CHAPTER 2 Objectives of Groundwater Modelling In the last two decades mathematical modelling techniques have increasingly proved their value in furthering the understanding of groundwater systems and, hence, in improving the evaluation, development, and management of groundwater resources, and the control of groundwater problems. 2.1 The Modelling Approach The question "why model" is still sometimes asked. The answer must be that combining the available hydrogeological data with the appropriate physical laws (in the form of equations) in a self-consistent mathematical model is generally the best way to make use of these data, for whatever purpose. Most commonly used are mathematical models, which express the behavior of groundwater systems in terms of a set of physical equations. In simple cases these partial differential equations can be solved analytically, but they normally require computerized numerical solution because of their complexity. For the most part, we are concerned with numerical simulation models, but increasingly a stochastic or statistical approach to model parameters and input data is being adopted. The equations describing groundwater flow in porous media are mathematically analogous to those governing the flow of electric current in a resistor-capacitor network. Such networks were used as the first quantitative models of groundwater systems. All physical analogue models have been largely superceded by numerical simulation, following the development of digital computers with adequate speed and capacity because numerical models need less time for construction and operation. All models are initially and primarily used to integrate available hydrogeological data and test the adequacy of the existing conceptual model of the groundwater system. -8-
2.2 Scale and Focus of Models Groundwater models can be constructed at widely-differing spatial scales, from one- or two-dimensional simulation of flow within a 10 to 100 m radius of a pumping well, to two- or three-dimensional simulation of major regional aquifers occupying areas of up to 10 6 km 2. Normally, modelling work is conducted either at the local project design scale or the regional resource evaluation scale. Models are most frequently constructed to simulate the response of hydraulic heads of groundwater to changes in pumpage or recharge. These models can be readily expanded to consider velocity distributions and contaminant transport. The mathematical equations underlying the groundwater flow model have been adequately verified and the physical meaning of the parameters involved is clearly understood. However, in the case of contaminant transport there is continuing controversy about the mathematical characterisation and measurement of hydrodynamic dispersion, and about the best way to identify, to measure and to model the chemical interactions and reactions that can occur in an a- quifer. Since the state-of-practice in respect of contaminant transport models is not well established, they receive only limited treatment here and it is suggested that the results of applying such models should still be interpreted with great caution. 2.3 Model Classification by Objective Groundwater models may be subdivided according to their objective, as follows: (a) prediction models; (b) identification or evaluation models; (c) management models. All three types are closely linked, prediction models forming the basis for the other two types. Each type is discussed individually below. 2.3.1 Prediction Models The majority of models in common use are prediction models based on the numerical simulation technique. They predict the response of a groundwater system, in terms of variation of hydraulic heads, to natural and/or artificial hydraulic stresses, especially those associated with pumped groundwater abstractions. Amongst the problems that can be considered with such models are included the prediction of: (a) long-term maximum drawdown of a pumped well in an aquifer with seasonal recharge; (b) short-term drawdown interference between pumped wells, and thereby associated reduction in yield; (c) long-term drawdown trends, and thus the useful life of pumped wells, in overdeveloped aquifers; (d) reduced flow in surface water courses in hydraulic connection with aquifers, as a result of groundwater abstraction, through calculation and interpretation of the appropriate draw-downs; -9-
(e) (f) increased flow in streams and rivers in hydraulic connection with aquifers, as a result of return flows from irrigation areas and leakage from artificial canals; groundwater changes resulting from reduced aquifer recharge due to such factors as drought or urbanization; (g) groundwater changes resulting from increased aquifer recharge due to such factors as irrigation, leakage from an artificial canal, artificial recharge works, or effects of urbanization; (h) movement of the saline-fresh water interface as a result of groundwater abstraction from coastal aquifers; (i) (j) pumping rates required to achieve a necessary engineering design; design of ditch, tile and other drainage schemes. In the case of contaminant transport, the concentration distribution associated with a given contaminant loading is also predicted. In view of the current limitations of such models, applications are commonly restricted to prediction of the distribution resulting from a simple, continuous point-source of pollution, with grossly-simplified representation of the processes of contaminant dispersion, sorption and degradation. The modelling of this problem is usually limited to a local site scale. Prediction of contaminant transport at the regional scale, the migration of diffuse-source groundwater pollutants and the behavior of those pollutants involved in more complex chemistry cannot yet be predicted reliably. It is relevant at this point to consider in outline the development of a prediction model using numerical simulation (Figure 2.1). This development involves a number of stages: (1) Decisions must be made on whether to opt for a steady or non-steady state formulation, on the appropriate number of spatial dimensions, on the boundary conditions to be used in the model, and on their relation to those of the aquifer as a whole. These decisions will be guided by a synthesis of available information, including any existing conceptual model of the groundwater system. (2) Formulation of the relevant set of mathematical equations, their expression in numerical form (normally by the finite element or finite difference technique) and their coding in the appropriate computer language. (3) Verification that the computer program is capable of solving the selected set of differential equations with convergence to acceptable accuracy. This is usually achieved through the consideration of some special cases, which lend themselves to analytical solution. Since some model formulations are valid for only a restricted range of parameter values, it is important to consider the widest possible range of aquifer conditions likely to be involved in the problem to be addressed. (4) Fitting of the model, by adjusting or calibrating values of parameters and boundary conditions, so as to best reproduce the observed field response to a known hydraulic stress and/or contaminant load, and hopefully to obtain statistics regarding the uncertainty of the calibrated parameters. Steps (2) and (3) lead to a computer code which may be used for many different cases. Steps (1) and (4) are specific to each study. Step (4) is fulfilled using either an -10-
