# Application of Artificial Neural Networks in Forecasting a Standardized Precipitation Evapotranspiration Index for the Upper Blue Nile Basin

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data Used

#### 2.1. Study Area

#### 2.2. Data Sources

## 3. Methodology

#### 3.1. SPEI

_{i}values were then aggregated at different time scales. Following the Vicente-Serrano et al. [14] approach, the log-logistic distribution F(x) was applied to transform the original D series into standardized units at different time scales. Finally, the F(x) distribution was utilized to calculate the SPEI following the inverse normal function discussed in Reference [51]. The complete derivation and theory of the index can be found in [52].

#### 3.2. Artificial Neural Networks (ANNs)

#### 3.3. ANN Model Development

#### 3.4. Statistical Performance Measures

^{2}), root-mean-square error (RMSE), Willmott’s index of agreement (d), and the Nash–Sutcliffe coefficient of efficiency (E). The following mathematical equations define these metrics.

_{i}is the observed SPEI value, and P

_{i}is the ANN-predicted SPEI value. RMSE was used to measure the average ANN model prediction error to indicate how close the predicted values were to the observed. Lower values of the index indicate high prediction accuracy. The coefficient of determination R

^{2}was determined from the scattered plot of the observed and predicted SPEI values from the fitted regression line. The best model should have an R

^{2}value close to unity. R

^{2}= 1 denotes an exact linear relationship between the observed and predicted values. However, correlation-based measures are oversensitive to extreme values. As a result, a model might appear to be a good predictor when it is not [60]. The Nash–Sutcliffe coefficient of efficiency [61] is 1 minus the absolute difference between the sum of the squared differences between the predicted and observed values, standardized by the variance of the observed values during the study period. The Nash–Sutcliffe coefficient of efficiency (E) statistical measure ranges from −Infinity to 1, and a value closer to unity indicates a better relationship of the observed to the predicted data. However, it has drawbacks, as the errors are calculated as square terms and hence larger values in a time-series are overestimated, whereas lower values are neglected [62]. To overcome the insensitivity of Nash–Sutcliffe coefficient of efficiency (E) and the coefficient of determination (R

^{2}), Willmott’s index of agreement (d) was proposed [63]. Willmott’s index of agreement (d) gives a value between 0 and 1, and a value close to unity indicates the realization of the best model, whereas a value close to 0 indicates no agreement at all. The index improves upon those mentioned above, yet remains sensitive to extreme events. For sound scientific model calibration and evaluation, a combination of different performance measures is recommended. The performance of the ANN in terms of the score metrics between the observed SPEI and predicted ANN outputs were examined and the results are presented in the next section. The best ANN architecture was trained with the resilient back-propagation learning algorithm with the tangent sigmoid hidden transfer function. Furthermore, the output transfer function was chosen to be linear.

## 4. Results and Discussions

#### 4.1. Model Performance

^{2}), RMSE, Willmott’s index of agreement (d), and the Nash–Sutcliffe coefficient of efficiency (E).

