Modelling the acidification of lakes: An Overview

Rajarishi Sinha, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.

Disclaimer: The views expressed in this document are those of the author only, and may not reflect those of the TAF working group or the NAPAP

Index

Summary:	

Emissions of sulphates and other acidic pollutants from anthropogenic sources results in the deposition of these acidic pollutants on the earth's surface, downwind of the source. These pollutants reach surface waters like lakes and acidify them, resulting in lower pH levels. Sometimes the pH levels drop sufficiently so that the lake can no longer support aquatic life. This document traces the efforts by many researchers to understand and quantify the effect of acid deposition on the water chemistry of populations of lakes. Beginning from the Eastern Lake Survey, which sampled lakes from several regions in the Eastern United States to obtain their pH, Acid Neutralising Capacity (ANC, used interchangeably with the term alkalinity, unless otherwise specified) and major ions, the document moves on to describe three classes of models used to predict these chemical variables for lake populations of lakes, viz. dynamic models, steady-state models and direct distribution models. Steady state and direct distribution models are discussed in some detail, as is the medium complexity mechanistic model MAGIC, since they relate directly to the authors proposed research effort in the coming months (see [16]). Finally, a few thoughts on nitrogen cycling in the soil and in surface waters are presented.

1. Background	

In the 1970s and early 80s, evidence from site-specific studies in the United States and Canada indicated that declines of pH and ANC in surface waters had occurred over time. These conditions had been caused by acidic deposition from anthropogenic sources releasing acidic pollutants into the atmosphere.

There was considerable uncertainty in extrapolating the site specific results to a regional or national scale because of (1) the degree to which individual study sites represent larger regional populations, (2) unknown bias in lake selection, (3) absence of measurements of chemical variables that are critical to assessing chemical or biological effects, (4) difficulty in comparing data collected by different and sometimes unknown methods and (5) inconsistent documentation of quality assurance protocols. The Eastern Lake Survey was conducted to determine the chemical variables pH, ANC, major ions like Al3+, Ca2+ and others for the lakes in the Eastern United States. The critical issue in the design of the survey was the chemical characterisation of regional lake populations. A pH and ANC value measured for a sample from a lake would be subject to spatial and temporal variability. It was recognised that it was not essential that the index sample be taken at a time of worst-case conditions. It was more important that the index sample be collected at a time when within lake spatial variability is small. Samples were collected in the fall when spatial variation within the lake is reduced as the lake undergoes a period of mixing that may last four to eight weeks. Samples were collected in the deepest part of the lake to represent the dominant water mass.

A stratified sampling method was used by which sample lakes were allocated equally among strata. There were three levels of stratification. The first was by region, and there were three regions, namely the North East, the Upper Midwest and the South East. Each region was divided into subregions, where each subregion in each region was relatively homogeneous with respect to water quality, physiography, vegetation, climate and soils. Based on this homogeneity, five subregions were identified in the Northeast, four in the Upper Midwest and two in the Southeast. Each subregion was divided into alkalinity map classes, based on the predominant range of surface water alkalinity values, namely < 100 (eq/L, 100-200 (eq/L and > 200 (eq/L. All three alkalinity map classes were found within each of the eleven subregions. Lakes were selected in such a way that each lake in a stratum had an equal probability of inclusion. Lakes with a surface area < 4 ha were an important resource that were not considered in this survey. Small lakes are often lower in pH and ANC than larger lakes in the same geographic area.

There is substantial evidence that surface water chemical characteristics during spring may be less favourable for biota than during fall (Landers et al., 1988), possibly due to snow melt and subsequent runoff into surface waters. Florida has been shown to have a high percentage of acidic lakes (22%) and this may be due to the warmer climate in the Florida region. But Florida is an area receiving only moderate loadings of sulphur. At the time when the results of the survey were made available, this anomaly could not be explained. But these new data made it possible to apply empirical models to evaluate lake acidification associated with loadings of sulphur deposition, explore the importance of organic acids and to test the hypothesis of regional scale lake acidification caused by neutral salts.

2. Models for Regional Lake Acidification	

2.1 Dynamic Models	

Since then, the state-of-the-art has advanced a great deal. Dynamic, mechanistic models have been developed to simulate the acidification processes with a high degree of detail. These models are useful to study individual lake systems in detail and they provide a framework for advancing the state of knowledge of the fundamental mechanisms of acidification (Small and Sutton, 1986). For assessing the acidification in an entire region, predictions are required for many lakes and generating and evaluating a dynamic model for each lake and calibrating the model for each lake system is a very difficult task. Dynamic models have been developed by Chen et al., 1982, Christophersen and Wright et al., 1981, Galloway et al., 1983, Cosby et al., 1985 and other workers.

