# Precipitation Forecasting in Northern Bangladesh Using a Hybrid Machine Learning Model

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}values up to 0.87 and 0.92 for the stations of Rangpur and Sylhet, respectively.

## 1. Introduction

## 2. Study Area and Datasets

_{max}), minimum temperature (T

_{min}), relative humidity (H), wind speed (V

_{wind}), cloud coverage (C) and a monthly average of daily bright sunshine (S), were used for the precipitation (P) forecasting, from January 1956 to December 2013. Cloud coverage was measured in okta, ranging from 0 oktas, which indicates a completely clear sky, to 8 oktas, completely covered sky.

^{2}), which assess how well the model replicates measured values and predicts future values, the mean absolute error (MAE), equal to the average magnitude of the difference between measured and predicted values, the root mean square error (RMSE), equal to the root of the average square difference between measured and predicted values, and the relative absolute error (RAE), equal to the ratio between absolute error and absolute value of the difference between average of the measured value and each measured value. These metrics are defined as:

## 3. Methods

#### 3.1. M5P

_{i}is the target variable value for the i-th unit, and y

_{m}is the target variable mean. The function Φ(s

_{p}, t) to be maximized is expressed as:

_{L}and p

_{R}are the portion units allocated to the left node t

_{L}and right node t

_{R}, and s

_{p}indicated the split value [33]. Different stopping rules were considered: minimum impurity level, minimum impurity change in the subdivision, minimum elements number for each node, and maximum tree depth. Furthermore, the pruning technique was considered to avoid overfitting problems for the fully developed tree. This technique removes branches that provide a low contribution to the prediction ability in order to reduce the tree size. The following parameters were considered: Batch size = 100; minimum number of instances to allow at a leaf node = 6.

#### 3.2. Support Vector Regression (SVR)

_{i}. Based on the following training dataset: {(x

_{i}, y

_{i}), i = 1, …, l} ⊂ X × R, where X indicates the space of the input arrays, the Euclidean norm ||w||

^{2}must be minimized, by solving a constrained convex optimization problem, in order to find a linear function f(x) = 〈w, x〉 + b, where b ∈ R and w ∈ X. In addition, slack variables were introduced to tolerate to allow deviations from ε.

#### 3.3. Hybrid Model M5P-SVR

#### 3.4. Particle Swarm Optimization (PSO)

## 4. Results

#### 4.1. Time Series Analysis

_{min}(Figure 4b) showed XCF peaks equal to 0.8, higher than those computed for T

_{max}(Figure 4a), equal to 0.6, highlighting a greater correlation of the minimum temperatures with the precipitation. Both peaks were observed for τ = 12 months. The cross-correlation between relative humidity and precipitation (Figure 4c) exhibited peaks at τ = 11 months for both stations. A higher correlation for Sylhet was computed, with XCF close to 0.8. However, Rangpur also showed a good correlation, with XCF higher than 0.5. For the cross-correlation between wind speed and precipitation, peaks were instead observed for a τ = 14 months (Figure 4d), with a lower correlation in comparison to temperature and humidity, with XCF = 0.4 for Rangpur and XCF = 0.3 for Sylhet. Cross-correlation between cloud coverage and precipitation (Figure 4e) showed high peaks at τ = 12 months, with XCF close to 0.8 for both stations.

#### 4.2. Rangpur Station

_{a}= 1 month, the best performances were obtained with the hybrid algorithm M5P-SVR and Model A, which included all the monitored exogenous inputs (R

^{2}= 0.89, MAE = 47 mm, RMSE = 68 mm, MAE = 27.42%, Figure 6a,b). Performances reduced passing to Model B, which did not consider T

_{max}and T

_{min}as exogenous inputs (R

^{2}= 0.87, MAE = 49 mm, RMSE = 71 mm, MAE = 28.31%). Model B was outperformed by Model C, which instead did not include the cloud overage and the daily bright sunshine as exogenous inputs, while it took into account both maximum and minimum temperatures (R

^{2}= 0.87, MAE = 47 mm, RMSE = 71 mm, MAE = 27.52%). This highlights a greater impact on the algorithms training of the temperature, in comparison with the cloud coverage and bright sunshine. However, Model D (R

^{2}= 0.80, MAE = 62 mm, RMSE = 85 mm, MAE = 36.44%), which included only H and V

_{wind}as exogenous inputs, exhibited much lower performances with respect to both Models B and C. Therefore, not considering the cloud overage and the daily bright sunshine as exogenous inputs still had a negative impact on the algorithms training. The worst performances were achieved for Model E (R

^{2}= 0.79, MAE = 64 mm, RMSE = 88 mm, MAE = 37.98%, Figure 6c,d), which included only the relative humidity as exogenous input. Both M5P and SVR algorithms showed similar performances reduction passing from Model A (M5P–R

^{2}= 0.88, MAE = 47 mm, RMSE = 10,471 mm, MAE = 28.05%; SVR–R

^{2}= 0.85, MAE = 51 mm, RMSE = 75 mm, MAE = 30.13%) to Model E (M5P–R

^{2}= 0.79, MAE = 67 mm, RMSE = 90 mm, MAE = 39.59%; SVR–R

^{2}= 0.77, MAE = 65 mm, RMSE = 92 mm, MAE = 38.12%). However, a marked difference between the algorithms was observed for Model B, with M5P (R

^{2}= 0.85, MAE = 53 mm, RMSE = 77 mm, MAE = 30.88%) that showed better performances in comparison with SVR (R

^{2}= 0.79, MAE = 61 mm, RMSE = 88 mm, MAE = 35.55%). As the lag time increases, from t

_{a}= 1 month to t

_{a}= 3 months, a slight performance reduction was observed for all algorithms and models. However, M5P-SVR with Model A was confirmed as the most performing algorithm (R

^{2}= 0.89, MAE = 47 mm, RMSE = 69 mm, MAE = 27.50%).

