Słupskie Prace Geograficzne

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1 Słupskie Prace Geograficzne 4 Ivan Kirvel Poeranian University in Słupsk kirviel@yandex.ru Piotr Shvedovskiy Aleksander Volchek Briest National University, Bialorussia ESTIMATING THE PROBABILITY OF OPTIMAL FUNCTIONING FOR ENVIRONMENT MANAGEMENT SYSTEMS AND FINDING WAYS TO IMPROVE THEIR ENVIRONMENTAL RELIABILITY OCENA PRAWDOPODOBIEŃSTWA OPTYMALNEGO FUNKCJONOWANIA SYSTEMÓW I ZARZĄDZANIA ŚRODOWISKIEM I WYZNACZENIE SPOSOBÓW POPRAWY ICH NIEZAWODNOŚCI Zarys treści: The optial functioning of both natural and antropogenic systes is adequately definable by paraeters of ecological safety and sustainability. Practice shows that ain factors deterining the status and functioning of environental anageent systes and environental safety are design flaws, low construction quality and poor aintenance. This allows to iprove ecological reliability by eans of the initial reservation or to perfor its gradual increase, ipleenting certain environental rehabilitation easures. Perfored analysis of Polesie water anageent systes had shown that optial degree of prolonging the operation tie by initial reservation should not exceed i.r. =.38, while the optial factor of the systes perfection should be not less than as. =.89, and factor of the allowable investents increase into ecological reliability should not exceed c. =.6. Therefore solution of providing the optial ecological sustainability, reduncancy, and environental anageent systes optial functioning should be considered as a ulti-criteria proble with the optiization on acceptable utility with axiu coherence, objective coproise, and preferability. Key words: water resources, functioning, probability, environental reliability, sustainability, analysis, optiization Słowa kluczowe: zasoby wodne, funkcjonowanie, prawdopodobieństwo, zrównoważony rozwój, stabilność, analiza, optyalizacja 49

2 Introduction As noted in Kirvel et al. (3) the optial functioning of natural, natureantropogenized, and antropogenic systes is enough definable by the paraeters of environental safety and sustainability. In this case, if the stability of the optial functioning of the syste deterines its ability to aintain its structure and functional properties when exposed to external factors and to return close to its original state after exposure to factors that bring fro balance, the probability of optial functioning characterizes the probability that, during operation, the transition syste fro one state to another will not lead to a breach of its balance and its ain paraeters will not go over the critical liits. And, as shown in studies (Kirvel et al. 3; Ivchenko, Martyshchenko 998; Volchek et al. 3), with a standard value of the required confidence probability γ =.9, lower confidence liit of the optial functioning probability of the syste (p) ust be at least p =.986, at the prevailing indirect relationship between environental coponents in range,697 R,73 for direct interconnection, if the nuber of coponents (N) does not exceed. In this case, regardless of the intended odalities and systes structure, their probability of optial functioning can be described by the dependence (Shvedovskiy, Luksha ), given the reserve of environental reliability level for all environental coponents N N = p qi ηi + qij ηij ( ) q,,, N, () i= i> j p... where p the probability of the optial functioning of the syste if there is no reduction of environental coponents reliability to a critical level; q i the probability of reaching the critical level of environental reliability of any fro the i-th coponent; η i weighting factor for the i-th coponent, which deterines its functional significance (redundancy); η ij, q ij, η, N, q, N coponents weights and probability of occurrence of double, triple, etc. superiposed processes of the environental coponents reliability reduction; η i = - p i /p ; p i the probability of optial functioning of the syste on reaching a critical level of environental reliability of i-th coponent (Loginov et al. 4). Accordingly, at independence of the processes of achieving critical levels of environental reliability by the coponents, i.e. when p, we have p = N ( q i η i ) i=. () Analysis of survey aterials of the environental anageent systes state and functioning allows to note that ain reasons of unsatisfactory perforance and, consequently, low ecological reliability are design errors (8.9%), poor quality of building (.%), poor aintenance (38.6%), and the set of all causes (.3%). At the 5

