SCOPE 35 - Scales and Global Change

INTRODUCTION

The International Geosphere-Biosphere Programme (IGBP) of the International Council of Scientific Unions (ICSU) is aimed at 'describing and understanding the interactive physical, chemical, and biological processes that regulate the total Earth system, the unique environment for life, the changes that are occurring in this system and the manner in which they are influenced by human actions. 'Each discipline involved has used its own spatial and temporal scales in describing the relevant processes quantitatively, thus generating its own specific resolution of the questions being asked. To succeed in obtaining an integrated approach to modelling the earth's resource systems. a consistent and coordinated use of scales is necessary across the various disciplines. This chapter describes the existing approaches to scale requirements in groundwater modelling and identifies further research to facilitate integration of groundwater systems into large-scale models of global processes.

Groundwater is a subsurface element of the hydrosphere, which is generally understood to encompass all the waters beneath, on, and above the earth's surface. Because groundwater systems occur in an irregular pattern allover the earth, they must be considered in any global analysis of the hydrosphere.

Many solar-powered processes occur in the hydrosphere, resulting in a continuous movement of water. This dynamic system is referred to as the hydrologic cycle. Its major elements are atmospheric water, surface water. water in the subsoil, groundwater, stream networks, lakes and ocean basins, and the water in the lithosphere (see Figure 11.1).

Movement of water occurs both within each element of the hydrologic cycle and as exchanges between the elements, and results in the dynamic character of  this relatively closed system. The exchange processes between the surface subsystem and the atmosphere include evaporation, precipitation (rainfall, fog, dew, hail, and snowfall), plant transpiration, and sublimation of snow. Infiltration, groundwater recharge from streams, and subsurface discharge into lakes and streams (both interflow and baseflow) are inter-element processes between surface and subsurface. Surface runoff forms the link between the stream network subsystem and the oceans (Domenico, 1972). Finally, juvenile, rejuvenated, and connate water is released from the lithosphere and becomes an active part of the hydrologic cycle. In addition, interactions take place between the subsurface hydrosphere and elements of the earth's biological environment.

Figure11.1 Elements of the hydrological cycle (after Domenico, 1972)

Each of these physical and biological elements can constitute a system and might consist of various subsystems, each with its own spatial and temporal characteristics. In studying the interactions among such systems, as well as in aggregating smaller systems into larger ones, the problem of scale arises.

This chapter explores the variability of spatial and temporal scales in modelling the dynamics of groundwater systems. Special attention is given to scaling aspects of modelling the subsurface hydrosphere relevant to interactions with terrestrial and aquatic ecosystems.

Scales in groundwater hydrology can be discussed from two perspectives. First is the physical scale on which the hydrological processes take place. These processes provide the physical setting in which human interaction can be studied, as they occur in unintentional or managed alterations in the natural system. Another perspective is that of resource management, where socioeconomic and political conditions are paired with the hydrological and engineering aspects of a groundwater system. Modelling is an instrument to organize the data collection and to structure the analysis of the studied system. In groundwater hydrology, modelling has become the principle tool in the management of the resource. The extensive scientific foundation of groundwater modelling and the large database available indicate that groundwater systems might be modelled successfully in order to study their role in the earth system. Further research is required to integrate quantitative descriptions of groundwater systems into large-scale models of global processes, and to facilitate proper scaling of intersystem hydrologic and biologic processes.

To provide a basis for the discussion of scales in groundwater modelling, this chapter begins with a description of major aspects of groundwater systems, including definitions, relevant orders of magnitudes of processes, subsystems, and classifications.

CHARACTERISTICS OF GROUNDWATER SYSTEMS

A groundwater system is an aggregate of rock in which water enters and moves, and which is bounded by rock that does not allow any water movement, and by zones of interaction with the earth's surface and with surface water systems (Domenico, 1972). In such a system the water may transport solutes and biota; interactions of both water and dissolved constituents with the solid phase (rock) often occur.

Water in the earth occurs in spaces within solid matter. Various types of such spaces or pores exist, and include fractures. The interstices may vary in size from large limestone caverns to miniscule capillary openings in which water is held primarily by adhesive forces (Bear, 1979).

Subsurface water or underground water occurs in four zones. Directly beneath the land surface is the zone of aeration, or unsaturated zone, which contains both water and air. Its thickness may vary widely in time and space. In wetlands this zone may be absent, while in arid areas the thickness of this zone (sometimes called the vadose zone) can exceed 1000 m (Bouwer, 1978). That part of the unsaturated zone that supports plant growth is the root zone; it generally extends to a maximum depth of 2 m beneath the land surface (Heath, 1983). The soil zone is a major interaction area between the subsurface hydrosphere and the biospheric elements of terrestrial ecosystems.

The unsaturated zone is almost always underlain by rock layers that are fully saturated with water. This is the saturated zone, and the water in it is commonly referred to as groundwater. Groundwater forms an important fraction of global fresh water resources. It is estimated that 4000 km³ of fresh water is stored up to a depth of 800 m under the land surface, comprising about 14% of the total amount of fresh water (L'vovich, 1979). After glaciers, which contain 85% of all fresh water, groundwater is the second largest global. source of fresh water.

At the boundary zone between the unsaturated and saturated zone, the attraction forces between water and rocks are balanced against the pull of gravity. As a result, the smaller pores are water-saturated while the larger pores contain both water and air. This boundary between groundwater and vadose or soil water is known as the water table or the phreatic surface.

A special type of subsurface water occurs as a zone of permafrost. In addition to ice, this frozen zone may also contain liquid water at subzero temperatures. This free water is often highly saline. Permafrost is present in the northern regions of Eurasia, of North America, all of Antarctica, and the high mountain areas within orogenic belts (Klimentov, 1983). The thickness of the frozen zone may exceed 100 m.

