INTEGRATED RISK ANALYSIS FOR SUSTAINABLE WATER RESOURCES MANAGEMENT

Transcription

1 INTEGRATED RISK ANALYSIS FOR SUSTAINABLE WATER RESOURCES MANAGEMENT JACQUES GANOULIS Laboratory of Hydraulics, Department of Civil Engineering Aristotle University of Thessaloniki, Thessaloniki, Greece Abstract Two main criteria are usually taken into consideration for engineering water resources management, namely technical reliability and economic efficiency (techno-economic approach). To obtain sustainability, one should consider not only technical and economic issues, but also environmental and social aspects. In this paper it is explained how integrated risk analysis considering risk indexes in four dimensions (technical, economical, environmental and social) can be used in order to quantify the degree of sustainability in water resources management. 1. Introduction Water resources management involves different disciplines, such as engineering, chemistry, ecology, economy, law and social sciences. Traditionally, the general objective of water management has been the satisfaction of demand for various uses, such as agriculture, drinking water or industry, using available water resources in technically reliable and economically efficient ways. This approach has led to structural and mostly technocratic solutions being suggested and implemented in several countries. However, in many cases building dams modifying riverbeds and diverting rivers has had serious negative repercussions on the environment and on social conditions. Moreover, waste in the use of this precious resource and rampant pollution in all areas of water use have raised doubts about this form of management. The concept of a sustainable management of water resources was first mentioned in Stockholm in 1972, during the United Nations World Conference and then at the Rio summit in 1992 with Agenda 21. The new philosophy is based on the integrated management of water at the watershed basin level. Emphasis is placed on environmental protection, the active participation of local communities, demand management, institutional aspects and the role of continuous and lifelong education of all water users. On the methodological level, integrated water management remains an open question and several different approaches seek to define a coherent paradigm. One possible paradigm is proposed in this paper and may be called the «4E paradigm»:

2 Epistemic, Economic, Environmental, and Equitable. It is based on integrated risk analysis, with a multidimensional characterization of different risks: scientific, economic, environmental and social. This paradigm uses either the theory of probability, or fuzzy logic, or both in order to assess and integrate technico-economic and socio-environmental risks in a perspective of sustainable management of water resources. The aim of this paper is to show how traditional engineering planning and design methods for reducing risks in water supply and management can be extended to consider environmental and social risks. Furthermore, a multiobjective decision-making methodology is suggested, in order to rank different feasible solutions 2. Risk Definition and Methodologies for Risk Quantification Engineering risk and reliability analysis provides a general framework to identify uncertainties and quantify risks. As shown in this paper, so far two main methodologies have been developed to assess risks (Ganoulis, 1994): (a) the stochastic approach, and (b) the fuzzy set theory. Stochastic variables and probability concepts are based on frequency analysis and require large amounts of data. Questions of independence between random variables and validation of stochastic relations, such as the well-known statistical regression, are often difficult to resolve. Fuzzy set theory and fuzzy calculus may be used as a background to what could be called "imprecision risk analysis". In this paper it is demonstrated how fuzzy numbers and variables may be used for estimating risks in cases where there is a lack of information or very little data available. 2.1 THE TECHNOCRATIC APPROACH Depending on the particular sector involved (e.g. drinking water, hydraulic engineering, agriculture or industry), various engineering specialities have been developed to address problems of water resources management. From a traditional and rather technocratic point of view, water resources planning may be defined as the process of developing alternative water quantities in order to satisfy demand over a given time period. This technocratic concept reduces water supply questions to the mere technical problem of collecting and distributing water volumes, in order to satisfy different water demands for drinking, irrigation or industrial use. Engineering planning and the design of structural or non-structural alternative solutions are the usual tools used by this profession for water management studies. The different steps involved in engineering planning are indicated in Fig. 1. The first step is to provide alternative technical solutions, by the use of data and mathematical modelling. Then, the decision making process is developed by introducing different criteria, such as technical reliability and economic efficiency.