_{a}= 1 month–R

^{2}= 0.87, MAE = 62 mm, RMSE = 88 mm, MAE = 38.09%, Figure 6e,f; t

_{a}= 3 months–R

^{2}= 0.87, MAE = 63 mm, RMSE = 89 mm, MAE = 38.45%). It should be noted that, passing from the training to the testing stage, only a slight performance reduction was observed. The difference in terms of performances between Model B and Model C, observed for the training stage in particular for SVR, has been observed also for the hybrid model M5P-SVR for the testing stage (t

_{a}= 1 month, Model B–R

^{2}= 0.82, MAE = 73 mm, RMSE = 91 mm, MAE = 43.15%; t

_{a}= 1 month, Model C–R

^{2}= 0.86, MAE = 65 mm, RMSE = 89 mm, MAE = 39.65%). However, the worst predictions were achieved with Model E, for both lag times (t

_{a}= 1 month, R

^{2}= 0.79, MAE = 79 mm, RMSE = 94 mm, MAE = 46.56%, Figure 6g,h; t

_{a}= 3 months, R

^{2}= 0.78, MAE = 83 mm, RMSE = 96 mm, MAE = 48.94%).

_{a}= 1 month, R

^{2}= 0.86, MAE = 69 mm, RMSE = 96 mm, MAE = 41.99%) led to slightly better prediction in comparison with SVR (t

_{a}= 1 month, R

^{2}= 0.84, MAE = 66 mm, RMSE = 91 mm, MAE = 40.51%), for Model E, SVR (t

_{a}= 1 month, R

^{2}= 0.78, MAE = 79 mm, RMSE = 98 mm, MAE = 46.89%) outperformed significantly M5P (t

_{a}= 1 month, R

^{2}= 0.72, MAE = 84 mm, RMSE = 103 mm, MAE = 49.41%) for both lag times.

#### 4.3. Sylhet Station

_{a}= 1 month–R

^{2}= 0.94, MAE = 55 mm, RMSE = 76 mm, MAE = 18.64%, Figure 7a,b; t

_{a}= 3 months–R

^{2}= 0.94, MAE = 56 mm, RMSE = 78 mm, MAE = 19.12%). As the number of exogenous inputs reduces, a performance decrease was observed. In particular, Models B and C exhibited performances similar to each other and lower to Model A, for both lag times. A further slight performance decrease occurs passing to Model D (t

_{a}= 1 month–R

^{2}= 0.91, MAE = 64 mm, RMSE = 91 mm, MAE = 22.38%; t

_{a}= 3 months–R

^{2}= 0.90, MAE = 69 mm, RMSE = 95 mm, MAE = 24.35%). However, a marked performance decrease occurs passing from Model D to Model E, with the latter that considered only the relative humidity as exogenous input (t

_{a}= 1 month–R

^{2}= 0.88, MAE = 82 mm, RMSE = 112 mm, MAE = 28.28%, Figure 7c,d; t

_{a}= 3 months–R

^{2}= 0. 88, MAE = 85 mm, RMSE = 114 mm, MAE = 28.99%).

^{2}values and lower values of MAE, RMSE, and MAE.

_{a}= 1 month (R

^{2}= 0.92, MAE = 68 mm, RMSE = 91 mm, MAE = 25.26%, Figure 7e,f) to t

_{a}= 3 months (R

^{2}= 0.91, MAE = 69 mm, RMSE = 93 mm, MAE = 25.57%). As for the training stage, performances of Model B and Model C were in line and lower than those computed for Model A. Model D (t

_{a}= 1 month–R

^{2}= 0.88, MAE = 77 mm, RMSE = 107 mm, MAE = 29.34%; t

_{a}= 3 months–R

^{2}= 0.86, MAE = 79 mm, RMSE = 109 mm, MAE = 30.07%) was slightly outperformed by both models B and C, proving its reliability despite it included only relative humidity and the wind speed as exogenous inputs. A lower prediction ability was observed for Model E (t

_{a}= 1 month, R

^{2}= 0.85, MAE = 86 mm, RMSE = 119 mm, MAE = 31.84%, Figure 7g,h; t

_{a}= 3 months, R

^{2}= 0.83, MAE = 89 mm, RMSE = 122 mm, MAE = 32.87%). However, the hybrid model M5P-SVR with Model E, even including the only relative humidity as exogenous input, was still able to properly detect the precipitations trend.