A primary unit in groundwater systems is the aquifer, a lithologic unit or combination of units capable of transmitting relatively significant amounts of water (Figure 11.2). An aquifer may coincide with a geologic formation; it may cover a group of such formations, or it may be a part of a formation or a group of formations. It is often bounded by poorly transmitting layers called confining beds.

A water-table or phreatic aquifer is characterized by a freely moving upper boundary. The location of this water table follows the variations in hydraulic head. Although the hydraulic or piezometric head in a confined aquifer may fluctuate, its upper and lower physical boundaries are fixed.

The largest hydrogeologic unit is a groundwater basin. It is a system containing the entire network of flow paths taken by all the water recharging the basin (Freeze and Witherspoon, 1966). A groundwater basin consists of a single aquifer or several connected and interrelated aquifers. The water divide between two adjacent groundwater basins is not necessarily the same as that between the surface water drainage basins overlying them. Watersheds can lose part of their water to neighbouring watersheds through subsurface interbasin transfers. In a valley between mountain ranges, the drainage basin of the surface stream coincides closely with the groundwater basin. In limestone areas and large alluvial basins, the drainage and groundwater basins may have entirely different configurations.

Figure 11.2 Groundwater system units (after Johnson, 1975)

As an illustration of the distribution of groundwater systems, areas with significant groundwater resources in the United States (areas with freshwater yields of more than 3.15l/sec) are shown in Figure 11.3.

The largest groundwater systems in the United States are formed by major alluvial basins such as that in the High Plains groundwater region where the Ogallala aquifer extends over more than 20000 km², and that in California's Central Valley. Other large regional aquifer systems exist in the Coastal Plain region, e.g. the Karitan and Magothy formations of unconsolidated sands and gravels underlying large regions in the south part of the northeastern and mid-Atlantic states, and the carbonate rock aquifer system formed by the Floridan formation in Florida and southeastern Georgia (Figure 11.3). Many smaller aquifer systems occur in these and other regions, and range from hundreds to a few thousand square kilometres. Numerous more localized aquifers of less than l00 km² are found in many parts of the country.

Figure 11.3 Groundwater resources in the United States (after Rickert et al., 1979)

Water enters the groundwater system in recharge zones and leaves the system in discharge areas. In a humid climate, the major source of aquifer recharge is the infiltration of water and its subsequent percolation through the soil into the groundwater subsystem. This type of recharge occurs in all instream areas except along streams and their adjoining floodplains, which are discharge areas. In arid parts of the world, recharge is often restricted to mountain ranges, to alluvial fans bordering these mountain ranges, and along the channels of major streams underlain by thick and permeable alluvial deposits.

In addition to these natural recharge processes, artificial or man-made recharge can be significant. This type of recharge includes injection wells, induced infiltration from surface water bodies, and irrigation.

Outflows from groundwater systems are normally the result of a combination of inflows from various recharge sources. Groundwater loss appears as interflow to streams (rapid near-surface runoff); as groundwater discharge into streams (resulting in baseflow); as springs and small seeps in hillsides and valley bottoms, quicksands, geysers, frost mounds, pingos; as wetlands such as lakes and marshes fed by groundwater; as capillary rise near the water table into a zone from which evaporation and transpiration can occur; and as transpiration by phreatophytes (plants whose roots can live in the saturated zone or can survive fluctuations of the water table) (Toth, 1971; Freeze and Cherry, 1979). Other outflows are artificial or human-induced, as agricultural drainage (tile-drains, furrows, ditches) and wells for water supply or dewatering (e.g. excavations and mining).

A significant difference between recharge and discharge zones is their areal extent. The discharge areas of a groundwater system are in general much smaller than the recharge areas. The concentration of flowlines near discharge areas indicates that horizontal flow is more efficient than vertical flow. Recharge areas are commonly found in topographic highs, while natural discharge areas are located in topographic lows. In recharge areas a rather thick unsaturated zone often occurs, while in discharge areas the water table is close to the land surface.

The unsaturated zone has a significant smoothing influence on the temporal characteristics of the recharge of groundwater systems. Highly variable (hourly) precipitation and diurnal evapotranspiration effects are dampened and seasonal and long-term variations in flow rates become more prominent further from the soil surface. In this dampening the higher frequency fluctuations are filtered, a proces which continues in the groundwater zone. Its ultimate effect can be observed in stream base flow which is characterized by seasonal and long-term components.

Figure 11.4 Schematic diagram of a regional groundwater flow system (after Toth, 1983)

Figure 11.5 Schematic overview of groundwater residence times in large regional systems

A groundwater system may consist of a single flow system between its recharge and discharge areas. This is generally the case when local relief is negligible and only a gentle regional slope is present. If the relief of the surface becomes more pronounced, local groundwater flow systems can develop: If the depth-to-width ratio of the system is small, a series of local flow systems adjacent to each other is the result. However, if the aquifer depth-to-width ratio increases, a combination of flow systems may develop, resulting in a hierarchically structured groundwater system with local, intermediate, and regional components (Figure 11.4). If the groundwater system consists of multiple aquifers, this hierarchical structure is even more evident (Figure 11.5). The notion that such a hierarchical structure exists has improved the effectiveness of modelling groundwater systems significantly (e.g. Freeze and Witherspoon, 1966).

MODELLING THE DYNAMICS OF GROUNDWATER

A groundwater system has two basic hydraulic functions: in storing water it acts as a reservoir, and in transmitting water from recharge to discharge areas it serves a conduit. A groundwater system can be considered as a reservoir that integrates various inputs (through mixing, among others) and dampens and delays the propagation of changes in inputs. The water movement is dictated by hydraulic gradients and geology-dependent hydraulic conductivity. In turn, these gradients are influenced by groundwater system boundary conditions such as those resulting from human-induced stresses on the system, climatic effects, and topography (land-surface and stream-related boundary conditions).

