property form because of lack of state system of safety control. Besides, the ...... An inventory about flood events and their respective damages is given from the ...... In case of Triangular Fuzzy Numbers (TFN) the operation is simpler and, as ...
COMMISSION OF EUROPEAN COMMUNITIES TEMPUS/TACIS PROGRAM INTERNATIONAL UNESCO CHAIR “ENVIRONMENT EDUCATION IN SIBERIA” OF ALTAI STATE TECHNICAL UNIVERSITY
RISK BASED ENVIRONMENTAL MANAGEMENT
Barnaul 2001
Risk-based environmental management / Tskhai, A.A. [et al]. Editors: Tskhai, A. A.; Ganoulis, J. – Barnaul: ―Azbuka‖ Publishing House. 2001. 227p. ISBN 5-93957-022-4 The objective of this monograph is to make an introduction into risk-based environmental modelling. Assessment of anthropogenic impact on the environment is characterized on the concrete examples. Theoretical approaches to probabilistic ecological and economic modelling of risks in nature use are presented, practical applications of the models are demonstrated. For specialists and graduates.
Authors: Tskhai, A.A.; Ganoulis, J.; Gorbachev, V.N.; Hubert, P.; Kirillov, V.V.; Mironenko, V.F.; Nachtnebel, H.-P.; Poulin, M. Responsible for issue: Belyaev, A.; Savinykh, L.; Solodky, O.
Funded by TEMPUS/TACIS Program (Commission of European Communities); Altai State Technical University © Altai State Technical University
CONTENTS INTRODUCTION .................................................................... 5 1
ANTHROPOGENIC
LOADS
AND
RISKS:
THE
ASSESSMENT OF IMPACT ON THE ALTAI TERRITORY ENVIRONMENT ..................................................................... 7 2 INDUSTRIAL RISK IN SIBERIA ...................................... 13 3 IMPACT ON AQUATIC ECOSYSTEMS IN SIBERIA: CRUCIAL
FACTORS,
ENVIRONMENTAL
EFFECTS,
ECOLOGICAL RISK ASSESSMENT .................................. 35 4 ENVIRONMENTAL RISK ................................................. 54 5 ENVIRONMENTAL MODELLING TOOLS FOR A RIVER AND ITS WATERSHED BASIN .......................................... 63 6 SOME ASPECTS OF SCALING IN HYDROLOGY ........ 82 7
FLOOD
RISK,
CONTROL
MEASURES
AND
STRATEGIES FOR RISK MITIGATION ............................. 88 8 UNCERTAINTY AND RISK IN MONITORING AND MANAGEMENT OF POLLUTED AQUIFERS ................. 105 9 RISK DEFINITION AND IDENTIFICATION IN WATER RESOURCES PROBLEMS ................................................. 122 10 RISK QUANTIFICATION IN WATER RESOURCES MANAGEMENT .................................................................. 179 11 RISK MANAGEMENT IN WATER RESOURCES PROJECTS............................................................................ 196
REFERENCES...................................................................... 216 LIST OF AUTHORS ............................................................ 226
INTRODUCTION This monograph is based on the materials of short intensive course ―Risk Based Environmental Management‖ organized within the framework of the project ―Educational Reform in Siberia for Environmental Protection‖ of TEMPUS/TACIS Programme on inter-university cooperation, held September 3 – 7, 2001 in Altai State Technical University, Barnaul (A. A. Tskhai – Introduction, Chapter 4; J. Ganoulis – Chapters 9, 10, 11; V.N. Gorbachev – Chapter 1; V.V.Kirillov – Chapter 3; V.F.Mironenko, I.V.Butakova, E.V.Likhoded – Chapter 2; H. P. Nachtnebel – Chapters 7, 8; M. Poulin - Chapter 5; P. Hubert – Chapter 6). This edition opens with Chapter 1 devoted to the assessment of anthropogenic impact on the environment and to the problem of risks in natural resources use of the region on the example of Altai Krai; many facts were pointed to. Chapter 2 tells about the peculiarities of ecological risks in connection with industrialization of Siberia. The impact on water ecosystems of Siberia, its defining factors and ecological effects in connection with basic notion of risk are characterized in Chapter 3. Mathematical notion of risk, its varieties and peculiarities for different ecological situations connected to toxic pollutants effect and pollution facts are considered in Chapter 4. Theoretical approach to hydrological processes modelling is developed in Chapters 5, 6. The problems of modelling in order to forecast and estimate flood risks, as well as considering uncertainty factor in natural ecosystems pollution monitoring are of great importance for water economy. These questions are considered in Chapters 7 and 8. On the basis of the above-said concepts and approaches it becomes possible to further formulate unified theory of risk based environmental management (Chapter 9), to give concrete examples and etc. The important application of the stated methodology is risk management in the projects connected to environment protection and natural resources use (Chapters 10 and 11). Per se this material is unique for Russian investigators due to the level of mathematical formalization and generalization what makes the publication of this book really interesting for specialists. It is necessary to mark a significant contribution of A. Belyaev, N..Dremova, M.Finadeeva, L .Metsker, L. Savinykh, O. Solodki, A. Scheglova, A. Vostrikova to preparation of the materials of Altai Annual International School on Water Resources Management for edition. In conclusion the organizers express their gratitude to Federal Programme ―Leading Research Schools‖ and to Academician Oleg F.
Vasiliev personally for financial assistance for the authors‘ participation in the activities connected to approbation of the research results received in the course of investigations. The significance of this assistance can not be overestimated in modern Russian conditions.
1 ANTHROPOGENIC LOADS AND RISKS: THE ASSESSMENT OF IMPACT ON THE ALTAI TERRITORY ENVIRONMENT Nowadays the Committee on Natural Resources of Altai Territory incorporating forestry, geological, aquatic and ecological services deals with problems of the environmental conservation. On May 17, 2000 the Russian State Committee on the Environment was abolished that resulted in reduction of the ecologist staff by 66% (compare: 109 specialists worked before reorganization and now only 38 ones are on the staff). The last reduction of staff that was in April 2001 practically liquidated regional and municipal environmental services. Thus, in Barnaul, regional center of Altai Territory, the independent Committee on the Environment doesn‘t exist at present. Of total pollutants 1058,1 th.t were discharged from point sources while 877,3 th.t (82,9%) came to treatment plants and 810,4 th.t (76,6%) of total pollutants were recovered and neutralized. 180,8 th.t were discharged to the atmosphere (17,1% of total emissions). Emergency and at one time discharges were not revealed in 2000 though only 94,1 th.t of hazardous wastes were utilized, 4,4% less than in 1999. 274 enterprises have the established standards on maximum allowable emission, 98 – temporary agreed ones. Despite some decrease in anthropogenic load on the environment, 191 enterprises increased emissions to the atmosphere from point sources by 22,6 th.t. On the average, in 2000 94 kg of hazardous wastes accounted for each resident of Altai Territory. High level of pollution was registered in Zarinsk, Biisk, Yarovoye, Barnaul as well as in Blagoveshchensky, Tabunsky, Kulundinsky and Loktevsky regions. Of 176 planned activities on emission reduction, 160 (90,9%) were realized with a consequent emission decrease by 1,0 th.t (the projected figure made up 1,2 th.t) in 2000. Besides, 18 new treatment plants were put into operation (85,7% of the scheduled ones); 115 (96,6%) activities aimed at raising operational effectiveness of treatment plants and 6 (60,0%) ones on improvement of technological processes were carried out; 7(100%) of pollution sources were eliminated; other activities made up 14 (73,7%). In 2000 year the registered industrial enterprises had 17105 point sources of pollution including unregistered ones (2687) which discharged 4,6% of all pollutants.
In Altai settlements motor transport contributes greatly to pollution as demonstrated ―Clean Air‖ action (Tab. 1.1). According to the data of state monitoring, deterioration of hydrochemical state of surface water bodies in the vicinity of Barnaul and Rubtsovsk was observed due to increased volume of discharged foul waters and pollutants from 74072, 04 t in 1999 to 76227,54 t in 2000. Table 1.1 - Index for pollutants at monitoring stations Location of sections Ob river, Fominskoye settlement Ob river, upstream and downstream Charysh river, Charyshsky collective farm Alei river, Rubtsovsk town (upstream, downstream)
1999 1,2 2,45 2,39 2,61
2000 1,02 2,52 2,62 2,14
2,38 2,51
2,84 2,71
2,62 3,08 3,98 4,21 2,74
2,54 2,87 3,4 2,35 2,76
Alei river, Aleisk town (upstream and downstream)
Barnaulka river, Barnaul, mouth Chumysh river, outskirts of Zarinsk Chumysh river, Talmenka settlement
The Altai Regional Committee on State Statistics reported that at the beginning of 2000 the inspected enterprises had 24102,5 th.t of toxic wastes. All in all, 492,2 th.t of wastes were produced and 136,7 th.t were used by enterprises; 28,9 –were recovered completely; 10,2 th.t were buried and forwarded to the sanctioned dumps. The overwhelming bulk of toxic wastes in 2000 were produced by industrial enterprises; 141,1 th.t of the most hazardous wastes fell on chemical and petroleum chemical ones; 7,0 th.t of moderately hazardous wastes – on iron works; 281,1 th.t of low hazardous wastes were produced by power plants. In the late 2000 agricultural enterprises had 1,3 th.t of unfit for use toxic chemicals, herbicides and other hazardous agricultural chemicals. The Committee on Natural Resources is responsible for control over storage and usage of pesticides and mineral fertilizers in Altai. The areas of coniferous forests in Altai Territory were reduced by 0,9 th.ha in 2000 year as a result of intensive cutting out. The plantings destruction by fires spanned 1435,9 th.ha.