3 2.2 COGNITIVE AND NON-COGNITIVE UNCERTAINTIES Uncertainties are actually due to a lack of knowledge about the structure of various physical and biochemical processes, and to the limited amount of data available ([2], [16], [5], [7]). Several authors have analysed different types of uncertainties and distinguished between uncertainties, which may be objective or subjective, basic or secondary and natural or technological. Another distinction should also be made between (1) non-cognitive or natural uncertainties or randomness, and (2) cognitive or man-induced or technological uncertainties. PROBLEM DEFINITION DATA MODELLING PROCESS MODELLING ALTERNATIVE SOLUTIONS ASSESSMENT OF THE ALTERNATIVES DECISION MAKING PROCESS DECISION Figure 1: Steps in engineering planning.

4 2.2.1 Non-cognitive uncertainties or randomness It is postulated that natural uncertainties are inherent to a specific process, and that they cannot be reduced by using an improved method or more sophisticated models. Uncertainties due to natural randomness or non-cognitive uncertainties may be taken into account by using stochastic or fuzzy logic-based methodologies, which are able to quantify uncertainties Cognitive or man-induced uncertainties Man-induced uncertainties are of different kinds: (a) data uncertainties, due to sampling methods (statistical characteristics), measurement errors and methods of data analysis, (b) modelling uncertainties, due to the inadequacy of the mathematical models in use and to errors in parameter estimation, and (c) operational uncertainties, which are related generally to the construction, maintenance and operation of engineering works. Contrary to natural randomness, cognitive uncertainties may be reduced by collecting more information, or by improving the mathematical model being used. 2.3 DETERMINISTIC, STOCHASTIC AND FUZZY VARIABLES Although rather exceptional, there are situations in water resources engineering which can be considered as deterministic. In such cases mathematical deterministic approaches relating inputs to outputs are sufficient, because uncertainties are low. Take, for example, the effect on water flow rate from a reservoir by changing the reservoir water level. There is a deterministic relation between the flow rate and the water level in the reservoir. In such a case risk and reliability techniques should not be used, because the situation is predictable. When the reservoir is filled by an inflow that varies randomly in time, various uncertainties produce a variation of water level in the reservoir that is no longer deterministic. It may be considered as a stochastic or probabilistic variable. Imprecision in boundary conditions and modelling coefficients can be quantified and propagated by use of fuzzy numbers and fuzzy logic-based modelling [8]. 2.4 DEFINITION OF THE ENGINEERING RISK In a typical problem of technical failure under conditions of uncertainty, there are three main questions, which may be addressed, in three successive steps. 1. When should the system fail? 2. How often is failure expected? 3. What are the likely consequences? The first two steps are part of the uncertainty analysis of the system. The answer to question 1 is given by the formulation of a critical condition, producing the failure of the system. To find an adequate answer to question 2 it is necessary to consider the frequency or the likelihood of failure. This can be done by use of the

5 TECHNICAL RELIABILITY TECHNICAL FAILURE ECONOMIC LOSSES ECONOMIC EFFECTIVENESS Ganoulis J.: Integrated Risk Analysis for Sustainable Water Resources Management probability calculus. Consequences from failure (question 3) may be accounted in terms of economic losses or profits It has been largely accepted that the simple definition of the engineering risk as the probability of failure (risk = probability) is much more appropriate. As shown in Fig. 2, the actual approach in engineering water resources planning methodology aims primarily to reduce technical and economic risks by achieving two main objectives Technical reliability or performance, and Economic effectiveness. ENGINEERING RISKS ECONOMY Figure 3: Technical and economic performances in water resources management. As explained in [7] we should define as load l a variable reflecting the behaviour of the system under certain external conditions of stress or loading. There is a characteristic variable describing the capacity of the system to overcome this external load. We should call this system variable resistance r. A failure or an incident occurs when the load exceeds this resistance, i.e., FAILURE or INCIDENT : l > r SAFETY or RELIABILITY : l r In a probabilistic framework, l and r are taken as random or stochastic variables. In probabilistic terms, the chance of failure occurring is generally defined as risk. In this case we have RISK= probability of failure= P( l > r) 2.5 INSTITUTIONAL AND SOCIAL ISSUES In recent years special attention has been paid to institutional and social approaches in water resources management and flood alleviation planning [8]. The institutional or administrative framework may be conceived as being the set of state owned agencies or private enterprises dealing with production, distribution and treatment of water. Of particular importance is their scale of operation (local, regional or state), their degree of autonomy from the central administrative body, and the involvement of

