A computationally efficient method for uncertainty analysis of SWAT model simulations

Original Paper
  • 25 Downloads

Abstract

The physically based distributed hydrological models are ideal for hydrological simulations; however most of such models do not use the basic equations pertaining to mass, energy and momentum conservation, to represent the physics of the process. This is plausibly due to the lack of complete understanding of the hydrological process. The soil and water assessment tool (SWAT) is one such widely accepted semi-distributed, conceptual hydrological model used for water resources planning. However, the over-parameterization, difficulty in its calibration process and the uncertainty associated with predictions make its applications skeptical. This study considers assessing the predictive uncertainty associated with distributed hydrological models. The existing methods for uncertainty estimation demand high computational time and therefore make them challenging to apply on complex hydrological models. The proposed approach employs the concepts of generalized likelihood uncertainty estimation (GLUE) in an iterative procedure by starting with an assumed prior probability distribution of parameters, and by using mutual information (MI) index for sampling the behavioral parameter set. The distributions are conditioned on the observed information through successive cycles of simulations. During each cycle of simulation, MI is used in conjunction with Markov Chain Monte Carlo procedure to sample the parameter sets so as to increase the number of behavioral sets, which in turn helps reduce the number of cycles/simulations for the analysis. The method is demonstrated through a case study of SWAT model in Illinois River basin in the USA. A comparison of the proposed method with GLUE indicates that the computational requirement of uncertainty analysis is considerably reduced in the proposed approach. It is also noted that the model prediction band, derived using the proposed method, is more effective compared to that derived using the other methods considered in this study.

