Advertisement

Toward a combined Bayesian frameworks to quantify parameter uncertainty in a large mountainous catchment with high spatial variability

  • Yousef Hassanzadeh
  • Amirhosein Aghakhani AfsharEmail author
  • Mohsen Pourreza-Bilondi
  • Hadi Memarian
  • Ali Asghar Besalatpour
Article
  • 119 Downloads

Abstract

Although hydrological models play an essential role in managing water resources, quantifying different sources of uncertainties is a challenging task. In this study, the application of two parameter uncertainty quantification methods and their performances for predicting runoff was investigated. Sequential Uncertainty Fitting version 2 (SUFI-2) and DiffeRential Evolution Adaptive Metropolis (DREAM-ZS) algorithms were employed to explore the output uncertainty of Soil and Water Assessment Tool (SWAT) at a multisite flow gauging station. In order to optimize the model and quantify the parameter uncertainty, S1 and S2 strategies, which belong to the SUFI-2 and DREAM-ZS algorithms, were defined. The prior ranges of the S1 were adopted from SWAT manual, and the prior ranges of the S2 were selected using a compromising approach between the prior and posterior ranges extracted from S1. P-factor, d-factor, Nash-Sutcliffe coefficient (NS), the dimensionless variant of average deviation amplitude (S), and the average relative deviation amplitude (T), as performance criteria, were assessed. The NS, S, and T for total uncertainty ranged 0.60–0.71, 0.46–0.51, and 0.94–1.01 under S1 strategy and 0.64–0.78, 0.07–0.22, and 0.39–0.64 under S2, respectively. In parameter uncertainty analysis, S and T indices ranged from 1.51 to 1.88 and 2.20 to 2.60, correspondingly. The results showed that the DREAM-ZS algorithm improved model calibration efficiency and led to more realistic values of the parameters for runoff simulation in SWAT model. However, the S2 strategy, which implicitly takes advantage of both formal and informal Bayesian approaches simultaneously, will be able to outperform the S1 for reducing the prediction uncertainties.

Keywords

Uncertainty analysis Multisite calibration SUFI-2 DREAM-ZS SWAT 

Notes

Funding

Financial support was provided by Iran National Science Foundation (INSF). The corresponding contract number is 96005746.

