lower the Tom River nearby Bragino and Karym-Kary settlements; the least values were marked in tributaries mouths and near Nizhnevartovsk (Figure. 1.4).
COMMISSION OF EUROPEAN COMMUNITIES TEMPUS/TACIS PROGRAM INTERNATIONAL UNESCO CHAIR “ENVIRONMENTAL EDUCATION IN SIBERIA” OF ALTAI STATE TECHNICAL UNIVERSITY
ECOLOGICAL MODELING INTRODUCTION
Barnaul 2001
Ecological Modeling Introduction / Tskhai A.A. [et al]. Editors: Tskhai A. A.; Poulin M. – Barnaul: “Azbuka” Publishing House. 2001. 269 p. ISBN 5-93957-006-2 The objective of this monograph is to make an introduction into environmental modeling. The subject matter of modeling, namely, river basin, its water ecosystems, monitoring and management in its nature-technical complex, is described on concrete examples. Theoretical approaches to environmental modeling are characterized; practical applications of the models are studied. For specialists and graduates.
Authors: Tskhai A. A.; Poulin M.; Beldeeva L. N.; Bezmaternykh D. M.; Ganoulis J.; Zherelina I. V.; Kvon V. I.; Kirillov V. V.; Liakhova S. A.; Nachtnebel H.-P.; Nechai N. Z.; Silantyeva M. M. Responsible for issue: O. G. Solodky, N. Y. Kim.
Funded by TEMPUS/TACIS Program (Commission of European Communities);
Altai State Technical University
© Altai State Technical University
CONTENTS INTRODUCTION................................................................................. 3 1 AQUATIC ECOSYSTEMS DIVERSITY OF THE OB RIVER BASIN.................................................................................................... 4 2 UPPER OB RIVER BASIN HYDROECONOMIC SITUATION AND WATER MANAGEMENT ................................................................. 34 3 THE BASIN APPROACH TO NATURE MANAGEMENT (ALEI RIVER AS A CASE STUDY) ............................................................. 49 4 ENVIRONMENTAL MONITORING OF BARNAULKA ............ 70 RIVER BASIN .................................................................................... 70 5 SPATIAL UNCERTAINTY IN GROUNDWATER SOLUTE TRANSPORT MODELLING............................................................. 76 6 HYDROLOGICAL BASIS FOR SOIL AND GROUNDWATER MODELLING ..................................................................................... 92 7 WATER POLLUTION: PHYSICAL AND MATHEMATICAL DESCRIPTION................................................................................. 112 8 PARTICLE TRACKING TECHNIQUES FOR WATER QUALITY ASSESSMENT .................................................................................. 146 9 THE HYDRODYNAMIC AND HYDROTHERMAL BASE OF THE ECOLOGICAL MODELING OF LAKES AND WATER BODIES176 10 NUMERICAL MODELLING OF LAKE AND RIVER ECOLOGY ........................................................................................................... 198 11 AQUATIC ECOSYSTEMS MODELLING................................. 218 12 GEOINFORMATION SYSTEMS FOR WATER ECONOMY.. 232 REFERENCES.................................................................................. 249 AUTHORS ........................................................................................ 265
INTRODUCTION The collective monograph “Introduction into Ecological Modeling” has been prepared on the materials of the same name intensive course (Polzunov Altai State Technical University, Barnaul, September 18 – 21, 2000), organized within the framework of TEMPUS/TACIS Programme project “ Educational Reform in Siberia aimed at Environment Protection” (A.A.Tskhai: Introduction, Chapter 11, 12; M. Poulin: Chapter 10; L.N. Beldeeva, D.M. Bezmaternykh, M.M. Silantyeva: Chapter 4; J. Ganoulis: Chapter 7,8; I.V. Zherelina: Chapter 3; V.I. Kvon: Chapter 9; V.V. Kirillov: Chapter 1; S.A. Liakhova: Chapter 2; H.P. Nachtnebel: Chapters 5, 6; N.Z. Nechai: Chapter 2). The objective of this monograph is to make an introduction into environmental modeling for river basin, its water ecosystems, monitoring and management in its nature-technical complex on concrete examples. Chapter 1 is devoted to the questions of content, structure and functioning of water ecosystems of Asian part of Russia. Chapter 2 relates the peculiarities of Upper Ob river basin and its Water Economy Directorate activity. The basing approach to nature management is being developed in Chapter 3 on the base of Aley-river. The part of the book devoted to the description of subject field of modeling closes with Chapter 4 characterizing ecological monitoring of a small river on the base of Barnaulka river basin. Theoretical approach to the modeling of hydrogeological processes is being developed in Chapters 5 and 6. The important role in ecological modeling is given to particles behavior description. The technique of their control and modeling methods of their random walk are described in Chapters 7 and 8. The change of water ecosystems condition, in many respects, is defined by the dynamics of their hydrological and hydrothermal characteristics. Chapter 9 is devoted to mathematical formalization of such processes. On the base of the above-stated material it becomes possible to formulate ecological models for lakes and rivers, to describe relative conceptual approaches, to give concrete examples, and etc. The important supplement of stated methodology is forecasting of water ecosystems state (Chapter 11). Chapter 12 gives the example of geoinformation system developed for water use management. In conclusion it is necessary to mark a substantial contribution of university staff members O.G. Solodky, N.L. Dremova, Y.S. Morozova, L.A. Metsker, M.V. Finadeeva to preparation and publication of the materials of AltSTU Annual International School of Water Resources Management. 3
1 AQUATIC ECOSYSTEMS DIVERSITY OF THE OB RIVER BASIN INTRODUCTION All geosystems are represented by natural waters inhabited by living organisms. Natural waters are the source of water circulation and water supply. Moreover, they are actually a source of life at present and in future. Living organisms, biocenoses of rivers, lakes and reservoirs (stagnant and flowing waters) act as a biofilter providing water quality required for human existence. Nowadays the contradiction between increased water consumption under strict requirement to water quality and progressive anthropogenic impact on water objects all over the world including Siberia is observed. To eliminate such a contradiction is possible under its consideration as an element of more general problem of social-economic and natural systems interrelations. A strategic trend in solving the problem of water supply for human needs of sufficient amount and of required quality is maintenance of aquatic ecosystems self-restoration potential. Aquatic ecosystems diversity and their extremely complicated structural-functional organization are of interest to all sciences as for classic ones like physics, chemistry, botany, zoology as for current achievements in physical-chemical biology, cybernetics and system analysis. 1 ECOSYSTEMS AS AN OBJECT OF MODERN ECOLOGY It is well-known that ecology grew out of biological knowledge system. The Darwin concept of natural selection which defined interaction between each biological species and habitat as a key factor for biological evolution determination played a crucial role in development of this biological trend. E. Hekkel who successfully developed this idea in 1866 suggested an "ecology term" (oikos means habitat, dwelling from Greek). "By ecology is implied the science on economy, living conditions for fauna organisms. It studies common relations of animals in respect to as nonorganic as organic environment; their friendly and hostile attitudes to other animals and plants with which they interact directly and indirectly or, in a word, all those intricate interrelations which Darwin characterised as a struggle for survival," – E. Hekkel wrote in 1869 (Biological History …, 1972). As may be seen from the foregoing, "ecology" and "economy" terms are practically synonims by origin. However, the latter term is applied to 4
define laws and rules for economic activity while an "ecology" term is widely used in biology in the sense mentioned above (Trusov, 1983). Ecology as a science on interrelations between organisms and environment hasn't lost its subject for study at present though one of living species has reached such a level of development that makes possible to deal with self-knowledge. Moreover, it has a strong desire to change the world in its favor. Meanwhile, a man exept for brains given to him by nature has currently few other prerequisites to do that in despite of the fact that increasing number of researchers concentrate themselves on interactions between human society and environment; a man as a part of Biosphere with its other components. Long-run process of sciences differentiating brought to methodological and staff unreadiness of scientific community to solve such a complicated interdisciplinary problem as optimisation of interrelations between social-economic and natural systems, though achievements made in these sciences are pronounced. Thus, ecology as a science which gave rise to the system approach as the basis for methodology, can be and currently becomes the starting point for problems formulation and analysis of the scientific results obtained. A special role of ecology as a science which integrates all the sciences is notable in view of specific nature of current postnonclassic science development characterized by present-day problem of scientific theories and sciences integration (Phylosophy of Science, 1995). Ecology, in more exact terms, as an ecological approach to phenomena studying has become a general scientific approach nowadays (Gerasimov, 1978). A distinguishing feature of current ecology development is an attempt to use its achievements for creation of scientific basis for human survival, human living being and in the long run for development of social-evolution strategy (Kirillov, 1997). If phylosophy considered to be a metascience and concentrate of methodology ecology, probably, is a basis for postnonclassic stage of phylosophy itself. It is professor A. Ptitsin (1995) opinion that ecology in future should be phylosophy of nature science and life since it deals with natural-science, economic, social, cultural and other aspects. The object of modern ecology is ecosystems including the largest one – Biosphere. Modern ecology is a science on ecosystems revealing mechanisms of their composition and structures. We can call a system any real or conceivable object entire features of which could be presented as a result of its parts interaction by recognising Platon statement that the entire is something larger than sums of its parts (Fedorov, Gilmanov, 1980). Ecosystem can be defined as a complicated system including jointly living 5
organisms (biocenosis) and environment components which are kept in constant interaction (Figure 1.1).
Figure1.1 - Scheme of ecosystem "Ecosystem" notion is close to “natural complex”. In both cases 1) a system approach is observed, 2) elements (or a set of elements) of the system coincide and 3) interest of investigators to studying these relations is marked. But if the notion on natural geosystems (including biocenosis) assumes equality of all elements, the ecosystem notion contains principle division of the system’s elements into two large subsystems: 1) "master" and 2) "dwelling" (oikos), "environment", "resources", thus inequality of elements is set into the notion. All the relations are evaluated above all due to their effect on the "master". If relations among the environment elements don't influence directly or indirectly on the "master" state they are considered to be insignificant under ecosystem studying (Figure 1.2). In other words, according to the ecosystem concept one of the element is certain to be placed in the system center or considered as the "subject". Hence the subject for the study changes greatly under the object invariability. Any component of the environment or society can act as the ecosystem "master". A centered approach is implicitly manifested in geomophological knowledge on morphosculpture where relief is considered as the "master" subjected to "environment" (climate, vegetation, water) influence. There is a "soils" notion as a "landscape image". Elements of environmental approach are distinctly expressed under considering the nature as "environment" and "resources" for industry and agriculture development ("master"). It immediately follows that biocentered variant of environmental approach (ecology of living beings) and environmental approach on the whole differ from each other (Trusov, 1983). 6
Figure1.2 - The differences between models of geosystem (I) and ecosystem (II) 1-4 – elements of system; 5 – relations among elements; 6 – subgroup "master"; 7 - subgroup "environment" We decided to consider the peculiarities of ecological (ecosystem) approach in detail, first, to clear up the issue whether thorough analysis of abiotic components under studying of composition, structure, functioning of natural and man-made ecosystems evolution is required; second, to note that the needs for biocentered approach at initial stage of investigations may be insufficient for relationships establishment of spatial-temporal entity of these complicated on structure and behaviour systems. Complexity of the structure is defined by system elements number – n and a number of relations among them – m; as for the system behavior complexity it is determined by character and diversity of responses to any impact (Fleishman, 1982). 2 THE FACTORS OF DIVERSITY AND TYPOLOGICAL INDICATOR OF AQUATIC ECOSYSTEMS Joint effects of numerous ecological factors of different spatial (global, regional, local) and temporal scales; natural and anthropogenic ones determined the ecosystems’ peculiarities. Type of ecosystem is defined by the largest on temporal and spatial scales, natural in origin factors. Thus, dynamics and gradient of global factors like heat and moisture determine all spatial and temporal consequences of ecosystems in accord with Law of geographical zonation formulated originally for soils by V.V. Dokuchaev. Azonality (extrazonality) are stipulated by regional and local factors capable to level the infuence of zonal features combination. The most 7
important factor of azonality is entering extra matter and energy competitive on intensity with zonal one. Ecosystem diversity is one of the biological diversity levels which is based on the study results of diversity at genetic and species levels as well as on the data on conditions diversity for forming and functioning biological systems. It is suggested to refer a number of different habitats, biotic communities and ecological processes to ecosystem diversity (Mc Neely et all., 1990) by means of ecosystem typification on the basis of their ecotopes which are more conservative and stable than biocenoses (Rysin, 1995). Intensity of water exchange is the governing characteristic to define water objects as reservoirs (stagnant waters) or as streams (flowing). Water objects are involved simultaneously in outer exchange, when waters and substances come from the outside and go far beyond the object limits, as well as in the inner one occured in water objects themselves (Bogoslovsky, 1975). The index for intensity of outer water exchange is conventional water exchange: Kwe=Vi/Va is the ratio of volume of average annual inflow to water object (Vi) to water object volume at the average level (Va) (Grigor'ev, 1959a; 1959b; Dolgov, 1954). For river sections Va=ωL, where ω – mean area of section at the site; L – the section's length. Another index of water exchange Кw=Vw/Va is the ratio of total water bulk involved in outer water exchange (precipitation and inflow from the basin or runoff from the water object and evaporation from aquatic surface) (Vw) to the same reservoirs volume (Va) (Butorin, 1965). Kwe and Кw are similar to flowing water reservoirs and Кw reflects best the specific nature of water balance in internal–drainage water objects. Water exchange is dependent on specific watershed ∆F=F/fo – the ratio of watershed area (F) to water surface (fo) (Grigor'ev, 1959a; 1959b; Bogoslovsky, 1960; Sokolov, 1959). Similarly to conventional water exchange "conventional salt exchange" of water objects (Kse= Psi/Psa) can be defined as the ratio of average annual ion inflow (Psi) to average salt stock in the water object (Psa=Sa*Va, where Sa - mean water salinity). Period of water stay in the water object and consequently the level of the reservoir autochthonous processes effect on the waters are connected wth intensity of outer exchange. Transition of waters and substances through the water object dominates in case of intensive outer exchange; under reduced one accumulation in water object predominates. Thus, two groups of water objects prevail, namely, transit and accumulative ones; as this takes place, 8
there are intermediate groups as well like transit-accumulative and accumulative-transit ones. Rivers distinquished by the most intensive exchange (Kwe or Kse 50300 and more) belong to a transit group. Runoff makes up input-output volume of water balance. The water quantity transported through the river site exceeds by tens and hundreds times the river's bed capacity and exchange occurs during one or several days at the sites of hundreds of kilometers. Heterogeneity (two currents which are differ in water properties) is observed under inflow of a large tributary distinguishing from the main river by velocity, turbidity, water salinity (Dolgov, 1954; Zenin, 1961; 1965). The ocean and undrained lakes belong to the accumulative group since transit of water and substances associated with the runoff is not observed. The world ocean has the least among world water objects indices for exchange (Kwe=326*10-6; Кse=6,4*10-6). Full exchange of its waters can be underway approximately for 3000 years. In large undrained lakes (e.g. Aral lake) water exchange increases by some percent, that is , it can be in progress for tens of years while salt exchange requires less time. Intermittent lakes of accumulative group are distinguished by specific exchange. Under Кwe=1 water loss by evaporation is marked. As for substances brought by the current they are left in the hollow and partially subjected to weathering. Transit-accumulative group is presented by reservoirs and drained lakes where runoff giving 90 % of waters to water objects and with higher input-output dominates in water balance. As for lakes this index is less a bit. Water exchange in most reservoirs is less significantly than in rivers (Kwe Ilmen' Lake – 3,4; Gorkovsky reservoir – 6,1; Dneprovsky reservoir – 15; Novosibirsk reservoir - 9), water exchange occurs several times per year. Salt exchange is lower there as well (Kse Ilmen' Lake – 3,4). Accumulative-transit group consists of large fresh water drained lakes similar on water exchange to accumulative group (Kwe Ladoga Lake, Telerskoye Lake – 0,07; Onega Lake – 0,05; Baikal – 0,003) but they differ from this group by constant weak transit of waters and substances due to runoff. Full water exchange can be in progress during tens or hundreds of years. Salt exchange is more intensive compared with accumulative reservoirs (Кse Ladoga and Onega Lakes – 0,06). The weaker outer exchange is the smaller role in its biocenosis formation and functioning the basin plays and larger role – the reservoir autochtoneous processes that results in more stable characteristics of the ecosystem on the whole. 9
S.S. Shwartz (1976) formulated universal law for ecosystem characteristic ("good ecosystem"): High level of production (biomass) of main chains of trophic systems. High compensatoring activity due to increase under multiplication of productivity by biomass up to maximum. High stability of ecosystem under change of outer conditions within wide range due to trophic diversity. High rate of matter and energy exchange due to high activity of reducing ecosystem element. Ability of quick reconstruction of the community structure under change of environment. To differentiate aquatic ecosystems with respect to biological and system features diversity of taxonomic composition; information structure complexity; completeness and balance of trophic structure of biocenoses; intensity of energy and substances fluxes with estimating of relalive share of allochthonous and autochthonous organic matter, degree of their transformation and accumulation; level of trophicity; distribution of typical life-time of biocenosis elements and dynamics of abiotic factors; rate and direction (tendency) of communities evolution (succession), biocenosis and the ecosystem on the whole are used. 2.1 Composition, structure and functioning of aquatic ecosystems in the Ob river basin
different types of
It is Professor’s I.V. Stebaev (1993) opinion that the watershed of the Ob basin can be called as a water area since there are numerous water objects here and the whole spectrum of ecosystems of stagnant and flowing waters: water ways of different size; mountainous and steppe lakes of different size and salinity; small and large reservoirs, marshes. The peculiarities of forming and functioning of the basin streams and reservoirs ecosystems are specified by diversity of natural conditions and character of vast territory use which makes up 15% of Russia. First investigations of aquatic ecosystems of the Ob basin were made in the 17th century. Necessity in making practical decisions on natural resource use in the region promoted and stimulated greatly such a research. For example, project on construction of hydropower station on Biya river gave rise to thorough studying of Teletskoye lake by State Hydrology Institute. In the 80th just this very lake attracted considerable interest again because of the need for giving ecological examination of Katun hydropower 10
station project. Specialists from numerous institutes studied Katun river and its tributaries as well as Lake Teletskoye as analogue for future reservoir. Long term complex research of Ob river and its basin for many years was made due to the project on Siberian rivers runoff redistribution including Nizhneobsk hydropower station and reservoir construction to solve hydroeconomic problems of Kazakhstan and Central Asia. Construction of Novosibirsk hydropower station in the 50 th gave impetus to carrying out investigations on the Ob, from Kamen-on-Ob up to Novosibirsk. Thus, Novosibirsk reservoir became the object under study for many years and to different specialists who investigated it as the reservoir of complex purpose including as a source of a water supply for Novosibirsk, as an ecosystem and as a model object for studying particular ecological communities and processes. Design and construction of Krapivinsky hydraulic power system resulted in the 80th in great bulk of various data on Tom river. Making prognosis on environment state changes as a result of construction and operating of Kansk-Achinsk fuel and energy complex (KAFEC) contributed to intensive complex investigations of rivers, lakes and reservoirs in Chulym river basin in the 70-80th. Information and data on ecosystems of Alei River basin and Ob-Irtysh interfluvial area were used to assess nuclear tests after effects at Semipalatinsk Test Site. Nowadays there is the need for assessment of aquatic ecosystems of Mid and Lower Ob as well as Tom River state and prognoses for their change since level of river waters contamination by petroleum products is rather high. Water objects of West Siberia were always of great concern to researchers because of the region’s stagnant and flowing waters use for fishing and recreational (including treatment) purposes as well. Natural prerequisites for human morbidity especially aggravated by anthropogenic factors are one more reason for carrying out research. Let us consider typological features of composition structure functioning and succession of the Ob basin aquatic ecosystems taking as an example the Ob itself in the part from mountainous tributaries up to KarymKary settlement; large oligotrophic lake Teletskoye; steppe mesotrophic lake Gorkoye-Peresheechnoye situated in Ob-Irtysh interfluve and coolingreservoirs of thermal power stations in Inya and Chulym river basins (Figure 1.3).
