Statistical Aspects of the Assessment Water Discharge Using the Tracer Dilution Method

Authors

  • Tatyana N. Sintsova Mining Institute of the Ural Branch of the Russian Academy of Sciences image/svg+xml
  • Anatoly P. Lepikhin Mining Institute of the Ural Branch of the Russian Academy of Sciences image/svg+xml

DOI:

https://doi.org/10.34753/HS.2025.7.3.286
+ Keywords

mixing method, distribution functio, inconsistency, water discharge

+ Abstract

The aim of this study is to assess the errors in measuring water discharge in streams using the dilution method. Instability in water discharge measurements during instantaneous and continuous tracer injections arises from the inconsistency of arithmetic mean estimators. This occurs because the distribution functions follow an inverse normal distribution, which results from the structure of the calculation formulas. Furthermore, discharge fluctuations follow an inverse normal distribution, for which estimates of mean values and variances are inconsistent. The ratio for estimating water flow contains tracer concentrations in the denominator, which are generally random variables. If its variability is determined solely by measurement errors and small-scale turbulent fluctuations, then the tracer concentrations fluctuations will be normally distributed, and the calculated discharge will follow an inverse normal distribution.

Mathematical modeling of water flow measurement errors using a Monte Carlo simulation showed that, with low marker concentration variability, their estimates are consistent. It was found that, at low tracer concentration variability (СvС < 0.1), their estimates are stable, while at СvС > 0.25, they are unstable. Mountain rivers, which are primarily targeted by the considered methods for estimating water discharge, are characterized by both high turbulence and rapid temporal variability in water discharge. Therefore, the distance from the tracer injection site to the control section should ensure sufficiently uniform and complete mixing of the marker across the flow cross-section. Furthermore, the characteristic time for tracking changes in concentrations at the control section with instantaneous tracers’ injection should be significantly shorter than the characteristic temporal variability of the water discharge itself.

Effective methods for improving the stability of water discharge measurements and reducing fluctuations in measured concentrations at the control section are proposed: increasing the distance between the injection and control section, and using sensor arrays.

+ Author Biographies

Tatyana N. Sintsova

leading engineer, Mining Institute of the Ural Branch of the Russian Academy of Sciences, Perm, Russia, SPIN-code: 7569-1702, https://orcid.org/0000-0003-0327-4894, Author ID Scopus: 57474212500, Author ID: 1226076, e-mail: tanya_sinzova@mail.ru.

Anatoly P. Lepikhin

D.Sc. (Geography), Head of the Laboratory, Mining Institute of the Ural Branch of the Russian Academy of Sciences, Perm, Russia, SPIN-code: 7621-8001, https://orcid.org/0000-0001-9874-3424, Author ID: 147950, Author ID Scopus: 56370650100, e-mail: lepihin49@mail.ru.

+ References

1. Wood P.J., Dykes A.P. The use of salt dilution gauging techniques: ecological considerations and insights. Water Research, 2002, vol. 36, pp. 3054–3062.

2. Acosta-Motos J.R., Ortuño M.F., Vicente A. B., Diaz-Vivancos P., Sanchez-Blanco M. J., Hernandez J. A. Plant Responses to Salt Stress: Adaptive Mechanisms. Agronomy, 2017. vol. 7 (18). 38 p.

3. Pang H., Xin X., He J., Cui B., Guo D., Liu S., Yan Z., Liu C., Wang X., Nan J. Effect of NaCl Concentration on Microbiological Properties in NaCl Assistant Anaerobic Fermentation: Hydrolase Activity and Microbial Community Distribution. Frontiers in Microbiology, 2020, vol. 11, pp. 1–10.

4. Бернадский Н.М. Измерение расходов воды химическим методом. СПб. 1913.

5. Риммар Г.М. Применение электропроводности для определения расходов воды методом смешения // Труды ГГИ, в. 36 (90): ГИМИЗ, 1952. С.18–48.

