# Runoff Estimation Using Advanced Soft Computing Techniques: A Case Study of Mangla Watershed Pakistan

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

^{†}

## Abstract

**:**

^{2}), and Nash–Sutcliffe efficiency (NSE). The outcomes of these computing techniques were evaluated with the multilayer perceptron (MLP). DTF was found to be a more accurate soft computing approach with the average evaluation parameters R

^{2}, NSE, RMSE, and MAE being 0.9, 0.8, 1000, and 7000 cumecs. Regarding R

^{2}and RMSE, there are about 57% and 17% of improvement in the results of DTF compared to other techniques. Flow duration curves (FDCs) were employed and revealed that DTF performed better than other techniques. This assessment revealed that DTF has potential; researchers may consider it an alternative approach for rainfall-runoff estimations in the Mangla watershed.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Single Decision Trees (SDTs)

^{(k−1)−1}

^{k}

#### 2.2. Decision Tree Forests (DTFs)

#### 2.3. Tree Boost (TB)

#### 2.4. Multi-Layer Perceptron (MLP)

#### 2.5. Study Area

^{2}, making it the second-largest tributary in the world after the Indus basin [22]. The Mangla watershed is situated on the Jhelum River and has a storage capacity of 7.475 MAF and a drainage area of 33,333.15 km

^{2}. The runoff of the Jhelum River basin drains into the Mangla watershed. This catchment supplies irrigation and hydropower with water. Six million hectares of land are irrigated from this reservoir as part of a 1000 MW hydroelectric power-producing capability. The Jhelum and its tributaries, Neelam, Poonch, Kanshi, and Naran, make up the Mangla watershed. In the catchment area, precipitation and snowmelt generated runoff, representing the reservoir’s intake. The water stored in various basins, such as the Neelam, Poonch, Kanshi, Jhelum, and Naran basin, will flow to the river Jhelum as runoff at the Mangla catchment.

#### 2.6. Dataset

#### 2.7. Performance Evaluation

^{2}is between 0 and 1. The model will be considered the most efficient when the correlation coefficient value approaches 1 or is equal to 1. The range of model efficiency RMSE values is between 0 and 1. The better the model, the lower the RMSE number, while the worse the model or data, the higher the RMSE value. Most hydrological studies provide NSE values as percentages [24,47]. In Equation (7), where m is the number of input–output training patterns, n is the number of parameters to be detected and RMSE is the root-mean-square error between the network output and target. The RMSE statistics are predicted to improve when more parameters are introduced to a model, whereas the AIC statistics punish the model for having more parameters and, as a result, tend to produce more parsimonious models [48].

## 3. Results

^{2}was 57%; for RMSE, it was found to be a 17% improvement.

^{2}and NSE values for DTF training and testing range between 0.24 to 0.32. The RMSE and MAE are approximately 24,000 and 19,000 cumecs. R

^{2}and NSE values for SDT are between 0.10 and 0.11 to 1 for training and testing. The figures for RMSE and MAE range between 27,000 and 20,000 cumecs. R

^{2}and NSE range between 0.15 and 0.10 for TB, whereas the other statistical measures, RMSE, and MAE, range between 26,000 and 19,000 cumecs. The typical technique MLP has a training and testing value of 0.15 for both R

^{2}and NSE.

^{2}and NSE for the DTFs fall in the range of 0.5 to 0.6, while the values calculated for RMSE and MAE are approximately 14,000 to 20,000 cumecs. The values of R

^{2}and NSE for SDTs are both 0.20, regardless of whether the model is being trained or tested, whereas the values of RMSE and MAE range between 25,000 and 19,000 cumecs. The TB values for R

^{2}and NSE are 0.20 and 0.18, respectively. RMSE and MAE both perform at a level of 25,000 to 18,000 cumecs. Both the training and testing phases of the MLP have R

^{2}and NSE values of 0.17 and 0.18, respectively. In the case of MLP, the performance evaluation of RMSE and MAE ranges from around 26,000 to 20,000 cumecs. All these results from Table 4 indicate that MLP is less efficient for analyzing runoff when a combination of the three is used. Table 5 shows that the values of R

^{2}and NSE are determined within the range of 0.6 to 0.7 for both training and validation for the DTFs. RMSE and MAE both have values that range between 16,000 and 12,000 cumecs. The values of R

^{2}and NSE are the same, with a value of 0.20, for both the training and the testing phases. RMSE and MAE both have performances that fall somewhere in the range of 25,000 to 18,000 cumecs. For TB, the values for R

