Development of Rating Curves: Machine Learning vs. Statistical Methods
2. Materials and Methods
2.1. The Statistical Approach—PINAX
- A test of the null hypothesis that the DC is equal to a selected value ρ0 against the alternative hypothesis to be less than ρ0 at a significance level α1.
- A test that the standardised departures from the regression estimations are less than an upper threshold (the acceptable threshold corresponds to a significance level α2).
- A test of the null hypothesis that the standardised deviation of the residuals is equal to a value σ0 against the alternative to be greater with a significance level α3.
- An upper threshold for consecutive positive or negative residuals (the acceptable threshold corresponds to a significance level α4).
- An upper threshold for standardised departures of inputs (stage) and outputs (discharge) from their corresponding mean values (the acceptable threshold corresponds to a significance level α5).
- An upper threshold b6 for the number of clusters.
- The known outliers and breakpoints.
2.2. The Machine Learning Approach
2.2.1. Data Clustering and Filtering
2.2.2. Approximate the Rating Curve with MLP
3.1. Case Study—Sakoulevas River
- Points 3 and 5. It is evident from Figure 5 that these two points lie far away from the cloud of the remaining points.
- Point 4. This point corresponds to a measurement with very low discharge (the second lowest, see Figure 3), which, however, has a significant stage (Figure 4). This is the only point of DBSCAN that was not deemed an outlier by PINAX. Indeed, geometrically, it looks like an outlier, but from a hydraulic perspective, this judgement can be disputed.
- Points 8, 12, and 13. These points could have formed a category on their own, but the lower limit to form a new category is 6 points (this was verified by setting m equal to 3).
- Points 1, 2, 6, and 7. The reason for this decision of DBSCAN is not obvious for these points.
3.2. Case Study—Trikeriotis River
3.3. Case Study—Agrafiotis River
4. Discussion and Conclusions
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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|(attained significance level of DC equal 0.9) > α1 = 0.05||✓||✓|
|(standardised departures) < b2 = 2.58||✓||X|
|(standard deviation of residuals) < σ0 = 0.35, with α3 = 0.05||✓||✓|
|(number of consecutive runs) < 9||✓||✓|
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Rozos, E.; Leandro, J.; Koutsoyiannis, D. Development of Rating Curves: Machine Learning vs. Statistical Methods. Hydrology 2022, 9, 166. https://doi.org/10.3390/hydrology9100166
Rozos E, Leandro J, Koutsoyiannis D. Development of Rating Curves: Machine Learning vs. Statistical Methods. Hydrology. 2022; 9(10):166. https://doi.org/10.3390/hydrology9100166Chicago/Turabian Style
Rozos, Evangelos, Jorge Leandro, and Demetris Koutsoyiannis. 2022. "Development of Rating Curves: Machine Learning vs. Statistical Methods" Hydrology 9, no. 10: 166. https://doi.org/10.3390/hydrology9100166