The paper contains the description of the feasible approach to modeling and forecasting of ecological processes that are the component of the sustainable development paradigm. The suggested mathematical apparatus is based on the statistical methods and comprises hidden Markov models with the linguistic modeling

T. V. Shulkevich

Y. M. Selin

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Computer Science Journal of Moldova, vol.24, no.2(71), 2016Feasible approach to modeling of ecologicalcomponent of the sustainable developmentparadigmT. V. Shulkevich, Y. M. SelinAbstractThe paper contains the description of the feasible approach tomodeling and forecasting of ecological processes that are the com-ponent of the sustainable development paradigm. The suggestedmathematical apparatus is based on the statistical methods andcomprises hidden Markov models with the linguistic modeling.Keywords: modeling, forecasting, ecological processes, math-ematical apparatus, hidden Markov models, linguistic modeling.According to the definition suggested by the Centre “For our com-mon future” (“For our common future”), that has been working inGeneva since 1988, and the United Nations Conference in Rio deJaneiro (1992), the sustainable development is understood as the kindof development that “satisfies the current needs, but does not compro-mise the abilities of the future generations to satisfy their own needs”,or that provides “the high quality of environment and the healthy econ-omy for all nations”. Therefore, the problem of the sustainable devel-opment is the problem of the mankind salvation from the consequencesof its own activity that, by the end of the 20th century, have becomecritical and manifested themselves in desertification, pollution of theatmosphere, oceans and soil, rapid population growth, poverty, star-vation, dangerous diseases, etc. The issues of scientific knowledge andeducation, industry and innovation technologies, ecological, social andmedical problems, international relations and political events and manyother phenomena of modern life have intertwisted into the single inter-related unit. The consciousness of the situation and the search of thec©2016 by T. V. Shulkevich, Y. M. Selin172Feasible approach to modeling of ecological component of . . .Figure 1. The triune concept of the sustainable developmentreasonable solutions to the problem have become an urgent matter. Itrequires focused attention not only on a global, but also on a national,regional and local basis [1].Usually, the sustainable development paradigm is presented in thefollowing way (Fig. 1).The growing rate of exploitation of natural resources, economicdecline of the economies in transition raise up the risk of the techno-genic disasters, keep the countries from spending considerable effortsand resources necessary for the implementation of measures to reducethe environmental impact. To accomplish the purpose of the sustain-able development the specific mechanisms for its implementation arerequired. The development and application of the “environmental as-sessment” system for the assessment of the transition to the sustainabledevelopment is of considerable significance in the world practice. Themost important are the two of its modes (local and strategic) that nowa-days are the well-established mechanisms of revelation and preventionof the environmental consequences of the human induced activity (refer173T. V. Shulkevich, Y. M. Selinto Fig. 2) [2].However, for better understanding of the ecological component ofthe sustainable development paradigm, it is necessary to analyze somenatural phenomena and biospheric processes and their interaction inthe “man-environment” system. We will pay careful attention to envi-ronmentally hazardous processes.Environmentally hazardous processes are generally understood asexogenous and endogenous (anthropogenic), short-term and long-termimpacts on the ecosystem as a whole or on its particular element, lead-ing to the violation or problems of its performance that in its turndisrupts the man-environment balance.1. Endogenous (anthropogenic) impacts are caused by anthro-pogenic activity (pollution by harmful organic and non-organic sub-stances of all kinds of the environment: the atmosphere, surface wa-ters, water-saturated underground layers, soil, animate environments;noise and electromagnetic pollution of the atmosphere; light pollution;flooding of soils and slopes; ozone depletion and creating conditionsfor the greenhouse