Application of environmental models to different ... - CiteSeerX

Ecological Modelling 125 (2000) 15 – 49 www.elsevier.com/locate/ecolmodel

Application of environmental models to different hydrological systems A. Ghosh Bobba a,*, Vijay P. Singh b, Lars Bengtsson c a b

National Water Research Institute, En6ironment Canada, 867 Lakeshore Road, Burlington, Ont., Canada L7R 4A6 Department of Ci6il and En6ironmental Engineering, Louisiana State Uni6ersity, Baton Rouge, LA 70803 -6405, USA c Department of Water Resources Engineering, Uni6ersity of Lund, S-22100, Lund, Sweden Accepted 14 June 1999

Abstract In recent years global problems such as climatic change, acid rain, and water pollution in surface and subsurface environments dominate discussions of world environmental problems. In this paper, the roles of hydrologic processes and hydrogeochemical processes are investigated through development, modification, and application of mathematical models for addressing point and non-point source water quality modelling of receiving waters: surface water, subsurface water and lake water. The paper describes the use of models to simulate the movements of pollutants and water: subsurface water, surface water and lake sediments. A hydrological model was applied to Northeast Pond River watershed to understand climate change effects in the watershed. Four watershed acidification models were applied to compute hydrogen ion, alkalinity and sulphate concentrations from Turkey Lakes watershed, Canada. The computed hydrogen ion was used to estimate acidic events, magnitude of hydrogen ion, and duration using a stochastic model. There exist uncertainties in environmental models due to imperfect knowledge of processes controlling water quality parameters as well as errors in data. Monte Carlo, first order, and inverse method analyses were used to assess uncertainty in models. SUTRA (saturated – unsaturated transport) and SUTRA − 1 models were applied to Lambton county, Ontario, Canada to locate groundwater discharge areas for St. Clair River, calculate discharge rates, and hydrogeologic parameters. A sediment contamination model was developed and applied to Great Lakes sediment data to estimate transport parameters by 210Pb data. It was then coupled with fatty acid data and results were compared with observed data. A contaminant transport model was developed and applied to two North American streams to compute stream water concentration. The computed data was compared with observed data using a simple statistical method. A hydrological model was coupled with water quality models and RAISON (regional analysis by intelligent systems on) expert system and applied to Canadian watersheds. Digital satellite data was used to locate groundwater discharge and recharge areas in the watershed. This data is useful as observed data for hydrological modelling and GIS (Geographical Information System) system. © 2000 Elsevier Science B.V. All rights reserved.

* Corresponding author. Tel.: + 1-905-3368911; fax: + 1-905-3364972. E-mail address: [email protected] (A.G. Bobba) 0304-3800/99/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 0 0 ( 9 9 ) 0 0 1 7 5 - 1

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A.G. Bobba et al. / Ecological Modelling 125 (2000) 15–49

Keywords: Climate change; Watershed acidification modelling; Pollution; Surface and ground water; Lake sediments; Water balance; Environmental modelling; Canada; Ontario; Turkey lakes watershed; Lake Ontario; St. Clair river; Uncertainty analysis; Satellite data analysis

1. Introduction Water is among the most essential requisites that nature provides to sustain life for plants, animals and humans. The total quantity of fresh water on earth could satisfy all needs of the human population were it evenly distributed and accessible. Different regions of the world are faced with largely different types of problems associated with water resources occurrence, use and control, which may endanger a sustainable development of these resources. If one considers the distribution of water resources, it is evident that some parts of the world are much better favoured with water resources than others. By and large, more developed coun-

tries are located in higher latitudes where the climate is mild and precipitation is sufficient. There are, of course, exceptions, and not only inside large countries like Canada, the United States, and the Russia (of the former Soviet Union) can the water conditions change drastically from region to region, but this may also occur in small countries. The prevalent types of water uses are evidently related to the types of water problems. To take three examples of large world regions, one can state that in a country such as Canada, and the United States water quality problems are the main overall concern, whereas in countries such as India or China the main concern is related to water quantity.

Fig. 1. Vertical cross section of a typical basin.


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2. Environmental system

Fig. 2. Linkages involving various physical locations and mathematical models.

Natural conditions of water resources occurrence and forms of water resources use are not the only reasons for different types of problems. The level of social and economic development and the available technology also contribute greatly to the nature of these problems. Good technology and, in particular, good engineering technology is essential for finding the best solution to the problems but is not, by itself, a guarantee that the problems will be solved in the best possible way. In many areas engineering technology is good but conditions are not created to ensure an efficient use of water resources. This is often the case with irrigation works in developing countries, where the social organisation does not allow full use of land and water resources. Similarly, in the case of water supply and sanitation works, the educational level of the populace does not ensure a full understanding of basic hygienic rules. The objective of the study is to apply different types of environmental models to different parts of a hydrological system.

The observed status of a system at any point in time results from the collective interaction of all these processes, both natural and anthropogenic. Processes in each of these categories occur along a time–space continuum and, depending on their location along this continuum, require different treatment or representation within the models. For example, the time-and spatial-scale formulations required to describe a storm hydrograph differ from those required to estimate the average annual discharge from a watershed. These distinct process formulations reflect the differing objectives for model development and application, as well as the differing philosophies of the model developers. The formulations and process representations, therefore, must be evaluated with respect to the model objectives, assumptions, and purposes for development, not in the context of whether they are ‘correct’ or ‘incorrect’. Evaluations should focus on identification of the types of systems (drainage lakes, seepage lakes, headwater streams), the regions and subregions, and the time scales for which model application is appropriate (i.e. the essence of the evaluation is bound to model application).

2.1. En6ironmental modelling Mathematical models have been used extensively over the past 50 years to address water quality problems and are currently used to investigate and assess virtually every type of water resource problem (Friedman et al., 1984). The U.S. Office of Technology Assessment (OTA) conducted an analysis of water resources models and their use by federal and state government agencies to address water resources problems (Office of Technology Assessment (OTA), 1982). Conclusions from this evaluation include Models are often the best available alternative for analysing complex resource problems; Models have the potential to provide even greater benefits for future water resource decision making; and

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Water resource models vary greatly in their capabilities and limitations and must be carefully selected and applied by knowledgeable professionals. Selecting appropriate procedures for analysing a particular problem is a major part of the modelling activity. In some instances, a decisionmaker requires only an order-of-magnitude estimate, whereas in other cases, increased precision might be important (Friedman et al., 1984). A different model might be used in each case, even though the problem is similar. Moreover, for many applications, there are no strategies for

developing or using models. In fact, the development of models has out-paced the corresponding documentation, support, and guidance for their use (Friedman et al., 1984). Some of the specific recommendations for model use are: Mathematical models should be based on a fundamental representation of physical mechanisms and incorporate, to the extent possible, state-of the-art understanding of the problem. Selection of mathematical models for regulatory applications requires a thorough understanding of the capabilities and limitations of the available models.

Fig. 3. Conceptualised hydrological model (Bobba and Lam, 1990).


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Fig. 4. Location of Northeast Pond river watershed.

Fig. 5. Computed total flows for different scenarios (Bobba et al., 1992b, 1997).

Proper development of models requires modellers that are well trained in the underlying physical

principles of the environmental system, as well as in the computational procedures of modelling.

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Fig. 6. Percentage change of different watershed variables for different scenarios (Bobba et al., 1997).

Fig. 7. Location map of the Turkey Lakes watershed.


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Fig. 8. Comparison of model simulated versus observed monthly runoff data for Batchawana lake watershed (Booty et al., 1992).

Fig. 9. Comparison of model simulated versus observed monthly averaged outflow flow for pH Values for Batchawana Lake watershed at station S1 (Booty et al., 1992).