Reforestation was performed on the area of 12439 ha. Trees were planted on the 8257 ha. Natural reforestation took place on the area of 3705 ha. Nowadays, great damage from fires is observed. The damaged areas have increased From 10,6 up to 14,5 ha as compared with the preceding five year period. It should be noted that in general such areas decreased from 1942 (32,2 th.ha) in 1999 to 612 (10,1 th.ha) in 2000. In other words, the forest areas damaged by fires reduced from 12,9 to 7,3 th.ha. The majority of fires (481 or 78,6%) were caused by people while the number of agricultural fires made up 11 (1,8%); fires as a result of thunderstorms – 110 (18%). These facts are indicative of insufficient agitation activity and enlightenment of population. To avoid conflagrations it is necessary to stimulate enlightenment among population and forest users. In spite of general reduction of the areas damaged by fires the total area of Rosleskhoz affected forests increased from 108,4 up to 154,4 th.ha because of two-time expansion of pest locations, from 76,5 to 140,8 th.ha to be exact. To eliminate pest locations the appropriate surface measures were undertaken on the area of 360 ha. For example, the sea buckthorn plantations and Siberian silkworm locations were treated by chemicals in Blagoveshchensky forestry farms. In Frunzensky forestry farm 17024 ha were treated by the use of aviation and biological means. Abolishment of environmental foundations brought to cutting off funding for nature protective measures. As a result, the chairmen of the Committees on Finance in many towns and regions of Altai Territory use the budget payments destined to control the environment pollution for any other purposes but not for solving environmental problems. All in all, total financial receipts obtained for pollution by the regional and local budgets in January-July, 2001 constituted 15114 th.rbls; 5284 th. rbls (34,9%) were given to carry out nature protective measures. These are some dramatic examples. The Barnaul budget received 1437 th.rbls and only 5 th.rbls (0,3%) were spent on ecological purposes; Zonalny region got 73,4 th.rbls and forwarded 3,6 th.rbls (4,9%) on ecological purposes; Zarinsk and Yarovoye towns were given 194 and 39 th.rbls, respectively. Note; nothing was spent to implement nature protection measures! In spite of the hard current situation big efforts to protect the environment are being made by the Administration and the Committee on Natural Resources of Altai Territory. The Altai Territory administration passed a resolution № 942 of 22.12.2000 on establishment of the regional state department ―On the environment conservation and natural resources reproduction‖ with the staff
of 190 members. The law of Altai Territory on ―Regional budget for 2001‖ envisages to assign 6250 th.rbls to cover the staff costs. The department is involved in: - ecological control over the sources of pollution, inspection of treatment plants operation, the observance of - emission standards on pollutant discharge and instructions on safe handling with wastes as well as environment quality standards, - ecological control over the use and conservation of lands, vegetation and animals, - inspection of realization of regional programs, plans and activities on environmental conservation; meeting the construction, operation, industrial sitting requirements. Taken together the measures mentioned above will promote improvement of ecological situation in Altai Territory. The primary aim of the Environmental Department of Altai Territory is carrying out the ecological control, state ecological examination, economical regulation of nature management and informationenlightenment activity. For 2000 and 6 months of 2001 year 4000 inspections of enterprises and organizations were made; violation in nature protection legislation was noted in 3131 cases, of which more than 2000 ones were eliminated. The materials on 900 objects were submitted to the State Ecological Examination Board (SEEB), as this takes place, 45 of them were not approved, materials on 57 objects were given back to the customers for further correction and completion. SEEB primarily deals with the following objects: - projects on filling stations construction –67, - documentation on licensing of water objects and mineral resources use – 103, - projects on agricultural products processing – 57, - projects on gas pipeline construction – 36, - projects on motorways and bridges construction – 21. To perform the State Ecological Examination 157 commissions with not on the staff experts and 171 joint ones with staff and not on the staff specialists were formed. For stabilization of ecological situation works on licensing are being continued. For example, 42 licenses were issued to carry out the activities in the field of environment conservation; 22 previously issued licenses were extended and 29 ones were terminated. In 2000 the Environmental Foundations of Altai Territory got 20,3 mln.rbls. Payments of 10 enterprises made for realization of nature
protective measures were subjected to adjustments in the sum of 1,6 mln.rbls. The prevented ecological damage for 2000 made up 1389,2 mln. rbls. In Altai there are 4 regions where the second stages of space vehicles launched from ―Baikonur‖ space port, zone Ю-30 (№ 306,307, 309, 310) fall. Total area of such a site is 2,8 th.km2. As a result of correction made by Rosaviakosmos specialists in August 2001, the area of falling has enhanced to 3,2 th. km2 ( Tretyakovsky and Charyshsky regions). It should be noted that social tension increases, especially in Ploskovsk, Novoaleisk settlements of Tretyakovsky region where sick rate is essentially higher than the region‘s center. In keeping with realization of the international agreement on nuclear arms limitation, 20 underground rocket units (СС-20 ―Satana‖) and 2 command posts were demolished. At present, the project on reclamation of the lands underwent due to 378/1,2 objects demolition is being considered and examined by the Russian Ministry of Nature. Final decisions on the project should be made immediately, otherwise the dates of land reclamation will not be realized. Much time is paid to environmental education and propaganda of ecological knowledge. Every week the regional radio broadcasts the informational ecological news. Moreover, people can weekly watch the ecological program ―Rassvet‖ on TV; the ―Vestnik of Ecology‖ and ―Kulunda Nature‖ newspapers are issued regularly. From April 15,2001 up to June 5,2001 All - Russian Days on nature protection and ecological safety were organized under ―Ecology-SafetyLife‖ motto. People in all regions were involved in trash removal from the green zones, banks and coasts of water bodies. They planted trees and put in good order their towns, settlements and villages. The ―Report on the Environmental State in Altai Territory‖ is issued annually. The 5th international medical-ecological exhibition called ―Man. Ecology. Health‖ was held in Barnaul where all the committees took part. The Altai Territory Soviet of People‘s delegates passed a law of Altai Territory on ― Safe handling with pesticides and agrochemicals‖ of 06.03.2000 as well as a resolution N 194 ― On approval of resolutions on the state natural complex reserves of regional importance‖ of 03.07.2000. In accordance with the resolution, 17 reserves gained the new status, namely, the complex national one (―Obskoy‖, ―Bolsherechensky‖, ―Zavyalovsky‖, ―Blagoveshchensky‖, ―Togulsky‖, ―Aleussky‖, ―Pankrushikhinsky‖, ―Chinetinsky‖, ―Neninsky‖, ―Urzhumsky‖, ―Volchikhinsky‖,
―Yegoryevsky, ―Kulundinsky‖, ―Mamontovsky‖, ― Gilevsky‖, ―Sokolovsky‖, ―Ondatrovy‖). As for now 33 persistent state complex natural reserves have been established in Altai Territory. In line with the law of the Russian Federation ―On especially protected natural territories‖ and the regional law ― On especially protected natural territories‖ the Altai administration passed a resolution № 251 of 06.04.2001 ―On development and location of especially protected natural areas in Altai Territory‖ aimed at regulation of unexhausted nature management and conservation of biological and landscape diversity of Altai. Currently, the Executive bodies of Altai Territory and municipal departments should jointly execute the Russian Federation Law ―On the environment conservation‖ (art. 9,10); ―On general principles of local selfgovernment in the Russian Federation‖ (art.6, 56); ―On local selfgovernment in the Russian Federation‖ (art.66, 67,71,73,74); ―The budget code of the Russian Federation‖ (art.85) to stabilize ecological situation in Altai Territory.
2 INDUSTRIAL RISK IN SIBERIA INTRODUCTION Transition to new economic mechanisms by means of all processes intensification is impossible without scientific and technical achievements, effective use of resources and decrease of losses due to accidents and traumatism. The solution of this problem requires scientifically justified approaches to organization and assurance of safety in all fields of industry, agriculture, transport and power engineering. At the same time, as practice shows, the increase of power available for society, and the use of new technologies and materials are usually followed by numerous human victims, serious moral and material loss. Undoubtedly, the problem of accidents is taking on special significance in nuclear power, chemical industry as well as under operation of the armament and defense technology equipped with powerful energy sources, high-toxic and deleterious substances. Experience suggests that underestimation of the factors mentioned above results in loss of life, equipment lay-up and environment pollution. Prevention from such accidents or decrease in loss requires well-directed activity in revealing the conditions for their occurrence, the use of estimation methods and safety increase. This work considers socio-economic issues and the strategy of Siberian cities development, and gives current methodological principles of risk in engineering systems. The system for industrial risk management in the most progressive region in Siberia, Krasnoyarsk Territory, is an example. Environmental approaches to risk assessment are given from the works conducted by Altai Technical University in reference to Altai Territory and Barnaul city. N.N.Moiseev indicated that ―to extend the history a Man should learn how to correlate his local and global activity with the Nature‘s abilities. People should realize the requirement for strict development limits and the necessity to correlate their activity with the development of biosphere. These requirements are so drastic that they can be called as environmental imperative‖. 1 SOCIO-ECONOMIC SITUATION AND THE STRATEGY OF SIBERIA DEVELOPMENT Up to the middle of the 20th century the industrial development of the world was at the expense and to the prejudice of nature. Even the
industrially developed countries with market economy started the restoration of natural resources when they improved their welfare. Thus, it can be assumed that if the fundamental improvement in socio-economic development of Russia doesn‘t take place, the degradation of habitat and natural resources potential will be aggravated. The volume of discharge, and processing and consumption wastes will reduce as the production curtails, but the specific discharge will increase. Socio-economic situation in Russia is characterized by the following changes. The decline in productivity that began in 1989 has embraced all republics and regions of Russia. Decline in standard of life reached the point when the problem of population life support was drastically dramatized. In many regions the decline in productivity reached its crucial point when the direct destruction of economic potential starts. The decline in standard of life is uneven within the country and is followed by growth of assymetry in the indices of regions social development. The regions differ in the part of population with income lower than the living wage. In Tuva, Buryatiya, Daghestan as well as in Chita, Irkutsk, Kemerovo, Tyumen regions and in Krasnoyarsk Territory this part constitutes 65-70%, and in Magadan, Rostov regions and in Stavropol and Krasnodarsk Territories it is 2 times lower. The loss of government regulation of social development resulted in essential disproportion in implementation of the state program on housing construction. Deterioration of population living conditions reflected on nation health, demographic and criminal situation. Decrease of mortality and depopulation takes place almost in the half of all republics, regions and territories. It should be noted that these processes covered primarily the main historical body of Russia: Russian North, North Western, Central, Central-Chernozem, Volgo-Vyarsk, Ural regions. The crisis and decline in productivity caused the growth of unemployment, which at present is 10 times as great as in 1991, and it continue in growth. Nowadays the process of conservation of raw material resources supported by new projects in mining industry, oil- and gas production is observed in Siberia. In so doing the majority of the projects to be implemented in Siberia and Far East do not provide the raw materials processing at the sites. It is supported by large volume of exports of Siberian raw materials as well as by specific direction of transport routes: from the source of raw materials to the ports and frontier points. Thus, it can be stated that share of exports from Siberia and Far East with preliminary processing increases.
