Forecasting Monthly Water Deficit Based on Multi-Variable Linear Regression and Random Forest Models
Abstract
:1. Introduction
2. Data and Methodology
2.1. Data Collection
2.1.1. Study Area and Weather Data
2.1.2. The Circulation Indices Data
2.2. Methodology
2.2.1. Variation of Water Deficit
2.2.2. Selection of the Key Circulation Indices
Preliminary Selection of the Independent Circulation Indices
Selection of the Key Circulation Indices
2.2.3. The Quantitative Relationship between D and the Key Circulation Indices
Multi-Variable Linear Regression Model
Random Forest Model
Model Performance Assessment
2.2.4. Prediction of Water Deficit Conditions
3. Results
3.1. Spatiotemporal Variations of Month D
3.2. Relationship between Monthly D and Circulation Indices
3.2.1. Preliminary Selected Circulation Indices Considering Multi-Collinearity
3.2.2. Screen of the Key Circulation Indices
3.3. Quantitative Relationship between Monthly D and the Key Circulation Indices
3.3.1. Model Performance Assessment
3.3.2. Importance Rank of Predictors
3.4. Forecasted Water Deficit Conditions in Northwestern China
4. Discussions
4.1. The Necessity of Selecting Key Circulation Indices from over 100 Indices
4.2. Relative Importance of Climate Drivers to Water Deficit
4.3. Prediction of Water Deficit Conditions
4.4. Limitations and Future Framework
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
AO | Artic oscillation |
D | difference of precipitation and ET0 |
ET0 | reference crop evapotranspiration |
ENSO | El Niño Southern Oscillation |
FAO | Food and Agriculture Organization |
IOD | Indian Ocean Dipole |
IPCC | Intergovernmental Panel on Climate Change |
LCCC | Lin’s Concordance Correlation Coefficient |
MAPE | mean absolute percentage error |
MLR | multi-variable linear regression model |
NAO | North Atlantic Oscillation |
PDO | Pacific Decade Oscillation |
Pr | precipitation |
R2 | coefficient of determination |
RMSE | root mean square error |
R | Pearson correlation coefficient |
SPI | standardized precipitation index |
SPEI | standardized precipitation and evapotranspiration index |
VIF | variance inflation factor |
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Initially Selected Circulation Indices | |||||
---|---|---|---|---|---|
NAHAI | WPSH | EPSH | NANRP | EPRP | SSRP |
WHWRP | APVA | PPVA | NAPVA | AEPVA | PPVI |
AEPVI | NVCL | NVCLI | EMC | AZC | AMC |
EATP | IBTI | AO | AAO | NAO | PNA |
EA | WP | EAWR | POL | SCA | 50ZW |
MPZW | WPTW | CPTW | EPTA | ACCP | NINO1 + 2 |
NINOW | NINOA | NINOB | TSA | WHWP | IOWPA |
