Application of Solar Activity Time Series in Machine Learning Predictive Modeling of Precipitation-Induced Floods
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area
2.2. Data Description
- Flood (F): (date, precipitations (mm), days from the beginning of the flood).
- Integral proton flux (IPF, ): .
- Differential electron and proton flux (DF, p/cs2-sec-ster). These blocks contained different sun energy characteristics for different periods during different flood events. The measured ranges for differential electron flux were 38–53 keV and 175–315 keV for all analyzed floods, while the measured ranges for differential proton flux varied depending on the period in which the flood occurred. The differential proton fluxes were measured in the following ranges: 47–65 keV, 47–68 keV, 65–112 keV, 112–187 keV, 115–195 keV, 310–580 keV, 761–1220 keV, 795–1193 keV, 1060–1900 keV, and 1060–1910 keV. However, the only common range for all flood events was 310–580 keV.
- Solar wind (SW): = ( ).
- Radio flux of 10.7 cm (RF, solar flux units): .
2.3. The impact of Precipitation on the Occurrence of Floods
2.4. Preliminary Processing of Input Data and Correlation Analysis
2.5. Machine Learning and Forecast of Precipitation
3. Results and Discussion
3.1. Lag Analysis
3.2. Gini Index
3.3. Evaluation Metrics
- If the error of the test and training sets is close (small variance) it indicates that the model is well fitted and predicts unknown values at the same level as the known ones. The absolute value shows how accurate such a model is.
- If the accuracy on the training set reaches 1, and on the test set it is close to 0.5, it indicates overfitting. That is, the known data are perfectly predicted, and the unknown ones are guessed (50:50) and are impossible to predict.
3.4. Forecasting Models
3.5. Discussion
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Sum of Squares | df | Mean Square | F | Sig. | |
---|---|---|---|---|---|
Between groups | 5018.900 | 10 | 501.890 | 11.665 | 0.000 |
Within groups | 9465.810 | 220 | 43.026 | ||
Total | 14,484.710 | 230 |
Post Hoc Test | Hochberg | Games–Howell | ||
---|---|---|---|---|
Day | −1 | 0 | −1 | 0 |
−10 | 0.000 | 0.000 | 0.000 | 0.000 |
−9 | 0.000 | 0.000 | 0.026 | 0.008 |
−8 | 0.000 | 0.000 | 0.003 | 0.002 |
−7 | 0.000 | 0.000 | 0.008 | 0.004 |
−6 | 0.000 | 0.000 | 0.007 | 0.003 |
−5 | 0.000 | 0.000 | 0.005 | 0.003 |
−4 | 0.000 | 0.000 | 0.018 | 0.007 |
−3 | 0.002 | 0.000 | 0.045 | 0.015 |
−2 | 0.002 | 0.000 | 0.049 | 0.016 |
−1 | 0.999 | 0.997 | ||
0 | 0.999 | 0.997 |
