Economic aspects of the delineation of well head protection areas under conditions of uncertainty

Transcription

1 Economic aspects of the delineation of well head protection areas under conditions of uncertainty N. Theodossiou * and D. Latinopoulos Division of Hydraulics and Environmental Engineering, Department of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece *Corresponding author: niktheod@civil.auth.gr, Tel: Abstract The determination of wellhead protection areas is a matter of major importance especially for wells supplying water for domestic use, since it allows water resources managers and local authorities to impose measures over the development of agricultural or industrial activities that could somehow affect the quality of groundwater. In this paper an investigation, using computer-based mathematical models, of the implications of uncertainty on the estimation of the hydrogeological parameters that affect the delineation of wellhead protection areas is performed. This investigation is based on a stochastic simulation of the soil material structure of the aquifer. The economic aspects of the measures imposed over the protected areas according to their resulting delineation are then analysed in order to establish a measure of the costs of information and of the degree of uncertainty of the hydrogeological parameters. Keywords: Well head protection areas; Stochastic analysis; Groundwater simulation; Water economics. 1. INTRODUCTION Groundwater pollution is considered to be one of the most important water related environmental problems. Protection of groundwater systems is not only imposed by the European Union Framework Directive 2000/60/EC and all the relevant European or National legislation that followed it, but it also considered to be an absolute necessity considering the multiple uses of groundwater in domestic supply, agriculture, industry etc. In order to protect pumping wells, a detailed scientific approach based on the determination of well head protection areas, is needed. A well head protection area (WHPA) is defined as the area that needs to be protected (by imposing restrictions on the activities that can be developed) so that no pollutants of concentrations higher than the permitable limits, can reach the pumping well, using a number of criteria and more commonly the time criterion considering the time needed for the pollutant to reach the well. Respectively, a capture zone (or contribution zone) defines the surface or subsurface surrounding area, which includes water and pollutants that will finally end up in a certain period and be abstracted by the well [1, 2, 3]. In this paper a methodology for the determination of well head protection areas under conditions of uncertainty is outlined. This methodology is based on a costbenefit analysis that takes into consideration the cost of acquiring more information in order to reduce the hydrogeological uncertainty of an aquifer against the benefit of imposing land-use restrictions only on, as much as necessary, of the surrounding area of a productive pumping well. 2. THE STOCHASTIC MODEL In order to present the proposed methodology a theoretical example will be used. This example is based on the respective example used in the tutorial of the T-Progs model [4]. T-Progs is a software package that performs transition probability geostatistics to generate multiple equally probable models of aquifer heterogeneity, all of which can be conditioned to borehole data. T-Progs is generally used in a stochastic modelling approach with the ModFlow 2000 model [5, 6]. Both Proceedings of the 2 nd International CEMEPE & Editors: A. Kungolos, K. Aravossis SECOTOX Conference, Mykonos, June 21-26, 2009 A. Karagiannidis, P. Samaras ISBN page 309

2 ModFlow 2000 and T-Progs are included in the Groundwater Modelling System GMS software [7]. The concept is to use all the available data from the boreholes s cross-sections in order to construct models of the geological structure of the aquifer. These models will then be used in order to simulate the function of the aquifer including the delineation of capture zones and thus the well head protection area of a selected pumping well. It is obvious that since the available borehole data are never enough, this procedure results in a stochastic approach of the structure of the aquifer. The less the available data, or the smaller their relevance, the higher the uncertainty introduced. T-Progs [4] is used to solve two significant statistical problems. The first one is to define the transition probability data for each geological material located in the boreholes. This is achieved by computing a set of transition probability curves as a function of lag distance for each material for a given sampling interval. The second is to generate the multiple material sets during the simulation stage. This is achieved by applying Markov Chains to formulate the equations used to estimate these material sets. The objective of this stage of the analysis is to fit the Markov Chain curves as accurately as possible to the measured transition probability curves. This process is similar to fitting a model variogram to an experimental variogram in a kriging exercise [4, 8]. In the following figure an example aquifer is presented along with a borehole network. The geological structure of the aquifer is presented in figure 2 in the form of a cross-section. Figure 1. Borehole distribution Figure 2. Borehole distribution and geological cross-section The application of T-Progs can result in a series of realisations of the material structure of the aquifer based on the transition probability curves and the adapted Markov Chains curves. One of the numerous realisations of this application is presented in figures 3 and Figure 3. Aquifer material structure