Keywords

Uncertainty GLUE Mutual Information Distributed hydrological models MCMC SWAT 

References

  1. Alazzy AA, Lü H, Zhu Y (2015) Assessing the uncertainty of the Xinanjiang rainfall-runoff model: effect of the likelihood function choice on the GLUE method. J Hydrol Eng 20(10).  https://doi.org/10.1061/(ASCE)HE.1943-5584.0001174
  2. Anand S, Mankin KR, McVay KA, Janssen KA, Barnes PL, Pierzynski GM (2007) Calibration and validation of ADAPT and SWAT for field-scale runoff prediction. J Am Water Resour Assoc 43(4):899–910CrossRefGoogle Scholar
  3. Arabi M, Govindaraju RS, Engel B, Hantush M (2007) Multiobjective sensitivity analysis of sediment and nitrogen processes with a watershed model. Water Resour Res 43(6):W06409.  https://doi.org/10.1029/2006WR005463
  4. Arnold JG, Fohrer N (2005) SWAT2000: current capabilities and research opportunities in applied watershed modeling. Hydrol Process 19(3):563–572CrossRefGoogle Scholar
  5. Arnold JG, Allen PM, Bernhardt G (1993) A comprehensive surface-ground water flow model. J Hydrol 142(1–4):47–69CrossRefGoogle Scholar
  6. Athira P, Sudheer KP (2015) A method to reduce the computational requirement while assessing uncertainty of complex hydrological models. Stoch Environ Res Rick Assess 29(3):847–859CrossRefGoogle Scholar
  7. Barlund I, Kirkkala T, Malve O, Kämäri J (2007) Assessing the SWAT model performance in the evaluation of management actions for the implementation of the water framework directive in a finnish catchment. Environ Model Softw 22(5):719–724CrossRefGoogle Scholar
  8. Beven KJ (2006) A manifesto for the equifinality thesis. J Hydrol 320:18–36CrossRefGoogle Scholar
  9. Beven KJ, Binley AM (1992) The future of distributed models: model calibration and uncertainty prediction. Hydrol Process 6:279–298.  https://doi.org/10.1002/hyp.3360060305 CrossRefGoogle Scholar
  10. Beven K, Binley A (2014) GLUE: 20 years on. Hydrol Process 28:5897–5918CrossRefGoogle Scholar
  11. Beven K, Freer J (2001) Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the glue methodology. J Hydrol 249(14):11–29CrossRefGoogle Scholar
  12. Blazkova S, Beven K (2009) A limits of acceptability approach to model evaluation and uncertainty estimation in flood frequency estimation by continuous simulation: Skalka catchment, Czech Republic. Water Resour Res 45:W00B16.  https://doi.org/10.1029/2007wr006726 CrossRefGoogle Scholar
  13. Carota C, Parmigiani G, Polson NG (1996) Diagnostic measures for model criticism. J Am Stat Assoc 91:753–762CrossRefGoogle Scholar
  14. Christensen S (2004) A synthetic groundwater modeling study of the accuracy of GLUE uncertainty intervals. Nord Hydrol 35(1):45–59Google Scholar
  15. Cibin R, Sudheer KP, Chaubey I (2010) Sensitivity and identifiability of stream flow generation parameters of the SWAT model. Hydrol Processes 24(9):1133–1148CrossRefGoogle Scholar
  16. Cibin R, Athira P, Sudheer KP, Chaubey I (2014) Application of distributed hydrological models for predictions in ungauged basins: A method to quantify predictive uncertainty. Hydrol Proces.  https://doi.org/10.1002/hyp.9721 Google Scholar
  17. Confessor RB Jr, Whittaker GW (2007) Automatic calibration of hydrologic models with multi-objective evolutionary algorithm and pareto optimization. J Am Water Resour Assoc 43(4):981–989CrossRefGoogle Scholar
  18. Demaria EM, Njissen B, Wagener T (2007) Monte Carlo sensitivity analysis of land surface parameters using the variable iniltration capacity model. J Geophys Res 112:D11113CrossRefGoogle Scholar
  19. Freer J, Beven KJ, Ambroise B (1996) Bayesian estimation of uncertainty in runoff prediction and the value of data: an application of the GLUE approach. Water Resour Res 32(7):2161–2173CrossRefGoogle Scholar
  20. Freni G, Mannina G (2010) Bayesian approach for uncertainty quantification in water quality modeling: the influence of prior distribution. J Hydrol 392:31–39CrossRefGoogle Scholar
  21. Gardner RH, O’Neill RV (1983) Parameter uncertainty and model predictions: a review of Monte Carlo results. In: Berk MB, Straten GV (eds) Uncertainty and forecasting of water quality. Springer, New York, pp 245–257CrossRefGoogle Scholar
  22. Gassman PW, Reyes MR, Geen CH, Arnold JG (2007) The soil and water assessment assessment tool: historical development, applications and future research directions. Trans ASABE 50(4):1211–1250CrossRefGoogle Scholar
