Skip to main content

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

Abstract

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.

Graphical Abstract

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Data Availability

All data and material used in this study are available on request and at http://www.iat.pr.gov.br/Pagina/Sistema-de-Informacoes-Hidrologicas.

References

  1. Bowes M, Loewenthal M, Read D, Hutchins M, Prudhomme C, Armstrong L, Harman S, Wickham H, Gozzard E, Carvalho L (2016) Identifying multiple stressor controls on phytoplankton dynamics in the river thames (uk) using high-frequency water quality data. Sci Total Environ 569:1489–1499

    Article  Google Scholar 

  2. Coelho M (2019) Uncertainty Analysis in the Statistical and Stochastic Context of Water Quality Time Series. PhD thesis, Federal University of Parana

  3. CONAMA (2005) (Conselho Nacional do Meio Ambiente). Resolução n 357/05

  4. Dadhich AP, Goyal R, Dadhich PN (2021) Assessment and prediction of groundwater using geospatial and ann modeling. Water Resour Manag pp 1–15

  5. Del Giudice D, Muenich RL, Kalcic MM, Bosch NS, Scavia D, Michalak AM (2018) On the practical usefulness of least squares for assessing uncertainty in hydrologic and water quality predictions. Environ Model Softw 105:286–295

    Article  Google Scholar 

  6. Elkiran G, Nourani V, Abba S (2019) Multi-step ahead modelling of river water quality parameters using ensemble artificial intelligence-based approach. J Hydrol 577:123962

    Article  Google Scholar 

  7. Fernandes CVS (2019) INTEGRA 2: Bases Técnicas para a Integraçáo de Instrumentos de Gest ao de Recursos Hídricos - Estudo de Caso da Bacia do Alto Iguaçu e Bacia do Alto Tietê (INTEGRA 2: Technical Bases for the Integration of Water Resources Management System Instruments - Case Study of the Upper Iguaçu Basin and Alto Tietê.). Technical report, University of Zurich, Department of Informatics

  8. Ferreira DM, Fernandes CVS, Kaviski E (2016) Curvas de permanência de qualidade da água como subsídio para o enquadramento de corpos d’água a partir de modelagem matemática em regime não permanente. RBRH 21(3):479–492

    Article  Google Scholar 

  9. Ferreira DM, Fernandes CVS, Kaviski E, Fontane D (2019) Water quality modelling under unsteady state analysis: Strategies for planning and management. J Environ Manag 239:150–158

  10. Ferreira DM, Fernandes CVS, Kaviski E, Fontane D (2020) Transformation rates of pollutants in rivers for water quality modelling under unsteady state: A calibration method. J Hydrol pp 124769

  11. Gholizadeh MH, Melesse AM, Reddi L (2016) A comprehensive review on water quality parameters estimation using remote sensing techniques. Sensors 16(8):1298

    Article  Google Scholar 

  12. Guzman JA, Shirmohammadi A, Sadeghi AM, Wang X, Chu ML, Jha MK, Parajuli PB, Harmel RD, Khare YP, Hernandez JE (2015) Uncertainty considerations in calibration and validation of hydrologic and water quality models. Transactions of the ASABE 58(6):1745–1762

    Article  Google Scholar 

  13. Helsel DR, Hirsch RM, Ryberg KR, Archfield SA, Gilroy EJ (2019) Statistical methods in water resources. Technical report, US Geological Survey

    Google Scholar 

  14. Hintze JL, Nelson RD (1998) Violin plots: a box plot-density trace synergism. Am Stat 52(2):181–184

    Google Scholar 

  15. Huang H, Wang Z, Xia F, Shang X, Liu Y, Zhang M, Dahlgren RA, Mei K (2017) Water quality trend and change-point analyses using integration of locally weighted polynomial regression and segmented regression. Environ Sci Pollut Res 24(18):15827–15837

    Article  Google Scholar 

  16. IAT (2018) Instituto Água e Terra (Water and Earth Institute)

  17. Leigh C, Alsibai O, Hyndman RJ, Kandanaarachchi S, King OC, McGree JM, Neelamraju C, Strauss J, Talagala PD, Turner RD et al (2019) A framework for automated anomaly detection in high frequency water-quality data from in situ sensors. Sci Total Environ 664:885–898

    Article  Google Scholar 

  18. Lim H, An H, Kim H, Lee J (2019) Prediction of pollution loads in the geum river upstream using the recurrent neural network algorithm. Korean J Agric Sci 46(1):67–78

    Google Scholar 

  19. Loucks DP, Beek EV (2017) Water Resource Systems Planning and Management. Springer International Publishing

  20. Marrin D (2017) Pattern-based approaches to evaluating water quality. In Multidisciplinary Digital Publishing Institute Proceedings vol 2

  21. Martin JL, McCutcheon SC (1998) Hydrodynamics and transport for water quality modeling. CRC Press

  22. Miller MP, Tesoriero AJ, Hood K, Terziotti S, Wolock DM (2017) Estimating discharge and nonpoint source nitrate loading to streams from three end-member pathways using high-frequency water quality data. Water Resour Res 53(12):10201–10216

    Article  Google Scholar 

  23. Onyutha C (2019) Hydrological model supported by a step-wise calibration against sub-flows and validation of extreme flow events. Water 11(2):244

    Article  Google Scholar 

  24. Strokal M, Spanier JE, Kroeze C, Koelmans AA, Flörke M, Franssen W, Hofstra N, Langan S, Tang T, van Vliet MT et al (2019) Global multi-pollutant modelling of water quality: scientific challenges and future directions. Curr Opin Environ Sustain 36:116–125

    Article  Google Scholar 

  25. Sturludottir E, Gunnlaugsdottir H, Nielsen OK, Stefansson G (2017) Detection of a changepoint, a mean-shift accompanied with a trend change, in short time-series with autocorrelation. Commun Stat Simul Comput 46(7):5808–5818

    Article  Google Scholar 

  26. Taherdoost H (2018) A review of technology acceptance and adoption models and theories. Procedia manufacturing 22:960–967

    Article  Google Scholar 

  27. Tung TM, Yaseen ZM (2020) A survey on river water quality modelling using artificial intelligence models: 2000–2020. J Hydrol 585:124670

  28. Uusitalo L, Lehikoinen A, Helle I, Myrberg K (2015) An overview of methods to evaluate uncertainty of deterministic models in decision support. Environ Model Softw 63:24–31

    Article  Google Scholar 

  29. Yao J, Wang G, Xue W, Yao Z, Xue B (2019) Assessing the adaptability of water resources system in shandong province, china, using a novel comprehensive co-evolution model. Water Resour Manag 33(2):657–675

    Article  Google Scholar 

  30. Yaseen ZM, Sulaiman SO, Deo RC, Chau K-W (2019) An enhanced extreme learning machine model for river flow forecasting: State-of-the-art, practical applications in water resource engineering area and future research direction. J Hydrol 569:387–408

    Article  Google Scholar 

  31. Zhang Q, Hirsch RM (2019) River water-quality concentration and flux estimation can be improved by accounting for serial correlation through an autoregressive model. Water Resour Res 55(11):9705–9723

    Article  Google Scholar 

Download references

Funding

No funding was received to assist with the preparation of this manuscript.

Author information

Affiliations

Authors

Contributions

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.

Corresponding author

Correspondence to Danieli Mara Ferreira.

Ethics declarations

Conflicts of Interest

The authors have no conflicts of interest to declare.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 501 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1007/s11269-021-02908-1

Download citation

Keywords

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