effect). They may be controlled and, in some cases,reduced or even prevented.2. Exogenous impacts are the manifestations of the outer space andinternal geological processes and changes (solar cycles, hurricanes, trop-ical cyclones, monsoons, volcanic activity, global warming as a resultof the precession of the Earth’s axis, and finally, the asteroid hazard).They are purely objective, cannot be controlled, but may be observedand forecasted. Therefore, it is possible to develop a set of measuresto minimize the damages or mitigate the consequences.It becomes clear from the mentioned earlier that the environmen-tally hazardous processes are of various nature and types. Also, it isevident that “not everything depends on a man”.In Fig. 3 there is a schematic classification of the environmentallyhazardous processes [3].The solar activity (Fig. 4) is a special type of an exogenous impacton the geological and biochemical processes taking place on Earth.The index for the solar activity characteristics, so called Wolf number,Zurich number or the relative sunspot number is calculated by the174Feasible approach to modeling of ecological component of . . .Figure 2. Environmental assessment system (EA)175T. V. Shulkevich, Y. M. SelinFigure 3. Environmentally hazardous processes classification176Feasible approach to modeling of ecological component of . . .Figure 4. Solar activity cyclical change. Source: US National Centrefor Environmental Information sitefollowing formula of R = k · (f + 10 · g), where R is the Wolf number;f is the total number of sunspots on the visible sun hemisphere; g isthe number of sunspot groups; k is the multiplier (less than 1) thattakes into account the total contribution of observing conditions, thetelescope type and that is observed by the standard Zurich numbers.According to the observation data for the last 304 years, the cy-cle length in actual practice varies from 8.5 to 14 years between theproximate minimums and from 7.3 to 17 years between the proximatemaximums. The connection between the solar cycles and the increasedoccurrence of land slides has been proved. The most adverse impactis on that of the innovate technology effects, high-frequency operatingdevices, such as mobile communications, satellites (and also the re-lated navigational safety problems), etc. Solar radiation is the sourceof the motion in the atmosphere-ocean system. The force, that thesolar radiation generates, produces buoyancy – the source of motion177T. V. Shulkevich, Y. M. Selinin the atmosphere. It determines the nature of hurricanes, tornadoes,tsunamis and other destructive processes. Also, the solar activity in-fluences the proliferation of some diseases, increases the frequency oftraffic accidents, etc.The climate change caused by the global warming is not only theresult of increased greenhouse gases concentrations (especially, carbondioxide) in the atmosphere, but also the result of the next cycle of theprecession of the Earth’s axis, thus it has an exogenous cause and itwill be intensified in the near future. Although, according to Kh.Y.Shelnhuber [4], Antarctic and Greenland’s ice sheet, Sahara desert,Amazonian rainforest, Asian monsoon system, Gulf Stream and sixmore “weak spots” of Earth influence the climate, and in the case ofat least one of them undergoing changes, the ecological disaster (ofthe continental level) will be inevitable, the risk may be decreased byreducing the emission rate of gases mentioned earlier.Considering the literature [3], we can define two principal directionsand accordingly, two methodological approaches to the mathematicalmodeling of the dynamics of the environmentally hazardous processesof various nature. The first approach comprises dynamic-computed ap-proaches based on computational methods for solving various kinds ofdifferential equations that describe the basic laws of physics, and alsoatmospheric and hydrodynamic processes. They are focused on solv-ing the following basic problems of the most important spatiotemporalpatterns of the current natural processes:• Exposure of the current spatiotemporal interrelations betweenvarious atmospheric processes in the observation dynamics;• Natural processes modeling for the forecasting of their develop-ment dynamics.The second approach, comprising empirical dynamic-statistical ap-proaches based on the use of the long-term field measurement statistics,belongs to the international system for the analysis and forecasting ofthe ecosystem components. They