_{a}= 1 month, R

^{2}= 0.85, MAE = 102 mm, RMSE = 133 mm, MAE = 35.96%; SVR-t

_{a}= 1 month, R

^{2}= 0.82, MAE = 92 mm, RMSE = 125 mm, MAE = 34.08%).

#### 4.4. Performance Comparisons of the Models

_{a}= 3 days and 55 mm for Model E-t

_{a}= 3 days, while outliers (indicated with the red crosses) with positive and negative absolute errors between −291 mm and 370 mm. Overall, Model E led to the higher underestimation of heavy rainfalls. A narrow box plot was computed for Model A with a notch between −70 mm and 9 mm, a median equal to −14 mm and the outliers between −240 mm and 190 mm. SVR box plot (Figure 8b) showed similar results, with the exception of the Model E for which the SVR algorithm led to a narrower box plot in comparison with the M5P one. The narrowest box plots and the lowest outliers where, however, computed for the hybrid model M5P-SVR (Figure 8c) with a notch for Model A between −54 mm and 14 mm and a median equal to −11 mm.

## 5. Discussion

^{2}values up to 0.63. Pham et al. (2020) [20] model the short-term daily rainfall for the tropical climate of Vietnam, reaching R

^{2}values up to 0.69 with the SVR algorithms. Diez-Sierra and Jesus (2020) [21] for the long-term rainfall time series for semi-arid climates of Tenerife reached the best performances with a neural network model (R

^{2}= 0.30) and with an individual SVR algorithm (R

^{2}= 0.27).

^{2}values equal to 0.78 and −1.01, respectively. Mahmud et al. (2017) [54] developed a seasonal autoregressive integrated moving average (SARIMA) model for the monthly rainfall forecast for different Bangladesh stations. However, the performances for the Rangpur and Sylhet division were lower compared to the present study, with R

^{2}values equal to 0.76 and 0.75, respectively, against values up to 0.87 and 0.92 obtained with the hybrid model M5P-SVR. Navid and Niloy (2018) [55] also developed a multiple linear regression (MLR) model for the rainfall prediction of the Rajshahi Division, showing however low correlation coefficient, equal to 0.315, between predicted and measured precipitation.

^{2}values up to 0.87 and 0.92 for the stations of Rangpur and Sylhet, respectively.