Groundwater systems are characterized by complex inflow-outflow-storage relations. System outflows are influenced by the origin and pathways of the groundwater. These relations are difficult to define directly from input and response data because of the dampening effect of storage on inflow, the lag or delay between the time water enters and exits the system, the variable rate and sometimes diffuse manner of recharge and discharge, and the heterogeneity of the geology. Therefore, mathematical models, based on a mechanistic description of the physical and chemical processes internal to the groundwater system, are widely used in groundwater hydrology.

The mathematical model for groundwater flow is derived by applying principles of mass conservation (resulting in the continuity equation) and  conservation of momentum (resulting in the equation of motion). The generally applicable equation of motion in groundwater is Darcy's law, which originated in the mid-nineteenth century as an empirical relationship. Later, a mechanistic approach related this equation to the basic laws of fluid dynamics (Bear, 1972). Variability of parameters in space and time and uncertainty in data are often incorporated in these models.

The rate of groundwater movement can be expressed in terms of time required for groundwater to move from a recharge area to a discharge zone. This time ranges from a few days in zones adjacent to discharge areas in small local systems, to thousands of years for water that moves through deeper parts of the groundwater system (Figure 11.5). The large residence time in groundwater basins gives relatively slow chemical processes a chance to influence the composition of the water.

The groundwater transport of dissolved chemicals and biota such as bacteria and viruses is directly related to the flow of water in the subsurface. Many of the constituents occurring in groundwater can interact physically and chemically with solid phases such as clay particles, and with various dissolved chemicals. As a consequence, their displacement is both a function of mechanical transport processes such as advection and dispersion, and of physicochemical interactions such as adsorption-desorption, ion exchange, dissolution-precipitation, reduction-oxidation, complexation, and radioactive decay. Biotransformations taking place during the transport can alter the composition of the groundwater significantly.

In modelling the transport of dissolved chemicals, the principle of mass conservation is applied to each of the chemical constituents present. The resulting equations include physical and chemical interactions, as between the dissolved constituents and the solid subsurface matrix, and among the various solutes themselves. These equations might include the effects of biotic processes. To complete the mathematical formulation of a solute transport problem, equations are added describing groundwater flow and chemical interactions, as between the dissolved constituents and the solid subsurface matrix, and among the various solutes themselves. In some cases equations of state are added to describe the influence of temperature variations and the changing concentrations on the fluid flow through the effect of these variations  on density and viscosity.

In a stochastic system the relationships governing the behaviour of the system are described in a probabilistic manner. If one element of a system is stochastic in nature, the system as a whole behaves stochastically, although the relationships themselves might be defined in a deterministic sense.

The solution of the equations describing a deterministic system is approached in three ways. If the solution is continuous in both time and space, it is called an analytical solution or model. For a solution that is discrete in either time or space, the term semianalytical model is used. A numerical model is discrete in both time and space and uses approximations for the derivatives in the governing equations. Spatial and temporal resolution in applying such models is a function of study objectives and availability of data.

No universal model can solve all kinds of groundwater problems; different types of models are appropriate for solving different types of problems. It is important to realize that comprehensiveness and complexity in a simulation do not necessarily equate with accuracy. An extensive discussion of the status of groundwater models is presented by Bachmat et al. (1985).

MULTIPLE SCALES IN MODELLING GROUNDWATER SYSTEMS

A wide range of both spatial and temporal scales is involved in the study of groundwater problems. Spatial scales range from less than a nanometre, for studying such phenomena as the interactions between water molecules and dissolved chemicals (Cusham, 1985), to hundreds of kilometres, for the assessment and management of regional groundwater systems (Toth, 1963). For temporal scales, two major categories can be distinguished: steady-state or average state, and a time-varying or transient state. Periodic fluctuations on a diurnal or seasonal scale are frequent in hydrogeology. Other processes display certain trends or occur rather randomly in nature (Table 11.1). Many processes exhibit a strong temporal effect immediately after their initiation but become stable after a while, moving to a steady-state. Other processes fluctuate on a scale that is often much smaller than necessary to include in the analysis of such systems. An averaging approach is then taken, resulting in steady-state analysis. The steady-state is also assumed when the analysis period is so short that temporal effects are not noticeable.

Dimensions in the time domain range from millenia in palaeohydrological simulations and risk-analysis for long-term isolation of radioactive waste through year-by-year, seasonal, monthly, weekly, daily, and hourly scales for field systems-to modelling of real-time systems on a basis of minutes and even seconds in certain laboratory experiments.

An important aspect of the scaling problem is related to the difference between the scale on which processes are mathematically described, and the subsequent aggregation into larger-scale formulations amenable to field analytical procedures. Small-scale descriptions are aggregated into large-scale models by applying averaging procedures. Such averaging applied to a statistical description of microscopic processes is commonly used to obtain continuous hydrodynamic field equations on the macroscopic scale (e.g. Bear , 1972, 1979). Although the resulting model requires less supporting field data than is required for a problem of the same physical extent, a certain amount of information regarding the real physical systems is lost. Also, in going to larger spatial and temporal scales, variations in system characteristics that could be ignored on the smaller scale may become important. Examples are the increasing importance of heterogeneities and anisotropy as related to the

Table 11.1 Summary of mechanisms tending to produce fluctuations in groundwater levels (after Freeze and Cherry, 1979)

geology of the system for larger spatial scales, and the effects of long-term recharge variations on the water balance of a system for long time periods. A major problem in this averaging process lies in evaluating the effects of assumptions made on the microscopic scale and the effects on the level of uncertainty in the modelling of a groundwater system. If such assumptions have to be incorporated in the macroscopic description, their formulation may be problematic. Another problem that may arise as a result of an averaging approach is that of defining the physical meaning of the resulting state variables and system parameters. Thusfar, no systematic evaluation of the consequences of this aggregation process in groundwater has been published, although an extensive database is available to carry out such a study.