6 different water stakeholders in the decision making process. The administrative systems and water laws and regulations, together with social perception on the use of water and traditions involved, make the issue of water resources management very complex. 2.6 FUZZY LOGIC BASED APPROACH Consider now that the system has a resistance %R and a load %L, both represented by fuzzy numbers. A reliability measure or a safety margin of the system may be defined as being the difference between load and resistance ([7], [19]). This is also a fuzzy number given by M = R L Taking the h-level intervals of %R and %Las R(h)=[R 1 (h), R 2 (h)], L(h)=[L 1 (h), L 2 (h)], then, for every h [0, 1], the safety margin M(h) is obtained by subtracting L(h) from R(h), i.e. M(h) = R(h) - L(h). Two limiting cases may be distinguished, as shown in Fig. 3: There is absolute safety if: whereas absolute failure occurs when: M(h) 0 h [0,1] M(h) < 0 h [0,1]. A fuzzy measure of risk, or fuzzy risk index R i may be defined as the area of the fuzzy safety margin, where values of M are negative. Mathematically, this may be shown as: R i = M m< 0 m µ ( m) dm µ ( m) dm M (1) The fuzzy measure of reliability, or fuzzy reliability index R e is the complement of (1), i.e. µ ( m) dm M m> 0 Re = 1 Ri = (2) µ ( m) dm m M

7 1 M = R- L : safety L R (a) x M = R - L : failure 1 R L (b) x 1 M = R - L RISK: Ri R L (c) Figure 3: Absolute safety (a), absolute failure (b) and fuzzy risk (c).

8 3. Fuzzy Modelling Fuzzy modelling has not yet been developed extensively, although fuzzy numbers and fuzzy relations have found many applications in control engineering and industrial devices. Fuzzy set theory ([22], [13], [23]), and its derivative fuzzy arithmetic [12], may be used in order to introduce imprecise data into a mathematical model in a direct way with minimal input data requirements. In fuzzy modelling only the range and the most confident values of the input variables are required, so it can be used successfully when the available data is too sparse for a probabilistic method to be applied ([7] [20]). In this model the various parameters and loads from external sources are considered as triangular fuzzy numbers (T.F.N.). In order to calculate the concentration of all pollutants at each node using finite differences or finite elements, a system of fuzzy equations needs to be solved. This is difficult from a mathematical point of view, and has stimulated a lot of interest because whatever possible technique is used, only enclosures for the range of the output variables can be produced. Shafike ([18]) introduced the fuzzy set theory coupled with the finite element method into a groundwater flow model. The algebraic system of equations with fuzzy coefficients was solved with an iterative algorithm [14]. The fuzzy set theory was also applied into a steady-state groundwater flow model with fuzzy parameters combined with the finite difference method. A non-linear optimisation algorithm was used for the solution of the groundwater flow equations with fuzzy numbers as coefficients for the hydraulic heads. Ganoulis et al. [9] used fuzzy arithmetic to simulate imprecise relations in ecological risk assessment and management. Specifically the technique was applied to a simplified domain with coastal circulation, in order to evaluate the risk of coastal pollution. For the solution of the algebraic system of equations with fuzzy coefficients direct interval operations were employed, instead of the iterative methods or non-linear optimisation techniques used in previous studies. Since triplets cannot be used for the multiplication and division operations, as explained in [12], mathematical operations have been performed at various h-level cuts by the use of the interval of confidence at each h-level. It is also important to mention that the solution of an interval equation using interval operations is always an enclosure of the exact solution ([11], [14], [15]). The best possible enclosure for an interval function, which is defined as the hull of the solution, is a fundamental problem of Interval Analysis and should be treated with care, as the solution accuracy depends on the shape of the interval function [17]. The technique was tested initially with a one-dimensional advection-dispersion model in the non-conservative form, using the finite difference method. The results derived from the numerical computation considering the dispersion coefficient as fuzzy parameter are very similar to those of the analytical solution, confirming the accuracy of the numerical technique. A finite element algorithm combined with fuzzy analysis was also used for the solution of the advection-dispersion equation.

