Uncertainty analysis of Porsuk River model

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1994Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 1994Bu çalışmada Porsuk Nehrin Modelinin kalibrasyonu ve QUAL2E-UNCAS programı ile modelin belirsizlik analizi yapılmıştır Bugüne kadar ki, bütün model çalışmalarında, simülasyon sonuçlan ile kalibrasyon sonuçlan arasındaki farklar sadece grafiksel olarak veya analitik olarak değerlendirilmiş,ancak istatiksel bir analize tutulmamıştır. Dolayısıyla, modeldeki sapma ve hataların hangi düzeyde olduğu, modelin güvenirliliği ve doğrusallığı hakkındaki tüm yorumlar, grafikler üzerinde yapılmıştır. Belirsizlik analizleri dünyada su kalite modelleri için sıkça kullanılır hale gelmiştir Artık model üzerinde çıplak gözle yapılan değerlendirmeler yetersiz kalmakta, istatiksel analiz gerekliliği ortaya çıkmaktadır. Bu amaçla, çalışmada QUAL2E-UNCAS bilgisayar pogramı kullanılmış, programın içerisindeki 3 ayn belirsizlik analizi ayn ayn tanıtılmıştır. Aynca QUAL2E modelinin son versiyonu kullanılarak yeniden kalibre edilen, Porsuk Nehri modeli verileri kullanılarak, model üzerinde birinci derece hata analizi yapılmış, elde edilen sonuçlar yorumlanmıştır. Belirsizlik analizinden elde edilen sonuçlar modelin yeniden yapılacak kalibrasyonuna ışık tutacaktır.As environmental controls become more costly to implement and the penalties of judgement errors become more sewere, environmental quality management requires more efficient management tools based on greater knowledge of the environmental phenomena to be managed. The stream water quality model QUAL2E is widely used for waste allocations, discharge permit determinations, and other conventional pollutant evaluations In this study, The Porsuk River model that was studied by Dr.Selmin Burak Baltaoğlu, using MODQUAL water quality model, in 1991, has been evaluated and calibrated once more by using the last version of QUAL2E But the main aimes of this study are to define the uncertainty analysis and to perform the one of selected uncertainty analysis of QUAL2E-UNCAS program including three different uncertainty analysis, to the calibrated Porsuk River Model QUAL2E-UNCAS has been shown to provide a useful framework for performing uncertainty analysis in steady-state water quality modelling. Application of the first order error analysis to a data set from Porsuk River Basin has highlighted some of the useful features of uncertainty analysis In this study, calibration of Porsuk River Model was done and three uncertainty analysis of QUAL2E-UNCAS were identified Finally, first order analysis was performed to the Porsuk River Model data şet and results were evaluated. XII UNCERTAINTY ANALYSIS Uncertainty analysis for model simulations is assuming a growing importance in the field of water quality management. The impetus for this concern is provided by recent public awareness over health risks from improper disposal of toxic wastes. One of the first steps in the chain of risk assesment is the quantification of the error in predicting water quality. Unfortunately, uncertainty analysis of water quality model forecasts has not received as much attention in practice as has the prediction of expected average values. Uncertainty analysis has been the subject of much discussion in the ecosystem modelling literature with Rose and Swartzman, 1981 and O'Neill and Gardner, 1979. In the water resorces literature, lake eutrophication models have been used to compare various methods of uncertainty analysis (Reckhow,1979; Scavia et al.,1981; and Malone et al., 1983). The methodologies described in this study represent a systematic approach to uncertainty analysis for the general purpose stream water quality model of Porsuk River. The objective is to provide some of the tools for incorporating uncertainty analysis as an integral part of the water quality modelling process. Three uncertainty anlysis can be employed in QUAL2E-UNCAS ; sensitivity analysis, first order error analysis and monte carlo simulation. Thge user is provided this array of options for flexibility, because the methods differ in teir assumptions and will no always agree with each other Discrepancies may be explained by by errors in the first order approximation or by errors duew to biased variance calculations. Monte Carlo simulation has the advantage of output frequency distributions, but it carries a high computational burden. First order error propagation provides a direct estiate of model sensitivity, but that variability is usually more indicative of the variance of model components than of the dynamics of model structure. The methodology provided in QUAL2E-UNC AS allows the model user to perform uncertainty analysis with relative ease and efficiently manages the