  23. Haan CT (2002) Statistical methods in hydrology. Iowa State Press, AmesGoogle Scholar
  24. Jeremiah E, Sisson SA, Sharma A, Marshall L (2012) Efficient hydrological model parameter optimization with Sequential Monte Carlo Sampling. Environ Model Softw 38:283–295CrossRefGoogle Scholar
  25. Jin X, Chong-Yu Xu, Zhang Q, Singh VP (2010) Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model. J Hydrol 383:147–155CrossRefGoogle Scholar
  26. Katz RW (2002) Techniques for estimating uncertainty in climate change scenarios and impact studies. Clim Res 20:167–185CrossRefGoogle Scholar
  27. Kuczera G, Parent E (1998) Monte Carlo assessment of parameter uncertainty catchment models: the Metropolis algorithm. J Hydrol 211:69–85CrossRefGoogle Scholar
  28. Li H, Wu J (2006) Uncertainty analysis in ecological studies. In: Wu J, Jones KB, Li H, Loucks OL (eds) Scaling and uncertainty analysis in ecology:methods and applications. Springer, NetherlandsGoogle Scholar
  29. Li L, Xia J, Xu CY, Singh VP (2010) Evaluation of the subjective factors of the GLUE method and comparison with the formal Bayesian method in uncertainty assessment of hydrological models. J Hydrol 390(3–4):210–221CrossRefGoogle Scholar
  30. MacKay DJC (2003) Information theory, inference and learning algorithms. Cambridge University Press, Cambridge. ISBN 0-521-64298-1Google Scholar
  31. Manache G, Melching CS (2008) Identification of reliable regression- and correlation-based sensitivity measures for importance ranking of water-quality model parameters. Environ Model Softw 23:549–562CrossRefGoogle Scholar
  32. Mantovan P, Todini E (2006) Hydrological forecasting uncertainty assessment: incoherence of the GLUE methodology. J Hydrol 330:368–381.  https://doi.org/10.1016/j.jhydrol.2006.04.046 CrossRefGoogle Scholar
  33. May RJ, Dandy GC, Maier HR, Nixon JB (2008) Application of partial mutual information variable selection to ANN forecasting of water quality in water distribution systems. Environ Model Softw 23(10–11):1289–1299CrossRefGoogle Scholar
  34. McMillan H, Clark M (2009) Rainfall-runoff model calibration using informal likelihood measures within a Markov chain Monte Carlo sampling scheme. Water Resour Res 45:W04418.  https://doi.org/10.1029/2008WR007288 CrossRefGoogle Scholar
  35. Migliaccio KW, Chaubey I (2008) Spatial distributions and stochastic parameter influences on SWAT flow and sediment predictions. J Hydrol Eng 13(4):258–269CrossRefGoogle Scholar
  36. Mirzaei M, Huang YF, El-Shafie A, Shatirah A (2015) Application of the generalized likelihood uncertainty estimation (GLUE) approach for assessing uncertainty in hydrological models: a review. Stoch Environ Res Risk Assess 29:1265–1273CrossRefGoogle Scholar
  37. Montanari A (2005) Large sample behaviors of the generalized likelihood uncertainty estimation (GLUE) in assessing the uncertainty of rainfall-runoff simulations. Water Resour Res 41:W08406.  https://doi.org/10.1029/2004WR003826 CrossRefGoogle Scholar
  38. Mukund Nilakantan J, Ponnambalam SG et al (2015) Bio-inspired search rithms to solve robotic assembly line balancing problems. Neural Comput Appl 26(6):1379–1393CrossRefGoogle Scholar
  39. Neitsch SL, Arnold JG, Kiniry JR, Williams JR, King KW (2002) Soil water assessment tool theoretical documentation version 2000. Texas Water Resource Institute, College Station (TWRI Report, TR-191) Google Scholar
  40. Nott DJ, Marshall L, Brown J (2012) Generalized likelihood uncertainty estimation (GLUE) and approximate Bayesian computation: what’s the connection? Water Resour Res 48:W12602.  https://doi.org/10.1029/2011WR011128 CrossRefGoogle Scholar
  41. Rastetter EB, King AW, Cosby BJ, Hornberger GM, O’Neill RV, Hobbie JE (1992) Aggregating fine-scale ecological knowledge to model coarser-scale attributes of ecosystems. Ecol Appl 2:55–70CrossRefGoogle Scholar
  42. Refsgaard JC, Sluijs JP, Hojberg AL, Vanrolleghem PA (2007) Uncertainty in the environmental modeling process—a framework and guidance. Environ Model Softw 22:1543–1556CrossRefGoogle Scholar
  43. Sadegh M, Vrugt JA (2013) Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation. Hydrol Earth Syst Sci 17:4831–4850CrossRefGoogle Scholar
  44. Schoups G, Vrugt JA (2010) A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-Gaussian errors. Water Resour Res 46:W10531.  https://doi.org/10.1029/2009WR008933 Google Scholar