2.2 Empirical Equilibrium/Steady State Models	

Steady state models have no time component. Most steady-state models use information describing the current state of the water chemistry in the lake to predict: (1) the original water chemistry before any acid deposition and (2) the eventual future condition assuming a constant deposition rate. The major advantage over dynamic models is that they require less data and can be applied where insufficient data exist to apply dynamic models.

Most steady state models explicitly consider only some of the components of lake ANC, namely bicarbonate (HCO3-), carbonate (CO32-) and hydroxide (OH-), and not organic anions or Al. Therefore these models predict the effect of acid deposition on alkalinity and not on ANC. In estimating pH from alkalinity, most of these models use time-independent empirical relationships derived from lake surveys which implicitly account for the effect of other constituents on pH such as organic anions and Al. None of these models consider the possibility of a change in organic acid concentrations as a result of acidification. However, recent studies suggest that this oversight is likely to cause only slight overestimates of acidification. Some steady-state models such as the Henriksen model cannot be applied to systems with significant watershed sulphur sources. However, such sources are not significant for low pH (pH<6) lakes in the Northeast. Also, some workers have suggested that forest growth is also responsible for acidification of soils and surface waters, but none of these models accounts for forest-growth related acidification.

Empirical equilibrium models have been developed that use steady state chemical weathering and ionic electroneutrality to calculate a steady state alkalinity given an acid deposition rate. These models are easier to apply than the dynamic models, but certain difficulties persist. Weathering rates vary significantly in different watersheds. Empirical equilibrium models have been developed by Wright and Henriksen, 1983, Schnoor et al., 1984 and others. The Henriksen-Wright model and the Schnoor model are described here as these form the basis for applications of the Direct Distribution model of Small and Sutton (1986).

2.2.1 Henriksen-Wright model	

The Henriksen-Wright model relates the equilibrium alkalinity (ANC) of a lake to the acid deposition rate, the annual rainfall, flow-through ratio and chemical weathering in the watershed. The model assumes that some fraction of the deposition of acid is neutralised in the watershed system. The neutralisation fraction NF is assumed to be constant and independent of the level of acid deposition. The remaining fraction (1-NF) acts to decrease the alkalinity of the lake, as given by :

(1)

where C is the acid concentration of the incoming precipitation adjusted upward to account for dry deposition and evapotranspiration.

In the Henriksen-Wright model, this neutralisation is assumed to occur entirely as a result of the exchange of base cations Ca and Mg and is measured relative to the change in the in-lake SO4 concentration, so that :

(2)

As long as the base cation exchange is the primary source of neutralisation and the increase in the SO4 concentration occurs as a result of increase in the acid deposition, F and NF are equivalent. The value of F was typically thought to vary between 0 and 0.4 and was assumed to be constant across all lakes. The early assumptions were based on highly elevated, poorly buffered Norwegian lakes. However, more recent studies have recognised the variability in F. The model output is very sensitive to the assumed value of F.

The basic hypothesis here is that acidified waters are a result of a large scale acid-base titration. Bases released by the weathering of primary rock are titrated with acids deposited from the atmosphere. It is also generally accepted that other processes like cation exchange and sulphate reduction dampen the effects of acid deposition.

Small and Sutton, 1986 and Labieniec et al., 1989 discussed the use of F to represent the neutralisation fraction.

2.2.2 Schnoor Trickle-Down Model	

Schnoor and co-workers (Schnoor et al., 1984, 1986) derive a similar acidification model based on the kinetics of weathering. In this model, the neutralisation fraction decreases as acid deposition increases, based on a non-linear relationship between the chemical weathering rate and the level of acid deposition.

(3)

where k0 is the rate constant in the absence of free acidity in (eq m-2 yr-1, kh is the rate constant for acid hydrolysis, D is the acid deposition rate and m is a fractional order constant.

2.3 Direct Distribution Models	

Such models are based on the empirical probability distribution of an indicator such as ANC in a sample of lakes. The distribution is coupled with an empirical model such as the Henriksen-Wright model or the Schnoor Trickle-down model. These models can also predict distributions of other indicators like pH. They can also characterise the probability distributions of the uncertainty in the model parameters.

