Application of the patient rule induction method to detect hydrologic model behavioural parameters and quantify uncertainty

Ashkan Shokri*, Jeffrey P. Walker, Albert I.J.M. van Dijk, Ashley J. Wright, Valentijn R.N. Pauwels

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)


Finding an operational parameter vector is always challenging in the application of hydrologic models, with over-parameterization and limited information from observations leading to uncertainty about the best parameter vectors. Thus, it is beneficial to find every possible behavioural parameter vector. This paper presents a new methodology, called the patient rule induction method for parameter estimation (PRIM-PE), to define where the behavioural parameter vectors are located in the parameter space. The PRIM-PE was used to discover all regions of the parameter space containing an acceptable model behaviour. This algorithm consists of an initial sampling procedure to generate a parameter sample that sufficiently represents the response surface with a uniform distribution within the “good-enough” region (i.e., performance better than a predefined threshold) and a rule induction component (PRIM), which is then used to define regions in the parameter space in which the acceptable parameter vectors are located. To investigate its ability in different situations, the methodology is evaluated using four test problems. The PRIM-PE sampling procedure was also compared against a Markov chain Monte Carlo sampler known as the differential evolution adaptive Metropolis (DREAMZS) algorithm. Finally, a spatially distributed hydrological model calibration problem with two settings (a three-parameter calibration problem and a 23-parameter calibration problem) was solved using the PRIM-PE algorithm. The results show that the PRIM-PE method captured the good-enough region in the parameter space successfully using 8 and 107 boxes for the three-parameter and 23-parameter problems, respectively. This good-enough region can be used in a global sensitivity analysis to provide a broad range of parameter vectors that produce acceptable model performance. Moreover, for a specific objective function and model structure, the size of the boxes can be used as a measure of equifinality.

Original languageEnglish
Pages (from-to)1005-1025
Number of pages21
JournalHydrological Processes
Issue number8
Publication statusPublished - 15 Apr 2018
Externally publishedYes


  • equifinality
  • hydrological model
  • parameter estimation
  • uncertainty quantification


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