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Fig. 10. The probabilities of the number and timing of acidification events above the selected truncation level for the Turkey Lakes watershed (Bobba et al., 1990, 1996d).

Fig. 11. Contaminant concentration at different locations in the stream (Bobba et al., 1996b,c).


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Fig. 12. Contaminant concentration with bottom sediment adsorption in the stream (Bobba et al., 1996b,c).

Fig. 13. Contaminant concentration with bottom sediment and aquatic vegetation adsorption in the stream (Bobba et al., 1996b,c).


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Models used for regulatory applications must be subjected to a two-stage confirmation with field data: (1) calibration, where the parameters of the model are estimated to allow a good match between the model predictions and an observed field data set; and (2) verification, where the model is compared to an independent data set without further modifying the parameter values and relationships in the model. Comparison of model predictions and observed field data as part of the confirmation process should include qualitative, graphical comparisons and, if appropriate, quantitative measures of the goodness of fit. Sensitivity and uncertainty analysis of environmental models should be performed to provide decision-makers with an understanding of the level of confidence in model predictions and to identify key areas for future study. The model, initial test applications and the modelling applications should be peer reviewed.

2.2. Model de6elopment Models are used in virtually every discipline, from physics to philosophy, for hypothesis formulation and testing, as heuristic tools for understanding system structure and function, and in assessing the effects of future control or management strate-

gies. This study emphasises mathematical models and their potential use in environmental assessment activities. Although the model variables and process representations differ across disciplines, many unifying factors or principles underlie most mathematical models. Two important factors for evaluating models, particularly water quality models, are model complexity and time–space relationships. These two factors are introduced here and are developed in subsequent sections of this study.

2.3. Bounding model applications For any analysis, and particularly for approaches that rely on the weight of evidence, appropriate procedures and techniques must be applied to the problem. Bounding model application for the purpose of assessing the effects of acidic deposition on future changes in surface water acid–base chemistry is one of the primary objectives of this study. The models that are considered in this study were developed specifically to address this issue. The emphasis in this study, therefore, is to bound their potential use and to determine the systems, regions, and time frame for which their application is most appropriate. Assessing the effects of acidic deposition, groundwater contamination, stream water quality and contaminant transport in lake sediment

Fig. 14. Observed and computed (solid line) chloride concentrations at three locations of Uvas creek, U.S.A. (Bobba et al., 1996b,c).

Model

Time step

TMWAM

Simulation daily Linked to hydrology model time step (three layer model)

ILWAS

Simulation daily Linked to hydrology model time step

ETD

Simulation daily Linked to hydrology model time step Simulation Linked to hydrology model monthly time step

RAINS

Hydrology

Inorganic S

Organic S

Sulphate adsorption fitted to lin- Same as inorganic S ear isotherm; weathering based on stoichiometric release from minerals and coupled with organic acids Same as above Only mineralization from organic matter and plant uptake based on decomposition rates and plant uptake nutrient needs Sulphate adsorption treated as Not considered linear isotherm Not considered

Reference Bobba and Lam, 1990; Lam et al., 1988

Chen et al., 1984

Schnoor et al., 1984; Nikolaidis, 1987 Kamari ,1985


Table 1 Comparison of different types of watershed acidification models (Bobba et al., 1995a)

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Table 2 Summary of basic governing equations for groundwater flow and transporta Name of equation

Equation

Groundwater flow

(f ( (f (f ( Kxx + = (x (z (z (t (x

Darcy velocity vectors

along x-direction 6x = −

Kxx (f u (x

Kzz (f along z-direction 6z = − u (z (C ( (C Contaminant transport Dxx RD − (t (x (x

Hydrodynamic dispersion coefficients

n

+

( (C ( (C Dxz + Dzz (x (z (z (z

+

( (C Dzx (z (x

+

( (6zC)+RalC= 0 (z

( (6xC) (x

+

x-component: Dxx = DL

6x6x

+ 62 6z6z DT 2 +Dmu 6 6x6x z-component: Dzz = DT 2 + 6 6z6z DL 2 +Dmu 6 xz-component: Dxz = Dzx = (DL− 6x6z DT ) 2 D =6a6;D = b6 L

Retardation coefficient

T

r Rd = 1+Kd u

a where F is hydraulic head (L), K is hydraulic conductivity (L/T), 6 is Darcy velocity (L/T), Kd is distribution coefficient (L 3/M), u is effective porosity (dimensionless), r is bulk density, Rd equilibrium constant (dimensionless), a is longitudinal dispersivity (L), b is transverse dispersivity (L), Dxx is x-component dispersion coefficient (L 2/T), Dzz is z-component of dispersion coefficient (L 2/T), l is decay constant (1/T), Dm is molecular diffusion coefficient (L 2/T), and C is concentration (M/L 3).

on aquatic systems is a multifaceted problem requiring the use of multiple techniques and procedures. Convergence of these multiple approaches to similar solutions enables increased confidence in the conclusions for the assessment. Divergence of results indicates that other factors might be influencing these systems and additional analyses might be required to understand the problem. The use of multiple techniques and procedures for assessments is a common practice for other water resources problems.

2.4. Model complexity Models can be conceptual, logical, mathematical, or of other type but, in all instances, they are an abstraction or simplification of the prototype system. Two general modelling philosophies serve as the basis for model development: (1) to improve understanding of system dynamics or (2) to control the system response. Although these two philosophies are not mutually exclusive, research models developed for hypothesis testing and system understanding typically have different structures, assumptions and limitations, input data requirements, and output formats than do decision or control models developed to evaluate different management strategies. In general, research models are more complex than control models. In many instances, these models are developed because insufficient field or laboratory data are available to test hypotheses or evaluate management strategies (Starfield and Cundall, 1988). Increased model complexity, however, typically implies increased data requirements, which can lead to a feedback loop of increased complexity requiring increased data requirements, which in turn require increasingly complex model formulations and so on. Unfortunately, models with available data sets appropriate for their application are few (Loague and Freeze, 1985). Complexity and incorporation of greater detail do not necessarily lead to a better model. In a comparison of increasingly complex rainfallrunoff models, regression model, a unit hydrograph (first principles), and a quasi-physically based model, the two simpler, less data-intensive models performed as well as or better in predictions than did the more complex, quasi-physically based model (Loague and Freeze, 1985). Scale problems associated with unmeasurable spatial variability of rainfall and soil hydraulic properties limited the successful application of the physically based model. Models are developed because the ‘real world’ is too complex to understand; if the models themselves are made too complex, they become less useful in elucidating the real-world structure and function, in testing and formulating hypotheses, and in conducting assessments (Starfield and Cun-


dall, 1988). The art of modelling lies in determining which watershed and surface water processes and data are essential for inclusion in the model. The challenge is to develop that art into a rigorous scientific methodology suitable for assessment (Starfield and Cundall, 1988).

2.5. Factors affecting reliability Five groups of factors are recognised that affect the reliability of model predictions. Among these, the most important is the formulation of the assessment question (specification of the problem). The assessment question affects the scale of time and space as well as the processes and mech-

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anisms that should be taken into account by the model. Changes in the assessment question may enhance the significance of previously assumed minor processes. Thus, errors and uncertainties associated with previously unimportant processes may suddenly dominate results when the model is applied to a new question. Even slight modifications to an assessment question may cause a model with an outstanding reliability record to grossly mispredict. Nevertheless, it is recognised that large errors can be introduced by simple typographical and programming mistakes. Unfortunately, quality assurance procedures are frequently compromised in the face of pressing deadlines and emergencies.

Fig. 15. Location map of Lambton county, Ontario, Canada.


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Fig. 16. Simulated hydraulic head map for Lambton county (Bobba, 1993).