3 Figure 4. Aquifer material structure (cross-section) Figure 5 presents the uncertainty distribution of this application. It indicates the possibility for the soil material of each cell of the discretisation network to be of a certain type. This figure presents the probability that the soil material of any cell of the first layer of the discretisation network is clay. The red color indicates certainty that the assumption (the material to be clay) is correct while the blue color indicates certainty that the assumption is in-correct. The latter is again a certainty since it indicates that another material is certain to be present in this particular cell. So the certain areas are indicated with both red and blue colors while the uncertain areas are presented with green and yellow colors. It is obvious that the more the available information the more the extent of the areas with higher certainty. Figure 5. Probability distribution of the soil material structure. 3. THE DELINEATION OF WELL HEAD PROTECTION AREAS According to the definitions presented earlier, the well head protection areas are defined as the capture zones that supply water to a pumping well in a certain time period. In cases of extreme uncertainty, meaning an aquifer that has no available data, then the capture zone is defined in circular form [1]. Figure 6. Well head protection areas under conditions of uncertainty 311

4 The more the available information, the more accurate the estimation of the capture zone, and thus, the less the resulting WHPA. Figure 6 presents different realizations of the resulting well head protection area in an unbounded aquifer. While the accuracy of the estimation of the protection area is increased the resulting area is decreased. The lower limit, presented in figure 6 by the inner curve, is one corresponding to the deterministic approach of the geological structure of the aquifer resulting from the theoretical and unrealistic assumption of infinite information and thus no uncertainty. 3. ECONOMIC ANALYSIS In order to provide economic efficiency during the specification of the boundaries of the wellhead protection area (WHPA), an environmental decision-making analysis is undertaken. The first step in this analysis is the determination of the main benefits, costs and risks that may arise from the groundwater protection policy. The direct benefit of all WHPAs is the provision of clean potable water to any potential user. This is a precondition for all protection alternatives, regardless of the size of the WHPA. Therefore, this benefit will be left out of the following analysis as it won t differentiate the economic outcome of the delineation alternatives. There are two categories of costs associated with the delineation of the WHPAs, which are going to be examined herein: (a) the cost of hydrogeological information and (b) the cost of uncertainty of the hydrogeological parameters. The first one is considered as the direct cost of installing a more sophisticated monitoring (observation) groundwater network. On the other hand, the cost of uncertainty is introduced in this paper to simultaneously assess the indirect benefit of information and the risk of misspecification of the WHPAs. This approach differs from other similar data-worth analyses [9],[10],[11] as it focuses on the alternative costs of groundwater prevention (land-use restrictions) and not on the risk of failure and the remediation costs. The cost of information (monitoring) consists of: (a) the cost of installing new observation boreholes and (b) the cost of gathering and analyzing all the necessary information (operational cost). If operational costs exhibit increasing economies of scale then the cost function will be a quasi-concave function. Otherwise, it can be assumed that the cost of information is a linear function of the number of boreholes. As already mentioned, the cost of uncertainty can be indirectly estimated by assessing the economic implications of the land-use restrictions. The reason for this is that the delineation of the total protected area is contingent on the degree of hydrogeological information (i.e. greater number of observation boreholes result to a more accurate delineation). Thus, the cost of uncertainty (CU) can be estimated as the foregone value of land-uses due to the misspecification (overestimation) of the protected area, according to the following equation: CU w i AU i (1) i where, w i is the total cost of land regulation per unit of area for the i-th land use and AU i is the total area of the i-th land use under uncertain hydrogeological conditions (protection status). Similarly, the indirect benefit from the hydrologeological information (BI) can be estimated as the change (reduction) in the cost of uncertainty under higher lever of information (greater number of boreholes). BI = CU x1 CU x2, x 1 <x 2 (2) where x is the number of boreholes in scenario j. In order to estimate both cost of uncertainty and benefit of information, it is essential to assess the total economic effect of land-use restrictions under various protection (information) scenarios. On this account, it is necessary to determine the following: 1. The time horizon in the assessment of the effects of land-use restrictions (how many years after the land-use restrictions have to be taken into account). 2. The discounting factor for future costs and/or benefits. 3. The change in land values (accrued per hectare of land) according to the current land-uses. 312