#### 4.2. Comparison of Different Models

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Wilhite, D.A.; Glantz, M.H. Understanding: The drought phenomenon: The role of definitions. Water Int.
**1985**, 10, 111–120. [Google Scholar] [CrossRef] [Green Version] - Cheng, C.-H.; Nnadi, F.; Liou, Y.-A. Energy budget on various land use areas using reanalysis data in Florida. Adv. Meteorol.
**2014**, 2014, 1–13. [Google Scholar] [CrossRef] [Green Version] - Dorjsuren, M.; Liou, Y.-A.; Cheng, C.-H. Time series MODIS and in situ data analysis for Mongolia drought. Remote Sens.
**2016**, 8, 509. [Google Scholar] [CrossRef] [Green Version] - Luo, L.; Apps, D.; Arcand, S.; Xu, H.; Pan, M.; Hoerling, M. Contribution of temperature and precipitation anomalies to the California drought during 2012–2015. Geophys. Res. Lett.
**2017**, 44, 3184–3192. [Google Scholar] [CrossRef] - Habibi, B.; Meddi, M.; Torfs, P.J.J.F.; Remaoun, M.; Van Lanen, H.A.J. Characterisation and prediction of meteorological drought using stochastic models in the semi-arid Chéliff–Zahrez basin (Algeria). J. Hydrol. Reg. Stud.
**2018**, 16, 15–31. [Google Scholar] [CrossRef] - Liou, Y.A.; Nguyen, A.K.; Li, M.H. Assessing spatiotemporal eco-environmental vulnerability by Landsat data. Ecol. Indic.
**2017**, 80, 52–65. [Google Scholar] [CrossRef] [Green Version] - Cheng, C.H.; Nnadi, F.; Liou, Y.A. A regional land use drought index for Florida. Remote Sens.
**2015**, 7, 17149–17167. [Google Scholar] [CrossRef] [Green Version] - Liou, Y.A.; Mulualem, G.M. Spatio-temporal assessment of drought in Ethiopia and the impact of recent intense droughts. Remote Sens.
**2019**, 11, 1828. [Google Scholar] [CrossRef] [Green Version] - Dutra, E.; Magnusson, L.; Wetterhall, F.; Cloke, H.L.; Balsamo, G.; Boussetta, S.; Pappenberger, F. The 2010–2011 drought in the Horn of Africa in ECMWF reanalysis and seasonal forecast products. Int. J. Climatol.
**2013**, 33, 1720–1729. [Google Scholar] [CrossRef] [Green Version] - Wu, X.; Hongxing, C.; Flitma, A. Forecasting monsoon precipitation using artificial neural networks. Adv. Atmos. Sci.
**2011**, 14, 123. [Google Scholar] [CrossRef] - Wu, C.L.; Chau, K.W.; Li, Y.S. Predicting monthly streamflow using data-driven models coupled with data-preprocessing techniques. Water Resour. Res.
**2009**, 45. [Google Scholar] [CrossRef] [Green Version] - Hao, Z.; Singh, V.P.; Xia, Y. Seasonal Drought Prediction: Advances, Challenges, and Future Prospects. Rev. Geophys.
**2018**, 56, 108–141. [Google Scholar] [CrossRef] [Green Version] - Zargar, A.; Sadiq, R.; Naser, B.; Khan, F.I. A review of drought indices. Environ. Rev.
**2011**, 19, 333–349. [Google Scholar] [CrossRef] - Vicente-Serrano, S.M.; Beguería, S.; López-Moreno, J.I.; Vicente-Serrano, S.M.; Beguería, S.; López-Moreno, J.I. A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index. J. Clim.
**2010**, 23, 1696–1718. [Google Scholar] [CrossRef] [Green Version] - Almedeij, J. Drought analysis for kuwait using standardized precipitation index. Sci. World J.
**2014**, 2014. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Yu, C.; Li, C.; Xin, Q.; Chen, H.; Zhang, J.; Zhang, F.; Li, X.; Clinton, N.; Huang, X.; Yue, Y.; et al. Dynamic assessment of the impact of drought on agricultural yield and scale-dependent return periods over large geographic regions. Environ. Model. Softw.
**2014**, 62, 454–464. [Google Scholar] [CrossRef] [Green Version] - Hayes, M.J.; Svoboda, M.D.; Wardlow, B.D.; Anderson, M.C.; Kogan, F. Drought monitoring: Historical and current perspectives. In Remote Sensing of Drought: Innovative Monitoring Approaches; CRC Press: Boca Raton, FL, USA, 2012; pp. 1–19. ISBN 9781439835609. [Google Scholar]
- Yusuf, A.A.; Francisco, H. Climate change vulnerability mapping for Southeast Asia vulnerability mapping for Southeast Asia. East