are focused on the exposure of thebasic spatiotemporal patterns typical of the atmospheric processes over178Feasible approach to modeling of ecological component of . . .decades. The main purpose of these approaches is, in fact, the estab-lishment of deep spatiotemporal correlations between various naturalprocesses based on the long-term statistics. Depending on the pur-poses of the study it is necessary to perform the development of themathematical apparatus for the analysis of the dynamics of the envi-ronmentally hazardous processes based on either dynamic-computed ordynamic-statistical approaches, taking into account the specific pecu-liarities and properties of the processes.Besides, there is the third type of processes that cannot be modeledwith the help of dynamic-computed methods, and due to the absenceof a peculiar particular periodicity (daily, monthly, annual or anotherpermanent periodicity) they are difficult to describe using empirical-statistical methods. Therefore, the problem of the development of theprocess analysis and the development of the forecasting methods of suchprocesses for the information support of the environmental situationcontrol and monitoring system is relevant.To sum up, the conducted analysis allows for the conclusion thatthe environmentally hazardous processes are characterized by the com-plex interrelations, interdependencies and interactions of various fac-tors and causes. They have the following characteristic properties andpeculiarities:• The heterogeneousness and diversity of causes and factors and anactivity that causes them;• The spatial distribution of the triggering events, temporal andspatial uncertainty of the growth dynamics and their impact onthe eco-surroundings;• The nonstationarity of properties and ambiguity of their charac-teristics.These properties and peculiarities determine the practical relevancyof studying of all the variety of characteristics, interrelations, interac-tions, interdependencies of the diverse factors and causes of the envi-ronmentally hazardous processes on the basis of the single systematicapproach from the perspective of achieving the globally defined objec-tive of the environmental situation management – early prevention and179T. V. Shulkevich, Y. M. Selin(or) minimization of the adverse effects of their action. However, theanalysis shows that nowadays the various types of natural and techno-genic environmental processes, their causes, progress, consequences andthe sphere of the action are studied separately, without regard to in-terrelations, interdependencies, and interactions.Such an approach does not consider some factors of primary impor-tance that influence the active processes, their adverse impact level, thepossibility and effectiveness of its prevention.Considering all of the above-mentioned, we propose the feasiblemathematical apparatus that may be used for the forecasting of theenvironmental processes of all three types [5].Hidden Markov models (HMM). The following diagram (Fig. 5)shows the general structure of HMM. Ellipses are the variables withthe random value. Accidental variable x(t) corresponds to the valueof the hidden variable at time t. Accidental variable y(t) is the valueof the variable under an observation at time t. The arrows on thediagram stand for the conditional dependences. As it can be seen fromthe diagram, the value of the hidden variable x(t) (at time t) dependsonly on the value of the hidden variable x(t − 1) (at time t− 1). It iscalled the Markov property. However, at the same time the value ofthe variable y(t) under an observation depends only on the value of thehidden variable x(t) (at time t).Figure 5. Solar activity cyclical changeThe probability of observing the sequence Y = y(0), y(1), ..., y(L −1) of the length L is P (Y ) =∑X P (Y/X) · P (X).Here, the sum runs over all possible sequences of hidden pointsX = x(0), x(1), , x(L − 1).180Feasible approach to modeling of ecological component of . . .The basic Markov models may be described through the followingvariables: N is the number of conditions; T is the number of obser-vations; θi=1,...,N is the parameter for the observation of the relationsbetween conditions; φi=1,...,N ;j=1,...,N is the probability of transfer fromcondition i to condition j; φi=1,...,N is N -dimensional vector consistingof j vectors φi=1,...,N ;j=1,...,N; xt=1,...,T is the condition of the observa-tion in a time t; yt=1,...,T is the result of the observation in a time t;F (y/θ) is the probability