Data Set | Time Interval |
---|---|
, | 5 min |
1 min | |
3 per day | |
1 per day |
Flood Event | Bulk Speed | Ion Temperature | Proton Density | 10.7 cm Radio Flux | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2001_0645 | 0.23 | 0.23 | 0.18 | 0.18 | 0.68 | - | - | 0.68 | - | 0.68 | 0.68 | - | 0.68 | - | 0.41 | 0.41 | 0.64 | 0.18 |
2002_0463 | 0.19 | 0.52 | 0.19 | 0.52 | - | - | 0.19 | 0.29 | - | 0.29 | 0.19 | - | 0.19 | - | 0.29 | / | 0.29 | 0.24 |
2002_0488 | / | / | 0.43 | 0.43 | - | - | / | 0.19 | - | 0.19 | 0.18 | - | 0.43 | - | 0.43 | 0.82 | / | 0.19 |
2002_0774 | 0.15 | 0.13 | 0.15 | 0.1 | - | 0.15 | - | - | 0.15 | - | 0.13 | - | 0.13 | - | 0.15 | 0.15 | 0.16 | 0.13 |
2004_0423 | 0.26 | 0.33 | 0.33 | 0.26 | - | / | - | - | 0.33 | 0.11 | 0.26 | - | 0.17 | - | 0.77 | 0.33 | 0.26 | 0.17 |
2007_0201 | 0.26 | 0.3 | 0.21 | / | - | 0.34 | - | - | 0.26 | 0.21 | 0.11 | - | 0.26 | - | 0.21 | 0.38 | 0.47 | 0.17 |
2007_0247 | / | 0.15 | 0.41 | 0.27 | - | 0.42 | - | - | 0.27 | 0.42 | 0.22 | - | 0.62 | - | / | 0.22 | 0.15 | 0.23 |
2007_0278 | 0.45 | 0.65 | / | 0.21 | - | 0.21 | - | - | 0.11 | 0.21 | / | - | 0.45 | - | / | 0.43 | / | 0.44 |
2008_0055 | / | 0.1 | 0.27 | 0.22 | - | 0.24 | - | - | 0.27 | 0.22 | 0.42 | - | 0.3 | - | 0.22 | 0.16 | 0.19 | / |
2008_0381 | 0.27 | / | 0.3 | / | - | 0.13 | - | - | 0.53 | 0.27 | / | - | 0.82 | - | 0.3 | 0.3 | 0.13 | 0.27 |
2009_0497 | 0.34 | / | 0.33 | 0.33 | - | 0.44 | - | - | 0.34 | 0.44 | 0.34 | - | 0.44 | - | 0.58 | 0.15 | 0.15 | / |
2012_0446 | 0.35 | 0.35 | 0.25 | 0.3 | - | 0.25 | - | - | 0.17 | 0.29 | - | / | - | / | 0.17 | 0.29 | / | 0.2 |
2012_0488 | 0.24 | 0.24 | 0.13 | 0.13 | - | 0.81 | - | - | 0.39 | 0.36 | - | 0.46 | - | 0.46 | / | / | 0.46 | 0.36 |
2012_0548 | 0.41 | 0.13 | / | / | - | / | - | - | / | / | - | / | - | 0.41 | 0.21 | 0.16 | 0.41 | 0.16 |
2012_0549 | 0.26 | 0.26 | 0.26 | 0.4 | - | 0.26 | - | - | 0.4 | 0.4 | - | 0.4 | - | 0.67 | 0.26 | 0.4 | 0.26 | 0.13 |
2012_0552 | 0.2 | / | 0.34 | 0.19 | - | / | - | - | 0.21 | / | 0.11 | - | 0.15 | - | / | 0.51 | / | / |
2013_0572 | 0.1 | / | / | 0.18 | - | 0.18 | - | - | 0.31 | 0.16 | 0.42 | - | / | - | 0.42 | 0.3 | / | 0.1 |
2015_0561 | 0.24 | 0.54 | 0.38 | 0.54 | - | 0.24 | - | - | 0.54 | 0.52 | 0.54 | - | / | - | 0.52 | 0.52 | 0.54 | 0.24 |
2017-0490 | 0.29 | 0.21 | 0.14 | 0.28 | - | 0.29 | - | - | 0.2 | 0.2 | 0.21 | - | 0.65 | - | 0.24 | 0.24 | 0.21 | 0.15 |
2019_0568 | 0.12 | 0.12 | 0.38 | 0.38 | - | 0.6 | - | - | 0.12 | / | 0.49 | - | / | - | 0.68 | 0.48 | 0.68 | 0.53 |
Classifiers | |
1. | DecisionTreeClassifier() |