## 6. Conclusions

^{2}), mean absolute error (MAE), root mean square error (RMSE), and relative absolute error (RAE). Box plots have been also employed to compare the predictions made with the different combinations of algorithms, exogenous inputs, and lag times. The hybrid model M5P-SVR outperformed both the individual M5P and SVR algorithms.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Murali, J.; Afifi, T. Rainfall variability, food security and human mobility in the Janjgir-Champa district of Chhattisgarh state, India. Clim. Dev.
**2014**, 6, 28–37. [Google Scholar] [CrossRef] - Lockart, N.; Willgoose, G.; Kuczera, G.; Kiem, A.S.; Chowdhury, A.K.; Parana Manage, N.; Twomey, C. Case study on the use of dynamically downscaled climate model data for assessing water security in the Lower Hunter region of the eastern seaboard of Australia. J. South. Hemisph. Earth Syst. Sci.
**2016**, 66, 177–202. [Google Scholar] [CrossRef] - Lehner, B.; Döll, P.; Alcamo, J.; Henrichs, T.; Kaspar, F. Estimating the impact of global change on flood and drought risks in Europe: A continental, integrated analysis. Clim. Chang.
**2006**, 75, 273–299. [Google Scholar] [CrossRef] - Kang, J.; Wang, H.; Yuan, F.; Wang, Z.; Huang, J.; Qiu, T. Prediction of Precipitation Based on Recurrent Neural Networks in Jingdezhen, Jiangxi Province, China. Atmosphere
**2020**, 11, 246. [Google Scholar] [CrossRef] [Green Version] - Chiang, Y.M.; Chang, L.C.; Jou, B.J.D.; Lin, P.F. Dynamic ANN for precipitation estimation and forecasting from radar observations. J. Hydrol.
**2007**, 334, 250–261. [Google Scholar] [CrossRef] - Grecu, M.; Krajewski, W.F. A large-sample investigation of statistical procedures for radar-based short-term quantitative precipitation forecasting. J. Hydrol.
**2000**, 239, 69–84. [Google Scholar] [CrossRef] - Peleg, N.; Ben-Asher, M.; Morin, E. Radar subpixel-scale rainfall variability and uncertainty: Lessons learned from observations of a dense rain-gauge network. Hydrol. Earth Syst. Sci.
**2013**, 17, 2195–2208. [Google Scholar] [CrossRef] [Green Version] - Morin, E.; Krajewski, W.F.; Goodrich, D.C.; Gao, X.; Sorooshian, S. Estimating rainfall intensities from weather radar data: The scale-dependency problem. J. Hydrometeorol.
**2003**, 4, 782–797. [Google Scholar] [CrossRef] [Green Version] - Barszcz, M.P. Quantitative rainfall analysis; flow simulation for an urban catchment using input from a weather radar. Geomat. Nat.
**2019**, 10, 2129–2144. [Google Scholar] [CrossRef] - Dash, S.S.; Sahoo, B.; Raghuwanshi, N.S. Comparative Assessment of Model Uncertainties in Streamflow Estimation from a Paddy-Dominated Integrated Catchment Reservoir Command; AGU Fall Meeting: Washington, DC, USA, 2018; p. H43C-2386. [Google Scholar]
- Chen, C.; Zhang, Q.; Kashani, M.H.; Jun, C.; Bateni, S.M.; Band, S.S.; Dash, S.S.; Chau, K.W. Forecast of rainfall distribution based on fixed sliding window long short-term memory. Eng. Appl. Comput. Fluid Mech.
**2022**, 16, 248–261. [Google Scholar] [CrossRef] - Di Nunno, F.; Granata, F.; Gargano, R.; de Marinis, G. Prediction of spring flows using nonlinear autoregressive exogenous (NARX) neural network models. Environ. Monitor. Assess.
**2021**, 193, 350. [Google Scholar] [CrossRef] - Granata, F.; Di Nunno, F. Forecasting evapotranspiration in different climates using ensembles of recurrent neural networks. Agric. Water Manag.
**2021**, 255, 107040. [Google Scholar] [CrossRef] - Fathi, M.; Kashani, M.H.; Jameii, S.M.; Mahdipour, E. Big Data Analytics in Weather Forecasting: A Systematic Review. Arch. Comput. Methods Eng.
**2022**, 29, 1247–1275. [Google Scholar] [CrossRef] - Ramesh Babu, N.; Bandreddy Anand Babu, C.; Dhanikar, P.R.; Medda, G. Comparison of ANFIS and ARIMA Model for Weather Forecasting. Indian J. Sci. Technol.
**2015**, 8 (Suppl. S2), 70–73. [Google Scholar] [CrossRef] - Xiang, Y.; Gou, L.; He, L.; Xia, S.; Wang, W. A SVR–ANN combined model based on ensemble EMD for rainfall prediction. Appl. Soft Comput.
**2018**, 73, 874–883. [Google Scholar] [CrossRef] - Tran Anh, D.; Duc Dang, T.; Pham Van, S. Improved Rainfall Prediction Using Combined Pre-Processing Methods and Feed-Forward Neural Networks. J
**2019**, 2, 65–83. [Google Scholar] [CrossRef] [Green Version] - Danandeh Mehr, A.; Nourani, V.; Karimi Khosrowshahi, V.; Ghorbani, M.A. A hybrid support vector regression–firefly model for monthly rainfall forecasting. Int. J. Environ. Sci. Technol.
**2019**, 16, 335–346. [Google Scholar] [CrossRef] - Danandeh Mehr, A.; Jabarnejad, M.; Nourani, V. Pareto-optimal MPSA-MGGP: A new gene-annealing model for monthly rainfall forecasting. J. Hydrol.
**2019**, 571, 406–415. [Google Scholar] [CrossRef] - Pham, B.T.; Le, L.M.; Le, T.T.; Bui, K.T.T.; Le, V.M.; Ly, H.B.; Prakash, I. Development of Advanced Artificial Intelligence Models for Daily Rainfall Prediction. Atmos. Res.
**2020**, 237, 104845. [Google Scholar] [CrossRef] - Diez-Sierra, J.; Jesus, M.d. Long-term rainfall prediction using atmospheric synoptic patterns in semi-arid climates with statistical and machine learning methods. J. Hydrol.
**2020**, 586, 124789. [Google Scholar] [CrossRef] - Ghamariadyan, M.; Imteaz, M.A. A Wavelet Artificial Neural Network method for medium-term rainfall prediction in Queensland (Australia) and the comparisons with conventional methods. Int. J. Climatol.
**2021**, 41, E1396–E1416. [Google Scholar] [CrossRef] - Danandeh Mehr, A. Seasonal rainfall hindcasting using ensemble multi-stage genetic programming. Theor. Appl. Climatol.
**2021**, 143, 461–472. [Google Scholar] [CrossRef] - Jahan, C.S.; Mazumder, Q.H.; Islam, A.T.M.M.; Adham, M.I. Impact of irrigation in Barind area, NW Bangladesh—an evaluation based on the meteorological parameters and fluctuation trend in groundwater table. J. Geol. Soc. India
**2010**, 76, 134–142. [Google Scholar] [CrossRef] - Rahman, M.S.; Islam, A.R.M.T. Are precipitation concentration and intensity changing in Bangladesh overtimes? Analysis of the possible causes of changes in precipitation systems. Sci. Total Environ.
**2019**, 690, 370–387. [Google Scholar] [CrossRef] [PubMed] - Di Nunno, F.; de Marinis, G.; Gargano, R.; Granata, F. Tide prediction in the Venice Lagoon using Nonlinear Autoregressive Exogenous (NARX) neural network. Water
**2021**, 13, 1173. [Google Scholar] [CrossRef] - Coulibaly, P.; Anctil, F.; Aravena, R.; Bobee, B. Artificial neural network modeling of water table depth fluctuations. Water Resour. Res.
