Dynamic model and estimation of the future eutrophication for the Lake Prespa

Transcription

1 Poceedings of the 2nd IASME / WSEAS Intenational Confeence on Enegy & Envionment (EE'07), Potooz, Slovenia, May 15-17, Dynamic model and estimation of the futue eutophication fo the Lake Pespa Kosta Miteski, Andeja Naumoski Depatment of Compute Technologies and Envionment Cente, Faculty of Electical Engineeing and Infomation Technologies at St. Cyil and Methodius Univesity of Skopje, Kapos II bb, 1000 Skopje, FYR OF MACEDONIA komit@etf.ukim.edu.mk, Andeja.Naumoski@etf.ukim.edu.mk Abstact: - This pape pesents a new computing analysis, based on Matlab Simulink, how to build a dynamic model fo aquatic suface wate bodies in ou case the Lake Pespa. The dynamic model, which is moe complex than the othe models, it involves equation that descibes the inside biological and chemical pocess of the lake and connections between living oganisms and phosphoous component, and can be used to longtem pediction of lake behaviou and it s eutophication. The model that we ae pesenting has some limitations, because the natue of the poblem is moe chaotic than deteministic. We ae limited by the changeable outside conditions and the othe inside pocess that ae existing into the lake, than we ae not have consideed. Ou model takes only the diffeential equation that descibes the phosphous cycle inside of the lake. The main contibution of building such model is poviding us with futue estimating of the eutophication inside of the lake. In aid of this study is softwae application called Matlab Simulink which it has unique possibility to simulate a dynamic development (evolution) of the ecosystem fo given paametes and input value of the measued components. Many scenaios that have been developed can show the futue development of the ecosystem in long-tem peiod, fo ove 10 yeas. The expeimental esults that we have gain ae compaed with measued values and it has eo not moe than 10%, which classify ou model as good. Key-wods: - Lake Pespa, Dynamic Model, Eutophication, Phosphous concentation, Scenaio ca, Scenaio cc. 1 Intoduction Aquatic ecological models can be classified into thee goups: empiical, dynamic and combine. These ecological models have poven to be vey useful in solving ecological poblems using computing technicians. Due to thei ability to used little measued paametes to achieve thei goal, the most successful ecological model fo long-tem pediction is the dynamic model. The dynamic model used with diffeent scenaios and build in vaious compute pogams has been vey successful in achieving optimal solution fo vaiety of poblems based on pediction of the futue state of the ecosystems. This pape intoduces the dynamic model fo Lake Pespa, a ae aquatic ecosystem with his own floa and fauna. Lake Pespa has he own geogaphical specification we have embedded into the model and we will show that state of the lake is coesponding with ou esults gain fom the model. The dynamic model has been evaluated with Matlab Simulink, which povide us with simulation with diffeent input paametes and possibility to change many constants that appeas in the simulated model [3]. We have achieved, only the simulation of the fist of the thee diffeential equations that descibes the behaviou of the biological and chemical pocesses in the lake and that s the diffeential equation fo available phosphoous cycle [5]. The eutophication of the lake is evaluated by using the Tophic State Index (TSI) with diffeent appoaching methods, which one of them includes empiical model pesented in section 2 and the othe, the Matlab Fuzzy Logic Toolbox which is pesented in section 3.2. In section 2 we pesent the fomal definition and inside pocess of the dynamic model and in section 3 the actual inside look of the dynamic model fo Lake Pespa in Matlab Simulink. The expeimental esults gain fom the model and the futue development scenaios ae given in section 3.1, while section 4 concludes the pape and ou aeas of futhe eseach.

