The Use of Large-Scale Climate Indices in Monthly Reservoir Inflow Forecasting and Its Application on Time Series and Artificial Intelligence Models
Abstract
:1. Introduction
2. Time Series and Artificial Intelligence Models
2.1. Seasonal AutoRegressive Integrated Moving Average (SARIMA) Model
2.2. SARIMA with eXogenous Variables (SARIMAX) Model
2.3. Artificial Neural Network (ANN) Model
2.4. Adaptive Neural-Based Fuzzy Inference System (ANFIS) Model
- Rule 1: if isandisthen
- Rule 2: ifisandisthen where and are the membership functions of each input and , and are the output functions and and are linear parameters. The ANFIS model consists of five layers as shown in Figure 2.
2.5. Random Forest (RF) Model
3. Data and Study Area
4. Input Variable Selection
4.1. Partial Autocorrelation Function (PACF)
4.2. Ensemble Empirical Mode Decomposition (EEMD)
4.3. Cross-Correlation Analysis
4.4. Backward Elimination Method
5. Application and Results
5.1. Model Input Variables
5.2. Model Parameters and Setting
5.2.1. SARIMA and SARIMAX Models
5.2.2. ANN Models
5.2.3. ANFIS Models
5.2.4. RF Models
5.3. Model Performance
6. Discussion
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Station | Type | Data Period | Basin Area (km2) | Volume (×103 m3) | Water Supply Capacity (×103 m3) | Mean Inflow (m3/s) | |
---|---|---|---|---|---|---|---|
Annual | Seasonal (JJAS) | ||||||
Soyangang dam | Multi-purpose (E.C.R.Da) | January 1974–December 2016 | 2703 | 9600 | 1,900,000 | 68.28 | 221.99 |
Chungju dam | Multi-purpose (C.G.Db) | January 1986–December 2016 | 6705 | 902 | 1,789,000 | 162.39 | 359.22 |
Goesan dam | Hydro-power (C.G.Db) | January 1982–December 2016 | 671 | 19.6 | 5700 | 13.72 | 30.18 |
Climate Index | Classification | Climate Index | Classification |
---|---|---|---|
NINO 1+2 (NINO12) | ENSO/SST:Pacific | Tropical Northern Atlantic Index (TNA) | SST:Atlantic |
NINO 3 (NINO3) | ENSO/SST:Pacific | Tropical Southern Atlantic Index (TSA) | SST:Atlantic |
NINO 4 (NINO4) | ENSO/SST:Pacific | Carribbean SST Index (CAR) | SST:Atlantic |
NINO 3.4 (NINO34) | ENSO/SST:Pacific | Pacific Decadal Oscillation (PDO) | Teleconnections |
Bivariate ENSO Timeseries (BEST) | ENSO | Northern Oscillation Index (NOI) | Teleconnections |
Multivariate ENSO Index (MEI) | ENSO | Pacific North American Index (PNA) | Teleconnections |
Trans-Nino Index (TNI) | SST:Pacific | Western Pacific Index (WP) | Teleconnections |
Western Hemisphere Warm Pool (WHWP) | SST:Pacific/SST:Atlantic | Eastern Atlantic/Western Russia (EAWR) | Teleconnections |
Oceanic Nino Index (ONI) | SST:Pacific | North Atlantic Oscillation (NAO) | Teleconnections |
Atlantic Multidecadal Oscillation (AMO) | SST:Atlantic | Southern Oscillation Index (SOI) | Atmosphere |