^{2}and NSE range from 0.21 to 0.19 for training and testing analyses, whereas the values range from around 25,000 to 20,000 cumecs for RMSE and MAE. Table 8 shows that the values of R

^{2}and NSE for DTFs range from 0.86 to 0.81, while RMSE and MAE are between 13,000 and 9000 cumecs. SDTs show 0.25 for R

^{2}and NSE, but 25,000 and 19,000 cumecs for RMSE and MAE. TB’s training and testing NSE and R

^{2}are 0.23 and 0.18, respectively. RMSE and MAE for TB ranges from 25,000 and 18,000 cumecs. MLP has the same values, 0.19 for R

^{2,}NSE, and 25,000 and 19,000 cumecs for RMSE and MAE. The findings in Table 7 indicate that the DTF is a more effective solution than SDT, TB, and MLP. The training and testing stages produce R

^{2}and NSE values for the DTF in the range of 0.89 and 0.83, while the RMSE and MSE values produce 13,000 and 9000 cumecs, respectively. In the SDT, 0.25 is specified for R

^{2}, and the exact value is specified for NSE. RMSE and MAE are between 25,000 and 19,000 cumecs. R

^{2}is found to be 0.26 using the TB technique, and NSE is 0.27. The final RMSE and MAE values fall somewhere in a range that goes from 24,000 to 17,000 cumecs. The exact value of 0.17 is shown for MLP’s R

^{2}and NSE. In contrast, RMSE and MAE range from 20,000 and 25,000 cumecs, respectively. Table 8 shows that R

^{2}and NSE for DTFs are between 0.90 and 0.80. RMSE and MAE are 12,000 and 9000 cumecs. SDTs and TB have a 0.25 square correlation and NSE. RMSE and MAE are 250,000 and 180,000 cumecs. 0.20 is MLP’s R

^{2}and NSE. RMSE and MAE range from 25,000 to 19,000 cumecs. MLP is underestimated compared to DTFs, TB, and SDTs. MLP has a lower potential than other techniques. Table 9 reveals that the R

^{2}and NSE values for DTFs are in the region of 0.9 to 0.8, giving it an advantage over TB, SDTs, and MLP. It is evidenced by the fact that DTFs come out on top. The results for RMSE and MAE range between 10,000 and 8000 cumecs. R

^{2}and NSE have 0.25 and 0.27 for SDTs, whereas RMSE and MAE have 25,000 and 17,000 cumecs, respectively. TB has an R

^{2}value of 0.35 and an NSE value of 0.30. Its RMSE value is 24,000 cumecs and its MAE value is 16,000 cumecs. The minimum likelihood proportionate has the lowest value of any statistical parameter. These are the results for R

^{2}, NSE, RMSE, and MAE: 0.20, 0.18, 26,000, and 18,000 cumecs, respectively. The DTFs models were the most accurate based on the R

^{2}, and NSE values lie between 0.9 and 0.8, as shown in Table 10. The RMSE and the MAE come in at 10,000 cumecs and 7000 cumecs, respectively. R

^{2}values of 0.30 and NSE values of 0.27 are comparable for SDTs and TB, whereas RMSE values of 24,000 cumecs and MAE values of 17,000 cumecs are reported for each. The MLP model has a value of 0.19 for R

^{2}and a comparable amount for NSE. However, the RMSE value is 25,000 cumecs and the MAE value is 19,000 cumecs.

^{2}, NSE, MAE, and RMSE for each input combination for the best DTFs model to examine the effect of the previously mentioned input combinations.

^{2}across input combinations. Figure 8a shows an increase in R

^{2}values from input combination 1 with a single P(t) precipitation value to input combination 4, which has P(t), P(t-1), P(t-2), and P(t-3) precipitation data, followed by a constant value. Figure 8b shows a similar pattern for NSE fluctuations. Similarly, Figure 8a,b illustrates the fluctuation of RMSE and MAE, respectively, with selected input combination changes. (c) depicts the overall RMSE and MAE values. Figure 8a,b demonstrates a significant reduction in error values from input combinations up to the input combination, which is consistent with the R

^{2}and NSE values (4). According to the findings, it is possible to assert that the precipitation P(t), P(t-1), P(t-2), and P(t-3) contain complete data about the watershed’s hydrological signature and that there is no vital information hidden in the lag precipitation data. This assertion can be supported by stating that the lag precipitation data do not contain any relevant information.

