Abstract
Two stochastic models are developed to describe the BOD output (i.e. effluent) variation of facultative aerated lagoons in series. One of the models uses the uncertainty analysis (UA) technique and the other is based on the moment equation solution methodology of stochastic differential equations (SDE's). The former considers a second-order approximation of the expectation (SOAE) and a first-order approximation of the variance (FOAV). The SDE model considers that output variability is accounted for by random variations in the rate coefficient. Comparisons are provided. Calibration and verification of the two models are aciieved by using field observations from two different lagoon systems in series. The predictive performances of the two models are compared with each other and with another SDE model, presented in a previous paper, that considers input randomness. The three methods show similar predictive performances and provide good predictions of the mean and standard deviation of the lagoon effluent BOD concentrations and thus are considered as appropriate methodologies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnold, L. 1974: Differential equations: theory and applications. New York: Wiley
Benefield, L.D.; Randall, C.W. 1980: Biological process design for wastewater treatment. Englewood Cliffs: Prentice Hall
Benjamin, J.R.; Cornell, C.A. 1970: Probability, statistics, and decision for civil engineers. New York: McGraw-Hill
Bodo, B.A.; Thompson, M.E.; Unny, T.E. 1987): A review on stochastic differential equations for applications in hydrology. Stoch. Hydrol. Hydraul. 1, 81–100
Burn, D.H.; McBean, E.A. 1985: Optimization modeling of water quality in an uncertain environment. Water Resour. Res. 21, 934–940
Cornell, C.A. 1972: “First order analysis and parameter uncertainty”. International Symposium on Uncertainties in Hydrology and Water Resource Systems, University of Arizona, Tucson
Finney, B.A.; Bowles, D.S.; Windham, M.P. 1982: Random differential equations in river water quality modelling. Water Resour. Res. 18, 122–134
Gaines, J.B. 1989: Pėak sewage flow rate: prediction and probability. J. Water Pollut. Control Fed. 61, 1241–1248
Gardiner, C.W. 1983: Handbook of stochastic methods for physics, chemistry and the natural sciences. New York: Springer-Verlag
Harr, M.E. 1987: Reliability-based design in civil engineering. New York: McGraw-Hill
Ito, K. 1951: On stochastic differential equations. Mem. Amer. Math. Soc. 4, 1–51
Jalbert J.M. 1983: “Les etangs facultatifs aeres-Theorie et pratique”, Proceedings, 6th Symposium on Wastewater Treatment, Montreal, November 16–17
Jazwinski, A.H. 1970: Stochastic processes and filtering theory. New York: Academic Press
Leduc, R., Unny, T.E.; McBean, E.A. 1986: Stochastic model of first-order BOD kinetics. Water Res. 20, 625–632
Leduc, R.; Unny, T.E.; McBean, E.A. 1987: Stochastic modeling of the insecticide fenitrothion in water and sediment compartments of a stagnant pond. Water Resour. Res. 23, 1105–1112
Leduc, R.; Unny, T.E.; McBean, E.A. 1988: Stochastic models for first-order kinetics of biochemical oxygen demand with random initial conditions, inputs, and coefficients. Appl. Math. Model. 12, 565–572
Metcalf; Eddy, 1979: Wastewater engineering: treatment, disposal, reuse. New York: McGraw-Hill
Mistry, K.J.; Himmelblau, D.M. 1975: Stochastic analysis of trickling filter. J. Env. Eng. Div. (ASCE) 101, 333–350
Niku, S.; Schroeder, E.D. 1981: Stability of activated sludge processes based on statistical measures. J. Water Pollut. Control Fed. 53, 457–470
Ouldali, S. 1988: Stochastic modeling of facultative aerated lagoons. M. Eng. thesis, McGill Univ., Montreal
Ouldali, S.; Leduc, R.; Nguyen, V.-T.-V. 1989: Uncertainty modeling of facultative aerated lagoon systems. Water Res. 23, 451–459
Randtke, S.J.; McGarty, P.L. 1977: Variations in nitrogen and organics in wastewaters. J. Env. Eng. Div. (ASCE) 103, 539–550
Reckhow, K.H.; Chapra, S.C. 1983: Engineering approaches for lake management Vol. 1: Data analysis and empirical modeling. Boston: Butterworth Publishers
Song, T.T. 1971: Pharmacokinetics with uncertainties in rate constants. Math. Biosc. 12, 235–243
Soong, T.T. 1973: Random differential equations in science and engineering. New York: Academic Press
Tanthapanichakoon, W.; Himmelblau, D.M. 1981: Simulation of a time dependent activated sludge wastewater treatment plant. Water Res. 15, 1185–1195
Tetreault, R.; Desjardins, R.; Beland, Y.; Briere, F. 1983: Evaluation de la constante d'utilisation de la DBO et du coefficient de temperature: comparaison de deux methodes. Sci. Tech. Eau 16, 255–259
Thirumurthi, D. 1979: Design criteria for aerobic aerated lagoons. J. Env. Eng. Div. (ASCE) 105, 135–148
Thirumurthi, D. 1980: Design guigelines for incompletely mixed or aerobic-anaerobic aerated lagoons. Can. J. Civ. Eng. 7, 27–35
Thomann, R.V. 1970: Variability of waste treatment plant performance. J. San. Eng. Div. (ASCE) 96, 819–837
Unny, T.E.; Karmeshu 1983: Stochastic nature of outputs from conceputal reservoir cascades. J. Hydrol. 68, 161–180
Wallace, A.T.; Zollman, D.M. 1971: Characterization of time-varying organic loads. J. San. Eng. Div. (ASCE) 97, 257–268
Wong, E. 1971: Stochastic processes in information and dynamical systems. New York: McGraw-Hill
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Leduc, R., Ouldali, S. Probabilistic modeling of aerated lagoons: A comparison of methodologies. Stochastic Hydrol Hydraul 4, 65–81 (1990). https://doi.org/10.1007/BF01547733
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01547733