4.11 Groundwater model

Transcription

1 4.11 Groundwater model 4.11 Groundwater model Introduction and objectives Groundwater models have the potential to make important contributions in the mapping and characterisation of buried valleys. Often the Quaternary infill of the buried valleys is characterised by a high fraction of sands (Sandersen & Jørgensen 2003) and the valleys are likely to provide interconnected bodies of high permeability. Buried valleys may therefore act as important groundwater reservoirs but they may also pose a threat to bounding deep aquifers as they may provide shortcuts for fast transport of surficial contamination. In areas with saltwater intrusion from salt domes the valley can act as a pathway from deeper aquifers to more shallow aquifers. Groundwater models can be used to quantify if the buried valley is an interesting aquifer from a water balance point of view. The models can also be used to map the flow paths and therefore the vulnerability of the valley itself and the surrounding sediments. For planning issues the model is a powerful tool for characterizing catchment areas to abstraction wells. Hydrogeologically, the buried valleys may roughly be divided into two categories. (1) Those incised into low permeable sediments, and (2) those incised into high permeable sediments or alternating layers of clay and high permeable sand. The first class of buried valleys may be cut down into clayey Paleogene sediments. In these environments the valley form a distinct feature with contrasting hydraulic properties compared to the surrounding sediments. The valley may constitute the primary aquifer in the area and serve as an important groundwater resource. Limited lateral exchange between the water inside the valley takes place with the surrounding layers and the groundwater flow patterns are therefore to a high degree controlled by the geometry of the valley. The valley may be recharged from surficial sand layers located outside the valley itself and the water flowing in the valley may therefore originate from places far away from the valley. In areas where several valleys are located, the valleys may form a network where groundwater flow paths are highly dependent on the hydraulic connection between the individual valleys. Quantification of the degree of connectivity between neighbouring or cross-cutting valleys may be crucial for the identification of flow paths and the spatial vulnerability of the valleys. For valleys incised into high permeable sediments like Neogene sand formations or alternating layers of clay and sand, the valley and the surrounding sandy layer may constitute one large aquifer system. The Quaternary sediments inside the valley are often characterised by larger grain sizes than the pre-quaternary sediments (Sandersen & Jørgensen 2003), and the yield of the valley may therefore be higher than for the pre-quaternary sediments. Hence, the valley serves as an attractive location for well fields. The valley may on the other hand cut through clay layers of otherwise large lateral extend that protects the deep Neogene aquifers from contamination from the surface. Since the valley penetrates the clay cover, the valley may create short-circuits between the shallow groundwater and the deep surrounding aquifers. Hence, the buried valley can pose a threat to the water quality of the otherwise well protected pre- Quaternary aquifers, and the motivation for mapping and analysis of the potential for pollution to reach the pre-quaternary aquifers is significant. In the following the steps involved in the construction of a groundwater model are shortly described. Then, special considerations involved in the modelling of buried valleys are addressed. Following, the possibilities to use the groundwater model to map and characterise buried valleys are outlined. Only a limited number of modelling studies on buried valley systems have been presented in the international literature. As a consequence, this chapter is not comprehensive and a number of problems involving buried valleys with different infill and located in different geological environments have to be examined in order to provide a complete description of the challenges and opportunities involved in numerical modelling of systems containing buried valleys. The aim of the chapter is to provide the reader with an overview of the procedures involved in the construction of groundwater models for systems dominated by buried valleys and to describe the possible benefits of setting up a 133