5 Figure 7: Conceptual framework of economic analysis Benefit of information TB TC 1 Max Revenue TB>TC Information (number of boreholes) Figure 8: Cost-benefit analysis of reducing uncertainty Time horizon and discounting factor are policy choices, usually defined by the decision maker. However, the most challenging part in this analysis is the assessment of all the relevant costs associated with land-use restrictions. Namely, land restrictions on industrial land uses bring about the following costs: (a) relocation cost (including all the construction and planning costs), (b) profit losses (for the period the industry is out of work) and (c) the higher cost of logistics (supposing that the current location was selected so as to minimise these costs). Concerning the land-use restrictions on agricultural activities, the most important types of costs are (a) the cost of the obsolete capital 313

6 (e.g. farming machinery that cannot be used on the new farming activities), (b) the productivity losses due to restrictions either on inputs (e.g. fertilisers, pesticides) or on agricultural products (high revenue products per cultivated area) and (c) the potential costs because of higher risk on agricultural production (e.g. new products in the local market). o further assess the effect of investing in observation boreholes, a cost-benefit analysis can be used. This analysis aims to maximise the net present value (NPV) of information by increasing the hydrogeologic data collection (see Figure 8). The cumulative net present value of the system over n years was computed using the following equation: n (BI t CI t ) NPV (3) t (1 r) 314 t 0 where, BI t and CI t are the total benefits and total cost of information in year t and r is the discounting factor. 4. CONCLUSIONS It is more than obvious that the delineation of well head protection areas is a matter that can not be handled lightly. The seriousness of imposing unnecessary restrictive measures over productive areas on the one hand, and not taking all the necessary precautions to protect water abstracted from pumping wells on the other, arises the need to introduce the cost of information in the decision making process in order to rationalise the whole procedure of the delineation of well head protection areas. References 1. U.S. Environmental Protection Agency, 1994, Ground water and wellhead Protection Handbook, EPA/625/R-94/ Theodossiou,., P. Latinopoulos and E. Fotopoulou, 2002, Estimation of wellhead protection areas under conditions of uncertainty, International Conference on Protection and Restoration of the Environment VI, 49-56, Skiathos. 3. Theodossiou, N., P. Latinopoulos and E. Fotopoulou, 2005, Application of Monte Carlo analysis in the delineation of well head protection areas, 9th International Conference on Environmental Science and Technology, , Rhodes Island. 4. Carle, Steven F., 1999, T-PROGS:Transition Probability Geostatistical Software Version 2.1, Hydrologic SciencesGraduate Group University of California, Davis Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, M.G., 2000, MODFLOW-2000, the U.S. Geological Survey modular ground-water model -- User guide to modularization concepts and the Ground-Water Flow Process: U.S. Geological Survey Open-File Report 00-92, 121 p. 7. Groundwater Modelling System, 2008, GMS 6.5 Software. 8. Theodossiou, N. And E. Fotopoulou, 2009, Delineation of well head protection areas using stochastic analysis approach, 11 th International Conference on Environmental Science and Technology, Chania, Crete, Greece. (submitted) 9. Freeze A., James, B., Massmann J., Sperling, T. and Smith, L., 1992, Hydrogeological decision analysis: The concept of data worth and its use in the development of site investigation strategies, Groundwater, Vol.30 (4), pp Bierkens, M., 2006, Designing a monitoring network for detecting groundwater pollution with stochastic simulation and a cost model, Stochastic Environmental Research and Risk Assessment, Vol.20, pp Wagner, B.J., Evaluating data-worth for ground-water management under uncertainty, Journal of Water Resources Planning and Management, Vol.125 (5), pp