**2001**, 37, 885–896. [Google Scholar] [CrossRef] - Guzman, S.M.; Paz, J.O.; Tagert, M.L.M.; Mercer, A.E. Evaluation of seasonally classified inputs for the prediction of daily groundwater levels: NARX networks vs support vector machines. Environ. Model. Assess.
**2019**, 24, 223–234. [Google Scholar] [CrossRef] - Mohammadi, B.; Mehdizadeh, S.; Ahmadi, F.; Lien, N.T.T.; Linh, N.T.T.; Pham, Q.B. Developing hybrid time series and artificial intelligence models for estimating air temperatures. Stoch. Environ. Res. Risk Assess.
**2021**, 35, 1189–1204. [Google Scholar] [CrossRef] - Di Nunno, F.; Granata, F. Groundwater level prediction in Apulia region (Southern Italy) using NARX neural network. Environ. Res.
**2020**, 190, 110062. [Google Scholar] [CrossRef] - Di Nunno, F.; Granata, F.; Gargano, R.; de Marinis, G. Forecasting of Extreme Storm Tide Events Using NARX Neural Network-Based Models. Atmosphere
**2021**, 12, 512. [Google Scholar] [CrossRef] - Quinlan, J.R. Learning with continuous classes. In Proceedings of the 5th Australian Joint Conference on Artificial Intelligence, Hobart, Australia, 16–18 November 1992; pp. 343–348. [Google Scholar]
- Granata, F.; Di Nunno, F. Artificial Intelligence models for prediction of the tide level in Venice. Stoch. Environ. Res. Risk Assess.
**2021**, 35, 2537–2548. [Google Scholar] [CrossRef] - Cortes, C.; Vapnik, V. Support-vector networks. Mach. Learn.
**1995**, 20, 273–297. [Google Scholar] [CrossRef] - Vapnik, V. Statistical Learning Theory; J. Wiley: New York, NY, USA, 1998. [Google Scholar]
- Collobert, R.; Bengio, S. SVMTorch: Support vector machines for large-scale regression problems. J. Mach. Learn. Res.
**2001**, 1, 143–160. [Google Scholar] - Granata, F.; Di Nunno, F. Air Entrainment in Drop Shafts: A Novel Approach Based on Machine Learning Algorithms and Hybrid Models. Fluids
**2022**, 7, 20. [Google Scholar] [CrossRef] - Kittler, J.; Hatef, M.; Duin, R.P.W.; Matas, J. On Combining Classifiers. IEEE Trans. Pattern Anal. Mach. Intell.
**1998**, 20, 226–239. [Google Scholar] [CrossRef] [Green Version] - Gandhi, I.; Pandey, M. Hybrid Ensemble of classifiers using voting. In Proceedings of the 2015 International Conference on Green Computing and Internet of Things (ICGCIoT), Greater Noida, India, 8–10 October 2015; pp. 399–404. [Google Scholar] [CrossRef]
- Adnan, R.M.; Mostafa, R.R.; Kisi, O.; Yaseen, Z.; Shahid, S.; Zounemat-Kermani, M. Improving streamflow prediction using a new hybrid ELM model combined with hybrid particle swarm optimization and grey wolf optimization. Knowl.-Based Syst.
**2021**, 230, 107379. [Google Scholar] [CrossRef] - Kilinc, H.C. Daily Streamflow Forecasting Based on the Hybrid Particle Swarm Optimization and Long Short-Term Memory Model in the Orontes Basin. Water
**2022**, 14, 490. [Google Scholar] [CrossRef] - Xu, Y.; Hu, C.; Wu, Q.; Jian, S.; Li, Z.; Chen, Y.; Zhang, G.; Zhang, Z.; Wang, S. Research on Particle Swarm Optimization in LSTM Neural Networks for Rainfall-Runoff Simulation. J. Hydrol.
**2022**, 608, 127553. [Google Scholar] [CrossRef] - Kennedy, J.; Eberhart, R.C. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neutral Networks, Perth, Australia, 27 November–1 December 1995; pp. 1942–1948. [Google Scholar]
- Zhang, F.; Dai, H.; Tang, D. A Conjunction Method of Wavelet Transform-Particle Swarm Optimization-Support Vector Machine for Streamflow Forecasting. J. Appl. Math.
**2014**, 2014, 910196. [Google Scholar] [CrossRef] - Tien Bui, D.; Shirzadi, A.; Amini, A.; Shahabi, H.; Al-Ansari, N.; Hamidi, S.; Singh, S.K.; Thai Pham, B.; Ahmad, B.B.; Ghazvinei, P.T. A Hybrid Intelligence Approach to Enhance the Prediction Accuracy of Local Scour Depth at Complex Bridge Piers. Sustainability
**2020**, 12, 1063. [Google Scholar] [CrossRef] [Green Version] - Feng, Z.K.; Niu, W.J.; Tang, Z.Y.; Jiang, Z.Q.; Xu, Y.; Liu, Y.; Zhang, H.R. Monthly runoff time series prediction by variational mode decomposition and support vector machine. based on quantum-behaved particle swarm optimization. J. Hydrol.
**2020**, 583, 124627. [Google Scholar] [CrossRef] - Danandeh Mehr, A.; Gandomi, A.H. MSGP-LASSO: An improved multi-stage genetic programming model for streamflow prediction. Inf. Sci.
**2021**, 561, 181–195. [Google Scholar] [CrossRef] - Dabral, P.P.; Murry, M.Z. Modelling and Forecasting of Rainfall Time Series Using SARIMA. Environ. Process.
**2017**, 4, 399–419. [Google Scholar] [CrossRef] - Alsumaiei, A.A. A Nonlinear Autoregressive Modeling Approach for Forecasting Groundwater Level Fluctuation in Urban Aquifers. Water
**2020**, 12, 820. [Google Scholar] [CrossRef] [Green Version] - Di Nunno, F.; Race, M.; Granata, F. A nonlinear autoregressive exogenous (NARX) model to predict nitrate concentration in rivers. Environ. Sci. Pollut. Res.
**2022**. [Google Scholar] [CrossRef] - Iannello, J.P. Time Delay Estimation Via Cross-Correlation in the Presence of Large Estimation Errors. IEEE Trans. Signal Process.
**1982**, 30, 998–1003. [Google Scholar] [CrossRef] [Green Version] - Chowdhury, A.F.M.K.; Kar, K.K.; Shahid, S.; Chowdhury, R.; Rashid, M.D.M. Evaluation of Spatio-temporal Rainfall Variability and Performance of a Stochastic Rainfall Model in Bangladesh. Int. J. Climatol.
**2019**, 39, 4256–4273. [Google Scholar] [CrossRef] - Rahman, M.; Islam, A.H.M.S.; Nadvi, S.Y.M.; Rahman, R.M. Comparative Study of ANFIS and ARIMA Model for Weather Forecasting in Dhaka. In Proceedings of the 2013 International Conference on Informatics, Electronics and Vision (ICIEV), Dhaka, Bangladesh, 17–18 May 2013; pp. 1–6. [Google Scholar] [CrossRef]
- Mahmud, I.; Bari, S.H.; Rahman, M.T.U. Monthly rainfall forecast of Bangladesh using autoregressive integrated moving average method. Environ. Eng. Res.
**2017**, 22, 162–168. [Google Scholar] [CrossRef] [Green Version] - Navid, M.A.I.; Niloy, N.H. Multiple Linear Regressions for Predicting Rainfall for Bangladesh. Communications
**2018**, 6, 1–4. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Location of the stations: with a representation of the Bangladesh divisions (