2 TORBEN O. SONNENBORG, DORTE SEIFERT & ROLF JOHNSEN numerical model for a buried valley with respect to mapping and characterisation of the valley Construction of groundwater models Construction of a groundwater model involves several steps and requires input and participation from different professions (Refsgaard & Henriksen 2004). In Figure a simplified version of the modelling protocol proposed by Refsgaard et al. (2005) is shown. The modelling process can be divided into five main steps: (1) Model study plan, where the problem is described and the objectives of the modelling work is defined. This part of the modelling process is very important since it determines to a large extend how many of the following tasks are carried out. (2) Data and conceptualization, where field data are collected and processed. This step includes the construction of the conceptual model, where one of the most important tasks is the construction of a three-dimensional digital hydrostratigraphical model. The hydrostratigraphical model is a simplified version of the geological model, where only the geological units important for the groundwater flow problem at hand is described explicitly as separate units and where the resulting units are categorised according to their hydraulic properties (hydrofacies) rather than the geological environment or stratigraphical belonging. When dealing with systems containing buried valleys, it is normally important to describe the structure and the geometry of the valleys with high precision. The details of the geological and hydrostratigraphical model will naturally decrease with depth as the density of geophysical and geological data falls. Besides the hydrostratigraphical model, this step also involves delineation and definition of model area and boundary conditions which both to a certain degree depends on the overall flow directions in the system of interest. This information is usually obtained from maps illustrating the distribution of hydraulic head in the area of interest. The choice of boundary conditions has large influence on the model performance and is therefore a task that should be given high attention. Additionally, the modelling code used for the actual problem is selected. The code should be able to address the objectives defined under step one. If, e.g., the interaction between streams and groundwater is important for the study, it is necessary to select a model code that is able to represent streams and can describe the flux between the two domains as a function of the variables that are important to examine in the study. If the problem is time variable, a code that can handle transient flow should be selected. Numerous similar questions should be considered when the model code is selected. (3) Model set-up, where the numerical model is constructed, including choices concerning design of the numerical grid and discretization, representation of the geology in the numerical model, and implementation of boundary conditions and stresses like groundwater abstraction. If transient simulations are carried out, additional parameters (storage parameters) have to be assessed, time step has to be chosen and initial conditions should be specified. Fig : Modelling protocol (Refsgaard et al. 2005). 134

3 4.11 Groundwater model (4) Calibration and validation, where the calibration method is selected, and the model parameters are adjusted using the selected calibration method to obtain the best reproduction of the physical system. Usually, the structure of the model is fixed during the calibration process, e.g., the hydrostratigraphical model is unchanged, while the parameters describing the hydraulic properties of the individual hydrostratigraphical units are changed. Before the calibration process is initiated the acceptable level of match to observed data is usually defined. If it is not possible to obtain the accuracy specified or if it is only possible if unrealistic model parameter values are used, it may be necessary to re-examine the conceptual model and make changes to e.g., the hydrostratigraphical model. The calibration process may be followed by a socalled validation test, where the prediction ability of the model is tested against independent observations, i.e., field data not used in the calibration process. The test can be carried out using different approaches (Refsgaard 1997, Henriksen et al. 2003). When a transient model is constructed, the strongest and most frequently used test is the so-called split-sample test, where the model is tested on data from a period not included in the model calibration. (5) Simulation and evaluation, where the model is used to produce the results required to fulfil the objectives of the study, and the results are analysed and interpreted. Basically, a groundwater model provides results on hydraulic head values at the defined grid cells, and based on these hydraulic head values fluxes between grid cells are calculated. Hence, the most basic use of the model is to obtain information about flow directions and the overall water balance of the modelled system. Often information about individual aquifers or water bodies is demanded and the model can be used to quantify the flux to and from such units. If streams or rivers are included in the model set-up, results on the groundwater flux to and from the rivers can be quantified. If information about flow paths and travel times are required, two basic requirements have to be fulfilled. The geology has to be described in higher detail than if only information on fluxes is required. The flow path of the water is highly dependent on heterogeneities in geology since water preferable flows in the high permeable sediments. The numerical grid also has to be designed such that the geological heterogeneities are resolved by the numerical model. Hence, a model designed for prediction of flow paths and travel times are usually more demanding with respect to input data and model set-up. In order to simulate flow paths and travel times, the basic groundwater model has to be combined with a particle tracking model. The particle tracking model is able to predict the travel path and time the water follows based on information from the groundwater flow model on hydraulic head and the specified hydraulic properties. This ability may be used to delineate the fate of water infiltrating at a particular location. It may also be used to simulate the age of the groundwater at a particular point in the system or in a certain aquifer. In groundwater protection studies particle tracking models are used intensively to delineate the recharge area to individual well fields in order to delineate the area on the ground surface that potentially can pose a threat to the well field. When information about concentration levels of contaminants or specific species are required, a transport model has to be build upon the flow model. Similar to the particle tracking model, the transport model uses the hydraulic head solution from the flow model to calculate flow paths and mass fluxes. A transport model requires a finer discretisation than a model designed for water balance and flow path considerations. Hence, the requirements to input data and computational demands are increased further. The individual hydrostratigraphical units usually have to be resolved by several numerical layers in order to obtain a transport solution with sufficient accuracy. The transport model can provide information on concentrations in time and space on the modelled species. The use of a transport model is relevant in relation to contaminant transport from a point source, where the development of the concentration of the substance of interest should be predicted, e.g., at a well field. A transport model can also be used to quantify the transport and fate of, e.g., nitrate in agricultural areas to estimate the nutrient load to lakes or fjords. Further details about model construction and application can be found in, e.g., Anderson & Woessner (1992) and Sonnenborg & Henriksen (2005). 135