Originally, at the beginning-middle of the 20th century the shift of productive forces to the East took place. Three stages of Siberia development were expected: establishment of transport and electric power infrastructures, development of industrial production and, finally, the advancement of research and educational institutes. It was assumed to complete the formation of the united power space including gasification of the south of Siberia; completion of transport system building, creation of food base, satisfaction of domestic requirements through the development of the own machine-constructing complex. The regional branches of the Russian Academy of Sciences were expected to form the entire scientific and educational space. For various reasons this program wasn‘t implemented. The state was unable to cope with the expensive projects of Siberia development. Therefore, large mining, raw materials and metallurgical companies such as ―LUKoil‖, ―UKOS‖, ―Siboil‘, ―SUAL‖, ―Gasprom‖, etc. are the major investors to the projects of the development of regions involved in raw materials export. At present Siberia and Far East face the need to choose the strategy of their development. In this case there are two ways of development: - extensive development of raw materials sources on the basis of currently available technological base; - innovation reconstruction of the whole technological platform including raw materials branches. The development of the first way is rather conjectural since the industrial belt constructed along the ―Transsib‖ Railroad failed in territory development management. Because this sector included mainly the military plants, it slightly mated with the raw materials one. Infrastructures constructed beyond the Urals were intended for another standard of economy management and life. Now they are functioning under overtolerance load that results in the loss of capacity and inefficient operation. Despite the fact that the consequences of the first way of development are evident, the second way is highly conjectural since the revision of the whole management system as well as of the production relations development is required. 2 INDUSTRIAL OBJECTS AND THEIR SAFETY For the last five years risk level and hazard effect due to industrial and natural accidents and catastrophes have become unacceptable for further social and economic development of Russian Federation (every year about 50th. people lose their lives and 250th. are traumatized; direct loss
constitutes 3-5% of the G.N.P., and the indirect one is 1,6-2,2 times larger, annual loss increases by 10-30%). If this problem isn‘t solved effectively in the nearest decade, the growth rate of the G.N.P. won‘t be able to compensate for the annual 8-10% loss due to accidents and catastrophes. Nowadays the problem of safe functioning of complex industrial objects takes on great significance. Technosphere is a threat to a Man. Since 1979 economic loss caused by industrial accidents has been larger than the loss due to natural catastrophes. There are about 100th. hazard production facilities, of which 2300 nuclear and 3000 chemical ones are characterized by rather high risk. The nuclear complex is supplied with ~1013 of fatal toxodoses, their quantity in the chemical one makes up ~1012 . The statistic analysis of accidents and catastrophes in Russia carried out by the state supervision service shows that the number of mortal cases increases annually by 10-25%. The situation is aggravated by the fact, that many potentially hazardous objects and productions are marked by the project resources working out. Further operation will result in sharp increase in failures caused by wear of equipment and structure damage. Over prolonged periods the concept of ―absolute safety‖ or ―zero risk‖ made up the basis for industrial enterprises operation. The ―zero risk‖ concept provides such organization of industrial object that excludes the possibility of accident. This concept has some shortcomings such as its unattainability, heavy material costs of its realization and personnel‘s inability to effective activity in case of emergency situation. Following the idea of full exclusion of accident many safe nuclearpower objects were constructed. Nevertheless, the accidents took place, and the effects were disastrous. The ―zero risk‖ concept gave way to the so-called ―acceptable risk‖ concept suggesting the ―foresee and prevent‖ principle. This concept allows for the accident and preventive measures. The ―background risk‖ concept is used in the ―acceptable risk‖ one. According to this concept there is a possibility that a man will lose his life due to an accident, crime or any other ―unnatural‖ occurrence in any region, no matter whether there are industrial objects. In statistics such category is called ―death due to unnatural reasons‖. It is evident, that the probability of death increases, if there are factors adversely affecting the human life. Therefore, individual mean statistical risk due to industrial activity is compared with this category. Individual risk is characterized by one
numerical value, i.e. the probability of death per one person in a year. It is a universal characteristic of danger for man that allows to normalize the level of acceptable individual risk. In line with the territories under consideration the universal, national (level of the country), regional and local background risks are distinguished. It is commonly supposed that there are two levels of risk: acceptable risk (the one which the society must put up with in order to get profit as a result of its activity) calling for further estimation; and unacceptable risk (it is assigned by the authorities as the maximum one, and in case of its excess, measures on its elimination should be taken). The level of acceptable individual risk has its standard only in some countries. In the Netherlands the ―acceptable risk‖ concept was legalized in 1985. According to the law the probability of death is considered to be unacceptable when it is caused by danger from technosphere of more than 10-6 (the probability of destruction of dam separating the country from sea). Under risk level of 10-6-10-8 decision is made on the basis of economic and social aspects. In Russian Federation the value of unacceptable risk makes up >10 -4, while the acceptable risk is equal to r (1) SAFETY or RELIABILITY : r (2) Loads and resistances are terms used in structural engineering. In the field of water resources engineering and environmental water quality these two variables have a more general meaning, as explained in Tab. (9.1). Failure or safety of the system may also be considered in relation to the consequences of failure, such as loss of lives or economic damage. To illustrate the concepts of loads, resistances, failures, incidents and consequences of failure, let examine the safety of an earth dam, shown in Fig. (9.1). The question is how to determine safely the height of the dam, when the level of water in the reservoir fluctuates according to the local hydrologic conditions. In this particular example, the load is the height of
water in the reservoir h and the resistance r of the system is the height of the dam H. There should be an incident or a failure when, because of a flood, the value of h exceeds H, i.e. FAILURE CONDITION : h>H on the contrary, the design will be successful and safe if we have SAFETY CONDITION : hH From the previous example we can see that "load" and "resistance" may take different meanings, depending on the specific problem we face. They can mean pollutant concentrations, water heights, receiving capacity to pollution or the height of a dam. Tab. (9.1) summarizes different definitions of "loads" and "resistances" according to the physical system they are applied to, in the context of Water Resources Engineering. Overtopping
H
h
Consequences
h
H
Time
failures
Fig. 9.2 - Risk of failure of an earth dam under hydrologic uncertainty conditions.
Tab. 9.1 Examples of "loads" and "resistances" in Water Resources Engineering. physical system hydraulic structure gate, dam, flood levee, . . . water system lake, aquifer, river, coastal area, . . .
scientific discipline civil and hydraulic engineering
"load"
"resistance"
type of failure structural failure
force,stress wind load flood rate
resisting stress dam height
water resources and environmenta l engineering
water demand pollutant load pollutant
water supply reservoir capacity receiving capacity
water shortfall
water system
hydrology
concentrati on flow rate flood rainfall
"t-years" flow rate flood rainfall
hydrologic exceedance floods
ecosystem
biological sciences
exposure
ecosystem capacity
ecosystem damage
human organism
health sciences
exposure
human capacity
health damage
water pollution
What is important, as for example for the earth dam shown in Fig. (9.2), is to take into account the consequences of an incident or failure. As shown in Fig. (9.2), in case of failure, a flood wave will be generated and propagated downstream. The loss in property and perhaps human lives caused by the flood are important parameters which need to be taken into consideration during the design of the dam. In a typical problem of failure under uncertainty conditions, we usually face three main questions which are addressed in three successive steps STEP 1 WHEN WOULD THE SYSTEM FAIL? STEP 2 HOW OFTEN FAILURE IS EXPECTED? STEP 3 WHAT ARE THE LIKELY CONSEQUENCES?
The two first steps form part of the uncertainty analysis of the system. The answer to question 1 is given by the formulation of the critical condition in Eq. (9.1), i.e,. when the load exceeds the resistance r of the system. To provide a satisfactory answer to question 2 we may consider the variables of the problem such as the load and resistance r, as nondeterministic. When time is taken also into consideration, we are referring to unsteady or time-dependent risk and reliability analysis. When loads and resistances are considered at time t constant, we speak about static risk and reliability analysis. 2.1 PROBABILISTIC RISK In a probabilistic framework, and r are taken as random or stochastic variables. In probabilistic terms, the chance of having a failure or the likelihood of failure are generally defined as risk. For example, in the case of the dam in Fig. (9.1), we will have RISK= probability of failure= P( h > H ) RELIABILITY= probability of success= P( h H ) If fuzzy logic is used, and r are considered as fuzzy numbers. Then risk and reliability are defined by means of appropriate fuzzy measures, which will be introduced later. By considering the system variables as random, uncertainties can be quantified on a probabilistic framework. Loads and resistances r previously defined are taken as random variables L and R, having the following probability distribution and probability density distribution functions FL(), fL() : load FR(r), fR(r) : resistance There are different definitions of risk in a probabilistic framework. The simpler one is the probability that load exceeds the resistance. This is the probability of failure p of one component, in a steady state system. F Risk is given by the following relation
p =P(RR
L=R f (,r)=Cte LR
L0: recharge
q 0, > 0 f ( k) exp[ ] 2 k 2
2
Independently if the inputs may be considered as deterministic or random variables, because of the stochastic character of the parameter K, the output variable h should have a probability distribution function. If this is evaluated in form of Eq. (5), then the aleatory uncertainties due to the random variation of aquifer parameter should be evaluated. The state-of knowledge stochastic modelling of aquifer flow includes multivariate normal distributions and exponential correlation function for the hydraulic conductivity random field.
One important question in the stochastic modelling of hydrological systems is the change in the spatial heterogeneity scales. Furthermore, various methods and tools have been extensively used in the past for stochastic simulation, such as - Time series analysis, filtering, krigging - Stochastic differential equations - Spectral analysis - Taylor series and perturbation analysis - Monte-Carlo simulation. 1.5 Monte Carlo simulation This is a general simulation technique which may be applied when some random variables are related with deterministic functional relationships. In the Monte Carlo method several possible realisations of a random variable would be produced, from which the statistical properties of the variable, such as mean value and variance, are obtained. The main point of the technique is to generate samples having a prescribed probability distribution function. The easiest way for doing this, is to start with samples of random numbers, which are realizations of the standard uniform random variable U. This is a random variable with a uniform probability density distribution fU(u) between 0 and 1 (Fig. 10.7).