References

  1. Abbaspour, K. C. (2011). SWAT-CUP4: SWAT calibration and uncertainty programs—a user manual. Swiss Federal Institute of Aquatic Science and Technology, Eawag.Google Scholar
  2. Abbaspour, K. C., Johnson, C. A., & Van Genuchten, M. T. (2004). Estimating uncertain flow and transport parameters using a sequential uncertainty fitting procedure. Vadose Zone Journal, 3(4), 1340–1352.Google Scholar
  3. Abbaspour, K. C., 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. Journal of Hydrology, 333(2), 413–430.Google Scholar
  4. Afshar, A. A., & Hassanzadeh, Y. (2017). Determination of monthly hydrological Erosion severity and runoff in Torogh dam Watershed Basin using SWAT and WEPP models. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 41(2), 221–228.Google Scholar
  5. Afshar, A. A., Hasanzadeh, Y., Besalatpour, A. A., & Pourreza-Bilondi, M. (2017a). Climate change forecasting in a mountainous data scarce watershed using CMIP5 models under representative concentration pathways. Theoretical and Applied Climatology, 129(1–2), 683–699.Google Scholar
  6. Afshar, A.A., Hassanzadeh, Y., Pourreza-Bilondi, M., & Ahmadi, A. (2017b). Analyzing long-term spatial variability of blue and green water footprints in a semi-arid mountainous basin with MIROC-ESM model (case study: Kashafrood River Basin, Iran). Theoretical and Applied Climatology, 1–15 (Published Online).Google Scholar
  7. Arnold, J. G., Srinivasan, R., Muttiah, R. S., & Williams, J. R. (1998). Large area hydrologic modeling and assessment part I: Model development. JAWRA Journal of the American Water Resources Association, 34(1), 73–89.Google Scholar
  8. Arnold, J. G., Kiniry, J. R., Srinivasan, R., Williams, J. R., Haney, E. B., & Neitsch, S. L. (2011). Soil and Water Assessment Tool input/output file documentation: Version 2009. College Station: Texas Water resources institute technical report, 365.Google Scholar
  9. Beven, K. (2006). A manifesto for the equifinality thesis. Journal of Hydrology, 320(1), 18–36.Google Scholar
  10. Beven, K., & Binley, A. (1992). The future of distributed models: Model calibration and uncertainty prediction. Hydrological Processes, 6(3), 279–298.Google Scholar
  11. Beven, K., & Freer, J. (2001). Equifinality, data assimilation and uncertainty estimation in mechanistic modeling of complex environmental system using the GLUE methodology. Journal of Hydrology, 249(1–4), 11–29.Google Scholar
  12. Beven, K. J., Smith, P. J., & Freer, J. E. (2008). So just why would a modeller choose to be incoherent? Journal of Hydrology, 354(1–4), 15–32.Google Scholar
  13. Bicknell, B. R., Imhoff, J. C., Kittle Jr, J. L., Donigian Jr, A. S., & Johanson, R. C. (1996). Hydrological simulation program-FORTRAN. user's manual for release 11. US EPA.Google Scholar
  14. Bilondi, M. P., & Abbaspour, K. C. (2013). Application of three different calibration-uncertainty analysis methods in a semi-distributed rainfall-runoff model application. Middle-East Journal of Scientific Research, 15.Google Scholar
  15. Box, G. E. P., & Tiao, G. C. (1992). Bayesian inference in statistical analysis (p. 608). New York: Wiley Interscience.Google Scholar
  16. Cho, J., Bosch, D., Lowrance, R., Strickland, T., & Vellidis, G. (2009). Effect of spatial distribution of rainfall on temporal and spatial uncertainty of SWAT output. Transactions of the ASABE, 52(5), 1545–1556.Google Scholar
  17. Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied hydrology, 572 pp. New York: Editions McGraw-Hill.Google Scholar
  18. Dumont, B., Leemans, V., Mansouri, M., Bodson, B., Destain, J. P., & Destain, M. F. (2014). Parameter identification of the STICS crop model, using an accelerated formal MCMC approach. Environmental Modelling & Software, 52, 121–135.Google Scholar
  19. Engeland, K., Steinsland, I., Johansen, S. S., Petersen-Øverleir, A., & Kolberg, S. (2016). Effects of uncertainties in hydrological modelling. A case study of a mountainous catchment in southern Norway. Journal of Hydrology, 536, 147–160.Google Scholar
  20. Flanagan, D. C., Frankenberger, J. R., & Ascough, J. C., II. (2012). WEPP: Model use, calibration, and validation. Transactions of the ASABE, 55(4), 1463–1477.Google Scholar