2.6. Important distinctions The evaluation of reliability in model predictions requires a thorough understanding of the assessment question. For each question there is a quantity of interest (e.g. concentration) and an associated reference unit (kg/m3/year per individual per population, etc.). Distinctions are made in the documented literature about whether the quantity of interest is a stochastic variable or whether it is invariant with respect to the reference unit. This distinction determines whether the assessment question has a probabilistic or a deterministic answer. The document therefore discriminates between two fundamentally different types of uncertainty: Type A and B. Type A uncertainty from the selection of an incorrect model with correct (deterministic) parameters. Type A uncertainty can be subdivided into in appropriate model selection and inherent modelling error due to process aggregation. Type B uncertainty assumes the use of a perfect model with parameters that are characterised by a degree of uncertainty. The presence of Type A uncertainty in the quantity of interest requires a probabilistic answer to

the question. A probabilistic answer represents stochastic variability in the quantity of interest in the form of a distribution. In practice, deterministic as well as probabilistic answers can be determined imprecisely because of Type B uncertainties. Type B uncertainties suggest a range, not of variability but of alternative, possibly true deterministic or probabilistic answers to the assessment question. Four possible prediction formats are discussed in the literature depending on the extent to which Type A and B uncertainties are present.

2.7. Model 6alidation The process of testing model predictions against independent data sets is referred to as ‘model validation’. Model validation is considered the best method for evaluating the accuracy in model predictions. For assessment questions in which the quantity of interest is invariant with respect to its reference unit, a single predicted value is compared with a single value, which is often an estimate obtained from a number of measurements. Examples are average concentrations or time-inte-


grated concentrations for a specific time period and location. The presence of Type B uncertainty requires that subjective confidence bounds be placed on the model prediction. Statistical techniques are then employed to evaluate the confidence that the true value is encompassed by uncertainty placed about the deterministic model prediction. For assessment questions in which the quantity of interest is a stochastic variable, comparisons are made of the empirical distribution of observed

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values with the predicted distribution. The presence of Type B uncertainty requires placement of subjective confidence bounds on the predicted distribution. Statistical techniques are then employed to evaluate the confidence that certain characteristic values (i.e. mean, median, 95th percentile, etc.) of the true distribution are encompassed by the uncertainty placed on those of the predicted distribution. For both types of questions, the validation process is repeated as many times as necessary to

Fig. 17. Observed hydraulic head map for Lambton county (Bobba, 1993).

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Fig. 18. Relative error map for Lambton county (Bobba, 1993).

encompass the range of conditions over which the model may be applied. Analyses are made of the potential for the model to over- or under-predict the true values and the extent to which these results confirm quantitative standards of performance that have been assigned to the model. For quantities of interest that vary as a function of time and space, the validation process analyses the temporal and spatial trends in the over- or under-predictions. These trends indicate the capacity of the model to simulate the dynamics and spatial resolution of a system as well as to produce accurate results for a specific time and location.

3. Description of the hydrological system Fig. 1 shows a vertical cross-section of a basin, and indicates some of the physical features and hydrologic processes, which are of interest in this study. The movement of water in the basin can be predicted using various hydraulic relationships. These relationships utilise values of initial and boundary conditions (e.g. rainfall) to determine the magnitude and direction of flow velocity at different locations. Associated with the movement of water are physical, chemical and biological processes that affect its quality. The processes acting upon a given water particle are largely


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Fig. 19. Comparison of hydraulic head distributions by inverse analysis (solid) to the observed distribution (dashed) (Piggott et al., 1996).

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determined by the particle’s location in the system. For instance, the scouring and deposition phenomena occur in surface runoff, while dispersion may occur in both surface and groundwater flow. A systematic approach was taken in this study for modelling the surface flow, unsaturated flow and groundwater phenomena: the flow or quantity aspects were simulated first, followed by the water quality aspects. At each time step, the velocities at various physical locations were determined from hydraulic formulations. The calculated velocity field was then used as input to the water quality models, which routed the movement of pollutants through the system. This sequential approach was required because certain

water quality phenomena (e.g. dispersion) were affected by velocity. From Fig. 1 it can be seen that the path of any water particle may cross different regions which, in turn involve different models. This fact points out the need to formalise methods for utilising these models sequentially and for transmitting information from one model to another. Some of these interfacing aspects are depicted in Fig. 2. The boxes in this figure represent physical locations in a basin, which may be sources or sinks of pollutants. The arrows denote movement of these pollutants among the various locations. Two major items are considered in routing this movement: flows and pollutant concentrations.

3.1. Application of en6ironmental models to hydrological system

Fig. 20. Variation of flux with deviation of ground surface elevation from the regional trend (Piggott et al., 1996).

Fig. 21. Two-layer representation of the sediment pore water matrix and the boundary conditions of the contaminant transport in the conceptual model.

Mathematical models have been used extensively over the past 50 years to address water quality problems and are currently used to investigate and assess virtually every type of water resource problem (van Grinsven et al., 1995). Models can be conceptual, logical, mathematical, or of other type but, in all instances, they are an abstraction or simplification of the prototype system. Two general modelling philosophies serve as the basis for model development: (1) to improve understanding of system dynamics or (2) to control the system response. Although these two philosophies are not mutually exclusive, research models developed for hypothesis testing and system understanding typically have different structures, assumptions and limitations, input data requirements, and output formats than do decision or control models developed to evaluate different management strategies. In general, research models are more complex than control models. In many instances, these models are developed because insufficient field or laboratory data are available to test hypotheses or evaluate management strategies. Increased model complexity, however, typically implies increased data requirements, which can lead to a feedback loop of increased complexity requiring increased data requirements, which in turn require increasingly complex model formulations and so on.


Fig. 22. Comparative representation of simulated and observed

Models are developed because the ‘real world’ is too complex to understand that if the models themselves are made too complex, they become less useful in elucidating the real-world structure and function, in testing and formulating hypotheses, and in conducting assessments. The art of modelling lies in determining which watershed and surface water processes and data are essential for inclusion in the model. The challenge is to develop that art into a rigorous scientific methodology suitable for assessment.

4. Watershed runoff modelling climate change Within the next few decades, the first global climatic changes resulting from increasing atmospheric concentrations of carbon dioxide and other trace gases are likely to appear. Indeed,

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210

Pb in sediment core in Lake Ontario (Bobba et al., 1996a).

there is some evidence that changes can now be detected. Yet despite recent improvements in our ability to model global climatic systems, major gaps remain in our understanding of the potential geophysical and socio-economic impacts of climatic changes. One of the most important impacts to society of future climatic changes will changes in regional water availability, specifically the timing and magnitude of surface runoff and soil moisture fluctuations. Unfortunately, our ability to assess the regional impacts of climatic change on water resources is seriously constrained, both by the difficulty in evaluating future climatic conditions and by uncertainty over appropriate methods for studying regional effects of global changes (Nielson et al., 1973). The objective of the study is to perform the water balance assessment of the effects of a range of hypothetical climate change scenarios on runoff in

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the watershed and to examine these effects in relation to natural variability. Recently, attempts have been made to translate change variables, such as temperature, into environmental and societal impacts. Such assessments have focused primarily on the effects of increases in atmospheric temperatures on agricultural productivity (Bach et al., 1981; Rosenberg, 1981, 1982; Parkinson and Bindschadler, 1984; Thomas, 1984), and sea level (Schneider and Chen, 1980; U.S. Environmental Protection Agency, 1983). Major changes in water availability caused by alterations in temperature and precipitation patterns may be even more important to society. Such hydrologic changes will affect nearly every

aspect of human well being, from agricultural productivity and energy use to flood control, municipal and industrial water supply, and fish and wildlife management. The tremendous importance of water for both societal and ecological need underscores the necessity of understanding how a change in global climate would affect regional water supplies (Hughes et al., 1980). In many areas of the world, existing water supplies are only marginally adequate to maintain acceptable levels of food production and to meet other basic human needs. In some regions, deficits occur on a seasonal or perennial basis, while the other areas catastrophic seasonal flooding results in major loss of life and

Fig. 23. Comparative representation of simulated and observed fatty acid in sediment core in Lake Ontario (Bobba et al., 1996a).


