UDC 556.531
DOI 10.35776/VST.2026.01.01

Ialaletdinova A. V., Yalaletdinov Radik, Vazhdaev Konstantine, Мартяшева В. А., Reziapov Timur

Estimation of the trends of daily values of the river water total hardness

Summary

While controlling water treatment processes, monitoring water quality indicators is essential, since modeling their seasonal variations provides for predicting changes in river water. Time series of daily total hardness values in river water over a 28-year period were analyzed. Regression analysis was used to describe the trend of the indicator of river water. Parameters of the linear regression equations were determined using the Regression tool built in the Data Analysis Package in MS Excel. Prediction of changes in daily total hardness values in the river water was made through statistical modeling – constructing discrete Markov chains that account for the changes in the indicator owing to the random factors. Using the linear regression method, an equation was obtained that described the trend of the total hardness in river water over time. The F-test value revealed statistical significance of the equation. It was established that the total hardness of river water exhibits an upward trend. Using a statistical method – constructing finite Markov chains – a short-term prediction of the total hardness values in river water for the next 10 days was made. It was found that the probability of the total hardness values falling within the first region of the lowest potential risk (S1 state up to 3.5 °H) increases, while the probability of values falling within the second region (S2 state from 3.5 to 7 °H) decreases. While the probability of the values falling within the third region (S3 state above 7 °H, increased potential risk) increases, the increase is no more than 0.2%. Therefore, no increase in the river water hardness values is expected in the next 10 days following the study period.

Key words

water quality , control arrangements , total hardness , regression , stochastic system , Markov processes , probability of event

For citation: Ialaletdinova A. V., Ialaletdinov R. F., Vazhdaev K. V., Martiasheva V. A., Reziapov T. R. Estimation of the trends of daily values of the river water total hardness. Vodosnabzhenie i Sanitarnaia Tekhnika, 2026, no. 1, pp. 4–9. DOI: 10.35776/VST.2026.01.01. (In Russian).

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