4 TORBEN O. SONNENBORG, DORTE SEIFERT & ROLF JOHNSEN Special requirement for buried valley models Many of the steps and tasks described above are similar for systems containing buried valleys as for other geological environments. However, special attention should be given to the discretisation and the design of the grid with presence of buried valleys. The discretisation, i.e., the distance between the grid points in the horizontal and vertical directions, is highly dependent on the purpose of the model study. When dealing with water resources problems and evaluation of groundwater vulnerability on larger scale (100 10,000 km 2 ) the model area is usually resolved by a relatively coarse grid. In the horizontal dimension grid cells with side lengths in the order of m are usually defined. When a system containing buried valleys is modelled it is important to use a cell size that is small compared to the width of the valley to resolve the flow in the valley. The cell size used in the valley should not exceed the valley width, and if the flow paths within the valley should be simulated several cells should be used to describe the valley. If the modelled valley (or network of valleys) is aligned in a dominant direction, it is recommended to rotate the model grid such that the grid axis follows the valley orientation. Hereby, the flux within the valley is calculated more accurately and local refinement of the discretization in the area occupied by the valley is more unproblematic. In the vertical dimension the number of model layers in water resource and groundwater protection models usually corresponds to the number of hydrostratigraphical layers. Hereby, each hydrostratigraphical layer is represented by one model layer. The flow in the individual geological units and the exchange between different layers are easily calculated and precisely determined. If hydrostratigraphical layers pinches out, the thickness of the model layer representing that unit is normally specified to a small value (e.g., 0.5 m). When dealing with systems containing buried valleys the design of the grid is a challenge. Consider the system illustrated in Figure , where a cross-section through a system containing a buried valley is sketched. The valley cuts through a sequence of pre-quaternary layers that are continuous on both sides of the valley. For such a system both the grid design and the discretisation have to be considered carefully. Two alternative grid designs are shown in Figure (B and C). In both cases the surrounding pre-quaternary layers are resolved by one model layer each, which is a common approach when dealing with resource and groundwater protection models. In case B each model layer represents only one hydrostratigraphical unit or (layer). When a geological layer disappears or pinches out, the model layers describing that pre- Quaternary layer have a small thickness and continues through the model area. This is illustrated in Figure B, where the thickness of the model layers describing the pre-quaternary layers are specified to a small value in the area occupied by the buried valley. The layer is continuous beneath the valley and attains the thickness corresponding to the pre-quaternary layer at the other side of the valley. This approach has the advantages that it is relatively easy to determine the location of the model layers. Each model layer represents only one hydrostratigraphic unit, and therefore the analysis and interpretation of the results from the model is straightforward. E.g., the flux to model layer 3 represents the inflow to the same geological layer. The disadvantages of this approach are that the numerical resolution of the buried valley is very coarse. In the sketched case, the Quaternary valley is only represented by one model layer, and considering that buried valleys are typically several hundred metres deep, this is not ideal for describing the internal flow in the valley. Additionally, the numerical layers at the periphery of the valley are aligned almost vertically which may result in numerical problems (mass balance errors, convergence problems). In Figure C an alternative grid design is illustrated. Here, the numerical layers describing the pre-quaternary geology are continued through the valley by interpolation between the valley boundaries. The model layer describing the bottom of the valley is adjusted to fit the boundary between the valley and the surrounding pre-quaternary sediment. This kind of grid may be more difficult to set up, but the two problems pointed out above are circumvented. The valley is now resolved by 136