2 Poceedings of the 2nd IASME / WSEAS Intenational Confeence on Enegy & Envionment (EE'07), Potooz, Slovenia, May 15-17, Eutophication of the Lake Pespa The eutophication of the lakes has been established as a scientific fact since 1977 when, Calson has povided methods to classified aquatic suface wate bodies like lake, into thee goups accoding to the level of the phosphous component, chloophylla(chl-a) and the secchi disk (SD) [6]. These thee paametes ae putting the lake into one of thee goups in a scale of 0 to 100: - oligothophic lake (low poductive lake); - mesotophic lake (medium poductive lake); - eutotophic lake (high poductive lake); Each of this goups has defined index as TSI, which is showing in which goup is the lake. Thee ae many methods to obtain TSI, but in this case we will use the empiical model [7]. Many softwae pogams have been developed to estimate the TSI, but we estimated using special module call, Lake Eutophication Analysis Pocedue (LEAP), which is a pat of softwae package, Wisconsin Lake Modelling Suite (WiLMS) [10]. This module has ability of automatic calculating TSI based on a Calson s TSI fomula. LEAP takes the esults of the wate quality that we have obseved and calculates the futue values of the thee main vaiables that we have measued. On a second hand we have futue esults of the chloophyll-a changing quantity depending of the model eo vaiations. In the end comes the summay of the TSI, which is epesented in Fig. 1. ecent papes Lake Ohid, has TSI of 22 indexes which is oligothophic [5]. Accoding Calson, the oligothophic lakes ae less eutophicated then mesotophic lakes, because they have lowe values fo TSI. This lead to a conclusion that this kind of lakes, in this case study Lake Pespa must have some system that will decease this TSI index. Deceasing can be only done by eliminating the phosphous component fom the lake and also this will have impact on the food chain of the living oganisms, also on the biological and chemical pocess inside of the lake. To pevent futhe eutophication of the Lake Pespa we must take inside look of the pocess that have occu in the past and now, and this only can be done by examine the dynamic model of the Lake Pespa. 2.1 Pocess inside of the Lake Pespa To undestand what casing and how to pevent the futhe eutophication of this ecosystem we have to undestand the way how the phosphous component is having effect on the Lake Pespa. Ou seach fo the cause stats with the conceptual diagam which illustates the flow of phosphoous though the food web. The model takes into account only the wate column (sediment laye has not been conside in this eseach). This conceptual diagam is showing how the phosphous component is effecting on the living oganisms and how they ae using it. But, the phosphous that comes fom the outside is the bigge poblem that we ae facing, so the lake faces acceleated deteioation of its wates and a change of the TSI of this aquatic ecosystem, mainly caused by nutient load. Man-made eutophication, in absence of contol measues, poceeds much faste than a natual phenomenon and is the majo eason fo aising eutophication of this lake. A conceptual/functional diagam which is a basis fo the dynamic model is pesented in Fig.2. Figue 1.Calson tophic state index fo Lake Pespa. As we can see fom the Fig.1 Lake Pespa has TSI of 46.3 indexes, which puts this lake into mesotophic goup of lakes. Accoding to some Figue 2.Conceptual diagam showing the components of the model of the phosphoous cycle. Such dynamic model, which tends to pedict futue eutophication and the tophic state lake-wide,

