Hello,

Since the data have been measured in one river, it can be done considering the assumption that the two period have the same coefficient of variation. Since the "correlation coefficient =0.87" is in acceptable level, it is recommended to define and approve the statistical significance of the above value.

You are extrapolating the solid loading. While this method of using correlation to fill missing data, you must be aware of its limitation. Firstly, you are assuming that solid loading is the same as the measure and predicted time periods. This may not always be true given changes in watershed land use and pollutant loading rates over time. Secondly, the solid needs to be explored further on its dissolution in liquid. Dissolved, suspended, and settled solids can vary by many factors.

So, carefully identifying and checking these caveats is important.

Thank you very much professors @Raoof mostafazadeh and @ timothy o randhir, for your valuable answers

To add to Prof. Radnhir's answer, seek out regression software that will provide you with not only the R-squared correlation coefficient, but the (a) fit uncertainty and (b) prediction uncertainty (which will be larger). These uncertainties should be included, or carried through, your extrapolations. Seek out any information about changes in the watershed from 1948 that would change the relationships between your variables. Treat your extrapolations with caution: There may have been historical episodes (e.g., floods, interannual channel storage) that diverged dramatically from your limited data set.

Thank you prof Ted swift for your answer and for your clarification to the answer of prof Randhir

I see that the extrapolation of such a databases requires a detailed knowledge in the studied field

Abdeldjalil, I'm not a professor, but thanks for the compliment. Yes, extrapolation (or interpolation) takes at least some knowledge of the field. "Correlation is not causation", though it is usually a useful hint. If possible, seek out the underlying mechanisms driving the correlation in collaboration with a "subject matter expert". Having a long-term data set is very valuable, if used properly.

What method do you use to find the correlation coefficient?, with your equation how is the residues behavior? For both, interpolation and extrapolation, the last is the most misleading.