## 4. Discussion

^{2}and NSE discovered during the training and testing of models were found to be more than other techniques, as shown in Table 5, Table 6, Table 7, Table 8, Table 9 and Table 10. The percent of improvement in terms of R

^{2}and RMSE in the outputs of DTFs up to the maximum value of 57% and 17%, respectively, compared to other techniques. Many researchers quoted that results from DTFs are generally equal to 1 and many others [22,49,50]. R

^{2}is one of the most significant model evaluation criteria that many hydrologists and researchers have found and utilized for predicting and forecasting the behavior of various hydrological cycle components [30]. The RMSE findings of all the different input combinations demonstrated that the DTFs have a higher ability to predict rainfall and runoff than SDTs and TB while the models are being trained and tested. The reduced value of the root-mean-square error (RMSE) demonstrates that the model is accurate [51]. DTFs and SDTs were previously used for streamflow forecasting and showed good potential [22]. In Figure 8a,b, TB and SDTs demonstrated the most effective results of 1.00 in training modeling techniques at all stations, according to the NSE results for both train and test cases of soft computing techniques. SDTs, TB, and MLP showed less efficient results. The higher NSE value shows the models’ efficiency [52]. Figure 8a,b shows that the DTF has better runoff prediction than SDT and TB, according to RMSE values. DTF is a more effective MLP than the conventional one [22]. A smaller value of the RMSE indicates the model’s fitness [53]. So, the DTFs are the most effective technique for rainfall and runoff prediction for the Mangla watershed, according to NSE results previously mentioned by [54]. Figure 9 shows that hydrographs of the low, medium, and high streams were made using soft computing techniques such as SDTs, DTFs, and MLP to analyze their capability. These techniques were used to create the hydrographs. DTFs have good potential for predicting runoff. For the evaluation of catchment features, the lower and upper regions of the FDCs are essential parts. The low flow component of the FDC indicates how well the catchment can support itself during hot and dry weather. The catchment is likely to have the flood regime indicated by the high flow portion [7,15].