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Fig. 24. The computer classification of groundwater regimes from the satellite digital data (LANDSAT, Band 7) of training centre, 20 March, 1974 (Bobba et al., 1992a).

property. Altering precipitation patterns may greatly affect the duration and severity of water shortages and excesses, significantly increasing the possibility of conflicts for existing water supplies and aggravating the consequences of flooding and drought. Methods for evaluating such regional hydrologic changes must be developed in order to predict such problems and to help formulate specific policies to reduce their severity.

In this study we use the watershed runoff model which includes a water balance model to calculate the runoff for both the present climate and a doubled CO2 climate. The principal focus in this study is on changes in the mean monthly runoff. Monthly changes have also been examined for the basin. The changes in runoff can occur due to the combined effects of changes in rainfall runoff and snowmelt runoff. Increased temperatures are

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likely to increase the ratio of rain to snow and to initiate snow melting earlier in the spring. The hydrological model of watershed acidification model was a modified version of watershed runoff model and applied to study hydrological conditions of watershed due to climate change (Fig. 3). The modified watershed runoff model was applied to Northeast Pond River watershed to study climate change effects (Bobba et al., 1992b, 1997) (Fig. 4). This study evaluates one of the most important regional impacts that may result from changes in global climate changes in water availability. Widely varying climate change sce-

Fig. 25. The computer classification of groundwater discharge areas (LANDSAT, Band 7) in the Big Creek and Big Otter basins, Ontario, on 20 March, 1974 (Bobba et al., 1992a).

narios were used to drive a water-balance model designed to evaluate the impacts of global climatic changes on runoff and soil moisture in the watershed. The scenarios studied include three scenarios with hypothetical temperature and precipitation changes. Application of the watershed runoff model to the Northeast Pond River suggests that variations of 30% in mean annual flow as a result of climatic change are not unrealistic, with even greater changes possible in most watersheds. The relationship between changes in precipitation and changes in annual runoff are nearly linear for the scenarios considered. A 50% decrease in precipitation causes a decrease in runoff of approximately 50%, assuming increases in temperature and evapotranspiration. The changes in annual flow could be aggravated or mitigated by changes in seasonal flow (Fig. 5). The magnitude of changes in annual flow induced by hypothetical scenarios ranged from decreases in mean annual runoff of 25% to increases in mean annual runoff of 15%. The greatest decrease in runoff was seen in the basin for a 2°C increase in temperature in conjunction with a 50% decrease in precipitation. A 100% increase in precipitation caused runoff to increase 100%. All relationships between runoff and precipitation are nearly linear for the range of scenarios studied. Runoff increases more slowly than precipitation (Fig. 5). Model biases undoubtedly affect this relationship. The percentage changes in runoff are dominated by low flow years (Fig. 6). Despite the uncertainties that surround the nature and timing of future climatic changes and their subsequent impacts, the results presented here raise serious concerns about regional water availability. In particular, observed decreases in summer soil moisture and runoff and increases in winter runoff are robust and consistent across widely varying scenarios. This consistency suggests strongly that hydrologic vulnerabilities will make the impacts of climatic changes on water resources an issue of major concern in many regions of the world. Four particularly important and consistent changes were observed: (1) Large decreases in summer soil moisture levels for all climate change scenarios, (2) decreases in summer runoff volumes for all climate change scenarios, (3) major shifts in the


timing of average monthly runoff throughout the year, and (4) large increases in winter runoff volumes for the climate change scenarios.

5. Watershed acidification modelling Acidic deposition entering the watershed or catchment can be a primary contributor changes in surface water quality (NAPAP Aquatic Effects Working Group, 1991). Atmospheric deposition to catchments occurs due to three physical processes: wet deposition, dry deposition, and interception of cloud water, fog, and mist droplets. Although watershed vegetation has minimal effect on the quantity of wet deposition entering the catchment, it can influence the quantity of dry deposition through aerosol and vapour capture. After wet deposition, interception by the canopy, however, exchange reactions can take place between the incoming acidic solution and the forest canopy that change the chemical composition of the throughfall solution. Organic acids such as fulvic acids, lignins, and tannins are released from the canopy, which combine with free hydrogen ions in solution. A number of process-oriented mathematical models have been developed that simulate the flow of acidic input through terrestrial systems and the resulting chemical response of surface waters. Over the past decade long-term data sets available from integrated monitoring programs have been analysed conceptually, statistically and with use of dynamic simulation models (Kirchner, 1992; Newell, 1993). Literature reviews have been made of either the principles or the performance of a small number of acidification models (Reuss et al., 1986; Schecher and Driscoll, 1988; Eary et al., 1989). Different watershed acidification models are shown in Table 1. The details of the models are explained earlier (Bobba et al., 1995a). Four different watershed acidification models were applied to a Canadian watershed and their results compared. The Batchawana sub-basin is the headwater sub-basin of the Turkey Lakes watershed and is approximately 2.06 km2 in surface area and receives approximately 1212 mm of precipitation annually. The (Turkey Mersey wa-

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tershed acidification model), TMWAM (Bobba and Lam, 1990; Lam et al., 1988, 1989), ETD (enhanced trickle down) (Nikolaidis, 1987), and ILWAS (integrated lake watershed) (Chen et al., 1984) models are all lumped parameter, deterministic models that were designed to operate on a daily time step in order to be able to examine watershed processes in real time. The RAINS (regional acidification information and simulation) (Kamari, 1985) model was developed to examine watershed responses to acidic precipitation over long intervals (monthly and annually, respectively). Also, as not all of the models are capable of simulating all of the major cations and anions, pH, alkalinity, and sulphate, which are common to all the models, and discussed for comparison purposes. All of the models were applied for the period 1 January 1981 to 31 December 1984, for data measured at station S1, shown in Fig. 7. The models were initially calibrated for the period 1 January 1981 to 31 December 1982. They were then run for the final 3 years of data without further calibration. The models were run using the same basic physical and chemical input constants and parameter values as well as meteorological input data. The models were all calibrated by trial and error rather than by an automatic numerical optimisation procedure. The model parameters were adjusted to minimise the errors between the observed and model calculated outputs, based on the principle of least squares. Additional statistics are used to evaluate model performance. Linear and rank correlation coefficients and regression slopes based on a statistical comparison of computed and observed values are also used to indicate model performance. The simulated versus the observed monthly watershed outflow data are presented in Fig. 8 and the associated model performance of statistical data are presented by Bobba (1996). The TMWAM and RAINS models show very similar simulated flows and have almost identical statistical performance. The ILWAS model, which has the most sophisticated hydrologic submodel, performed as equally well as the TMWAM and RAINS models, except with respect to its coefficient of efficiency, in predicting monthly outflows from the watershed. The hydro-