Fig. 10.7 - The standard uniform random variable U. As shown in Fig. (10.7) the cumulative function F U(u) is the bisectrice line in the plane u-FU(u). We have
FU ( u ) = P (U u ) =
u 0
dx = u
(17)
The methods for generating random numbers with uniform probability distribution are mainly based on recursive relations in the form x k 1 (axk b)(mod m) (18) where a and b and m are non-negative integers. The Eq. (18) means that residuals of modulus m are first computed as
xk 1 (axk b) m {Int (
axk b )} m
(19)
where Int is the integer part of the number. Then random numbers between 0 and 1 are obtained by the ratio
uk 1
xk 1 m
(20)
Numbers generated by the use of this procedure are not real random numbers. They have a pattern cyclically repeated. For this reason they are called pseudo-random numbers. In order to avoid small periods of cycles,
the constants a, b and m should be given large values. Samples of pseudorandom numbers U, such as (u1, u2,...,un), are generated nowadays on modern computers by means of appropriate internal functions. Numbers generated by such procedure should be tested for statistical independence and uniform distribution. Having generated a sample of uniformly distributed random numbers uk, the corresponding number xk which belongs to a sample of probability distribution function FX(x), may be generated by use of the following relations (Fig.10.8)
Fx (x k ) = FU (u k ) = u k -1
x k = FX (u k )
(21) F (x)
F (u)
X
U
1
u
450
1
u
x
Fig. 10.8 - Relation between random variables X and U. For reliability computations, the Monte Carlo simulation technique proceeds in three steps (1) generation of synthetic samples of random numbers, following specified probability distributions. This may be done for input variables, loads and resistances (2) simulation of the system by means of a model, where values of generated random variables are taken into account (3) reliability assessment of the system by counting the number of satisfactory realisations over the total number of realisations. Thus, the probability of success, or the system reliability, may be estimated. The Monte Carlo simulation technique is a powerful tool, capable of representing complex systems with a non-linear structure. It is equivalent to the experimental methodology, in which testing of a system is performed by repetition of experiments. Therefore, the Monte Carlo simulation technique
suffers from some drawbacks as any experimental method: lack of insight in the structure of the system and difficulty in making synthesis of the results. Also, for complex systems, a considerable amount of computing may be necessary and sometimes inconsistent result could be obtained because of sampling variabilities. APPENDIX 2.1 - Definition of fuzzy numbers Fuzzy Numbers
may be formally defined as a set of ordered pairs X = {( x, (x)) : x R; (x) [ 0, 1 ]} (22) X X X and (x) represents its where x is a particular value of X X A fuzzy number
membership function. Values of the membership function are located in the closed interval [0,1]. The closer (x) is to 1, the more ―certain‖ one is
X
about the value of x.
is normal and convex when its membership A fuzzy number X function takes one maximum value equal to 1 and is always increasing to the left of the peak, and decreasing to the right. As can be seen in Fig. (10.9), there are two values of x where the membership function reaches zero, and at least one where it reaches a value of 1. A fuzzy number can be characterized by these three points and the shape of the curve defined by a pair of functions, one to the left and one to the right of the peak, since leftright symmetry is not a necessary condition. A real, or crisp number, is a fuzzy number whose elements comprise only one number with a non-zero membership value, which is equal to 1.
μ~(x) X
1 convex non-convex
h=0.5 h
X(h) x
0 1 1.20 Figure 10.9
8.60
10
Convex (a) and non-convex (b) fuzzy numbers.
Triangular Fuzzy Numbers The simplest type of fuzzy number is the triangular, that is, one having linear membership functions on either side of the peak. A fuzzy triangular number can be characterized by three real numbers: two values of x where the membership function reaches zero and one where it reaches a value of 1. Fig. (10.10) gives an example of a triangular fuzzy number (TFN). This may be described by the values of x at points x1, x2 and x3.
ì (x) ~X 1
0
x
x 1 x2
Fig. 10.10
x3 Triangular Fuzzy Number.
Thus,
= (x , x , x ) completely characterizes a triangular number. X 1 2 3
It follows that any real or ―crisp‖ number can be defined as a triangular fuzzy number, with x1=x2=x3. A more general definition and further details about fuzzy numbers may be found in Dubois and Prade (1980) and Zimmermann (1985). h-level of a Fuzzy Number The h-level set of a fuzzy number X (h), defined as
X
X (h)={x: (x) h)} X
is the ordinary set or interval
(23)
Fig. (10.9) illustrates the above definition. Referring to the Fig. (10.9), at the so called credibility level h=0.5 corresponds the 0.5-level cut, which is the ordinary set [1.2,8.6]. For h=0, the 0-level cut is [1,10]. Appendix B: Fuzzy Number Operations Extension Principle The extension principle is a method of computing membership functions of fuzzy sets which are functions of other fuzzy sets. Using this principle, which is a basic tool of fuzzy arithmetic, we can perform point-topoint operations on fuzzy sets. Let X and Y be two ordinary sets and f a one-to-one mapping from X to Y i.e. f = xy
x X, y=f(x), y Y
(24)
Function f is deterministic and can be extended to the fuzzy set situation as follows.
be a fuzzy set in X with membership function ( x) . The X X image of X in Y is the fuzzy set Y with membership function given by the Let
extension principle as follows
~ ( x); y f ( x), x X, y Y} sup{ X (25) ~ ( y) Y 0 otherwise
Arithmetic Operations on Fuzzy Numbers
~
~
Let us define two triangular fuzzy numbers A and B by the triplets
~ ~ A = (a1, a2, a3) and B = (b1, b2, b3) . We have ~ ~ A + B = (a1 b1, a2 b2, a3 b3) i) Addition: ~ ~ Subtraction: A - B = (a1 b3, a2 b2, a3 b1)
(26) (27)
Multiplication or division between two triangular fuzzy numbers does not give a triangular fuzzy number. However we can approximate them as follows iii) Multiplication
~ ~ A * B = [min (a1 * b1, a1 * b3, a3 * b1, a3 * b3), a2 * b2 ,
(28)
iv) Division
~ ~ a1 a1 a3 a3 a2 a1 a1 a3 a3 A / B = [min ( , , , ), , max ( , , , )] b1 b3 b1 b3
b2
b1 b3 b1 b3
(29)
Algebraic Properties of Fuzzy Numbers
~ ~
~
Assume that A , B and C are fuzzy numbers. The following laws hold:
~ ~ ~ ~ A + B= B+ A ~ ~
~
~ ~ ~ ~ A B=B A ~
~ ~
( A + B ) C = A +( B C ) Associativity
Cummutativity
~ ~ ~
~ ~ ~
( A B)C = A (B C )
However, subdistributivity and subcancellation is not always valid. In particular we have
~ ~ ~ ~ ~ ~ ~ A ( B C ) A B A C
~ ~ ~
( A B)C
~ ~ ~ ~ A C B C
Subdistribution
~ ~ ~ ~ ~ ~ A - B ( A + C )-( B + C )
~ ~ ~ ~ ~ ~ A /B A C /B C
Subcancellation Overestimation usually occurs because of the failure of the distributive and cancellation laws.
11 RISK MANAGEMENT IN WATER RESOURCES PROJECTS ABSTRACT The simple definition of engineering risk as the probability of failure does not reflect completely the characteristics of the physical system operating under risk. It gives just an indication about the state of safety of the system or how this would behave under some uncertainty conditions. In a more general way, we can say that engineering risk is an index characterising the degree of performance of the system. If the system is performing safely, then engineering risk tends to zero. Inversely, when risk approaches to 1, the system is likely to fail. In order to describe in more detail the behaviour of a water system under risk, some other performance indices and figures of merit will be defined in this lecture. Some of these factors are better known as resilience, grade of service, vulnerability and availability. Among the figures of merit perhaps the most important is the one incorporating the consequences of failure. The function L of consequences may be expressed in economic units (costs, benefits) or in more general terms e.g. environmental consequences or lives. For every particular numerical value of engineering risk the consequences may be evaluated. As shown in this lecture, this should be an essential element for the management of risks and decision analysis. In this lecture, the role of risk into the decision theory is briefly presented. In simple cases an objective function can be formulated. The minimization of losses or maximization of profits may be used as design criteria. For multiple objectives probabilistic or fuzzy trade-offs of various risk indexes should be considered by introducing the multi-objective decision analysis under risk. 1 PERFORMANCE INDICES AND FIGURES OF MERIT A water resources system operating under risk should be designed in such a way that safety prevails during its life-time. On the other hand, the notion of safety does not imply that the system is risk-free. Because of uncertainties a value of risk always exists; for engineering purposes this should be maintained as small as possible. However, the engineering risk as an index characterizing the state of safety of the system is not sufficient to indicate all the properties of a system under risk conditions. This is why performance indices and figures of merit have been introduced.
-Performance indices (PIs) are measures indicating how the system performs when external conditions create adverse effects such as extreme loading. During some time periods incidents may occur which would render the system unable to accomplish its function. These incidents are not catastrophic events, but the system may possibly recover. Characteristic examples of the behaviour of a hydrosystem under risk is a pipe distribution system which can deliver for some time only part of the demand, or a sewer system overflowing at certain time periods. PIs should provide quantitative information about the incident related properties of the system. Duckstein and Parent (1994) report nine different incidentrelated PIs which may be calculated at every time t PI1: grade of service PI2: quality of service PI3: speed of response PI4: reliability PI5: incident period PI6: mission reliability PI7: availability PI8: resilience and PI9: vulnerability. The latter two PIs are of special interest to describe the characteristics of the system in cases of incident or failure -Resilience: this is a measure of the reaction time of the system in order to return to safe operating conditions. A system of high resilience responds quickly to a given incident and returns quickly to normal state. A low resilience system needs long times to recover. -Vulnerability: it is an index measuring the degree of damage which an incident causes to a system. It is known that highly sophisticated systems are the most vulnerable: an incident could cause complete destruction to its components. Examples of high vulnerable systems are complex electronic devices, sophisticated computer systems and structures such as arch dams with very small safety factor. -Figures of merit (FMs) are defined as functions of the performance indices. In a sense they are considered as "super criteria." If PI1, PI2, . . ., PIk are different PIs, then a FMi may be expressed as FMi = FMi (PI1, PI2, . . ., PIk) Two FMs are of particular interest (Duckstein and Plate (eds.), 1987) a. sustainability (SU) and b. engineering risk (RI) Sustainability is a combination of high resilience and low vulnerability. Engineering risk may be generally expressed by a joint probability distribution over all possible FMs. For example risk may be defined as the probability of having a given reliability and resilience. A special case is to define the engineering risk as the complement of the reliability or as the probability of failure. Economic consequences, such as costs and benefits may be expressed as function of risk.
