A cost function for neutralizing acidic Adirondack surface waters

JOURNAL

OF ENVIRONMENTAL

ECONOMICS

ANJJ MANAGEMENT

12,

277-285

(1985)

A Cost Function for Neutralizing Acidic Adirondack Surface Waters’ DONALDDUTKOWSKYANDFREDRICC.MENZ Department

of Economics,

Clarkson

Received

July 18,1983;

University, revised

Potsdam, October

New York,

13676

1984

A cost function for neutralizing acidic surface waters by base addition (liming) is derived based upon constrained cost minimization. The model is estimated using a sample of 547 acidic Adirondack lakes with total costs projected for neutralizing each lake to one of six possible target alkalinity levels. Empirical findings indicate that relatively accurate forecasts of lake neutralization costs can be obtained given target alkalinity levels and various limnological characteristics. The results provide a model for predicting lake neutralization costs which can potentially be used in evaluating the relative merits of alternative strategies for reducing acidic 0 1985 Academic Press, Inc. deposition damages.

It is widely believed that long distance transport and deposition of acidic pollutants has become an important environmental problem in several areas of the world. Recent scientific findings indicate that air pollution may be causing significant adverse effects on ecosystems in geographical areas remote from major sources of emissions. Results from a considerable body of research have documented the known or potentially harmful effects of “acid precipitation,” or acidic deposition, on aquatic ecosystems [l, 15,171. Effects on terrestrial environments and materials are also being extensively studied [ll]. There is by no means a consensus regarding appropriate strategies for managing the acidic deposition problem [4]. The obvious way to eliminate the problem of acid precipitation is to reduce anthropogenic emissions of sulfur and nitrogen oxides. In the United States, these emissions largely result from the combustion of fossil fuels and from transportation-related activity [ll, 131. Possibilities for controlhng emissions at stationary sources include using fuels with a lower sulfur content, reducing the sulfur content of presently used fuels by physical cleaning, and installation of flue gas desulfurization (or other technological) processes. However, for political and economic reasons, and because the response to reduced emissions has not been well-defined, other strategies for controlling acidification damages have been proposed. One strategy that has received attention is lake neutralization, or “liming,” which refers to the addition of lime or other alkaline substances to protect or possibly renovate acidified surface waters. Liming temporarily mitigates certain symptoms of surface water acidification, but is not considered a permanent solution to the problem. Nevertheless, liming has been practiced in Sweden [2], Canada [7], and in the Adirondack region of New York State [3]. The most extensive lake neutralization ‘Gregory N. Smith and Donald Wilton provided research assistance. We also thank Thomas Cracker, Joseph DePinto, Charles T. Driscoll, and an anonymous referee for their comments on an earlier version. This research was partially supported by the U.S. Environmental Protection Agency. 277 0095-0696/85

$3.00

Copyright 0 1985 by Academic Press. Inc. All rights of reproduction in any form reserved

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program is in Sweden, where more than 3000 lakes and waterways are currently being treated for acidification damages. While experience with liming indicates that short-term mitigation of damages to surface waters is possible, important questions remain regarding the long-term impact of chemical neutralization on aquatic resources. In this paper, we present estimates of a cost function for neutralizing acidic Adirondack surface waters by adding sufficient base dosage (agricultural lime, CaCO,) to achieve a desired target alkalinity level. This cost function relates neutralization costs for an individual lake to the desired target alkalinity level as well as to corresponding physical features of these water bodies. Results of an earlier study which computed liming costs for acidic Adirondack lakes [12] provide the data for this analysis.