2. | RandomForestClassifier(max_depth = 5, max_features = 1, n_estimators = 10, 100) |
3 | KNearestNeighborsClassifier(n_neighbors = 3) |
Ensembles | |
4. | AdaBoostClassifier(n_estimators = 100, random_state = 0) |
5. | GradientBoostingClassifier(learning_rate = 1.0, max_depth = 1, random_state = 0) |
6. | BaggingClassifier(base_estimator = SVC(), random_state = 0) |
Flood Event | Accuracy for the Training Set at Consecutive Addition of Lags | Accuracy for the Test Set at Consecutive Addition of Lags | Error Variance between Test and Training Data Sets | |||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
2001_0645 | 0.87 | 1.00 | 0.87 | 0.87 | 1.00 | 0.80 | 1.00 | 1.00 | 0.87 | 1.00 | 1.00 | 0.60 | 1.00 | 1.00 | 0.80 | 1.00 | 1.00 | 0.80 | 1.00 | 1.00 | 0.13 | 0.13 | 0.13 | 0.07 | 0.07 | 0.07 | 0.07 | 0.07 | 0.07 | 0.00 |
2002_0463 | 0.86 | 1.00 | 1.00 | 1.00 | 0.86 | 1.00 | 0.86 | 1.00 | 1.00 | 1.00 | 0.25 | 0.50 | 0.75 | 0.75 | 1.00 | 1.00 | 1.00 | 0.75 | 0.75 | 1.00 | 0.20 | 0.15 | 0.15 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.00 |
2002_0488 | 1.00 | 0.87 | 1.00 | 0.87 | 1.00 | 0.87 | 1.00 | 1.00 | 1.00 | 0.87 | 0.80 | 0.80 | 0.40 | 0.40 | 0.40 | 0.80 | 0.80 | 0.60 | 0.80 | 1.00 | 0.21 | 0.21 | 0.21 | 0.21 | 0.18 | 0.18 | 0.13 | 0.13 | 0.13 | 0.07 |
2002_0774 | 0.93 | 0.75 | 0.93 | 1.00 | 1.00 | 0.93 | 0.93 | 1.00 | 0.93 | 1.00 | 0.87 | 1.00 | 0.87 | 0.75 | 0.87 | 0.87 | 1.00 | 0.87 | 1.00 | 0.87 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.04 | 0.04 | 0.04 | 0.04 |
2004_0423 | 0.93 | 0.87 | 1.00 | 1.00 | 1.00 | 1.00 | 0.87 | 1.00 | 1.00 | 0.87 | 0.87 | 0.25 | 0.75 | 1.00 | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 | 1.00 | 0.19 | 0.19 | 0.14 | 0.14 | 0.14 | 0.14 | 0.14 | 0.08 | 0.08 | 0.08 |
2007_0201 | 0.93 | 1.00 | 0.91 | 1.00 | 0.91 | 1.00 | 1.00 | 0.91 | 1.00 | 1.00 | 0.87 | 0.83 | 0.67 | 0.83 | 0.83 | 0.83 | 0.50 | 1.00 | 0.83 | 0.50 | 0.15 | 0.15 | 0.15 | 0.10 | 0.10 | 0.10 | 0.10 | 0.10 | 0.06 | 0.06 |
2007_0247 | 0.83 | 0.83 | 0.92 | 0.92 | 1.00 | 1.00 | 0.92 | 1.00 | 1.00 | 0.92 | 0.57 | 0.71 | 0.71 | 0.71 | 0.71 | 0.00 | 0.71 | 0.86 | 0.71 | 0.86 | 0.22 | 0.22 | 0.19 | 0.19 | 0.17 | 0.17 | 0.13 | 0.13 | 0.13 | 0.13 |
2007_0278 | 1.00 | 0.90 | 1.00 | 0.90 | 0.90 | 1.00 | 1.00 | 0.80 | 1.00 | 0.90 | 0.80 | 0.80 | 0.40 | 0.80 | 0.60 | 1.00 | 0.40 | 1.00 | 0.60 | 1.00 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | 0.16 | 0.16 | 0.16 | 0.12 | 0.12 |
2008_0055 | 1.00 | 1.00 | 1.00 | 0.87 | 1.00 | 0.87 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.80 | 0.60 | 0.60 | 0.60 | 0.80 | 0.80 | 0.20 | 1.00 | 1.00 | 0.18 | 0.18 | 0.18 | 0.18 | 0.13 | 0.13 | 0.07 | 0.07 | 0.00 | 0.00 |