WPWPA | AMO | OC | WWDC | EM | NE |
TIOD | SIOD | WNPTN | NLTC | TSN | SOI |
AMM | QBO | NAT |
No. of Site | Fitted MLR Equation | R2 | LCCC | MAPE (%) | RMSE (mm) |
---|---|---|---|---|---|
51053 | 0.0088PPVI12 + 0.21NAHAI6 − 1.68SSRP10 − 1.13NANRP11 − 3.32PPVA6 − 0.76MPZW5 + 3.10WPWPA4 − 1.10EPRP11 + 0.0046AEPVI12 − 2.06WNPTN10 − 36.57 | 0.863 | 0.927 | 44.3 | 22.4 |
51238 | +0.0071PPVI12−1.41SSRP11 + 3.43WPWPA4 + 4.13 PPVA12 − 0.84NANRP11 + 0.0045AEPVI12 − 0.60MPZW5 − 0.77NAHAI12 − 2.07WNPTN10 − 0.17EPRP11 − 186.38 | 0.872 | 0.931 | 28.8 | 19.0 |
51334 | − 0.50NAHAI12 − 1.08NANRP11 − 0.78EPRP11 − 1.34SSRP10 + 4.55NAPVA12 + 0.0082PPVI12 + 0.0056AEPVI12 − 0.67 MPZW5 + 3.96WPWPA4 − 2.14WNPTN10 − 211.16 | 0.919 | 0.958 | 11.2 | 17.1 |
51811 | − 0.0073PPVI6 + 4.78PPVA11 − 0.19SSRP10 − 1.55EPRP11 + 0.50IOWPA9 + 0.75NAHAI5 + 1.92WPWPA4 − 1.28 NANRP10 + 0.007AEPVI12 − 2.29WNPTN10 − 0.02MPZW5 − 147.04 | 0.900 | 0.948 | 28.7 | 17.5 |
51573 | − 2.29SSRP10 + 0.012PPVI12 + 5.70PPVA11 − 0.95WPWPA10 − 1.55NANRP11 + 0.79NAHAI11 − 0.62MPZW5 − 0.92 EPRP11 − 0.09IOWPA3 + 0.0113AEPVI12 − 4.59WNPTN10 − 150.71 | 0.903 | 0.949 | 27.6 | 21.9 |
51477 | − 0.0078PPVI6 − 2.30SSRP10 + 2.62NANRP5 − 0.0068 AEPVI6 − 3.98PPVA6 − 0.37IOWPA9 − 1.12EPRP10 + 0.03 NAHAI6 + 1.63WPWPA4 − 2.05WNPTN10 − 0.54MPZW5 + 10.87 | 0.891 | 0.942 | 21.3 | 21.0 |
52203 | − 0.0087PPVI6 + 0.52IOWPA9 − 1.76SSRP10 − 0.0086 AEPVI6 + 0.15NAHAI5 + 2.85WPWPA4 − 2.09APVA6 − 2.51 WNPTN10 − 0.46MPZW5 − 4.56PPVA5 − 1.03NANRP10 − 0.69EPRP10 +88.96 | 0.905 | 0.950 | 36.7 | 19.8 |
52112 | − 0.01PPVI6 − 5.51WNPTN10 − 3.32SSRP10 + 0.0169 AEPVI12 − 0.28IOWPA9 + 3.26WPWPA4 − 6.71PPVA6 − 1.61NANRP10 − 0.31APVA6 + 1.13NAHAI5 − 0.59MPZW5 − 0.72EPRP10 + 53.11 | 0.930 | 0.964 | 19.2 | 26.8 |
51567 | − 1.96NAPVA5 − 0.0053PPVI6 + 1.75SSRP4 + 0.0092 AEPVI12 + 0.31IOWPA9 − 0.61MPZW5 + 1.48WPWPA4 − 1.21NANRP10 + 0.12NAHAI5 − 1.66APVA6 + 2.66 WNPTN4 − 0.74EPRP10 − 48.82 | 0.895 | 0.945 | 21.1 | 17.4 |
No. of Site | Predictor Variables Importance Ranking (%) |
---|---|
51053 | PPVI12 (37.1), NAHAI6 (30), SSRP10 (29.3), NANRP11 (29.1), PPVA6 (28.4), MPZW5 (25), WPWPA4 (24.2), EPRP11 (22.1), AEPVI12 (21.7), WNPTN10 (17.5) |
51060 | IOWPA9 (32.5), PPVI12 (32.5), SSRP10 (31.7), NANRP6 (27.4), NAHAI11 (26.9), PPVA6 (26.8), WPWPA4 (24.1), EPRP12 (23.7), AEPVI11 (23), MPZW5 (22.8), WNPTN10 (14.3) |
51068 | PPVI12 (35.5), WPWPA10 (35.2), SSRP4 (33.9), EPRP12 (28.8), NANRP11 (26), PPVA11 (25.6), MPZW5 (23.5), WNPTN12 (22.7), AEPVI10 (21), NAHAI11 (19.9) |
