### Abstract

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 (DREAM_{ZS}) 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 language | English |
---|---|

Pages (from-to) | 1005-1025 |

Number of pages | 21 |

Journal | Hydrological Processes |

Volume | 32 |

Issue number | 8 |

DOIs | |

Publication status | Published - 15 Apr 2018 |

### Keywords

- equifinality
- hydrological model
- parameter estimation
- PRIM-PE
- uncertainty quantification

### Cite this

*Hydrological Processes*,

*32*(8), 1005-1025. https://doi.org/10.1002/hyp.11464

}

*Hydrological Processes*, vol. 32, no. 8, pp. 1005-1025. https://doi.org/10.1002/hyp.11464

**Application of the patient rule induction method to detect hydrologic model behavioural parameters and quantify uncertainty.** / Shokri, Ashkan; Walker, Jeffrey P.; van Dijk, Albert I. J. M.; Wright, Ashley J.; Pauwels, Valentijn R. N.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Application of the patient rule induction method to detect hydrologic model behavioural parameters and quantify uncertainty

AU - Shokri, Ashkan

AU - Walker, Jeffrey P.

AU - van Dijk, Albert I. J. M.

AU - Wright, Ashley J.

AU - Pauwels, Valentijn R. N.

PY - 2018/4/15

Y1 - 2018/4/15

N2 - 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.

AB - 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.

KW - equifinality

KW - hydrological model

KW - parameter estimation

KW - PRIM-PE

KW - uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85044226097&partnerID=8YFLogxK

U2 - 10.1002/hyp.11464

DO - 10.1002/hyp.11464

M3 - Article

VL - 32

SP - 1005

EP - 1025

JO - Hydrological Processes

JF - Hydrological Processes

SN - 1099-1085

IS - 8

ER -