2008_0381 | 0.93 | 1.00 | 0.93 | 1.00 | 0.86 | 1.00 | 0.86 | 1.00 | 1.00 | 1.00 | 0.87 | 0,62 | 0.75 | 0.75 | 0.62 | 0.62 | 0.87 | 0.75 | 0.87 | 0.87 | 0.12 | 0.12 | 0.12 | 0.12 | 0.12 | 0.12 | 0.12 | 0.08 | 0.08 | 0.08 |
2009_0497 | 1.00 | 0.89 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.89 | 0.80 | 0.60 | 0.80 | 0.60 | 0.60 | 0.80 | 1.00 | 0.80 | 0.80 | 1.00 | 0.17 | 0.17 | 0.12 | 0.12 | 0.07 | 0.07 | 0.07 | 0.07 | 0.07 | 0.07 |
2012_0446 | 0.90 | 1.00 | 1.00 | 0.80 | 1.00 | 1.00 | 1.00 | 0.80 | 1.00 | 1.00 | 0.80 | 0.80 | 0.40 | 0.60 | 0.80 | 0.80 | 0.60 | 1.00 | 0.80 | 1.00 | 0.16 | 0.16 | 0.16 | 0.16 | 0.12 | 0.12 | 0.12 | 0.12 | 0.06 | 0.06 |
2012_0488 | 1.00 | 1.00 | 1.00 | 0.86 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.00 | 0.75 | 0.50 | 1.00 | 0.50 | 1.00 | 0.75 | 0.75 | 0.75 | 0.75 | 0.23 | 0.23 | 0.23 | 0.20 | 0.20 | 0.15 | 0.15 | 0.15 | 0.08 | 0.08 |
2012_0548 | 1.00 | 0.87 | 1.00 | 1.00 | 0.87 | 1.00 | 0.87 | 1.00 | 0.87 | 1.00 | 0.75 | 0.75 | 0.75 | 0.50 | 1.00 | 0.50 | 0.75 | 0.75 | 1.00 | 1.00 | 0.22 | 0.22 | 0.19 | 0.19 | 0.19 | 0.14 | 0.14 | 0.08 | 0.08 | 0.00 |
2012_0549 | 1.00 | 1.00 | 0.87 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.87 | 0.75 | 0.75 | 1.00 | 1.00 | 0.75 | 1.00 | 0.75 | 0.75 | 0.75 | 1.00 | 0.14 | 0.14 | 0.14 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 |
2012_0552 | 0.88 | 0.96 | 0.88 | 0.92 | 0.84 | 0.96 | 0.84 | 0.96 | 0.88 | 0.92 | 0.69 | 0.31 | 0.77 | 0.62 | 0.54 | 0.62 | 0.69 | 0.46 | 0.62 | 0.62 | 0.22 | 0.22 | 0.21 | 0.21 | 0.21 | 0.19 | 0.19 | 0.19 | 0.19 | 0.19 |
2013_0572 | 0.92 | 0.92 | 0.92 | 0.92 | 0.85 | 0.92 | 0.85 | 0.92 | 0.92 | 1.00 | 0.72 | 0.57 | 0.14 | 0.57 | 0.71 | 0.43 | 0.57 | 0.57 | 0.57 | 0.86 | 0.23 | 0.23 | 0.23 | 0.21 | 0.21 | 0.19 | 0.19 | 0.19 | 0.16 | 0.16 |
2015_0561 | 1.00 | 0.86 | 1.00 | 0.86 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.50 | 1.00 | 0.75 | 0.50 | 0.75 | 0.75 | 0.75 | 1.00 | 1.00 | 0.20 | 0.20 | 0.15 | 0.15 | 0.15 | 0.15 | 0.08 | 0.08 | 0.00 | 0.00 |
2017-0490 | 0.87 | 1.00 | 1.00 | 1.00 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.60 | 1.00 | 0.60 | 1.00 | 0.80 | 0.20 | 1.00 | 1.00 | 1.00 | 0.12 | 0.12 | 0.12 | 0.12 | 0.12 | 0.06 | 0.06 | 0.00 | 0.00 | 0.00 |
2019_0568 | 0.86 | 1.00 | 1.00 | 0.75 | 1.00 | 1.00 | 0.87 | 1.00 | 1.00 | 1.00 | 0.75 | 0.25 | 0.50 | 1.00 | 0.25 | 0.50 | 0.25 | 0.50 | 0.25 | 0.75 | 0.24 | 0.24 | 0.22 | 0.22 | 0.22 | 0.19 | 0.19 | 0.14 | 0.14 | 0.08 |
