Comparison Between Complete And Simplified Water Quality Models. Case Study In A Large River In Brazil

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1 e20634a Comparison Between Complete And Simplified Water Quality Models. Case Study In A Large River In Brazil Marcos von Sperling, Mauro da Costa Val, Nilo Oliveira Nascimento Department of Sanitary and Environmental Engineering, Federal University of Minas Gerais, Belo Horizonte, Brazil, marcos@desa.ufmg.br ABSTRACT The paper investigates modelling of dissolved oxygen using water quality model QUAL2E in its complete version (all oxygen demanding and producing components included) and in sequentially simplified versions (excluding sedimentation, benthic demand and/or nitrogen cycle). A case study is investigated, comprising River Paraopeba, a large river that crosses the metropolitan area of Belo Horizonte, the third largest in Brazil. A reach with a length of 243 km, 15 tributaries, 20 towns and 3 lentic systems was the subject of the modelling studies. Special attention was given to the two most important coefficients in the model structure: K 1 (deoxygenation coefficient) and K 2 (reaeration coefficient). The complete and simplified versions of QUAL2E were able to represent satisfactorily well DO concentrations along the river. Considering the great difficulty in data (input data and parameter values) acquisition in developing countries, the utilisation of simpler model versions is frequently an imperious necessity. Due to the representativeness of the scale of the studied river and its catchment area, it is believed that the methodology may be used in other planning studies in which financial, time or technical constraints indicate the use of simpler models. KEYWORDS Water quality, mathematical modelling, QUAL2E, simplified models INTRODUCTION Complete and more sophisticated water quality models are frequently accepted as being able to best represent reality. However, their requirements for input data and model parameters are intensive, and in many cases unaffordable in developing countries. On the other hand, simpler models are usually considered to be more limited in the representation of a wider spectrum of intervening conditions, but have the advantage of less requirements for input data, what may be a significant aspect in those situations where financial constraints play an important role in the scope definition of the simulation studies. The present paper investigates modelling of dissolved oxygen using water quality model QUAL2E (Brown and Barnwell, 1987) in its complete version (all oxygen demanding and producing components included) and in sequentially simplified versions (excluding sedimentation, benthic demand and/or nitrogen cycle), according to the following five structures: Structure 1: complete QUAL2E model Structure 2: QUAL2E model without sedimentation Structure 3: QUAL2E model without benthic demand

2 Structure 4: QUAL2E model without nitrogen cycle Structure 5: QUAL2E model in its simpler structure, without sedimentation, benthic demand and nitrogen cycle, similar to the Streeter-Phelps model A case study is investigated, comprising River Paraopeba, a large river with 510 km of length and various tributaries, which crosses the metropolitan area of Belo Horizonte, the third largest in Brazil. A reach with a length of 243 km was the subject of the modelling studies, its selection being a result of importance, better data availability, as well as of its location with respect to the main sources of pollution in the metropolitan area. The reach under study has 6 tributaries in the left bank, 9 tributaries in the right bank, 20 towns and 3 lentic systems. Historical data, based on several years, have been used to calibrate and validate the model. The flow data were based on four flow-measuring points and the quality data were derived from seven monitoring stations along the reach under study. Two different periods are investigated in the paper: dry period (April to September) and wet period (October to March). In the studied region, the seasonal variations are mainly defined by the amount of rainfall (dry and wet seasons). Average flow and quality data from each of these six-month periods were used to calibrate and validate the models. In the model calibration and verification, special attention was given to the two most important coefficients in the model structure: K 1 (deoxygenation coefficient) and K 2 (reaeration coefficient). The relevance of the paper lies in the conclusion that, with the proper selection of coefficients, a simpler model can give almost the same results as a more complete one. Naturally each simulation is case specific, but the large size and diversity of the catchment area studied is likely to allow extrapolation for a wide variety of similar situations in developing countries world-wide. SIMULATIONS IN DRY PERIOD (CALIBRATION) Table 1 presents a summary of the main simulations undertaken with QUAL2-E for the dry period. The study (Costa Val, 2001) comprised tens of runs, with only the most important of those being discussed in this paper. In the table, the best value found for the deoxygenation coefficient K 1 is presented, together with the resulting Coefficient of Determination (COD), which was used as a measure of the model adherence to the observed data. The best K 1 value is that which leads to the lowest sum of the squared errors, or, in other words, to the highest COD values. COD is given by Equation 1, and its values may vary between - and +1,0, with values closer to +1,0 indicating better fittings. COD = 1 [ Σ (y obs - y est ) 2 ] / [ Σ (y obs - y obs mean ) 2 ] (1) where: y obs = observed DO value (average of the six-month values, in each monitoring station) y est = estimated DO value (in each monitoring station) y obs mean = mean value of observed DO (mean value of observed DO in all seven monitoring stations along the river reach)