  21. Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457–472.Google Scholar
  22. Hargreaves, G. H., & Samani, Z. A. (1985). Reference crop evapotranspiration from temperature. Applied Engineering in Agriculture, 1(2), 96–99.Google Scholar
  23. He, J., Jones, J. W., Graham, W. D., & Dukes, M. D. (2010). Influence of likelihood function choice for estimating crop model parameters using the generalized likelihood uncertainty estimation method. Agricultural Systems, 103(5), 256–264.Google Scholar
  24. Hernandez-Lopez, M. R., & Frances, F. (2017). Bayesian joint interface of hydrological and generalized error models with the enforcement of total laws. Hydrology and Earth System Sciences, 1–40.  https://doi.org/10.5194/hess-2017-9.
  25. Jin, X., Xu, C. Y., Zhang, Q., & Singh, V. P. (2010). Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model. Journal of Hydrology, 383(3), 147–155.Google Scholar
  26. Joseph, J. F., & Guillaume, J. H. (2013). Using a parallelized MCMC algorithm in R to identify appropriate likelihood functions for SWAT. Environmental Modelling & Software, 46, 292–298.Google Scholar
  27. Koren, V., Reed, S., Smith, M., Zhang, Z., & Seo, D. J. (2004). Hydrology laboratory research modeling system (HL-RMS) of the US national weather service. Journal of Hydrology, 291(3), 297–318.Google Scholar
  28. Kozelj, D., Kapelan, Z., Novak, G., & Steinman, F. (2014). Investigating prior parameter distributions in the inverse modelling of water distribution hydraulic models. Journal of Mechanical Engineering, 60(11), 725–734.Google Scholar
  29. Kuczera, G., & Parent, E. (1998). Monte Carlo assessment of parameter uncertainty in conceptual catchment models: The Metropolis algorithm. Journal of Hydrology, 211(1), 69–85.Google Scholar
  30. Kumar, N., Singh, S. K., Srivastava, P. K., & Narsimlu, B. (2017). SWAT model calibration and uncertainty analysis for streamflow prediction of the tons River Basin, India, using sequential uncertainty fitting (SUFI-2) algorithm. Modeling Earth Systems and Environment, 3(1), 1–13.Google Scholar
  31. Laloy, E., & Vrugt, J. A. (2012). High-dimensional posterior exploration of hydrologic models using multiple-try DREAM (ZS) and high-performance computing. Water Resources Research, 48(1).Google Scholar
  32. Laloy, E., Fasbender, D., & Bielders, C. L. (2010). Parameter optimization and uncertainty analysis for plot-scale continuous modeling of runoff using a formal Bayesian approach. Journal of Hydrology, 380(1–2), 82–93.Google Scholar
  33. Leta, O. T., Nossent, J., Velez, C., Shrestha, N. K., van Griensven, A., & Bauwens, W. (2015). Assessment of the different sources of uncertainty in a SWAT model of the river Senne (Belgium). Environmental Modelling & Software, 68, 129–146.Google Scholar
  34. Leta, O. T., van Griensven, A., & Bauwens, W. (2016). Effect of single and multisite calibration techniques on the parameter estimation, performance, and output of a SWAT model of a spatially heterogeneous catchment. Journal of Hydrologic Engineering, 22(3), 05016036.Google Scholar
  35. Li, X., Weller, D. E., & Jordan, T. E. (2010). Watershed model calibration using multi-objective optimization and multi-site averaging. Journal of Hydrology, 380(3–4), 277–288.Google Scholar
  36. Li, B., Liang, Z., He, Y., Hu, L., Zhao, W., & Acharya, K. (2017). Comparison of parameter uncertainty analysis techniques for a TOPMODEL application. Stochastic Environmental Research and Risk Assessment, 31(5), 1045–1059.Google Scholar
  37. Lin, B., Chen, X., Yao, H., Chen, Y., Liu, M., Gao, L., & James, A. (2015). Analyses of landuse change impacts on catchment runoff using different time indicators based on SWAT model. Ecological Indicators, 58, 55–63.Google Scholar
  38. Mantovan, P., & Todini, E. (2006). Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology. Journal of Hydrology, 330(1), 368–381.Google Scholar
  39. Marhaento, H., Booij, M. J., Rientjes, T. H. M., & Hoekstra, A. Y. (2017). Attribution of changes in the water balance of a tropical catchment to land use change using the SWAT model. Hydrological Processes, 31(11), 2029–2040.Google Scholar