**2009**, 181, 1–19. [Google Scholar] - Mishra, S.S.; Nagarajan, R. Forecasting drought in Tel River Basin using feedforward recursive neural network. Int. Conf. Environ. Biomed. Biotechnol.
**2012**, 41, 122–126. [Google Scholar] - Pulwarty, R.S.; Sivakumar, M.V. Information systems in a changing climate: Early warnings and drought risk management. Weather Clim. Extrem.
**2014**, 3, 14–21. [Google Scholar] [CrossRef] [Green Version] - Khashei, M.; Bijari, M. An artificial neural network (p, d, q) model for timeseries forecasting. Expert Syst. Appl.
**2009**, 37, 479–489. [Google Scholar] [CrossRef] - Barua, S.; Ng, A.W.M.; Perera, B.J.C. Artificial Neural Network–Based drought forecasting using a nonlinear aggregated drought index. J. Hydrol. Eng.
**2012**, 17, 1408–1413. [Google Scholar] [CrossRef] - Hardwinarto, S.; Aipassa, M. Rainfall monthly prediction based on Artificial Neural Network: A case study in Tenggarong station, East Kalimantan–Indonesia. Procedia Comput. Sci.
**2015**, 59, 142–151. [Google Scholar] [CrossRef] [Green Version] - Morid, S.; Smakhtin, V.; Bagherzadeh, K. Drought forecasting using artificial neural networks and time series of drought indices. Int. J. Climatol.
**2007**, 27, 2103–2111. [Google Scholar] [CrossRef] - Liou, Y.A.; Liu, S.F.; Wang, W.J. Retrieving soil moisture from simulated brightness temperatures by a neural network. IEEE Trans. Geosci. Remote Sens.
**2001**, 39, 1662–1672. [Google Scholar] - Belayneh, A.; Adamowski, J.; Khalil, B. Short-term SPI drought forecasting in the Awash River Basin in Ethiopia using wavelet transforms and machine learning methods. Sustain. Water Resour. Manag.
**2016**, 2, 87–101. [Google Scholar] [CrossRef] - Deo, R.C.; Şahin, M. Application of the Artificial Neural Network model for prediction of monthly standardized precipitation and evapotranspiration index using hydrometeorological parameters and climate indices in eastern Australia. Atmos. Res.
**2015**, 161–162, 65–81. [Google Scholar] [CrossRef] - Le, M.H.; Perez, G.C.; Solomatine, D.; Nguyen, L.B. Meteorological drought forecasting based on climate signals using Artificial Neural Network—A case study in Khanhhoa Province Vietnam. Procedia Eng.
**2016**, 154, 1169–1175. [Google Scholar] [CrossRef] [Green Version] - Schubert, S.D.; Stewart, R.E.; Wang, H.; Barlow, M.; Berbery, E.H.; Cai, W.; Hoerling, M.P.; Kanikicharla, K.K.; Koster, R.D.; Lyon, B.; et al. Global meteorological drought: A synthesis of current understanding with a focus on SST drivers of precipitation deficits. J. Clim.
**2016**, 29, 3989–4019. [Google Scholar] [CrossRef] [Green Version] - Roundy, J.K.; Wood, E.F.; Roundy, J.K.; Wood, E.F. The attribution of land–Atmosphere interactions on the seasonal predictability of drought. J. Hydrometeorol.
**2015**, 16, 793–810. [Google Scholar] [CrossRef] - Lyon, B. Seasonal drought in the greater horn of Africa and its recent increase during the March–May long rains. J. Clim.