3 sae tie 6% of the are already seen in the period of adaptation of systes, 9% in the period of optial functioning, and 45% in the period of ass anifestations of failure and the foration of a critical level of environental safety. Hence it follows that environental reliability can be fored as by a priary reservation, so by its staged increase through the ipleentation of relevant environental reediation. Let us consider this proble for the nature-antropogenized water anageent systes. Results and discussion 3 Research carried out for the ost coon water anageent and agrolandscape Polesie systes with use of functional Bellan equations have revealed the estiated ters of systes reconstruction to ensure axial effect, which are: first reconstruction 8, second 33, third 48, fourth 67, fifth 83 years. However, in practice, the optial reconstruction between lifespan of water systes is 5 8 years at the axiu ter of operation up to 3-33 years. For these tie steps, we will optiize the environental reliability and the probability of systes optial functioning. Since the function of ecological reliability of any anthropogenic degree is definable by three regions ( P ), four states of functioning ( S i i = risk ( S r 4 j j = ), ten factor variables of ) and the set of real states of ajor groups of eleents and coponents, then the following relationship can be used to optiize it: C opt co = A t [( + t α) ] + i= θ, (3) which takes into account both the initial capital investent, and the costs of providing the required ecological reliability of the ain group eleents and the syste as a whole. Here: А one-tie capital costs; θ т current annual cost of aintaining the syste perforance at the required degree of environental reliability; t [( + α ) ] factor of costs reoteness; α norative coefficient of effectiveness; t period of coparison. Then, the econoic effect of increasing the level of environental reliability regardless of the ethod of its ipleentation can be deterined by the following dependence θ = k y E n t (λ λ ) (C C ), (4) where λ liit of costs increase of the syste at increased calculation period and iproved ecological reliability by ties; λ phasing factor of the ipleentation of conservation and restoration activities over life of the syste T ; E n nora- 5

4 tive factor of bringing costs; k y specific capital investents; C and C the variant-wise costs, respectively, of the eleents ain groups of the syste, which are causing its environental reliability as a whole. It should be noted that the period of optial environental reliability is deterined by the period lof optial functioning (T к ) (Braun et al. 997; Heuvelink 998; Kalinin et al. 7). Plots of the specific econoic effect of increasing the calculation period and the level of environental reliability of the syste are shown in Fig.. ӨЭо l eк ct эк l ц eк ct эк b ц b а,5 а,,7 5,,6,5 3а,5,,3 4а 3 4,5 3, 4,5 6, 7,5 Fig.. Plots of the econoic effect of iproving the environental reliability at (С - С ) = (a, a, 3a, 4a) and its econoically allowable reduced costs increase at E =.8 (,, 3, 4) and the reduced costs increase for providing the optiu environental reliability at increase of the calculation period and the level (5): at T = 5 and T = 3; at T = and T = 3; 3 at T = 5 and T = 3; 4 at T = 3 and T = 3 years Ryc.. Ryciny zależności efektu ekonoicznego od wzrostu bezpieczeństwa ekologicznego przy (С - С ) = (a, a, 3a, 4a) i ekonoicznie optyalnych wydatków przy E =,8 (,, 3, 4) oraz zwiąkszenia trat na zabezpieczenia optyalizacji bezpieczeństwa ekologicznego, przy zwiększeniu okresu obliczanego i poziou (5): dla T = 5 i T = 3; dla T = i T = 3; 3 dla T = 5 i T = 3; 4 dla T = 3 i T = 3 lat Analysis of the chart allows to note that the increase in calculation period and the level of environental reliability is ost appropriate to the period of foration of the critical level of environental reliability (Т k ) when optiizing the iniu allowable level of environental reliability and at the end of the initial (adaptation) period of operation when optiizing the initial reservation. 5