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logic submodel used in the ETD model is intermediate in complexity between the ILWAS and TMWAM, and RAINS models. However, for this particular application, it shows the largest deviation from the measured values for both the monthly and cumulative flows, as reflected by all four-model performance statistics. Considering each model performance statistic separately, it can be seen that with respect to the linear correlation coefficient, the RAINS and TMWAM models performed the best with values of r =0.987 and 0.986, respectively, followed closely by the ILWAS model with r =0.967, and the ETD model was the least precise with r=0.896. The rank correlation coefficient indicates how well the models simulate the timing and magnitude of the peaks of flows as compared to the linear correlation coefficient. In this case, the TMWAM, ILWAS, and RAINS models perform equally well, with R=0.988, 0.985, and 0.984, respectively. Considering the coefficient of efficiency, the RAINS and TMWAM models perform best with respect to the mean-as-model, with E = 0.970 and 0.961 respectively, followed closely by the ILWAS model with R= 0.915, and finally the ETD model with R= 0.762. The models show a significant range in their abilities to simulate monthly and seasonal changes represented by the observed outlet chemistry data. The model predicted versus the observed outlet stream pH data is presented in Fig. 9. It can be seen in the Fig. 9 that the RAINS model tends to overpredict the fluctuations of observed pH and alkalinity (Bobba, 1996). The ETD model tends to underpredicts the fluctuations of observed pH but does the best job of simulating the observed alkalinity (Bobba, 1996). The TMWAM model appears to do the satisfactory job of simulating the observed pH data and is second to the ETD model in simulating the measured alkalinity data. The TMWAM predictions most closely simulate both the magnitude and the timing of the observed sulphate stream concentration peaks, as confirmed by the rank correlation coefficient of 0.680 (Bobba, 1996). The ILWAS model also performs well in predicting the timing of the peaks in stream sulphate concentration, with R = 0.610. However, the magnitudes of the peaks,

especially in the spring of 1983 and 1984, are significantly different from the observed values. As was the case for pH, the ETD model predictions for SO4 show the smallest fluctuations of magnitude over the period of study. The RAINS model underpredicts the stream sulphate concentrations over the entire period of study. It also fails to predict the timing of the peaks, as verified by the very low rank correlation coefficient. ILWAS model needs more parameters and more input data. It only runs on main frame. TMWAM model includes organic acids in hydrogeochemical model. RAINS model runs only on a monthly time step. All the models were not tested for long term validation. All these models were tested only for the short term. As a result, the models have to be run on a long-term basis for testing of their performance. The watershed acidification might change due to atmospheric change effects. At least the models have to be run for climatic scenarios.

5.1. Prediction of acid shocks in the watershed The acid shock model (ASM) is a probabilistic model based on developments in the theory of extreme values (Bobba et al., 1990, 1996d) and represents an attempt to develop a more general stochastic model to describe and predict the behaviour of acid shocks. The objective of this study was to derive stochastic models to predict the probability of higher hydrogen ion concentration flow events due to snowmelt and rainfall in acid sensitive watersheds. The daily computed hydrogen ion concentration data was used in this analysis. There is a good relationship between flow and outflow pH values for Batchawana Lake watershed at station S1 (Booty et al. 1992). The daily computed data compared well with observed data (Bobba and Lam, 1989, 1990). Two sets of higher hydrogen concentration flow events were recognised by rain or rain on snow or snow melting processes. At the selected truncation level (Ho), the watersheds reveal distinct statistical characteristics of the two generating processes. The mean magnitude of snowmelt generated events is larger than that of rainfall events and snowmelt events tend to last longer than rainfall events. These observations reflect the control of


the physical and hydrometeorlogical processes. Rainfall affects larger areas of the watershed simultaneously, but its duration is limited. Snowmelt usually occurs from the middle of March or the beginning of April and is restricted to short periods. Rain generated hydrogen ion concentrated flow events are most frequent in November, but can occur at any time in autumn or winter. The probability of acid shock events, measured as H+ concentrations, is defined for pH B6 in Turkey Lake watershed. Fig. 10 illustrates the fit of the nonhomogeneous Poisson distribution to the number and timing of events. The proposed distributions satisfactorily represent the mixture of physical and hydrometeorlogical processes that are operating. They reveal the sharp increase in probability of hydrogen ion concentration flow events during snowmelt followed by high hydrogen ion concentration flows during summer. Snowmelt generated hydrogen ion concentration flows occur over a longer period and produce a more gradual change in the probabilities of flooding between October and February. For the period of observation, there was a maximum of three events per year, as indicated by a maximum PE (probability of events) of three for this watershed. Similarly, the probability of duration of an event is presented for the watershed. It can be seen, for example, that 50% of such events last less than approximately 35 days. The predicted (using exponential distribution) magnitudes of high hydrogen ion concentration flows generated by snowmelt and rainfall processes were computed.

6. Water quality modelling in streams The water quality models reflect the complexity of the water resources issues ranging from minimum stream flows for water supply, irrigation, fish and wildlife habitat, water quality, recreation, and aesthetics to basin wide waste load allocation or eutrophication studies to assessing the fate, transport, and transformation of pollutants and hazardous substances in our surface waters (Booty and Lam, 1989). Multiple desired water resources uses result in multiple, interactive water

39

resources issues that must be resolved (Jorgensen, 1984). Surface water models provide a flexible, efficient, and cost-effective approach for integrating many process interactions and evaluating the effects of various management alternatives on surface water quantity and quality (Orlob, 1983). Recently, the requirement to perform environmental exposure assessments for toxic substances, including pesticides, has led to increased use of pesticide runoff loading models to enhance estimates of environmental risk arising from specific chemical change (Donigian et al. 1977; Dean and Mulkey, 1979). The objective of the study was to develop a simple water quality model to aquatic stream. Many mathematical models have been developed to describe the transport of various contaminants in stream ecosystems. The mathematical models usually assume an eddy diffusivity mechanism (DiToro et al., 1981; Ambrose et al., 1988). The basic transport equation can be written for a three dimensional system as: (C (C (C ( ( (C ( Kx + K + K = (x (y y (y (z z (z (t (x

(C (C (C + + uy + uz S (1) (x (y (z − where, Kx, Ky and Kz are turbulent dispersion coefficients in the x, y and z directions; ux, uy and uz are fluid velocities in each of the co-ordinate directions; C is the concentration at any point (x, y, z), t is the time; and S is the source or sink. The above equation states that changes in conservative substances are due to turbulent dispersion and convection in three directions. Eq. (1) is complex and difficult for practical applications. Therefore, in numerous studies simplified versions of the equation have been proposed to describe chemical waste contamination transport in one or two dimensions. In order to simulate the uptake in the regions of low velocity and by sediments and plants, other parameters have been added to the equation. Transport functions was derived by applying the sorption and desorption concepts to the mass balance principal. A one-dimensional mathematical model for the transport of chemical waste contamination in an aquatic environment is: − ux

40


(C ( 2C (C −u +%m = DL j = 1 Sj (t (x 2 (x

(2)

where C is the concentration of chemical waste or a particular contaminant in the flowing stream at any point x, and time t; x is the distance in the direction of flow; DL is the longitudinal dispersion coefficient; u=Q/A, u is the average velocity of flow; Q is the flow rate; A is the cross-section of the stream; Sj is uptake or release from the j th of m adsorption phases; and j is the index number for each adsorption phase. The first two terms in Eq. (2) define the mixing characteristics and dilution, while the third term describes uptake and release of contamination. The mathematical model equations are solved by a finite difference method (Bobba et al., 1996a,b,c). The model was applied to a hypothetical waste disposal site sitting on the bank of a stream. The leachate is seeping into the stream. The data was used from the available literature (Schnoor et al., 1984, 1987). The shapes of the contaminant profiles are shown in Fig. 11 at different locations in the stream. From the shape and maximum values of the simulated data, it can be seen that initial dispersion of a point source does not follow Taylor’s equation (1954), but rather takes the shape of a skewed normal distribution because of dominance of advection over dispersion. However, at some point downstream, the curves approach a form where the Taylor (1954) expression is valid. The results obtained with an adsorption term for bottom sediments added to the dispersion equation are shown in Fig. 11. Bell shape curves were observed at different locations. As expected, peak concentrations are observed near the source. The time lag of peak concentration increases at different locations with less peak concentration. This might be happening due to adsorption on the sediments. This Fig. 12 is similar to Fig. 11 but that shows the tails of the concentration profiles are different. The contamination concentration was longer in the stream without aquatic adsorption. Aquatic vegetation adsorbed some of the contaminants. Continuous release of contaminants may also be modelled with this solution. The transport equation with adsorption terms for bottom sediments and vegetation was used for the continuous release case and the results are shown in Fig. 13.