**2014**, 27, 7953–7975. [Google Scholar] [CrossRef] - Hoell, A.; Funk, C.; Hoell, A.; Funk, C. The ENSO-related West Pacific Sea surface temperature gradient. J. Clim.
**2013**, 26, 9545–9562. [Google Scholar] [CrossRef] - Behrangi, A.; Nguyen, H.; Granger, S. Probabilistic seasonal prediction of meteorological drought using the bootstrap and multivariate information. J. Appl. Meteorol. Climatol.
**2015**, 54, 1510–1522. [Google Scholar] [CrossRef] - Allam, M.M.; Jain Figueroa, A.; McLaughlin, D.B.; Eltahir, E.A.B. Estimation of evaporation over the upper Blue Nile basin by combining observations from satellites and river flow gauges. Water Resour. Res.
**2016**, 52, 644–659. [Google Scholar] [CrossRef] [Green Version] - Tekleab, S.; Mohamed, Y.; Uhlenbrook, S. Hydro-climatic trends in the Abay/Upper Blue Nile basin, Ethiopia. Phys. Chem. Earth, Parts A/B/C
**2013**, 61–62, 32–42. [Google Scholar] [CrossRef] - Samy, A.; Ibrahim, M.G.; Mahmod, W.E.; Fujii, M.; Eltawil, A.; Daoud, W. Statistical assessment of rainfall characteristics in Upper Blue Nile Basin over the period from 1953 to 2014. Water
**2019**, 11, 468. [Google Scholar] [CrossRef] [Green Version] - Broman, D.; Rajagopalan, B.; Hopson, T.; Gebremichael, M. Spatial and temporal variability of East African Kiremt season precipitation and large-scale teleconnections. Int. J. Climatol.
**2020**, 40, 1241–1254. [Google Scholar] [CrossRef] - Giannini, A.; Biasutti, M.; Held, I.M.; Sobel, A.H. A global perspective on African climate. Clim. Chang.
**2008**, 90, 359–383. [Google Scholar] [CrossRef] - Siam, M.S.; Wang, G.; Demory, M.E.; Eltahir, E.A.B. Role of the Indian Ocean sea surface temperature in shaping the natural variability in the flow of Nile River. Clim. Dyn.
**2014**, 43, 1011–1023. [Google Scholar] [CrossRef] - Diro, G.T.; Grimes, D.I.F.; Black, E. Teleconnections between Ethiopian summer rainfall and sea surface temperature: Part II. Seasonal forecasting. Clim. Dyn.
**2011**, 37, 121–131. [Google Scholar] [CrossRef] - Alhamshry, A.; Fenta, A.A.; Yasuda, H.; Shimizu, K.; Kawai, T. Prediction of summer rainfall over the source region of the Blue Nile by using teleconnections based on sea surface temperatures. Theor. Appl. Climatol.
**2019**, 137, 3077–3087. [Google Scholar] [CrossRef] - Segele, Z.T.; Lamb, P.J.; Leslie, L.M. Seasonal-to-Interannual variability of Ethiopia/Horn of Africa monsoon. Part I: Associations of wavelet-filtered large-scale atmospheric circulation and global sea surface temperature. J. Clim.
**2009**, 22, 3396–3421. [Google Scholar] [CrossRef] - Berhane, F.; Zaitchik, B.; Dezfuli, A. Subseasonal analysis of precipitation variability in the Blue Nile River Basin. J. Clim.
**2014**, 27, 325–344. [Google Scholar] [CrossRef] - Gebremicael, T.G.; Mohamed, Y.A.; Betrie, G.D.; van der Zaag, P.; Teferi, E. Trend analysis of runoff and sediment fluxes in the Upper Blue Nile basin: A combined analysis of statistical tests, physically-based models and landuse maps. J. Hydrol.
**2013**, 482, 57–68. [Google Scholar] [CrossRef] - Coffel, E.D.; Keith, B.; Lesk, C.; Horton, R.M.; Bower, E.; Lee, J.; Mankin, J.S. Future hot and dry years worsen Nile basin water scarcity despite projected precipitation increases. Earth’s Futur.
**2019**, 7, 967–977. [Google Scholar] [CrossRef] [Green Version] - Broad, K.; Agrawala, S. The Ethiopia food crisis—Uses and limits of climate forecasts. Science
**2000**, 289, 1693–1694. [Google Scholar] - Conway, D. The climate and hydrology of the Upper Blue Nile river. Geogr. J.
