Environmental and Ecological Statistics

, Volume 26, Issue 1, pp 87–105 | Cite as

A history matching approach for calibrating hydrological models

  • Natalia V. Bhattacharjee
  • Pritam Ranjan
  • Abhyuday MandalEmail author
  • Ernest W. Tollner


Calibration of hydrological time-series models is a challenging task since these models give a wide spectrum of output series and calibration procedures require significant amount of time. From a statistical standpoint, this model parameter estimation problem simplifies to finding an inverse solution of a computer model that generates pre-specified time-series output (i.e., realistic output series). In this paper, we propose a modified history matching approach for calibrating the time-series rainfall-runoff models with respect to the real data collected from the state of Georgia, USA. We present the methodology and illustrate the application of the algorithm by carrying a simulation study and the two case studies. Several goodness-of-fit statistics were calculated to assess the model performance. The results showed that the proposed history matching algorithm led to a significant improvement, of 30% and 14% (in terms of root mean squared error) and 26% and 118% (in terms of peak percent threshold statistics), for the two case-studies with Matlab-Simulink and SWAT models, respectively.


Contour estimation Gaussian process model History matching Hydrology Inverse problem Prediction 



The authors would like to thank the Editor, the Associate Editor and two reviewers for their thorough and helpful reviews. Ranjan’s research was partially supported by the Extra Mural Research Fund (EMR/2016/003332/MS) from the Science and Engineering Research Board, Department of Science and Technology, Government of India. Mandal and Tollner’s research was partially supported by 104B State Water Resources Research Institute Program, USA Grant G16AP00047. We would like to thank NASA DEVELOP National Program’s node at the Center for Geospatial Research, UGA for providing resources on SWAT modeling.


  1. Abbaspour K, Johnson C, Van Genuchten M (2004) Estimating uncertain flow and transport parameters using a sequential uncertainty fitting procedure. Vadose Zone J 3(4):1340–1352CrossRefGoogle Scholar
  2. Abbaspour K, Yang J, Maximov I, Siber R, Bogner K, Mieleitner J, Zobrist J, Srinivasan R (2007) Modelling hydrology and water quality in the pre-alpine/alpine thur watershed using swat. J Hydrol 333(2):413–430CrossRefGoogle Scholar
  3. Arnold J, Williams J, Srinivasan R, King K, Griggs R (1994) Swat: soil and water assessment tool. US Department of Agriculture, Agricultural Research Service, Grassland, Soil and Water Research Laboratory, TempleGoogle Scholar
  4. Boyle DP, Gupta HV, Sorooshian S (2000) Toward improved calibration of hydrologic models: combining the strengths of manual and automatic methods. Water Resour Res 36(12):3663–3674CrossRefGoogle Scholar
  5. Chu W, Gao X, Sorooshian S (2010) Improving the shuffled complex evolution scheme for optimization of complex nonlinear hydrological systems: application to the calibration of the sacramento soil-moisture accounting model. Water Resour Res 46:W09530. CrossRefGoogle Scholar
  6. Dile Y, Berndtsson R, Setegn S (2013) Hydrological response to climate change for gilgel abay river, in the lake tana basin-upper blue nile basin of ethiopia. PLoS ONE 8(10):e79296CrossRefGoogle Scholar
  7. Duan Q, Sorooshian S, Gupta V (1992) Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour Res 28(4):1015–1031CrossRefGoogle Scholar
  8. Duncan O, Tollner E, Ssegane H (2013) An instantaneous unit hydrograph for estimating runoff from windrow composting pads. Appl Eng Agric 29(2):209–223CrossRefGoogle Scholar
  9. Franchini M, Galeati G (1997) Comparing several genetic algorithm schemes for the calibration of conceptual rainfall-runoff models. Hydrol Sci J 42(3):357–379CrossRefGoogle Scholar
  10. Jayakrishnan R, Srinivasan R, Santhi C, Arnold J (2005) Advances in the application of the swat model for water resources management. Hydrol Process 19(3):749–762CrossRefGoogle Scholar
  11. Johnson M, Moore L, Ylvisaker D (1990) Minimax and maximin distance designs. J Stat Plan Inference 26(2):131–148CrossRefGoogle Scholar
  12. Kalaba L, Wilson B, Haralampides K (2007) A storm water runoff model for open windrow composting sites. Compost Sci Util 15(3):142–150CrossRefGoogle Scholar
  13. Krysanova V, Srinivasan R (2015) Assessment of climate and land use change impacts with swat. Reg Environ Change 15(3):431CrossRefGoogle Scholar
  14. Loeppky J, Sacks J, Welch W (2009) Choosing the sample size of a computer experiment: a practical guide. Technometrics 51:366–376CrossRefGoogle Scholar
  15. Lohani AK, Goel N, Bhatia K (2014) Improving real time flood forecasting using fuzzy inference system. J Hydrol 509:25–41CrossRefGoogle Scholar
  16. MacDonald B, Ranjan P, Chipman H (2015) GPfit: an R package for fitting a Gaussian process model to deterministic simulator outputs. J Stat Softw 64(12):1–23CrossRefGoogle Scholar
  17. Montanari A, Toth E (2007) Calibration of hydrological models in the spectral domain: an opportunity for scarcely gauged basins? Water Resour Res 43:W05434. CrossRefGoogle Scholar
  18. Nash J, Sutcliffe J (1970) River flow forecasting through conceptual models part i—a discussion of principles. J Hydrol 10:282–290CrossRefGoogle Scholar
  19. Ranjan P, Bingham D, Michailidis G (2008) Sequential experiment design for contour estimation from complex computer codes. Technometrics 50(4):527–541CrossRefGoogle Scholar
  20. Ranjan P, Thomas M, Teismann H, Mukhoti S (2016) Inverse problem for a time-series valued computer simulator via scalarization. Open J Stat 6(03):528–544CrossRefGoogle Scholar
  21. Srinivasan M, Gérard-Marchant P, Veith T, Gburek W, Steenhuis T (2005) Watershed scale modeling of critical source areas of runoff generation and phosphorus transport. JAWRA J Am Water Resour Assoc 41(2):361–377CrossRefGoogle Scholar
  22. Tigkas D, Christelis V, Tsakiris G (2015) The global optimisation approach for calibrating hydrological models: the case of medbasin-d model. In: Proceedings of the 9th world congress of EWRA, pp 10–13Google Scholar
  23. Vernon I, Goldstein M, Bower R (2010) Galaxy formation: a Bayesian uncertainty analysis. Bayesian Anal 5(4):619–669CrossRefGoogle Scholar
  24. Wilson B, Haralampides K, Levesque S (2004) Stormwater runoff from open windrow composting facilities. J Environ Eng Sci 3(6):537–540CrossRefGoogle Scholar
  25. Zhang R, Lin CD, Ranjan P (2018) A sequential design approach for calibrating a dynamic population growth model. arXiv:1811.00153

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Health Metrics and EvaluationUniversity of WashingtonSeattleUSA
  2. 2.OM&QTIndian Institute of Management IndoreIndoreIndia
  3. 3.Department of StatisticsUniversity of GeorgiaAthensUSA
  4. 4.College of EngineeringUniversity of GeorgiaAthensUSA

Personalised recommendations