51076 | NAHAI6 (33.5), SSRP10 (32.8), NANRP12 (31.5), AEPVI11 (31.1), PPVI6 (30.9), MPZW5 (29.4), WPWPA4 (26.4), PPVA6 (23.8), EPRP11 (21), WNPTN10 (13.2) |
51087 | PPVA11 (34.2), PPVI12 (33.8), NANRP12 (32.7), SSRP10 (32), MPZW5 (25), EPRP11 (24.8), WPWPA10 (22.4), AEPVI10 (15.9), NAHAI12 (14.1), WNPTN11 (13) |
51133 | PPVI6 (36.5), AEPVI12 (36.4), SSRP11 (33.9), PPVA10 (25.8), WPWPA11 (25.5), NANRP12 (24.6), NAHAI11 (18.8), EPRP12 (18.4), WNPTN10 (12.9) |
51156 | PPVI12 (36.5), SSRP10 (34.4), MPZW5 (32.6), WPWPA10 (30.5), PPVA12 (23.9), NANRP12 (22.8), AEPVI11 (22.4), WNPTN10 (17.7), EPRP11 (15.3) |
51232 | PPVI12 (41.2), WPWPA4 (36.3), NAHAI6 (33.1), SSRP12 (31.7), AEPVI11 (29.2), NANRP11 (27.9), PPVA6 (27.6), MPZW5 (26.2), EPRP11 (21.2), WNPTN10 (16.3) |
51238 | PPVI12 (40.6), SSRP11 (32.2), WPWPA4 (31.6), PPVA12 (27.6), NANRP11 (27.3), AEPVI5 (25.8), MPZW12 (23.9), NAHAI12 (21.2), WNPTN11 (17.2), EPRP10 (16.6) |
51241 | AEPVI6 (43), PPVI12 (36.8), SSRP11 (30.9), NANRP11 (20), EPRP11 (18.9), PPVA12 (18.6), WNPTN10 (11.8) |
51243 | PPVI6 (42.5), IOWPA11 (31.2), NAHAI9 (30.1), NANRP6 (29.8), SSRP10 (25.3), EPRP11 (22.2), PPVA6 (21), AEPVI5 (15.8), WPWPA6 (15.7), MPZW4 (15), WNPTN10 (6.1) |
51334 | PPVI12 (37.8), SSRP10 (36.9), WPWPA4 (34.3), PPVA11 (30.6), NANRP5 (28.3), NAHAI12 (27.8), AEPVI12 (26.9), MPZW12 (26.6), EPRP11 (21.4), WNPTN10 (12.6) |
51367 | WPWPA4 (40.3), SSRP11 (39.4), PPVI12 (36.7), AEPVI12 (31.4), MPZW5 (30.3), NANRP11 (26.3), PPVA12 (24), NAHAI12 (22.1), IOWPA3 (20.2), EPRP11 (15.9), WNPTN10 (14.9) |
51477 | PPVI6 (37.4), SSRP10 (29.1), NANRP6 (28.8), AEPVI5 (25.3), PPVA9 (25.1), IOWPA6 (24.2), EPRP6 (17.6), NAHAI10 (17.4), WPWPA4 (15), WNPTN10 (13.1), MPZW5 (11.1) |
51526 | PPVI4 (34.9), SSRP6 (34.7), PPVA12 (28.7), NANRP9 (28.4), IOWPA5 (25), WPWPA10 (23.2), AEPVI6 (23), NAHAI5 (19.9), EPRP10 (18.8), MPZW6 (17.3), APVA5 (16.7), WNPTN4 (11.6) |
51567 | PPVI6 (37.1), SSRP4 (32), AEPVI12 (31.1), IOWPA9 (29.8), MPZW5 (25), WPWPA4 (24.1), NANRP5 (22.3), NAHAI5 (21.5), APVA10 (20.4), PPVA6 (19.7), WNPTN4 (17.9), EPRP10 (16) |
51573 | SSRP10 (39.5), PPVI12 (36.7), PPVA10 (31.8), WPWPA11 (31.3), NANRP11 (29.5), NAHAI11 (28.2), MPZW3 (26), EPRP11 (24.8), IOWPA5 (24.3), AEPVI10 (24.1), WNPTN12 (21.7) |
51628 | WNPTN4 (37.9), PPVI12 (37.7), SSRP10 (31.5), PPVA11 (30.4), WPWPA10 (27.6), NANRP11 (24.9), MPZW10 (24), EPRP10 (21.9), NAHAI11 (20.7), AEPVI12 (19.3), APVA12 (15) |
51656 | WPWPA4 (36.8), SSRP4 (34.6), PPVI6 (33.6), IOWPA9 (33.1), MPZW5 (28.9), PPVA5 (26), NANRP4 (24.6), WNPTN4 (24.4), NAHAI5 (21.8), APVA6 (21), AEPVI6 (17.7), EPRP4 (17.5) |