5 Then the degree of econoically reasonable increase in the cost of the syste or basic groups of its eleents is deterined by the relation L l = + θ eк, and the degree of increase of reduced costs to increase the calculation period or the level of ct L С eк ' environental reliability ( b ) and the corresponding econoic effect ( ct θ ) by the relations b eк = C / C and, where C ct the costs of raising the calculation period and the level of environental reliability, given to the tiing of environental rehabilitation works; L and L are respectively the perissible costs for construction and environental reliability iproveent of the ain group of eleents fro the tiing of T and T to the period T c of the syste operation (Rusin 99; Jeffers 98). Accordingly, the allowable tie frae to iprove the calculation period and the level of environental reliability at the construction stage deterined by Y M = L / L indicator, and during the operational phase by k д = k Y, where k М the total cost of the basic version of the syste. Then the optial degree of increase in the calculation period and the level of environental reliability of a group of eleents of the syste under construction is to be deterined by the depen-dence (Truhaeva 976) L (.953 ) opt = ln T, T L. c (5) where T the duration of adaptation period of the syste to for the ecological environent state. Accordingly, the period of optial functioning (Т оpt ) and the index of technical perfection of the syste (α k ) are defined by L Т оpt = ln ln ( + E T ) L + ( + E) c, k T T T Tc ( ) ( ) ( ). α = + E + E + E (6) A graphical representation of these characteristics gives the generalized diagra of environental safety and quality of systes (see Fig. ). Analysis of the ain characteristics (,, 3, 4) suggests the following. At increase of the calculation period and the level of environental reliability in the operation period the curve approaches the straight line, with кр Т = Т с, i.e. at equality of environentally safe operation period of the whole syste and ajor groups of eleents (Т = Т с ) perissible degree of increase in costs ( pr ) reaches the ceiling at the point B, where Y = L. Iproving the calculation period and the level of environental reliability can also be achieved by increasing the perfection of ain groups of eleents, but the ties increase in the calculation period and the level of environental reliability 53

6 δ α к, Lp α c к L con, L o,у, L, L P C K K А опт n ' K 5 6 M B D H ' H Fig.. Generalized diagra of the level of environental reliability and of technical perfection of the syste: L = f (Т, Т с ); Y = f (, Т); 3 L = f 3 (, Т); 4 α k = f 4 (, Т); 5 L с = f 5 (, Т); 6 L c = f 6 (,T ); 7 L b р = f7 (,T ) Ryc.. Ugólniony diagra poziou bezpieczeństwa ekologicznego i technicznego udoskonalenia systeów: L = f (Т, Т с ); Y = f (, Т); 3 L = f 3 (, Т); 4 α k = f 4 (, Т); = f, T ; 7 = f (,T ) 5 L с = f 5 (, Т); 6 ( ) L c 6 L b р 7 causes an increase in the level of technical perfection, which asyptotically approaches its liiting value at D point (α к = ). This eans that the rate of cost of environental protection and restoration activities in the operation of the syste decreases while the period of optial functioning increases. With a sall optial functioning calculation period the costs of raising the calculation period and the level of environental reliability are insignificant (at point А, L = L ). The point P is characterized by indicators equality of costs for iproving environental reliability in the operation and providing the initial reservation of its calculation period. M point of intersection of lines and 3, characterized by an optiality (Y = L ) of functioning period with a given degree (level) of ecological reliability also defines the liits of the econoic feasibility of iproving perforance by using the initial reservation (if the increase the calculation period of the ain group of eleents is less than опт ties), and a phased ipleentation of conservation and restoration activities under other conditions. 54