output from the analysis. The preprocessing and postprocessing algorithms used are, in principle, applicable to many water quality models. The preprocessor allows the user to select th variables and/or parameters to be altered, without having to manually restructure the input data set. This task is XIII performed automatically by the preprocessor for as many uncertainty conditions as the users wishes to simulate. The postprocessor stores and manipulates only the output of interest, thus reducing potential vouminous output. The user must select the important variables and locations in the strem network where uncertainty effects are desired for analysis. SENSITVITY ANALYSIS With sensitivity analysis option in QUAL2E-UNCAS, the user may vary the inputs singly, in groups, or using factorial design strategies. The input requirements for sensitivity analysis of consist of identifying the input variables to be perturbed and specifying the magnitude of perturbation. The outputfor each sensitivity analysis simulation consists of the change (i.e., the sensitivities)in the valus of each output variable (AY) resulting from the changes in the values of the input variables (AX). This output is provided in tabular format. FIRST ORDER ERROR ANALYSIS First order error analysis utilizes the first order approximation to the relationship for computing variances im multivariate situations. The input variables are assumed to act independently and the model to be linear. The first order approximations to the components of output variance is often good. The QUAL2E-UNCAS output for first order error analysis consists of two parts : a) a tabulation of normalized sensitivity coefficients b) a listing of the components of variance. The normalized sensitivity coefficients represent the percentage change in the ouput variable resulting from a 1 percent change in each input variable, and are computed as follows: Sy =(AYj / Yj) / (AX( / Xj) S: sensitivity coefficients X: base value of input variable AX: magnitude of input perturbation Y: base value of output variable AY: sensitivity of output variable XIV The components of variance for each output variable Y are the percentages of output variance attributable to each input variable X, computed in the following manner. Var (Yj) = Z Var (X i)(AYj / AXj )2 Var(Y): variance of output variable Var(X): variance of input variable The components of the output variance, represent a weighting of the input variances, by the square of the sensitivity of model output output to rthe input. The input requirements for first order error analysis consist of (a) the magnitude of the input perturbation, AX and (b) the value of the variance of the input variable, Var(X). MONTE CARLO SIMULATION Monte Carlo simulation is a method for numerically oiperating complex syatem that has random components. Input variables are sampled at random from pre-determined probability distribution and the distribution of output values from repeated simulations is analyzed statistically. The validity of this method is not affected by nonlinearities in the water quality model. The monte carlo simulation computations in QUAL2E-UNC AS provide summary statistics and frequency distributions for the state variables at specific locations in the system. The summary statistics include: mean (base and simulated), bias, minimum, range, standart deviation, coefficient of variation, and skew coefficient Frequency and cumulative frequency distributions are tabulated in işncremnets of one-half a standart deviation. Comparison of the standart deviation estimates from monte carlo simulations with those from first order error analysis provide an indication of the extent model nonlinearities. Cumulative frequency distributions are useful in evaluating overall dispersion in the model predictions and in assesing the likelihood of violating a water quality standart. The input requirements for monte carlo simulation option in QUAL2E-UNCAS consist of (a) the varince of the variable, (b) the probability density function of the input variable, and (c) the number of simulations to be performed. XV First order analysis was performed to the Porsuk River Model, and folllowing results were obtained from Biocheical oxygen demand and dissolved oxygen simulations BOD TOTAL STANDART DEVIATION TOPLAM I 0.156 fl 0.912 g 0.765 fl 0.615 M 0 696 DISSOLVED OXYGEN TOTAL STANDART DEVIATION TOPLAM M 0.348 1 0.290 ft 0.188 1 0.237 tf 0.231 An evaluation of the input factors which contribute the most to the level of uncertainty in an output variable will lead us in the direction of nost efficient data gathering research. In this manner the risk of imprecise forecasts and recommend measures for reducing the magnitude of that imprecision can be asssed.Yüksek LisansM.Sc