2 BASIC DECISION THEORY 2.1 Main Elements of Decision Making Decision theory is concerned with alternative actions that an engineer or a decision maker should undertake under different environmental conditions. As environment we mean not only the physical environment but also economic, social, political or legal conditions. There are three basic elements in a decision making situation (Berger, 1985) (1) Candidate alternatives or alternative actions, designated as ai. These are alternative design solutions, which engineers control and can select as candidate solutions to the problem. Because of various limitations, such as technological or modelling constraints, it is not possible to find all possible alternatives. This means that the set {ai} is non exhaustive. However, the members of the set {ai} are mutually exclusive. Any combination between ai may be considered as a different alternative. (2) States of nature noted as {i}. These are environmental conditions in which any action ai should operate. Such conditions are called "nature". In a decision-making situation nature can include technical, physical, political, economic and social considerations. These different conditions are not significantly influenced by the actions a i, but affect significantly the consequences. The members of the set {i} are mutually exclusive and exhaustive. (3) Outcomes, which are the consequences associated to an action and a state of nature. For every alternative action ai, given a state of nature j an outcome Yij may be obtained. For every combination of action and state of nature, several measures of an outcome are possible. These may be expressed as risks, costs, environmental impacts, social values, etc. Take, for example, the extension of an existing wastewater treatment plant in a big city, in order to remove nitrates. In view of different technological processes, which are available for nitrate removal, the following alternative actions should be taken: a1 : bio-denitrification a2 : ion exchange a3 : blending of water a4 : combination of a1 and a2
a5 : cancel the program a6 : delay the decision concerning a1, a2 and a4 to obtain more information. We may observe that the list of a1 - a6 is not exhaustive and that a1 a6 are mutually exclusive. Every candidate action ai may be described by a set of variables called control variables. For example, a1 depends on the amount of oxygen used and the type of bacteria. Action a 3 is defined by the proportion of two different types of water, such as groundwater and surface water. Now, because of the particular size of the installation, there is uncertainty about the efficiency of each of the processes. We should distinguish three different states of nature, such as 1 : low efficiency 2 : medium efficiency 3 : high efficiency 1, 2, 3 are mutually exclusive and exhaustive. For every combination of an alternative ai and a state of nature j we obtain an outcome Yij. This relates to wastewater with a certain amount of nitrates. Different measures may be used to describe each outcome, such as the cost and environmental impact. Actions {ai}, states of nature {i} and outcomes {Yij} may be represented in form of a decision tree (Fig. 2.1) or a decision table (Fig. 11.2). A decision tree has two types of nodes (1) the decision nodes, from which alternative actions begin and (2) the chance nodes, which are the origin of the states of nature (Fig. 11.1).
CHANCE NODE
1
Y12
2
DECISION NODE
a1
i
Y1i
a2
ai
Actions a i
Fig. 11.1
Yij
j
States of Nature
j
Outcomes
Yij
Elements of a decision tree.
If the number of actions and states of nature is great, the decision tree becomes complicated. A matrix representation may be preferable in such case (Fig. 11.2).
States nature Actions a1 a2 a3 . . . ai .
of
1
2
3
.
k
.
Y11 Y21 Y31 . . . Yi1 .
Y12 Y22 Y32 . . . Yi2 .
Y13 Y23 Y33 . . . Yi3 .
. . . . . . . .
Y1k Y2k Y3k . . . Yik .
. . . . . .
Fig. 11.2
.
Elements of a decision matrix.
From the above elements, two considerations are important in a decision problem (1) Uncertainties (2) Preferences or Criteria. Combination between (1) and (2) gives the decision rule which is the tool for taking the final decision. In relation with different types of uncertainties, we should distinguish four main categories of decision situations. (1) Decision under certainty: There are different alternative actions and for each alternative only one outcome occurs with certainty. This is the case, when only one state of nature is possible and one outcome is obtained for every alternative action. In effect, the decision matrix of Fig. (11.2) reduces to a single column. The selection of the best alternative may be based on ranking the outcomes in order of preference and choosing the most preferred outcome. The problem in this case consists of ranking the outcomes according to a preference. (2) Decision under risk: Different states of nature may exist with known objective probabilities. For every action ai and state of nature j the engineer can deterministically identify the outcome Yij. This case may be represented by the decision tree shown in Fig. (11.1) or by the decision matrix of Fig.
(11.2) except that objective probabilities P k associated to the states of nature k should be added. (3) Decision under uncertainty or imprecision: The decision maker can evaluate the outcome, given an alternative action and a state of nature, but he is not able to express objectively and quantitatively the probabilities of the states of nature. The problem is to select the optimal alternative ai under such imprecise conditions. (4) Decision under conflict: The states of nature represent situations where an opponent tries to maximize his own objectives. This is the topic of game theory (Fraser and Hipel, 1984). 2.2 Decision Criteria The different criteria or preferences we can use in order to define a decision rule depend on personal attitudes but also on the type of the decision problem in relation with different situations of uncertainties. The most complicated case for decision making is when no objective information is available about the occurrence of the states of nature. This is the case of decision making under uncertainty. 2.2.1
Decision Making under Uncertainty
To clarify the discussion let us consider the example (1) of water supply in Athens, formulated slightly differently. Example 1 After a severe drought in 1993, to ensure the water supply of Athens, Greece over the next year, the following alternative actions have been considered: a1 : transport of water by tankers a2 : transport of water by trucks a3 : drilling of new wells. Three different states of nature are taken for autumn 1993: 1 : Wet period (W) 2 : Medium precipitation (M) 3 : Dry period (D) Due to a severe drought over the past seven years if was difficult to quantify the probabilities of the states of nature.
The various costs, in billions of Drachmas (Dra), associated to various combinations of actions and states of nature are given in Tab. (11.1). Tab. 11.1 (1).
Economic loss matrix (in billions of Dra) for the example
States of Nature
1 W
2 M
3 D
Actions a1 : transport by tankers a2 : transport by trucks a3 : new drillings
2.5 0.5 0.2
3 4 2
5 7 10
In the costs not only expenses for infrastructure are included (e.g. pumping the water from tankers and transportation to the water treatment plant) but also operation costs and economic losses in case that water supply is still not sufficient (e.g. the combination of new wells and a dry season). We can distinguish two different decision attitudes ranging from the more pessimistic (MINI-MAX or MAXI-MIN) to the more optimistic (MAXI-MAX or MINI-MIN) point of view. The Pessimist: (MINIMAX or MAXIMIN) The decision maker is pessimistic or conservative, believing that the worst can happen. If we consider losses, then he first looks at the maximum loss (worst case) and then he tries to minimize it (Tab. 11.2). Using this rule, the action a1 (transport by tankers) will be chosen. If we have gains or utilities instead of losses, then the pessimist tries to maximize the minimum utility (MAXIMIN rule).
Tab. 11.2 Illustrative economic loss matrix (in billions of Dra) and decision rules under uncertainty. States of nature
Actions
W
M
D
a1
2.5
3
5
a2 a3
0.5 0.2
4 2
7 10
Pessimist or MINIMAX
Optimist or MINIMIN
Row Maxima
Row Minima 2.5
5 7 10
0.5
0.2
The Optimist: (MINIMIN or MAXIMAX) An optimistic person thinks that nature works with him. In case of losses, for every action, he thinks the minimum loss will occur (best case). Then he will take the decision which minimize the minimum particular loss (Tab. 11.2). For this example, the action a 3 (new wells) will be chosen. In case of benefits or utilities, the optimistic decision maker will try to maximize the maximum particular benefit. This is the maximax rule. The Regretist: Loss of Opportunity This is the person who has the attitude to compare the difference between the outcome he actually realizes and the maximum he could have realized with the best possible action under the particular state of nature. This difference is called the degree of regret or loss of opportunity. For example, if the state of nature Wet is considered in Tab.(11.1) and action a3 is selected, the regret is 0. However, if a2 or a1 had been selected, the excess of cost or the loss of opportunity would be respectively 0.3 and 2.3 units. The objective now is to minimize regret. To do that, first the original economic loss or utility matrix is rewritten with the outcomes representing the losses due to imperfect prediction. Such a matrix is called a regret matrix. For the example of Tab. (11.3) the regret matrix is written as follows (Tab. 11.3).
Tab. 11.3
Regret matrix (in billions of Dra) of Example (1).
States of nature
Row maxima
Actions
W
M
D
a1: tankers
2.3
1
0
2.3
a2: trucks
0.3
2
2
2
a3: wells
0
0
5
5
Suppose now that we would like to minimize maximum regret. This is the MINIMAX regret criterion, which guarantees a lower limit to the maximum regret. Using this criterion, first the maximum regret for each row is recorded (Tab. 11.3). The action a2 (transport by trucks) is selected, which corresponds to the minimum value of regret, in the column on the righthand side of the regret matrix (Tab. 11.3). The outcomes in the regret matrix are also called opportunity costs. 2.2.2
Decision Making under Risk
Suppose now that a hydrologic analysis is made from available data over the past 100 years. Classification of the past 100 autumns has shown that 60 were wet (W), 30 were medium (M) and 10 were dry (D). If we suppose that there is no reasonable evidence that the future will be radically different from the past we assign the probabilities of the different states of nature 0.6, 0.3 and 0.1 respectively. The decision tree shown in Fig. (11.3) incorporates the probabilities P(1) = 0.6, P(2) = 0.3 and P(3) = 0.1.
a1
a2
P( 1 )= 0.6
2.5
P( 2 )= 0.3
3
P( 3)= 0.1 P( 1 )= 0.6
0.5
P( 2 )= 0.3
4
P( 3)= 0.1 a3
7
P( 1 )= 0.6
0.2
P( 2 )= 0.3
2
P( 3)= 0.1
Fig. 11.3
5
10
Decision tree under risk (Example 1).
For every action, the mean expected cost may be evaluated as E(L1) = 0.6(2.5) + 0.3(3) + 0.1 (5) = 2.9 E(L2) = 0.6(0.5) + 0.3(4) + 0.1 (7) = 1.3 E(L3) = 0.6(0.2) + 0.3(2) + 0.1(10) = 1.6 Since E(L2) is the minimum expected cost, the action a2 (transport by trucks) should be preferred. In case of benefits instead of costs, the decision rule becomes the maximum expected benefit. 2.2.3
Discontinuous Decision Problems
A more general presentation of the decision theory and multiobjective analysis is given in the following section. A simple case occurring in for decision problems is the dichotomy between two and alternatives: (a1) taking an action and (a2) none at all. To these two possible actions a1 and a2 may correspond two characteristic failure modes or states of nature 1 and 2 (Rubinstein, 1986). For example, a decision is to be taken on whether or not it is better to build a flood level for the protection of an inhabited area (Duckstein and Bogardi, 1991). For a given protection level from floods Qo, we have two possible states of nature: (1) Q Qo : failure and (2) Q < Qo : safety. For
any combination between two alternative actions and two states of nature there are annualized protection costs and losses due to floods. In this case we have a discontinuous economic loss function, which may displayed in matrix form (Tab. 11.4).