Conceptual aquifer model Mathematical equations Physical laws equilibrium state boundary conditions Numerical formulation T Computer program y Model verif ied~)-»-( No j Field data (variables) (Model validated')-»-!. No Aquifer parameters (constants) Hydraulic stresses (variables) Aquifer prediction model S Prediction runs Figure 2.1. Development sequence for a prediction model using numerical simulation. (Calibration runs)- -11-
inverse model, or by trial and error using the "prediction model" in an "identification or evaluation" mode as defined in the next section. The fitting of a model through this calibration process is not straightforward because various combinations of parameters and boundary conditions will often give equally close predictions when the data on observed aquifer behavior are limited. That is, there is not a unique solution to the calibration problem. If field data are only available for a condition of low hydraulic stress, spurious calibration results may be obtained. For example, gross overestimates of average unconfined storativity can easily occur with consolidated aquifers. Such a model will invariably indicate vast volumes of groundwater storage, at least on paper, and there is danger that this "paper water" may pass into resource plans without further consideration of the validity of its physical basis. Considerable hydrogeological judgement and caution is thus required at the model validation stage. Once a model is validated, the associated computer program assumes the status of a working model which can be used to predict aquifer behavior in response to other natural and artificial variations in hydraulic stress or contaminant load. However, in the first few years of its existence, a model will normally be subject to regular recalibration and refinement as field data corresponding to a wider range and a larger scale of applied stresses are collected. Thus the early predictions of a model which was validated with only limited field data may be subject to especially large errors and need to be interpreted with appropriate caution. It should not be assumed that field data are unreliable, simply because they cannot be readily simulated by the prediction model developed. Frequently the model selected proves to be inappropriate, and thus inadequate to represent actual groundwater flow mechanisms. When fundamental modifications are made, dramatic improvements are often obtained in the correlation between model output and field data. Aspects of groundwater flow and types of aquifer characteristics which have proved likely to lead to serious error if ignored include: drastic variations of transmissivity and abrupt changes of storativity (specific yield) with saturated aquifer thickness, major vertical flow and recharge components, and partial penetration of wells and rivers. In addition, all groundwater problems are in reality three-dimensional and time-variant. Such models make larger demands on the provision of data as well as computer time and storage. The approach usually adopted is to reduce the number of dimensions represented and/or to consider only the steady state. This is only acceptable if the model still adequately reflects the predominant groundwater flow mechanism. 2.3.2 Identification or Evaluation Models A numerical simulation model may be developed primarily to identify or evaluate the parameters and boundaries of a little known aquifer. This can be undertaken using the simulation model exclusively in calibration mode (Figure 2.1), adjusting the value of parameters and/or boundary conditions to reproduce the observed aquifer response to known stresses. This important issue will be discussed in more detail in Chapter 5. 2.3.3 Management Models Prediction models employing numerical simulation methods and heterogeneous aquifer parameters have often been utilized to explore groundwater management alternatives. For this purpose the model is executed repeatedly under various scenarios designed to achieve a particular objective, such as obtaining a sustainable water-supply, dewatering an excavation area for construction, preventing saline water encroachment or controlling a contaminant plume. Use of such an approach, however, avoids rigorous formulation of groundwater management goals and may fail to consider important operational restrictions. It is thus unlikely that optimal management solutions will be arrived at using numerical simulation models alone. -12-
More recently, true management models have been developed incorporating rigorous formulation of management objectives and/or policy constraints, through use of decision criteria or linear optimization programming, with numerical simulation of groundwater hydraulic or contaminant behavior. Such models must be based on decision criteria, such as maximum total water-supply, minimum total project cost or maximum project economic benefit, or on a given policy constraint, such as minimum required water-supply, conforming to some water quality standard or a ceiling for capital and/or running costs. By their nature, management models will only be developed for aquifers, or parts of aquifers, for which a soundly validated prediction model and broad-based reliable field data exist. Aquifer management modelling methods involving both water quantity and quality considerations were reviewed by Gorelick (1983). The idea behind such models is that one often wishes to know where to best locate wells and how much to pump or inject at each location. It is a straightforward matter to formulate aquifer management problems as optimization problems. There, the objective might be to minimize pumping costs or contaminant clean-up costs, for example. In addition, there will be a series of restrictions on hydraulic heads, drawdowns, velocities, and solute concentrations. Economic, logistic, and legal considerations may also be reflected in the constraint set. In such models the groundwater flow and/or contaminant transport equations are included as constraints. Therefore, optimal management solutions simulate the behavior of the system of interest. Prior to 1983 the models generally enabled one to handle linear systems (confined aquifers). Since that time, methodology has been developed to account for nonlinearities and for model uncertainties. Developments along these lines are described in Gorelick (1988) and Wagner and Gorelick (1987). 2.4 Concluding Remarks The development and application of a mathematical model should be an exercise in thinking about how a groundwater system works. Models must be regarded as a tool to aid decision-making, but decisions should not be reached exclusively from results generated by the model. If the basic principles of groundwater flow (and, where appropriate, contaminant transport) and the underlying assumptions of modelling are lost sight of, there is serious danger of gross misinterpretation of model output. This is more likely to occur when models are packaged and automated. In the application of all models, and most especially of groundwater quality models, a high degree of scientific judgement tempered with wide experience of field observation is desirable to produce sound interpretations. -13-