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Deterministic and Stochastic Principles to Convert Discrete Water Quality Data into Continuous Time Series


Limited water quality data is often responsible for incorrect model descriptions and misleading interpretations in terms of water resources planning and management scenarios. This study compares two hybrid strategies to convert discrete concentration data into continuous daily values for one year in distinct river sections. Model A is based on an autoregressive process, accounting for serial correlation, water quality historical characteristics (mean and standard deviation), and random variability. The second approach (model B) is a regression model based on the relationship between flow and concentrations, and an error term. The generated time series, here referred to as synthetic series, are propagated in time and space by a deterministic model (SihQual) that solves the Saint-Venant and advection-dispersion-reaction equations. The results reveal that both approaches are appropriate to reproduce the variability of biochemical oxygen demand and organic nitrogen concentrations, leading to the conclusion that the combination of deterministic/empirical and stochastic components are compatible. A second outcome arises from comparing the results for distinct time scales, supporting the need for further assessment of statistical characteristics of water quality data - which relies on monitoring strategies development. Nonetheless, the proposed methods are suitable to estimate multiple scenarios of interest for water resources planning and management.

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D.M.F, M.C., C.V.S.F., E.K. and D.H.M.D. contributed to the study conception and design. Material preparation, data collection and analysis were performed by D.M.F and M.C. The first draft of the manuscript was written by D.M.F; M.C., C.V.S.F., E.K. and D.H.M.D. commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Danieli Mara Ferreira.

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Ferreira, D.M., Coelho, M., Fernandes, C.V.S. et al. Deterministic and Stochastic Principles to Convert Discrete Water Quality Data into Continuous Time Series. Water Resour Manage 35, 3633–3647 (2021).

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  • Water quality time series
  • Stochastic modeling
  • Deterministic modeling
  • SihQual model
  • Water resources planning and management