The model was applied to Uvas Creek which is located near Monterev, CA, USA. Chloride was injected at a constant rate for 3 h and its concentration reached a maximum value of 11.9 mg/l. The background concentration was measured to be 3.7 mg/l. The computations based on the leading edges observed at 38, 281, and 619 m are shown in Fig. 14. The computed data with observed data is good. The significant features of the concentration data are (a) the decrease in the maximum concentration at the downstream locations, (b) the clipping of the shoulders of the leading edges, (c) the extent of the tails, and (d) an apparent loss of mass at 619 m. The injected concentration was 11.4 mg/l, and flow was 0.0125 m3/s. The model was fitted by a trial and error method. The best-fit model parameters were determined in a downstream sequence for each of the three reaches between locations. The dispersion coefficient calculated by the numerical method was 0. 50 m2/s. Similarly, this model was applied to Ice Water Creek, Canada (Bobba et al., 1996b). The computed data compared well with observed data. The dispersion calculated by the model was 0.35 m2/s.

7. Groundwater and contamination modelling Groundwater modelling is concerned with the behaviour of subsurface systems. Essentially all models are simplified representations of these subsurface systems (Bear, 1979; Freeze and Cherry, 1979). Modelling, therefore, may be considered as an exercise in systems analysis whereby theories concerning the behaviour of groundwater systems are organised into models which are used for their predictive capability (Bobba and Singh, 1995). Contaminant transport models simulate movement and concentration in groundwater systems of various contaminants, in particular pollutants such as leached contaminants from landfills. These models generally contain a flow submodel, which provides flow directions and velocities. A quality submodel utilises these velocities to simulate advective transport, allowing for dispersion and reactions. Mass transport models include both conservative and non-conservative transport


by containing such factors as chemical adsorption and ion exchange. The purpose of the study is to identify groundwater seepage areas to St. Clair River by applying the numerical model, (saturated unsaturated transport) SUTRA. Basic equations for development of any deterministic model for the study of groundwater flow and contaminant transport phenomena for a two dimensional aquifer are described in Table 2. The contaminant models consider dispersion, diffusion, convection, and chemical adsorption processes affecting contaminant propagation in sub-surface systems (Bobba and Singh, 1995). The SUTRA (Voss, 1984) groundwater flow model was applied to Lambton county to identify groundwater seepage areas to Lake Huron and St. Clair river. The Lambton County (Ontario, Canada) is located along an international boundary between USA and Canada. St. Clair flows from Lake Huron to lake St. Clair. The SUTRA groundwater flow model was applied to Lambton county, Ontario, Canada (Fig. 15). The details of geology and hydrogeology are described earlier (Bobba, 1993). The steady state calibration of the model of the fresh water aquifer was made using the piezometric record during the field season. This involved a laborious procedure consisting of several simulations with different input data by varying, in particular, the transmissivity distribution and the boundary conditions at the eastern side. Simple statistical models were applied to compare computed and measured data. Fig. 18 shows the contours of relative percentage errors between observed and computed data. The various statistical parameters illustrate favourable agreement between the observed and calculated results. Maximum error magnitudes are observed on the eastern edge boundary. This may be due to an error recharge boundary condition. Large error magnitudes are also observed near the St. Clair river. This may be due to a poor description of the buried valley; that is, the thickness and hydraulic conductivity of the aquifer in the buried valley might have contributed to the error. The topography and hydraulic head of the freshwater aquifer apparently follow the westerly trend of the bedrock surface.

41

By observing Figs. 16 and 17, we can locate groundwater discharge areas of the St. Clair River. These locations compared well with observed data. The maximum error is observed at the centre of the area (Fig. 18). This may be due to heterogeneity in this area. Flow rates in the drift are generally slow because the deposits that comprise the drift are fine textured and are characterised by low hydraulic conductivity. The hydraulic conductivity of the bedrock valley formation ranges from 4 × 10 − 8 to 2 × 10 − 6 m/s. A fresh water aquifer was encountered in the bedrock valley and is considered to be continuous along the bedrock valley. The water level contours in the bedrock valley indicate a generally westward groundwater flow system. Since hydraulic gradient varies across the bedrock valley, the rates of groundwater flow also vary. Calculations indicate that groundwater flux into and out of the valley is about 0.9 and 0.5 m3/s, respectively, for a 100 m strip of aquifer. The difference of about 0.4 m3/s is lost within the valley and may flow downward into the overlying Hamilton formation. The amount water that flow westward out of valley (0.5 m3/s) probably discharges to the St. Clair River. The relative percentage errors have shown uncertainty in hydrological parameters, boundary conditions and recharge rates to an aquifer. The following section explains the application of inverse model to compute the hydrological parameters.

7.1. Application of in6erse analysis to groundwater flow model Inverse analysis is an increasingly popular method of calibrating models of groundwater flow systems through the use of conventional methods of groundwater flow and transport simulations in conjunction with methods of function optimisation (McLaughlin and Townley, 1996). The purpose of this study was to describe an application of inverse analysis of SUTRA model to Lambton County. The inverse analysis model was developed and coupled with SUTRA model and applied to existing data. In this application, inverse analysis is used to derive a best estimate of the values of hydrogeologic parameters controlling

42


groundwater levels in the Lambton county aquifer where the groundwater flow occurs at a steady rate and is two-dimensional, with horizontal flow within the aquifer dominant over vertical flow within the till and bedrock. Piggott and Bobba (1993) presented the details of the development of SUTRA − 1. Inverse analysis was performed using SUTRA − 1, an inverse implementation of the SUTRA groundwater flow and transport algorithm (Voss, 1984). SUTRA − 1 invokes SUTRA as a subroutine and co-ordinates the transfer of information to and from SUTRA and the AMOEBA polytope optimisation algorithm of Press et al. (1986). SUTRA − 1 (Piggott et al., 1994, 1996) is based on the indirect approach to inverse analysis in which an error function quantifies the discrepancy between observed and simulated spatial and temporal distributions of hydraulic head and solute concentration or fluid temperature, and the parameters regulating the simulated results are manipulated until the minimum value of the error function is obtained. Only steady state hydraulic head data is considered in this analysis. The nodal hydraulic heads computed by SUTRA are a function of many input parameters. Factors such as the discretization of the aquifer are invariant and are permanently defined in the problem specification. Other factors such as spatial distributions of aquifer thickness and hydraulic conductivity and specified head and flux boundary conditions are subject to considerable uncertainty and become candidate parameters for determination by inverse analysis. Correlating flux to the deviation of ground surface elevation from the regional trend consistently yields a better approximation of the observed hydraulic head distribution than does correlating flux to ground surface elevation. The improved match is apparent in the RMS errors and is manifest in the observed and simulated distributions of hydraulic head illustrated in Fig. 19. On the basis of this evidence, it is concluded that elevation deviation is the dominant factor in defining the distribution of groundwater levels in Lambton County. The control of groundwater levels by elevation deviation is expressed by varying rates of net recharge and depletion of the