 To understand the effect of the various processes active in groundwater systems, each of these processes must be described on an appropriate scale. The optimal scale for an individual process can be quite small. However, for the management of groundwater systems, such small scales are not required. The result is that the scales used in groundwater modelling range from microscopic to macroscopic (Bonnet, 1982; Table 11.2; Figure 11.6). On the microscopic scale, processes occur on atomic and molecular scales, such as the interactions between water molecules, organics, and clay surfaces and between organics and microbes, or processes on a particular scale involving large numbers of molecules. The granular scale represents the processes that occur on the scale of individual pore spaces and their adjacent grains. Significant for the formulation of most groundwater flow and transport equations is the scale of continuous equivalent media. The scale unit is defined as the Representative Equivalent Volume (REV) and contains many pores and grains (Bear, 1979). It is also the smallest macroscopic scale. Going to even larger scales, Bonnet (1982) defines the geologic or structural scale as a part of an aquifer containing sedimentological and elementary stratigraphical heterogeneities, and the hydrogeological or regional scale as an aquifer or groundwater basin. In groundwater modelling, the scales of interest for the study of interrelationships between the geohydrosphere and ecosystems range from site and local to intermediate and regional (Table 11.3). Significant characteristics on each scale vary for different hydrogeological interests.

Table 11.2 Principal scales in hydraulics of subsurface porous media (after Bonnet, 1982)

Figure 11.6 Scales pertinent to hydrology (Bonnet, 1982)

The processes of water movement and the transport of energy and dissolved constituents through porous media are well understood and are mathematically described on a macroscopic scale, using a representative equivalent volume (Bear, 1979). Such an approach can also be applied to flow and transport in fractured rock (Wang and Narasimhan, 1984). One way to make a system of fractures of varying size and orientation accessible to quantitative analysis is through the concept of equivalent porous media. Another approach often taken is based on applying stochastic principles to obtain representative parameters. Such approaches can be used to extend the results of small-scale studies to larger-scale problems.

Some of these approaches involve a direct relation between the spatial and temporal scales. This is especially the case in researching the physical principles underlying the responses of groundwater systems to varying stresses. In other cases the choice of temporal scales is related more to the type of problem under study and the materials of interest, such as the long-term storage of radioactive waste, where time scales up to thousands of years apply. Simulation of such large time periods may be limited by stability criteria inherent to the mathematical solution procedures included in the model.

The essential scaling problem is how to distinguish between the variables that can be considered as constants or as being uniform across discrete intervals of pertinent dimension (space, time), and the variables that cannot be so considered (Beck, 1985). Problem decomposition in space or time is often applied to obtain optimal resolution in relation to computational efficiency. An example of such spatial and temporal decomposition is found in the modelling of infiltration into the soil and subsequent percolation toward the saturated zone. A distinction has been made between spatial discretization and connectiveness for local (Figure 11.7a) and for regional (Figure 11.7b) scales. Runoff from precipitation is split into a surface component (lumped horizontal segment) and infiltration (one- or two-dimensional, vertical). The infiltrated water percolates to the groundwater where a two-dimensional horizontal or three-dimensional model is used. For each of the submodels a different timestep is used, from hourly for the surface runoff and daily for the percolation, to weekly or monthly for the flow in the saturated zone.

                                                                                                                                             
Table 11.3 Scales in groundwater modelling

Figure 11.7(a) Typical dimensionalities used to represent surface, unsaturated, and saturated zones in local-scale groundwater models (after Boutwell et al., 1985). (b) Typical dimensionalities used to represent surface, unsaturated, and saturated zones in regional groundwater models

In groundwater models, a significant distinction exists between local and regional discretization of the surface zone. This distinction reflects the difference in physiographic character between the subsurface and the surface, resulting in different approaches in aggregating small-scale phenomena into large-scale models. Also, limitations in presently existing data acquisition techniques influence the resolution used in modelling the surface zone.

Note the difference in treatment of the vertical components in groundwater models. In the regional models the flow in soils and between aquifers is mainly one-dimensional and vertical, to reduce the computational load. In the local model, second-order effects may be important enough to warrant the use of two-dimensional vertical simulation in the soil zone.

Another example can be found in simulating solute transport in fractured porous media where the movement of the solute in the fractures can be two orders of magnitude greater than in the porous matrix. A split-time approach increases the efficiency of the simulations (DeAngelis et al. , 1984).

With the increasing capacity and decreasing cost of computers, a trend prevails toward using smaller time scales for the same types of problems, resulting in higher temporal resolution.

 SCALES RELEVANT TO GROUNDWATER MANAGEMENT SCALES

The scales used in groundwater modelling are determined by the characteristics of the groundwater system, by the availability of data, and by the nature of the system's management. These influences often include both natural and human-induced influences, such as the effects of climate, pumping, deep-well injection, and agricultural irrigation and drainage.

A discussion of spatial and temporal scales with respect to groundwater quality runs parallel with that of groundwater quantity. In general, human-induced influences affect local and intermediate scale, while large, regional-scale phenomena are of natural origin. Some human-induced quality changes are also on a regional scale, such as the amalgamated effect on water levels of groundwater withdrawal for irrigation; nonpoint pollution caused by use of fertilizers, herbicides, and pesticides in agriculture; acidification of groundwater as a result of acid precipitation; and the change in quality resulting from urbanization.

From a management point of view a system can be hierarchical, divided into administrative elements such as townships, counties, states, and river basins. If modelling is intended to provide optimal courses of action in the management of the water resources, an approach based on administrative elements can be successful. However, such as approach does not follow natural boundaries and elements.