Tab. 11.4 States of nature Actions a1 : protect a2 : not to protect Probability
Discontinuous economic loss function. 1 : Q Qo failure
2 : Q < Qo safety
C
C
K
O
P
1-p
where C : is the annualized protection cost, and K : the annualized flood losses If the information on the states of nature is not perfect, we introduce the probabilities of occurrence of these states. In Tab. (11.4) we assume p to be the probability of failure and (1-p) that of safety. The economic losses are Action a1 : L (a1) = C p + C (1-p) = C Action a2 : L (a2) = K p + 0 (1-p) = K p Action a1 (protect) will be preferred if L (a1) < L (a2) and action a2 (do not protect) will be better if L (a2) < L (a1) In more general cases we may have i possible actions and k states of nature. Uncertainty, which includes aleatory or natural randomness and epistemic or controllable uncertainties may be expressed by probabilities
pk. Alternatively, the fuzzy set analysis or a mixed fuzzy set / probabilistic approach may be used. These are illustrated in the following examples. Example 2 In summer 1993 water supply reserves for the metropolitan area of Athens, Greece have been estimated to be sufficient to meet the demand only for the next few months. The main cause for this water deficiency was a multi-years drought. Having estimated between the cost of taking action (e.g. transport of freshwater by tankers or trucks) and the economic losses from possible failure to meet the demand, find the optimal decision. The key issue to the problem was whether or not precipitation in autumn would be sufficient to replenish the water reservoirs and satisfy the demand for the next hydrological year. We could assume three possible states of nature ranging from the most pessimistic to most optimistic scenario. 1 : weak precipitation will occur 2 : normal precipitation 3 : strong precipitation To simplify it, we would assume two cases or states of nature 1 : weak rainfalls (W) 2 : strong rainfalls (S) Assuming p to be the probability for weak-precipitation and (1-p) that of strong precipitation we should write the economic loss matrix as Tab. 11.5 States of nature
Economic loss matrix for the example (2). 1 : (W)
2 : (S)
a1 : Take action a2 : Do not take further action
C
C
K
0
Probabilities
P
1-p
Actions
where C is the cost for taking action and K the economic losses in case of failure. Let suppose that K>>C for example K=10 C. The opportunity losses for the case a1 are (1): L (a1) = p C + (1-p) C = C For the case a2, we have (2): L (a2) = p K +(1-p) 0 = p K Action a1 should be preferable if L (a1) < L (a2) or C < p K or p > C/K = 1/10 rom hydrological data it should be estimated that the probability for having weak precipitation would be less than 1:10. This means that L(a 2) < L(a1) and the action a2 is preferable. Example 3 Examination of samples of groundwater has indicated that contamination of groundwater has occurred from an industrial disposal site. The extent of groundwater pollution is such, that there is risk of pollution in the river (Fig. 11.4).
DISPOSAL SITE
PUMPING WELLS
GROUNDWATER FLOW
RIVER
Fig. 11.4
Groundwater and river pollution from an industrial disposal site.
A decision has to be taken, whether or not to undertake the drilling of a series of pumping wells in order to reduce the risk of water pollution in the river. Results from mathematical modelling of groundwater flow, including conditional simulation, turning bands and random walks, has indicated the probability of river pollution. The risk of pollution p 1 with pumping wells has been found to range between 4x10 -8 to 6x10-8, although there is more risk of contamination p2, ranging between 5x10-3 to 8x10-3 if no action is taken. Risk is here the probability that the concentration of chemicals in the river Criver exceeds the maximum allowable by the standards, Cm, i.e. RISK = P (Criver > Cm) Because of the uncertainties, both risks p1 and p2 may be taken as triangular fuzzy numbers. We denote this as p 1 = (4, 5, 6) x 10-8 p 2 = (5, 6, 8) x 10-3 Also the protection C and the damage costs K, due to a possible pollution of the river, should be considered as fuzzy numbers. We have = (3, 4, 5) x 104 US $ C and
= (5, 6, 10) x 106 US $ K both in form of annualized costs. In this situation we have two possible actions a1 : undertake the river protection works, and a2 : do not act. Two states of nature exist, as 1 : pollution of water in the river 2 : no pollution. The decision problem may be represented as a decision tree (Fig. 11.5). By use of fuzzy arithmetics (see Chapter 2) we can estimate the fuzzy opportunity losses for actions a1 and a2 as
(a1) = C p 1 + C (1- p 1 ) = C = (3, 4, 5) x 104 L p 2 + 0 (1- p 2 ) = K p 2 = (a2) = K L
={(5, 6, 10) x 106}.{(5, 6, 8) x 10-3} = (2.5, 3.6, 8.0) x 104
1
~ C
pollution a1 : protect
2 no pollution
1 a2 : do not protect
~ C ~ K
pollution
2 no pollution
Fig. 11.5
0
Decision tree representation of the river pollution problem.
To compare two fuzzy numbers, we use the definition of a fuzzy mean.
is the triangular fuzzy number (x1, x2, x3) then its fuzzy mean is X ) x1 x2 x3 FM( X 3 Taking the FM( L (a1)) and FL( L (a2)) we have If
(a1)) FM( L or
3 4 5 (a 2 )) 2.5 3. 6 8 4. 7 4 FM( L 3 3
(a1)) < FM ( L (a2)) FM ( L As a conclusion, the action a1 (protect) is preferable on a purely economic basis. Considering the most confident values C = 4 x 104 , K = 6 x 106 , p2 = 6 x 10-3
we have, as for the case of Eqs. (5.28) and (5.29) L (a1) = C = 4 x 104 L (a2) = K p2 = 3.6 x 104 or L (a2) < L (a1) Thus, the action a2 (do not protect) is preferable. It is interesting to note that, if uncertainties were not taken into account as fuzzy numbers, the decision may have been the opposite. This example illustrates the fact that preference may be influenced by the consequences (amount of money). Therefore the form of the relation between the utility and the amount of monetary values (utility function) may reflect the attitude of the decision maker against the risk. Three different attitudes may be distinguished (Fig. 11.6) (i) risk adverse (ii) risk indifferent (iii) risk seeking
1
Utility function Risk indifferent
Risk adverse
Risk seeking 0 0$
Fig. 11.6
100$
Monetary value
Different forms of the utility function.
The fundamental question is how to determine utilities given several measures of outcomes. Utility theory is a general methodology to determine numerical values of utilities given different possible outcomes in a decision making situation. Empirical relations have been proposed by several scientists in the past. D. Bernoulli (1730) has proposed the following formula u(A) = log A, where A is a certain amount of money and u(A) the utility function. Buffon (French naturalist), stated that if one adds an amount a to an existing sum of money A then u(a) is given by
u(a) (1 / a) (1 / (A a))
Modern utility theory has been developed on an axiomatic basis by Von Neumann and Mongasten (1947). More details may be found in the literature ( Raiffa, 1968). 3. MULTIOBJECTIVE DECISION ANALYSIS Preferences or decision criteria Yj are not objectively defined; they rather reflect what the decision maker wants. From what has been exposed previously in this Chapter it may be concluded, that the prevailing preference under risk is the maximization of the expected utility. Preferences or decision criteria constitute the objectives, which have been formulated in Section (2). Following the systems approach, an objective Yj is a function of the decision variables x1, x2,..., xn . This may be written as Yj=fj(x1, x2,..., xn) During the last decade it became more and more evident that engineering decisions are subject to multiple objectives. In environmental engineering, for example, the treatment and disposal of sewage is subject not only to minimization of environmental impacts but also to minimization of costs, minimization of adverse reaction of environmentalists and possibly others. These objectives are usually conflicting. Improvement of one is obtained with deterioration of others. In the case of a wastewater treatment plant, for example, even if we restrict ourselves only to economic objectives, these could be in conflict, whether they are defined by the owner or operator of the plant or by the regulatory agency. The introduction of the utility function is a way to reduce a multiobjective decision making problem to another with only one objective. The latter is expressed in monetary units. Such a transformation is of course practical but has many limitations: it is not unique, it depends on the individual experience of the engineer and it may be wrong. In Multiobjective Decision Analysis (MDA) the question is not to obtain an optimal solution as in the case of One Objective. Instead of an optimum solution we speak about a "non-inferior" or "non-dominant" solution. This is a solution for which all objective functions are improved. Otherwise no other solution can improve one objective without causing a degradation to at least another. Let us consider, for example, the problem of maximixing two conflicting objectives Y1 and Y2 subject to a set of constraints gj(x1, x2,..., xn) = 0 j = 1, 2, .., m
Each couple of values Y1 and Y2 that satisfy the constraints lies within the feasible region or feasible space (Fig. 11.7). This region is limited by a curve ABCD called as feasibility frontier. This is the set of "noninferior" or "nondominated" solutions. Every decision vector on this curve is defined by a maximum value of the objective Y 2 given a value of the objective Y1. This particular solution is "optimal" in the sense that there can be no increase in one objective without a decrease in the value of the other objective. A selection of one particular between the non-inferior solutions depends on the preferences of the decision maker. This may be indicated by a family of iso-preference or indifference curves (Fig. 11.7). The optimal solution is defined by the point B on the feasibility frontier that has the maximum level of preference. Y2 A
I1 I3
Iso-preference or Indiferrence Curve
I2 B
Feasibility Frontier Feasible Region
C
Nondominated Solution
D
Y1
Fig.11.7 Nondominated solutions for a two-objective problem. In planning problems a general class of methodology has been developed to rank different alternatives with various conflicting objectives under risk. This is called Multi-Criterion Decision Making (MCDM) (Goicoechea et al., 1982). One of the methods which is very promising is the Composite or Compromise Programming. First, trade-offs between objectives may be done in different levels to obtain some composite economic or ecological indicators. When data are imprecise or missing the fuzzy set theory is very useful (Woldt et al. 1991, Dahab and Lee, 1991). Then, ranking between different strategies or options may be done using different techniques, as the one based on the minimum composite distance from the ideal solution (Fig. 11.8) (Stansbury et al., 1991).
Worst situation 1 Strategy 1
Composite Ecological Index
Strategy 2
Strategy 3
0 Ideal point
Fig. 11.8
0
Composite Economic Index 1
Ranking between different options expressed in terms of economic and ecological indexes.
REFERENCES for the Chapter 2: 1. 2. 3. 4. 5.
6. 7.
Izmailov V.N. Industrial and ecological safety, risk management; M., 1998-461p Catastrophes and education. Edited by Vorobyev Yu.L.; 1999.177p Malkov A.V Modern industrial objects and their safety. In: ―Ecology and Environment of Russian‖ journal, 2001.- 33-34pp Alymov V.T., Krapchatov V.P., Tarasova N.P. Analysis of industrial risk, M.;Krugly stol (Round table), 2000. Issues of population and territory protection from emergency situations. Works of the All-Russian Conference, Krasnoyarsk: KSTU Pbl., 1997.- 271 p Belov P.G. Theoretical principles of system engineering safety. M.:SSTL ―Safety‖, 1996- 424 p. Kukin P.P., Lapin V.L., et al. Safety of industrial processes and enterprises, M.:Vysshaya shkola‖, 2001- 318 p.
for the Chapter 4: 1. 2. 3.