3 Poceedings of the 2nd IASME / WSEAS Intenational Confeence on Enegy & Envionment (EE'07), Potooz, Slovenia, May 15-17, is the fist attempt undetaken in descibing the ecological state of Lake Pespa. On the basis of the biological and chemical pocesses in the lake, the dynamical model is composed fom the diffeential equation that is descibing the behaviou of the available phosphoous (AvlP). AvlP which is the only diffeential equation taken in consideation hee (1), is descibed mathematically as the sum of the decomposition and the algae espiation pocesses, minus pimay poduction, which ae highly phosphoous dependable. davlp P = ( D P + R a ) (1) dt C The AvlP is only a component that has enomous impact on the live inside of the Lake, but we must not foget that this AvlP comes as pat of the Total Phosphous (TP) inside of the lake which is sum of the existed phosphous inside of the Lake and phosphous concentation that comes fom manmade eutophication. So, the task that we have put in font of us is to calculate AvlP and TP fo the next yeas, so we could be able to pedict the futhe eutophication of the lake. 1 ( K + K * UP) * T B Ra= * (3) D =β T X (4), whee P m stands fo maximal ate of gowing, UP 1 is edacting the phosphous component, K and K ae constants that epesents the ate of espiation and ate of popotional, espectively, T epesents tempeatue facto, B is biomass. The T component epesents input tempeatue, β is constant that descibes the ate of tansfomation and X stands fo input of the phosphous concentation. As we can see fom the equation (2), (3) and (4) the model is complex, consideing moe inside look between impotant components [8]. All this is consideed when we have built the dynamic model. The illustated diagam is shown in Fig.3. The model allows us fo given input of two vaiables that ae esponsible fo the eutophication of the lake, the tempeatue and the phosphous component to see how they contibuted in the futue development of the ecological sate of the Lake Pespa. Measued data is taken fom diffeent measuement stations aound the Lake, fo one yea peiod, 03/ /2006 [11]. 3 The dynamic model of Lake Pespa In the pevious section we have look the cause of the eutophication and the basis of the pocess that we have to model them now, to get futue development of the eutophication. The dynamic model of the Lake Pespa has been built with Matlab Simulink, pogam that allows us to obtain esults fo long-tem peiod with satisfied accuacy. The model that we have built has thee main pats, which epesents the dynamical pocess of the phosphous component inside of the lake. Diffeential equation (1) contains fom thee main pats. The P epesents the pimay poductions of algae; Ra epesents espiation of the algae and D the decomposition. P/C is constant that we have to change to gain minimal diffeence between measued values and pedicted values fo the given peiod of time. The thee main pats ae consisted with moe mathematical equation that moe closely ae descibing the pocess of phosphous component and the diect impact on living oganisms. The equations that ae descibing these pocesses ae P = P * UP * T B (2) m * Figue 3.The dynamic model of the Lake Pespa in Matlab Simulink The phosphous component is vey impotant, because it has diect impact on the state of the lake and the eutophication. The AvlP epesents the left component of the diffeential equation (1), so the will be epesented as output of the dynamic model and then using discete mathematics we will calculate TP which is pesent inside of the lake. To develop fast esponse of the dynamic model between the measued and the esults gain fom the model fo long-tem peiod we have to modify the model to conside diffeent changes between the two input paametes. This model is epesented on Fig.4. As we pointed ealie, now we can examine the long-tem peiod of the eutophication of the lake by

4 Poceedings of the 2nd IASME / WSEAS Intenational Confeence on Enegy & Envionment (EE'07), Potooz, Slovenia, May 15-17, taking input measued tempeatue values and values of the phosphous component. Figue 4.The dynamic model of the Lake Pespa modified fo diffeent input paametes. 3.1 Expeimental esults Now, let s simulate. Fist we do with the model is calibation. We have been changing the paametes constants to gain elevant output with the measued values. Afte we have done this, with acceptable eo, we have extended the pediction peiod fom 12 months to 120 months, o 10 yeas. Of couse, thee will be an eo between the values that we have gain fom the model, but we expect that these eos not extent the value of 10 % between these esults and the values fom the measued paametes. Afte the simulation is un fo the peiod of 12 months the output gaphic is given on Fig.5. Fo this pupose we give peiodical concentations that ae fiction, but moe closely epesents the past