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

TB | Tree Boost |

DTFs | Decision tree forests |

SDTs | Single decision trees |

MLP | Multilayer perceptron |

RMSE | Root means square error |

MAE | Mean absolute error |

R^{2} | Coefficient of determination |

NSE | Nash–Sutcliffe efficiency |

FDCs | Flow duration curves |

ANN | Artificial neural network |

ANFIS | Adaptive neuro-fuzzy inference system |

GP | Genetic programming |

GEP | Gene expression programming |

SVM | Support vector machine |

BPA | Back-propagation algorithm |

RGA | Real-coded genetic algorithm |

SOM | Self-organizing map |

MCS | Monte Carlo simulation |

SORM | Simplified order reliability method |

FORM | First-order reliability method |

ME | misclassification error |

km^{2} | Square kilometers (area) |

MAF | Million acre feet (storage capacity) |

MW | Megawatts (electric power) |

°C | Degrees Celsius (temperature) |

Inches | Precipitation |

## References

- Nawaz, Z.; Li, X.; Chen, Y.; Guo, Y.; Wang, X. Temporal and Spatial Characteristics of Precipitation and Temperature in Punjab, Pakistan. Water
**2019**, 11, 1916. [Google Scholar] [CrossRef] [Green Version] - Fahad, S.; Wang, J. Climate change, vulnerability, and its impacts in rural Pakistan: A review. Environ. Sci. Pollut. Res.
**2020**, 27, 1334–1338. [Google Scholar] [CrossRef] [PubMed] - Asadi, S.; Shahrabi, J.; Abbaszadeh, P.; Tabanmehr, S. A new hybrid artificial neural networks for rainfall–runoff process modeling. Neurocomputing
**2013**, 121, 470–480. [Google Scholar] [CrossRef] - Waqas, M.; Saifullah, M.; Hashim, S.; Khan, M.; Muhammad, S. Evaluating the Performance of Different Artificial Intelligence Techniques for Forecasting: Rainfall and Runoff Prospective. In Weather Forecasting; IntechOpen: London, UK, 2021; p. 23. [Google Scholar]
- Gholami, V.; Sahour, H. Simulation of rainfall-runoff process using an artificial neural network (ANN) and field plots data. Theor. Appl. Climatol.
**2022**, 147, 87–98. [Google Scholar] [CrossRef] - Solomatine, D.; See, L.M.; Abrahart, R.J. Data-driven modelling: Concepts, approaches and experiences. In Practical Hydroinformatics; Abrahart, R.J., See, L.M., Solomatine, D.P., Eds.; Springer: Berlin/Heidelberg, Germany, 2009; pp. 17–30. [Google Scholar]
- Shoaib, M.; Shamseldin, A.Y.; Melville, B.W.; Khan, M.M. A comparison between wavelet based static and dynamic neural network approaches for runoff prediction. J. Hydrol.
**2016**, 535, 211–225. [Google Scholar] [CrossRef] - Verma, R. ANN-based Rainfall-Runoff Model and Its Performance Evaluation of Sabarmati River Basin, Gujarat, India. Water Conserv. Sci. Eng.
**2022**, 1–8. [Google Scholar] [CrossRef] - Nourani, V.; Baghanam, A.H.; Adamowski, J.; Kisi, O. Applications of hybrid wavelet–Artificial Intelligence models in hydrology: A review. J. Hydrol.
**2014**, 514, 358–377. [Google Scholar] [CrossRef] - Fama, E.F.; French, K.R. The Cross-Section of Expected Stock Returns. J. Financ.
**1992**, 47, 427–465. [Google Scholar] [CrossRef] - Jang, J.-S.R. ANFIS: Adaptive-Network-Based Fuzzy Inference System. IEEE Trans. Syst. Man Cybern.
**1993**, 23, 665–685. [Google Scholar] [CrossRef] - Koza, J.R. Evolution of subsumption using genetic programming. In Toward a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life; MIT Press: Cambridge, MA, USA, 1992. [Google Scholar]
- Savic, D.A.; Walters, G.A.; Davidson, J.W. A genetic programming approach to rainfall-runoff modelling. Water Resour. Manag.
**1999**, 13, 219–231. [Google Scholar] [CrossRef] - Joachims, T. Text categorization with Support Vector Machines: Learning with many relevant features. In Machine Learning: ECML-98; Springer: Berlin/Heidelberg, Germany, 1998; pp. 137–142. [Google Scholar]
- Shoaib, M.; Shamseldin, A.Y.; Melville, B.W. Comparative study of different wavelet based neural network models for rainfall–runoff modeling. J. Hydrol.