In the Direct Distribution model of Small and Sutton (1986), a 3-parameter lognormal function is used to describe the distribution of the ANC :

(4)

A range of correlation coefficients between the model parameters are required. These are difficult to estimate.

The pH-alkalinity relationship developed by Small and Sutton (1986) is used to transform an alkalinity distribution to the corresponding pH distribution :

(5)

Measured ANC is used to estimate pH using an empirical titration curve approximated by the above equation. The shape of this titration curve is assumed to be invariant. This assumption works well for regions with low-ANC lakes, such as the Adirondacks. In regions with fewer low ANC lakes, predictions are inaccurate at the extremes of the ANC distribution. Also, this model is difficult to apply to empirical distributions that are not easily parametrised.

In another study, Small et al. (1988) examined the distribution of ANC in four subregions of the Eastern Lake Survey and found that bimodal pH curves were obtained for two subregions. Results were obtained which were similar to those of Small and Sutton (1986).

2.4 MAGIC: The Model of Acidification of Groundwater in Catchments

Regional mechanistic models attempt to represent actual chemical reactions in the catchment under consideration using kinetic and equilibrium expressions for the underlying geochemical processes. In such models, for the sake of simplicity, spatial variations within the watershed are not considered. Regionalisation is achieved using Monte Carlo methods which produce a set of statistically representative lakes for the region. This set of lakes (the artificial or simulated data set) is identified by selecting parameter distributions from the expected range of values for typical lakes in the region. These distributions are randomly sampled and the model is calibrated by accepting a set of parameter inputs which generates the current distribution of lake chemistry. Accepted parameter sets are stored and form the set of simulated lakes. This set is then used to simulate the response of the region to future changes in deposition.

There are two principal regional mechanistic models currently in use, namely the RAINS Lake Model and the MAGIC model. MAGIC is an intermediate complexity process oriented model of catchment soil and stream water chemistry (Cosby et al., 1985). It incorporates a small number of processes which are assumed to be important in influencing the long-term response of surface waters to acidic deposition. These soil processes are: (1) base cation exchange in soils, (2) dissolution of aluminium hydroxide, (3) solution of carbon dioxide in soil solution and subsequent carbonic acid dissociation, (4) sulphate adsorption in soils and (5) mineral weathering.

Processes 1 through 3 are modelled based on the Reuss-Johnson soil chemistry model. Sulphate is assumed to have an adsorbed phase and to follow a Langmuir isotherm. The first four processes equilibrate rapidly and are assumed to occur instantaneously in soils. A simultaneous equilibrium is computed at each time step. Changes over time steps are calculated by computing a mass balance for the total amount of base cations and strong acid cations in the watershed. Inputs are by acidic deposition and net uptake and release in the watershed, primarily mineral weathering minus biological uptake.

MAGIC represents the watershed with two soil-layer compartments arranged vertically and assumed to be areally homogeneous. Typical temporal resolution is annual but monthly output can also be obtained. Numerical integration techniques are used in which the two soil compartments and the lake compartment are treated as continually stirred tank reactors. The efflux of a given chemical component from a compartment is calculated as the difference between the influx product of the rates and durations of reactions occurring within the compartment at each time step. Watershed flow data are averaged to obtain monthly or yearly values before being used in MAGIC.

MAGIC was specifically formulated for the purpose of conducting long-term simulations. It does not simulate short term episodic events. MAGIC has been modified to include organic acids, based on the work of Driscoll et al. (1994). Labieniec et al. (1989) showed that the Direct Distribution model of Small and Sutton (1986) could mimic the predictions of MAGIC. More recently, Small et al. (1994, in press) have shown that the Direct Distribution model can be used as a simplified approximation to MAGIC for the Adirondack subregion, albeit with two shortcomings, as discussed below.

3. Future Directions	

This section of this document deals with the research proposal pending with the Department of Energy, Office of Energy Research. Prof. Mitchell J. Small is a principal investigator for this project.

This project involves modelling the lake acidification effects for the Tracking Analysis Framework (TAF), an integrated model proposed by Henrion and Marnico (1993). MAGIC is currently being updated to incorporate nitrogen cycling and nitrate leaching, an improved representation of aluminium reactions and equilibrium and improved representation of organic acids. The shortcomings of the Direct Distribution model identified by Small et al. (1994, in press), namely the failure to consider the effect of changes in base cation deposition and the failure to represent small long-term reductions in the watershed acid neutralisation fraction NF associated with simulated depletion of base cations in soils will be addressed.

