CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Na tentativa de facilitar o diagnÃstico dos diversos fatores que afetam a qualidade da Ãgua e antever possÃveis impactos futuros sobre o meio ambiente , sÃo adotadas aÃÃes que racionalize m o uso da Ãgua a partir da otimizaÃÃo de processos naturais ou tecnolÃgicos. A modelagem matemÃtica à um exemplo disso e, em conjunto com a Teoria Fuzzy , que permite fazer a anÃlise dos resultados sem necessidade de significativos bancos de dados, pode - se estabelecer o risco como indicador de contaminaÃÃo das Ãguas de rios, sendo de valor prÃtico na tomada de decisÃo e concessÃo de outorga de lanÃamentos. Neste estudo, foi desenvolvido um modelo matemÃtico aplicado Ãs equaÃÃes completas de Streeter - Phelps utilizando a Teoria dos nÃmeros Fuzzy , a fim de analisar o risco de contaminaÃÃo de um curso d'Ãgua que recebe agentes poluentes de mÃltiplas fontes de lanÃamento. Pelas simulaÃÃes do modelo, foram analisados diferentes cenÃrios, verificando a influÃncia d os seus parÃmetros, bem como o lanÃamento de fontes poluidoras pontuais e difusas, nos percentuais de risco. De acordo com os resultados, observou - se que a quantidade de carga lanÃada tem influÃncia no tempo de diluiÃÃo desta massa no sistema, de forma que , para maiores valores de lanÃamento, o tempo de diluiÃÃo à menor, favorecendo os processos de decaimento e formaÃÃo da camada bentÃnica; em relaÃÃo Ãs reaÃÃes fÃsicas, quÃmicas e biolÃgicas, verifica - se que os processos de sedimentaÃÃo, fotossÃntese e res piraÃÃo, para os dados mÃdios encontrados em literatura, tem pequena influÃncia no comportamento das curvas de concentraÃÃo de OD e curvas de risco, enquanto que o processo de nitrificaÃÃo tem forte influÃncia; jà a temperatura desempenha um significativo papel no comportamento do OD, onde, para valores maiores, maior serà o dÃficit OD e, em consequÃncia, aumento dos percentuais de risco. Por fim, o modelo desenvolvido como proposta de facilitar a tomada de decisÃo no controle de lanÃamento de efluentes em rios mostrou - se uma alternativa viÃvel e de valor prÃtico de anÃlise, jà que os objetivos foram alcanÃados / In an attempt to facilitate the diagnosis of the various factors that affect water quality and predict possible future impacts on the environment, actions to rationalize the use of water from the optimization of natural and technological processes are adopted. Mathematical modeling is one example and, together with Fuzzy Theory, which allows the analysis of the results without the need for significant databases, one can establish the risk as an indicator of contamination of rivers, and of practical value in decision making and allocation of grant releases. In this study, the full Streeter-Phelps equations, using the Fuzzy set Theory, was applied, in order to analyze the risk of contamination of a watercourse that receives multiple sources release pollutants. Through the model simulations, different scenarios were analyzed, and the influence of its parameters as well as the launch point and nonpoint pollution sources, in the calculation of the risk. According to the results, it was observed that the amount of discharge released influences the time of the mass dilution in the system, so that for higher values of launch, the dilution time is less favoring the formation and decay processes of benthic layer; regarding the physical, chemical and biological reactions, it appears that sedimentation processes, photosynthesis and respiration, concerning with the average data found in literature, have little influence on the behavior of the curves of DO concentration curves and risk, while the nitrification process has a strong influence; with respect to the temperature, the results showed that it plays a significant role in the behavior of DO, where, for larger values of it, the higher the DO deficit and, consequently, increase in the risk. Finally, the model developed as a proposal to facilitate the decision making in the control of discharge of effluents into rivers proved to be a viable and practical analytical alternative way, since the goals were achieved.