THE GENERAL

MODEL

We assume that the derived cost function arises from an economic unit seeking to minimize the total cost of neutralizing a given acidic lake in order to achieve a predetermined desired target alkalinity level. Assuming that the appropriate inputs consist of chemical base dose, labor, and capital requirements to spread and transport the lime, total cost can be expressed as C = WI LIME + W,L + W,K,

0)

where C is the total cost in dollars; LIME, L, and K refer, respectively, to the input levels of lime, labor, and capital; and w denotes the exogenously determined unit input cost associated with the i th unit (i = 1,2,3). The constraint to this optimization problem involves liming the lake so that the alkalinity will be increased to a predetermined target level. We assume that the process of neutralizing a given acidic lake can be described by the classical microeconomic production function. This production function, which is assumed to be increasing and strictly quasiconcave with respect to chemical dose, labor, and capital, is given by ALK = f(LIME,

L, K, LAKE);

fiYf29.h ’ 0;

fil,f22~.f33

< 0;

(2)

where f( ) is the production function; ALK denotes the resulting alkalinity after neutralization; LAKE refers to a vector of exogenous physical lake characteristics including ambient alkalinity prior to liming; and LIME, L, and K are defined as before. The effect of the LAKE variable on resulting alkalinity, denoted by fLAKE, will vary in sign depending upon the lake’s physical characteristics. The constraint to the cost minimization problem is that the resulting alkalinity of the lake after neutralization either exceeds or is equal to an exogenously given target alkalinity level. Under the above assumptions, the appropriate Lagrangian for this constrained minimization problem is given by

219

COSTS FOR LAKE NEUTRALIZATION

Z?= (wi LIME + w,L + w,K) + h(TALK

- f(LIME,

L, K, LAKE)),

(3)

where TALK is the target alkalinity; h is the Lagrange multiplier; and all other variables are defined as before. If the economic unit optimizes according to the above problem a unique, optimal input combination (LIME*, L*, K*) will be obtained.2 Upon substituting the above solution into Eq. (l), the following minimized cost function results: C* = F(W,,W,,W,,TALK,

LAKE),

(4

where the effect of any unit input price on total cost will be positive. The effect of the variable TALK on total minimized cost is equal to A*, the shadow price of increasing the target alkalinity level. Given the assumptions of diminishing marginal returns for all inputs and that the target alkalinity is achieved with equality after chemical neutralization, this effect is also expected to be positive. Finally, for a given physical lake characteristic, its effect on total cost is given by CfAKE = -X*fL,,kz. Hence, the effect of this variable upon total cost will be opposite in sign from its effect in increasing alkalinity after neutralization. Physical characteristics which tend to hinder the process of raising the alkalinity, ceteris paribus, will lead to increased costs of neutralizing that lake to the target alkalinity level.

EMPIRICAL

ESTIMATES

Estimation of Eq. (4) was performed using data from 547 acidic Adirondack lakes partitioned into accessible (218) and remote (329) classifications based upon their proximity to roads. It was assumed that lime is to be spread by boat in accessible lakes, whereas neutralization of remote lakes would be accomplished by helicopter. Total cost was computed for each lake based upon projected chemical, labor, and capital requirements for six target alkalinity values ranging in increments of 50 from 150 to 400 microequivalents (peq) per liter.3 Base dosage was sufficient to neutralize each lake to the target alkalinity level for a period of 5 years. For a more complete description of the base dosage and cost computation procedure, see [12]. Because the sample consists of cross-section data gathered at a single point in time, unit input ‘In adopting the familiar microeconomic constrained cost minimization problem to the question of lake neutralization, some of the regularity conditions assumed may warrant closer examination. In the production function, while labor and capital can be readily assumed to possess positive and decreasing marginal product at the optimum, these assumptions may not hold for the variable LIME. For a highly acidic lake with a short hydraulic retention time, it may not be possible to achieve the desired target alkalinity level, except for extremely brief periods, no matter how much lime is applied [6]. We also assume that the constraint will always hold with equality; this implies a positive marginal cost of seeking a higher target alkalinity level. For a given acidic lake, it is possible that the given target either cannot be met at all or that errors in the application of lime may occur which would cause the target to be exceeded. ‘Alkalinity is a measure, expressed in microequivalents per liter, of the sensitivity of surface waters to changes in pH upon addition of a strong acid. Acidification of a water body is most conveniently recognized as the loss in alkalinity that has occurred [lo]. New York State Department of Environmental Conservation [14] classifies lakes with an alkalinity range of 0 to 40 peq/liter as being extremely sensitive, 41 to 200 neq/liter as moderately sensitive, 201 to 500 ueq/liter as exhibiting low sensitivity, and greater than 500 neq/liter as being not sensitive to acid deposition. The alkalinity level of 200 peq/liter is the most commonly used threshold for sensitive waters [ll].

