Articles | Volume 26, issue 20
https://doi.org/10.5194/hess-26-5341-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-26-5341-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
27 Oct 2022
Research article |
| 27 Oct 2022
| 27 Oct 2022
Pitfalls and a feasible solution for using KGE as an informal likelihood function in MCMC methods: DREAM(ZS) as an example
Yan Liu
CORRESPONDING AUTHOR
Chair of Hydrological Modeling and Water Resources, University of
Freiburg, 79098 Freiburg, Germany
Institute of Groundwater Management, Technical University of Dresden, 01069 Dresden, Germany
Jaime Fernández-Ortega
Department of Geology and Centre of Hydrogeology, University of
Málaga (CEHIUMA), 29071 Málaga, Spain
Matías Mudarra
Department of Geology and Centre of Hydrogeology, University of
Málaga (CEHIUMA), 29071 Málaga, Spain
Andreas Hartmann
Institute of Groundwater Management, Technical University of Dresden, 01069 Dresden, Germany
Chair of Hydrological Modeling and Water Resources, University of
Freiburg, 79098 Freiburg, Germany
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- High-Resolution Estimation of Soil Saturated Hydraulic Conductivity via Upscaling and Karhunen–Loève Expansion within DREAM(ZS) Y. Xia & N. Li https://doi.org/10.3390/app14114521
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- Proposing New Wetland Health and Risk Indicators Using Hydroclimatic Variables and Data-Driven Models for a Coastal Wetland A. Elyasi et al. https://doi.org/10.1007/s12237-025-01647-5
- Historical memory in remotely sensed soil moisture can enhance flash flood modeling for headwater catchments in Germany Y. Liu et al. https://doi.org/10.1016/j.jhydrol.2024.132395
- Sensitivity of montane grassland water fluxes to warming and elevated CO2 from local to catchment scale: A case study from the Austrian Alps M. Vremec et al. https://doi.org/10.1016/j.ejrh.2024.101970
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- Drought in a warmer, CO 2 -rich climate restricts grassland water use and soil water mixing J. Radolinski et al. https://doi.org/10.1126/science.ado0734
- Explainable residual learning for diagnosing infiltration model limitations: A Loess Plateau case study H. Zhu et al. https://doi.org/10.1016/j.envsoft.2026.107151
15 citations as recorded by crossref.
- Efficacy of evapotranspiration products on improving streamflow prediction in ungauged catchments under various hydrological models and climates S. Wu et al. https://doi.org/10.1016/j.jhydrol.2026.135857
- Assessment of left-censored data treatment methods using stochastic simulation F. Silva & É. Pinto https://doi.org/10.1590/2318-0331.282320230087
- Selecting a conceptual hydrological model using Bayes' factors computed with replica-exchange Hamiltonian Monte Carlo and thermodynamic integration D. Mingo et al. https://doi.org/10.5194/gmd-18-1709-2025
- High-Resolution Estimation of Soil Saturated Hydraulic Conductivity via Upscaling and Karhunen–Loève Expansion within DREAM(ZS) Y. Xia & N. Li https://doi.org/10.3390/app14114521
- Explainable PSO-optimised machine learning models for multi-pollutant air quality forecasting in major African cities with transfer learning G. Mazuruse et al. https://doi.org/10.3389/fenvs.2026.1828162
- Improved representation of soil moisture processes through incorporation of cosmic-ray neutron count measurements in a large-scale hydrologic model E. Fatima et al. https://doi.org/10.5194/hess-28-5419-2024
- Randomized block quasi-Monte Carlo sampling for generalized likelihood uncertainty estimation C. Onyutha https://doi.org/10.2166/nh.2024.136
- A multi-hydrological model ensemble prediction uncertainty estimation (e-PRUNE) framework C. Onyutha https://doi.org/10.2166/nh.2025.116
- Analysis of climatic extremes in the Parnaíba River Basin, Northeast Brazil, using GPM IMERG-V6 products F. Batista et al. https://doi.org/10.1016/j.wace.2024.100646
- Proposing New Wetland Health and Risk Indicators Using Hydroclimatic Variables and Data-Driven Models for a Coastal Wetland A. Elyasi et al. https://doi.org/10.1007/s12237-025-01647-5
- Historical memory in remotely sensed soil moisture can enhance flash flood modeling for headwater catchments in Germany Y. Liu et al. https://doi.org/10.1016/j.jhydrol.2024.132395
- Sensitivity of montane grassland water fluxes to warming and elevated CO2 from local to catchment scale: A case study from the Austrian Alps M. Vremec et al. https://doi.org/10.1016/j.ejrh.2024.101970
- Comparing hydraulic and water quality constraints in pollutant discharge estimation under data-scarce monitoring: a bayesian case study in the Cikakembang River, Indonesia D. Yudianto & C. Kieswanti https://doi.org/10.1007/s10661-026-15052-3
- Drought in a warmer, CO 2 -rich climate restricts grassland water use and soil water mixing J. Radolinski et al. https://doi.org/10.1126/science.ado0734
- Explainable residual learning for diagnosing infiltration model limitations: A Loess Plateau case study H. Zhu et al. https://doi.org/10.1016/j.envsoft.2026.107151
Saved (final revised paper)
Latest update: 02 Sep 2026
Short summary
We adapt the informal Kling–Gupta efficiency (KGE) with a gamma distribution to apply it as an informal likelihood function in the DiffeRential Evolution Adaptive Metropolis DREAM(ZS) method. Our adapted approach performs as well as the formal likelihood function for exploring posterior distributions of model parameters. The adapted KGE is superior to the formal likelihood function for calibrations combining multiple observations with different lengths, frequencies and units.
We adapt the informal Kling–Gupta efficiency (KGE) with a gamma distribution to apply it as an...
