Forecasting Quarterly Inflow to Reservoirs Combining a Copula-Based Bayesian Network Method with Drought Forecasting
Abstract
:1. Introduction
2. Methodology
2.1. Procedures of Quarterly Inflow Forecasting
2.2. Copula-Based Bayesian Network
2.3. Drought Forecasting Using Drought Index
2.4. Quarterly Inflow Forecasting Combined with Drought Forecasting
- (1)
- Use the probability distribution of the next quarter inflow (like that in Figure 3) to calculate the cumulative probability that corresponds to a specific inflow of the next quarter.
- (2)
- Use the cumulative probability to calculate the SII.
- (3)
- When the calculated SII is the same as the lower bound value of each drought stage, set the corresponding quarterly inflow as the quarterly inflow that represents that drought stage (for D4, the inflow where the SII is −2.5).
- (4)
- Repeat Steps (1) to (3) for all quarters and quarterly inflows.
3. Results
3.1. Two Selected Dams in This Study
3.2. Quarterly Inflow Forecasting Curves Conforming to Drought Stages
3.3. Quarterly Drought Forecast Results
3.4. Quarterly Inflow Forecast Results
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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SII Range | Drought Category |
---|---|
2.00 ≤ SII | Extreme wet |
1.50 ≤ SII < 2.00 | Very wet |
1.00 ≤ SII < 1.50 | Moderately wet |
0.00 ≤ SII < 1.00 | Near normal |
−1.00 ≤ SII < 0.00 | Mild drought (D1) |
−1.50 ≤ SII < −1.00 | Moderate drought (D2) |
−2.00 ≤ SII < −1.50 | Severe drought (D3) |
SII < −2.00 | Extreme drought (D4) |
Engineering Data | Soyanggang Dam | Andong Dam |
---|---|---|
Basin area (km2) | 2703 | 1584 |
Year completed | 1973 | 1976 |
Total storage capacity (× 106 m3) | 2900 | 1248 |
Average yearly inflow (× 106 m3) | 1750 | 940 |
Yearly water supply (× 106 m3) | 1213 | 926 |
industrial water | 1200 | 450 |
agricultural water | 13 | 300 |
instream flow | - | 176 |
Dam | Distribution | Quarter | Threshold Value | |||
---|---|---|---|---|---|---|
First | Second | Third | Fourth | |||
Soyanggang | Lognormal | 0.0724 | 0.0636 | 0.0898 | 0.1242 | 0.219 |
Gamma | 0.1062 | 0.0898 | 0.1110 | 0.1583 | ||
Gumbel | 0.2189 | 0.2029 | 0.1534 | 0.2334 | ||
Weibull | 0.1169 | 0.1127 | 0.1261 | 0.1601 | ||
Gaussian | 0.1691 | 0.1570 | 0.1438 | 0.2082 | ||
Andong | Lognormal | 0.0915 | 0.1001 | 0.1057 | 0.0813 | 0.232 |
Gamma | 0.1267 | 0.1123 | 0.0771 | 0.1072 | ||
Gumbel | 0.2457 | 0.1930 | 0.1288 | 0.2396 | ||
Weibull | 0.1394 | 0.1038 | 0.0736 | 0.1380 | ||
Gaussian | 0.1871 | 0.1205 | 0.0932 | 0.1713 |
Dam | First and Second Quarters | Second and Third Quarters | Third and Fourth Quarters | Fourth and First Quarters |
---|---|---|---|---|
Soyanggang | 0.4781 | 0.0543 | –0.1770 | 0.0739 |
Andong | 0.3767 | 0.4828 | 0.1281 | 0.1831 |
Cases | Absolute Error for the Third Quarter 2014 (%) | Absolute Error for the Third Quarter 2015 (%) | Range of Absolute Error for the Third Quarter (%) | Range of Absolute Error for All Quarters (%) |
---|---|---|---|---|
BN forecast without drought forecast | 103.6 | 93.3 | 4.1–103.6 | 3.2–103.6 |
BN forecast with drought forecast by 50% criteria | 14.2 | 18.6 | 4.1–48.0 | 3.2–100.1 |
Cases | Absolute Error for the Third Quarter 2013 (%) | Absolute Error for the Third Quarter 2015 (%) | Range of Absolute Error for the Third Quarter (%) | Range of Absolute Error for All Quarters (%) |
---|---|---|---|---|
BN forecast without drought forecast | 169.7 | 355.6 | 2.2–355.6 | 1.2–355.6 |
BN forecast with drought forecast by 50% criteria | 169.7 | 32.1 | 32.1–169.7 | 1.2–169.7 |
BN forecast with drought forecast by 55% criteria | 169.7 | 9.4 | 9.4–169.7 | 1.2–169.7 |
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Kim, K.; Lee, S.; Jin, Y. Forecasting Quarterly Inflow to Reservoirs Combining a Copula-Based Bayesian Network Method with Drought Forecasting. Water 2018, 10, 233. https://doi.org/10.3390/w10020233
Kim K, Lee S, Jin Y. Forecasting Quarterly Inflow to Reservoirs Combining a Copula-Based Bayesian Network Method with Drought Forecasting. Water. 2018; 10(2):233. https://doi.org/10.3390/w10020233
Chicago/Turabian StyleKim, Kwanghoon, Sangho Lee, and Youngkyu Jin. 2018. "Forecasting Quarterly Inflow to Reservoirs Combining a Copula-Based Bayesian Network Method with Drought Forecasting" Water 10, no. 2: 233. https://doi.org/10.3390/w10020233