In many management situations the selection of the scale of analysis is influenced by the restrictions in data availability. In part, such restrictions are imposed by the lack of techniques for obtaining higher-resolution data. For example, in groundwater modelling the recharge term of the subsurface water balance is directly related, through precipitation and evaporation, to atmospheric processes and conditions. These exchange variables between atmosphere and soil surface are obtained either through direct measurement (rainfall) or indirectly through calculation (evaporation), using various atmospheric variables. Such data were formerly available only for a limited number of sampling stations. Consequently, such stations are considered to represent a rather large area (Figure 11.7b), thus limiting severely the accuracy with which the recharge can be determined. In recent years remote sensing has developed as a promising means for obtaining areal values for a number of significant parameters (e.g. soil moisture and snow cover). As atmospheric scientists discuss simulations of global atmospheric exchanges based on a grid with cells circa 100 by 100 km (Dickinson, 1988), the possibility of using remote sensing to obtain important data for modelling groundwater systems and addressing problems of scale, becomes increasingly interesting.

The following discusses spatial and temporal scales from a phenomenological point of view.

Spatial scales

Water supply problems are generally related to availability of sufficient water to cover water needs, and to drawdown of groundwater levels and reduction of pressures and storage as a result of the exploitation of the resource. Industrial and municipal water supply requires well fields with the wells relatively closely spaced (50-200 m) in order to obtain an efficient connection with the distribution network. Their area of influence can range from less than 1 km² to more than 10 km². Private, single-household wells have a small area of influence (often less than l00 m), but in some areas the combined drawdown of a large number of private wells can cause serious aquifer depletion. This is especially true with agricultural water use. Although individual irrigation wells may have a significant influence on a system (up to a few thousand metres), the total effect of large-scale irrigation from groundwater may have serious detrimental effects on the water levels and the storage in large aquifer systems, e.g. the long-term depletion of the Central Valley aquifers in California, and of the Ogallala aquifer in the High Plain region. This problem occurs most often in areas with low to moderate recharge from precipitation.

Groundwater pumpage aimed at lowering water levels may assume large- scale proportions, as with dewatering for mining operations. An example is the open-pit mining of lignite in the northern part of the Rhenish lignite mining district in West Germany, where drawdowns of more than 100 m occur to keep the pit dry. The influence of this dewatering is felt more than 20 km off site, and the affected area is still expanding as a result of continuing dewatering (Boehm, 1983).

Operation of groundwater systems and conjunctive management of coupled groundwater-surface water systems have their special scale requirements, ranging from the scale of a major watershed or river basin (for policy decisions) to that of sections of the aquifer or stretches of the river (for local planning and engineering purposes).

So-called human-induced point-source groundwater contamination, as from spills, leaching from landfills or lagoons, and underground tank failures, often occurs on a much more local scale (100-1000 m). However, if nothing is done about such groundwater deterioration, the affected area can become quit extensive (1000-10000 m).

Some basins are affected by a large group of individual point sources such a septic tanks or landfills and dumps. The aggregated effect of these is comparable with that of nonpoint pollution. In such cases, individual mitigation has no effect and regulatory action for the entire basin is required.

Temporal scales

For water management purposes, temporal scales are important. Incidental local situations, such as construction site dewatering and chemical spills, have mainly short-term effects-weeks or months. Seasonal effects are related to agricultural uses and the use of aquifers as thermal energy sources or storage. Mid-to long-term scales (1-20 years) apply to many wellfield operations dewatering of mining sites, and local pollution problems. Long-term effects  (20-100 years) are of special interest in regional water resource development  hazardous waste displacement, and regional nonpoint pollution. Historical periods (100 years to millions of years) are of interest for palaeohydro geological studies and for isolation of highly toxic, nondegradable chemicals and long-living radionuclides.

A typical example of temporal scales as applied in groundwater models is the study of the South Platte River in Colorado (Morel-Seytoux and Restrepo 1985). This model currently simulates about a 100-mile stretch of river and hydraulically connected aquifer. The model is used for two types of analysis:

1. daily operation of the conjunctive use river-aquifer system aimed at allocation of irrigation water according to availability and water rights

2. evaluation of policies and legislation.

In the operational mode a daily simulation time-step is used for the surface water system and a weekly simulation is used for the groundwater away from the river. To account for the more rapid responses of the groundwater near the river, a correction is made to the results of the weekly simulations for the parts of the aquifer along the river. The scale for the use of the model in the development of policies and in evaluating new legislation, as in the formulation of new water-distribution rules, is much larger because long-term effects are of interest. In the South Platte River study, a weekly timestep is used for surface water, a monthly timestep for groundwater.

In planning remedial action, temporal scales are directly dependent on the extent of the polluted area, the geology, the important hydrological and biochemical processes, and the remedial action itself. For example, remedial actions designed for control of erosion and runoff, such as grading and surface water diversion, could require transient simulation with short timesteps for the rainfall and runoff processes that fluctuate rapidly (daily scale). In the saturated zone the flow is more regular and changes occur within a time frame of months or even years. Dynamically linked sub models, each with its own time scale, are then required for efficient simulation. To evaluate the threat of pollution on humans and the environment, or to analyse the effects of remedial action, simulation periods of 20-100 years are common. Much longer-term effects may have to be included, as in the case of long-living radionuclides and chemically inert toxic organics.

An example of temporal scale is radioactive waste storage in unsaturated systems, where effects must be evaluated for time periods up to ten thousand years (US EPA, 1982). Because of the strongly nonlinear character of the flow and transport equations for the unsaturated zone, the time steps cannot be too large (Reisenauer et al. , 1982; Tripathi and Yeh, 1985). Tripathi and Yeh ( 1985) used variable time steps up to 20 000 years to simulate an unsaturated system for such an extended time.

GROUNDWATER-ECOSYSTEM RELATIONSHIPS

Ecology is concerned with the influence of external factors on organisms and with the way organisms modify their surroundings. The study of the inter-action between water systems and ecological systems, or ecosystems, is important because water is a major environmental factor in most ecosystems.