dynamic of the measued tempeatue and phosphous values. Afte simulation has ended we have gain data fo diffeent scenaios given in the Table 1.These scenaios epesents diffeent change of the measued values that ae moe likely to happen. Fo instance, the most used change fo tempeatue values is -5 to +10 %, because we don t expect damatic change of this measued value in the next peiod, but the phosphous component has to be teated with moe pecision, because it has diect impact on the living envionment. Name of the scenaio Change of tempea tue values (in %) input value fo the model Change of phosphous concentati on (in %) input value fo the model Change of TP concent ation (Pedicte d/input) output value fo the model Scenaio AA Scenaio AB Scenaio BA Scenaio BB Scenaio BC Scenaio CA Scenaio CB Scenaio CC Scenaio DA Scenaio DB Table 1 Table of output values of the model fo peiod of 5 yeas. Figue 5.Gaphic output of the dynamic model fo the Lake Pespa fo 12 months peiod. Yellow line epesents the AvlP concentation inside of the lake and the magenta colou line epesents TP, which is impotant fo the living envionment. The next task is to gain esults fo the futue development of the TP concentation. This is accoding to Integovenmental Panel fo Climate Change (IPCC) the exteme events that pobably could happen in next yeas in the Southen Euope, hee ae consideed [9]. The cold wintes with vey low tempeatues and day summes with high tempeatues with little ain will have majo impact on the suface wate esouces and its pollution. Many wateshed aeas will dain-out and the concentation of the phosphous in the lake will emain high, depending fom the esidence time of the wate in the lake. So the change of he concentation is in the ange of -90% which epesent s system that has implemented wate waste management, till +30 %

5 Poceedings of the 2nd IASME / WSEAS Intenational Confeence on Enegy & Envionment (EE'07), Potooz, Slovenia, May 15-17, which will epesent a system that is left with ou cae fom the authoities. Scenaio CC is most possible to happen, because in next few yeas we expect to ise the tempeatue coefficient fom +5 till +10% and change of phosphous component to ise fom +10 to +20%. tempeatue change will be not moe than + 5%. The dynamic evolution is epesented on Fig.7. The scenaio CA clealy indicates that if we want to pevent futhe pollution of the lake we must build a wate waste management system to emove phosphous component fom the lake to educe the eutophication of the ecosystem. Next step is to calculate the TSI in ode to show the incease of the eutophication inside of the lake. Figue 6.Evolution diagam of Lake Pespa dynamics fo scenaio CC in next 10 yeas The evolution of the ecological system is given on Fig.6. The ed line epesents TP changed with paametes accoding scenaio CC, and the magenta line epesent evolution without influence to the main paametes. Even without any man-kind change of the inputted phosphous, the dynamical model has pointed, that it need immediately building a wate waste management system to eliminate phosphous component fom the suface wate. 3.2 Estimating the futue TSI of the Lake Pespa A model fo lake tophic state foecast has been developed based on a fuzzy expet system using a ule-based scheme in Matlab Fuzzy Logic Toolbox. Fuzzy logic is applies in ode to obtain moe ealistic pictue about the status of the lake and its eutophication. A fuzzy infeence pocedue is used to evaluate the ules leading the lake system and to poduce a tophic state index. Figue 8.Fuzzy ule system fo the futue developed TSI of Lake Pespa Because fuzzy theoy deals with membeship functions, we have to define membeship function fo the input and output vaiables. Afte defining membeship functions fo the input and output vaiables, a fuzzy expet system can be consulted. Name of the scenaio Concent ation of phospho us (mg/l) Value of TSI fo given scenaio TSI state Figue 7.Evolution diagam of Lake Pespa dynamics fo scenaio CA in next 10 yeas If we estimate that the wate waste system can eliminate -40% and even -80% of phosphous concentation fom the suface wate, we have scenaio CB and scenaio CA and we assume that Scenaio AB Scenaio CA Scenaio CC 19,8 47 mesotophic 4 23 oligothophic eutotophic Table 2 Summay of dynamic model fo Lake Pespa with calculated TSI state