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costs are considered constant with respect to the estimated model and were thus removed from the regressions.4 Characteristics considered for remote lakes were the summer ambient alkalinity level, that is, the existing alkalinity of a water body prior to neutralization (in peq/liter, MALK); total lake watershed area less the drainage area of other limed lakes (in hectares, NETWS); surface area of the lake (in hectares, SURF); distance from the chemical storage site to the lake (in kilometers, DIST); and elevation of the lake above sea level (in meters, ELEV). Summary statistics for these variables for remote and accessible lakes in the sample are reported in Table I. With the exception of ambient alkalinity, each of the above physical characteristics is expected to have a positive effect on total cost. For given amounts of lime, labor, and capital, acidic lakes larger in size and net watershed area will bring about a smaller alkalinity gain after neutralization in comparison to smaller lakes of the same ambient alkalinity level. Therefore, greater amounts of chemical dose and more liming applications would be needed to neutralize these lakes to the desired target alkalinity level. Similarly, for remote water bodies at higher elevations, greater costs for transporting base from the chemical storage site imply greater expense incurred for a single application of a given amount of lime, again indicating a positive effect on total cost. We assume that the impact of elevation on total cost is significant only for remote lakes and that the appropriate chemical storage site for any accessible lake would be located in close proximity to that site. Ambient alkalinity is expected to be inversely related to total cost. Clearly, for two lakes identical in all other characteristics, the neutralization cost will be greater for the more acidic body, that is, the lake with the lower ambient alkalinity level. In the estimation, we initially assumed that all variables were linear functions of cost. It became apparent, however, that the relationship between cost and ambient alkalinity for both lake types was noticeably nonlinear. Hence, additional polynomial terms for the variable MALK were included in the regression.5 The results are as follows (numbers in parentheses are t statistics): For accessible lakes: C* = -32751.6 ( - 9.6)

+ 117.2 TALK (10.3) - 0.06 MALK3 (- 6.6)

N = 1308,

R2 = 0.90.

- 158.8 MALK (-3.5) + 16.8 NETWS (72.9)

+ 6.2 MALK2 (10.8) + 27.9 SURF, (11.5) (5)

“We performed some experiments involved with reestimating the model for both remote and accessible lakes after changing some of the unit input costs. The robustness of the cost function was analyzed by changing one of the unit input cost assumptions, recomputing cost, and estimating the model with the adjusted data. The specific assumptions we investigated were using a wage rate of $550/hr instead of $4SO/hr; increasing the cost of lime by 20%; and increasing the rental rates for the boat and helicopter each by 20%. It should be noted that we may not have considered all of the extreme bounds of the plausible assumptions regarding the unit input costs. Nevertheless, the estimated function was found in all cases to be quite robust with regard to parameter significance and fit. Similar parameter estimates were obtained as well. ‘Cost functions were also estimated having the form C* = a,exp(atMALK)TALKa2 NETWSaJDISTa4ELEVas, with findings similar to those of the polynomial type.

COSTS

FOR

LAKE

TABLE Variable

Variable name

Definitions

I

and Summary

Total cost ($) Target alkalinity level (peq/liter) Summer ambient alkalinity (peq/liter) Lake watershed area net of other limed lakes Surface area (ha.) Distance from the chemical storage site (km) Elevation above sea level (m)

TALK MALK NETWS SURF DIST ELEV

TABLE Projected

and Forecasted

Costs

Statistics 218 Accessible lakes Standard Mean deviation

Variable definition

c*

281

NEUTRALIZATION

for Selected

(ha.)