**a**); with the elevation in meter above the sea level (

**b**).

**Figure 4.**XCF between precipitation and: maximum temperature (

**a**); minimum temperature (

**b**); relative humidity (

**c**); wind speed (

**d**); cloud coverage (

**e**); bright sunshine (

**f**).

**Figure 6.**Rangpur station–M5P-SVR, t

_{a}= 1 month–Measured vs. predicted precipitation (on the

**left**): Training stage—Model A (

**a**), Training stage—Model E (

**c**), Testing stage—Model A (

**e**), Testing stage—Model E (

**g**); time series with the measured and predicted precipitation (on the

**right**): Training stage—Model A (

**b**), Training stage—Model E (

**d**), Testing stage—Model A (

**f**), Testing stage—Model E (

**h**).

**Figure 7.**Sylhet station–M5P-SVR, t

_{a}= 1 month–Measured vs. predicted precipitation (on the

**left**): Training stage—Model A (

**a**), Training stage—Model E (

**c**), Testing stage—Model A (

**e**), Testing stage—Model E (

**g**); time series with the measured and predicted precipitation (on the

**right**): Training stage—Model A (

**b**), Training stage—Model E (

**d**), Testing stage—Model A (

**f**), Testing stage—Model E (

**h**).

Model | Exogenous Inputs |
---|---|

A | T_{max}, T_{min}, H, V_{wind}, C, S |

B | H, V_{wind}, C, S |

C | T_{max}, T_{min}, H, V_{wind} |

D | H, V_{wind} |

E | H |

Variable | Rangpur | Sylhet | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Mean | σ | CV | Max | Min | Mean | σ | CV | Max | Min | |

T_{max} (°C) | 32.9 | 3.6 | 0.11 | 43.3 | 21.6 | 33.2 | 2.8 | 0.08 | 39.6 | 25.8 |

T_{min} (°C) | 19.9 | 5.5 | 0.28 | 27.7 | 7.3 | 20.3 | 4.5 | 0.22 | 26.3 | 10.6 |

P (mm) | 179.1 | 203.9 | 1.14 | 1344.0 | 0.0 | 333.7 | 336.3 | 1.01 | 1394.0 | 0.0 |

H (%) | 80.6 | 7.1 | 0.09 | 92.0 | 40.0 | 78.7 | 8.1 | 0.10 | 93.0 | 47.0 |

V_{wind} (m/s) | 1.2 | 0.6 | 0.50 | 3.3 | 0.2 | 1.5 | 0.7 | 0.47 | 5.4 | 0.3 |

C (okta) | 3.3 | 2.0 | 0.61 | 7.2 | 0.1 | 4.3 | 2.2 | 0.51 | 7.7 | 0.3 |

S (hours) | 6.4 | 1.5 | 0.23 | 10.8 | 1.7 | 6.3 | 2.0 | 0.32 | 10.6 | 0.0 |

Stage | t_{a} | Algorithm | Metrics | Model | ||||
---|---|---|---|---|---|---|---|---|