4.
Izmalkov, V.I.; A.V.Izmalkov. Safety and risk under industrial impact. P.1, 2. M; 1994 Alymov V.T., Krapchatov V.P., Tarasova N.P. Analysis of industrial risk, M.;Krugly stol (Round table), 2000. Protsenko, A.N.; Makhutov, N.A.; Artem‘ev, A.Ye. Population and environment safety in Moscow: study and management // Safety problems under emergency situations. Ed. 2, M.: UISTI, 1997 Kiselev, Ye.Ye.; Fridman, K.B. Risk for health. Approaches to the use in medical and ecological study, and environment quality management: Technical manual. International Institute on risk for health, 1997
for the Chapter 5: 216
1.
2.
3.
4.
5.
6.
7.
8.
9.
Billen G., Servais P., (1989). Modélisation des processus de dégradation bactérienne de la matière organique en milieu aquatique. In: Micro-organismes dans les écosystèmes océaniques, Masson, 219-245. Brisson N., Mary B., Ripoche D., Jeuffroy M., Ruget F., Nicoullaud B., Gate P., Devienne-Barret F., Antonioletti R., Durr C., Richard G., Beaudoin N., Recous S., Tayot X., Plenet D., Cellier P., Machet J., Meynard J., Delécolle R. (1998). STICS : a generic model for the simulation of crops and their water and nitrogen balances. 1- theory and parameterisation applied to wheat and corn. Agronomie 18,311-346. Even S., Poulin M., Garnier J., Billen G., Servais P., Chesterikoff A., Coste M., (1998). River ecosystem modelling : application of the Prose model to the Seine river (France), Hydrobiologia, Vol. 373-374, 27-45. Gomez E., Ledoux E., (2000). Modélisation intégrée des écoulements et du transfert des itrates sur le bassin de la Seine. Rapport d‘activité du Programme PIREN-Seine, UMR CNRS 7619 Sisyphe Paris Jussieu. Garnier J., Billen G., Coste M., (1995). Seasonal succession of diatoms and chlorophyceae in the drainage network of the Seine river : observations and modelling, Limnologie and Oceanography, Vol. 40(4), 750-765. King D., Le Bas C., Jamagne M, Daroussin H.R. et J., (1995). Base de données géographique des sols de France à l‘échelle du 1/1000000. Notice générale d‘utitlisation. Rapport technique, UNRA. Service d‘étude des sols et de la carte pédologique de France. Lancelot C., Mathot S., Owens N.J.P., (1986). Modelling protein synthesis, a step to an accurate estimate of net primary production : Phaeocystis pouchetii colonies in Belgian coastal waters, Marine Ecology Progress Series, Vol. 32, 193-202. Ledoux E., Girard G., Villeneuve J.P., (1984). Proposition d‘un modèle couplé pour la simulation conjointe des écoulements de surface et des écoulements souterrains sur un bassin hydrologique. La Houille Blanche, 101-110. Poulin. M., Even S., Billen G., Mouchel J.M., Garnier J., Levassor A., Leviandier T., 1998, Chapitre « Modèles », dans : « La Seine 217
en son bassin : Fonctionnement écologique et activité humaine, Meybeck M. Editeur, ELSEVIER, pages 679-717. 10. Poulin. M., Even S., Mouchel J.M., Billen G., Garnier J., Levassor A., Leviandier T., de Marsily G., 1999, Models of a river system. The Piren-Seine Program, in « Advances in Environmental and Ecological Modelling», Blasco F., Weill A., Editors, ELSEVIER, pages 17-45.
for the Chapter 6: 1. 2.
Raudkivi, A.J. (1979) Hydrology. Pergamon Press, New York. Remenieras, G. & Hubert, P. (1990) Hydrologie. In Encyclopedia Universcilis, vol. no XI, 796-806. 3. Schertzer, D. & Lovejoy, S. (1986) On the dimension of atmospheric motion. Turbulence and chaotic phenomena in fluids. Ed. by T. Tatsumi , North Holland, 505-508. 4. Schertzer, D. & Lovejoy, S. (1987) Physical modeling and analysis of rain and clouds by anisotropic scaling and multiplicative processes. J. Geophys. Res., 92, (D8), 9693-9714. 5. Schertzer, D. & Lovejoy, S. (1991) Scaling nonlinear variability in Geodynamics: Multiple singularities, observables, universality classes, nonlinear variability. In : 6. Geophysics, Scaling and Fractals, ed. by D. Schertzer and S. Lovejoy , 41-82, Kluwer, Dordrecht. 7. Tessier, Y., Lovejoy, S., Hubert, P., Schertzer, D. & Pecknold, S. (1996) Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions../. Geophys. Res., 101, (D21), 26427-26440. 8. Turcotte, D.L. and Greene, L. (1993) A scale-invariant approach to liood-irequenc} analysis. Stochastic Hydrol. Hydraul., 7, 33-40. 9. Bendjoudi, H. & Hubert, P. (1998) A propos de la distribution statistique des cumuls pluviometriques annuels. Faut-il en finir avec la normalite ? Rev. Sci. Eau, 4, 617-630. 10. Hubert, P. & Carbonnel, J. P. (1988) Caracterisation fractale de la variabilite et de 1'an-isotropie des precipitations intertropicales. C.R. Acad. Sci. Paris, II (307), 909-914.
218
11. Hubert, P. & Carbonnel, J.P. (1989) Dimensions fractales de 1'occurrence de pluie en climat soudano-sahelien. Hydrologie Continentale , 4, 3-10. 12. Hubert, P., Friggitt, F. & Carbonnel, J. P. (1995) Multifractal structure of Rainfall Occurrence in West Africa. In New Uncertainty Concepts in Hydrology and Water Resources , ed. by Z.W. Kundzewicz , 109-113, Cambridge University Press, Cambridge (UK). 13. Ladoy, P., Schmitt, F., Schertzer, D. & Lovejoy, S. (1993) Analyse multifractale de la variabilite pluviometrique a Nimes. C.R. Acad. Sci. Paris, II (317), 775-782. 14. Lovejoy, S. & Schertzer, D. (1986) Scale invariance, symmetries, fractals and stochastic simulations of atmospheric phenomena. Bull. of the AMS, 6'7, 21-32. 15. Lovejoy, S., Schertzer, D. & Tsonis, A.A. (1987) Functional boxcounting and multiple elliptical dimensions in rain. Science, 235, 1036-1038. 16. Mandelbrot, B.B. (1977) The Fractal Geometry of Nature, Freeman, San Francisco. 17. Olson, J. (1996) Validity and applicability of scale-independant, multifractal relationship for rainfall../. Atm. Res. , 42, 53-65. 18. Pandcy, G., Lovcjoy.S. & Schertzer. D. (1998) Multifractal analysis of daily river flows including extremes for basin of five to two million square kilometres, one day to 75 years. J. ofllydrol. , 208, 62-81.
for the Chapter 7: 1. 2.
3. 4.
Ang, A.H. and W.H. Tang (1984) Probability concepts in engineering, planning and design. Vol.1 and 2.J. Wiley, NY. Duckstein L. and E.J. Plate (1987) Engineering reliability and risk in water resources. Martinus Nijhoff Publishers, Dordrecht, The Netherlands. Henley, E.J. and H. Kumamoto (1981). Reliability Engineering and risk assessment. Prentice Hall Publ. Englewood Cliffs, NY. Ribamod, Final Workshop Proceedings, R. Casale et al. Published by the European Commission. RIver BAsin MODelling Management and Flood Mitigation. ENV4-CT96-0263 219
5. 6.
7.
Schulz, E.F., V.A. Koelzer and K. Mahmood (1972) Floods and Droughts. Water Resources Publications. Fort Collins, CO, USA. UNDRO (1991) Office of United Nations Desaster Relief Coordinator. Mitigating natural disasters: phenomena, effects, and options. A manual for policy makers and planners. UN. NY,USA. Vose, D. (1996) Quantitative risk analysis. J. Wileyand Sons. Chichester.
for the Chapter 8: 1.
2.
3.
4.
5.
6.
7. 8.
Bardossy A., H.P. Nachtnebel: Effect of the observation Geometry on Groundwater Solute Transport Modeling. Proc. Int. Symposium on Contaminant Transport in Groundwater, Stuttgart, FRG, 1989. Boyd, S., A. Jones, A. Knaus, and C. McGrath. 1986. Drinking water: A community action guide . Concern, Inc., Washington, DC. Brumaster, D.E. 1981. "Contamination of groundwater by toxic organic chemicals." Report prepared by the Council on Environmental Quality, Washington, DC. CAST. 1987. Health issues related to chemicals in the environment: A scientific perspective. Comments from CAST. Council for Agricultural Science and Technology, Ames, IA. 25 pages. Chu Wen-Sen, E.W. Strecker, D.P. Lettenmaier: An Evaluation of Data Requirements for Groundwater Contaminant Transport Modeling; Water.Res.Research, Vol. 23, No. 3, p. 408-424, (1987). Cohen, S.Z., S.M. Creeger, R.F. Carsel, and C.G. Enfield. 1984. "Potential for pesticide contamination of groundwater resulting from agricultural uses." In : "Treatment and Disposal of Pesticide Wastes," (Edited by: R.F. Krueger and J.N. Seiber), pages 297325, ACS Symposium Series No.259 , American Chemical Society, Washington, DC. Federal Register , Volume 50, Issue 219, page 46930. November 13, 1985. Journel A.G., C.J. Huijgbregts: Mining Geostatistics; Academic Press (1978).
220
9.
10.
11.
12.
13.
14.
15.
Konikow L.F., J.D. Bredehoeft: Computer Model for Twodimensional Solute Transport and Dispersion in Groundwater; US Geological Survey, Reston, VA, (1978). National Academy of Sciences. 1977. Drinking Water and Health . Chapter 6, Volume I. National Academy of Science, Washington, DC. National Research Council. 1983. Risk assessment in the federal government: Managing the process. National Academy Press, Washington, DC. 191 pages. Rao, M. P., and P.S.C. Rao. 1987. "Organic pollutants in groundwater: 1. Health effects." Soil Sci. Fact Sheet SL 54, Institute of Food & Agric. Sci., Univ. of Florida, Gainesville, FL. Smith L., F.W. Schwartz: Mass Transport; Role of Hydraulic Conductivity Data in Prediction; Water Res. Research, Vol. 17, No. 5, p. 1463-1479, (1981). Smith L., R.A. Freeze: Stochastic Analysis of Steady State Groundwater Flow in a Bounded Domain; 2. Two-dimensional Simulations; Water Res. Research, Vol. 15, No. 6, p. 1543-1559, (1979). Sykes J.F., J.L. Wilson, R.W. Andrews: Sensitivity Analysis for Steady State Groundwater Flow Using Adjoint Operators; Water.Res.Research, Vol. 21, No. 3, p. 359-371, (1985).
for the Chapter 9: 1.