**2014**, 515, 47–58. [Google Scholar] [CrossRef] - Zounemat-Kermani, M.; Kisi, O.; Rajaee, T. Performance of radial basis and LM-feed forward artificial neural networks for predicting daily watershed runoff. Appl. Soft Comput.
**2013**, 13, 4633–4644. [Google Scholar] [CrossRef] - Srinivasulu, S.; Jain, A. A comparative analysis of training methods for artificial neural network rainfall–runoff models. Appl. Soft Comput.
**2006**, 6, 295–306. [Google Scholar] [CrossRef] - Setiono; Hadiani, R. Analysis of Rainfall-runoff Neuron Input Model with Artificial Neural Network for Simulation for Availability of Discharge at Bah Bolon Watershed. Procedia Eng.
**2015**, 125, 150–157. [Google Scholar] [CrossRef] [Green Version] - Elsafi, S.H. Artificial Neural Networks (ANNs) for flood forecasting at Dongola Station in the River Nile, Sudan. Alex. Eng. J.
**2014**, 53, 655–662. [Google Scholar] [CrossRef] - Farajzadeh, J.; Fard, A.F.; Lotfi, S. Modeling of monthly rainfall and runoff of Urmia lake basin using "feed-forward neural network" and "time series analysis" model. Water Resour. Ind.
**2014**, 7–8, 38–48. [Google Scholar] [CrossRef] [Green Version] - Napolitano, G.; See, L.; Calvo, B.; Savi, F.; Heppenstall, A. A conceptual and neural network model for real-time flood forecasting of the Tiber River in Rome. Phys. Chem. Earth Parts A/B/C
**2010**, 35, 187–194. [Google Scholar] [CrossRef] - Waqas, M.; Shoaib, M.; Saifullah, M.; Naseem, A.; Hashim, S.; Ehsan, F.; Ali, I.; Khan, A. Assessment of Advanced Artificial Intelligence Techniques for Streamflow Forecasting in Jhelum River Basin. Pak. J. Agric. Res.
**2021**, 33, 580–598. [Google Scholar] [CrossRef] - Rajurkar, M.; Kothyari, U.; Chaube, U. Modeling of the daily rainfall-runoff relationship with artificial neural network. J. Hydrol.
**2004**, 285, 96–113. [Google Scholar] [CrossRef] - Shamseldin, A.Y. Application of a neural network technique to rainfall-runoff modelling. J. Hydrol.
**1997**, 199, 272–294. [Google Scholar] [CrossRef] - Shin, M.-J.; Guillaume, J.H.A.; Croke, B.F.W.; Jakeman, A.J. A review of foundational methods for checking the structural identifiability of models: Results for rainfall-runoff. J. Hydrol.
**2015**, 520, 1–16. [Google Scholar] [CrossRef] - Tokar, A.S.; Johnson, P.A. Rainfall-Runoff Modeling Using Artificial Neural Networks. J. Hydrol. Eng.
**1999**, 4, 232–239. [Google Scholar] [CrossRef] - Wu, C.L.; Chau, K.W.; Fan, C. Prediction of rainfall time series using modular artificial neural networks coupled with data-preprocessing techniques. J. Hydrol.
**2010**, 389, 146–167. [Google Scholar] [CrossRef] [Green Version] - Devak, M.; Dhanya, C.; Gosain, A. Dynamic coupling of support vector machine and K-nearest neighbour for downscaling daily rainfall. J. Hydrol.
**2015**, 525, 286–301. [Google Scholar] [CrossRef] - He, Z.; Wen, X.; Liu, H.; Du, J. A comparative study of artificial neural network, adaptive neuro fuzzy inference system and support vector machine for forecasting river flow in the semiarid mountain region. J. Hydrol.
**2014**, 509, 379–386. [Google Scholar] [CrossRef] - Kisi, O.; Cimen, M. A wavelet-support vector machine conjunction model for monthly streamflow forecasting. J. Hydrol.
**2011**, 399, 132–140. [Google Scholar] [CrossRef] - Kundu, S.; Khare, D.; Mondal, A. Future changes in rainfall, temperature and reference evapotranspiration in the central India by least square support vector machine. Geosci. Front.
**2017**, 8, 583–596. [Google Scholar] [CrossRef] - Noori, R.; Karbassi, A.R.; Moghaddamnia, A.; Han, D.; Zokaei-Ashtiani, M.H.; Farokhnia, A.; Gousheh, M.G. Assessment of input variables determination on the SVM model performance using PCA, Gamma test, and forward selection techniques for monthly stream flow prediction. J. Hydrol.
**2011**, 401, 177–189. [Google Scholar] [CrossRef] - Rasouli, K.; Hsieh, W.W.; Cannon, A.J. Daily streamflow forecasting by machine learning methods with weather and climate inputs. J. Hydrol.
**2012**, 414–415, 284–293. [Google Scholar] [CrossRef] - Keskin, M.E.; Taylan, D.; Terzi, Ö. Adaptive neural-based fuzzy inference system (ANFIS) approach for modelling hydrological time series. Hydrol. Sci. J.
**2006**, 51, 588–598. [Google Scholar] [CrossRef] - Shoaib, M.; Shamseldin, A.Y.; Melville, B.W.; Khan, M.M. Runoff forecasting using hybrid Wavelet Gene Expression Programming (WGEP) approach. J. Hydrol.
**2015**, 527, 326–344. [Google Scholar] [CrossRef] - Quinlan, J.R. Simplifying decision trees. Int. J. Man-Mach. Stud.