  45. Smith PJ, Beven K, Tawn JA (2008) Informal likelihood measures in model assessment: theoretic development and investigation. Adv Water Resour Res 31:1087–1100CrossRefGoogle Scholar
  46. Stedinger JR, Vogel RM, Lee SU, Batchelder R (2008) Appraisal of the generalized likelihood uncertainty estimation (GLUE) method. Water Resour Res.  https://doi.org/10.1029/2008wr006822 Google Scholar
  47. Steuer R, Kurths J, Daub CO, Weise J, Selbiq J (2002) The mutual information: detecting and evaluating dependencies between variables. Bioinformatics 18:S231–S240CrossRefGoogle Scholar
  48. Talebizadeh M, Morid S, Ayyoubzadeh SA, Ghasemzadeh M (2010) Uncertainty analysis in sediment load modeling using ANN and SWAT model. Water Resour Manag 24:1747–1761.  https://doi.org/10.1007/s11269-009-9522-2 CrossRefGoogle Scholar
  49. Uniyal B, Jha MK, Verma AK (2015) Parameter identification and uncertainty analysis for simulating streamflow in a river basin of Eastern India. Hydrol Process 29:3744–3766CrossRefGoogle Scholar
  50. Vrugt JA, Gupta HV, Bouten W, Sorooshian S (2003) A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters. Water Resour Res 39(8):1201.  https://doi.org/10.1029/2002wr001642 Google Scholar
  51. Vrugt JA, Braak CJF, Clark M, Hyman JM, Robinson BA (2008a) Treatment of input uncertainty in hydrologic modeling: doing hydrology backward with Markov chain Monte Carlo simulation. Water Resour Res 44:W00B09.  https://doi.org/10.1029/2007wr006720 CrossRefGoogle Scholar
  52. Vrugt JA, Braak CJF, Gupta HV, Robinson BA (2008b) Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling? Stoch Environ Res Risk Assess 23:1011–1026.  https://doi.org/10.1007/s00477-008-0274-y CrossRefGoogle Scholar
  53. Warmink JJ, Janssen JAEB, Booij MJ, Krol MS (2010) Identification and classification of uncertainties in the application of environmental models. Environ Model Softw 25:1518–1527CrossRefGoogle Scholar
  54. West M (1993) Approximating posterior distributions by mixture. J R Stat Soc B 55(2):409–422Google Scholar
  55. Wiwatenadate P, Claycamp HG (2000) Error propagation of uncertainties in multiplicative models. Hum Ecol Risk Assess 6:355–368CrossRefGoogle Scholar
  56. Wu Y, Liu S (2012) Automating calibration, sensitivity and uncertainty analysis of complex models using the R package flexible modeling environment (FME): SWAT as an example. Environ Model Softw 31:99–109CrossRefGoogle Scholar
  57. Xiong LH, Wan M, Wei XJ, O’Connor KM (2009) Indices for assessing the prediction bounds of hydrological models and application by generalised likelihood uncertainty estimation. Hydrol Sci J-Journal Des Sciences Hydrologiques 54(5):852–871CrossRefGoogle Scholar
  58. Yen H, Jeong J, Feng QY, Deb D (2015) Assessment of input uncertainty in SWAT using latent variables. Water Resour Manag 29:1137–1153CrossRefGoogle Scholar
  59. Zhang Z (2012) Iterative posterior inference for Bayesian Kriging. Stoch Environ Res Rick Assess 26(7):913–923CrossRefGoogle Scholar
  60. Zhang W, Li T (2015) The influence of objective function and acceptability threshold on uncertainty assessment of an urban drainage hydraulic model with generalized likelihood uncertainty estimation methodology. Water Resour Manag 29:2059–2072CrossRefGoogle Scholar
  61. Zhang X, Srinivasan R, Liew MV (2008) Multi-site calibration of the SWAT model for hydrologic modeling. Trans ASABE 51(6):2039–2049CrossRefGoogle Scholar
  62. Zhang Y, Xia J, Shao X (2011) Water quantity and quality simulation by improved SWAT in highly regulated Huai river basin of China. Stoch Environ Res Risk Assess.  https://doi.org/10.1007/s00477-011-0546-9 Google Scholar
  63. Zhang J, Li Q, Guo B, Gong H (2015) The comparative study of multi-site uncertainty evaluation method based on SWAT model. Hydrol Process 29:2994–3009CrossRefGoogle Scholar
  64. Zhenyao S, Lei C, Tao C (2012) The influence of parameter distribution uncertainty on hydrological and sediment modeling: a case study of SWAT model applied to the Daning watershed of the three Gorges Reservoir Region China. Stoch Env Res Risk Assess.  https://doi.org/10.1007/s00477-012-0579-8 Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringIndian Institute of Technology PalakkadPalakkadIndia
  2. 2.Department of Civil EngineeringIndian Institute of Technology MadrasChennaiIndia

Personalised recommendations