Atlantic Meridional Mode (AMM) | SST:Atlantic | Quasi-Biennial Oscillation (QBO) | Atmosphere |
North Tropical Atlantic SST Index (NTA) | SST:Atlantic | Artic Oscillation (AO) | Atmosphere |
Station | Autoregressive Variables (AR-) | A Combination of Autoregressive and Exogenous Variables (ARX-) |
---|---|---|
SY dam | Lag1, Lag12, Lag24, Lag36 | Lag12, Lag36, NTA(12), AMO(6), NINO4(12), NINO12(10), AMM(12) |
CJ dam | Lag36, TNI(12), AMO(12), NINO12(11), NTA(11), NINO12(5) | |
GS dam | Lag12, Lag36, NINO12(5), QBO(9), AMO(1) |
SY Dam | CJ Dam | GS Dam | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
IMFs | CI | Lag | r | IMFs | CI | Lag | r | IMFs | CI | Lag | r |
IMF1 | NINO12 | 10 | 0.21 | IMF1 | NINO12 | 11 | 0.22 | IMF1 | NINO12 | 11 | 0.19 |
IMF2 | NINO12 | 5 | 0.42 | IMF2 | NINO12 | 5 | 0.48 | IMF2 | NINO12 | 5 | 0.45 |
IMF3 | NINO12 | 4 | 0.76 | IMF3 | NINO12 | 5 | 0.75 | IMF3 | NINO12 | 5 | 0.75 |
IMF4 | QBO | 7 | −0.32 | IMF4 | QBO | 8 | −0.33 | IMF4 | QBO | 9 | −0.29 |
IMF5 | NTA | 12 | −0.21 | IMF5 | NTA | 11 | −0.42 | IMF5 | NTA | 12 | −0.40 |
IMF6 | AMM | 12 | −0.29 | IMF6 | NINO4 | 12 | −0.38 | IMF6 | TNI | 12 | 0.32 |
IMF7 | NINO4 | 12 | −0.15 | IMF7 | AMO | 12 | 0.49 | IMF7 | AMO | 1 | 0.30 |
IMF8 | AMO | 6 | −0.57 | RES | TNI | 12 | −0.21 | RES | AMO | 1 | 0.25 |
RES | AMO | 1 | 0.47 |
Station | SARIMA (p, d, q)(P, D, Q)[s] | SARIMAX (p, d, q)(P, D, Q)[s] |
---|---|---|
SY dam | SARIMA(0,0,0)(2,1,2)[12] | SARIMAX(0,0,0)(3,1,1)[12]. Lag12 |
−0.926, −0.271, −0.155, −0.732 | −0.117, −0.202, 0.148, −0.954, 0.326 | |
CJ dam | SARIMA(0,0,0)(1,1,3)[12] | SARIMAX(0,0,0)(2,1,1)[12] Lag36 |
−0.758, −0.147, −0.887, 0.148 | −0.071, 0.052, −0.949, 0.133 | |
GS dam | SARIMA(0,0,1)(1,1,1)[12] | SARIMAX(0,0,0)(1,1,1)[12] Lag12 |
0.171, −0.066, −0.888 | 0.152, −0.937, −0.254 |
Station | AR-ANN | ARX-ANN |
---|---|---|
SY dam | 3 | 5 |
CJ dam | 4 | 4 |
GS dam | 2 | 2 |
Station | AR-ANFIS | ARX-ANFIS | ||||
---|---|---|---|---|---|---|
Optimal MF | Number of Input MF (Layer2) | Number of Rules (Layer3) | Optimal MF | Number of Input MF (Layer2) | Number of Rules (Layer3) | |
SY dam | BS | 8 | 16 | BS | 14 | 128 |
CJ dam | BS | 8 | 16 | BS | 12 | 64 |
GS dam | BS | 8 | 16 | NG | 10 | 32 |
Station | AR-RF | ARX-RF |
---|---|---|
SY dam | 200 | 500 |
CJ dam | 200 | 300 |
GS dam | 100 | 200 |
Station | Model | r | RMSE | NSE | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Train. | Vali. | Test | Train. | Vali. | Test | Train. | Vali. | Test | ||
SY dam | SARIMA | 0.65 | 0.53 | 84.17 | 83.69 | 0.42 | −0.04 | |||
SARIMAX | 0.65 | 0.38 | 84.52 | 93.82 | 0.42 | −0.31 | ||||
AR-ANN | 0.66 | 0.70 | 0.58 | 82.89 | 89.18 | 72.28 | 0.44 | 0.49 | 0.22 | |