51704 | PPVI6 (39.9), NANRP11 (32.2), IOWPA10 (28.9), SSRP9 (28), AEPVI10 (23.8), NAHAI4 (23.4), WNPTN6 (21.6), WPWPA5 (19.6), EPRP11 (18.1), MPZW6 (16.9), PPVA6 (16.5) |
51705 | EPRP11 (37), PPVI10 (35.4), SSRP12 (34.1), WNPTN10 (31.5), AEPVI12 (26.1), NANRP11 (22.2) |
51709 | PPVI12 (37.5), WPWPA11 (36.9), SSRP10 (33.8), PPVA5 (33.6), MPZW10 (30.2), EPRP10 (29.1), WNPTN11 (28.9), NANRP11 (25.2), AEPVI3 (21.9), IOWPA12 (21), NAHAI11 (19.4) |
51720 | PPVI6 (36.3), WPWPA4 (36), NANRP4 (26.4), SSRP9 (26), AEPVI5 (23.9), IOWPA6 (23.7), PPVA6 (23.1), NAHAI10 (21.2), WNPTN5 (20.3), EPRP5 (14.7) |
51730 | PPVI6 (38.2), IOWPA10 (35.8), SSRP9 (28.6), WNPTN10 (27.4), AEPVI4 (23.3), WPWPA6 (23), NAHAI5 (21.7), NANRP10 (20.7), PPVA6 (18.1), MPZW5 (17.8), APVA10 (17.3), EPRP5 (15.5) |
51765 | PPVI6 (38.2), IOWPA9 (32), SSRP4 (31), NANRP4 (29.3), WPWPA10 (28.7), WNPTN4 (24.8), PPVA5 (24.3), MPZW6 (23.6), AEPVI6 (23.1), APVA5 (20.2), NAHAI5 (18.6), EPRP10 (16.8) |
51810 | PPVI6 (43.8), IOWPA4 (38.8), WPWPA11 (31.8), PPVA9 (30.3), SSRP10 (25.9), WNPTN10 (25.7), AEPVI12 (20.6), MPZW5 (18.1), NANRP10 (18), NAHAI11 (17.5), EPRP10 (11.5) |
51811 | PPVI6 (46.9), PPVA9 (28.8), SSRP11 (27.5), EPRP5 (26.8), IOWPA10 (25.8), NAHAI11 (25), WPWPA4 (22.2), NANRP10 (20.1), AEPVI12 (19.5), WNPTN10 (18.9), MPZW5 (14.3) |
51818 | NANRP6 (36.7), PPVI5 (34.1), SSRP4 (31.9), AEPVI12 (27.9), PPVA11 (27.3), NAHAI11 (25.8), MPZW10 (21.2), WPWPA5 (21.1), EPRP10 (16.8), WNPTN4 (13.7) |
51828 | AEPVI5 (33.6), SSRP6 (32.9), PPVI12 (32.6), NANRP4 (32.5), NAHAI11 (27.2), MPZW5 (22.9), PPVA11 (21.9), WPWPA10 (21.1), IOWPA9 (17.2), EPRP12 (15.5), APVA10 (13.7), WNPTN4 (13) |
51839 | AEPVI12 (36.5), PPVI6 (34.3), PPVA11 (33.6), SSRP4 (33.4), NANRP5 (31.6), WPWPA10 (28.2), IOWPA5 (23.1), APVA6 (22), NAHAI10 (20.8), EPRP9 (18.3), WNPTN4 (16), MPZW5 (12.5) |
51855 | WPWPA4 (35.7), SSRP4 (34.1), PPVI6 (31.1), IOWPA9 (29), NANRP5 (26.6), AEPVI6 (25.9), PPVA5 (24.3), EPRP5 (23.8), APVA6 (21.8), NAHAI5 (18.8), MPZW5 (16.8), WNPTN4 (9.8) |
51931 | PPVI5 (35.7), SSRP6 (33.7), NANRP4 (31.6), APVA4 (25.1), AEPVI6 (24.7), WPWPA9 (23.9), IOWPA6 (23.3), PPVA5 (23.3), MPZW10 (22.7), EPRP5 (21.3), NAHAI5 (19.8), WNPTN4 (11.4) |
52101 | WNPTN4 (38.8), PPVI12 (36.6), WPWPA10 (25.3), EPRP10 (23.8), SSRP10 (23.3), PPVA6 (22.5), MPZW10 (17), NANRP5 (16.5), AEPVI12 (14.2) |
52112 | PPVI6 (43.2), WNPTN9 (33.4), SSRP10 (29.5), AEPVI12 (28.8), IOWPA10 (28.5), WPWPA4 (26.7), PPVA6 (26.1), NANRP10 (20.8), APVA5 (20.4), NAHAI6 (15.5), MPZW10 (14.7), EPRP5 (13.7) |