11
Figure1.3 - The scheme of the Ob river basin 2.2 Ob River Rivers are considered to be the most dynamic component of Hydrosphere since changes of river bed waters are registered in the average every 11 days (L'vovich, 1986). Rivers as the system of removal of water and wind erosion products as well as wastes from the territory redistribute anthropogenic load within geo- and hydrosystems. As this takes place, in addition to standard classification of rivers by sites on morphological features (upper, middle, lower) it is suggested to consider changes of substances' flows, fluxes of energy and information, succession of river biocenoses and genesis of water quality along the stream. If we broaden the 12
trophicity notion as the basis for limnetic system classification, oligo-, meso- and eutrophic sites could be detected in the river. Trophicity change as a characteristic for living organisms development level, intensity of substances and energy fluxes along the river takes place due to natural reasons but its significant shift towards as increase ( in case of entering allochthonous organic and biogenic substances) as decrease (due to toxic substances and pollutants coming to the river) can be observed. Selfpurification potential of the river is followed by trophicity. Heterogeneity of features and the greatest changes in chemical composition of water downstream the river occurs when the river crosses different geographical zones, i.e. rivers running in meridianal direction (Alekin, 1970). One glowing example of such a river is the main water way of West Siberia – Ob River. Its ecosystem is subjected to intensive anthropogenic load factors increasing in the direction from the source towards the river mouth. Katun River with its Yarly-Amry, Chibitka, Chuya, Chemal tributaries as well as Lake Teletskoye tributaries with average monthly annual t0 not higher than 200C, high oxygen content, rapid flow, rocky and stony-pebbly ground are considered to be ritral (Illies, Botosaneanu, 1963). Biocenoses features are the following: absence of true zoo-and phytoplankton mass development of cold-loving stenothermic amphibiotic insects larvas (103 taxones, biomass is up to 69g/m2). Biomass in the Katun basin was presented mainly by caddis flies (Trichoptera) larvas; in Tevenek river (Lake Teletskoye tributary) – gammarides. Mountainous water ways of the Upper Ob are similar to rivers of Far East regions by taxonomic content and relative role of particular incect order in zoobenthos. Drift of bottom invertebrates reached its maximum during floodplain in Chemal river (up to 16 smpl./m3) and in Tevenek river (up to smpl./m3) when increased benthos mass due to breeding was observed. Use of integral water quality index, i.e. the Vudiviss index which reflects, probably, specific hydrobionts response to habitat degradation enables one to ascertain that favorable conditions for hydrobionts (in Katun, Chemal, Chuya rivers) are marked exept for insignificant deterioration in Chibitka river and unfavorable conditions in Yarly-Amry river (Rudneva, 1995). Major vegetation of mountainous water ways are lithophile phytoovergrowings presented mainly by diatoms. Values of total biomass for the Katun reached 76g/m2 due to Hydrurus foetidus golden algae development; for the tributary of the second order, i.e. Chibitka river 116g/m2 due to Didimosphenia geminata diatoms; and in the tributary of the third order, i.e. Yarly-Amry river - up to 208 g/m2 due to Ulothrix zonata green conferva. It should be noted that kseno-and oligosaprobic species 13
prevailed (Kim et al, 1992). All in all, 323 species and 133 types and forms of algae from 90 genera and 48 groups among which diatoms types (76,5%) prevailed and green (10,8%) and bluegreen (7,4%) algae played a subordinated role, were found in the Katun and its tributaries in 1988-1989. Algae runoff formation due to washing off benthos algae from their natural places of habitat is distinguished by significant diversity (up to 63 form in a sample) in biomass (0,129-0,898 g/m3). Specific algae content in Katun river, absence of phytoplankton as well as unstable character of benthos groups indicate that the rivers capability to self-purification is low (Safonova, 1993). The Ob site situated upper of Novosibirsk reservoir is typically flat but its ecosystem (which is considered complete on biotic communities content) is influenced by mountainous Katun and Biya rivers which form the Ob. Average monthly water temperatures are maximum in June and don’t exceed 19,2 0C. Investigations made there in 1989 and 1993 showed various phytoplankton (179 species) occurrence with predominance of green, diatom and to lesser degree bluegreen algae and essential fluctuations in number (9,4-501 th.cells/l) and biomass (0,03-1,1 mg/l) downstream the river. The maximum values for biomass were registered in the mouth part of Biya river (near Biya town) and Chroomonas acuta dinophite algae - one of dominants of Teletskoye Lake was found. Species of algae belong to βmesosaprobic ones. Approximately 50 species with predominance of Rotiferia wheel animalcules under maximum values of total number - up to 91,4 th.smpl./m3 and biomass - up to 1,817 g/m3 were revealed in zooplankton. One of the methods for investigation of spatial-temporal heterogeneity of living organisms distribution and revealing of integral changes in the river and watershed area under influence of natural processes and anthropogenic load is phytoplankton pigments concentration studying. Seasonal, annual dynamics and distribution of major photosynthetic pigment of phytoplankton along the Ob were studied (Kirillova et al., 2000). As for annual aspect trophic status of the upper Ob is stable one. Content of "a" chlorophyll varied within 2,9-51,2 mg/m3. In AugustSeptember, 1999 in the course of complex experiments water sampling was made on the river site from the Tom river up to Irtysh river mouth and the content of "a" chlorophyll was within 2,9-51,2 mg/m3 which differed little from the content obtained during studying of phytoplankton photosynthetic pigments near Barnaul in the period of low water in previous years: 14,2 and 13,0 mg/m3, respectively. Its minimum was registered in July lower Krasny Yar settlement and maximum - in August at the site situated lower the Tom river mouth. The 14
Kruskall-Vallis nonparametrical criterium for comparison of several independent samplings was used to characterise spatial distribution and temporal dynamics of "a" chlorophyll and other photosynthetic pigments for analysis of the data obtained in July and August (Zaks, 1976). Analysis of calculations showed that for 95% of confidential interval reliable differences between single points of sampling in July were absent. Considerable differences between the river banks and water ways and 0-1 m horizons were not found as under assessment of mid stream tributaries effects on "a" chlorophyll content in the Ob river waters. As for temporal aspect, increase in pigment characteristics values was marked in August as compared with ones in July under 1-5% level of importance. Sharp fluctuations of "a" chlorophyll concentrations, practically by 5 times, were registered at the water surface of water way in the course of investigations carried out in the 3d decade of August - first decade of September, 1999 at the site of Mid and Low Ob river. The highest values for "a" chlorophyll concentration were observed lower the Tom River nearby Bragino and Karym-Kary settlements; the least values were marked in tributaries mouths and near Nizhnevartovsk (Figure 1.4). Reliable differences between 3 points on cross section for all sites studied during this period weren't revealed. Differences in content of key photosynthetic pigment in Mid Ob tributaries and main river bed (namely, in the Tom waters near the mouth average on section value (15,4±1,5 mg/m3) was less (p>DM and Eq. (17) may take the form:
C C Vi t x i x i
C D(ii ) xi
(18)
If turbulent diffusion is isotropic then all coefficients D(ii) take the same value DT and Eq. (18) is written in the form:
C C 2 C Vi DT t x i x i x i 133
(19)
In the special case of one-dimensional flow with constant velocity U, this formula is simplified to:
C C 2 C U DT 2 t x x
(20)
If M is the amount of mass added into the flow field at position x=0 and time t=0 then, the solution of the above equation is:
C ( x, t )
( x Ut ) 2 M exp 4 DT t 4DT t
Analytical solutions may also be found for turbulent diffusion in twodimensional space, but the main difficulty of the problem is not so much the mathematical solution but rather the physical and mathematical description of the coefficient of turbulent diffusion DT. In fact, on the basis of the definition of this coefficient as given in Eq. (16), the value of DT depends upon the physical characteristics of the flow field. A basic question which arises is to find how the coefficient of turbulent diffusion is related with the physical characteristics of the flow field and, in particular, the scale of the turbulent flow. It is obvious that the value of DT becomes larger as the characteristic length l of turbulent vortices increases, but the correlation between these two variables differs depending upon whether it refers to free turbulent flow or to shear turbulent flow influenced by solid walls. For a free and homogeneous turbulent flow, Batchelor has used the spectral theory of Colmogoroff to define that
D T ( const .)1 3l 4
3
(21)
where is the mean value of energy losses due to viscosity per unit mass, and l is the scale of turbulent vorticity involved in diffusion. The relationship (21) has been corroborated experimentally by Orlob. To define the coefficient of turbulent diffusion a number of semiempirical theories have been developed in the past, such as the Prandtl characteristic length or theories which are based on the method of Lagrange, i.e., the monitoring of the motion of one or two fluid particles (Taylor, 1921). 134
The study of turbulent diffusion in cylindrical or prismatic channels and in one- or two-dimensional flows with free surfaces (rivers, coastal areas, etc.) has been advanced substantially with the hydrodynamic dispersion approach explained below. Turbulent Dispersion We have seen earlier that the description of turbulent diffusion is based on a change of scale. At the microscopic scale of molecules, molecular diffusion predominates. The superposition of stochastic motions due to turbulence leads to turbulent diffusion, which develops at a greater scale and is based on the temporal mean turbulent variables at every point. If we now consider a larger scale and treat the phenomenon on the basis of mean velocities in a cross-section perpendicular to the direction of the flow, then we introduce the definition of convective dispersion by means of dispersion coefficients Dx, Dy which correspond to the turbulent dispersion coefficients DTx, DTy respectively. Frequently, a coastal region or a water body have a geometry which does not allow the modelling of the circulation of the fluid in one dimension. We must, therefore, consider both velocity components parallel to directions x and y. These velocities are caused by tides, wind currents or other reasons and may be described with the equations of motion and continuity. If H is the depth of the flow, we introduce the mean velocities along the depth U and V from
1 U H
H
1 V H
udz 0
H
vdz
(22)
0
Let C be the mean pollutant concentration along the depth H, then the convective diffusion equation for two dimensional flow yields
C C C C U V Dx t x y x x y
C D y (4.26) y
The dispersion coefficients Dx and Dy depend upon the flow characteristics and vary according to the velocities U and V. It must be stated that, if the turbulent mixing of the pollutant occurs at the surface of the flow (surface diffusion), we may still use Eq. (23) by integrating the velocities and the concentrations at a given depth below the surface. 135
The dispersion of pollutants in a two dimensional and homogeneous flow of infinite width has been studied by Elder (1959). If qx and qy are the flow rates per unit width parallel to directions x and y, ë is the frictional loss coefficient and yo the depth of the flow stream, the dispersion coefficients are given by:
Ds 5, 9 / 2 Dn 0, 2 / 2
q 2x q 2y yo q 2x q 2y
yo where s and n indicate the direction of the flow and that normal to it, respectively. To describe specific cases of pollution Eq. (23) may be integrated numerically. For the dispersion coefficients one may use any theoretical or empirical formula, as long as the numerical results describe satisfactorily in situ measurements. Growth Kinetics Wastewaters contain various microbial organisms in the form of dispersions or flocculates. The main types are - Bacteria: these constitute the major group of micro-organisms (Total Coliforms, E-Coli). - Protozoa: single-cell animal organisms feeding on bacteria - Algae: single-cell plant organisms In aerobic digestion conditions the fundamental reaction occurring is BACTERIA + ORGANIC MATTER + OXYGEN + NUTRIENT SALTS = CO2 + H2O + NEW BACTERIA The organic matter consists of carbon compounds such as proteins, carbohydrates, oils, fats, etc. Since their exact chemical composition may not be determined with ease, these are treated quantitatively all together through the parameters BOD (biological oxygen demand), COD (chemical oxygen demand) or TOC (total organic carbon). BOD is the amount of oxygen required for aerobic biological digestion of the organic effluents. This parameter was first introduced in England. Its measurement has been specified to be performed at 20oC at the end of 5 days (BOD5). This was deemed necessary to simulate water 136
temperature in English rivers, given that these are of relatively short lengths. After 5 days the wastewaters reach the sea where dilution becomes so large that the occurrence of septic or anaerobic conditions is prevented. As shown schematically in figure 7.11, at 20oC, all available organic matter is oxidised after approximately 6-10 days. Subsequently, only biological oxidation of the ammoniac nitrogen into nitrates occurs.
