standard deviations of the corresponding calculated sulfate values in each range were determined. These are plotted, along with minimum and maximum calculated values for each quantile, in Figure 1. For comparison, the line Y = X is also included. By inspection, the average calculated value systematically overestimates actual sulfate by -20 pequiv/L in each quantile. The magnitude of the discrepancy is not correlated with the measured sulfate value, but may be inversely related to the number of observations in each quantile. The systematic error results from the departure of equivalent conductance from limiting equivalent conductance at noninfinite dilution, as well as from the fact that certain components of the waters are omitted from the model (most notably organic acids and Environ. Sci. Technol., Vol. 22, No. 12, 1988
1461
Table 11. Measured and Calculated Sulfate from 23 Sites in the RILWAS Data Set and Other Features of Water Chemistry'
site name Andes Creek Arbutus Pond Barnes Lake Big Moose Outlet Black Pond BUB/SIS Cascade Lake Clear Pond Constable Dart Lake Heart Lake Little Echo Pond Merriam Lake Moss Inlet Moss Lake Otter Lake Pancake Lake Rondaxe Lake Squash Lake Townsend Pond West Pond Windfall Lake Woodruff Pond
[SO~Irnem~t [ S O ~ I ~ ~ Ipropr C~, sum N pequiv/L pequiv/L error propr mean DOC, [H+l, MMAL, COND, cations, (months) mean SD mean SD means abs error pmol of C/L pequiv/L pH pmol/L pmho/cm pequiv/L 23 17 24 26 25 27 27 25 27 27 24 25 24 26 27 25 20 27 21 27 27 27 25
136 137 53 139 132 130 135 126 148 138 105 73 133 135 138 137 122 132 131 153 112 139 134
18 11 14 11 8 13 12 10 18 7 9 13 11
28 9 20 36 7 17 15 13 26 30
163 52 156 36 77 46 153 38 151 50 157 38 155 44 151 41 161 43 152 37 134 31 85 49 136 44 149 40 162 33 153 37 136 35 150 33 127 44 145 38 141 35 164 45 143 123
0.20 0.13 0.44 0.10 0.14 0.20 0.14 0.19 0.09 0.10 0.28 0.17 0.02 0.10 0.17 0.12 0.11 0.14 0.03 0.05 0.26 0.18 0.07
0.23 0.17 0.62 0.19 0.32 0.29 0.23 0.26 0.18 0.19 0.30 0.47 0.22 0.21 0.21 0.22 0.20 0.20 0.18 0.17 0.28 0.23 0.63
566 422 418 339 354 279 326 318 417 321 307 1038 485 330 310 202 525 303 580 255 679 387 714
13.9 0.6 21.8 10.1 0.1 0.9 0.5 0.2 12.4 7.9 0.7 59.6 35.1 2.7 0.6 5.1 10.0 2.1
40.0 7.1 9.2 1.9 0.2
4.9 6.2 4.7 5.0 6.8 6.0 6.3 6.7 4.9 5.1 6.2 4.2 4.5 5.6 6.2 5.3 5.0 5.7 4.4 5.1 5.0 5.7 6.7
11.4 1.0 1.1 8.9 0.3 1.8 2.8 0.8 10.5 7.6 0.6 1.2 19.3 6.1 2.2 5.0 12.5 4.4 19.2 9.9 6.6 5.6 1.0
30 27 18 29 40 27 34 30 30 28 23 30 33 30 32 26 27 28 34 30 36 30 70
174 235 67 169 347 193 271 240 176 171 167 118 142 219 247 165 175 198 156 188 182 222 636
"Abbreviations: [SO,],d, measured sulfate concentration; [SO4lcaIcd,calculated sulfate concentration from eq 5; SD, standard deviation; propr error means, proportionate error in means of calculated and measured sulfate; propr mean abs error, proportionate mean absolute error, the mean of the absolute values of sample specific errors, expressed as a proportion of mean measured sulfate; DOC, dissolved organic carbon; MMAL, monomeric aluminum; COND, specific conductance; sum cations, sum of calcium, magnesium, sodium, potassium, and hvdronen. on an eauivalents basis.