3 Table 1. Simulations for dry period, showing best-fit K 1 value and the resulting COD. Structure Model components K 1 Coefficient of Sedimentation Benthic demand N cycle (d -1 ) Determination (COD) 1 0,17 0,74 2 0,17 0,57 3 0,17 0,52 4 0,17 0,67 5 0,65 0,67 It is seen that the complete model achieved a COD value of 0,74 (74% of the variance explained by the model). However, the simpler model, without sedimentation, benthic demand and nitrogen cycle, was able to reach a COD of 0.67, which is only 9% lower than that achieved by the complete model. K 1 value needed to be readjusted, in this case leading to a higher value (Table 1), in order to encompass all oxygen-consuming components into the single carbonaceous matter component in the simplified structure. The reaeration coefficient K 2 was investigated by the use of three empirical equations (Owens et al, apud Branco 1978; Churchill et al, 1962; Thackston & Krenkel, 1969), correlating K 2 with liquid velocity and depth. None of these equations led to a good fitting of the DO values, and the simpler proposal of Arceivala (1981), with a range of fixed K 2 values as a function of a qualitative description of the river in terms of velocity and depth, was adopted. Figure 1 presents the simulation results from both model structures (1 = complete; 5 = simple), together with the observed DO values (mean +/- 1 standard deviation). 9,0 DO PROFILE - DRY PERIOD 8,5 8,0 DO (mg/l) 7,5 7,0 6,5 Complete model Simple model 6,0 5,5 5, DO mean DO mean+ St.dev. DO mean - St.Dev. Simple model Complete model Fig. 1. Observed (mean +/- 1 standard deviation) and simulated DO values (dry period). Complete model (K 1 =0.17d -1, COD=0.74) and simplified model (K 1 =0.65 d -1, COD=0.67). SIMULATIONS IN WET PERIOD (VALIDATION) Simulations were also undertaken with the different model structures for the wet period. In this period, the reaeration coefficient K 2 needed to be reduced, as a result of the greater

4 flow depth in the river in the wet period. For the complete model, K 2 suffered a reduction of 1/3, whereas for the simplified structure, K 2 had a reduction of 2/3. The lower value of K 2 (greater reduction) in the simplified model is probably due to the non-consideration of BOD removal by sedimentation. The best K 1 values were: (a) complete model: K 1 =0.35 d -1 ; (b) simplified model: K 1 =0.23 d - 1. The resulting COD values were very similar (0.75 and 0.74, respectively, for the complete and simplified models). Figure 2 shows the similarity of both curves. DO PROFILE - WET PERIOD 9,0 8,5 8,0 7,5 DO (mg/l) 7,0 6,5 6,0 Simple model Complete model 5,5 5, DO mean DO + St.Dev. DO - St.Dev. Complete model Simple model Fig. 2. Observed (mean +/- standard deviation) and simulated DO values (wet period). Complete model (K 2 with 1/3 reduction; K 1 =0.35d -1, COD=0.75) and simplified model (K 2 with 2/3 reduction; K 1 =0.23 d -1, COD=0.74). CONCLUSIONS The complete and simplified versions of QUAL2E were able to represent satisfactorily well DO concentrations along the river, as measured by the Coefficient of Determination. Considering the great difficulty in data (input data and parameter values) acquisition in developing countries, the utilisation of simpler model versions is frequently an imperious necessity. Therefore, the results obtained may be considered relevant in this context. Also, due to the representativeness of the scale of the studied river (243 km) and its catchment area (15 tributaries, 20 towns and 3 lentic systems), it is believed that the methodology may be used in other planning studies in which financial, time or technical constraints indicate the use of simpler models. REFERENCES ARCEIVALA, S. J. (1981). Wastewater treatment and disposal: engineering and ecology in pollution control. New York: Marcel Dekker, Inc. 892 p. BRANCO, S.M. (1978). Hidrobiologia aplicada à engenharia sanitária. São Paulo, CETESB. 620 p. (in Portuguese).

5 BROWN, L. C. ; BARNWELL, T. O. (1987). The enhanced stream water quality models QUAL2E and QUAL2E-UNCAS : documentation and user manual. Athens GA: Environmental Protection Agency. 189 p. (EPA/600/3-87/007) CHURCHILL, M.A.; ELMORE, H.L.; BUCKINGHAM, R.A. (1962). The prediction of stream reaeration rates. Journal Sanitary Engineering Division, ASCE, 88 (4). July p COSTA VAL, M. (2001). Aplicação do modelo de simulação da qualidade das águas de rios QUAL2E: análise do balanço de oxigênio dissolvido em um trecho da bacia hidrográfica do Rio Paraopeba em Minas Gerais. MSc dissertation, UFMG. (In Portuguese) THACKSTON, E., KRENKEL, P. (1969). Reaeration prediction in natural streams. J. Environ. Eng. Div., ASCE, 95. Contact: Prof. Marcos von Sperling Department of Sanitary and Environmental Engineering Federal University of Minas Gerais Av. Contorno o andar Belo Horizonte BRAZIL marcos@desa.ufmg.br