distribution function of observations param-eterized by θ.The result of the environmental process observation with the helpof HMM is the sequence of conditions the system undergoes during thetime of observation.Markov model of weather with three conditions will be used asan example. We will consider that the observations are made daily(for example, at noon), the weather may have one of the followingconditions:• S1 – rain (snow);• S2 – cloudy;• S3 – clear.The weather on the day t is described by one of the abovemen-tioned conditions, and the transition-probability matrix has the fol-lowing form:A =(aij)=0, 4|0, 3|0, 30, 2|0, 6|0, 20, 1|0, 1|0, 8. (1)Thus, having the process model in the form of the probability ma-trix and the start state probability matrix, we can calculate any con-dition sequence probability, that is any observation probability.Linguistic modeling. According to the specific rules the numericvalues are replaced with the symbols. The forecasting is made throughthe search of the symbol strings and their correlation with the strings181T. V. Shulkevich, Y. M. Selinfrom the observation database. Obtained symbols make up the V al-phabet from which, in its turn, the words are formed.Herein, the grammar (or formal grammar) is understood as theway of description of a formal language, that is the discrimination of acertain subset from the whole set of words of a certain finite alphabet.The forecasting is performed with the help of a stochastic context-free grammar. Stochastic context-free grammar is the context-freegrammar in which each deduction rule has a corresponding probability.Context-free grammar G is the tuple (N,T, P, S): S ∈ N ; N andT are the bounded disjoined sets; P is a finite subset N × (N⋃T ).Herein, the following names are used: N is the nonterminal set, Tis the terminal set, P is the deduction rules set. Rules (α, β) ∈ P arespecified as α → β. The left part of the deductive rule must contain onevariable (nonterminal symbol). Formally, α ∈ N , β ∈ (N ∪ T )⋆α ∈ N ,β ∈ (N ∪ T )⋆, | β |≥ 1 should be realized.In stochastic context-free grammars the deduction rules correlatewith the probability of use:ρ : p → R, (2)where∑pr∈Prρ (pr) = 1. (3)It is necessary to combine both methods to improve the accuracy ofthe forecast.Conclusion. Thus, we proposed the mathematical apparatus thatmight be used for the modeling and forecasting of the environmentalprocesses of the sustainable development paradigm. The common prob-lem of the statistical methods is the lack of the historical information.However, the mankind is engaged in the monitoring of the environ-ment, observation of the weather and natural processes throughout thelife. Therefore, the use of the statistical methods in particular is fullyjustified.182Feasible approach to modeling of ecological component of . . .References[1] United Nations, Agenda 21-United Nations Environment Pro-gramme, New York, United States: United Nations, April 23, 1993,300 p. ISBN: 978-92-1-100509-7.[2] S. V. Patoka, E. V. Khlobistov, “The theoretical basis of environ-menttal safety research development and deployment of industrialcapacity,” in Ekonomika promyslovosti Ukrainy (Zb. nauk. prac.),Kiev, Ukraine: RVPS Ukrainy NAN Ukrainy, 2001, pp. 29–37. (inUkrainian)[3] Y. N. Selin, “System analysis of ecologically dangerous processes ofdiferent nature,” System Research and Information Technologies,no. 2, pp. 22–32, 2007. (in Ukrainian)[4] S. Rahmstorf, H. J. Schellnhuber, Der Klimawandel. Diagonose,Prognose, Therapie, Seoul, Korea: Dosol Publishing Co., 2007, 144p. ISBN: 3-406-50866-9. (in German)[5] I. V. Baklan, Y. N. Selin, T. V. Shulkevich, “Mathematicalmodels predict time series of diferent nature,” Vestn. Kherson-skogo nacionalnogo universiteta, vol. 3(50), pp. 213–218, 2014. (inUkrainian)Tatiana Shulkevich, Yurii N. Selin Received April 2, 2016Tatiana ShulkevichNational Technical University of Ukraine “Kyiv Polytechnic Institute”Ukraine, Kiev, Peremogy ave., 37Phone: +380937256753E–mail: tatyana-victorovna@ukr.netYurii N. SelinEducational-scientific complex “Institute for applied system analysis”Ukraine, Kiev, Peremogy ave., 37, bild.35Phone: +380672388649E–mail: selinyurij@online.ua183

Feasible approach to modeling of ecological component of the sustainable development paradigm

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Feasible approach to modeling of ecological component of the sustainable development paradigm

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