Finally, a Bayesian Monte Carlo method will be incorporated into TAF to be able to modify the uncertainty distributions in TAF based on observed data.

3.1 Nitrogen Cycling	

The two major pathways of nitrogen input to terrestrial ecosystems are atmospheric deposition and biological fixation. Deposited nitrogen can remain on plant surfaces for some time, only to be moved again by wind or dissolved by rain so that it can enter the soil or run off into surface waters. When atmospheric nitrogen is deposited on land, various processes determine its fate. Because many of these processes are mediated by biological agents, they are seasonal and highly dynamic.

Some specialised organisms convert atmospheric N to NH3, thereby making it biologically active. Nitrogen mineralisation is the conversion of organic nitrogen to inorganic forms, primarily NH4+ and NO3-. There are two processes involved in this conversion. The first is ammonification, by which organic nitrogen is converted to NH3 which in turn is converted to NH4+ in the soil. The second is nitrification, which involves the bacterial conversion of NH4+ to NO3-. Ammonification is carried out by micro-organisms that are favoured by warm temperatures, high organic content and high soil moisture. As a result of the diversity of the micro-organisms involved, the process takes place over a wide range of environmental conditions. Nitrifying bacteria are very sensitive to soil moisture content. Nitrification is more rapid in well-aerated and drained soils. Total nitrogen in the soil declines sharply with depth, while the proportion of fixed NH4+ increases with depth.

Therefore, important factors to be considered in studying the effect of nitrogen cycling and runoff to surface waters are :

1. Atmospheric nitrogen deposition rate.
2. Vegetation cover over the region under consideration.
3. "Residence time" of nitrogen on the vegetation before it is removed by wind or rain.
4. Whether nitrogen is removed from vegetation primarily by rain or some nitrogen is returned to the atmosphere by wind.
5. Whether nitrogen fixing micro-organisms are present in the soil.
6. Whether environmental conditions are favourable for ammonification of nitrogen by these micro-organisms.
7. The rate of ammonification.
8. Whether the soil moisture content is suitable to support nitrifying micro-organisms.
9. The rate of nitrification.
10. How much of the NO3- produced is assimilated by organisms in the soil.
11. How much of the remaining "free" NO3- is able to leach into surface waters or ground water.
12. Whether the rate of transport of NO3- from the soil to surface waters is rapid or hindered by assimilation of NO3- or denitrification by organisms during the process of transport.

4. Acknowledgements	

The author would like to thank Prof. Mitchell J. Small for his encouragement and advice throughout the period over which this study was conducted.

