Water Resources Management

, Volume 33, Issue 1, pp 229–243 | Cite as

Enhancement of Model Reliability by Integrating Prediction Interval Optimization into Hydrogeological Modeling

  • K. S. Kasiviswanathan
  • Jianxun He
  • Joo-Hwa Tay
  • K. P. Sudheer


This paper presents a single-objective optimization-based perturbation analysis to quantify model prediction uncertainty. A new index named coverage width index (CWI), which combines two commonly used uncertainty indices, the percentage of coverage (POC) and the average width (AW), was proposed to facilitate the optimization. Considering the outperformance of the wavelet neural network (WNN) among various data-driven modeling approaches in hydrogeological modeling, the proposed approach was integrated into WNN (called OPWNN). A case study was conducted to demonstrate the application of OPWNN in groundwater level forecasting at two wells in the Amaravathi River Basin, India. The sensitivity analysis of the effect of initial perturbation range on CWI suggested that uncertainty is sensitive to the selected perturbation range and a small perturbation does not guarantee an acceptable prediction interval (PI). The modeling results demonstrated that the OPWNN can optimize the PI effectively with minimized AW corresponding to an expected high POC. Therefore, this approach can yield more reliable predictions/forecasts for water resources management.


Hydrogeological modeling Model reliability Perturbation analysis Prediction interval Optimization Wavelet neural network 



The authors would like to thank the University of Calgary (Eyes High Program), Canada, for the financial support of this study. The data used in this study are available upon request from the corresponding author via email.

Compliance with Ethical Standards

Conflict of Interest



  1. Adamowski J, Chan HF (2011) A wavelet neural network conjunction model for groundwater level forecasting. J Hydrol 407:28–40. CrossRefGoogle Scholar
  2. Alvisi S, Creaco E, Franchini M (2012) Crisp discharge forecasts and grey uncertainty bands using data-driven models. Hydrol Res 43(5):589–602. CrossRefGoogle Scholar
  3. Asefa T (2009) Ensemble streamflow forecast: a glue-based neural network approach. J Am Water Resour Assoc 45:1155–1163. CrossRefGoogle Scholar
  4. Benaouda D, Murtagh F, Starck JL, Renaud O (2006) Wavelet-based nonlinear multiscale decomposition model for electricity load forecasting. Neurocomputing 70:139–154. CrossRefGoogle Scholar
  5. Creaco E, Berardi L, Sun S, Giustolisi O, Savic D (2016) Selection of relevant input variables in storm water quality modeling by multiobjective evolutionary polynomial regression paradigm. Water Resour Res 52:2403–2419. CrossRefGoogle Scholar
  6. Crochemore L, Perrin C, Andréassian V, Ehret U, Seibert SP, Grimaldi S, Gupta H, Paturel J-E (2015) Comparing expert judgement and numerical criteria for hydrograph evaluation. Hydrol Sci J 60(3):402–423. CrossRefGoogle Scholar
  7. Dhanesh Y, Sudheer KP (2010) Predictions in ungauged basins: can we use artificial neural networks? American Geophysical Union Joint Assembly, Foz doIguassu, Brazil, August 8–13Google Scholar
  8. Goldberg D (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, ReadingGoogle Scholar
  9. Jaafar WZW, Jiu J, Han D (2011) Input variable selection for median flood regionalization. Water Resour Res 47:W07503. CrossRefGoogle Scholar
  10. Kasiviswanathan KS, Sudheer KP (2013) Quantification of the predictive uncertainty of artificial neural network based river flow forecast models. Stoch Env Res Risk A 27:137–146. CrossRefGoogle Scholar
  11. Kasiviswanathan KS, Cibin R, Sudheer KP, Chaubey I (2013) Constructing PI for artificial neural network rainfall runoff models based on ensemble simulations. J Hydrol 499:275–288. CrossRefGoogle Scholar
  12. Liao Q, Zhang D, Tchelepi H (2017) A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media. J Comput Phys 330:828–845. CrossRefGoogle Scholar
  13. Liu Y, Gupta HV (2007) Uncertainty in hydrologic modeling: toward an integrated data assimilation framework. Water Resour Res 43:W07401. CrossRefGoogle Scholar
  14. Maier HR, Jain A, Dandy GC, Sudheer KP (2010) Methods used for the development of neural networks for the prediction of water resource variables in river systems: current status and future directions. Environ Model Softw 25:891–909. CrossRefGoogle Scholar
  15. Mallat SG (1989) A theory for multi-resolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11(7):674–693CrossRefGoogle Scholar
  16. Nourani V, Komasi M, Mano A (2009) A multivariate ANN-wavelet approach for rainfall-runoff modeling. Water Resour Manag 23:2877–2894. CrossRefGoogle Scholar
  17. Sun S, Bertrand-Krajewski JL (2013) Input variable selection and calibration data selection for storm water quality regression models. Water Sci Technol 68(1):50–58. CrossRefGoogle Scholar
  18. Xiong L, Wan M, Wei X, O’Connor KM (2009) Indices for assessing the prediction bounds of hydrological models and application by generalised likelihood uncertainty estimation. Hydrol Sci J 54:852–871. CrossRefGoogle Scholar
  19. Ye L, Zhou J, Zeng X, Gou J, Zhang X (2014) Multi-objective optimization for construction of prediction interval of hydrological models based on ensemble simulations. J Hydrol 519:925–933. CrossRefGoogle Scholar
  20. Yu JJ, Qin XS, Larsen O (2015) Uncertainty analysis of flood inundation modelling using GLUE with surrogate models in stochastic sampling. Hydrol Process 29:1267–1279. CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • K. S. Kasiviswanathan
    • 1
    • 2
  • Jianxun He
    • 2
  • Joo-Hwa Tay
    • 2
  • K. P. Sudheer
    • 3
  1. 1.School of EngineeringIndian Institute of Technology MandiKamandIndia
  2. 2.Department of Civil Engineering, Schulich School of EngineeringUniversity of CalgaryCalgaryCanada
  3. 3.Department of Civil EngineeringIndian Institute of Technology MadrasChennaiIndia

Personalised recommendations