Thesis (MEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Water Quality Models are mathematical representations of ecological systems and they play a major role in the planning and management of water resources and aquatic environments. Important decisions concerning capital investment and environmental consequences often rely on the results of Water Quality Models and it is therefore very important that decision makers are aware and understand the uncertainty associated with these models. The focus of this study was on the use of Monte Carlo Simulation for the quantification of prediction uncertainty associated with Water Quality Models. Two types of uncertainty exist: Epistemic Uncertainty and Aleatory Uncertainty. Epistemic uncertainty is a result of a lack of knowledge and aleatory uncertainty is due to the natural variability of an environmental system. It is very important to distinguish between these two types of uncertainty because the analysis of a model’s uncertainty depends on it. Three different configurations of Monte Carlo Simulation in the analysis of uncertainty were discussed and illustrated: Single Phase Monte Carlo Simulation (SPMCS), Two Phase Monte Carlo Simulation (TPMCS) and Parameter Monte Carlo Simulation (PMCS). Each configuration of Monte Carlo Simulation has its own objective in the analysis of a model’s uncertainty and depends on the distinction between the types of uncertainty. As an experiment, a hypothetical river was modelled using the Streeter-Phelps model and synthetic data was generated for the system. The generation of the synthetic data allowed for the experiment to be performed under controlled conditions. The modelling protocol followed in the experiment included two uncertainty analyses. All three types of Monte Carlo Simulations were used in these uncertainty analyses to quantify the model’s prediction uncertainty in fulfilment of their different objectives. The first uncertainty analysis, known as the preliminary uncertainty analysis, was performed to take stock of the model’s situation concerning uncertainty before any effort was made to reduce the model’s prediction uncertainty. The idea behind the preliminary uncertainty analysis was that it would help in further modelling decisions with regards to calibration and parameter estimation experiments. Parameter uncertainty was reduced by the calibration of the model. Once parameter uncertainty was reduced, the second uncertainty analysis, known as the confirmatory uncertainty analysis, was performed to confirm that the uncertainty associated with the model was indeed reduced. The two uncertainty analyses were conducted in exactly the same way. In conclusion to the experiment, it was illustrated how the quantification of the model’s prediction uncertainty aided in the calculation of a Total Maximum Daily Load (TMDL). The Margin of Safety (MOS) included in the TMDL could be determined based on scientific information provided by the uncertainty analysis. The total MOS assigned to the TMDL was -35% of the mean load allocation for the point source. For the sake of simplicity load allocations from non-point sources were disregarded. / AFRIKAANSE OPSOMMING: Watergehalte modelle is wiskundige voorstellings van ekologiese sisteme en speel ’n belangrike rol in die beplanning en bestuur van waterhulpbronne en wateromgewings. Belangrike besluite rakende finansiële beleggings en besluite rakende die omgewing maak dikwels staat op die resultate van watergehalte modelle. Dit is dus baie belangrik dat besluitnemers bewus is van die onsekerhede verbonde met die modelle en dit verstaan. Die fokus van hierdie studie het berus op die gebruik van die Monte Carlo Simulasie om die voorspellingsonsekerhede van watergehalte modelle te kwantifiseer. Twee tipes onsekerhede bestaan: Epistemologiese onsekerheid en toeval afhangende onsekerheid. Epistemologiese onsekerheid is die oorsaak van ‘n gebrek aan kennis terwyl toeval afhangende onsekerheid die natuurlike wisselvalligheid in ’n natuurlike omgewing behels. Dit is belangrik om te onderskei tussen hierdie twee tipes onsekerhede aangesien die analise van ’n model se onsekerheid hiervan afhang. Drie verskillende rangskikkings van Monte Carlo Simulasies in die analise van die onsekerhede word bespreek en geïllustreer: Enkel Fase Monte Carlo Simulasie (SPMCS), Dubbel Fase Monte Carlo Simulasie (TPMCS) en Parameter Monte Carlo Simulasie (PMCS). Elke rangskikking van Monte Carlo Simulasie het sy eie doelwit in die analise van ’n model se onsekerheid en hang af van die onderskeiding tussen die twee tipes onsekerhede. As eksperiment is ’n hipotetiese rivier gemodelleer deur gebruik te maak van die Streeter-Phelps teorie en sintetiese data is vir die rivier gegenereer. Die sintetiese data het gesorg dat die eksperiment onder beheerde toestande kon plaasvind. Die protokol in die eksperiment het twee onsekerheids analises ingesluit. Al drie die rangskikkings van die Monte Carlo Simulasie is gebruik in hierdie analises om die voorspellingsonsekerheid van die model te kwantifiseer en hul doelwitte te bereik. Die eerste analise, die voorlopige onsekerheidsanalise, is uitgevoer om die model se situasie met betrekking tot die onsekerheid op te som voor enige stappe geneem is om die model se voorspellings onsekerheid te probeer verminder. Die idee agter die voorlopige onsekerheidsanalise was dat dit sou help in verdere modelleringsbesluite ten opsigte van kalibrasie en die skatting van parameters. Onsekerhede binne die parameters is verminder deur die model te kalibreer, waarna die tweede onsekerheidsanalise uitgevoer is. Hierdie analise word die bevestigingsonsekerheidsanalise genoem en word uitgevoer met die doel om vas te stel of die onsekerheid geassosieer met die model wel verminder is. Die twee tipes analises word op presies dieselfde manier toegepas. In die afloop tot die eksperiment, is gewys hoe die resultate van ’n onsekerheidsanalise gebruik is in die berekening van ’n totale maksimum daaglikse belading (TMDL) vir die rivier. Die veiligheidgrens (MOS) ingesluit in die TMDL kon vasgestel word deur die gebruik van wetenskaplike kennis wat voorsien is deur die onsekerheidsanalise. Die MOS het bestaan uit -35% van die gemiddelde toegekende lading vir puntbelasting van besoedeling in die rivier. Om die eksperiment eenvoudig te hou is verspreide laste van besoedeling nie gemodelleer nie.