**1987**, 27, 221–234. [Google Scholar] [CrossRef] [Green Version] - Preis, A.; Ostfeld, A. A coupled model tree–genetic algorithm scheme for flow and water quality predictions in watersheds. J. Hydrol.
**2008**, 349, 364–375. [Google Scholar] [CrossRef] - Etemad-Shahidi, A.; Mahjoobi, J. Comparison between M5′ model tree and neural networks for prediction of significant wave height in Lake Superior. Ocean Eng.
**2009**, 36, 1175–1181. [Google Scholar] [CrossRef] - Xu, M.; Watanachaturaporn, P.; Varshney, P.K.; Arora, M.K. Decision tree regression for soft classification of remote sensing data. Remote Sens. Environ.
**2005**, 97, 322–336. [Google Scholar] [CrossRef] - Deo, R.C.; Kisi, O.; Singh, V.P. Drought forecasting in eastern Australia using multivariate adaptive regression spline, least square support vector machine and M5Tree model. Atmos. Res.
**2017**, 184, 149–175. [Google Scholar] [CrossRef] [Green Version] - Clay, D.E.; Alverson, R.; Johnson, J.M.; Karlen, D.L.; Clay, S.; Wang, M.Q.; Bruggeman, S.; Westhoff, S. Crop Residue Management Challenges: A Special Issue Overview. Agron. J.
**2019**, 111, 1–3. [Google Scholar] [CrossRef] [Green Version] - Sherrod, P.H. DTREG Predictive Modeling Software; DTREG: Brentwood, TN, USA, 2003; Available online: http://www.dtreg.com (accessed on 30 December 2003).
- Sherrod, P. Classification and Regression Trees and Support Vector Machines for Predictive Modeling and Forecasting; DTREG: Brentwood, TN, USA, 2006; Available online: http://www.DTREG.com/DTREG.pdf (accessed on 30 December 2006).
- Friedman, J.; Hastie, T.; Tibshirani, R. Additive logistic regression: A statistical view of boosting (With discussion and a rejoinder by the authors). Ann. Stat.
**2000**, 28, 337–407. [Google Scholar] [CrossRef] - McGarry, K.; Wermter, S.; MacIntyre, J. Knowledge extraction from radial basis function networks and multilayer perceptrons. In Proceedings of the IJCNN’99, International Joint Conference on Neural Networks (Cat. No.99CH36339), Washington, DC, USA, 10–16 July 1999; IEEE: Piscataway, NJ, USA, 1999. [Google Scholar]
- Mahmood, R.; Babel, M.S. Evaluation of SDSM developed by annual and monthly sub-models for downscaling temperature and precipitation in the Jhelum basin, Pakistan and India. Theor. Appl. Climatol.
**2012**, 113, 27–44. [Google Scholar] [CrossRef] - Jacquin, A.P.; Shamseldin, A.Y. Development of rainfall–runoff models using Takagi–Sugeno fuzzy inference systems. J. Hydrol.
**2006**, 329, 154–173. [Google Scholar] [CrossRef] - Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control
**1974**, 19, 716–723. [Google Scholar] [CrossRef] - Tayyab, M.; Ahmad, I.; Sun, N.; Zhou, J.; Dong, X. Application of Integrated Artificial Neural Networks Based on Decomposition Methods to Predict Streamflow at Upper Indus Basin, Pakistan. Atmosphere
**2018**, 9, 494. [Google Scholar] [CrossRef] [Green Version] - Sharma, V.; Mishra, V.D.; Joshi, P.K. Implications of climate change on streamflow of a snow-fed river system of the Northwest Himalaya. J. Mt. Sci.
**2013**, 10, 574–587. [Google Scholar] [CrossRef] [Green Version] - 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] - Chai, T.; Draxler, R.R. Root mean square error (RMSE) or mean absolute error (MAE)?—Arguments against avoiding RMSE in the literature. Geosci. Model Dev.
**2014**, 7, 1247–1250. [Google Scholar] [CrossRef] [Green Version] - Archer, D.; Fowler, H. Using meteorological data to forecast seasonal runoff on the River Jhelum, Pakistan. J. Hydrol.
**2008**, 361, 10–23. [Google Scholar] [CrossRef] - Babur, M.; Babel, M.S.; Shrestha, S.; Kawasaki, A.; Tripathi, N.K. Assessment of Climate Change Impact on Reservoir Inflows Using Multi Climate-Models under RCPs—The Case of Mangla Dam in Pakistan. Water
**2016**, 8, 389. [Google Scholar] [CrossRef] [Green Version] - Hayat, H.; Akbar, T.A.; Tahir, A.A.; Hassan, Q.K.; Dewan, A.; Irshad, M. Simulating Current and Future River-Flows in the Karakoram and Himalayan Regions of Pakistan Using Snowmelt-Runoff Model and RCP Scenarios. Water
**2019**, 11, 761. [Google Scholar] [CrossRef] - Searcy, J.K. Flow-Duration Curves; US Government Printing Office: Washington, DC, USA, 1959. [Google Scholar]