Oxygen Consumption
BOD
Nitrification
BOD
u
BOD
6 to 10 days
5
5 days
Time
Time
Figure 7.11 - Oxygen demand and residual (BOD)u. At higher temperatures the oxidation of ammoniac nitrogen may proceed faster. In figure 7.11 the dashed curve shows the total oxygen demand with no nitrification. In this case, an asymptotic value (BOD)u is reached. As a first approximation, the exponential relationship
BOD ( BOD ) u 1 exp( kt ) applies. Then, BOD5 is approximately equivalent to 65% of (BOD)u. COD is the amount of oxygen required for complete chemical oxidation of the organic content. Bacteria, being living organisms, need special conditions of temperature, nutrients, etc., to grow. Vitamins and metabolic compounds may catalyse growth, while poisons delay the process. 137
In figure 7.12 a typical growth curve for bacteria is shown; the time scale is only indicative. Introducing the bacterial load in solution containing organic matter, the growth of micro-organisms is very slow initially (adjustment period). This is followed by exponential growth during which the consumption of organic nutrients is substantial. When food is diminished, an equilibrium condition is reached, followed by a reduction in the cellular organisms (endogenous stage).
(Log ) number of cells
equilibrium
8 exponential
decrease
7
6
5
15
10
Time (h)
Figure 7.12 - Growth curve for bacterial load The biochemical kinetics of various compounds reacting with each other (bacteria, oxygen, organic matter and nutrients) may be described quantitatively with various formulations. These are based on different modelling of the underlying molecular kinetics. Let define as C the concentration of organic compounds (in ppm or g/l or mol/l). For biochemical kinetics the most important parameter is the biological decay or growth rate dC/dt. This rate increases with increasing probability that the various reacting compounds come in contact with each other. In an analogy, the number of possible collisions between the two 138
black and three white spheres in figure 7.13 is proportional to the product of the number of black and white spheres. Indeed, sphere M1, as well as M2, may collide with any one of the three spheres A1, A2 or A3. The total number of collisions per time is proportional to the product between the numbers of white and black spheres (2x3).
A1 M
1
A2 M2
A3
Figure 7.13 - Influence of particle concentration on the collision rate Let define as Xa the number of bacteria per litre, O the concentration of oxygen and N the concentration of nutrients. Then, the biological decay rate is
dC k C XaO N dt
(24)
We now assume that the number of white spheres in figure 7.13 is very large. Since white spheres are present everywhere, the frequency of collisions depends only upon the number of black spheres. For the case of a constant microbial concentration X a in excess of oxygen and nutrients, Eq. (24) may be rewritten as 139
dC k Xa C dt
(25)
Eq. (25) describes the biochemical kinetics only for small values of concentration C. When concentration C increases saturation occurs, so that the growth rate becomes independent of concentration (figure 7.14).
dC dt saturation
C
Figure 7.14 - Growth rate curve of organic load Eq. (25) may be generalised as follows
dC k k X a C k m C k X a m 1 dt C
(26)
When C then dC/dtconstant. In fact, the digestion rate is influenced by the autocatalytic action of bacteria, which grow during the reaction. As shown in figure 7.15, starting from point a (high concentration C), the rate increases with the growth of new bacteria. At the same time, the concentration of organic load drops and we reach an equilibrium region (optimal region, point b). Past point b the reaction rate is reduced, since the organic load concentration drops asymptotically to zero. Eq. (26) represents the fact that the biological digestion rate of organic matter depends upon the microbial concentration and the concentration of organics. 140
dC dt b
c
a
C Figure 7.15 - Curve of autocatalytic growth of organic matter 3 RIVER WATER QUALITY Rivers and streams are natural drainage systems not only for rainfall water but also for different substances which may be dissolved in various concentrations. Overland flows discharge into rivers and streams pollutants from non-point sources distributed over the entire catchment area. Also wastewaters of industrial, domestic and agricultural origin are discharged into rivers. For relatively low quantities of pollutant loads, turbulent mixing, re-aeration, sedimentation and re-suspension in rivers transport wastewaters from the source away into the sea (James (ed.) 1993). If, however, wastewater loading from municipal sewage overcomes the receiving capacity of the river, negative effects may appear, as shown in figure 7.16: (1) decrease in the concentration of dissolved oxygen (DO); (2) increase in organic matter (BOD) and nutrients; (3) increase in the population density of certain microbes; (4) decrease in the variability of different species. If toxic substances are discharged into a river, then biological species may disappear within a certain distance from the discharge point (figure 7.17a). A rapid decrease followed by a progressive increase of populations may be observed (figure 7.17b) in case of large amounts of suspended solids, which are discharged into the river. 141
DO
Sewage
Dissolved Oxygen DO
Species variability Population density
x or t
Figure 7.16 - Effects on river water quality and species populations from sewage disposal To assess the risk of river pollution, different mathematical models have been developed. Most of them refer to the relation between organic matter (BOD) and dissolved oxygen (DO). These apart, models describing the transport and fate of nitrates into rivers have also been developed. Numerical simulation, application of the Monte-Carlo technique and analysis of time series of water quality data may be used to quantify the risk of pollution. The above are briefly discussed in the following sections. Physically Based Mathematical Models For river water quality, physically based mathematical models describe the mechanisms controlling the transport and fate of pollutants in one-dimensional space. These are (1) advection, with mean velocity U; (2) turbulent dispersion, with coefficient DT; (3) biochemical interactions.
142
Toxics
Species variability Population density
x or t
(a) Suspended material Species variability Population density
x or t
(b) Figure 7.17 - Impacts on the ecosystems in the river from the disposal of (a) toxic chemicals and (b) suspended solids The mass conservation of n related chemical species Ci, i = 1, 2,..., n may be expressed by a set of n coupled, nonlinear, partial differential equations of the form 143
C i C 1 C U i ( ) {( D T ) i } fi (C1 , C 2 , . . ., C n ) t x i x x (27) where is the cross section of the river and fi(C1,C2,...,Cn) the temperature-dependent biochemical production or depletion rate of species i. If only one pollutant is considered, for and DT = constant, Eq. (27) is reduced to the one-dimensional advective dispersion equation in the form
C C 2C U DT 2 t x x
(28)
In the classic work of Streeter and Phelps, two species are considered, such as: C1: organic matter BOD ® C (29) and C2:
oxygen deficit
D=Cs-DO
(30)
where Cs is the saturation dissolved oxygen (figure 7.18). Using the symbols (28) and (29), the relationship between the rate of BOD discharge and the resulting concentration of DO, take the form of the following two coupled, partial differential equations. Sewage
D=Cs -DO C
s
DO sag DO RIVER
Figure 7.18 Schematic view of the oxygen deficiency sag curve 144
C C 2C U D T 2 K1C K 3C t x x
(31)
D D 2 D U D T 2 K1C K 2 D t x x
(32)
where K1 is the deoxygenation rate (T-1), a function of temperature and composition of the organic matter; K1 is of the order of 10-6 s-1; K2 the reaeration rate (T-1), which depends on the turbulent flow near the free surface of the water, the wind speed, etc. An empirical relation gives:
K2
4. 5 10 5 U1/ 2 -1 [s ] H3/ 2
(33)
where U is the mean velocity (m/s), and H the mean water depth (m). Solution of Eqs. (31), (32) gives the oxygen sag curve (figure 7.18): near the site of wastewater disposal the BOD is high and the oxygen deficit will increase downstream. Then, because of reaeration, the deficit will gradually decrease. More sophisticated physically based models may be developed by use of Eq. (27). For example, first order chemical kinetics may be used to represent the nitrification process, i.e. the decay of organic nitrogen and ammonia-nitrogen to nitrate-nitrogen through nitrite-nitrogen conversion (Thomann et al., 1971).
145
8 PARTICLE TRACKING TECHNIQUES FOR WATER QUALITY ASSESSMENT ABSTRACT This lecture deals more specifically with the assessment of water pollution problems. The quantification of pollution risks in coastal, river and aquifer systems is analysed by appropriate particle tracking numerical techniques, simulating transport, dispersion and physico-chemical reactions. A case study from coastal pollution in the Bay of Thermaikos (Greece) is presented. 1 RANDOM WALK SIMULATION Let consider the one-dimensional diffusion of a mass M introduced at time t = 0 in an infinitesimal distance around x = 0 (Figure 8.1). Mathematically, this initial condition is written as
C0 C( x , 0) M ( x )
(1)
where (x) is the Dirac delta function. Assuming that the mass M is diffusing without transport, the concentration C(x,t) is a solution of the one-dimensional diffusion equation
C 2 C D 2 t x
(2)
The well-known solution of Eq. (2) with the initial condition (1) is
C ( x, t )
x2 exp 4Dt 4 Dt C0
(3)
If 2 = 2Dt is substituted into Eq. (3), the Gaussian distribution with zero mean and variance 2 is obtained:
146
x2 C ( x, t ) 1 exp 2 C0 2 2
(4)
C (x, t)
t=0 mass M
t x x=0 Figure 8.1 - Diffusion of mass M introduced at time t = 0 at x = 0 Suppose now that a particle located at x = 0 oscillates randomly between maximum distances either +x or -x, with equal probability. For homogeneous probability distribution function p(x) we will have
p(x) = 0 p(x) =
if
1 2x
p(x) = 0
x < - x
i f - x < x < + x
if
(5)
x > + x
The mean value m = E(x) and the variance E(x - m)2 of this movement are
m = E(x) =
2 s
+ x - x
2
= E(x - m)
xp(x)dx = 0 + x - x
147
x 2 x p(x)dx = 3 2
(6) (7)
According to the central limit theorem, after n steps, the probability density distribution function P(x,t) is Gaussian, with mean value
nm=0 and variance 2 2
S = n s
This means that
x2 P( x, t ) exp 2 2 (n s2 ) 2(n s ) 1
(8)
Comparison between Eqs. (8) and (3) or (4) indicates that the two solutions become identical if 2
n s 2 D t or 2 t s = 2 D ( ) = 2 D t n
(9)
From Eqs. (9) and (7) we can evaluate x as
x 2 s = = 2 D t 3 x = 6 D t 2
or (10)
If we introduce a random variable rnd(-1, +1), which is distributed uniformly between -1 and +1, then Eq. (10) takes the form
x =
6 D t rnd (-1, + 1)
(11)
A random walk simulation of the one-dimensional diffusion equation (2), subject to the initial condition (1), should be performed according to the following steps (Ganoulis, 1977): (1) A large number N of particles is introduced at x = 0, t = 0; (2) Particles move by time increments t. If xn,p is the position of the particle p at time nt, then its position xn+1,p at time (n+1)t should be: 148
x n+1,p = x n,p +
6 D t rnd (-1, +1)
(12)
(3) Counting the number of particles located between x - x/2 and x + x/2 and dividing by the total number N of particles, a numerical approximation of Eq. (4) or Eq. (8) may be obtained. We may now extend the above for the case in which the fluid moves in the three-dimensional space. If V:( u , v , w ) is the velocity vector, considering N particles located at time t t at positions
r n ,p ( x n , p , y n , p , zn , p )
p = 1, 2,. . .,N
(13)
According to the random walk principle, the probability to find a particle at a given position after time t follows a Gaussian distribution with mean value 0 and variance s2=2 t D, where D is the dispersion coefficient. Now the particles are moving from time t= t to time t+ t=(n+1) t according to the relations
x n 1, p x n, p ut x1 y n 1, p y n, p vt x 2 z n 1, p z n , p wt x 3
(14) (15) (16)
where u, v, w are the velocity components of the current and x1, x2, x3 random variables following a normal distribution with mean value 0 and variance s2=2 t D. The procedure is illustrated in figure 8.2 for three particles initialy located at the same point A. Every particle is moving according to the relations (14) and (15). After 10 time steps the particles occupy three different positions A1, A2 and A3.
149
A2 A1
A
A3
Figure 8.2 - Random walk of three particles after 10 time steps
A2 A1
A
A3
Figure 8.3 - Grid overlay in the random walk of three particles 150
To evaluate probabilities and concentrations of the particles, the area is covered by a regular grid (figure 8.3). Knowing the velocity components u, v at the grid points, particle velocities are computed by linear interpolation. The probability for reaching a given grid cell and consequently the particle concentrations are evaluated by counting the number of particles which fall within the grid square. If instead of the initial condition (1) a continuous mass concentration is introduced at x=0 as
C( x 0, t ) Co
(17)
Then, the analytical solution of the diffusion equations (2) with advection velocity U is given by
x Ut C Co 1 erf , x 0 4 Dt
(18)
The validation of this random walk simulation is given in Figs. 8.4 and 8.5 for D=1 and D=0.01 m2/s respectively. In all cases we have U=1 m/s and x =1 m; this means that Peclet numbers based on x take values 1 and 100. Even if we introduce 10 times more particles (Figure 8.4) oscillations of the random walk simulation persist, although the front of the wave is well described (Figure 8.5) at high Peclet numbers (Ganoulis, 1977). An example of a two-dimensional random walk simulation is given in figure 8.6 and 8.7.
151
(a)
24
16 t=8s
32
D= 1 U= 1 x=1
(b)
D= 1 U= 1 x=1
Figure 8.4 - Comparison between the analytical solution and random walk simulation for (a) N=1,000 and (b) N=10,000 (Low Peclet number)
152
t=8s
16
24
32 D=0.01 U=1 x=1
Figure 8.5 - Comparison between random walk simulation and the analytical solution for a high Peclet number
Figure 8.6 - Two-dimensional random walk simulation
153
Figure 8.7 - Contours shown the impact probabilities from a local source emitting a pollutant with constant concentration Co=105 (Probability is in log coordinates) This method suffers from some drawbacks, however: first, to obtain statistically meaningful results a large number of particles, at least 103, has to be used. When continuous emissions of pollutant sources take place the necessary number of particles becomes very large. Secondly, because of the statistical origin of the method, the concentration field shows oscillations and averaging in time may be necessary to obtain smooth results. When a deterministic current velocity field is used in Eqs. (14) and (15), the solution obtained approaches that of the two-dimensional convective-dispersion equation. 2 DISPERSION BY WIND GENERATED CURRENTS Impact risk from wastewater discharges in the far field is more realistically assessed by using the time data recordings of currents. The time series of wind-generated current velocities which are measured over one whole season are usually stationary. Thus all statistical properties of the random variables, such as the current velocity and direction are independent from the time origin. 154
Now consider a large number of particles (Csanady, 1983; Ganoulis, 1991d; Roberts, 1989) initially located at the same point (point source), but departing at different times t=n t. Each particle moves during a given travel time T>t, where T=t+m t=(n+m) t. The final position r (t+T) of the particle after time T may be evaluated using the randomly varying current velocity field V (t)
r
(t+T) =
T V (t )dt
(19)
It is obvious that the final position of every particle depends on the initial departing time t. By allocating different values of t to each particle, different final positions of the particles after time T are found. Because of the stationarity of the random process, the concentration field and the probability of reaching a given location are independent of t. Having a relatively long record of time series of currents Vi, the impact probabilities and consequently the risk assessment of pollution at a given location are evaluated. After travel time T=(n+m) t, Eq. (19) takes the form: n m r (t,t+T) = Vi t i=n, ....n+m (20) n Counting of the particles at every location is done by using a grid overlay as in the case of random walk simulations. Pollutant concentrations are proportional to the number of particles located within every square of the grid. The statistical characteristics of the current velocity components are given in table 8.1. It may be recognised that standard deviations are larger than average values. This indicates the high temporal variability of currents. The autocorrelation functions of current velocity components u and v are shown in Figure 8.8. The form of these functions means that after an initial time lag greater than about 500s, the autocorrelation function takes very small values. This means that that wind generated velocities become uncorrelated or random and that autocorrelation tends to zero as time tends to infinity.
155
E stim ated Autocorrelatio ns 1
u-component
coefficient
0 .5
0
-0 .5
-1 0
20 0
400
lag 1
600
800
(x 1 0 ) s
v-component
coefficient
0 .5
0
-0 .5
-1 0
200
400 600 tim e la g (x1 0 ) s
80 0
Figure 8.8 - Autocorrelation functions of current velocity components u and v The results of this simulation are shown in figure 8.9 in the form of lines of equal probability. The pollution field varies with time T after the first release of particles which represent the discharged wastewater.