9 4. Towards a Sustainable Water Resources Management Approach To integrate risk assessment into the socio-technical decision-making process of water resources management, the Multi-Risk Composite-Method (MRCM) is proposed. This is a variant of a Multi-Criteria Decision-Making methodology (MCDM). MCDM has been extensively used in the past for ranking different alternative options under multiple criteria or objectives. Different analytical techniques for MCDM are available in literature ([10], [21], [4]). Recently, the following have received much more attention: ELECTRE I to III Compromise Programming Goal Programming Sequential Multiobjective Optimization Game Theory. In selecting the most appropriate method, important criteria are the kind of objectives (quantitative or qualitative), the number of decision-makers (one or a group) and whether objectives are involved a priori, a posteriori or interactively. ELECTRE I to III techniques are more suitable for qualitatively expressed criteria [1]. Game and team theories [3] are mainly interactive techniques. Uncertainties and risk may be quantified by using probabilities or fuzzy sets, and can be handled better by Compromise Programming Techniques ([8], [6]). The Multi-Risk Composite-Method (MRCM) belongs to this kind of method. As shown in Fig. 4, four main objectives or criteria are to be taken into consideration: 1. Engineering Reliability: some measures for technical performance are: technical effectiveness, service performance, technical security, availability and resilience. 2. Environmental Safety: environmental indicators may be positive or negative environmental impacts, such as increase or decrease in the number of species, public health issues, flora and fauna modifications, losses of wetlands, landscape modification 3. Economic Effectiveness: costs and benefits are accounted, such as project cost, operation and maintenance costs, external costs, reduction of damages benefits, land enhancement and other indirect benefits 4. Social Equity: social impacts are for example related to risk of extremes, duration of construction, employment increase or decrease and impacts on transportation.

10 After the definition of the objectives, the steps to be undertaken for the Multi-Risk Composite Method planning are the following [7]: 1. Define a set of alternative actions or strategies, which includes structural and non-structural engineering options. 2. Evaluate the outcome risks or risk matrix containing an estimation of the risks corresponding to each particular objective (technical, environmental, economic and social) 3. Find by use of an averaging algorithm the composite risk index for technical and ecological risks (eco-technical composite risk index) and the same for the social and economic risks (socio-economic composite risk index). 4. Rank the alternative actions, using as criterion the distance of any option from the ideal point (zero risks). As shown in Fig. 4, in the two-dimensional plane with coordinates the composite eco-technical and socio-economic indexes, strategies 1, 2 and 3 are ranked using as criterion the distance of any strategy from the ideal point (0,0). Worst situation Composite Eco-technical Risk Index Strategy 1 Strategy 2 Strategy 3 0 Ideal point 0 Composite Socio-economic Risk Index Figure 4: Ranking different strategies based on eco-technical and socio-economic risks.