**Figure 9.**(

**a**) FDCs between DTF, MLP and Qobs with input combination R(t). (

**b**) FDCs between DTF, MLP and Qobs with input combination R(t-3). (

**c**) FDCs between DTF, MLP and Qobs with input combination R(t-5). (

**d**) FDCs between DTF, MLP and Qobs with input combination R(t-8). (

**e**) FDCs between DTF, MLP and Qobs with input combination R(t-10).

Name of Station | Elevation (MSL) in Meters | Latitude | Longitude | Mean Yearly Precipitation (Inches) | Mean Yearly Temperature (°C) | Country |
---|---|---|---|---|---|---|

Naran | 2409 | 34.909° N | 73.6507° E | 1.83 | 19 | Pakistan |

Balakot | 975 | 34.548° N | 73.3532° E | 48.7 | 25.1 | Pakistan |

Muzaffarabad | 679 | 34.359° N | 73.47105° E | 45.67 | 27.6 | Pakistan |

Gharidopatta | 817 | 34.225° N | 73.6154° E | 3.85 | 25.9 | Pakistan |

Murree | 2291.2 | 33.907° N | 73.3943° E | 5.91 | 17.7 | Pakistan |

Plandri | 1400 | 33.715° N | 73.6861° E | 5.91 | 21.8 | Pakistan |

Kotli | 3000 | 33.518° N | 73.9022° E | 5.48 | 28.5 | Pakistan |

Rawlakot | 1638 | 33.866° N | 73.7666° E | 19.99 | 24.7 | Pakistan |

Kupwaara | 1522 | 34.033° N | 74.266° E | 42.00 | 13.9 | India |

Qazigund | 1670 | 33.624° N | 75.145° E | 3.30 | 27.0 | India |

Gulmerg | 2650 | 34.05° N | 74.38° E | 67.1 | 4.1 | India |

Sirinagar | 5000 | 34.083° N | 74.797° E | 32.5 | 11.8 | India |

Input Combinations | AIC |
---|---|

P(t) | 4.5432 |

P(t), P(t-1) | 4.2015 |

P(t), P(t-1), P(t-2) | 4.1534 |

P(t), P(t-1), P(t-2), P(t-3) | 3.9812 |

P(t), P(t-1), P(t-2), P(t-3), P(t-4) | 3.9678 |

P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5) | 3.9561 |

P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5), P(t-6) | 3.8911 |

P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5), P(t-6), P(t-7) | 3.6582 |

P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5), P(t-6), P(t-7), P(t-8) | 3.5121 |

P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5), P(t-6), P(t-7), P(t-8), P(t-9) | 3.3140 |

P(t), P(t-1), P(t-2), P(t-3), P(t-4), P(t-5), P(t-6), P(t-7), P(t-8), P(t-9), P(t-10) | 3.1480 |

Training Results with P(t) | Testing Results with P(t) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Model | R2 | NSE | RMSE | MAE | Model | R2 | NSE | RMSE | MAE |

DTFs | 0.329 | 0.322 | 25,905.668 | 20,441.804 | DTFs | 0.247 | 0.245 | 23,431.452 | 18,356.359 |

SDTs | 0.072 | 1.000 | 30,319.632 | 21,709.896 | SDTs | 0.116 | 0.116 | 25,354.221 | 19,403.642 |

TB | 0.169 | 0.164 | 28,804.129 | 20,771.767 | TB | 0.118 | 0.093 | 25,975.933 | 18,769.243 |

MLP | 0.145 | 0.144 | 29,107.893 | 21,653.686 | MLP | 0.163 | 0.163 | 24,671.509 | 19,676.838 |

Training Results with P(t-1) | Testing Results with P(t-1) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Model | R2 | NSE | RMSE | MAE | Model | R2 | NSE | RMSE | MAE |

DTFs | 0.607 | 0.573 | 20,552.859 | 16,087.144 | DTFs | 0.555 | 0.517 | 18,743.686 | 14,051.887 |

SDTs | 0.283 | 0.283 | 26,655.355 | 20,296.326 | SDTs | 0.143 | 0.143 | 24,957.492 | 18,966.122 |

TB | 0.247 | 0.234 | 27,574.589 | 19,787.896 | TB | 0.179 | 0.157 | 24,902.517 | 17,934.826 |

MLP | 0.202 | 0.201 | 28,125.942 | 21,264.919 | MLP | 0.150 | 0.149 | 24,873.708 | 19,182.440 |

Training Results with P(t-2) | Testing Results with P(t-2) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Model | R2 | NSE | RMSE | MAE | Model | R2 | NSE | RMSE | MAE |

DTFs | 0.721 | 0.670 | 18,066.618 | 13,873.521 | DTFs | 0.684 | 0.625 | 16,512.014 | 12,073.647 |

SDTs | 0.307 | 0.307 | 26,196.097 | 19,778.782 | SDTs | 0.180 | 0.180 | 24,422.021 | 18,304.985 |

TB | 0.254 | 0.242 | 27,432.893 | 19,339.867 | TB | 0.185 | 0.159 | 24,930.989 | 17,685.465 |

MLP | 0.214 | 0.214 | 27,899.405 | 20,915.020 | MLP | 0.138 | 0.137 | 25,058.222 | 19,672.974 |

Training Results with P(t-3) | Testing Results with P(t-3) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Model | R2 | NSE | RMSE | MAE | Model | R2 | NSE | RMSE | MAE |

DTFs | 0.861 | 0.812 | 13,654.807 | 9663.240 | DTFs | 0.829 | 0.776 | 12,776.157 | 8996.971 |

SDTs | 0.312 | 0.312 | 26,105.991 | 19,558.401 | SDTs | 0.184 | 0.184 | 24,360.689 | 18,264.990 |

TB | 0.257 | 0.246 | 27,367.762 | 19,095.066 | TB | 0.203 | 0.167 | 24,850.153 | 17,518.771 |

MLP | 0.217 | 0.217 | 27,850.550 | 20,693.155 | MLP | 0.164 | 0.160 | 24,717.335 | 19,418.675 |

Training Results with P(t-4) | Testing Results with P(t-4) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Model | R2 | NSE | RMSE | MAE | Model | R2 | NSE | RMSE | MAE |