156
Table 8.1 - Statistical characteristics of velocity components u and v Variable Sample size Average Variance Standard deviation Minimum Maximum Range
U (cm/s) 2047 5.06 53.19 7.29 -19.22 - 25.25 44.47
v (cm/s) 2047 -1.39 14.38 3.79 -18.39 11.92 0.31
T=6h
T=12h
T= 24h
Figure 8.9 - Contours of equal environmental impact probability after time T= 6, 12 and 24h from initial release (Wind generated currents and continuous constant discharge with Co=1 from a point source) 157
3 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 (Figure 8.10).
U
1 u
1 U
u
45 0 1
Figure 8.10 - The standard uniform random variable U Cumulative function FU(u) is the bisectrice line in the plane u-FU(u). We have:
FU ( u ) = P (U u ) = 158
u 0
dx = u
(21)
The methods for generating random numbers with uniform probability distribution are mainly based on recursive relations in the form:
x k 1 ( ax k b )(mod m)
(22)
where a and b and m are non-negative integers. The Eq. (22) means that residuals of modulus m are first computed as:
x k 1 ( ax k b ) m {Int (
ax k b )} m
(23)
where Int is the integer part of the number. Then random numbers between 0 and 1 are obtained by the ratio:
u k 1
x k 1 m
(24)
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 (figure 8.10)
Fx (x k ) = FU (u k ) = u k -1
x k = FX (u k )
(25)
For reliability computations, the Monte Carlo simulation technique proceeds in three steps: 159
(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. F (x)
F (u)
X
U
1
u
45 0
1
u
x
Figure 8.11 - Relation between random variables X and U 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. 4 ACASE STUDY: COASTAL POLLUTION: THERMAIKOS GULF (MAKEDONIA, GREECE)
THE
Using the results of monitoring in twelve stations over the time period 1984-1990, the water quality in the Thermaikos bay area is presented. In all these stations temperature, salinity, pH, dissolved oxygen, nitrites, nitrates, ammonia, phosphates, silicates, heavy metals, total coliforms and E-coli have been measured in the water column with seasonal frequency. There is 160
a general trend in water pollution to increase from south to north and from the open sea to the river estuaries. This reflects the effect of pollutant loads from human population in the northern region and from river flow. Mathematical modelling of the transport and fate of pollutants in the bay are used to assess the risk of pollution. The use of the models in analysing various combinations between the choice of the disposal site and the degree of sewage treatment is discussed. Meteorological and local climatic information is essential in analysing the long-term quality characteristics of coastal waters. More specifically, with respect to any global warming, it is useful to see the likely effect of the speculated climate change scenarios on coastal water quality. This can be studied by simulation, as presented below for a typical case in the Mediterranean, the Thermaikos Gulf, Makedonia, Greece. The question is: what would the consequence be on the water quality of Thermaikos Gulf from a doubling in the carbon dioxide content of the atmosphere (2xCO2 scenario)? In the case study, only the direct influence of temperature changes on water quality will be considered. Indirect effects, caused by variations in the amount of runoff or rainfall precipitation entering the water body, have not been included. Description of Thermaikos Gulf Thermaikos Gulf is located at the north-west corner of the Aegean sea with a width of 15 km at its maximum opening between Aherada Peninsula, on the west, and Epanomi on the east (figure 8.12). The maximum "height" of the gulf, from north to south, is 45 km and its total surface 473 km2; Figure 8.13 sketches its bathymetry. Thermaikos is open only on the south side. It constitutes the discharge basin for one major (Axios) and three minor in terms of flowrate (Aliakmon, Loudias, Galikos) rivers (Figure 8.12). All three carry water year-round, with flow rates varying between 10 m3/s and 400 m3/s from summer to winter. The flow rates vary greatly also due to irregular drainage from agricultural irrigation (Ganoulis, 1988a, 1990, 1991a). In addition, the sewage from the town of Thessaloniki (1,000,000 inhabitants) is also discharged into the gulf.
161
Thessaloniki AEGEAN SEA
THERMAIKOS GULF
GREECE
Figure 8.12 - Geographic location of Thermaikos Gulf
162
Thessaloniki
Bay Area
Epanomi Aherada Figure 8.13 - Bathymetry of Thermaikos Gulf (in [m])
The main climatological data in the region are shown in tables 8.2 and 8.3. The prevailing winds are S-SE, during summer, and N-NW during winter. Strong winds (>15 m/s) are infrequent and of short duration, lasting one or two days and arising usually during winter. Table 8.2 - Meteorological characteristics in Thermaikos Gulf: temperature during period 1930-75 (from Ganoulis, 1988a) Temp [oC] Min Max Ave
J
F
M
A
M
J
J
3.0 10.5 6.0
2.9 11.3 7.3
6.3 13.7 10.0
12.1 17.4 14.8
17.5 22.3 19.6
22.6 25.4 24.0
25.4 28.3 26.8
163
J 25.4 28.3 26.8
A 25.4 28.4 26.5
S 20.2 25.4 22.4
O 14.2 21.5 17.2
N 9.5 14.5 12.4
D 5.2 11.5 8.0
Year 15.3 17.5 16.2
Tab. 6.2 - Meteorological characteristics in Thermaikos Gulf: precipitation during period 1930-75 (from Ganoulis, 1988a) Month Precip.[mm]
J 41
F 35
M 40
A 41
M 49
J 37
J 27
A 20
S 31
O 51
N 56
D 55
Year 483
Beaufort strength [m/s]
1-2
3-5
6-7
>=8
1-3
3-10
10-17
>=17
The initial design of the sewerage system of the city of Thessaloniki is shown in Figure 8.1.4. The Figure focus on the upper part of the gulf, known as Bay of Thessaloniki. The main sewer collector (SC) is a tunnel of 2m in diameter, located in an averaged depth of 20m. This pipe collects all the sewage of the city from the eastern to the western part of the greater Thessaloniki metropolitan area. It ends in the sewage treatment plant (TP), located close to the river Gallikos (Figure 8.14). An advanced treatment of sewage has been decided, including bio-oxydation of wastewater. After this treatment, the disposal of wastewater has been initially provided into the river Axios using a twin-pipe system between the sewage treatment station and the river Axios (Figure 8.14). Because of the environmental concern about the water quality in the river and estuary, the design has been modified. This is due to the fact that the flow rate of the river Axios has been constantly decreased during the last few years, leading to lower wastewater dilution. In the same time, for the protection of river and coastal waters, the new water quality standards should be applied, according to the directives issued by the European Union. The coastal area close to the river mouth is considered as a protected area of very great importance from the ecological point of view. According to the RAMSAR convention this area is a special protected estuary. An estimation of the pollutant loads discharging into the bay is given in table 8.4. 164
GALLIKOS TP SC
THESSALONIKI
AXIOS PE
S1
BAY
Figure 8.14 - Sewage collection and treatment plant in the city of Thessaloniki Until a biological treatment of all wastewater would implemented in the near future, a preliminary operation of the treatment plant is provided (1992). During this transitional period, the wastewater disposal is made in the upper part of the bay (point PE), by using a ditch parallel to the bed of the river Gallikos (Figure 8.14). The local environmental impacts in this area and especially the concentrations in coliforms have been studied by application of risk assessment and mathematical modelling techniques (Ganoulis, 1991d; 1992). Important questions raised for the design are: a. is a submarine outfall (S1 in Figure 8.14) needed? b. if so, what is its best location? c. what is the optimum degree of wastewater treatment in relation to a possible eutrophication in the bay?
165
Table 8.4 - Pollutant loads in the bay of Thessaloniki Pollutant Sources
Flowrate (m3/day)
BOD5 (kg/day)
N (kg/day)
P (kg/day )
Sewage
150,000
60,000
10,000
4,000
Industrial wastewaters Axios
60,000
10,000
5,000
?
Winter 170 m3/s Summer 20 m3/s
50,000
16,000
4,000
Aliakmon
Winter 80 m3/s Summer 10 m3/s
20,000
3,000
900
Loudias
Winter 30 m3/s Summer 10 m3/s
20,000
3,000
900
Pumping stations
Winter 15 m3/s Summer 2 m3/s
20,000
4,000
400
Water Circulation Patterns A 3-D hydrodynamic model, which simulates the wind-induced circulation at various depths has been developed. The hydrodynamic model integrates the Navier-Stokes equations in the finite-difference grid; this is described on a regular Cartesian coordinate system, in the x-y plane, and the transformed coordinate ( z ) H along the vertical -z. H is the water depth and the surface elevation. On the basis of mathematical simulation work and in situ measurements the average water circulation patterns during winter and summer have been determined (Ganoulis, 1988a; 1990). Tidal currents are insignificant; total tidal elevation in the inner bay do not exceed 30 cm. The measurements show that, during summer, strong stratification of the water occurs with the warmer surface layers remaining stable over the colder depth layers; this leads to relatively anoxic conditions at the bottom. In 166
contrast, during winter, the colder and denser surface layers destroy the stratification and satisfactory vertical mixing in the water column results. Consequently, the worst conditions for pollution occur during summer. The understanding of the water circulation is of great importance. Previous measurements of currents using drogues, driftcards and currentmeters (Balopoulos and James, 1984; Ganoulis and Koutitas, 1981) and the application of hydrodynamic models (Ganoulis and Koutitas, 1981; Krestenitis and Ganoulis, 1987) have led to the following conclusions: (a) tidal currents are very low(< 5 cm/s); (b) external circulation from the N. Aegean sea creates a current entering the bay along the eastern coast and creating a cyclonic circulation; (c) currents are mainly due to the winds.
x
y
y
H
z
x
z
Figure 8.15 - The 3-D grid used in hydrodynamic computations During the summer, sea breezes create a residual water circulation, which is very characteristic for the pollutant transport. In fact, this is the most critical circulation state for the pollutant advection because, as the currents are small, an increase in pollutant concentration is observed. In the present development of mathematical modelling, steady state hydrodynamic conditions corresponding to the prevailing winds are used. To assess the risk of pollution in the gulf, the convective dispersion model has been used. For the numerical integration of the equations involved, various numerical algorithms have been developed during the last decade. Algorithms based on finite differences or finite elements suffer from numerical diffusion and trailing effects. Lagrangian models based on random walk simulation (cf. chapter 4) or using a mixed Eulerian167
Lagrangian approach have been found reliable to simulate the fate of pollutants in the Thermaikos Gulf (Ganoulis, 1990; 1991a). These models have been tested in simple cases where analytical solutions are available and validated by using the data collected. They have been adopted as tools for studying the environmental impacts from several alternatives of remedial measures aiming to protect the water quality in the gulf. Water Quality Assessment Monitoring of water quality characteristics and data processing is the basis for formulating computerized mathematical models and decide the appropriate remedial measures for environmental protection. The main objective of this study is the assessment of the present environmental situation in the bay of Thermaikos and the environmental impact analysis of the sewage works, actually under completion in the city of Thessaloniki. As shown in Figure 8.16 appropriate sampling stations non-uniformly distributed in space have been selected. Using the research vessel "THETIS" (13m long) during the period 1984-90, more than 2,500 water samples have been collected and analysed. Apart from the currents and winds, the following parameters have been monitored with seasonal frequency near the surface, the mean depth and near the bottom of the water column: (a) Temperature, salinity, density, dissolved oxygen, Ph; (b) Nutrients as NO2-, NO3-, NH4+, PO43-, SiO44- ; (c) Total coliforms and E-coli; (d) Heavy metals as Cd, Pb and Cu. Heavy metals have been also analysed in sediments. Variations of the water quality parameters are very large both in time and space. As an example the time series of nitrates at the station 1, located near the city of Thessaloniki is shown in Figure 8.17. These variations are due to the irregular physical conditions which prevail in the Mediterranean. In fact, the tides are very low and the wind induced circulation is strongly unsteady and variable in space. In view of the large variations of the data a statistical analysis has been performed. The contour lines of equal dissolved oxygen concentrations are shown in Figure 8.19. These are mean values over the time period 1984-89 near the seafloor. From these data a statistical trend is deduced for increasing of the water pollution from south to north (high population density) and to the river estuaries (high pollutant loads). In fact four different zones are distinguished, ranged from very bad to excellent water quality situation (Ganoulis, 1988a). 168
AXIOS
TH ES SA LO NI 1 KI
ÁA
9
2
8 3
7
N 4
6
5
Figure 8.16 - Location of sampling stations in the Thessaloniki bay NO -3 (ppm) 1.2 1 0.8 0.6 0.4 0.2 0
0
4
8
12
16
20
24
Time (x3 months)
Figure 8.17 - Time series of nitrates (NO3-) recorded at station 1 near the surface 169
Figure 8.18 - Distribution of dissolved oxygen (DO) in the Thermaikos Gulf (mean values over 1984-89 measured near the seafloor)
(a)
170
(b) Figure 8.19 - Experimental results for the distribution of DO near the bottom of the Gulf (averaged annual values (a) 1992 and (b) 1991) (from Ganoulis, 1988a; 1990) It should be noticed (Figs. 8.18 and 8.19) that mean annual values of dissolved oxygen are not constant, especially for the years 1991 and 1992. A general improvement can be observed in 1992, possibly due to the operation of the wastewater treatment plant (started beginning 1992). Ecologically sensitive coastal zones in the bay area, requiring special protection measures, are shown in Figure 8.20. These include the major part of the western coast near the rivers, where the water depth is small and large quantities of nutrients are discharged from the rivers. In this part of the bay, oyster farms have been developed, producing several millions of tonnes of oysters every year. With the new operation of the wastewater treatment plant, the risk of contamination of shellfishes by coliform bacteria should be evaluated. Chlorination for sewage desinfection has to be used very carefully (Ben Amor et al., 1990) in order to avoid formation of THM (Tri-Halo-Methanes) in coastal waters.
171
THESSALONIKI
ALIAKMON AXIOS
PE
Wetland Oyster farms
Submarine Outfall
Figure 8.20 - Sensitive zones in the bay of Thessaloniki The assessment of risk of water contamination has been made by using two methodologies, which are explained in chapter 4: (1) the random walk simulation and (2) the use of data of wind generated currents in form of time series To validate the random walk simulation, the actual situation has been studied near the site where the wastewater is discharged (Paliomana, site PE in Figure 8.21). The validation has been based on a choice of the "best" values of two parameters: the dispersion coefficient D and the time T90 of the bacteria decay. By use of data from sampling, the best choice of these coefficients has been made by calibration (Ganoulis, 1991d, 1992). This is the case shown in Figure 8.22a, where the values D=4 m2/s and T90=5h have been found.
172
City
Khinarou
PE Paliomana
PO S
1
Bay
Oyster farm Monitoring station
Submarine Outfall
Figure 8.21 - Sensitive zones near Paliomana 104 particles have been used over the total time simulation period. Small oscillations due to the statistical character of the method are not very important for the applications. By using a fixed grid and counting the number of particles located in a given grid cell, the lines of equal concentration are obtained (Figure 8.22(a) and (b)). It is noticed that sampling has made also during the night. The value T90=5h represents a mean value between day and night time situations. The results of simulation shown in Figure (6.13a) are in good agreement with the measurements (Ganoulis, 1992). Comparison has been based on the C80 concentrations (80% of the samples having C < C80). These concentrations must comply to EU standards within the oysters growing area. To obtain a further dilution of wastewater, the use of a short submarine outfall is a good solution (Figure8.22b).
173
City
Khinarou 5 4 3 2 1
Bay
Oyster farm Monitoring station
Submarine Outfall
(a) City
Khinarou
4 3 2 1
5
Bay
Oyster farm Monitoring station
Submarine Outfall
(b)
Figure 8.22 - Contours of E-coli concentrations: simulation of the actual situation (a) and using a submarine outfall S1 (b) 174
When time series of currents is available (Figure 8.23), the direct simulation method based on the displacement of particles with the random velocities of the currents gives more realistic results. This method has been used to evaluate the risk of pollution from two different discharge sites in the Bay.