2. 3. 4. 5. 6.
Ang, A.H. and W.H.Tang, (1984) Probability concepts in engineering planning and design Vo1.2, J.Wiley, New York, pp. Apostolakis, G. (1990) The concept of probability in safety assessments of technological systems. Science 250: 1359-1364 Berger, J.B. (1985): "Statistical decision theory and Bayesian analysis" Springer, New York Bogardi,l. and L.Duckstein (1978): "lnput for a stochastic control model of P-loading" Ecological Modelling, No.4 pp.173 -195 Dubois, D. and H. Prade (1980) Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 393 pp. Duckstein, L. ,B.P. Shrestha and E.Z. Stakhiv (1992) Multicriterion Risk and Reliability Analysis in Hydrologic System 221
7.
8.
9.
10.
11.
12.
13.
14. 15.
16.
17.
Design, in: Water Resources Engineering Risk Assessment, Ganoulis, J.(ed.), NATO ASI Series, Vol.G29, p.363-406, Springer-Verlag, Heidelberg Duckstein, L. and E.Plate (eds.) (1987) Engineering Reliability and Risk in Water Resources, E.M. Nijhoff, Dordrecht, The Netherlands, 565 pp. Ganoulis, J. (ed.) (1991) Water Resources Engineering Risk Assessment, NATO ASI Series, Vol G 29, Springer-Verlag, Heidelberg, 552 pp. Ganoulis, J., H. Morel-Seytoux (1985) Application of stochastic methods to the study of aquifer systems. Technical Documents in Hydrology, UNESCO,Paris. Ganoulis, J. (1994): Engineering Risk Analysis of Water Pollution: Probabilities and Fuzzy Sets, VCH, Weinheim, New York, Basel, Cambridge, Tokyo, 306 pp. Kaufmann, A. and M.M. Gupta (1985) Introduction of Fuzzy Arithmetic: Theory and Applications, Van Nostrand Reinhold, New York, 351 pp. Kaufmann, A. and M.M. Gupta (1988) Fuzzy Mathematical Models in Engineering and Management Science, North Holland, Amsterdam, 338 pp. P1ate, E.J. and L.Duckstein (1988): "Reliability based design concepts in hydraulic engineering" Water Resources Bulletin, AWRA, Vo1.24 pp 235-245 Papoulis, A. (1965): "Probability, random variables and stochastic processes", McGraw Hill Co.,N.Y. Plate, E. (1991) Probabilistic Modelling of Water Quality in Rivers, In: Water Resources Engineering Risk Assessment, Ganoulis, J.(ed.), NATO ASI Series, Vol.G29, p.363-406, Springer-Verlag, Heidelberg p.137-166 Shresta, B.P., K.R. Reddy and L. Duckstein (1990) Fuzzy reliability in hydraulics. In: Proc. First Int. Symp. on Uncertainty Mod. and Analysis, Univ. of Maryland, College Park Zimmerman, H.J. (1985) Fuzzy Set Theory and its Application, Martinus Nijhoff, 363 pp.
for the Chapter 10: 222
1. 2. 3. 4. 5. 6.
7.
8.
9.
10.
11.
12.
13.
14.
Ang, A.H. and W.H.Tang, (1984) Probability concepts in engineering planning and design. Vo1.2, J.Wiley, New York, pp. Apostolakis, G. (1990) The concept of probability in safety assessments of technological systems. Science 250: 1359-1364 Berger, J.B. (1985): "Statistical decision theory and Bayesian analysis" Springer, New York Bogardi,l. and L.Duckstein (1978): "lnput for a stochastic control model of P-loading" Ecological Modelling, No.4 pp.173 -195 Dubois, D. and H. Prade (1980) Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 393 pp. Duckstein, L. ,B.P. Shrestha and E.Z. Stakhiv (1992) Multicriterion Risk and Reliability Analysis in Hydrologic System Design, in: Water Resources Engineering Risk Assessment, Ganoulis, J.(ed.), NATO ASI Series, Vol.G29, p.363-406, Springer-Verlag, Heidelberg Duckstein, L. and E.Plate (eds.) (1987) Engineering Reliability and Risk in Water Resources, E.M. Nijhoff, Dordrecht, The Netherlands, 565 pp. Ganoulis, J. (ed.) (1991) Water Resources Engineering Risk Assessment, NATO ASI Series, Vol G 29, Springer-Verlag, Heidelberg, 552 pp. Ganoulis, J., H. Morel-Seytoux (1985) Application of stochastic methods to the study of aquifer systems. Technical Documents in Hydrology, UNESCO,Paris. Ganoulis, J. (1994): Engineering Risk Analysis of Water Pollution: Probabilities and Fuzzy Sets, VCH, Weinheim, New York, Basel, Cambridge, Tokyo, 306 pp. Kaufmann, A. and M.M. Gupta (1985) Introduction of Fuzzy Arithmetic: Theory and Applications, Van Nostrand Reinhold, New York, 351 pp. Kaufmann, A. and M.M. Gupta (1988) Fuzzy Mathematical Models in Engineering and Management Science, North Holland, Amsterdam, 338 pp. P1ate, E.J. and L.Duckstein (1988): "Reliability based design concepts in hydraulic engineering" Water Resources Bulletin, AWRA, Vo1.24 pp 235-245 Papoulis, A. (1965): "Probability, random variables and stochastic processes", McGraw Hill Co.,N.Y. 223
15. Plate, E. (1991) Probabilistic Modelling of Water Quality in Rivers, In: Water Resources Engineering Risk Assessment, Ganoulis, J.(ed.), NATO ASI Series, Vol.G29, p.363-406, Springer-Verlag, Heidelberg p.137-166 16. Shresta, B.P., K.R. Reddy and L. Duckstein (1990) Fuzzy reliability in hydraulics. In: Proc. First Int. Symp. on Uncertainty Mod. and Analysis, Univ. of Maryland, College Park 17. Zimmerman, H.J. (1985) Fuzzy Set Theory and its Application, Martinus Nijhoff, 363 pp.
for the Chapter 11: 1. 2. 3. 4. 5. 6.
7.
8.
9.
Ang, A.H. and W.H.Tang, (1984) Probability concepts in engineering planning and design. Vo1.2, J.Wiley, New York, pp. Apostolakis, G. (1990) The concept of probability in safety assessments of technological systems. Science 250: 1359-1364 Berger, J.B. (1985): "Statistical decision theory and Bayesian analysis" Springer, New York Bogardi,l. and L.Duckstein (1978): "lnput for a stochastic control model of P-loading" Ecological Modelling, No.4 pp.173 -195 Dubois, D. and H. Prade (1980) Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 393 pp. Duckstein, L. ,B.P. Shrestha and E.Z. Stakhiv (1992) Multicriterion Risk and Reliability Analysis in Hydrologic System Design, in: Water Resources Engineering Risk Assessment, Ganoulis, J.(ed.), NATO ASI Series, Vol.G29, p.363-406, Springer-Verlag, Heidelberg Duckstein, L. and E.Plate (eds.) (1987) Engineering Reliability and Risk in Water Resources, E.M. Nijhoff, Dordrecht, The Netherlands, 565 pp. Ganoulis, J. (ed.) (1991) Water Resources Engineering Risk Assessment, NATO ASI Series, Vol G 29, Springer-Verlag, Heidelberg, 552 pp. Ganoulis, J., H. Morel-Seytoux (1985) Application of stochastic methods to the study of aquifer systems. Technical Documents in Hydrology, UNESCO,Paris.
224
10. Ganoulis, J. (1994): Engineering Risk Analysis of Water Pollution: Probabilities and Fuzzy Sets, VCH, Weinheim, New York, Basel, Cambridge, Tokyo, 306 pp. 11. Kaufmann, A. and M.M. Gupta (1985) Introduction of Fuzzy Arithmetic: Theory and Applications, Van Nostrand Reinhold, New York, 351 pp. 12. Kaufmann, A. and M.M. Gupta (1988) Fuzzy Mathematical Models in Engineering and Management Science, North Holland, Amsterdam, 338 pp. 13. P1ate, E.J. and L.Duckstein (1988): "Reliability based design concepts in hydraulic engineering" Water Resources Bulletin, AWRA, Vo1.24 pp 235-245 14. Papoulis, A. (1965): "Probability, random variables and stochastic processes", McGraw Hill Co.,N.Y. 15. Plate, E. (1991) Probabilistic Modelling of Water Quality in Rivers, In: Water Resources Engineering Risk Assessment, Ganoulis, J.(ed.), NATO ASI Series, Vol.G29, p.363-406, Springer-Verlag, Heidelberg p.137-166 16. Shresta, B.P., K.R. Reddy and L. Duckstein (1990) Fuzzy reliability in hydraulics. In: Proc. First Int. Symp. on Uncertainty Mod. and Analysis, Univ. of Maryland, College Park 17. Zimmerman, H.J. (1985) Fuzzy Set Theory and its Application, Martinus Nijhoff, 363 pp.
225
LIST OF AUTHORS 1. Vladimir N. Gorbachev – Deputy Chairman of the Altai State Environmental Committee. 2. Vitaly F. Mironenko - Professor, Doctor of Sciences in Engineering, Head of the «Life safety» Chair at the ASTU. 3. Vladimir V. Kirillov - Candidate of Biological Science, Head of Water Ecology Laboratory, IWEP SB RAS. 4. Alexander A. Tskhaу – Professor, Doctor of Sciences in Engineering, Head of the UNESCO Chair «Environmental Education in Siberia». 5. Michele Poulin - Centre d‘Informatique Géologique, Ecole des Mines de Paris. 6. Pierre Hubert - UMR Sisyphe, Centre d'lnformatique Geologique, Ecole des Mines de Paris. 7. Hans-Peter Nachtnebel - Dept. of Water Resources Management, Hydrology and Hydraulic Engineering, University for Agricultural Sciences. Vienna, Austria. 8. Jacques Ganoulis – Professor, Head of the Hydraulics Laboratory, Department of Civil Engineering, Aristotle University of Thessaloniki.
226