52118 | PPVI6 (45), IOWPA9 (31.6), PPVA10 (28.3), AEPVI6 (25.8), SSRP12 (25.4), MPZW5 (22.9), WNPTN5 (20.9), NAHAI10 (19), NANRP10 (17.1), WPWPA10 (14.7), EPRP4 (13.8) |
52203 | PPVI6 (41.1), IOWPA9 (33.5), SSRP10 (27.8), AEPVI5 (24.9), NAHAI4 (24.2), WPWPA6 (23.7), APVA5 (23.2), WNPTN10 (22.3), MPZW10 (20.2), PPVA6 (20.2), NANRP5 (16.5), EPRP10 (12) |
52313 | EPRP11 (39.2), PPVI6 (38.6), SSRP4 (34.5), NANRP5 (28.1), MPZW10 (21.4), WPWPA6 (21.1), WNPTN10 (20.5), AEPVI6 (20.4), NAHAI6 (19.4), PPVA5 (17.5), APVA6 (14.4) |
52323 | WNPTN4 (48), SSRP10 (33.7), PPVI12 (32.7), MPZW5 (32.7), EPRP11 (28.6), WPWPA10 (26.8), AEPVI11 (24.6), NANRP12 (24.2), NAHAI12 (22.5), APVA12 (20.5), PPVA12 (18.3) |
52546 | PPVI6 (40.5), IOWPA9 (28), NAHAI5 (26.9), WNPTN12 (24.4), AEPVI11 (23.4), SSRP4 (23.3), PPVA10 (22.8), NANRP10 (20.5), MPZW5 (17.3), WPWPA10 (16.8), EPRP4 (16.3) |
52652 | WNPTN4 (48.1), PPVA11 (31.9), SSRP10 (29.2), PPVI12 (28.6), AEPVI10 (27), MPZW5 (25.4), EPRP12 (24.8), WPWPA10 (23.1), NANRP10 (22.7), NAHAI11 (10.7) |
52674 | EPRP10 (55.5), NANRP10 (49.2) |
52679 | EPRP10 (31.7), PPVA11 (31.2), SSRP10 (28.6), NANRP10 (25.9), NAHAI11 (19.9), AEPVI12 (15.7), PPVI11 (14.9) |
52681 | PPVA11 (33.6), WPWPA12 (31.3), APVA10 (29.1), PPVI10 (28.6), NANRP12 (28), SSRP10 (26.4), EPRP10 (25.2), WNPTN10 (22.5), NAHAI5 (18.6), MPZW11 (16.3), AEPVI12 (15.7) |
52797 | SSRP10 (42.2), EPRP10 (35.4), NANRP10 (31.9), PPVI11 (27.2) |
Circulation Index | PPVI | SSRP | WPWPA | NANRP | PPVA | IOWPA | AEPVI | WNPTN | NAHAI | MPZW | EPRP | APVA |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Rankid,NW | 2.959 | 1.928 | 1.135 | 0.962 | 0.941 | 0.900 | 0.856 | 0.631 | 0.507 | 0.406 | 0.401 | 0.141 |
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Li, Y.; Wei, K.; Chen, K.; He, J.; Zhao, Y.; Yang, G.; Yao, N.; Niu, B.; Wang, B.; Wang, L.; et al. Forecasting Monthly Water Deficit Based on Multi-Variable Linear Regression and Random Forest Models. Water 2023, 15, 1075. https://doi.org/10.3390/w15061075
Li Y, Wei K, Chen K, He J, Zhao Y, Yang G, Yao N, Niu B, Wang B, Wang L, et al. Forecasting Monthly Water Deficit Based on Multi-Variable Linear Regression and Random Forest Models. Water. 2023; 15(6):1075. https://doi.org/10.3390/w15061075
Chicago/Turabian StyleLi, Yi, Kangkang Wei, Ke Chen, Jianqiang He, Yong Zhao, Guang Yang, Ning Yao, Ben Niu, Bin Wang, Lei Wang, and et al. 2023. "Forecasting Monthly Water Deficit Based on Multi-Variable Linear Regression and Random Forest Models" Water 15, no. 6: 1075. https://doi.org/10.3390/w15061075