**2000**, 166, 49–62. [Google Scholar] [CrossRef] [Green Version] - Wagesho, N.; Goel, N.K.; Jain, M.K. Temporal and spatial variability of annual and seasonal rainfall over Ethiopia. Hydrol. Sci. J.
**2013**, 58, 354–373. [Google Scholar] [CrossRef] - Mellander, P.-E.; Gebrehiwot, S.G.; Gärdenäs, A.I.; Bewket, W.; Bishop, K. Summer rains and dry seasons in the upper blue Nile Basin: The predictability of half a century of past and future spatiotemporal patterns. PLoS ONE
**2013**, 8, e68461. [Google Scholar] [CrossRef] [Green Version] - Thornthwaite, C.W. An approach toward a rational classification of climate. Geogr. Rev.
**1948**, 38, 55. [Google Scholar] [CrossRef] - Barton, D.E.; Abramovitz, M.; Stegun, I.A. Handbook of mathematical functions with formulas, graphs and mathematical tables. J. R. Stat. Soc. Ser. A
**1965**, 128, 593. [Google Scholar] [CrossRef] [Green Version] - Beguería, S.; Vicente-Serrano, S.M.; Reig, F.; Latorre, B. Standardized precipitation evapotranspiration index (SPEI) revisited: Parameter fitting, evapotranspiration models, tools, datasets and drought monitoring. Int. J. Climatol.
**2014**, 34, 3001–3023. [Google Scholar] [CrossRef] [Green Version] - Seo, Y.; Kim, S. River stage forecasting using wavelet packet decomposition and data-driven models. Procedia Eng.
**2016**, 154, 1225–1230. [Google Scholar] [CrossRef] [Green Version] - Schuman, C.D.; Birdwell, J.D. Dynamic Artificial Neural Networks with affective systems. PLoS ONE
**2013**, 8, e80455. [Google Scholar] [CrossRef] [PubMed] - Günther, F.; Fritsch, S. neuralnet: Training of neural networks. R J.
**2010**, 2, 30–38. [Google Scholar] [CrossRef] [Green Version] - Riedmiller, M.; Riedmiller, M.; Braun, H. A direct adaptive method for faster backpropagation learning: The rprop algorithm. IEEE Int. Conf. Neural Netw.
**1993**, 16, 586–591. [Google Scholar] - Remesan, R.; Mathew, J. Hydrological Data Driven Modelling: A Case Study Approach; Springer International Pu: New York City, NY, USA, 2016; ISBN 9783319092355. [Google Scholar]
- Sheela, K.G.; Deepa, S.N. Review on methods to fix number of hidden neurons in neural networks. Math. Probl. Eng.
**2013**, 2013. [Google Scholar] [CrossRef] [Green Version] - Stathakis, D. How many hidden layers and nodes? Int. J. Remote Sens.
**2009**, 30, 2133–2147. [Google Scholar] [CrossRef] - Legates, D.R.; McCabe, G.J. Evaluating the use of “goodness-of-fit” Measures in hydrologic and hydroclimatic model validation. Water Resour. Res.
**1999**, 35, 233–241. [Google Scholar] [CrossRef] - Nash, J.E.; Sutcliffe, J. V River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef] - Krause, P.; Boyle, D.P.; Bäse, F. Comparison of different efficiency criteria for hydrological model assessment. Adv. Geosci.
**2005**, 5, 89–97. [Google Scholar] [CrossRef] [Green Version] - Willmott, C.J. On the validation of models. Phys. Geogr.
**1981**, 2, 184–194. [Google Scholar] [CrossRef] - Beck, M.W. NeuralNetTools: Visualization and analysis tools for neural networks. J. Stat. Softw.
**2018**, 85, 1. [Google Scholar] [CrossRef] [PubMed] - Garson, G.D. A comparison of neural network and expert systems algorithms with common multivariate procedures for analysis of social science data. Soc. Sci. Comput. Rev.
**1991**, 9, 399–434. [Google Scholar] [CrossRef]