uncommon inorganic ions) yet contribute something to the overall ion balance and conductivity. The 23 water bodies included in the RILWAS data set differ considerably with respect to ionic strength, pH, and dissolved organic carbon (Table 11). The predictive success of eq 5 was examined on a site-specific basis, using two different tests. First, the average measured and average calculated sulfate values of each site were determined and are displayed with their proportional errors in Table 11, columns 2-6. The proportional errors in means ranged from 0.02 to 0.44; only three sites had proportional errors greater than 0.20. This indicates that at most sites, eq 5 can predict annual average sulfate to within -10% of measured, even without correcting for the systematic error noted above. The generally good agreement (aside from the systematic error) between mean measured and calculated sulfate conceals the deviation of individual sulfate measurements from the corresponding eq 5 based estimates, since positive and negative deviations cancel one another out in the average. The sample specific error probably results from measurement error and large fluctuations in the concentrations of solutes excluded from the model. In an effort to quantify the sample by sample error, the mean of the absolute values of the sample specific errors was found and is expressed as a proportion of mean measured sulfate in Table 11, column 7. These proportionate mean absolute errors are necessarily greater than the proportionate errors in means described above and range from 17 to 63%. Only three sites had mean absolute errors over 32%. These three sites are all outliers with respect to water chemistry. Woodruff Pond had the highest ionic strength and the largest error (63%). Barnes Lake had the lowest ionic strength and nearly the same error (62%). Little Echo Pond had the highest dissolved organic carbon (DOC) and the third highest error (47%). While Little Echo Pond and Barnes Lake are also the only two sites having average sulfate values under 100 pequiv/L, low sulfate, per se, does 1462 Envlron. Sci. Technol., Vol. 22, No. 12, 1988
not appear to be associated with poor predictions, by inspection of Figure 1. Low pH and high monomeric aluminum levels are not associated with inaccurate estimates, in spite of the omission of aluminum from the model. Summary
Annual average sulfate time series may now be determined from reliable time series of conductivity, DIC or bicarbonate, chloride, nitrate, and pH, where these terms were measured simultaneously. Sample-specific historical values may be determined with far less confidence, particularly if the model is applied to waters having ionic strengths below 100 or above 600 pequiv/L, or DOC values above 600 pmol of C/L. The model may permit the determination of the effects of sulfur deposition on surface water sulfate concentrations at some sites lacking sulfate data. This is of interest because of the significance of sulfate levels to the study of the effects of acid rain on the environment. At sites in the northeastern United States, we can in some instances date when fisheries were lost (12) or when alkalinities declined (ref 13; p 71). Better knowledge of long-term sulfate trends would allow testing of the hypothesis at specific sites that these changes resulted from atmospheric sulfur deposition. Acknowledgments
I thank Gene Likens, Richard Bopp, George Hendry, and Michael Oppenheimer for constructive criticism, Floyd Taylor for encouragement, and Charles Driscoll and the Electric Power Research Institute for access to the RILWAS data set. Jane Ceraso was of great assistance with computations. Literature Cited (1) Galloway, J. N.; Norton, S. A.; Church, M. R. Enuiron. Sci. Technol. 1983,17, 541A-546A. (2) Hendry, G. R.; Hoogendyk, C. G.; Gmur, N. F. Analysis of Trends in the Chemistry of Surface Waters of the
Environ. Sci. Technol. 1988, 22, 1463-1468
(8) King, E. J. Qualitative Analysis and Electrolytic Solutions; Harcourt: New York, 1959. (9) MacInnes,D. A. The Principles of Electrochemistry; Dover: New York, 1932. (10) Driscoll, C. T.; Newton, R. M. Environ. Sci. Technol. 1985, 19, 1018-1024. (11) Butler, J. N. Carbon Dioxide Equilibria and Their Applications; Addison Wesley: Reading, MA, 1982. (12) Schofield, C. L. Ambio 1976,5, 228-230. (13) Massachusetts Department of Environmental Quality Engineering Acid Rain and Related Air Pollutant Damage: A National and International Call for Action; Common-
United States; U.S. EPA, Office of Research and Development: Corvalis, OR, 1984. U.S. EPA T h e Acid Deposition Phenomenon and its Effects. Critical Assessment Review Papers, (Effects Sci-
ences);US. Government Printing Office: Washington, DC, 1984; Vol. 11, Chapter 4. National Academy of Science Acid Deposition: Long Term Trends; National Research Council: Washington, DC, 1986. Smith,R. A.; Alexander, R. B. “Evidencefor Acid Precipitation Induced Trends in Stream Chemistry of Hydrologic Bench-Mark Stations”;USGS Circular No. 910, 1982. Henriksen, A. Changes in Base Cation Concentration Due to Freshwater Acidification; Norwegian Institute for Water Research: Oslo, Norway, 1982. Stumm, W.; Morgan, J. J. Aquatic Chemistry, 2nd ed.; Wiley: New York, 1981.
wealth of Massachusetts: Boston, MA, 1984. Received for review December 2, 1986. Revised manuscript received January 26, 1988. Accepted June 20, 1988.