39565.8 275.0 21.9 1908.3 164.6

329 Remote Mean

109603.4 85.4 42.8 5548.8 527.8 -

23178.0 275.0 6.3 413.7 14.4 7.5 591.5

-

lakes

Standard deviation 48071.6 85.4 42.1 464.2 21.4 3.9 104.2

II Adirondack

Ambient alkalinity (geq/liter)

Water Net watershed (hectares)

Bodies,

1982 Dollars”

Projected total costb ($)

Forecasted total costC (9

Accessible

Big Moose Lake (752) Sagamore Lake (313) Little Independence Pond (65) Mean: 218 accessible ponds

-48.0 40.7 - 25.0 21.9

7384.0 1802.3 489.4 1908.3

316,269 22,778 7,846 30,722

156,994 22,817 7,732 30,776

Remote

Toad Pond (369) Upper South Pond (200) GuU Lake (969) Mean: 329 remote ponds

- 98.0 - 16.7 2.0 6.3

326.8 203.0 523.9 413.7

125,047 6,867 17,678 19,519

287,195 6,334 18,062 19,562

“Data apply to target alkalinity of 200 peq/liter, identification numbers are in parentheses. bProjected using data from Menz and Driscoll [12]. ‘Forecasted with equations in text.

5-year

base

dose.

Water

bodies’

For remote lakes: C* = -28623.2 ( - 7.4)

+ 48.2 TALK (8.1)

- 0.2 MALK3 (- 39.2) + 75.7 SURF (2.9) N = 1974,

R2 = 0.78.

+ 110.8 MALK (4.5)

+ 2.6 MALK2 (4.0)

+O.OOl MALK4 (17.4)

+ 38.2 NETWS (32.1)

+ 667.6 DIST (3.0)

+ 16.0 ELEV, (3.0) (6)

Several interesting results emerge. First, all estimated parameters possess theoretically predicted signs and are significant at the 1% level.6 Second, based upon the R2 measure, the estimated cost functions for both lake classes fit unusually well, particularly for a cross-sectional study. The relationship between cost and target alkalinity level was found to be linear for both lake types although the estimated 6 With polynomial peq/liter),

regard to the effect of ambient alkalinity on total cost, some of the regression coefficients in the exhibit positive signs. Still, for the relevant range of the variable MALK (- 110 to + 100 the estimated cost functions are decreasing with respect to ambient alkalinity.

282

DUTKOWSKY

AND

AMBIENT

FIG.

1.

Estimated

total

liming

costs

for existing

MENZ

ALKALINITY

alkalinity

levels,

547 Adirondack

lakes.

marginal cost of treating lakes to the next highest target alkalinity level is more than twice as great for accessible lakes. This probably results from the fact that lakes in the accessible sample are generally larger in size with considerably greater net watershed areas (see Table I). Hence, greater amounts of lime would be required for these lakes as the target alkalinity level is increased. The forecasting ability of the estimated cost functions in Eqs. (5) and (6) was also investigated. In Table II, projected costs (from [12]) and forecasted cost estimates are reported for selected remote and accessible Adirondack lakes in our sample. A target alkalinity level of 200 peq/liter is assumed. For certain water bodies, neutralization costs can be forecasted quite accurately, whereas the prediction error was larger for other lakes. Large differences in forecasting ability may result from our highly disaggregated sample or from other physical characteristics not available for our regressions. Since cost functions estimated in loglinear functional form (see footnote 5) produced similar goodness of fit with a dependent variable considerably smaller in scale, it would appear that these functions may be more promising in terms of forecasting neutralization cost for a given lake. The fitted regression polynomials describing the effect of ambient alkalinity on total cost are illustrated in Fig. 1. Intercepts used in the plots are based upon the regression intercepts and the mean values of the remaining variables. In addition, the ambient alkalinity variable on the horizontal axis is displayed so that higher acidity is described in reading from left to right on the graph. From Fig. 1, it is seen that for both remote and accessible lakes, predicted cost is roughly constant with respect to ambient alkalinity when the variable is approximately -20 peq/liter or higher. When lakes are more acidic, however, predicted costs increase at an increasing rate, more so for the remote lakes. The high costs of neutralizing low alkalinity lakes can be attributed to the extremely short hydraulic retention times usually characteristic of these water bodies.’ In illustrating the dramatic increase in neutralization expenses incurred when a lake acidifies beyond a critical level, our findings lend empirical support to the hypothesis of Cracker and Forster [5]. Further, these results raise the question of whether highly acidic lakes should be neutralized at all. For such water bodies, the large short-run costs of neutralization may outweigh any benefits of this action.8 ‘We are indebted to Charles Driscoll for this point. 6There may exist other criteria in the decision of whether to neutralize a given acidic lake. For example, in New York State, current practice is to give priority to neutralizing ponds containing unique strains of native brook trout and/or having a history of high angler use and natural reproduction [3].