DTFs | 0.892 | 0.838 | 12,669.483 | 8868.312 | DTFs | 0.863 | 0.803 | 11,980.313 | 8415.763 |

SDTs | 0.294 | 0.294 | 26,447.197 | 19,776.773 | SDTs | 0.200 | 0.200 | 24,118.012 | 18,123.016 |

TB | 0.267 | 0.257 | 27,152.242 | 18,731.501 | TB | 0.298 | 0.288 | 22,771.702 | 16,219.624 |

MLP | 0.214 | 0.214 | 27,906.102 | 20,439.615 | MLP | 0.144 | 0.144 | 24,957.346 | 19,268.403 |

Training Results with P(t-5) | Testing Results with P(t-5) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Model | R2 | NSE | RMSE | MAE | Model | R2 | NSE | RMSE | MAE |

DTFs | 0.910 | 0.859 | 11,802.909 | 8361.152 | DTFs | 0.886 | 0.822 | 11,381.253 | 8046.244 |

SDTs | 0.296 | 0.296 | 26,405.846 | 19,680.738 | SDTs | 0.201 | 0.201 | 24,107.606 | 18,224.162 |

TB | 0.317 | 0.310 | 26,148.224 | 18,184.550 | TB | 0.281 | 0.267 | 23,123.848 | 16,485.957 |

MLP | 0.234 | 0.234 | 27,556.290 | 20,657.409 | MLP | 0.161 | 0.160 | 24,719.766 | 19,027.579 |

Training Results with P(t-9) | Testing Results with P(t-9) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Model | R2 | NSE | RMSE | MAE | Model | R2 | NSE | RMSE | MAE |

DTFs | 0.943 | 0.884 | 10,728.798 | 7399.087 | DTFs | 0.934 | 0.871 | 9672.249 | 6975.412 |

SDTs | 0.302 | 0.302 | 26,299.122 | 19,562.380 | SDTs | 0.216 | 0.216 | 23,882.899 | 17,811.067 |

TB | 0.293 | 0.274 | 26,855.594 | 18,116.157 | TB | 0.375 | 0.359 | 21,614.152 | 15,211.614 |

MLP | 0.230 | 0.230 | 27,622.395 | 19,999.241 | MLP | 0.117 | 0.089 | 25,938.759 | 20,903.000 |

Training Results with P(t-10) | Testing Results with P(t-10) | ||||||||
---|---|---|---|---|---|---|---|---|---|

Model | R2 | NSE | RMSE | MAE | Model | R2 | NSE | RMSE | MAE |

DTFs | 0.945 | 0.885 | 10,671.543 | 7273.468 | DTFs | 0.940 | 0.876 | 9511.740 | 6840.659 |

SDTs | 0.325 | 0.325 | 25,870.455 | 19,120.118 | SDTs | 0.217 | 0.217 | 23,867.600 | 17,791.516 |

TB | 0.351 | 0.339 | 25,613.232 | 17,437.303 | TB | 0.325 | 0.308 | 22,469.118 | 15,777.656 |

MLP | 0.215 | 0.214 | 27,903.246 | 20,319.296 | MLP | 0.145 | 0.144 | 24,965.553 | 19,058.321 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Humphries, U.W.; Ali, R.; Waqas, M.; Shoaib, M.; Varnakovida, P.; Faheem, M.; Hlaing, P.T.; Lin, H.A.; Ahmad, S.
Runoff Estimation Using Advanced Soft Computing Techniques: A Case Study of Mangla Watershed Pakistan. *Water* **2022**, *14*, 3286.
https://doi.org/10.3390/w14203286

**AMA Style**

Humphries UW, Ali R, Waqas M, Shoaib M, Varnakovida P, Faheem M, Hlaing PT, Lin HA, Ahmad S.
Runoff Estimation Using Advanced Soft Computing Techniques: A Case Study of Mangla Watershed Pakistan. *Water*. 2022; 14(20):3286.
https://doi.org/10.3390/w14203286

**Chicago/Turabian Style**

Humphries, Usa Wannasingha, Rashid Ali, Muhammad Waqas, Muhammad Shoaib, Pariwate Varnakovida, Muhammad Faheem, Phyo Thandar Hlaing, Hnin Aye Lin, and Shakeel Ahmad.
2022. "Runoff Estimation Using Advanced Soft Computing Techniques: A Case Study of Mangla Watershed Pakistan" *Water* 14, no. 20: 3286.
https://doi.org/10.3390/w14203286