Figure 8.23 - Time series of current velocity u
175
9 THE HYDRODYNAMIC AND HYDROTHERMAL BASE OF THE ECOLOGICAL MODELING OF LAKES AND WATER BODIES INTRODUCTION A water environment, in which hydrobionts live, interacting with the other components of ecosystem, has the certain temperature and is constantly moving. The rates of bio-chemical processes in the ecosystem depend on water temperature. Hydrobionts, products of their metabolism and nutrients move together with the water motion. Thus, it is necessary to have the values of water flow velocity and water temperature as the input data for the mathematical modeling of water ecosystems. The latter are usually calculated basing on a proper flow and heat transport model, which is usually regarded as the component (or sub-model) of more general waterecological model. 1 THE MODELS OF TURBULENT FLOWS AND HEAT TRANSPORT The flows in natural water bodies are usually turbulent. Turbulent water motion and heat transport processes in the water bodies are described by the following governing set of equations [2, 9, 14]: the x-direction momentum equation 0
z u uu vu wu 1 lv g dz t x y z x 0 z u u u K K K ; x x x y y y z z z
(1)
the y-direction momentum equation 0
z v uv vv wv 1 lu g dz t x y z y 0 z
(2)
v v v K K K ; x x x y y y z z z
the continuity equation and the equation of state – u v w T ; 0; x y z the heat transport equation -
(3)
(4) 176
T uT vT wT T T T D D D , t x y z x x x y y y z z z where t - time; u , v и w - components of velocity in x y и z directions respectively; T - water temperature; g - acceleration of gravity; l - the factor of Coriolis; K x , K y and K z ( Dx , D y and Dz ) - eddy viscosity (eddy diffusivity) in horizontal ( x , y ) and vertical( z ) directions respectively; - deviation of the water surface elevation from it’s 0 undisturbed level z ; - ambient fluid density and 0 - it’s referential value. There is a variety of different empiric formulas for the determination of eddy viscosity and eddy diffusivity. For example, "4/3" formula of Richardson. They can be also determined using the models of turbulence and particularly, k models, containing the equations for turbulence and rate of it’s dissipation. The system of equations (1) – (4) of 3-D model demands a big amount of computational resources for it’s numerical realization. Thus, it is often simplified in practice and the models of lesser dimension are used: 2-D (vertical and horizontal), 1-D (vertical and horizontal) and 0-D (volumetric) models. For example, 2-D vertical model is a result of lateral averaging of hydrodynamic and hydrothermal conditions under the assumption of it’s uniformity in lateral direction over the water body. Such simplification is possible for the water bodies of an oblong form, when their width is much lesser than their length. Such water bodies include river reservoirs and lakes of an oblong form, such as Lake Teletskoye. 2 MODELING OF FLOWS AND ICE-THERMAL CONDITIONS IN LAKE TELETSKOYE The first works for the mathematical modeling of ice-thermal conditions of Lake Teletskoye were based on unsteady 1-D vertical models. In the work [5] the vertical thermal conditions and the turbulent structure of the lake in the period of autumn-winter cooling and spring warming as far as the ice thickness dynamics are modeled. In the work [7] the annual thermal conditions of Lake Teletskoye are studied basing on the vertical 1D model. The methods of heat balance equation, momentums and turbulence parameters averaging over the horizontal planes were used there. The heat content of ice layer was taken into account while modeling of ice growth and melting processes. 177
But it must be taken into account that the significant changes in the seasonal dynamics of the lake thermal structure take place not only in vertical direction, but along it’s longitudinal axis also because of the big length of the lake and it’s relatively small width. Thus the approach proposed in [24] is used in the works [12, 13] for the modeling of this lake. This approach includes the averaging of the momentums equations, the mass conservation equation, the heat transport equation and the equations for turbulent energy and it’s dissipation rate over the width of the lake. The investigation of thermal conditions of Lake Teletskoye was carried out in that works not taking into account water compressibility. It was assumed that the value of water density, which was used in the equation of state, depended only on temperature. But the recent theoretical studies (look, for example [10, 21,26]) of deep lakes, and especially lake Baikal, have displayed that water compressibility, or, more precisely, the dependence of water density on pressure in the equation of state, plays the big role in the behavior of deep water in that lakes. This is mainly determined by the fact, that the maximum density temperature decreases with the depth increase (with the water pressure increase) from 4˚ C at the water surface by 0.2˚ each 100 m. 2.1 Formulation of the problem [11] The equations of laterally averaged model of hydrothermal processes in the lake [13], taking into account water compressibility, are: z0 bu buu bwu 1 gb dz t x z x 0 z u u bKx bKz sr u u ; x x z z
bu bw q; x z bT buT bwT T T bDx bDz qTin ; t x z x x z z w
1.0 p
(5)
(6) (7) (8)
kp , 12
b 2 b 2 i where s 1 i , x axis is directed z i 1 x along the lake from the river Biya towards the river Chulyshman, z - up; 2
178
u and w - components of velocity in x and z directions respectively; q
- lateral inflow per unit area; Tin - lateral inflow temperature; b x , z lake width; b b2 b1 ; b1 and b2 - ordinates of lateral surfaces of the lake; K x and K z ( Dx and Dz ) - eddy viscosity (eddy diffusivity) in horizontal ( x ) and vertical ( z ) directions respectively; r - shear stress factor of a lateral surface of the lake; - ambient fluid density and 0 -
it’s referential value; w T , S - density of water under a standard atmospheric pressure; S - water salinity, which is assumed here to be
constant and equal 75 mg/l [20]; k p T , S , p
- volumetric module of
water elasticity; p - hydrostatic pressure. The formulas recommended by UNESCO are used here for the definition of
w T , S and k p T , S , p
functions (look, for example, [3]). The initial and boundary conditions must be adjoined to the set of equations (1) – (4). In the initial moment of time velocity, temperature and water surface level distributions are set. On water surface at z the kinematics condition, wind shear stress and heat flux are set:
u w T u w ; K z ; c p Dz qn , (9) t x z z where w - wind shear stress, q n - heat flux through the water surface, c p - specific heat of water; At the bottom of the lake at z z0 the normal velocity and the heat flux are set to zero and the shear stress is expressed by the quadratic law:
w 0 ; Kz
u T kb u u , k b 014 . ; 0. z z
At the inlet vertical boundary of the lake , where the water of the river Chulyshman inflows to it, velocity, water discharge, and the temperature of inflowing water are set. At the outlet vertical border of the lake, where the river Biya outflows from it, velocity and water discharge (or the relationship between discharge and water level known as a rating curve) and the diffusive heat flux equal to zero are set. The wind shear stress and the heat flux at the water surface [9] are calculated using solar radiation and daily-averaged meteorological data 179
(wind speed, air temperature and humidity, atmospheric pressure and cloud) by the following formulas:
w a cwW 2 , 11 . 10 3 if W 6 m / s ; cw 3 . 10 0.72 0.063W if W 6 m / s , 10 where a 13 . kg/m3 – air density, W - wind velocity (look, for example, [1]);
q n q sr q ar qbr q e q c ,
(10)
where q sr - short wave solar radiation, q ar - long wave atmospheric radiation, qbr - long wave water surface radiation, q e - heat flux caused by evaporation, q c - heat flux caused by heat conductivity and convection. The following formulas are used for the calculation of this [23, 27], where the fluxes are expressed in kcal/(h·m2):
q sr q sc 1 w 1 0.65 C 2 ; 6
q ar 4.46 10 13 Ta 27315 . 1 017 . C2 ; 4
qbr 4.74 10 8 Ts 27315 . ;
q e f W2 es e2 ;
(11)
q c 0.459 f W2 Ts Ta ,
(12)
where q sc - solar radiation at clear sky per unit of horizontal area per unit of time, kcal/(h·m2); C - cloud in parts of 1;
w - water albedo; Ta air temperature at 2 m altitude, ˚C; Ts - water surface temperature, ˚C; W2 - wind velocity at 2 m altitude, m/s; e2 - partial pressure of water vapor at 2 m altitude, mm of mercury column. Saturated water vapor pressure at water 180
surface temperature es , mm of mercury column, and wind function
f W2 are calculated by the following formulas: 5278 ; es 25.4 exp 17.62 Ts 27315 . 4.3 W2 , if v 0.0148 W2 3 ; f W2 3 3.54 W2 , if v 0.0148 W2 ,
v Tsv Tav ,
Tsv Ts 27315 . 1 0.378 e s pa , Tav Ta 27315 . 1 0.378 ea pa , where Tsv - virtual temperature of a thin layer of vapor in contact with water surface, Tav - virtual temperature of air, pa - atmospheric pressure, mm of mercury column. The longitudinal distribution of the lateral inflows ) was set as the delta–functions in the inlet points. The measurement data of the lateral inflows water temperature was used while setting Tin in the heat transport equation (7). The vertical eddy viscosity and eddy diffusivity are defined using the equation for the turbulent energy e and its dissipation rate [19]:
be bue bwe e e bKxe bKze b P G b ; t x z x x z z b bu bw bKx bKz t x z x x z z 2 c1 b P 1 c3 G c2 b , e e e2 c1 144 . , c3 08 . , c2 2.0 10 . 0.3exp ReT 2 , ReT .
181
(13)
(14)
Here K xe ( K x ) and K ze ( K z ) - eddy diffusivity for the turbulent energy (its dissipation rate) in horizontal ( x ) and vertical ( z ) directions respectively; - cinematic water viscosity. The border conditions, described in details in [12, 13], are used in the turbulence model (13) and (14). Taking into account water compressibility and lateral wind shear stress, the terms of turbulence generation in this equations look as:
u 2 v 2 T P K ; G g T K a , z z z where the factor of thermal expansion is determined by the formula
1 T
, p
a - adiabatic temperature gradient, equal to 10-5 ˚C/m (this is the value for the fresh lake water according to D.Farmer, look, for example,, [4]), T 0.8 . For the purpose of parameterisation of the influence of lateral currents on the turbulence generation P , the lateral velocity shear v z was introduced into the expression for the turbulence generation, using the mathematical model of wind-generated current [8] following the idea of B.V. Arhipov and V.V. Solbakov [1]. Horizontal eddy viscosity and eddy diffusivity are determined using the formula of Richardson [18]. And their specific values were brought in [13]. The model of ice cover forming and development in this work is represented by the ice thickness ( t ) , equation, expressing the heat balance in it [25]:
i L f
d q ni q w , dt
(15)
i - ice density, L f - latent heat of ice melting, q ni - heat flux, incoming to the ice cover through it’s top surface, q w - heat flux, where
182
outcoming from the ice cover to water through it’s bottom surface (through the border separating ice with water). The heat flux, outcoming from the ice cover to water is determined by formula:
q w k w Tw T f ,
(16)
where k w - integral factor of heat conductivity, Tw - water temperature at the ice surface, T f - freezing point. The heat flux through the top ice surface q ni }$ is calculated by formula (10) for q n , in which the water surface temperature is replaced with the temperature of ice cover top surface, and water albedo is replaced with the ice albedo calculated by formula [25]:
0.45 , if Ta 0 C ; i . exp 0.07 Ta , if Ta 0 C . 0.25 016 Also, the corrective factors must be introduced into formulas (11) and (12) in the case of ice cover existence:
q e k e f W2 e s e2 ; q c k e 0.459 f W2 Ts Ta , where k e - the empiric factor, expressing the difference between water and ice roughness, Ti - the temperature of the ice cover top surface. Temperature Ti is found using the equation of heat fluxes balance at the top surface of ice cover:
q ni qi 0,
(17)
where qi is calculated by formula
183
qi k i
T f Ti
(18)
,
in which k i - ice heat conductivity factor.
Ti is obtained by solving the algebraic equation (17) with the iterative method of Newton. If the obtained value Ti is higher than the freezing point T f , what corresponds to the ice melting and appearance of water on it’s surface, we set Ti to T f . Here we neglect the thickness of water layer on the ice surface like in [25]. The reaching of freezing point by water is used as a condition of ice appearance. In the case of ice cover existence on the water surface (on the surface separating ice and water) the heat flux from ice to water q w is set instead of heat flux from air to water q n in the equation (9):
c p Dz
T qw. z
Also, we assume that the wind influence is absent on the water surface ( w 0 in the equation (9)). Basing on the results of numerical experiment, it was assumed that the mentioned conditions began to act when the ice thickness t exceeded 2 mm. Note, that there is no turbulence generation source caused by the wind-induced shear current in the case of ice cover existence. According to [22], seiches are the important source of turbulence in the case of ice cover existence. They are not directly taken into account in this work, but the turbulence, which they generate, is accounted via the eddy viscosity factor, which is equal to10-4 m2/s [22]. 2.2 The numerical results The model is numerically realized using the semi-implicit finite difference scheme [13]. The algorithm based on splitting by physical processes is used for the numerical solution of the motion equations. At the first fractional step the momentum transport is performed by advection and diffusion and at the second fractional step the hydrodynamic fields 184
adaptation is simulated [15]. Ice thickness equation (15) is solved by a method of The Runge-Kutta. Let us remind, that Lake Teletskoye is a deep flowing water body of an oblong form (Figure 9.1). The length of the lake is 77.8 km, maximum width is 5.2 km and the maximum depth is 325 m. The main part of inflow comes to the lake from the Chulyshman river in the southern part of the lake and the outflow takes place through the Biya river in the opposite northwestern part [20]. The simulations of the thermal structure of Lake Teletskoye were performed for the 1968-1969 hydrologic year, because that year measurements are the most completely presented in the literature and field measurements data [16, 17, 20]. According to this data the homothermal condition was reached by May 20 1968 [20]. This date was used as the beginning of the simulations listed below. Let us remind, that the hydrologic year begins in the April, thus our annual period of simulation has some shear in comparison with it. The simulations were begun from the quiescence with a uniform distribution of the initial temperature with a value equal to 2.3 ˚C, according to the measurements data. For the numerical analysis of the influence of water compressibility on the seasonal dynamics of thermal regime of Lake Teletskoye the numerical simulations, not taking into account water compressibility, were performed (pressure p 0 in the water state equation, what is in accordance with the atmospheric pressure) with the same input data. The results of the simulations display (Figure 9.2b), that not taking into account water compressibility leads to more intensive water mixing in the deep zone of the lake. According to the numerical solution, a uniform temperature distribution in the mentioned zones under the isotherm 4 ˚C with the value about 4 ˚C take place. This is connected with the loss of stability and appearance of turbulent convection. The mechanism of penetrative convection is well known (look, for example, [6]). The essence of it is in the rise of turbulence under the hydrostatic instability. In the current model this mechanism is realized via turbulence generation by the buoyancy force. When taking into account water compressibility (Figure 9.2a), the deep zones of the lake are less undergone convective mixing connected with the loss of hydrostatic stability. Although the temperature difference is small, the processes of turbulent exchange and, consequently, heat exchange, gas exchange, and oxygen exchange in particular, qualitatively differ in the deep zones of the lake. So, the results of the numerical simulations display that water compressibility must be used for the more accurate description of thermal conditions and turbulent mixing processes in Lake Teletskoye. 185
According to the observations data, the characteristic feature of the hydrothermal behavior of Lake Teletskoye is the formation of thermal bar fronts at its ends. and their movement to the central part of the lake. A thermal bar rises in the lake twice in a year: in the middle of May in spring and in the beginning of November in autumn. The duration of the springsummer thermal bar is almost 2 months, and of the autumn one – about a month. A thermal bar divides the lake to 2 parts, which have the different thermal conditions, chemical composition and distribution of hydrobionts [20]. The rising of the mentioned thermal bars is conditioned by the fact that water is heated more at the ends of the lake than in its deep central part where the water temperature is less than 4 ˚C in the period of thermal bar development. In the north-western part of the lake water is warmed more rapidly because of its relatively small depth, and in the southern part water warming is aided also by the warmer water inflow from the Chulyshman River. In the zones of cold and warm water mixing, where the water temperature reaches the value of maximal density 4 ˚C, the powerful thermal gravity circulations with the down-flows are developed (Figure 9.3). The mentioned circulations may play an important role in the function of lake ecosystem. Although the water velocity in it is relatively small, they can carry oxygen down to the bottom zones of the lake and carry nutrients up to the water surface. The thermal gravity currents accompanying a thermal bar are superposed by the Biya and Chulyshman inflow-induced and wind-induced currents. The results of the numerical simulations display the movement of the spring-summer thermal bar fronts towards the central part of the lake with their following confluence (Figure 9.4 and Figure 9.5). According to the measurements data “by the July 15 the fronts of the thermal bar are closed up and the lake becomes uniform” [20] in the longitudinal direction. According to the numerical results, the closing up of the thermal bar fronts and the setting in uniformity along the length of the lake (at least in the significant part of it) takes place approximately since July 13-15. The temperature field in the longitudinal-vertical section of Lake Teletskoye (isotherms) is given at Figure 9.6. It describes the thermal bar behavior in the period of autumn cooling of the lake. The autumn thermal bar fronts also rise in the north-western and southern parts of the lake and then move towards its center. The comparison of the calculated and observed temperature distribution at the vertical in the central part of the lake (road vertical № 26) is given at Figure 9.7 for June 20, July 20, August 20, September 20, October 20 and November 20 (sequentially from left to right and from top 186
to bottom). According to the results of the numerical simulations, the values of water temperature in the bottom zone of the lake are 3.6 - 3.8 ˚C by August 20, and the uniform vertical temperature distribution with the value 4.0 ˚C is set in by November 20, what corresponds to the field measurement data [20]. The comparison of the calculated and measured vertical temperature distributions at the different road verticals, situated along the lake (look at Figure 9.1), at August 20 is given at Figure 9.8. The comparison of the calculated and measured [17] ice thickness at the observation point near the settlement Yailu at the different moments of time is given at Figure 9.9. At last, the distributions of the calculated ice thickness along the lake at the different moments of time are given at Figure 9.10. Let us remind, that the wind of speed usually increases when moving from land to a lake. The meteorological data were obtained at land, at the lakeside meteorological station Yailu. The following values of the lake wind to land wind ratio were used in this work: 1.18 in June and July, 1.36 in August and 1.5 in September [20]. For the other months of a year this ratio was set to 1.5, because the long-time average annual data provides for this ratio a value about 1.5 for October-December [20]. Also, a small value of wind influence on the thermal conditions of the lake, caused by the ice cover, was taken into account. The additional simulations, not taking into account the mentioned correction of wind speed by moving from land to the lake, where carried out. The comparison of this simulations results with the results of basic simulations displayed that they provide the reasonable difference of the thermal conditions of the lake. Nevertheless, taking this correction into account has the significant influence on the ice thickness distribution along the lake, making it more smooth and realistic. So, the results of simulations and its comparison with the measurement data displays that the mathematical model describes the main futures of the thermal and ice conditions of Lake Teletskoye.