aquifer. This does not imply a mechanistic relation between elevation deviation and flux; that is, there is no physical mechanism by which a change in elevation deviation enforces a change in flux. Instead, allocating flux according to elevation deviation corresponds to allocating flux according to the dominant topographic features of the region. The uniform flux returned by the model implies a net recharge at a relatively low rate. This model yields only a modest improvement in RMS error relative to that obtained from the model, which assumes no recharge or depletion. More substantial reductions in RMS error for models in which flux varies with elevation deviation suggests that the region is most appropriately characterised by variable flux. Fig. 20 indicates that the relation between flux and elevation deviation is reasonably consistent across the various models and that the net depletion is predominant. The net recharge is confined to a small portion of the study region, largely the area corresponding to zone 4 in the four-zone mode. The topographic feature that is coincident with the Wyoming Moraine in the eastern portion of the study region extends completely across the region, following the trend defined by the moraine. This is well illustrated by zone 4 of the four-zone model (Piggott et al., 1994, 1996). Additional inverse analyses were performed using a two-zone flux zonation model in which one zone is represented the extent of the Wyoming Moraine and the second zone represented the remainder of the region. This model replicated the elevated groundwater levels over the extent of the moraine but failed to reproduce the extension of elevated groundwater levels across the region. By extending the zone representing the moraine across the region, the pattern of elevated groundwater levels was reproduced. Elevated fluxes were determined for the zone representing the moraine in both analyses. These observations suggest that the influence of the Wyoming Moraine extend beyond the limits of the moraine identified by Chapman and Putnam (1984). Dorr and Eschman (1970) recognise the extension of the Wyoming Moraine across the tip of Lake Huron and along the western shore of the lake as the Port Huron Moraine.


The RMS error returned from inverse analysis is smallest where elevation deviation is used as the correlation variable, is least for the functional flux distribution models, and decreases with the number of parameters to converge toward a non flux parameter. While decreasing values of RMS error are obtained as the models are refined, the values appear to converge toward a non-zero limit that represents variations in hydraulic head which are not explicable in terms of groundwater flow modelling, errors perhaps in the observed data. The semivariogram functions indicate that, in contrast to surface elevation, the subsurface data sets exhibit a substantial nugget effect that may reflect a combination of smallscale variability and measurement error. Smallscale variability is probable for the physiographic data but is less reasonable in the case of the hydraulic head data as the governing equation for groundwater flow mandates a continuous distribution of hydraulic head. Measurement error due to the misinterpretation of stratigraphy is likely for the subsurface physiographic data. Hydraulic head is prone to measurement error due to the misinterpretation of water levels and is subject to deviations imposed by differing pumping rates in neighbouring wells. The SUTRA − 1 model was applied only to one test site and groundwater flow only. The model has to be tested in other regions with different hydrogeological conditions by including the transport model.

8. Contaminant transport modelling through lake sediments Numerous contaminants introduced into the aquatic environment accumulate in lake bottom sediments. The ultimate fate of toxic contaminants which penetrate the water-sediment interface is governed by the combined properties of the contaminants themselves, those of the porous materials comprising the lake bed and the illdefined kinetics of biogeo-chemical processes (Berner, 1980; Cochran, 1985). A numerical transport model based on the mass balance technique, which includes time-dependent parameters

43

such as particle settling velocity, concentration or flux of particles, and depth dependent variables in sediments such as the bioturbation rate and porosity was developed and applied to the Great Lakes data. The purpose of this work was to utilise the numerical transport model in conjunction with directly measured contamination concentration profiles beneath the water–sediment interface. Following Schink and Guinasso (1978) and Bobba et al. (1996a), Fig. 21 illustrates the water–sediment interface, along with the one-dimensional sedimentation of contaminants into the interface and the subsequent one-dimensional transport of contaminants below it. Since the current work is concerned solely with activity and chemical reaction occurring beneath the water sediment interface, the following assumptions are made: (a) the lake water is well mixed with constant volume, (b) the model is one dimensional, (c) groundwater flow is ignored, (d) physical mixing, including molecular diffusion, occurs in the sediment water and varies with depth and different types of sediments, (e) biological mixing (bioturbation) is important, (f) the sediment can be divided into layers, each of which is considered to be homogeneous and isotropic, (g) the sedimentation rate is constant, and (h) chemical reactions (e.g. ion-exchange, adsorption, first order decay mechanisms) between pore water and sediments are important. The bioturbation effects are taken to be the consequence of the burrowing activity of benthic organisms. It is further assumed that below some depth (Z= L) such burrowing activity will cease to exist. In the present work, therefore, a two-layer representation is considered (Fig. 21), i.e. a bioturbation zone defined by 0B ZB L, and a non-bioturbation zone defined by Z \ L. Each of the two layers requires an average but constant value of diffusion coefficients (bulk coefficients). Consistent with the above assumptions, the one-dimensional mass transport equation governing the diffusion, advection, radioactive decay and adsorption processes that propagate chemical components within the lake bed sediments may be written as follows:

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(C = (x

(C (C ( Ds (x 1 (x (C + −Vs (x 1 +K (x (x

( DB

+


1 1+ K

Rd +

n

(1 −u) rs % Rs u

(3)

Eq. (3) can be further simplified for sediments below the zone of bioturbation where DB =0. Under this condition, the equation reduces to:

(C Ds ( 2C (C = −Vs 2 (x 1+ K (x (x +

n

1 (1 −u) rs % Rs % Rd + u 1+K

(4)

where C is the concentration of the contamination, t is time, x is depth, Ds is average molecular diffusion coefficient, DB is the average bioturbation (mixing) coefficient, Vs is sedimentation the rate, u is porosity,rs is density of sediment, K is adsorption coefficient, Rd is retardation coefficient and Rs sum of reaction coefficient. The equations are coupled with boundary conditions and solved by numerical methods. The finite-element model was developed and successfully applied to predict the 210Pb and total extractable fatty acid concentrations at different depths by using different transport parameters. The computed results were compared well with observed data and computed transport parameters from 210Pb data (Fig. 22). These parameters were used to simulate the fatty acid concentrations at different depths (Fig. 23). Simple statistical methods were used to compare computed and predicted results. This model is useful to predict the contaminant transport in Lake Sediments with different geological, physical, chemical and biological parameters and reactions. This model has to be applied to other locations with other organic chemical contaminants. 9. Uncertainty analysis in environmental modelling In any mathematical modelling, there are inevitable uncertainties in the model structure and parameter input values. The conventional deterministic modelling approach lacks mechanisms for

estimating the effects of uncertainties on the model response. Sensitivity analysis provides some insight, but is limited. Procedures for uncertainty or error estimation in contamination modelling have been described by Spear and Hornberger (1980), Thomann (1982), Reckhow (1979), Beck (1987), and Bobba (1996). These procedures include a variety of techniques such as first-order error analysis, regional sensitivity analysis, Monte Carlo simulations, methods of moments and maximum likelihood estimation. These procedures, although not discussed here, permit an evaluation of prediction uncertainty. Model developers typically focus on prediction uncertainty and increasing model resolution. While this is obviously desirable, quantifying the prediction uncertainty can be more important. Model users must be able to assess prediction uncertainty, which should be a critical research area for model developers. The main objective of this study was to develop and apply first-order and Monte Carlo analysis models to water quality models. In the paper (Bobba et al., 1996c) two error analysis techniques were applied in water quality modelling process, first order error analysis (FOEA) (Cornell, 1972; Berthouex, 1975) and Monte Carlo simulation (MCS) (Burges and Lettenmaier, 1975; Tiwari and Hobbie, 1976; Hornberger, 1980; O’ Neill et al. 1980; Ford, et al., 1981; Scavia et al., 1981; Walker, 1982; Malone et al., 1984), and are discussed in detail and some examples of their use are provided by (Bobba, (1996). The following is a summary of the application of the models with hypothetical data. (a) The applicability of the first-order error analysis (FOEA) is inherently restricted by three factors: (1) degree of nonlinearly in the model; (2) distribution of errors in each random variable; and (3) magnitude of errors. (b) One particular advantage of the first-order error analysis is that it provides the components of total uncertainty in model output caused by each random input variable. When the model is highly non-linear, firstorder error analysis may need to be extended to some higher order-error analysis. (c) Monte Carlo simulation is conceptually simple, theoretically sound, and flexible. Two important factors to be considered in any application of Monte Carlo


