Rainfall modeling using two different neural networks improved by metaheuristic algorithms

Creative Commons License

Sammen S. S., Kisi O., Ehteram M., El-Shafie A., Al-Ansari N., Ghorbani M. A., ...More

Environmental Sciences Europe, vol.35, no.1, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1186/s12302-023-00818-0
  • Journal Name: Environmental Sciences Europe
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, IBZ Online, Agricultural & Environmental Science Database, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, Environment Index, Geobase, Pollution Abstracts, Veterinary Science Database, Directory of Open Access Journals
  • Keywords: Markov chain, MLP, Probability matrix, Rainfall modelling, RBFNN
  • Istanbul Technical University Affiliated: Yes


Rainfall is crucial for the development and management of water resources. Six hybrid soft computing models, including multilayer perceptron (MLP)–Henry gas solubility optimization (HGSO), MLP–bat algorithm (MLP–BA), MLP–particle swarm optimization (MLP–PSO), radial basis neural network function (RBFNN)–HGSO, RBFNN–PSO, and RBFGNN–BA, were used in this study to forecast monthly rainfall at two stations in Malaysia (Sara and Banding). Different statistical measures (mean absolute error (MAE) and Nash–Sutcliffe efficiency (NSE) and percentage of BIAS (PBIAS)) and a Taylor diagram were used to assess the models’ performance. The results indicated that the MLP–HGSO performed better than the other models in forecasting rainfall at both stations. In addition, transition matrices were computed for each station and year based on the conditional probability of rainfall or absence of rainfall on a given month. The values of MAE for testing processes for the MLP–HGSO, MLP–PSO, MLP–BA, RBFNN–HGSO, RBFNN–BA, and RBFNN–PSO at the first station were 0.712, 0.755, 0.765, 0.717, 0.865, and 0.891, while the corresponding NSE and PBIAS values were 0.90–0.23, 0.83–0.29, 0.85–0.25, 0.87–0.27, 0.81–0.31, and 0.80–0.35, respectively. For the second station, the values of MAE were found 0.711, 0.743, 0.742, 0.719, 0.863 and 0.890 for the MLP–HGSO, MLP–PSO, MLP–BA, RBFNN–HGSO, RBFNN–BA, and RBFNN–PSO during testing processes and the corresponding NSE–PBIAS values were 0.92–0.22, 0.85–0.28, 0.89–0.26, 0.91–0.25, 0.83–0.31, 0.82–0.32, respectively. Based on the outputs of the MLP–HGSO, the highest rainfall was recorded in 2012 with a probability of 0.72, while the lowest rainfall was recorded in 2006 with a probability of 0.52 at the Sara Station. In addition, the results indicated that the MLP–HGSO performed better than the other models within the Banding Station. According to the findings, the hybrid MLP–HGSO was selected as an effective rainfall prediction model.