187
Figure 9.1 - Plain view of Lake Teletskoye (V.V. Selegei, T.S. Selegei [20])
188
Figure 9.2 - Calculated distribution of temperature (isotherms) in the longitudinal-vertical section of Lake Teletskoye along it’s length at August 20 1968, taking (a) and not taking (b) into account water compressibility
189
Figure 9.3 - The fields of temperature and velocity in the longitudinalvertical section of Lake Teletskoye along it’s length at June 20 1968. the road vertical № 26
190
Figure 9.4 - The dynamics of the spring-summer thermal bar fronts advancement: the distribution of temperature (isotherms) in the longitudinal-vertical section of Lake Teletskoye along it’s length at July 5 and July 8
191
Figure 9.5 - The dynamics of the spring-summer thermal bar fronts advancement: the distribution of temperature (isotherms) in the longitudinal-vertical section of Lake Teletskoye along it’s length at July 11 and July 15
192
Figure 9.6 - The dynamics of the autumn thermal bar fronts advancement: the distribution of temperature (isotherms) in the longitudinal-vertical section of Lake Teletskoye along it’s length at November 20 and November 25
193
Figure 9.7 - The comparison of the calculated (solid lines) and the measured (rectangles) distributions of temperature in Lake Teletskoye at 20.06.68, 20.07.68, 20.08.68, 20.09.68, 20.10.68 and 20.11.68 at the road vertical № 26 (from left to right and from top to bottom respectively)
194
Figure 9. 8 - The comparison of the calculated (solid lines) and the measured (rectangles) distributions of temperature in Lake Teletskoye at 20.08.68 at the road verticals № 22, № 24, № 6, № 26, № 13 and № 27 (from left to right and from top to bottom respectively; look at Figure 9.1)
195
Figure 9.9 - The dynamics of ice thickness in Lake Teletskoye near Yailu settlement (road vertical № 6). Solid line – the calculated values, bullets – the observed values
Figure 9.10 - The distributions of ice thickness along the length of Lake Teletskoye (from north to south) at 20.11.68 (XI), 20.12.68 (XII), 20.01.69 (I), 20.02.69 (II), 20.03.69 (III), 20.04.69 (IV), 20.05.69 (V). Solid lines correspond to the even months, dotted lines -- to the odd months 196
197
10 NUMERICAL MODELLING OF LAKE AND RIVER ECOLOGY 1 MODELLING What is a model: - a small scale copy of something; - a text written to understand (ecologist, geographer, sociologist write to understand, assemble concepts); - a set of concepts, translated or not into mathematical equations. I will talk about mathematical modelling of lakes and rivers ecological processes. Let’s build a model M(L, Q*), (figure 10.1) which is a suitable representation of a lake or a river L, model which is built to give an answer to the question Q, consistent with the model M, derived from the question Q*. The model will give an answer R in the virtual world that we have to transfer (translate) to the real world.
answer R*
lake, river... L
question Q*
analogy, analogy, analogy, analogy, analogy... answer R
Vi rt ual w orl
Model M(L, Q)
question Q
s
l od e m , s t d, repres p ent ation, conce Figure 10.1 - Modelling
198
1.1 River and lakes ecosystem modelling River and lakes ecosystem modelling implies a great number of interacting processes concerning physic, chemistry and biology. Each process, through concepts will be described by equations. Equations link variables, state variables and forcing variables. State variables includes the unknowns, the results given by the model. Forcing variables includes the input data. Parameters are numbers used in the equations; their value is measured or guessed or taken from literature.
Input data
Equations
Results
1.2 Classification of physical and biological complexity The following graph (figure 10.2) gives a simple classification of ecological models types used for lakes and river. The horizontal axis indicates the physical discretisation from 0D to 3D. OD means that the domain is considered to be well mixed. 1D means that in the domain we take into account heterogeneity along one direction. 3D means that the domain is divided in three directions. Each volume where concentration is considered to be homogeneous is also called a representative elementary volume (REV). The way discretisation is done will be described further on. The vertical axis indicates the possible biological complexities of ecological models. It goes from very simple model like the one designed by Vollenweider (OECD, 1969) to complex models with hundreds of state variables. This will be detailed later. Physical complexity Figure 10.3 shows what we mean by physical complexity. This figure shows different types of discretisation. The modelled domain is transformed in a set of boxes (or representative elementary volume or REV) where concentrations, state variables are homogeneous.
199
PHYSICAL COMPLEXITY
BIOLOGICAL COMPLEXITY
0D
Biochemical, phosphorus balance
1D
2D
3D
Vollenweider 1969
Simple trophic chain
Divided trophic levels, species
trophic network
MONSTER MODEL!!!!!
Figure 10.2 - Physical and biological complexity A zero dimension (0D) model is related to a well mixed water body. A 1DV, one dimensional, vertical, model describes vertical heterogeneity like temperature stratification, distribution of micro algae or chemical gradients in a lake. A 1DL, one dimensional, longitudinal, model describes concentration evolution of the state variables between the entrance and the outlet in a reservoir or between two sites in a river. A 2DV, bi dimensional, vertical, model describes the heterogeneity of the concentrations in a vertical plane: concentrations are supposed homogeneous in the transversal direction. A 2DH, bi dimensional, horizontal, model describes the heterogeneity of the concentrations in an horizontal plane: concentrations are supposed homogeneous in the vertical direction. A 3D, three dimensional model is built to describe heterogeneities along three axes, x, y and z, longitudinal, transversal and vertical. Biological complexity - Vollenweider : phosphorus trophic state (to be detailed later); 200
- Simple trophic chain : nutrients phytoplankton zooplankton (figure 10.4); - Trophic chain with divided trophic level: 4 species of phytoplankton, 2 types of zooplankton (figure 10.5); - Trophic network: trophic chain + bacteria + bacterioplankton + ciliates + flagellates. Physical and biological complexity must be adapted to the reality and to the question to solve: Small is beautiful.
Vertical section, view from the left bank 0D 1DV 1DL X
Z
Y X
View from above Vertical section, view from the left bank
2DV X
X
2DH
3D
Z
Y
View from above
DICRETISATION IN SPACE
Figure 10.3 - Physical complexity, discretisation in space
201
SIMPLE TROPHIC CHAIN ZOOPLANKTON
PHYTOPLANKTON
NO3
PO4
NH4 POP
NOP
Figure 10.4 - Conceptual model of a simple trophic chain DIVIDED TROPHIC LEVELS FISH
ZOO1
ZOO2
Chloro
B.G.
B.G. N2
Si
P
NO3 NH4
N2
Sip
Pop
Nop
Figure 10.5 - Conceptual model of a trophic chain with divided tophic levels 202
2 SOME PHYSICAL PROCESSES INFLUENCING LAKE ECOLOGY -Bathymetry : depth, shape, size. -Tributary discharge, lake volume, residence time of water. -Solar energy, temperature stratification, penetration depth, Photosynthetic Active Radiation (PAR). -Wind mixing. -Surface waves, seiches, internal waves. 2.1 Bathymetry
Depth
Len gth
tch Fe nd Wi Figure 10.6 - Depth, fetch Comparison of Baikal and Lake Superior with respect to volume, surface and mean depth: Mean depth = Volume : Surface -Lake Baikal (RF) 23000 km3 : 31500 km2 = 0.73 km -Lake Superior (USA) 12000 km3 : 83300 km2 = 0.14 km 203
2.2 Hydrological aspects P I V
O
3
V : volume
(m )
O : outflow
(m /y)
I : inflow
3
3
(m /y)
P : precipitation
3
(m /y)
Flushing time : T1 = V/O
(y) -1
Flushing ratio : = O/V (y ) Residence time : T2 = V/(P+I) (y)
Figure 10.7 - Flushing time, residence time 2.3 Solar energy Solar spectrum (figure 10.8) : high % of the energy in the visible range (0.4 to 0.75 ).
Figure 10.8 - Solar spectrum 204
Daily energy balance for a lake (figure 10.9): Qc : short wave QL1 : long wave emitted by the lake QL2 : long wave from the atmosphere Qs : sensible heat exchange (conduction) Qe : evaporation latent heat exchange Qtot : total
Figure 10.9 - daily energy balance for a lake Yearly energy balance for a lake (figure 10.10): energy decreases from September to February.
Figure 10.10 - Annual energy balance for a lake 205
Penetration depth (figure 10.11): Most of the energy will be kept in the first meter of a dirty lake. Since heat conduction is low in water, since density of water decreases with temperature above 4°C, the temperature of the surface layer will increase from march to august.
Figure 10.11 - Absorption of light by water in a lake at a 1 meter depth (expressed in % of the light intensity received at the surface), for different waters. A : pure water, B : oligotrophic lake, C : meso-eutrophic lake, D : lake with high concentrations in organic matter Water colour: absorption vs. reemission, the colour seen corresponds to the less absorbed wave length, dirty water is seen brown to red, clean water is seen blue to green (figure 10.11).
206
2.4 Some useful expressions The following expressions should not be used for all locations in the world : they were established for temperate climate (Europe). They should be adapted to local situations by interpretation of measurements and experiments. They might be used to obtain orders of magnitude and to illustrate relations between variables. A weather station might be used to measure : - Cloud cover and insulation duration (CC or ID) - Air temperature - Air humidity - Wind speed and direction - Atmospheric pressure - Solar radiation - Rain fall. Qc: short wave radiation Qext = 1350 W m-2 on top of the atmosphere CC : cloud cover CC = 1- ID/DD 0 < CC H + HCO3 -
+
HCO3 < > H +
-
2CO3
pK1 = 6.43 pK2 = 10.43
3.2 Carbonate equilibrium and photosynthesis Ca(HCO3)2 CaCO3+CO2+H2O calcium bicarbonate calcium carbonate 212
13
- Photosynthesis consume CO2 then the equilibrium moves to the right direction, CaCO3 precipitates up to a new equilibrium. - Respiration produces CO2, CaCO3, if any, might be solubilised, if no more pH decreases. -If CaCO3 precipitates, P might be adsorbed (co-precipitation of 3PO4 ) 3.3 Biochemical aspects of eutrophication The figure 10.14 demonstrates the chemical consequences of eutrophication. The larger the vertical “line”, the higher the concentration of a chemical species. Let’s examine what happens in a eutrophic lake and compare with an oligotrophic one. Oxygen concentration decreases with depth in a eutrophic lake. Respiration is high and photosynthesis is limited to the surface layer. CO2 concentration increases with depth for the same reasons. Denitrification eliminate nitrate in the hypolimnion. Ammonia is produced from mineralisation of organic matter, organic matter brought to the lake from outside or produced in the lake (dead phytoplankton). Phosphorus (PO4), iron and manganese are solubilised due to anoxy close to the bottom. For this lake the mixing by wind in the epilimnion is sufficient to maintain oxygen down to the thermocline. In some worst situations it is possible to observe chemocline (interface between oxic and anoxic layer) above the thermocline. For physical reason, very deep lakes, though oligotrophic, might be anoxic in part of the epilimnion. The deepest layers are not mixed every year with the upper layers because the water column is strongly stratified (temperature or chemical stratification) and/or the wind cannot mix the whole water column in case of great “depth to fetch” ratio.
213
Depth (m)
EUTROPHICATION 0-
02
C02
N03 NH4
P
Fe
Mn
10Thermocline
203040-
Depth (m)
EUTROPHIC LAKE
0-
02
C02 N03 NH 4
P
Fe
Mn
10203040OLIGOTROPHIC LAKE
Figure 10.14 - eutrophic and oligotrophic lakes, chemical aspects 4 MODELLING BIOLOGICAL PROCESSES Population dynamics of the following state variables called C : macrophytes, phytoplankton, zooplankton, bacteria, fish…
[ div ( K C C U ) S]dv dC dv V V dt This equation describes the transportation of the state variable C by advection and diffusion. S = (production – loss) of the state variable C Production = f(,r) P /(KP + P) [C] f : from experiments : growth rate of the species 214
r = Il / Iopt Il : measured or calculated light energy (W m-2) KP : phosphorus half saturation ratio Loss : Mortality, Excretion, Respiration Note : I know some biologists who hate modellers because they call “state variable C” wonderful species of plankton, full of life, unpredictable, with lovely silhouette, figures, colours… 5 ADVECTION-DIFFUSION EQUATION FOR A 1DV MODEL
dv V div(KC CU)dvV dC dt
(1)
K is a diffusion coefficient(m2 s-1)
U is the velocity vector U(u,v,w) (m s-1)
C is a concentration (kg m-3) For a 1DV model this equation gives :
dC CU)dv div ( K dv V V dC dz dt
(2)
Following Ostrogradsky (2) becomes :
d C .n CU.n)ds ( K dv S dz V dC dt diffusion
advection
(3)
right side
Layer # i
Ai,i+ 1
Ki,i+ 1
n Ci Vi
z Ai,i-1
n
U
Layer # i+ 1 Layer # i
Ki,i-1 Layer # i-1 215
diffusion t t
t t
Ai 1,i K i 1,i
C
t t
t t
t t
t t
C i 1 t t t t Ai,i1 K i,i1 Ci1 C i z z
i
advection (upstream scheme)
t t
t t
t t
t t
t t
t t
Ai 1,iui 1,iC i 1 Ai,i 1ui,i 1C i
right side (implicit scheme)
VC
t t i
i
t
C i t
This system of equations might be written as :
MC
tt
C
t
And the solution is :
C
t t
M C 1
t
6 CONCLUSION Environmental management is a task for a team. Many scientific disciplines are involved: - physics: hydrology, hydrodynamics, meteorology, energy transfer (radiation, light, heat) between lake, river and atmosphere and in the water column. - chemistry: oxygen, chemical speciation of nitrogen, phosphate, carbon. - biology: phyto and zoo plankton eco physiology, bacteria (organic matter transformation). Mathematical modelling is a tool for science and management. 216
Ecological modelling teaching should be done taking the following points into consideration. - students should learn to work in teams mixing different specialists (mathematics, physics, chemistry, biology). - measurements, data treatment and interpretation, modelling, should be taught altogether. - modelling should help a team to produce insights, not only numbers and graphs. - environmental knowledge should be given to all engineers. - models are research tools and are useful to managers. Modelling environment is a common goal for scientists and managers.