  40. Memarian, H., Balasundram, S. K., Abbaspour, K. C., Talib, J. B., Boon Sung, C. T., & Sood, A. M. (2014). SWAT-based hydrological modelling of tropical land-use scenarios. Hydrological Sciences Journal, 59(10), 1808–1829.Google Scholar
  41. Moriasi, D. N., Arnold, J. G., Van Liew, M. W., Bingner, R. L., Harmel, R. D., & Veith, T. L. (2007). Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Transactions of the ASABE, 50(3), 885–900.Google Scholar
  42. Narsimlu, B., Gosain, A. K., Chahar, B. R., Singh, S. K., & Srivastava, P. K. (2015). SWAT model calibration and uncertainty analysis for streamflow prediction in the Kunwari River basin, India, using sequential uncertainty fitting. Environmental Processes, 2(1), 79–95.Google Scholar
  43. Nash, J. E., & Sutcliffe, J. V. (1970). River flow forecasting through conceptual models part I—A discussion of principles. Journal of Hydrology, 10(3), 282–290.Google Scholar
  44. Neitsch, S. L., Arnold, J. G., Kiniry, J. R., & Williams, J. R. (2011). Soil and water assessment tool theoretical documentation version 2009. Texas Water Resources Institute.Google Scholar
  45. Nossent, J., & Bauwens, W. (2012). Multi-variable sensitivity and identifiability analysis for a complex environmental model in view of integrated water quantity and water quality modeling. Water Science and Technology, 65(3), 539–549.Google Scholar
  46. Nourali, M., Ghahraman, B., Pourreza-Bilondi, M., & Davary, K. (2016). Effect of formal and informal likelihood functions on uncertainty assessment in a single event rainfall-runoff model. Journal of Hydrology, 540, 549–564.Google Scholar
  47. Parajuli, P. B., Jayakody, P., & Ouyang, Y. (2018). Evaluation of using remote sensing evapotranspiration data in SWAT. Water Resources Management, 32(3), 985–996.Google Scholar
  48. Pourreza-Bilondi, M., Samadi, S. Z., Akhoond-Ali, A. M., & Ghahraman, B. (2016). Reliability of semiarid flash flood modeling using Bayesian framework. Journal of Hydrologic Engineering, 22(4), 05016039.Google Scholar
  49. Rivera, D., Rivas, Y., & Godoy, A. (2015). Uncertainty in a monthly water balance model using the generalized likelihood uncertainty estimation methodology. Journal of Earth System Science, 124(1), 49–59.Google Scholar
  50. Rostamian, R., Jaleh, A., Afyuni, M., Mousavi, S. F., Heidarpour, M., Jalalian, A., & Abbaspour, K. C. (2008). Application of a SWAT model for estimating runoff and sediment in two mountainous basins in Central Iran. Hydrological Sciences Journal, 53(5), 977–988.Google Scholar
  51. Sayari, N., Bannayan, M., Alizadeh, A., & Farid, A. (2013). Using drought indices to assess climate change impacts on drought conditions in the northeast of Iran (case study: Kashafrood basin). Meteorological Applications, 20(1), 115–127.Google Scholar
  52. Schoups, G., & Vrugt, J. A. (2010). A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-Gaussian errors. Water Resources Research, 46(10).Google Scholar
  53. Setegn, S. G., Srinivasan, R., Melesse, A. M., & Dargahi, B. (2010). SWAT model application and prediction uncertainty analysis in the Lake Tana Basin, Ethiopia. Hydrological Processes, 24(3), 357–367.Google Scholar
  54. Shi, X., Ye, M., Curtis, G. P., Miller, G. L., Meyer, P. D., Kohler, M., Yabusaki, S., & Wu, J. (2014). Assessment of parametric uncertainty for groundwater reactive transport modeling. Water Resources Research, 50(5), 4416–4439.Google Scholar
  55. Singh, V., Bankar, N., Salunkhe, S. S., Bera, A. K., & Sharma, J. R. (2013). Hydrological stream flow modelling on Tungabhadra catchment: Parameterization and uncertainty analysis using SWAT CUP. Current Science, 104(9), 1187–1199.Google Scholar
  56. Srivastava, P. K., Han, D., Ramirez, M. R., & Islam, T. (2013). Machine learning techniques for downscaling SMOS satellite soil moisture using MODIS land surface temperature for hydrological application. Water Resources Management, 27(8), 3127–3144.Google Scholar
  57. Surfleet, C. G., & Tullos, D. (2013). Uncertainty in hydrologic modelling for estimating hydrologic response due to climate change (Santiam River, Oregon). Hydrological Processes, 27(25), 3560–3576.Google Scholar
  58. Ter Braak, C. J. (2006). A Markov chain Monte Carlo version of the genetic algorithm differential evolution: Easy Bayesian computing for real parameter spaces. Statistics and Computing, 16(3), 239–249.Google Scholar