COSTS FOR LAKE NEUTRALIZATION

DISCUSSION

283

AND CONCLUSIONS

Our empirical findings are consistent with scientific evidence concerning the acidification process in aquatic ecosystems. Lake acidification has been characterized in the scientific literature as being equivalent to a large-scale acid titration of a bicarbonate solution [lo, 161. Acidic inputs are thought to result in a decrease in alkalinity in the early stages of acidification, but bicarbonate buffering capacity can maintain pH values at a level of about 6.0. No significant impacts on fish populations have been observed at this level of acidification [16]. As acidification continues, bicarbonate acid neutralizing capacity diminishes and temporal fluctuations in pH occur, with associated biological consequences such as recruitment failure and physiological stresses on fish populations. After alkalinity is depleted, lakes are characterized by chronically depressed pH levels (less than pH 5.0). At this stage, surface water quality will tend to resemble precipitation chemistry. Severe damage to fish populations and other biological consequences at this stage of acidification result from a combination of low pH values, low levels of calcium, and elevated aluminum concentrations [8,16]. If a water body becomes highly acidic, efforts to neutralize it may prove to be very costly and offer little chance of permanently restoring the system to its original state. Furthermore, while the addition of basic substances improves water quality in certain respects, detrimental effects of liming have been noted. One problem that has received attention is occasional fish mortality during the transition period after the addition of lime. Despite the resulting increase in pH, metals (particularly, aluminum) will not have precipitated and, thus, will become more toxic to fish [2]. Mortality to aquatic organisms may also result from pH shock with the introduction of alkaline substances [7]. In addition, enhanced accumulation of metals in sediments has been observed to accompany an increase in lake pH [7,8]. Unless neutralized lakes are carefully monitored and maintained, reacidification will take place. The biological consequences of repetitive neutralization and reacidification have not been studied, but there may be significant problems associated with this cyclic stress [12]. Finally, liming has been known to strip dissolved organic carbon (DOC) from the water column. Since DOC represents a source of buffering capacity, this may make certain waters more subject to reacidification. Loss of DOC also increases the potential for aluminum toxicity in acidic lakes [9]. Our results are of potential interest for setting policy at the national and state levels. The findings indicate that relatively accurate forecasts of lake neutralization costs can be obtained given data on lake characteristics such as the existing alkalinity level, surface acreage, net watershed size, elevation, and chemical costs.9 Empirical cost functions based upon this model can be employed to forecast the cost of liming other lakes within and outside the Adirondacks. Certain precautions should be noted, however, before this function is adopted to the problem of forecasting liming costs for acidic water bodies in another area. First, Adirondack lakes may not be representative of the types of acidic lakes in other regions. Important factors affecting base dosage requirements include characteristics which will vary by watershed. The more important characteristics include 91t should be noted that we have not considered several important costs of implementing a wide-scale lake neutralization program at the national or state level. For example, we did not include costs of establishing and administering an extensive liming program as well as costs of obtaining morphological and other data necessary to estimate the cost function.