Evaluation of an Annular DenuderIFilter Pack System To Collect Acidic Aerosols and Gases Petros Koutrakls,” Jack M. Wolfson, James L. Slater,+ Michael Brauer, and John D. Spengler
Harvard University, School of Public Health, 665 Huntington Avenue, Boston, Massachusetts 021 15 Robert K. Stevens
U S . Environmental Protection Agency, Research Triangle Park, North Carolina 2771 1 Charles L. Stone
University Research Glassware, Carrboro, North Carolina 27510
rn A glass impactor was designed and evaluated along with an annular denuder/filter pack system. The glass impactor has a 50% aerodynamic cutoff of 2.1 pm a t a flow of 10 L m i d and allows a quantitative transfer of gases and fine particles to the annular denuder and filter pack components. Fine particle and gas concentrations, determined by using the glass impactor along with the annular denuderlfilter pack, were in good agreement with those obtained with colocated reference samplers. Measurements of SO2,“OB, and HN02 gases showed mean collection efficiencies of 0.993, 0.984, and 0.952, respectively, which compare well with predicted values. Additionally, it was found that artifact formation of nitrate and nitrite ions, representing about 5-10% of the concentrations of HNO, and HN02,occurs in the Na2C03-coatedannular denuder. Corrections for these artifacts were made with a second Na2COB-coatedannular denuder. The results of this pilot study suggest that the glass impactor/annular denuder/ filter pack sampling system is suitable for measuring acidic aerosols and gases.
Introduction During the last decade, diffusion denuders have been used in a variety of atomospheric monitoring studies to collect gaseous atmospheric pollutants (1-6). These previous studies have relied on the use of tubular denuder designs. Possanzini et al. (7) described the application of an annular denuder configuration that quantitatively collects reactive atmospheric gases 15-20 times more efficiently, per unit length, than the tubular denuders. Recently, Vossler et al. (8) evaluated a sampler (EPA system) consisting of a glass impactor followed by two annular denuders and a filter pack. The glass impaction plate is permanently attached to the inlet section. The ‘On leave from the University of Steubenville, Steubenville, OH. 0013-936X/88/0922-1463$01.50/0
impactor removes coarse particles, while gases and fine particles are quantitatively transferred into the annular denuder and filter pack components. Subsequently, HNO,, HN02, and SO2 vapors are trapped by a Na2C03-coatedannular denuder. A second Na2C03-coated annular denuder is used to determine artifact formation of nitrate and nitrite, to correct the apparent concentrations of HNO, and HN02 on the first denuder. The last component of the sampling system is a filter pack containing a Teflon filter followed by a nylon filter. The first filter collects fine particles, while the second traps HN03 originating from the dissociation of “,NO3 collected on the Teflon filter. Recently, we developed a substantially more versatile and convenient impactor design for an annular denuder/filter pack system, the Harvard-EPA annular denuder system (HEADS). In this system the impaction plate is decoupled from the inlet housing and placed onto the top of the first annular denuder. The impaction plate is a porous glass disk which is impregnated with mineral oil to minimize bounce-off of the collected coarse particles. After sampling, the impaction plate and its holder are removed and the first denuder is extracted with no interference from the coarse particles. The HEADS was evaluated in a pilot study in Boston, MA, during the summer of 1987. The results of this air sampling are presented and discussed in this paper. D e s i g n a n d Description o f C o m p o n e n t s
The sampling system, shown in Figure 1, consists of a borosilicate glass impactor, two glass annular denuders, and a FEP Teflon filter pack. As illustrated in Figure 2, the impactor consists of an entrance elutriator section containing the inlet tube followed by an acceleration jet and the impaction plate. The plate is mounted at the entrance to the first annular denuder. The elutriator section is 9.5 cm in length, with 1.1-cm i.d. The acceler-
0 1988 American Chemical Society
Environ. Sci. Technol., Vol. 22, No. 12, 1988 1463