For example, soil moisture influences the type of vegetation present; without soil moisture autotrophic plant covers could not exist (Budyko, 1977). Three areas of interaction between ecosystems and groundwater systems can be distinguished: terrestrial ecosystems in groundwater recharge areas, terrestrial ecosystems in groundwater discharge areas, and wetland aquatic ecosystems having complex interactions with groundwater.

Groundwater is influenced by the surface ecosystem through which it is recharged. For example, water consumption by plants can control the amount of water percolating into the saturated zone, and the chemical composition of groundwater can be affected significantly by transformation processes occurring in the litter and soil. A secondary interaction occurs as groundwater moves from its area of recharge to its point of discharge, often traversing distances greater than the extent of the ecosystem from which it originated. During its subsurface movement groundwater mixes with water originating from other recharge areas. Thus, ecosystems in groundwater discharge areas are indirectly influenced by remote ecosystems in recharge areas, in the same way as downstream ecosystems can be influenced by the headwaters of drainage systems (Loucks, 1983).

Numerous studies have shown groundwater to be a major component of stream and wetland ecosystems (Loucks, 1983). As groundwater discharges into streams and lakes, it tends to stabilize discharge and water levels, as well as water quality and biological productivity. Interactions between groundwater and terrestrial ecosystems also take place in various subsurface layers, mostly the unsaturated zone. Here, groundwater often functions as a source of transpiration water for plants, as a transporting agent of dissolved nutrients and other chemicals, and as the essential environment for various subsurface organisms (Loucks, 1983; Gerba, 1985).

Changes in natural conditions and human activities can significantly alter the physical and chemical characteristics of groundwater and ecosystem interactions. For example, the widespread problems of soil salinization and desertification are promoted by irrigation and other practices that alter the water balance.

Ecosystems in recharge areas

Interactions between ecosystems and groundwater systems in recharge areas are rather one-sided. Plants take water from soil moisture fed by infiltrating precipitation, a process that shows wide daily and seasonal fluctuations. Water thus removed from the soil decreases the amount of water available for recharge of the groundwater system. The water requirements of the plants can be so great that little or no water is left for recharging the groundwater, and a seasonal depression in the water table results (Figure 11.8), especially in areas with a low precipitation-evaporation ratio. As groundwater in recharge zones is generally too far below the surface to be accessible directly or indirectly through capillary rise, groundwater level and quality does not affect ecosystems in these zones.

Figure 11.8 Seasonal fluctuations in groundwater levels; groundwater hydrograph of observation well 16-D, The Netherlands, for the period 1935-1980. Bottom of filter is at 14.15 m below surface; ground surface is 4.65 m above sea level

Ecosystems in discharge areas

The contact between groundwater and surface water in discharge areas takes three forms:

1. through free-flowing springs and seeps, groundwater collects in surface channels and feeds into a stream (Figure 11.9a)

2. through direct subsurface interaction between stream, lake, or sea and , groundwater system (Figure 11.9b)

3. through complex interactions in an extended area such as wetlands (Figure 11.9c) and in lakes where in time discharge is reversed into recharge, or discharge and recharge can occur at the same time in different parts of the contact zone (Figure 11.9d).

As indicated, the several types of outflows from groundwater systems induce direct relationships between the type of discharge and specific ecosystems; often, however, other indirect influences are present. Such distinctive relationships occur between groundwater seeps at the foot of slopes and phreatophyte-dominated ecosystems; in springfed pond ecosystems and streams; and in estuarine systems and shelf seas where freshwater seeps create a local brackish environment hosting a specialized aquatic biota.

Periodic fluctuations in regional recharge may affect surface water systems in discharge areas through variations in outflow; this is especially important for stream base flow. Because of the hydraulic contact often present between surface water and groundwater systems, surface water levels can cause fluctuations in groundwater levels; when streams and lakes are not subject to large variations in levels, the subsurface water table is not subject to large fluctuations. In turn, as fluctuations in surface water levels affect groundwater levels in discharge areas, outflow from the groundwater system to the surface water system is also affected (Figure 11.9e). Such fluctuations result in variations in water availability for plants. In areas where such a regime is present, ecosystems tolerant of large variations in moisture may exist. However, such variations in water availability do not always coincide with the seasonal water needs of the plants, as the variations are influenced by climatic cycles (e.g. wet and dry periods, temperature fluctuations in recharge areas) and by the wave propagation and dampening mechanisms in the groundwater system.

Evapotranspiration is an important process in many discharge areas. A major component of evapotranspiration is plant transpiration during the day with subsequent depletion of soil moisture and decline of groundwater levels resulting from capillary rise, as the water tables in these areas are close to the ground surface. During the night, recovery of groundwater levels from regional groundwater flow toward the discharge area, and increase of soil moisture content from capillary rise, can take place as the transpiration process is slowed. In some situations, when the water needs of the plants exceed the daily supply from groundwater and the discharge area extends away  from the draining stream, a seasonal water table depression may result, (although it is often less pronounced than in recharge areas). In turn, plant growth may then be impeded by restricted water availability resulting from the extended decline of the water table.

Figure 11.9 Various types of surface water-groundwater contacts in discharge areas

Phreatophytes, such as cottonwood trees along southwestern mountain streams, root in or near the saturated zone; their roots are accommodated to a low-oxygen environment. Thus they are able to survive high water table levels that may submerge their roots temporarily. However, they also can survive long periods of low precipitation because they are not dependent on local infiltration (Miller, 1977) .

Groundwater and wetland ecosystems

Probably the most complex relationships exist between groundwater and wetland ecosystems. The transport of water and nutrients in such systems results in quite distinctive ecosystem types and unique biota. Changed conditions in the groundwater recharge system often result in stresses on the receiving system, as when springs become seasonally or permanently dry, and when streams receive polluted groundwater discharge. Conversely, wetlands and lake systems can have a regulating function if they are in the path of groundwater flow (Figure 11.9d). The interactions in such systems work in two directions and at multiple scales: groundwater from upstream sources discharging into the surface water system affects aquatic ecosystem processes and productivity, while surface water infiltrating into the subsurface affects groundwater quality over large areas. These processes can be altered greatly by various natural or human-induced conditions, as in the case of wetlands that have been ditched and drained.