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AND MENZ

those of watershed geology (nature of bedrock and soils; history of weathering), hydrology, and morphometry (lake depth and area; watershed area). Second, base dosage requirements for the 547 ponds (out of approximately 3000 Adirondack ponds in total) were based upon certain important assumptions regarding water chemistry. Some of these assumptions concern sediment demand for base, acid/base reactions between sediments and the water column, and base dissolution efficiency (see [12]). Assumptions pertaining to physical characteristics such as estimated watershed areas, annual runoff, and lake surface areas affect the rate of chemical application and represent possible sources of error in cost projections. Finally, possible adverse biological and chemical consequences of liming were not explicitly considered and the values placed on these events may vary among regions. In short, this study offers a model which can be employed regionally to determine neutralization costs, given projected costs and relevant lake characteristics for a sample of acidified water bodies in that region. The estimated parameters we obtained, however, may be specific to the acidic deposition problem in the Adirondacks and the assumptions used to construct total costs. Renovation of lakes to a preacidic condition may not be possible in some cases if liming cannot fully meet the needs of that aquatic ecosystem or if it negatively effects that ecosystem. Scientific understanding of these needs and effects is incomplete. However, any management strategy for the control of acidification damages is likely to involve a combination of control at the source of emissions and remedial or interim treatment in certain sensitive receptor environments. Therefore, information on the cost of lake neutralization is critical for an evaluation of the relative merits of alternative strategies for controlling acidification damages. REFERENCES 1. R. Beamish and H. Harvey, Acidification of the LaCloche mountain lakes, Ontario, and resulting fish mortalities, J. Fish Res. Board Canad. 29, 1131-1143 (1972). 2. B. Bengtsson, W. Dickson, and P. Nyberg, Liming acid lakes in Sweden, Ambio 9, 34-36 (1980). 3. L. Blake, Liming acid ponds in New York, N. Y. Fish GameJ. 28(2), 209-214 (1981). Views, 4. Comptroller General of the United States, “The Debate over Acid Precipitation-Opposing Status of Research,” Report EMD-81-131, Washington, D.C. (1981). 5. T. D. Cracker and B. A. Forster, Decision problems in the control of acid precipitation: Nonconvexities and irreversibilities, J. Air Pollut. Control Assoc. 331, 31-37 (1981). 6. J. V. DePinto and J. K. Edzwald, “An Evaluation of the Recovery of Adirondack Acid Lakes by Chemical Manipulation,” Research Project Technical Completion Report, Project No. B-095-NY, Department of Environmental Engineering, Clarkson University, Potsdam, N.Y. (1982). 7. P. Dillon, N. Yan, W. Scheider, and N. Conroy, Acidic lakes in Ontario: Characterization, extent, and responses to base and nutrient additions, Arch. Hydrobiol. 13, 317-336 (1979). 8. C. T. Driscoll, J. P. Baker, J. J. Bisogni, and C. L. Schofield, Effect of aluminum speciation on fish in dilute acidified waters, Nafure (London) 2S4, 161-164 (1980). 9. C. T. Driscoll, J. R. White, G. Schafran, and J. D. Rendall, Calcium carbonate neutralization of acidified surface waters, J. Enuiron. Eng. Diu. (Amer. Sot. Ciu. Eng.) 12, 1128-1145 (1982). 10. A. Hemicksen, A simple approach for identifying and measuring acidification of freshwater, Nuture (London) 278,5 April, 542-545 (1979). 11. Interagency Task Force on Acid Precipitation, “Annual Report, 1983 to the President and Congress,” National Acid Precipitation Assessment Program, Washington D.C. (1983). 12. F. C. Menx and C. T. Driscoll, An estimate of the costs of liming to neutralize acidic Adirondack surface waters, Water Res. Res. 19(5), 1139-1149 (1983). 13. National Academy of Science, “Atmosphere-Biosphere Interactions: Toward a Better Understanding of the Ecological Consequences of Fossil Fuel Combustion,” National Academy Press, Washington D.C. (1981).

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14. New York State Department of Environmental Conservation, “Acidity Status Update of Lakes and Streams in New York State,” WM P-83, Albany, N.Y. (1984). 15. C. L. Schofield, Acid precipitation: Effects on fish, Ambio 5, 228-230 (1976). 16. C. L. Schofield, Processes limiting fish populations in acidified lakes, in “Atmospheric Sulfur Deposition: Environmental Impact and Health Effects” (Shriner, Richmond, and Lindberg, eds.), 345-356, Ann Arbor Science, Ann Arbor, Mich. (1980). 17. R. F. Wright and E. T. Gjessing, Acid precipitation: Changes in the chemical composition of lakes, Ambio 5, 219-223 (1976).