5 4.11 Groundwater model several numerical layers, and the problem with model layers with vertical orientation is avoided. However, the properties of the individual numerical layer are necessarily heterogeneous, as one layer describes both the Quaternary and the pre-quaternary sediments. Hence, some kind of zonation of the hydraulic properties within the individual model layers is required to describe the different properties of the valley and the surrounding sediments. In other areas alternative approaches can be relevant. In Chapter 5.2 an example of a different model setup for the Tyrsting valley is presented. In Figure a field case (Bording, Denmark, cf. Chap. 5.1) where the grid approach illustrated in Figure C has been applied is illustrated. The model area is discretized horizontally in uniform cells of 200 m. The valley cross section is resolved by about 18 numerical cells at the widest place near the surface. In the following we will use the notation geological layers for the defined geological units and numerical layers as the vertical discretization of the numerical model. In the example the numerical layers follow the pre-quaternary geology, resulting in 13 numerical layers, including one for the Quaternary unit and 12 for the pre-quaternary units of alternating sand and clay. Hence, each pre-quaternary formation is resolved by one numerical layer. If a geological layer pinches out or is absent, the numerical layer is given a thickness of 0.5 m, and the cells of such a layer is given the hydraulic properties of the underlying geological model. A cross section of the geological model and the discretization in the hydrogeological model for the focus area is shown in Figure The numerical layers are continuous through the buried valley, and the vertical boundaries of the numerical layers are initially determined by interpolation of the geological layers outside the buried valley. Subsequently, the bottom elevations of the cells located within the valley are adjusted using the following procedure. At the periphery of the valley, the bottom elevations of the numerical cells that are located just above the valley bottom known from the geological model are extended downwards to the boundary between the valley and the pre-quaternary given by the geological model. If, e.g., the buried valley cuts down into model layer 13, the bottom elevation of the cell in layer 12 at the particular location is shifted downwards to match the periphery of the valley. The top elevation of the cell in the underlying layer 13 is therefore defined by the bottom elevation of the buried valley, see example at the deepest point of the buried valley in Figure Fig : Illustration of a buried valley incised in a sequence of pre-quaternary layers. A) The geological settings, B) Numerical layers following the geological layers, and C) Numerical layers cutting through the valley. 137

6 TORBEN O. SONNENBORG, DORTE SEIFERT & ROLF JOHNSEN assess the credibility of the geological model is significant. The model results will be highly sensitive to the mapped valley structure (the geometry of the valley) and the connectivity between individual valleys (Sonnenborg 2006). A groundwater model therefore has the potential to (1) point out where the conceptual model is weak, e.g., indicated by a weak reproduction of observed data, and (2) to pinpoint the locations and areas in the model setup that are especially important for simulation of groundwater flow, e.g., found during a sensitivity study on the hydrostratigraphical model. These areas should be given special attention in subsequent field investigation of the system. Fig : Cross section of buried valley at Bording, Denmark, showing A) the geological model and B) the discretisation and grid design. Red represents the Quaternary deposits, while light blue and dark blue represent pre-quaternary sand and clay formations Using the model for mapping and characterisation A groundwater model can be used to obtain different kind of information about groundwater systems with buried valleys. First, the model may be used to test if the conceptual model proposed for the valley system is correct. If it is not possible to reproduce measured data of, e.g., hydraulic head and groundwater age from the valley and its surroundings using realistic hydraulic properties of the predefined geological units, the credibility of the model input like geological settings or boundary conditions is relatively low. This result is normally found during the calibration of the model, where the parameters of the geological units are adjusted to make the model able to reproduce historical observations from the system. Especially for valleys and networks of valleys located in low permeable pre- Quaternary sediments the ability of the model to A successful calibration process results in the estimation of hydraulic properties of the defined hydrostratigraphical units. Often, independent information on model parameters, e.g., hydraulic conductivity or transmissivities derived from pumping tests (cf. Sect. 4.14), is scarce, and it is therefore difficult to obtain representative values of hydraulic conductivity, storage coefficients and porosity based on a few field measurements. The model calibration produces these representative parameter values and provided that the quality of the conceptual model and the observation data used for calibration are good, the estimated parameters will be close to the true physical values. If an automatic parameter estimation procedure formulated in a statistical framework is used (e.g. Carrera & Neuman 1986), uncertainty estimates of the parameters are also produced. This information is valuable when judging the reliability of the individual parameter estimates and can be used in subsequent sensitivity studies and uncertainty analysis of the model results (Højberg & Refsgaard 2005). Secondly, a model that is well calibrated can be used to obtain information about the flow dynamics and the water balance of the simulated system. Inflows and outflows to the valley can be quantified, and the flux to and from neighbouring formations can be assessed. If the model has been designed with a sufficient detail with respect to geological description and discretisation, the flow paths and travel times in the valley can be simulated. If field information about water chemistry or groundwater age (cf. Sect. 4.12) is available from sampling of wells, the model predictions can be evaluated, and 138