Soil salinization

A major environmental problem occurring at the interface of groundwater systems and the soil surface is soil salinization, which results from evaporation of mineralized capillary moisture from the upper horizons of the soil. Depending on the chemical composition of the soil moisture, saline soils of sodium chloride, sulphate, and nitrate occur in the United States, the USSR, Egypt, Iraq, Tunisia, Syria, Pakistan, India, and China, among others (Kovda, 1983). Saline soils, which are found in both recharge and discharge areas, generally result from natural or man-made changes in the hydrological regime. Changes in drainage patterns, such as those caused by irrigation under poor drainage and by construction of reservoirs and canals, may cause rising groundwater levels, so that water logging of previous relatively dry surface areas may occur. Another example of soil salinization is the aridization of dry land, sometimes in combination with the changing natural drainage patterns that may result from the relative lowering of sea levels (Kovda, 1983). Wherever the flow of mineralized water is more or less constant, as in discharge areas in lowlands near the sea, salinization continues over a long time period.

Inadequate drainage conditions from man-made recharge often cause the water table to rise from significant depth to within a metre of the soil surface. Minerals present in irrigation water and leachate formed by dissolving agricultural chemicals in the irrigated soil can aggravate the soil salinization problem. In Egypt, for example, almost all irrigated land is potentially affected by this process and at least half of it is now salt-affected (Kishk, 1986).

Quantification of exchanges through budgets

Water and chemicals are stored within an ecosystem and move from one ecosystem to another. The fluxes involved can be quantified by analysing transport paths and water, energy, or mass budgets (Miller, 1977; Loucks, 1983). Balancing water system outflows with inflows provides a tool for understanding the relative importance of various transport and exchange mechanisms, and also assures that all the important mechanisms are accounted for. By comparing the budgets for neighbouring ecosystems, inconsistencies in the budgets may surface. However, the components of such budgets cannot always be measured in the field, and the unmeasured component is taken as the residual of the budget calculation. Uncertainties inherent in field determination of certain budget components may reduce the accuracy of such an analysis.

Groundwater-ecosystem interaction: a matter of scale

Ecosystems vary widely in spatial scale; some are as large as groundwater systems, while others are much smaller and may even coincide with soil units. In the latter case, a single groundwater system may be a common element shared by many different ecosystems. Thus, ecosystem research across a range of scales must recognize the potential differences among the spatial and temporal scales of the ecosystem and the associated groundwater system.

The prerequisite for quantifying relationships between groundwater systems and ecosystems is a quantitative understanding of each type of system. Conceptualization of the interactions between the systems can then proceed through interdisciplinary study and is a first step toward integral analysis of the combined system. In many instances the scales on which the systems are analysed are quite different (Figure 11.10); but resolving these differences is a crucial part of modelling the interactions between the surface and subsurface water, and the ecosystems influenced by the water system.

Figure 11.10 Scales and relative sizes of various hydrological systems and ecosystems

DISCUSSION AND RESEARCH NEEDS

This paper has focused on the principles of groundwater modelling and surveyed the problems of scale that are pertinent to such modelling. It has also addressed the linkages between groundwater systems and aquatic and terrestrial ecosystems. These relationships often take the form of stresses put on one system by the other, at various scales. To quantify the stresses and their effects on the systems being considered, several scales for data collection and modelling must be selected and defined. However, the scales on which interfacing groundwater-ecosystem processes are usually modelled are not identical. Hence, research on the available approaches to this problem is needed, including averaging over larger elements, spatial or temporal decomposition, and selection of the smallest relevant scale as the basic element of measurement and modelling. This latter approach requires extensive computer resources, now increasingly available.

Many other questions implicit in the previous sections also need to be answered so that physical and biological subsystems can be integrated into large-scale models, with all under a single scale. Studies are necessary to quantify interrelationships at various scales between hydrologic and biological subsystems. One element of such studies is improved definition of the most elementary units appropriate for work on the various subsystems. These basic units may be required as the foundation on which hierarchical modelling and integration can take place, leading to further definition of units at the scale required for regional modelling. In quantifying subsystem interactions, an illustrative study of the information loss and changing information requirements among groundwater systems aggregated at different scales from the basic units should be helpful. Such studies will be particularly important for modelling ecosystems influenced by groundwater discharge. Such research on aggregation could draw on the vast amount of existing regional groundwater data.

Another problem concerns selection of the appropriate scales for modelling studies. Here, the appropriate scales are determined by the objectives and by the level of resolution currently feasible for collecting and summarizing data on regional and global processes. In this context, the dynamic behaviour of the atmosphere, the hydrosphere, and the chemicals transported in air and water must be considered. The arbitrary scales associated with conventional modelling approaches in the various disciplines pose challenges for research on the integration between physical and biological subsystems.

Adapting the grid requirements from atmospheric modelling (on the scale of 10000 km²) into corresponding groundwater units may involve either parts of larger aquifers, or some number of smaller aquifers. In the latter case, representation at the prescribed scale may require calculation of equivalent variables describing storage throughput, transformations, and mixing in a large groundwater system. To unify optimally the modelling of the associated hydrological and biological systems, further research is necessary into the methodology of aggregation and decomposition of basic units. As part of such research, questions need to be asked concerning the relationships between spatial and temporal resolution and accuracy at the larger, aggregated scales. In this context, considerations as to the availability and quality of the databases will be significant. If we are to evaluate theoretical solutions to the indicated scaling problems of linked hydrologic and biologic systems, explicit criteria may be needed for selection of both small and large study basins and watersheds.

ACKNOWLEDGEMENTS

This paper has been prepared with support of the Holcomb Research Institute (HRI). The author acknowledges the resourceful discussions on large-scale ecological modelling with Orie L. Loucks and Richard A. Park of HRI and their constructive comments during the preparation of this paper .