ARX-ANN | 0.64 | 0.68 | 0.63 | 85.56 | 91.63 | 80.64 | 0.40 | 0.46 | 0.03 | |
AR-ANFIS | 0.65 | 0.73 | 0.53 | 84.54 | 88.49 | 74.97 | 0.42 | 0.49 | 0.16 | |
ARX-ANFIS | 0.61 | 0.71 | 0.41 | 87.93 | 89.53 | 86.96 | 0.37 | 0.48 | −0.13 | |
AR-RF | 0.94 | 0.83 | 0.47 | 42.61 | 75.33 | 77.78 | 0.85 | 0.63 | 0.10 | |
ARX-RF | 0.95 | 0.66 | 0.50 | 42.45 | 93.76 | 75.71 | 0.85 | 0.43 | 0.15 | |
CJ dam | SARIMA | 0.65 | 0.57 | 203.35 | 179.26 | 0.41 | −0.93 | |||
SARIMAX | 0.63 | 0.57 | 205.62 | 180.51 | 0.40 | −0.96 | ||||
AR-ANN | 0.64 | 0.71 | 0.52 | 204.71 | 202.42 | 162.32 | 0.40 | 0.48 | −0.58 | |
ARX-ANN | 0.61 | 0.74 | 0.67 | 209.49 | 191.73 | 151.26 | 0.37 | 0.53 | −0.37 | |
AR-ANFIS | 0.63 | 0.70 | 0.46 | 205.29 | 208.25 | 162.20 | 0.40 | 0.45 | −0.58 | |
ARX-ANFIS | 0.64 | 0.76 | 0.41 | 203.89 | 186.34 | 203.91 | 0.41 | 0.56 | −1.50 | |
AR-RF | 0.93 | 0.68 | 0.42 | 110.41 | 207.17 | 157.52 | 0.83 | 0.46 | −0.49 | |
ARX-RF | 0.93 | 0.79 | 0.40 | 108.83 | 174.11 | 169.53 | 0.83 | 0.62 | −0.73 | |
GS dam | SARIMA | 0.65 | 0.52 | 17.44 | 15.55 | 0.42 | −1.56 | |||
SARIMAX | 0.67 | 0.51 | 17.14 | 17.86 | 0.44 | −2.38 | ||||
AR-ANN | 0.62 | 0.72 | 0.37 | 17.88 | 15.37 | 13.67 | 0.39 | 0.51 | −0.98 | |
ARX-ANN | 0.69 | 0.63 | 0.51 | 16.48 | 17.41 | 14.21 | 0.48 | 0.37 | −1.14 | |
AR-ANFIS | 0.65 | 0.71 | 0.35 | 17.31 | 15.58 | 14.37 | 0.43 | 0.50 | −1.19 | |
ARX-ANFIS | 0.77 | 0.68 | 0.42 | 14.77 | 16.69 | 19.40 | 0.58 | 0.42 | −2.99 | |
AR-RF | 0.93 | 0.59 | 0.38 | 9.13 | 18.02 | 13.45 | 0.84 | 0.33 | −0.92 | |
ARX-RF | 0.94 | 0.68 | 0.46 | 8.69 | 16.35 | 16.76 | 0.86 | 0.45 | −1.98 |
Station | Model | r | RMSE | NSE | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2013 | 2014 | 2015 | 2016 | 2013 | 2014 | 2015 | 2016 | 2013 | 2014 | 2015 | 2016 | ||
SY dam | SARIMA | 0.62 | 0.43 | 0.78 | 0.75 | 102.18 | 99.57 | 59.86 | 63.84 | 0.38 | −9.02 | −2.31 | 0.38 |
SARIMAX | 0.53 | 0.10 | 0.67 | 0.69 | 110.61 | 131.76 | 43.73 | 60.81 | 0.28 | −16.54 | −0.77 | 0.44 | |
AR-ANN | 0.53 | 0.18 | 0.75 | 0.93 | 110.56 | 75.68 | 43.94 | 31.80 | 0.28 | −4.79 | −0.79 | 0.85 | |
ARX-ANN | 0.50 | 0.58 | 0.71 | 0.99 | 114.18 | 80.57 | 49.75 | 63.31 | 0.23 | −5.56 | −1.29 | 0.39 | |
AR-ANFIS | 0.50 | 0.23 | 0.80 | 0.90 | 112.66 | 80.56 | 44.31 | 36.59 | 0.25 | −5.56 | −0.82 | 0.80 | |
ARX-ANFIS | 0.27 | 0.14 | 0.75 | 0.96 | 130.77 | 104.71 | 39.43 | 25.02 | −0.01 | −10.08 | −0.44 | 0.91 | |
AR-RF | 0.41 | 0.29 | 0.82 | 0.68 | 121.48 | 58.62 | 49.12 | 59.95 | 0.13 | −2.47 | −1.23 | 0.45 | |
ARX-RF | 0.36 | 0.21 | 0.69 | 0.97 | 122.78 | 72.36 | 45.84 | 22.66 | 0.11 | −4.29 | −0.94 | 0.92 | |
CJ dam | SARIMA | 0.81 | 0.45 | 0.58 | 0.76 | 115.63 | 227.95 | 189.39 | 165.34 | 0.64 | −7.96 | −28.82 | −0.52 |