Lag | Feature Name | Feature Importance |
---|---|---|
t-4 | Ion temperature | 0.097 |
t-9 | 10.7 cm radio flux | 0.097 |
t-5 | 38–53 | 0.093 |
t-2 | Ion temperature | 0.092 |
t-0 | 47–68 | 0.089 |
t-6 | Ion temperature | 0.087 |
t-3 | 38–53 | 0.087 |
t-7 | 47–68 | 0.087 |
t-8 | 47–68 | 0.086 |
t-1 | Bulk speed | 0.079 |
Classifier | Forecast 0 | Forecast 1 | Forecast 2 | Forecast 3 | Forecast 4 | Forecast 5 | Forecast 6 | Forecast 7 | Forecast 8 | Forecast 9 |
---|---|---|---|---|---|---|---|---|---|---|
DecisionTree | 0.75 | 0.73 | 0.71 | 0.72 | 0.73 | 0.77 | 0.73 | 0.78 | 0.70 | 0.70 |
RandomForest | 0.70 | 0.73 | 0.59 | 0.73 | 0.70 | 0.78 | 0.70 | 0.70 | 0.69 | 0.65 |
KNearestNeighbors | 0.63 | 0.72 | 0.61 | 0.74 | 0.63 | 0.70 | 0.70 | 0.62 | 0.71 | 0.71 |
AdaBoost | 0.73 | 0.71 | 0.73 | 0.71 | 0.70 | 0.74 | 0.69 | 0.78 | 0.71 | 0.70 |
GradientBoosting | 0.73 | 0.73 | 0.73 | 0.71 | 0.60 | 0.74 | 0.71 | 0.76 | 0.72 | 0.69 |
BaggingClassifierSVC | 0.80 | 0.77 | 0.74 | 0.76 | 0.74 | 0.81 | 0.74 | 0.78 | 0.71 | 0.70 |
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Malinović-Milićević, S.; Radovanović, M.M.; Radenković, S.D.; Vyklyuk, Y.; Milovanović, B.; Milanović Pešić, A.; Milenković, M.; Popović, V.; Petrović, M.; Sydor, P.; et al. Application of Solar Activity Time Series in Machine Learning Predictive Modeling of Precipitation-Induced Floods. Mathematics 2023, 11, 795. https://doi.org/10.3390/math11040795
Malinović-Milićević S, Radovanović MM, Radenković SD, Vyklyuk Y, Milovanović B, Milanović Pešić A, Milenković M, Popović V, Petrović M, Sydor P, et al. Application of Solar Activity Time Series in Machine Learning Predictive Modeling of Precipitation-Induced Floods. Mathematics. 2023; 11(4):795. https://doi.org/10.3390/math11040795
Chicago/Turabian StyleMalinović-Milićević, Slavica, Milan M. Radovanović, Sonja D. Radenković, Yaroslav Vyklyuk, Boško Milovanović, Ana Milanović Pešić, Milan Milenković, Vladimir Popović, Marko Petrović, Petro Sydor, and et al. 2023. "Application of Solar Activity Time Series in Machine Learning Predictive Modeling of Precipitation-Induced Floods" Mathematics 11, no. 4: 795. https://doi.org/10.3390/math11040795
APA StyleMalinović-Milićević, S., Radovanović, M. M., Radenković, S. D., Vyklyuk, Y., Milovanović, B., Milanović Pešić, A., Milenković, M., Popović, V., Petrović, M., Sydor, P., & Gajić, M. (2023). Application of Solar Activity Time Series in Machine Learning Predictive Modeling of Precipitation-Induced Floods. Mathematics, 11(4), 795. https://doi.org/10.3390/math11040795