**Figure 1.**The geographical location of the Upper Blue Nile (UBN) river basin and metrological stations used in this study.

**Figure 2.**Land cover map of the UBN river basin in 2016 at 20 m spatial resolution, extracted from the European Space Agency.

**Figure 3.**Monthly climatology of rainfall and climatic water balance, CWB

_{i}= P

_{i}− PET

_{i}(precipitation − potential evapotranspiration) for the 1986–2015 period.

**Figure 8.**Density plots and histograms of the prediction error (PE) values calculated for the test period.

**Figure 11.**(

**a**) A scatterplot of the observed versus predicted plots for the two-layer ANN (ANN_2), one-layer ANN (ANN_1), and linear models (LM) with a 1:1 reference line plot. (

**b**) The 10-fold cross-validation root-mean-square errors for the two-layer ANN and one-layer ANN models.

Station Name | Geographical Locations | Elevation ASL | Annual Mean Rainfall (mm) | Mean Annual Temperature (°C) |
---|---|---|---|---|

Alemketema | 10.03° N, 39.03° E | 2280 m | 1049.16 | 19.74 |

Asossa | 10.02° N, 34.52° E | 1590 m | 1198.57 | 24.61 |

Bahir Dar | 11.59° N, 37.38° E | 1770 m | 1387.37 | 20.43 |

Bedele | 8.45° N, 36.33° E | 2030 m | 1809.18 | 17.92 |

Chagni | 10.97° N, 36.5° E | 1620 m | 1699.58 | 20.34 |

Debremarkos | 10.33° N, 37.74° E | 2515 m | 1334.15 | 16.27 |

Gondar | 12.61° N, 37.45° E | 1967 m | 1145.87 | 19.89 |

**Table 2.**Drought characterization based on standardized precipitation evapotransporation index (SPEI) values.

SPEI Values | Drought Category |
---|---|

SPEI ≥ 2 | Extremely wet |

1.5 ≤ SPEI < 1 | Severely wet |

1 ≤ SPEI < 1.5 | Moderately wet |

−1 ≤ SPEI < 1 | Near normal |

−1.5 ≤ SPEI < −1 | Moderately dry |

−2 ≤ SPEI < −1.5 | Severely dry |

SPEI < −2 | Extremely dry |

Model | No. of Input Variables | Year | Month | Rainfall | Max T | Min T | PET | SOI | IOD | PDO | N3 SST | N3.4 SST | N4 SST |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

M1 | 12 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

M2 | 11 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |

M3 | 10 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

M4 | 8 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

M5 | 6 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||||

M6 | 6 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||||

M7 | 4 | ✓ | ✓ | ✓ | ✓ |

**Table 4.**A measure of ANN model performance based on all statistical measures of the observed SPEI and predicted SPEI.

Station Name | R^{2} | RMSE | d | E |
---|---|---|---|---|

Alemketema | 0.870 | 0.335 | 0.965 | 0.863 |

Asossa | 0.892 | 0.349 | 0.966 | 0.884 |

Bahir Dar | 0.820 | 0.428 | 0.946 | 0.818 |

Bedele | 0.856 | 0.338 | 0.959 | 0.854 |

Chagni | 0.908 | 0.290 | 0.975 | 0.905 |

Debremarkos | 0.865 | 0.363 | 0.964 | 0.862 |

Gondar | 0.949 | 0.263 | 0.987 | 0.949 |

Overall station average | 0.880 | 0.338 | 0.966 | 0.876 |

Station Name | Maximum PE | Minimum PE | Standard Deviation |
---|---|---|---|

Alemketema | 1.674 | −0.631 | 0.337 |

Asossa | 0.877 | −1.561 | 0.346 |

Bahir Dar | 1.614 | −1.189 | 0.430 |

Bedele | 0.956 | −0.588 | 0.338 |

Chagni | 1.075 | −0.518 | 0.288 |

Debremarkos | 0.799 | −0.964 | 0.364 |

Gondar | 0.690 | −0.653 | 0.265 |

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**MDPI and ACS Style**

Mulualem, G.M.; Liou, Y.-A.
Application of Artificial Neural Networks in Forecasting a Standardized Precipitation Evapotranspiration Index for the Upper Blue Nile Basin. *Water* **2020**, *12*, 643.
https://doi.org/10.3390/w12030643

**AMA Style**

Mulualem GM, Liou Y-A.
Application of Artificial Neural Networks in Forecasting a Standardized Precipitation Evapotranspiration Index for the Upper Blue Nile Basin. *Water*. 2020; 12(3):643.
https://doi.org/10.3390/w12030643

**Chicago/Turabian Style**

Mulualem, Getachew Mehabie, and Yuei-An Liou.
2020. "Application of Artificial Neural Networks in Forecasting a Standardized Precipitation Evapotranspiration Index for the Upper Blue Nile Basin" *Water* 12, no. 3: 643.
https://doi.org/10.3390/w12030643