5. References	

1. Brakke, David F., Landers, Dixon H., and Ellers, Joseph M., Chemical and Physical Characteristics of Lakes in the Northeastern United States, Environ. Sci. Technol., Vol. 22, No. 2, 1988, 155-163.
2. Chen, C.W., Gherini, S.A., Dean, J.D., Hudson, R.J.M., Goldstein, R.A., Development and Calibration of the Integrated Lake-Watershed Acidification Study Model, Modelling of Total Acid Precipitation Impacts, J.L. Schnoor, Ed., Butterworth Publishers, Boston, 1984, 175-203.
3. Chen, C.W, Dean, J. David, Gherini, Steven A., Goldstein, Robert A., Acid Rain Model: Hydrologic Module, J. of the Env. Engg. Div., Proceedings of the ASCE, Vol. 108, No. EE3, June 1982, 455-472.
4. Chen, C.W., S.A. Gherini, N.E. Peters, P.S. Murdoch, R.M. Newton and R.A. Goldstein, 1984, Hydrologic analyses of acidic and alkaline lakes, Water Resour. Res., 20:1875-1882.
5. Christophersen, Nils, and Wright, R.F., Sulphate Budget and a Model for Sulphate Concentrations in Stream Water at Birkenes, a Small Forested Catchment in Southernmost Norway, Water Resour. Res., 17:377-389, 1981.
6. Cosby B.J., Hornberger, G.M, and Galloway, J.N., Modeling the Effects of Acid Deposition: Assessment of a Lumped Parameter Model of Soil Water and Streamwater Chemistry, Water Resour. Res., 21:51-63, 1985.
7. Driscoll, C.T., and Bisogni, J.J., Weak Acid/Base Systems in Dilute Acidified Lakes and Streams of the Adirondack Region of New York State, Modelling of Total Acid Precipitation Impacts, J.L. Schnoor, Ed., Butterworth Publishers, Boston, 1984, 53-72.
8. Galloway, James N., Norton, Stephen A., Church, M. Robbins, Freshwater Acidification from atmospheric deposition of sulphuric acid: A conceptual model, Environ. Sci. Technol., Vol. 17, No. 11, 1983, 541A-545A.
9. Kramer, James, and Tessier, André, Acidification of aquatic systems: A critique of chemical approaches, Environ. Sci. Technol., Vol. 16, No. 11, 1982, 606A-615A.
10. Labieniec, Paula A., Small, Mitchell J., and Cosby, Bernard J., Regional Distributions of Lake Chemistry Predicted by Mechanistic and Empirical Lake Acidification Models, Regional Acidification models: Geographic extent and time development, J. Kämäri, D.F. Brakke, A. Jenkins, S.A. Norton, and R.F. Wright, Eds., Springer-Verlag, Berlin, Germany, 1989, 185-202.
11. Landers, Dixon H., Overton, W. Scott, Linthurst, Rick A., and Brakke, David E., Eastern Lake Survey: Regional estimates of lake chemistry, Environ. Sci. Technol., Vol. 22, No. 2, 1988, 128-135.
12. Rubin, Edward S., Small, Mitchell J., Bloyd, Cary N., and Henrion, Max, Integrated Assessment of Acid Deposition Effects on lake Acidification, Journal of Environmental Engineering (ASCE), Vol. 118, No. 1, January/February 1992, 120-134.
13. Schnoor, J.L., Nikolaidis, Nikolaos P., Glass, Gary E., Lake Resources at risk to acidic deposition in the Upper Midwest, J. of the Water Poll. Con. Fed., Vol. 58, No. 2, 1986, 139-148.
14. Schnoor, J.L, Palmer, Jr., W.D., and Glass, G.E., Modelling Impacts of Acid Precipitation for Northeastern Minnesota, Modelling of Total Acid Precipitation Impacts, J.L. Schnoor, Ed., Butterworth Publishers, Boston, 1984, 155-173.
15. Small, Mitchell J., Cosby, Bernard J., Marnico, Ronald J., and Henrion, Max, Joint Application of an Empirical and Mechanistic Model for Regional Lake Acidification, submitted to Environmental Monitoring and Assessment in August 1994.
16. Small, Mitchell J., and Kalagnanam, J., Modeling Control Costs and Lake Acidification Effects for the Tracking Analysis Framework, Research proposal submitted to U.S. Department of Energy, Office of Energy Research, November 1994.
17. Small, Mitchell J., and Sutton, Michael C., A Direct Distribution Model for Regional Aquatic Acidification, Water Resour. Res., 22:1749-1758, 1986.
18. Small, Mitchell J., Sutton, Michael C., and Milke, Mark W, Parametric Distributions of Regional Lake Chemistry: Fitted and Derived, Environ. Sci. Technol., Vol. 22, No. 2, 1988, 196-204.
19. Stedinger, J.R., Fitting Log Normal Distributions to Hydrologic Data, Water Resour. Res., 16:481-490.
20. Sullivan, T.J., Historical Changes in Surface Water Acid-Base Chemistry in Response to Acid Deposition, NAPAP State of Science and Technology Report No. 11, National Acid Precipitation Assessment Program, Washington, DC.
21. Thornton, Kent W., Methods for Projecting Future Changes in Surface Water Acid-Base Chemistry, NAPAP State of Science and Technology Report No. 14, National Acid Precipitation Assessment Program, Washington, DC.
22. Turner, Robert S., Watershed and Lake Processes affecting Surface Water Acid-Base Chemistry, NAPAP State of Science and Technology Report No. 10, National Acid Precipitation Assessment Program, Washington, DC.
23. Wright, R.F., Norwegian Models for Surface Water Chemistry: An Overview, Modelling of Total Acid Precipitation Impacts, J.L. Schnoor, Ed., Butterworth Publishers, Boston, 1984, 73-87.
24. Wright, R.F., and Henriksen, A., Restoration of Norwegian Lakes by reduction in sulphur deposition, Nature, Vol. 305, 1983, 422-424.

Other Readings :

• Small, M.J., Sutton, M.C., A Regional pH-Alkalinity Relationship, Water Research Vol.20, No.3, March 1986, 335-343.

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