A | B | C | D | E | ||||

Training | 1 month | M5P | R^{2} | 0.88 | 0.85 | 0.87 | 0.80 | 0.79 |

MAE (mm) | 47 | 53 | 48 | 64 | 67 | |||

RMSE (mm) | 71 | 77 | 73 | 86 | 90 | |||

RAE (%) | 28.05 | 30.88 | 28.04 | 37.55 | 39.59 | |||

SVR | R^{2} | 0.85 | 0.79 | 0.85 | 0.78 | 0.77 | ||

MAE (mm) | 51 | 61 | 52 | 62 | 65 | |||

RMSE (mm) | 75 | 88 | 78 | 89 | 92 | |||

RAE (%) | 30.13 | 35.55 | 30.09 | 37.05 | 38.12 | |||

M5P-SVR | R^{2} | 0.89 | 0.87 | 0.87 | 0.80 | 0.79 | ||

MAE (mm) | 47 | 49 | 47 | 62 | 64 | |||

RMSE (mm) | 68 | 71 | 71 | 85 | 88 | |||

RAE (%) | 27.42 | 28.31 | 27.52 | 36.44 | 37.98 | |||

3 months | M5P | R^{2} | 0.88 | 0.84 | 0.87 | 0.79 | 0.78 | |

MAE (mm) | 48 | 54 | 49 | 65 | 69 | |||

RMSE (mm) | 71 | 78 | 73 | 86 | 89 | |||

RAE (%) | 28.22 | 31.48 | 28.24 | 38.25 | 40.69 | |||

SVR | R^{2} | 0.85 | 0.77 | 0.84 | 0.76 | 0.74 | ||

MAE (mm) | 52 | 62 | 52 | 65 | 67 | |||

RMSE (mm) | 76 | 91 | 78 | 94 | 95 | |||

RAE (%) | 30.33 | 36.46 | 30.35 | 38.42 | 39.52 | |||

M5P-SVR | R^{2} | 0.89 | 0.87 | 0.87 | 0.79 | 0.78 | ||

MAE (mm) | 47 | 49 | 47 | 63 | 66 | |||

RMSE (mm) | 69 | 71 | 71 | 87 | 90 | |||

RAE (%) | 27.50 | 28.73 | 27.50 | 37.20 | 39.25 | |||

Testing | 1 month | M5P | R^{2} | 0.86 | 0.82 | 0.86 | 0.80 | 0.72 |

MAE (mm) | 69 | 75 | 69 | 83 | 84 | |||

RMSE (mm) | 96 | 91 | 96 | 95 | 103 | |||

RAE (%) | 41.99 | 44.84 | 42.02 | 48.64 | 49.41 | |||

SVR | R^{2} | 0.84 | 0.79 | 0.83 | 0.78 | 0.78 | ||

MAE (mm) | 66 | 74 | 67 | 79 | 79 | |||

RMSE (mm) | 91 | 94 | 92 | 97 | 98 | |||

RAE (%) | 40.51 | 43.73 | 41.05 | 46.46 | 46.89 | |||

M5P-SVR | R^{2} | 0.87 | 0.82 | 0.86 | 0.80 | 0.79 | ||

MAE (mm) | 62 | 73 | 65 | 76 | 79 | |||

RMSE (mm) | 88 | 91 | 89 | 92 | 94 | |||

RAE (%) | 38.09 | 43.15 | 39.65 | 45.04 | 46.56 | |||

3 months | M5P | R^{2} | 0.86 | 0.82 | 0.86 | 0.79 | 0.72 | |

MAE (mm) | 69 | 75 | 69 | 86 | 87 | |||

RMSE (mm) | 97 | 93 | 97 | 98 | 104 | |||

RAE (%) | 42.35 | 50.81 | 42.39 | 44.35 | 51.70 | |||

SVR | R^{2} | 0.83 | 0.79 | 0.83 | 0.77 | 0.77 | ||

MAE (mm) | 67 | 75 | 68 | 82 | 83 | |||

RMSE (mm) | 92 | 95 | 92 | 99 | 100 | |||

RAE (%) | 40.81 | 44.83 | 41.40 | 48.38 | 49.05 | |||

M5P-SVR | R^{2} | 0.87 | 0.82 | 0.86 | 0.80 | 0.78 | ||

MAE (mm) | 63 | 75 | 65 | 78 | 83 | |||

RMSE (mm) | 89 | 93 | 90 | 93 | 96 | |||

RAE (%) | 38.45 | 44.25 | 39.71 | 46.16 | 48.94 |

Stage | t_{a} | Algorithm | Metrics | Model | ||||
---|---|---|---|---|---|---|---|---|