217
11 AQUATIC ECOSYSTEMS MODELLING ABSTRACT The methods of information technologies for water quality monitoring and management in river basin is proposed. This integrated approach is oriented to nature resources conservation and sustainability. The forecasting experience for Siberian reservoirs ecosystems states by model “Biogen” is considered. INTRODUCTION The important problem of water use management is forecasting of water object ecological state under the given scenario of external impacts. Theoretical basis of water quality forecasting with implementation of mathematical methods had been formulated and partially applied by 1980-s in the research works of Hydrochemical Institute, State Hydrological Institute , VNII VODGEO and others ( see, for example, Nikanorov, Skakal’sky et al 1989, 1991, and etc). Along with it, by now the choice of effective description of biochemical processes mechanism in channels and water bodies is still actual. Every new work on modeling of water economy objects state in the RF is connected with the development of new technologies, methods and tools, which allow to determine the character of chemical and biological processes in a definite water ecosystem and to answer the question set before specialists. The important meaning is also given to the modeling of hydro thermal processes, conditioning the terms of water biocenose functioning. The given work did not imply the detailed consideration of this field of the RF water economy objects modeling. Nevertheless, the research schools of Academician O.F. Vasiliev, V. M. Belolipetskiy, V. I Kvon, N. N. Filatov should be noted. Many of their works are devoted to ecological tasks and used in modeling of water ecosystems state of the lake Baikal, Ladozhskoe lake, the Teletskoe lake, and artificial lakes of the rivers Enisey, Ob and etc. (Vasiliev et al 1991; Vasiliev et al 1994; Belolipetskiy et al 1991, and etc.). Simulation water ecosystems models, as a rule, represent natural biogeo-chemical cycles of phosphorous and / or nitrogen combinations limiting the development of hydrobionics in reservoirs. Such an approach is developed in the research works on ecological modeling of different water objects of Russia: Leonov et al, 1999, 2000 (the Caspian sea), Menshutkin 218
1993 ( lakes Baikal, Dalnee and Ladozhskoe); Umnov 1997 ( Narochanskoe lake) and etc. The given researches open the stage of development of Russian water objects simulation models, and they are mainly devoted to technological questions of models construction. Natural data are used mainly to check the adequacy of the models, though sometimes it is possible to receive quantitative assessments of the processes of production and destruction, mass transfer and power interchange in ecosystems what could be of interest from the research point of view and could not be found by the other way. The use of the given models in practice of water economy organizations is limited so far on the reason that to calculate them it is necessary to have the data of special natural observations, which are not included in the list of standard parameters controlled by the monitoring service of OSSNC (Tskhai 1995; Tskhai et al, 1998). Applied empiric models designed for minimal volume of source information can be implemented just for interpretation of observations data. The attempts to use such models for forecasting lead sometimes to unrealistic results. In connection with this the elaboration of special simulation models of water ecosystems is actually. Such models must reproduce natural bio-geo-chemical cycles of combinations transformation, and all input information must be compared to the data of State Observation Service. In the opinion of specialists such models must be instruments and tools of water monitoring in Russia (Safronova et al 1997). For this purpose simulation model “Biogen” is offered (Tskhai et al 1997), for realization of which it is enough to have the standard data of Roscomhydromet (Federal Service of Hydrometeorology and Environmental Monitoring). When designing reservoirs it often happens that a water object does not exist yet, and the question is just in ecological assessment of the future reservoir with the help of simulation modeling. The results of such forecasting along with experts assessments and other indirect considerations serve additional arguments, in particular, when making a decision on river regulation in definite physical and geographical, and technological conditions. In this case the priority task is to choose the existing reservoir, analogous for the designed one due to the character of ecosystem thermal and biochemical processes. This is necessary for using numerical values of internal parameters of simulation model, calibrated on analogous water body, in forecasting calculations for designed object. The selection of the analogue, completely identical to the future reservoir is insoluble task. However, in the majority of cases it is possible to find a water body, located in the same geographical zone, with similar morphometric, hydrological characteristics. 219
The simplest case of water quality forecasting in the future reservoir is limited by the assessment of the two more common indicators: biochemical oxygen demand (BOD), characterizing spectrum content of easy oxidizing organic compounds and dissolved oxygen (DO). Further on such an approach is being laid out on the example of Boguchanski reservoir. For more complex forecasting the scheme of biogeneous compounds biochemical transformation is selected on the base of which it becomes possible to assess the dynamics of ecosystem components content. The most important criteria for selecting is the provision of the scheme with monitoring observation input data. The next step is preliminary assessment of biogeneous compounds coming to reservoir from both tributaries and lateral inflows, and also from flood land and with precipitation. Then mathematical model of the future object is described. It can be different due to spatial complexity of the construction: from point, in the majority of cases, when it is necessary to just assess the dynamics of water quality averaged characteristics, to one-, two-, three-dimensional model, depending on the question to which the answer must be given with the help of modeling. It should be taken into account that any complication or dimensionality increase of the model leads as a rule to sharp increase in volume of necessary source information which is by itself approximate in the majority of cases, and consequently, affects the exactness of the results received. In connection with this researchers try to use the simplest tools, and, if it is possible, to do without simulation modeling implementation in , for example, water body trophicity forecasting, but with the help of substances external flows analysis, similar to that one made in Vollenweider’s work (Vollenweider, 1975). In case, when the simulation model should still be built the special task is to elaborate great number of input data changes scenario, also completely covering limiting cases, in order to receive necessary results of modeling which will be specially analyzed later on. When designing water-cooling reservoirs for hydroelectric and atomic power stations being built the important question is forecasting of eutrophication spreading in tail race, and, actually, in a river basin. The peculiarity of the given situation is that to build a model of water-cooling reservoir ecosystem it is necessary to solve nonstationary three-dimensional hydrothermal and biochemical task for the water body of complex geometry, what is a difficult, time-consuming task today. Further on, on the example of Verchne-Uriupski hydrosystem (Ob river basin) the simplified approach is laid out, which, anyway, allows to compare variants of 220
ecological impacts on the river when realizing different project decisions on the complex water technical system. 1 MODEL APPROACH This day is noted by enlarging influence of anthropogenic factor on nature, ecological systems with or without human component, surface water and so on. The number of environmental and socio-economic problems are emerging, and hence - the need to all-roundly and accurately account water quality changes, to use these data for natural resources management, to inform population about water problems, to provide the base for collaboration of all constructive groops and movements in this field. Reliable data of environmental monitoring is a necessary base for regional water quality management. Information systems for support of administrative decisions in the field of water using are distributed more and more in water economies of developed countries. The aim of this work is to originate effective mathematical models and information means, based on assessment of real opportunities of control bodies on nature resources use and acting basic norms, which provide moving of the system of water quality monitoring and management in river basin to present-day information level. Main investigation results are the following: - realized common complex approach for assessment, forecasting and management of surface water quality in river basin with the help of modern mathematical modeling methods and informatics means in accordance with current legal and economic mechanisms of nature resources use in Russia; - scheme of regional water quality management in river basin made on the basis of acting basic norms accounting real opportunities of control organizations on water use and water protection; - created; - simulation models of aquatic ecosystem state for number of water objects; - water quality model of river system for main kinds of pollution; - optimization model of water protective activity for water user under present-day conditions. Scientific newness of investigation results in: - methodological field is following: the investigation methodology of nature-technical complex was developed by accounting of interrelation changes of environmental, economic and technological factors; - methodical field is following: methods of mathematical modeling and informatics were used for assessment, forecasting and management of 221
water quality in river basin on the basis of economic reform period norms and standard data of the Russian state observation services using; - mathematical modeling is following: complex of original simulation and optimization mathematical models which allow in particular to assess environmental effects of fulfillment of administrative decisions was originated and used in practice; - technological field is following: information geotechnology for water quality monitoring and regional management in river basin is offered. The Upper Ob river basin in the Altai administrative region boundaries was taken as an example. All original models of aquatic ecosystem state and water quality were verified according to observation data for some years at water objects under investigation. In case of forecasting of projected reservoir characteristics the models were verified carefully using data of analogous reservoir. Received quantitative results make qualitative forecasts more precise and in some cases simulation models are the only opportunity to forecast ecological state of water object under anthropogenic influence. Obtained results are theoretical and methodical base for solution of important problem of forecasting of aquatic ecosystem state and water quality management in river basin. The means originated by the author were used while his investigation of the Upper Ob river basin on the Altai administrative region; ecosystem state of the Novosibirskoye, Krapivinskoye, Ust-Srednekanskoye, Katunskoye, Verhne-Uryupskoye and other reservoirs. 2 ENVIRONMENTAL MONITORING IN RIVER SYSTEMS Environmental monitoring in river system is a multi-special hierarchical information system which includes repeating observations, assessment and forecasting anthropogenic changes of water quality and aquatic ecosystem state. The main tasks of environmental monitoring should be considered the following one: - achieving reliable and operative information on aquatic ecosystems and aquatic environment on the whole, on quantity of toxic substances and temporal dynamic of their content in industrial and agricultural waste (as well as in air pollution and waste storage accounting transformation processes), on high and extremely high pollution levels; - analysis and assessment of freshwater ecosystem state including those ones influenced by anthropogenic factors in accordance with acting norms; 222
- finding out such factors and defining their influence degree upon aquatic ecosystems as well as water quality regarding chemical factors; - forecasting changes in both aquatic ecosystem state and water environment pollution transport under concrete variants of outer influence including economic actions fulfillment; - necessary data preparation for optimal administrative decision making on rational water management; location, rendering harmless, prevention of high pollution in aquatic environment; - data use for investigations including finding out environment pollution impact, first of all fresh water supply sources on population health; for assessment and forecasting toxicants migration in underground and surface waters and in food chains of aquatic ecosystems; - provision governmental and social organizations, population of the region with data on the state of underground and surface waters. It seems to be expedient successive development of environmental monitoring information base: from simple to complex versions as information accumulation, improvement of interaction coordination between interested departments, mastering and elaboration of new technologies. Information subsystems must be created simultaneously, easy to adapt and locally distributed; as being prepared they must be integrated into general information system. It is very important from the very begining to provide with common ideology for projecting data base of all types, on the same numeric models on concrete territories (basins, zones and so on). An obligatory condition of system functioning shall be computer networks development for data transmission for timely solution of emerging problems by users belonging to different departments. The following tasks could appear as the result of information system of environmental monitoring in river systems besides mentioned above main tasks: - maps of environmental tension and anthropogenic pollution of different river basin sections; - assessment of concrete water users activity which influences on environmental state of natural water bodies: lakes, reservoirs, rivers and river flood-lands on the whole; - revealing the conditions of above-normative pollution in water supplying objects; - defining top anthropogenic load regarding separate ingredients in concrete river basin sections. 3 MODELS OF AQUATIC ECOSYSTEM STATE FORECASTING FOR RESERVOIRS 223
Pollution load into aquatic ecosystem causes aquatic bioceonosis reaction in return and also influences on population health by passing through every stage of food chain. Conditional character of water quality assessment according to MPC (maximum permissible concentration) indexes has emerged the need to develop variety of biological assessment of aquatic bioceonosis state. Hydrobiological methods give an opportunity to see in complex integral aquatic ecosystem reaction in return to anthropogenic pollution in difference with hydrochemical methods which allow to see predominantly intensity of anthropogenic press towards separate pollutants concentrations. Now the number of effective aquatic ecosystem models created in this field is much enough (see, e.g. Straskraba & Gnauck 1985 and others). To make simulation for these models however special observations on location are necessary and they are often absent under concrete conditions. Applied empirical models calculated for minimal number of input data are applied according to their structure only for interpretation of observed data. Attempts to apply such models for forecasting bring often to unreal results. In this connection development of aquatic ecosystems models is an actual task for applied purposes. From the one hand these models must be simulating, i.e. natural biogeochemical cycles of compounds transformation have to be reproduced in them. From the other hand all input information for these models must be assessed as standard data of national water monitoring system. The offered technology for mathematical models construction for biogeochemical cycle of biogen elements may be applied for preliminary assessment of environmental effects of reservoir construction. Projecting Beryozovskaya power plant-2 at the boundary of the Krasnoyarsk and Kemerovo administrative regions the problem to reduce eutrophication (warm water strongly polluted by phytoplankton and bacteria) distribution from chilling reservoir along the Uryup-river after dam (the Enisey river basin) has emerged. The aim of this work was to choose optimal projected variant of construction and maintenance of projected power station. The following approach was chosen. The change under complex influence of natural and anthropogenic factors of ecosystem component concentrations in a single water volume unit, moving in river after reservoir along river-bed flow was discussed. Quite natural supposition was used, that functional characteristics of future biocenosis in river after dam under permanent anthropogenic press would be nearly like similar ones in 224
eutrophical water body. The simulation was made for low water level year. Such suppositions helped to assess the worst variant of eutrophication in projected water object. Equations of biochemical phosphorus compound transformation in water body may be written as:
( w Ci ) (u w Ci ) Ri w Ji B Gi t x
(1)
where Ci is for concentration of water ecosystem components in phosphorus units gP/m3, i=1 - for bacteria biomass; i=2 - for phytoplankton biomass; i=3 - for dissolved organic phosphorus; i=4 - for dissolved mineral phosphorus; i=5- for suspended detritus phosphorus; Ri - transformation rate of i-th phosphorus fraction, gP/m3·day; Ji -for flow of i-th phosphorus fraction into bottom sediments, g/m2 ·day; Gi - rate of components load including lateral load within sections connected with washoff and waste, g/m·day. Defining the type of Ri members the following processes were taken into account: production of phytoplankton and phosphate consumption by aquatic algaes, bacteria production and mineralization of dissolved organic phosphorus, metabolic secretion of phytoplankton and bacteria, their mortality with detritus formation and its subsequent decomposition; transformation processes in bottom sediments as well as processes of biogen substance change in «water-bottom» layer. The model calibration of biochemical transformation of biogen elements was done on observed data for the eutrophical Balaton lake influenced, as it is known, by intensive anthropogenic pollution. Comparison of numeric modeling results for hydrothermic, chemical and biological water flow regime allowed to choose the most preferable variant (from the three project ones) regarding degree of influence upon eutrophication in river after reservoir. There is often a need to account non-stationary dynamic processes. The model «Biogen» (Tskhai & Ageikov, 1997) is formulated for this purpose. It includes thirteen components: compounds of nitrogen and phosphorus. Eight of them relate to water medium: ammonium nitrogen NH4 (variable number 1), nitrite one NO2 (2), nitrate one NO3 (3), biomass of phytoplankton F (4), suspended D (5) and dissolved C (7) organics in phosphorus units, orthophosphate phosphorus I (6), dissolved oxygen O2 (8). The other five components relate to bottom sediments: organics CB (9), 225
interstitial phosphorus PB (10) and nitrogen NB (12), and at last phosphorus PS (11) and nitrogen NS (13) both sorbed on solid phase. Main ecosystem component interactions accounting in model are shown at figure 11.1. To define the values of mass flows at the boundary «sediments-water» special model block which describes transformation of biogen compounds in bottom sediments is realized.
Figure 11.1 - Diagram of nitrogen and phosphorus compounds biochemical transformation for the «Biogen» model The following simplifying assumptions were used when input information for the model was prepared. First: it was considered that stoicheometric relations of carbon, nitrogen and phosphorus contents in ecosystem components are constant and equal to 106:16:1 (see, for example, Nikanorov, 1989). Second: the carbon content in dead organics of ecosystem components makes about half of the total weight (Nikanorov, 1989). Third: the main source of suspension in river water are soil particles washed off a watershed area. That is why the organics contents in suspension at an input correlates with its contents in a surface soil layer to be dominant on watershed area. It was considered that the organics content makes up 10 % of total soil weight. Such assumption is unacceptable for a reservoir, where the main suspension source is plankton mortality. 226
The unknown parameters of the "Biogen" model were determined on the data of observations for the Novosibirskoye reservoir within the limits of typical values intervals by minimization of the statistical Teil (Teil 1971) criterion values for each aquatic ecosystem component. Study of the Novosibirskoye reservoir ecosystem executed in 1981-82 hydrological year on the basis of the "Biogen" model application has shown, that this reservoir has a steady-state trophic status of an oligomesotrophic type. The dynamic processes of biogen compounds transformation are of the balanced character with account of seasons. Most important source of biogen load on reservoir (more than 85 %) is the Ob river. During a flood period more than 70 % of annual runoff of nitrogen and phosphorus is a river input. The "secondary pollution" from the bottom makes less than 10 % of general biogen load. The reservoir renders smoothing influence on a variation of biogen forms contents in a river. It detains more than 15 % of nitrogen and about 20 % of phosphorus transported with river flow. Suspension carrying out the reservoir makes about the one seventh part of load from the Ob-river. Most productive for reservoir phytoplankton was a period since June till August. Destructive processes intensity during open water period was rather uniform. The main factor of oxygen regime forming in reservoir was its high content in the Ob-river within whole year. The “Biogen” model was used for assessment of ecological effect after acceptance of the important municipal decision about change of water level regulation regime in the Novosibirskoye reservoir. The model simulation has shown that the process of dilution is the main factor of substances concentrations dynamics in the Novosibirskoye reservoir in winter. The offered variants of regime changes for the Novosibirskoye reservoir in winter to make it 1-3 m lower than a level of dead volume result in variation of average volume pollutants concentration in second meaning figure, contents dynamics of which was simulated, i.e. the influence of this factor is negligible.