simulation are: (1) probability distribution for each random input variable needs to be selected, and (2) number of simulation requires specification. (d) These two error analysis procedures were incorporated, as options, in a BOD-DO model. This new model is capable of simulating water quality in a complex stream system as well as estimating uncertainties in predicted BOD and DO values which would result from uncertain input conditions. (e) The result of applying these procedures to the model is summarised as follows: (1) If the random input variables are linearly related to BOD and DO in the stream, such as wasteload from treatment plants, and their distributions are normal, FOEA provides an exact solution for errors associated with predicted BOD, DO values. (2) If a limited number of non-linear input variables are randomised, MCS provides the option of choice. (3) When a reasonably large number of input variables are randomised, the model output tends to be normally distributed. If moderate departures from normality are present in the random input variables, FOEA provides good estimates of uncertainties in model response. (4) The maximum uncertainty in predicted DO values occur well beyond the DO sag point for the example selected. (5) The magnitude of influence of uncertainty in each random variable varies with the location along the stream. (6) One or two random variables exhibited a major influence on uncertainty in predicted DO values at any particular point in the stream for the example considered. (7) These error analysis procedures can be used to estimate the probability of violation of minimum DO requirements in stream. (8) The error analyses should be considered in effluent management programs. Monte Carlo analysis was applied to three existing groundwater analytical pollution transports models (Bobba et al., 1995b). The models consider the transport mechanisms of advection, dispersion, adsorption, radioactive decay, hydrolysis, and biodegradation. The Monte Carlo technique can be used to examine the uncertainty in output variables: either pollution arrival time or concentration. In this example, two schemes of assigning probability distributions are used: normal for all input parameters and mixed distributions. The

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two schemes show different results, which suggest that the probability function for each input parameter must be carefully selected. It is demonstrated that the type of probability distribution for arrival time or concentration is dependent on the mathematical structure of the model and the selected probability functions. The models were applied using only hypothetical data.

10. Expert systems—remote sensing technology to water resources In the early 1970’s, satellite technology was developed for assessing environmental and natural resources issues. Ever since the classic paper by Nielson et al. (1973) concerning the variability of field measured soil water properties, scientists have been aware of the spatial complexity of soil, and the complexity of solute transport in soil. Because of the spatial complexity of soil, modeling the movement of pollutants in the watershed is a spatial problem well suited for the coupling of a transport model with a GIS (Geographic Information System). Corwin et al. (1997) defined GISlinked models as an integrated system of three basic components: model, GIS, and data. The thermal gradients present in the groundwater flow systems were directly attributable to the presence of subsurface groundwater flow. LANDSAT digital radiance data was used to delineate the principal groundwater regimes according to the proximity of the water table to the surface. Based on this hypothesis, the groundwater recharge and discharge areas were located from LANDSAT and thermal pictures. The major benefit arising from this effort in environmental research and management of resources is that this technique allows the delineation of pollutant source areas from river systems to lakes. The remotesensing data is major input data in GIS and expert system applications in watershed hydrology. The objective of this study was to apply the remote sensing technology to surface and subsurface water resources. The investigation described here was primarily designed to determine whether appropriately processed digital satellite data would provide satisfactory information, which

46


could be used operationally. LANDSAT digital data was used to delineate the subsurface flow systems such as recharge and discharge areas (Fig. 24). The results indicate quite clearly that the standard digital processing techniques of contrast enhancement and cross correlation by using Bands 7 and 5 do allow the basin to be discriminated from snow and vegetation background information to discriminate the groundwater flow systems (Fig. 25). Satellite pictures are very useful to select sites for waste disposal and for modelling purposes. Wintertime satellite digital data is very useful to delineate groundwater flow systems in Canadian environment. The same digital data can be used to delineate the active and variable source areas in surface runoff modelling (Bobba et al., 1992a). The RAISON expert system was coupled with hydrological and water quality models and applied to field data (Bobba et al., 1992b). This work is still in preliminary stage. The remote sensing, including GIS may apply in future to get confidence in application.

11. Conclusions A description of above environmental models has been given following a logical framework. When conducting an impact assessment, models of differing nature are put together. All the stated models played an essential role. However, it must be recognised that several problems are related to the utilisation of these tools. The following general conclusions have been observed after applying the models in real world. It is current practice among universities, research institutes and consulting firms to think of mathematical models when doing an environmental impact assessment. However, sophisticated Models are not always a necessity. Frequently, the simpler the approach, the better. Model outputs are a function of assumptions made when writing the fundamental equations. In many models, there is some degree of uncertainty in the formulation of Physio-chemical mechanisms involved. The outputs are a function of available data, but data collection can encounter difficulties. Sometimes the detection level of

equipment is too low. Nevertheless, the previous example demonstrates the need for continuous monitoring of the maximum number of parameters. Automatic remote stations and teledetction could play a valuable role. Mathematical models may help to reduce the number of stations and to analyse the collected data. Redundancies and poor location of stations sometimes result from surveys done by different levels of government or public agencies. Good databases could be established if measurements were integrated. Very few attempts have been made to validate mathematical models. Proportions are usually not interested in this study. However, many environmental impact assessments result in compulsory monitoring programs for the proponents. Data are collected and not always used. Compatibility exists between physical and mathematical models. Thus, a mathematical model calibrated with physical model can be directly validated on-site without any ‘tuning’ of parameters. Compatibility exists between mathematical models. TMWAM is a good example of this point. A watershed runoff model was used, which had been validated for several years (30 years) with the same set of parameters (Bobba et al., 1997) As a new question was introduced to describe water quality, it was found necessary to modify calibration which previously was thought correct. Biological models are not as developed as water quality models. Biological systems are more difficult to simulate due to their complex nature. In conclusion, some important features should be emphasised: a) A study can include several applications of models of increasing complexity. Each intermediate model gives indications, which can be used to verify the next more sophisticated model. As seen previously, a simpler model can help define boundary conditions for a more complex one (Bobba, 1993). b) Models must be made more credible. Public perception is not always related to actual hazard. It is well known that the risk associated with nuclear power stations is feared much more than risk associated with cigarette smoking or road casualties. To obtain that confidence, several actions can be undertaken: 1) Validation of impacts predicted by past studies and follow up of the projects with moni-


toring efforts; 2) organisation of comparisons between physical and mathematical models; 3) organisation of comparisons of various mathematical models in the same field (e.g. WMO); 4) consulting firms could be asked to publish complete documentation when using a mathematical model in an impact assessment study; external experts and other research centres might then be in a position to evaluate the work done; and 5) the federal and state governments could increase the financial support for research.

Acknowledgements The senior author is grateful to D.S. Jeffries, D.C. Lam, A.R. Piggott, R. Bourbonniere and W.G. Booty for their contributions and help in this work. The encouragement and support from J. Carey are also appreciated. The authors acknowledge the publishers to permit to publish the figures. The constructive comments of anonymous reviewers and editor of the journal on the original manuscript are appreciated.

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