  59. Ter Braak, C. J., & Vrugt, J. A. (2008). Differential evolution Markov chain with snooker updater and fewer chains. Statistics and Computing, 18(4), 435–446.Google Scholar
  60. USDA-SCS. (1986). US Department of Agriculture-soil Conservation Service (USDASCS): Urban hydrology for small watersheds. Washington, DC: USDA.Google Scholar
  61. Van Griensven, A., & Meixner, T. (2006). Methods to quantify and identify the sources of uncertainty for river basin water quality models. Water Science and Technology, 53(1), 51–59.Google Scholar
  62. Van Griensven, A., Meixner, T., Grunwald, S., Bishop, T., Diluzio, M., & Srinivasan, R. (2006). A global sensitivity analysis tool for the parameters of multi-variable catchment models. Journal of Hydrology, 324(1), 10–23.Google Scholar
  63. Vrugt, J. A., Gupta, H. V., Bouten, W., & Sorooshian, S. (2003). A shuffled complex evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters. Water Resources Research, 39(8).Google Scholar
  64. Vrugt, J. A., Ter Braak, C. J., Clark, M. P., Hyman, J. M., & Robinson, B. A. (2008). Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation. Water Resources Research, 44(12).Google Scholar
  65. Vrugt, J. A., Ter Braak, C. J. F., Diks, C. G. H., Robinson, B. A., Hyman, J. M., & Higdon, D. (2009a). Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling. International Journal of Nonlinear Sciences and Numerical Simulation, 10(3), 273–290.Google Scholar
  66. Vrugt, J. A., Ter Braak, C. J., Gupta, H. V., & Robinson, B. A. (2009b). Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling? Stochastic Environmental Research and Risk Assessment, 23(7), 1011–1026.Google Scholar
  67. Vrugt, J. A., Ter Braak, C. J., Diks, C. G., & Schoups, G. (2013). Hydrologic data assimilation using particle Markov chain Monte Carlo simulation: Theory, concepts and applications. Advances in Water Resources, 51, 457–478.Google Scholar
  68. Wang, X., Williams, J. R., Gassman, P. W., Baffaut, C., Izaurralde, R. C., Jeong, J., & Kiniry, J. R. (2012). EPIC and APEX: Model use, calibration, and validation. Transactions of the ASABE, 55(4), 1447–1462.Google Scholar
  69. Wu, H., & Chen, B. (2015). Evaluating uncertainty estimates in distributed hydrological modeling for the Wenjing River watershed in China by GLUE, SUFI-2, and ParaSol methods. Ecological Engineering, 76, 110–121.Google Scholar
  70. Xiong, L., Wan, M., Wei, X., & O'connor, K. M. (2009). Indices for assessing the prediction bounds of hydrological models and application by generalised likelihood uncertainty estimation. Hydrological Sciences Journal, 54(5), 852–871.Google Scholar
  71. Xu, T., Valocchi, A. J., Ye, M., Liang, F., & Lin, Y. F. (2017). Bayesian calibration of groundwater models with input data uncertainty. Water Resources Research, 53(4), 3224–3245.Google Scholar
  72. Yang, J., Reichert, P., Abbaspour, K. C., Xia, J., & Yang, H. (2008). Comparing uncertainty analysis techniques for a SWAT application to the Chaohe Basin in China. Journal of Hydrology, 358(1), 1–23.Google Scholar
  73. Zahmatkesh, Z., Karamouz, M., & Nazif, S. (2015). Uncertainty based modeling of rainfall-runoff: Combined differential evolution adaptive metropolis (DREAM) and K-means clustering. Advances in Water Resources, 83, 405–420.Google Scholar
  74. Zeng, X., Ye, M., Wu, J., Wang, D., & Zhu, X. (2018). Improved nested sampling and surrogate-enabled comparison with other marginal likelihood estimators. Water Resources Research, 54, 797–826.  https://doi.org/10.1002/2017WR020782.Google Scholar
  75. Zhang, J., Li, Q., Guo, B., & Gong, H. (2015). The comparative study of multi-site uncertainty evaluation method based on SWAT model. Hydrological Processes, 29(13), 2994–3009.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Water Engineering, Faculty of Civil EngineeringUniversity of TabrizTabrizIran
  2. 2.Department of Water Engineering, College of AgricultureUniversity of BirjandBirjandIran
  3. 3.Department of Watershed Management, Faculty of Natural Resources and EnvironmentUniversity of BirjandBirjandIran
  4. 4.Department of Soil Sciences, College of AgricultureVali-e-Asr University of RafsanjanRafsanjanIran

Personalised recommendations