SARIMAX | 0.75 | 0.40 | 0.59 | 0.78 | 140.97 | 221.25 | 204.75 | 139.94 | 0.47 | −7.45 | −33.85 | −0.09 | |
AR-ANN | 0.58 | 0.38 | 0.64 | 0.83 | 181.56 | 210.36 | 147.21 | 80.67 | 0.12 | −6.63 | −17.02 | 0.64 | |
ARX-ANN | 0.62 | 0.83 | 0.42 | 0.99 | 169.29 | 137.67 | 190.67 | 86.89 | 0.23 | −2.27 | −29.22 | 0.58 | |
AR-ANFIS | 0.54 | 0.30 | 0.68 | 0.76 | 182.45 | 214.87 | 131.65 | 91.90 | 0.11 | −6.96 | −13.41 | 0.53 | |
ARX-ANFIS | 0.39 | 0.50 | 0.45 | 0.74 | 212.50 | 237.39 | 211.93 | 141.02 | −0.21 | −8.72 | −36.34 | −0.10 | |
AR-RF | 0.43 | 0.36 | 0.66 | 0.78 | 182.52 | 167.42 | 172.71 | 89.85 | 0.11 | −3.84 | −23.80 | 0.55 | |
ARX-RF | 0.35 | 0.47 | 0.61 | 0.69 | 230.87 | 162.34 | 153.13 | 108.92 | −0.43 | −3.55 | −18.49 | 0.34 | |
GS dam | SARIMA | 0.87 | 0.47 | 0.05 | 0.62 | 9.52 | 16.66 | 19.43 | 14.87 | −0.02 | −4.11 | −49.30 | −0.16 |
SARIMAX | 0.88 | 0.48 | 0.10 | 0.62 | 9.32 | 18.26 | 22.81 | 18.30 | 0.02 | −5.14 | −68.31 | −0.75 | |
AR-ANN | 0.82 | 0.50 | −0.21 | 0.01 | 10.10 | 15.14 | 13.00 | 15.70 | −0.15 | −3.22 | −21.52 | −0.29 | |
ARX-ANN | 0.82 | 0.79 | −0.39 | 0.71 | 8.89 | 15.67 | 18.74 | 11.49 | 0.11 | −3.52 | −45.80 | 0.31 | |
AR-ANFIS | 0.79 | 0.44 | −0.20 | 0.10 | 10.11 | 17.06 | 14.50 | 14.90 | −0.15 | −4.36 | −27.00 | −0.16 | |
ARX-ANFIS | 0.77 | 0.58 | −0.33 | 0.57 | 8.11 | 24.36 | 21.03 | 20.11 | 0.26 | −9.93 | −57.96 | −1.12 | |
AR-RF | 0.85 | 0.46 | 0.02 | 0.11 | 7.63 | 14.51 | 13.74 | 16.29 | 0.34 | −2.88 | −24.17 | −0.39 | |
ARX-RF | 0.80 | 0.61 | -0.16 | 0.59 | 7.98 | 18.23 | 20.88 | 17.07 | 0.28 | −5.12 | −57.10 | −0.52 |
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Kim, T.; Shin, J.-Y.; Kim, H.; Kim, S.; Heo, J.-H. The Use of Large-Scale Climate Indices in Monthly Reservoir Inflow Forecasting and Its Application on Time Series and Artificial Intelligence Models. Water 2019, 11, 374. https://doi.org/10.3390/w11020374
Kim T, Shin J-Y, Kim H, Kim S, Heo J-H. The Use of Large-Scale Climate Indices in Monthly Reservoir Inflow Forecasting and Its Application on Time Series and Artificial Intelligence Models. Water. 2019; 11(2):374. https://doi.org/10.3390/w11020374
Chicago/Turabian StyleKim, Taereem, Ju-Young Shin, Hanbeen Kim, Sunghun Kim, and Jun-Haeng Heo. 2019. "The Use of Large-Scale Climate Indices in Monthly Reservoir Inflow Forecasting and Its Application on Time Series and Artificial Intelligence Models" Water 11, no. 2: 374. https://doi.org/10.3390/w11020374
APA StyleKim, T., Shin, J. -Y., Kim, H., Kim, S., & Heo, J. -H. (2019). The Use of Large-Scale Climate Indices in Monthly Reservoir Inflow Forecasting and Its Application on Time Series and Artificial Intelligence Models. Water, 11(2), 374. https://doi.org/10.3390/w11020374