227
Figure 11.2 Comparison of observated and simulated for three project variant for the Novosibirsk reservoir for conditions of the 1981-1982 hydrological year. 228
Figure 11.3 Comparison of simulated (Novosibirsk reservoir) and observated nutrient releases for different water bodies. When the reservoir is created on the river a hydrological regime is varied essentially and as a consequence the conditions of aquatic ecosystem functioning vary, and hydrochemical and hydrobiological parameters vary too. The scientifically grounded forecast of ecosystem state in designing reservoir is one of the main requirements of a decision acceptance stage about river regulation. Special importance belongs to the study devoting the future character of an oxygen regime change, eutrophication level and features of nitrogen and phosphorus compounds circulation, that is regulated by the requirements to water quality in reservoirs and rivers. On the basis of the "Biogen" model application the ecosystem state forecast in the designing Ust-Srednekanskoye reservoir after a making period, in the Magadan administrative region on the Kolyma-river was executed. In simulation the rates characteristics of natural biochemical processes were used. They were assessed on laboratory and experimental 229
investigations. These data were also received as the result of water quality modeling in the Novosibirskoye reservoir which has technical parameters to be compared with the Ust-Srednekanskoye one and besides it is of the same river bed type. The obvious distinctions in reservoirs ecosystems conditions were taken into account. Such input information for modeling as biogen load into a reservoir, water and thermic regime, sedimentation and so on were receipt from the analysis of designing reservoir functioning conditions. For model verification the special simulation on the Kolymskoye reservoir data for 1987 was carried out. It is of a directly above prospective arrangement than the Ust-Srednekanskoye reservoir is, along Kolyma river bed, and it can be used as an analogue for designing one regarding physical, geographical and morthometric characteristics. Such approach allows to take into account correctly whole set of existing data on designing water object on the Kolyma river when forecast assessment of future ecosystem dynamics is executed. Forecasting simulation for average hydrological year by the “Biogen” model, describing the Ust-Srednekanskoye reservoir state after a making period with present-day volume of biogen load, have resulted to conclusions to be important for the designers. The designing reservoir will relate to oligotrophic type. It will not essentially differ regarding phytoplankton content from the Kolymskoye reservoir being in its present-day state. Average phytoplankton biomass to reservoir volume in summer period will reach 0,13 mg/l. Nitrite and nitrate concentrations in reservoir will change in the limits of MPC. The ammonium nitrogen concentration in some periods can reach two - three norms. Average oxygen concentration to reservoir volume within one year will change within the limits of 10,0-13,5 mg/l that is much higher of MPC. The BOD content in reservoir will change in MPC limits within all year, except for a period of the maximum phytoplankton vegetation intensity in August. The availability of enough hydrobiological data allows to introduce such kinds of plankton as bacteria, phyto-, zooplankton and protozoa into the scheme of biogen compounds transformation and to assess their interaction with abiotic part of aquatic ecosystem as it was made for the designing Krapivinskoye reservoir (Tskhai & Ageikov, 1994; Tskhai & Leonov, 1995).
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Figure 11.4 Scheme of biogeochemical transformation of nutrient compounds in the “Biogen” model
CONCLUSIONS Original investigations based on a common methodical approach resulted in a complex of mathematical models and information systems which were used in practice and corresponds to main inquiries of water quality assessment and forecasting in river basin under anthropogenic activity influence with the purpose to achieve environmental safety for population and sustainable development of regions: - tasks of environmental monitoring in river basin were formulated. - models of biogeochemical cycle of nitrogen and phosphorus compounds for preliminary assessment of environmental state of future reservoir ecosystems were elaborated. These models are oriented to use standard information of projecting and operating organizations, the Russian water monitoring system.
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12 GEOINFORMATION SYSTEMS FOR WATER ECONOMY ABSTRACT The technology of water quality management in basin scale is proposed. This integrated approach is oriented to resources conservation and sustainability and contains admistrative and economic actions of exposure to water users. The management information system "Hydro-manager" is elaborated for optimization of water protective activity on the basin scale, assessment and forecasting of ecological consequences under management decisions. MIS "Hydro-manager" includes problem-oriented geoinformation system of water quality of river basin in urban areas within boundaries of administrative region. Firstly, for construction of production functions, the optimization model of water user behaviour is realized. The enterprise water user pays for its water pollution and receives the financial support for its water protective actions. Further, the final variant is found with help of comparison criterion of the annual pollution minimum for few control river sections (for example, near sections where urban works intakes). Integrated MIS "Hydro-manager" for the Upper Ob-river basin on the territory of Altai administrative region is realized and analysed. INTRODUCTION MIS “Hydro-manager” is an example of geoinformation technology elaborated for the use in water economy of Russia (Tskhai, et al,1996; Tskhai, 1997). MIS “Hydro-manager” is intended for river basing water quality monitoring and management, and designed as GIS for general purposes ArcView GIS 3.0a with Spatial Analyst (Tskhai 1998). Mathematical model of ecological and economic processes in natural-technical complex of a river basin was realized in the given project accounting current regulations basis. Information basis for mathematical description is standard data of water monitoring and statistics state services. Some procedures in GIS produce river net water quality information modeling black, water protective activity at both an enterprise level and basing level. The project consists of the following components: - cartographic database with functional part of the system; - attributive database of the system objects’; - external programs realizing model calculations.
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Figure 12.1 – Electronic map of the Altai administrative region
Figure 12.2 – GIS “Hydromanager”
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To realize methodical approach it is necessary for the user to fill GIS database with water monitoring information, and also data on economic and water management activities of enterprises. Besides, when elaborating MIS “Manager” the information of coordinate part of diagrammatic map, the value of dam location relative significance were used as source information. As a result of self-purification models parametrization due to water monitoring data of Upper Ob-river basin equation coefficients were evaluated. Thus, to apply MIS “Hydromanager” to unspecified river basin of Russian Federation it is enough to have the map of the last extended scale (e.g. 1:500000) and standard information of State Services of the RF. 1 ENVIRONMENTAL MONITORING IN RUSSIAN RIVER BASINS The economic crisis of last ten years in Russia, reduction of industrial and agricultural production have decreased anthropogenic pollution of rivers and water bodies and improved surface waters quality apparently. But not so much. For example, the annual pollution contents in Ob-river near Barnaul – administrative centre of Altai region – constitute about six maximum allowable concentrations for oil-pollution, two - for phenol, above maximum allowable concentration - for nitrogen compounds and so on. Now federal subsidies for environmental purposes are steadfastly decreased. Even the federal allowance for many state water monitoring stations is stopped. Therefore, the sources for water quality improvement may be found only by the regions themselves. In fact, for solving water quality problems the change of many established by society ideas is required. The rational water resources use, restoration and protection need it. Recently the Law "About environmental protection" (1992) was adopted in Russia. Many of obsolete administrative procedures are replaced by new economic methods in environmental management like as developed market economies. Now the enterprise's payments for environmental pollution form the regional ecological foundations (briefly, REF) resources used for support of water protective activity. The special state environmental committees had appeared in the regions. But serious changes in environmental protection are not observed. Why is it so? The reason is not in absence of interested organizations. The water quality protection in region is the object of activity for local departments of Ministry of Ecology and Natural Resources, Federal Service of 234
Hydrometeorology and Environmental Monitoring, Russian Committee of Water Economy and many other water users. The reason is not in absence of Federal and Regional Water Resources Programmes. There are many such documents in Russia nowadays. Three of State "Water" Programmes: for drinking water supply, flood consequences, Volga-river restoration are preparing this year. The idea about programme between regions "The Clean Ob-river" was appeared within Ob-river Basin Agreement. But the effect of these documents realization is small for the present. Any goal-related programme will be effective only if on regional level it: - contains flexible complex strategy defining and redefining final, intermediate and next purposes of resources restoration and sustainability in dependence on society changes; - demarcates powers of every organizations using and controlling regional water resources state; - includes mechanisms for realization, control and informing officers and inhabitants; - shows the sources of necessary material, working and financial resources and so on. The top priority task for every water resources goal-related programme is creation of effective management mechanism including such elements as: - the detailed order of interaction between water users themselves and with control organizations according to normative base in Russia; - the procedure of economic regulators definition for water users behaviour: principles of REF resources distribution and so on; - the definition order of the enterprise as "ecological bankrupt", the analysis and forecasting of ecological consequences for its closing; - the additional measures for reduction of prior contaminants concentrations in control river sections; - the procedure substantiation of "long-term projects" investment (the results of this realization will be observed only in a few years); - the interaction in the system "industrial subscriber - enterprise of water municipal economy - environment protection organization"; - the control of nonpoint sources of anthropogenic pollution; - the development of information base for water quality monitoring and management in the river basin; - the scheme for water quality management in basin-scale. The creation problems of such mechanism with necessary information support system (MIS "Hydro-manager") are considered in this paper. 235
2 THE ENTERPRISE BEHAVIOUR MODEL IN THE LIGHT OF THE RECENT LAW Our model (Tskhai 1996) is formulated in accordance with modern Russian normative basis. The input data for this model is standard information about enterprise economic activity. The enterprise - water user pays for its water pollution in accordance with differentiated rates. The payments for permissible pollution refer to the manufactured product cost, for the beyond-permissible pollution - of the enterprise's profit. The optimality criterion is maximum enterprise net profit corresponding on level of subsidization of its water protective activity from all sources. Variable "j" determines the j-th environmental protection actions set with cost Xj. For simplification all actions are considered as investment. Then the model is formulated as
Фj = Bj - Nj - Fj - Gj max Xj Tj + vXj + Gj Fj B j - N j 0 Gj Bj - Nj - Fj for Xj, Tj, Fj, Bj, Nj 0.
(1) (2) (3) (4)
Here Фj and Bj are the net and balance profit of the enterprise after the realization of j-th actions set; Gj characterizes voluntary expenses of the enterprise from its profit for financial water protection actions. Tj is receipts from REF for realization of j-th actions set. The term v·Xj characterizes the depreciation charges included in product cost on water protection constructions put into operations. The enterprise payments Rj to REF after the realization of j-th actions set consist of
R j = P j + Fj
(5)
Here the payments for permissible pollution Pj and for beyondpermissible pollution Fj is the payment after the realization of j-th actions set are calculated as 236
Pj Pi j , F j min{ Fi j ; c[ B j N j ]} , i
i
where Pij=Li·min[mij(х); Mai];
Fij(x)=Ki·max{0; min[mij - Mai; Mbi - Mai]} + 5Ki·max[0; mij - Mbi]. Here c is limited level of beyond-permissible pollution payment in the percents of profit tax; Li – rate for normative and Ki – for beyondnormative pollution for i-th contaminant. Mai and Mbi are values of maximum allowable and temporary concerted waster masses of i-th contaminant, mij is real waster mass of i-th contaminant after realization of j-th actions set. The corresponding profit tax for enterprise Nj with rate may be calculated in accordance with the Law as
Nj = Bj - min[0,3Xj; 0,5Bj]
(6)
The formulated problem is related to discrete and nonlinear type. The method of its solving is concerned by exhaustion of variants j. For every j minimal value Gj satisfying the presented constraints is found. A number n determines the variants of j-th set and doesn't exceed values 20-30 in practice. The different mechanisms of distribution of REF resources are compared. Their influence on water protective strategy of the enterprise is assessed. The situations when the enterprise has interest to finance of water protective actions from its own net profit are considered (Tskhai 1995). Therefore the most profitable conditions for the enterprise realizing the specific water protection actions set may be found by means of our ecologico-economic model. The possibility of wastewater quality management with the help of the economic methods is appeared. For every variant of REF standing rules the optimal enterprise behaviour (including the contaminants masses in wastes) may be determined. This model is the basic element of MIS "Hydro-manager" supporting water quality management in basin scale. 3 THE GEOINFORMATION SYSTEM FOR ANTHROPOGENIC WATER QUALITY CHANGES ASSESSMENT AND FORECASTING IN THE RIVER BASIN 237
The geoinformation system is elaborated for support of management decisions on the base of regional economic mechanism on water quality in the river basin (Tskhai et al 1995). The information block of system consists of three parts: text data base; map-graphical data base; modelling data base. The text data base is intended for gathering, keeping and use of monitoring information of the river basin and data on the corresponding water-technical complex. There are the observed hydrological and hydrochemical data, the information on intensity and composition of the point and diffuse sources of the watershed pollution in this data base. This information is stored in the files of DBF BDMS dBASE III+ format. The map-graphical data base is realized on the example of the real watershed and is intended for holding the map-diagrams of administrative and river basin boundaries, the situations of towns and settlements, the posts of hydrological and water quality observations, the morphometry of rivers and so on. Water quality is estimated and forecasted by means of mathematical modelling methods (see, for example, Shnoor et al 1987). The information of the text data base is used. Our water quality model (Tskhai 1997) uses standard data of Russian State Service for Observations as input information. The dependencies of the model coefficients on hydrologic characteristics were calibrated by means of the monitoring data on the same river. Water quality model simulates the river spatial distribution for the values of twenty contaminants: (1) BOD, (2) oxygen deficit, (3) suspended matter, (4) COD, (5) ammonia, (6) nitrite, (7) nitrate, (8) synthetical surface-active matter, (9) oil-pollution, (10) phenol, (11) hexachloran, (12) chlorine, (13) sulphate, (14) magnesium, (15) calcium, (16) lindane, (17) iron, (18) copper, (19) lead, (20) phosphate for 18 periods of the year. The model equations in quasi-steady one-dimensional horizontal approach are defined as
d (Q Ci ) d dC E w i w Hi Gi , dx dx dx
(7)
where x and w are the longitudinal coordinate and the area of the cross-section; Q is the rate of water discharge; Ci is the concentration of the i-th chemical compound (index i varies from 1 to 20); E is the coefficient of
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longitudinal dispersion; Hi characterizes the rate of kinetic transformation for i-th chemical compound; Gi is the lateral load per unit length of channel. The scheme of river system includes Ob-river and its tributaries: Alei and Chumysh where enterprises-users are situated. The unevenness of dynamic processes along the river-bed is taken into account under simulation. In the model the channel form is described as a sequence of parts separated by cross-sections. The width of the cross-sections is calculated by means of a linear interpolation depending on the true level. For this purpose data of regime measurements of present-day river characteristics are used. Therefore it is supposed that natural deformation of the channel is negligible. Hydraulic model block is based on one-dimensional equations for quasi-steady longitudinal nonuniform flow with the lateral inflow in nonprismatic channel (Spitsin & Sokolova 1990). First, the lateral inflow per unit length of channel is calculated by means of specified discharges in the cross-sections and the point tributaries (or agri-industrial wastes). Then in accordance with an equation of continuity the discharge distribution in nodal points of the calculated network is found. Further the depth and true level in final cross-section is determined by means of the empirical curve of the connection between discharges and levels. The spatial distribution of the depth h, the area of the flow crosssection w and the mean discharge velocity of flow u are determined using the Eiler's method for the dynamic equation solution. The crude values of river-bed parts are found from condition of equality for simulated and observed average depth with the help of special iteration procedure. It repeats for every ten-day interval in flood (April-June) and for every month in another hydrological periods. An assumption of kinetics of the first order is used in the model for main part of compounds. The form of dependencies Hi from hydrological characteristics and the determined values of nonconservative constants are given in (Tskhai et al 1994). The value Gi may be defined as
Gi Cib q
(8)
where Cib is the content of i-th compound in lateral inflow q (if q