A | B | C | D | E | ||||

Training | 1 month | M5P | R^{2} | 0.92 | 0.90 | 0.91 | 0.89 | 0.88 |

MAE (mm) | 62 | 68 | 66 | 73 | 84 | |||

RMSE (mm) | 85 | 95 | 92 | 102 | 114 | |||

RAE (%) | 21.14 | 24.21 | 22.98 | 25.32 | 28.87 | |||

SVR | R^{2} | 0.90 | 0.86 | 0.88 | 0.84 | 0.84 | ||

MAE (mm) | 62 | 75 | 68 | 81 | 88 | |||

RMSE (mm) | 89 | 106 | 98 | 116 | 124 | |||

RAE (%) | 21.45 | 25.95 | 23.54 | 28.42 | 30.30 | |||

M5P-SVR | R^{2} | 0.94 | 0.93 | 0.93 | 0.91 | 0.88 | ||

MAE (mm) | 55 | 59 | 58 | 64 | 82 | |||

RMSE (mm) | 76 | 84 | 83 | 91 | 112 | |||

RAE (%) | 18.64 | 20.67 | 20.28 | 22.38 | 28.28 | |||

3 months | M5P | R^{2} | 0.92 | 0.90 | 0.91 | 0.89 | 0.88 | |

MAE (mm) | 63 | 70 | 67 | 75 | 86 | |||

RMSE (mm) | 85 | 97 | 93 | 104 | 118 | |||

RAE (%) | 21.50 | 24.38 | 23.30 | 26.48 | 34.30 | |||

SVR | R^{2} | 0.89 | 0.85 | 0.88 | 0.84 | 0.84 | ||

MAE (mm) | 64 | 75 | 69 | 82 | 90 | |||

RMSE (mm) | 90 | 108 | 99 | 117 | 126 | |||

RAE (%) | 21.89 | 26.24 | 24.08 | 28.77 | 30.64 | |||

M5P-SVR | R^{2} | 0.94 | 0.92 | 0.92 | 0.90 | 0.88 | ||

MAE (mm) | 56 | 62 | 60 | 69 | 85 | |||

RMSE (mm) | 78 | 85 | 85 | 95 | 114 | |||

RAE (%) | 19.12 | 21.37 | 20.83 | 24.35 | 28.99 | |||

Testing | 1 month | M5P | R^{2} | 0.91 | 0.87 | 0.87 | 0.87 | 0.85 |

MAE (mm) | 77 | 83 | 83 | 89 | 102 | |||

RMSE (mm) | 99 | 113 | 111 | 121 | 133 | |||

RAE (%) | 28.60 | 31.13 | 31.16 | 33.27 | 35.96 | |||

SVR | R^{2} | 0.91 | 0.84 | 0.86 | 0.82 | 0.82 | ||

MAE (mm) | 69 | 78 | 73 | 83 | 92 | |||

RMSE (mm) | 92 | 106 | 99 | 118 | 125 | |||

RAE (%) | 25.38 | 27.58 | 27.39 | 31.74 | 34.08 | |||

M5P-SVR | R^{2} | 0.92 | 0.89 | 0.89 | 0.88 | 0.85 | ||

MAE (mm) | 68 | 73 | 73 | 77 | 86 | |||

RMSE (mm) | 91 | 99 | 99 | 107 | 119 | |||

RAE (%) | 25.26 | 27.45 | 27.12 | 29.34 | 31.84 | |||

3 months | M5P | R^{2} | 0.90 | 0.87 | 0.87 | 0.85 | 0.83 | |

MAE (mm) | 80 | 86 | 87 | 92 | 106 | |||

RMSE (mm) | 103 | 117 | 117 | 130 | 147 | |||

RAE (%) | 29.31 | 32.26 | 32.63 | 34.79 | 37.70 | |||

SVR | R^{2} | 0.90 | 0.84 | 0.87 | 0.83 | 0.82 | ||

MAE (mm) | 70 | 80 | 75 | 86 | 93 | |||

RMSE (mm) | 93 | 108 | 102 | 116 | 126 | |||

RAE (%) | 25.86 | 28.03 | 27.95 | 32.03 | 34.37 | |||

M5P-SVR | R^{2} | 0.91 | 0.87 | 0.88 | 0.86 | 0.83 | ||

MAE (mm) | 69 | 75 | 74 | 79 | 89 | |||

RMSE (mm) | 93 | 102 | 100 | 109 | 122 | |||

RAE (%) | 25.57 | 27.94 | 27.73 | 30.07 | 32.87 |

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## Share and Cite

**MDPI and ACS Style**

Di Nunno, F.; Granata, F.; Pham, Q.B.; de Marinis, G.
Precipitation Forecasting in Northern Bangladesh Using a Hybrid Machine Learning Model. *Sustainability* **2022**, *14*, 2663.
https://doi.org/10.3390/su14052663

**AMA Style**

Di Nunno F, Granata F, Pham QB, de Marinis G.
Precipitation Forecasting in Northern Bangladesh Using a Hybrid Machine Learning Model. *Sustainability*. 2022; 14(5):2663.
https://doi.org/10.3390/su14052663

**Chicago/Turabian Style**

Di Nunno, Fabio, Francesco Granata, Quoc Bao Pham, and Giovanni de Marinis.
2022. "Precipitation Forecasting in Northern Bangladesh Using a Hybrid Machine Learning Model" *Sustainability* 14, no. 5: 2663.
https://doi.org/10.3390/su14052663