7 4.11 Groundwater model model results can assist in the interpretation of the observation data with respect to flow path and travel distances that result in the measured concentrations. The model results may also serve as the basis for assessment of the vulnerability (cf. Sect. 4.13) of the modelled valley. Using information on travel time, recharge locations and flow path the vulnerability of the aquifers can be assessed with high spatial resolution. The vulnerability of a specific aquifer is a function of travel time, but it also depends on the travel path since some soil layers have higher potential for natural remediation of contaminants. Therefore, it may be important not only to predict the groundwater age at an abstraction well but also to delineate the travel paths of the water reaching the well. The model can be used to map well head protection zones for well fields or individual abstraction wells. The hydrogeologist and planer should explicitly consider if the unsaturated zone is an integrated part in the model. The transport of water in the unsaturated zone is defined as vertical and the flow is sensible to the properties of the sediments in the unsaturated zone. An important aspect to the vulnerability study is therefore whether the unsaturated zone is clayey or sandy and to notice whether this should be added in the study. Further, the model can be beneficial for predicting the effects of changes on the system. The model can predict the response to changes in abstraction patterns, e.g., increasing pumping at existing wells or installation of new well fields, and quantify the effects on the location of the groundwater table, the effect on wet land areas and the discharge to rivers. The model may also be used to investigate the effects of land use changes or future climate changes on the groundwater resources. Here, the changes in the temporal and spatial distribution of groundwater recharge are of particular interest, and eventual changes may affect the flow pattern and sustainable groundwater resource of the system under consideration Conclusions As outlined in the paragraphs above, numerical modelling of buried valleys is associated with special considerations especially concerning discretisation and grid design in the area where the valley is located. However, a groundwater model has the potential to assist in the mapping and characterisation of buried valleys. Here the most important contributions with respect to mapping and characterisation are: To test the credibility of the conceptual model for the buried valley systems including the hydrostratigraphical model To provide quantitative information on the hydraulic properties of the geological units and uncertainty estimates on the parameter values To assess the water balance of the buried valley and to quantify the exchange of water (flux) with neighbouring formations To analyse the flow patterns in the valley and to quantify the groundwater age distribution within the valley To evaluate the vulnerability of aquifers in the valley by providing information on the area on the ground surface that recharges the aquifer, the travel path including the geological units the water has passed through on its way to the aquifer, and the time required to reach the aquifer To delineate well head protection zones of well fields in the valley To quantify the effect of changes on the systems with respect to the groundwater. Examples of possible changes includes land use changes, climate changes, changes in groundwater abstraction pattern. If a groundwater transport model is constructed the concentration development within the valley as a consequence of, e.g., point sources on the ground surface or contamination from agricultural loads may be assessed. 139

8 TORBEN O. SONNENBORG, DORTE SEIFERT & ROLF JOHNSEN References Anderson MP, Woessner WW (1992): Applied Groundwater Modeling, Simulation of flow and advective transport. Academic Press, London. Carrera J, Neuman SP (1986): Estimation of aquifer parameters under transient and steady-state conditions, 1. Maximumlikelihood method incorporating prior information. Water Resources Research 22(2): Henriksen HJ, Troldborg L, Nyegaard P, Sonnenborg TO, Refsgaard JC, Madsen B (2003): Methodology for construction, calibration and validation of a national hydrological model for Denmark. Journal of Hydrology 280 (1 4): Højberg AL, Refsgaard JC (2005): Model uncertainty parameter uncertainty versus conceptual models. Water Science and Technology 52 (6): Refsgaard JC (1997): Parameterisation, calibration and validation of distributed hydrological models. Journal of Hydrology 198 (1 4): Refsgaard JC, Henriksen HJ, Harrar WG, Scholten H, Kassahun A (2005): Quality assurance in model based water management review of existing practice and outline of new approaches. Environmental Modelling & Software 20(10): Refsgaard JC, Henriksen HJ (2004): Modelling guidelines terminology and guiding principles. Advances in Water Resources 27 (1): Sandersen PBE, Jørgensen F (2003): Buried Quaternary valleys in western Denmark occurrence and inferred implications for groundwater resources and vulnerability. Journal of Applied Geophysics 53: Sonnenborg TO (2006): Review of the modelling study in the Southern Aarhus area (in Danish). GEUS rapport 2006/15, Geological Survey of Denmark and Greenland. Sonnenborg TO, Henriksen HJ (2005): Handbook in groundwater modelling (in Danish). GEUS report no. 2005/80, Geological Survey of Denmark and Greenland. 140