11 4. Conclusions Integrating environmental and social issues into the engineering water resources management and flood alleviation planning is a challenge and a shift to a new scientific paradigm. A methodology is proposed to integrate multiple risk analysis into a multiobjective planning and decision-making process. In order to assess and rank different alternative strategies for water resources management the methodology called Multi- Risk Composite Method takes into consideration four main objectives, namely. technical, economic, environmental and social. Ranking of different alternatives is based on the least distance from the ideal point of zero risk by use of two composite risk indexes: 1. the eco-technical risk, and 2. the socio-economic risk. In order to achieve sustainability, by comparing this hydro-social approach to the traditional one of engineering water resources management, not only technical reliability and cost effectiveness are taken into account but also environmental safety and social equity. 5. References [1] Bogardi, I. and H.P. Nachtnebel, Multicriteria Decision Analysis in Water Resources Management, IHP, UNESCO, Paris, 469 pp. [2] Duckstein, L. and E.Plate (eds.), 1987 Engineering Reliability and Risk in Water Resources, E.M. Nijhoff, Dordrecht, The Netherlands, 565 pp. [3] Fang, L., K.W. Hipel and D.M. Kilgour, Interactive Decision-Making - The Graph Model for Conflict Resolution, J. Wiley and Sons, N.Y. [4] Fraser, N.M., and K.W. Hipel, Conflict Analysis: Models and Resolutions, North Holland, N.Y., 377 pp. [5] Ganoulis J., Water Quality Assessment and Protection Measures of a Semi-enclosed Coastal Area: the Bay of Thermaikos, Marine Pollution Bulletin, 23, [6] Ganoulis J., Floodplain Protection and Management in Karst Areas, In: Defence from Floods and Floodplain Management, Gardiner J. et al. eds., NATO ASI Series, Vol. 299 : , Kluwer Academic, Dordrecht, The Netherlands. [7] Ganoulis, J.,1994. Risk Analysis of Water Pollution: Probabilities and Fuzzy Sets. VCH, Weinheim, Oxford, NY, 306 pp. [8] Ganoulis, J., L. Duckstein, P. Literathy and I. Bogardi (eds.), 1996: Transboundary Water Resources Management: Institutional and Engineering Approaches. NATO ASI SERIES, Partnership Sub-Series 2. Environment, Vol.7, Springer-Verlag, Heidelberg, Germany, 478 pp. [9] Ganoulis, J., Mpimpas, H., Duckstein, L. and Bogardi, I., Fuzzy Arithmetic for Ecological Risk Management. In: Y. Haimes, D. Moser and E. Stakhin (Eds.), Risk Based Decision Making in Water Resources VII, ASCE, NY, pp [10] Goicoechea, A., D.R. Hansen and L. Duckstein, Multiobjective Decision Analysis with Engineering and Business Applications. J. Wiley, New York, 519 pp. [11] Hansen, E., Topics in Interval Analysis. Claperton Press, Oxford.

12 [12] Kaufmann, A. and Gupta, M., Introduction to Fuzzy Arithmetic: Theory and Applications. Van Nostrand Reinhold, New York. [13] Klir, G. and Folger, T., Fuzzy Sets, Uncertainty and Information. Prentice Hall. [14] Moore, R.E., Methods and Applications of Interval Analysis. SIAM, Philadelphia, PA. [15] Neumaier, A., Interval Methods for Systems of Equations. Cambridge University Press [16] Plate, E., Probabilistic modelling of water quality in rivers. In: Ganoulis, J. (ed.) Water Resources Engineering Risk Assessment. NATO ASI Series, Vol. G29, Springer-Verlag, Heidelberg, pp [17] Rall, L.B, Improved Interval Bounds for Range of Functions. In: Interval Mathematics 1985, Springer-Verlag, Berlin. [18] Shafike, N.G., Groundwater flow simulations and management under imprecise parameters. Ph.D thesis, Dept. of Hydrology and Water Resources, University of Arizona, Tucson, Arizona. [19] Shresta, B.P., K.R. Reddy and L. Duckstein, Fuzzy reliability in hydraulics. In: Proc. First Int. Symp. on Uncertainty Mod. and Analysis, Univ. of Maryland, College Park [20] Silvert, W., Ecological impact classification with fuzzy sets. Ecol. Model., 96: [21] Vincke, P.,1989. L aide multicritere a la decision, Editions de l Universite de Bruxelles. [22] Zadeh, L.A., Fuzzy sets. Information and Control, 8: [23] Zimmerman, H.J., Fuzzy Set Theory and its Applications (2 nd Ed.). Kluwer Acad. Publishers, Dordrecht, The Netherlands.