6. Schloeseng M. Th. Nouvelle methode pour juger les fluids. Comples rendus du deuxieme semester de l’Acadamie des Sciences. Paris, 1863.

7. Юхно А.В., Бузмаков С.В., Лубенцов А.С., Пнюшков А.Д. Измерение малых расходов воды методом постоянного пуска соляного раствора // Cб.: Рос. форум изыск.. Сб. докл. IV Межд. научно-практ. конф. М. 2022. С. 159–171.

8. Юхно А.В., Бузмаков С.В., Кулешов А.В. О развитии метода ионного паводка для определения расхода воды // Cб. тр. конф. «Гидрометеорология и экология: достижения и перспективы развития» им. Л. Н. Карлина, С.-П. / MGO-2022. М.: Изд-во «Перо». – 2022. – С. 257–260.

9. Юхно А.В., Бузмаков С.В., Лубенцов А.С. Метод ионного паводка как инструмент гидрологического мониторинга в горных районах. Специфика и перспективы // Водные ресурсы в условиях глобальных вызовов: экологические проблемы, управление, мониторинг. Ростов-на-Дону. Из-во: ООО «Лик» (Новочеркасск). 2023. С. 176–181.

10. Johnson N.L., Kotz S., Balakrishnan N. Continuous Univariate Distributions. Wiley. 1994. Vol. 1. 171 p.

11. Springer M.D. The Algebra of Random Variables. Wiley. 1979. 492 p.

12. Sappa G., Ferranti F., Pecchia G. M. Validation of Salt Dilution Method for Discharge Measurements in the Upper Valley of Aniene River (Central Italy). Recent Advances in Environmental, Ecosystem and Development, 2015, pp. 42–48.

13. Merz J., Doppmann G. Measuring Mountain Stream Discharge Using the Salt Dilution Method: A Practical Guide. Kathmandu, Nepal: International Centre for Integrated Mountain Development (ICIMOD), 2006, pp. 1–14.

14. Lane S.N., Parsons D.R., Best J.L., Orfeo O., Kostaschuk R.A., Hardy R.J. Causes of rapid mixing at a junction of two large rivers: Rio Parana and Rio Paraguay, Argentina. JGR: Earth Surface, 2008, vol. 113, F02024. DOI:10.1029/2006JF000745.

15. Любимова Т.П., Лепихин А.П., Паршакова Я.Н., Колчанов В.Ю., Gualtieri C., Lane S.N., Roux B. Гидродинамические аспекты слияния рек с различными плотностями вод // Вычислительная механика сплошных сред. 2020. Т. 13. № 4. С. 381–392.

16. Bouchez J., Lajeunesse E., Gaillardet J., France-Lanord C., Dutra-Maia P., Maurice L. Turbulent mixing in the Amazon River: The isotopic memory of confluences. Earth Planet. Sci. Lett., 2010, vol. 290, pp. 37–43. DOI:10.1016/j.epsl.2009.11.054.

17. Mackay J.R. Lateral mixing of the Liard and Mackenzie rivers downstream from their confluence // Canadian Journal of Earth Sciences, 1970, vol. 7., pp. 111–124. DOI:10.1139/e70-008.

18. Монин А.С., Яглом А.М. Статистическая гидромеханика. М.: Наука, 1965. Ч. 1. 639 с.

19. Математическое моделирование в управлении водопользованием (под ред. А.М. Черняева). Екатеринбург: Аква-Пресс, 2001. 520 с.

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Published

2025-12-15

Issue

Vol. 7 No. 3 (2025): Hydrosphere. Hazard processes and phenomena

Section

Conference materials

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Copyright (c) 2025 Татьяна Николаевна Синцова, Анатолий Павлович Лепихин

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How to Cite

Sintsova, T. N., & Lepikhin, A. P. (2025). Statistical Aspects of the Assessment Water Discharge Using the Tracer Dilution Method. Hydrosphere. Hazard Processes and Phenomena, 7(3), 286-295. https://doi.org/10.34753/HS.2025.7.3.286