7 Accordingly, the definition of the achieved rate of the syste perfection for any degree (the calculation period and level) can be done graphically designing опт ' ' point on the curve 4 ( K ) and then on the y-axis ( K ). Analysis of additional dependencies (5, 6, 7) shows that the iproveent of environental reliability deterines concoitant increase in capital investents (L c ), b costs in conjugate area ( L ) and reduces the cost of aintenance services ( L c р ). These paraeters are defined by ( L )/( L ) L c = ; = L / L b L c and L = Y ( L )/( L ) р. (7) Drawing a vertical line at certain i values, one can deterine the values of the above defined indicators and thereby ore fully and accurately evaluate the effectiveness of easures to iprove the calculation period and the level of environental safety. Let s analyze all these paraeters and calculated dependence for the syste, which is characterized by the following indicators: design life of the syste 3 years; period of operation of the syste before the foration of the critical levels of environental reliability at I variant T = years and at II Т =5 years; specific capital investents C = $ 4.5 / ha and C = $ 6. / ha; norative to bring the ulti-teporal costs E =.. Let s plan to increase the calculation period of functioning with the calculated level of environental reliability at I variant to 5,, 5 and 3 years and at II, 5 and 3 years. Being analyzed, the efficiency diagra of capital investents in the increase of ecological reliability of systes allows to note the following: optial degree of the life functioning increasing by the initial reservation opt I =.46 and =.38; II opt perissible degree of the capital investents increase for the construction of an object Y I =.86 and Y II =.6; best perfection indicator of systes αk I =.89 and k =.89; the optial duration of operation with confidence probability of optial functioning of γ =,9 and accordingly with the required environental reliability, fro the condition of iniizing the initial capital investent will be respectively T I =.3 years and = 6.9 years. T II α II Conclusion Water anageent and construction related to environental anageent, environental engineering in the field of water resources, fored today the variety of environental probles threatening not only the individual socio-econoic interests of society, but also its whole vital activity through the deterioration of the environent. 55

8 Solving these probles requires both the developent of ethodologies for evaluating the probability of optial operation of water systes and ethodologies for evaluating changes in the level of environental safety, stability, and reliability, especially at insufficient a priori inforation. According to our research, the deterining criterion of all the coponents causing environental sustainability, reliability, and optiu perforance of systes is not only the value of specific capital investents, but also the knowledge of an optial tiing of operation, the perfection index of a syste, etc. Hence, this proble should be considered as a ulticriteria proble with optiization at an affordable usefulness with the greatest consistency and target coproise. At the sae tie it should be based on the criteria of efficiency and preference. References Braun, P., Molnar T., Kleeberg H.B., 997, The proble of scaling grid-related hydrological process odeling, Hydrological Processes,, p Jeferrs J., 98, Introduction to syste analysis and ecology application, Moscow Heuvelink G.B.M., 998, Uncertainty analysis in environental odeling under a change of spatial scale, Nutrient Cycling in Agroecosystes, Vol. 5, p Ivchenko B.P., Martyshchenko L.A., 998, Inforation technology, St. Petersburg Kalinin M., Volchek A., Shvedovsky P., 7, Hazardous Natural Disasters in Belarus, Natural Disasters and Water Security: Risk Assessent, Eergency Response. and Environental Manageent: abstract book, Yerevan, Arenia, 8- October 7, International Geographical Union, Yerevan, p. 5-6 Kirvel I., Shvedovskaya D., Shvedowskii P., Volchek A., 3, Ocena ekologiczna optyalnego funkcjonowania systeów naturalnych i antropogenicznych, Słupskie Prace Geograficzne,, p. 5-6 Loginov V.F., Volchek A.A., Shvedovskiy P.V., 4, Application practice of statistics ethods at natural processes analysis and prediction, Brest Rusin I.I., 99, Ecologization of the econoics: regional anageent ethods, Moscow Shvedovskiy P.V., Luksha V.V.,, Matheatical odelling specifics of the developent jups in ecology systes and processes, Vestnik Brestskogo universiteta,, 8, p. 9-3 Truhaeva R.I., 976, The applied approach in researches of the decision aking procedure, Moscow Volchek А.А., Poita P.S, Shvedovskiy P.V., 3, Matheatical ethods in environental engineering. Workbook for higher educational institutions, Minsk Suary The research is targeted at estiating the optial functioning probability of natural, natural-anthropogenic, and anthropogenic systes, and at deterining ecological reliability and sustainability paraeters for the hydroeconoic Polessie systes. Analysis of the research results shows that solution of these probles is deanding their consideration as a ulti-criteria ones with optiization at acceptable utility, with axial coherence and objective coproise. 56