6 Poceedings of the 2nd IASME / WSEAS Intenational Confeence on Enegy & Envionment (EE'07), Potooz, Slovenia, May 15-17, This is an expet system that uses a collection of fuzzy membeship functions and ules, instead of Boolean logic, to eason about data. The ules in a fuzzy system ae usually of a tem IF-THEN ules and it has 27 ules, 3 fo each of the thee paametes. This esults in one fuzzy subset to be assigned to each output vaiable fo each ule. Unde composition, all of the fuzzy subset assigned to each output vaiable ae combined togethe to fom a single fuzzy subset fo each output vaiable. Finally the defuzzyfication pocess is pefomed, which is used when it is useful to convet the fuzzy output set to a cisp numbe. On Fig.8 we can see the fuzzy ule system that has been built fo Lake Pespa. Fo ou pupose we will only use the pocedue to obtain the esults and only give the expeimental esults that we have gain fom the model. Afte enteing the new values fo the futue scenaios we can epesent the eutophication pocess in a cetain moment of time. The esults ae epesented in Table 2 which summaizes the esults of ou eseach. 4 Conclusion This pape descibes the dynamic model fo Lake Pespa built and simulated in Matlab Simulink with tendency to pedict long-tem peiod eutophication pocess of the ecosystem. We popose a new decision making mechanism with a new way of pesenting the mathematical methods integate within ecology and methods to pesent the futue state tough tophic state and estimating eutophication. The esult is faste and moe eliably model, able to integate moe changes and flexible pediction pocedue that can be modified fo diffeent time peiods. Using paamete estimated histoy; this model can be ecalibated fo moe pecise pediction of output paametes and also can be updated to povide useful feedback fo the eutophication of the ecosystem. Fom this point of view we can say that eutophication of the Lake Pespa is climbing and it have a modeate supply of nutients, ae pone to modeate algal blooms, and have occasional oxygen depletions at depth. We have shown that ecosystems, in ou case Lake Pespa can be easily detached fom the balance point and put into a state whee envionment is unable to be a place fo the living oganisms. Ou esults have clealy pointed of alaming condition of the suface wate and it s pollution with phosphoous component. Building a wate waste management can pevent this futhe gowth of available phosphoous inside of the lake, so with this we ae peventing this ae aquatic system fom extinction of many fish spices and living oganisms. Based on these encouaging esults, futhe eseach of building such model will be pefomed. Its implementation is moe complex, but the othe two diffeential equations will give us moe eliable data and this will povide moe details of the model quality and advantages. Refeences: [1] MATLAB Fuzzy Logic Toolbox, the Math Woks Inc. Ve (R14) SP2, 2005 [2] Dale M. Robetson, William J. Rose, and David A. Saad, Wate Quality and the Effects of Changes in Phosphous Loading to Muskellunge Lake Vilas County Wisconsin, U.S. Geological Suvey Wate-Resouces Investigations Repot , 2005 [3] MATLAB Simulink, the Math Woks Inc. Ve (R14) SP2, 2005 [4] Miteski, K., Miteska. E., Web-based Infomation System fo Pollution Monitoing of Lake Pespa, Ballwois, 2006 [5] Miteski. K., Ecological model fo Lake Ohid, Faculty of Electical engineeing and Infomation Technology, PhD 2002 [6] Calson, R.E. A tophic state index fo lakes, Limnology Oceanogaphy, 22, pp , 1977 [7] Kichne, W.B., and Dillon, P.J., An empiical method of estimation the etention of phosphous in lakes, Wate Resou.Res., 11, 1975, [8] Janse, J.H., Aldenbeg, T., Kame, P.R.G., A mathematical model of the phosphous cycle in lake Loosdecht and simulation of additional measues, Hydobiology, 233, pp , 1992 [9] Matin Beniston, David B. S., Futue Exteme Events in Euopean Climate: An Exploation of Regional Climate Model Pojections, PRUDENCE-WP,5 pp. 4-24, 2004 [10] Wisconsin Lake Modelling Suite, Help File, ve , 2001, Wisconsin Depatment of Natual Resouces [11] TRABOREMA Poject WP3, EC FP6- INCO poject no. INCO-CT ,