REFERENCES

Bachmat, Y., Bredehoeft, J. D., Andrews, B., Holtz, D., and Sebastian, S. (1985). Groundwater Management: The Use of Numerical Models. 2nd Edition, edited by P . K. M. van der Heijde. Water Resources Monograph 5, American Geophysical Union, Washington, D.C.

Bear, J. (1979). Hydraulics of Groundwater. McGraw-Hill, New York.

Bear, J. (1972). Dynamics of Fluids in Porous Media. American Elsevier, New York. 

Beck, M. B. (1985). Water Quality Management: A Review of the Development and Application of Mathematical Models. IIASA 11, Springer-Verlag, Berlin.

Boehm, B. (1983). Conceptual Plan for Water Management Schemes in the Northern Part of the Rhenish Lignite Mining District, pp. 571-579. Publication N142, Intern. Assoc. Hydrol. Sc.

Bonnet, M. (1982). Methodologie de Modeles de Simuation en Hydrologie. Document 34, Bureau de Recherches Geologique et Minieres, Orleans, France.

Boutwell, S. H., Brown, S. M., Roberts, B. R., and Atwood, D. F. (1985). Modeling Remedial Actions at Uncontrolled Hazardous Waste Sites. EPA/540/2-85/001, U.S. Environmental Protection Agency, Cincinnati, Ohio.

Bouwer, H. (1978). Groundwater Hydrology. McGraw-Hill, New York.

Budyko, M. I. (1977). Global Ecology. English translation 1980. Progress Publishers, Moscow.

Cusham, J. H. (1985). The Need for Supercomputers in Clay-Water-Organic Mixtures. Presented at DOE Seminar on Supercomputers in Hydrology, Water Resources Research Center, Purdue University, West Lafayette, Indiana, September 10-12.

DeAngelis, D. L., Yeh, G. T., and Huff, D. D. (1984). An Integrated Compartment Model for Describing the Transport of Solute in a Fractured Porous Medium. ORNL/TM-8983, Oak Ridge National Laboratory, Oak Ridge, Tennessee.

Dickinson, R. E. (1988). Atmospheric systems and global change. (Chapter 5, this volume.)

Domenico, P. (1972). Concepts and Models in Groundwater Hydrology. McGraw-Hill, New York.

Freeze, R. A., and Cherry, J. A. (1979). Groundwater. Prentice-Hall, Englewood Cliffs, New Jersey.

Freeze, R. A., and Witherspoon, P. A. (1966). Theoretical analysis of regional groundwater flow: 1. Analytical and numerical solutions to the mathematical model. Water Resources Research, 2, 641-656.

Gerba, C. P. (1985). Microbial Contamination of the Subsurface. In Ward, C. H., McCarty, P. L., and Giger, W. (Eds.) Ground Water Quality. John Wiley and Sons, New York.

Heath, R. C. (1983). Basic Ground-Water Hydrology. Water Supply Paper 2220, U.S. Geological Survey, Reston, Virginia.

Johnson Division. (1975). Ground Water and Wells. Johnson Division, UOP Inc., Saint Paul, Minnesota.

Kishk, M. A. (1986). Land degradation in the Nile valley. Ambio, 15 (4), 226-230. Klimentov, P. P. (1983). General Hydrogeology. English Translation, MIR Publishers, Moscow, USSR.

Kovda, V. A. (1983). Loss of productive land due to salinization. Ambio, 12(2), 91-93.

Loucks, O. L. (1983). Wetland Characteristics- Their Land- Water Interactions.  Proceedings 2nd. SCOPE Workshop on Wetland Management, Songkla, Thailand, April 1983 (in press).

L'vovich, M. I. (1979). World Water Resources and Their Future. English Translation, American Geophys. Union, Washington, D.C.

Miller, D. H. (1977). Water at the Surface of the Earth. Academic Press, New York.

Morel-Seytoux, H. J., and Restrepo, J. I. (1985). SAMSON Computer System. HYDROWAR Program, Colorado State University, Fort Collins, Colorado.

NRC, (1981). Coal Mining and Ground-Water Resources in the United States. National Academy Press, Washington, D.C.

Reisenauer, A. E., Key, K. T., Narasimhan, T. N., and Nelson, R. W. (1982). TRUST:. A Computer Program for Variable Saturated Flow in Multidimensional, Deformable Media. NUREG/CR-2360, PNL-3975, Battelle Pacific NW Lab, Richland, Washington.

Rickert, D. A., Ulman, W. J., and Hampton, E. R. (1979). Synthetic Fuels Development, Earth-Sciences Considerations. U .S. Geological Survey, Reston, Virginia.

Toth, J. (1963). A Theoretical Analysis of Groundwater Flow in Small Drainage Basins. J. Geophys. Res. , 68, 4795-4811.

Toth, J. (1971). Groundwater Discharge: a Common Generator of Diverse Geologic and Morphologic Phenomena. Int. Assoc. Hydrol. Sci. Bull., 6, 7-24.

Tripathi, S., and Yeh, G. T. (1985). HYDROGEOCHEM on the Hypercube Computer. Presented at DOE Seminar on Supercomputers in Hydrology, Water Resources Research Center, Purdue University, West Lafayette, Indiana, September 10-12, 1985.

U.S. Environmental Protection Agency. (1982). Environmental Standards for the Management and Disposal of Spent Nuclear Fuel, High-level and Transuranic Radioactive Wastes (40 CFR Part 191). Federal Register (47 FR 58196), Washington, DC.

Wang, J. S. Y., and Narasimhan, T. N. (1984). Hydrologic Mechanisms Governing Fluid Flow in Partially Saturated, Porous Tuff at Yucca Mountain. LBL-18473, Lawrence Berkeley Lab., Berkeley, California.