- #1
mattmaci
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- TL;DR
- I question a conductivity-based dilution model that treats BOD₅ as a conservative tracer. Regression results show almost no linear relationship between BOD₅ and conductivity and different slopes for effluent and river water.
This is a real exploratory analysis conducted by a company and submitted to my country's environmental authority.
I would like to know your opinion on the analysis and whether my observations are valid. In particular, I would like to know whether, based on the formulation of the problem, it is correct to assume that there must necessarily be a linear relationship between BOD₅ and conductivity, and whether the data presented in the analysis contradict that assumption.
Below is my assessment. I have attached to this post the exploratory analysis submitted by the company.
The validity of the methodology proposed in the report relies on three hypotheses concerning the behavior of conductivity. In particular, Hypothesis 2 assumes that there is a linear relationship between conductivity and the total amount of dissolved compounds in the water, and that this relationship is the same for both the effluent and the receiving water body.
Although this hypothesis is questionable, considering that the two matrices — river water and effluent — have substantially different ionic compositions and conductivity values that differ by two orders of magnitude, I do not rule it out at this stage, since doing so would require a specific analysis for which the necessary information is not available.
Notwithstanding the above, this hypothesis is used to derive dilution equation (5), which is based on an assumed linear relationship between a tracer and conductivity. In this derivation, the relationship is assumed to be the same in both the effluent and the river, so that the dilution equation becomes independent of the parameters of the straight line (α and β).
Then, before deriving equation (6), the model introduces the assumption that BOD₅ can be treated as a conservative tracer over the temporal and spatial scales of the problem under analysis. This equation estimates BOD₅ as a function of the dilution calculated from conductivity measurements, and is used in an attempt to demonstrate that the observed results would not be exclusively attributable to the plant discharge.
Under the hypotheses and assumptions described above, the methodological development implies that there should be a linear relationship between BOD₅ and conductivity in both the effluent and the receiving water body, and that this relationship should be the same in both media.
However, when a linear regression is applied using the monitoring data presented by the company in its own report — taken from Tables 3 and 4 — the statistical results appear to contradict this assumption.
For the receiving water body, the regression between conductivity and BOD₅ yields a very low coefficient of determination: R² = 0.0002. This indicates that, within the measured ranges, a linear relationship between the two variables cannot be supported.
For the effluent, the coefficient of determination is R² = 0.078. This suggests that conductivity explains only a very small proportion of the variability in BOD₅, meaning that the relationship between the two variables is weak.
Finally, the estimated slopes for the two datasets are not equivalent. While the estimated slope α for the receiving water body is 0.0007, the corresponding value for the effluent is 0.0022. This means that the slope for the effluent is approximately three times greater than the slope for the receiving water body, which contradicts the assumption of a common relationship between conductivity and BOD₅ in both fluids.
Is my reasoning correct? Please take a look at the attached analysis that I am attempting to challenge.
I would like to know your opinion on the analysis and whether my observations are valid. In particular, I would like to know whether, based on the formulation of the problem, it is correct to assume that there must necessarily be a linear relationship between BOD₅ and conductivity, and whether the data presented in the analysis contradict that assumption.
Below is my assessment. I have attached to this post the exploratory analysis submitted by the company.
The validity of the methodology proposed in the report relies on three hypotheses concerning the behavior of conductivity. In particular, Hypothesis 2 assumes that there is a linear relationship between conductivity and the total amount of dissolved compounds in the water, and that this relationship is the same for both the effluent and the receiving water body.
Although this hypothesis is questionable, considering that the two matrices — river water and effluent — have substantially different ionic compositions and conductivity values that differ by two orders of magnitude, I do not rule it out at this stage, since doing so would require a specific analysis for which the necessary information is not available.
Notwithstanding the above, this hypothesis is used to derive dilution equation (5), which is based on an assumed linear relationship between a tracer and conductivity. In this derivation, the relationship is assumed to be the same in both the effluent and the river, so that the dilution equation becomes independent of the parameters of the straight line (α and β).
Then, before deriving equation (6), the model introduces the assumption that BOD₅ can be treated as a conservative tracer over the temporal and spatial scales of the problem under analysis. This equation estimates BOD₅ as a function of the dilution calculated from conductivity measurements, and is used in an attempt to demonstrate that the observed results would not be exclusively attributable to the plant discharge.
Under the hypotheses and assumptions described above, the methodological development implies that there should be a linear relationship between BOD₅ and conductivity in both the effluent and the receiving water body, and that this relationship should be the same in both media.
However, when a linear regression is applied using the monitoring data presented by the company in its own report — taken from Tables 3 and 4 — the statistical results appear to contradict this assumption.
For the receiving water body, the regression between conductivity and BOD₅ yields a very low coefficient of determination: R² = 0.0002. This indicates that, within the measured ranges, a linear relationship between the two variables cannot be supported.
For the effluent, the coefficient of determination is R² = 0.078. This suggests that conductivity explains only a very small proportion of the variability in BOD₅, meaning that the relationship between the two variables is weak.
Finally, the estimated slopes for the two datasets are not equivalent. While the estimated slope α for the receiving water body is 0.0007, the corresponding value for the effluent is 0.0022. This means that the slope for the effluent is approximately three times greater than the slope for the receiving water body, which contradicts the assumption of a common relationship between conductivity and BOD₅ in both fluids.
Is my reasoning correct? Please take a look at the attached analysis that I am attempting to challenge.