Articles | Volume 23, issue 4
https://doi.org/10.5194/hess-23-2147-2019
© Author(s) 2019. 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-23-2147-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
30 Apr 2019
Research article |
| 30 Apr 2019
| 30 Apr 2019
A likelihood framework for deterministic hydrological models and the importance of non-stationary autocorrelation
Lorenz Ammann
CORRESPONDING AUTHOR
Swiss Federal Institute of Aquatic Science and
Technology (Eawag), Dubendorf, Switzerland
Department of Environmental Systems Science, ETH Zurich,
Zurich, Switzerland
Fabrizio Fenicia
Swiss Federal Institute of Aquatic Science and
Technology (Eawag), Dubendorf, Switzerland
Peter Reichert
Swiss Federal Institute of Aquatic Science and
Technology (Eawag), Dubendorf, Switzerland
Department of Environmental Systems Science, ETH Zurich,
Zurich, Switzerland
Viewed
Total article views: 5,001 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 13 Aug 2018)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 3,160 | 1,630 | 211 | 5,001 | 306 | 210 | 231 |
- HTML: 3,160
- PDF: 1,630
- XML: 211
- Total: 5,001
- Supplement: 306
- BibTeX: 210
- EndNote: 231
Total article views: 3,822 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 30 Apr 2019)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 2,446 | 1,177 | 199 | 3,822 | 306 | 186 | 209 |
- HTML: 2,446
- PDF: 1,177
- XML: 199
- Total: 3,822
- Supplement: 306
- BibTeX: 186
- EndNote: 209
Total article views: 1,179 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 13 Aug 2018)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 714 | 453 | 12 | 1,179 | 24 | 22 |
- HTML: 714
- PDF: 453
- XML: 12
- Total: 1,179
- BibTeX: 24
- EndNote: 22
Viewed (geographical distribution)
Total article views: 5,001 (including HTML, PDF, and XML)
Thereof 4,585 with geography defined
and 416 with unknown origin.
Total article views: 3,822 (including HTML, PDF, and XML)
Thereof 3,496 with geography defined
and 326 with unknown origin.
Total article views: 1,179 (including HTML, PDF, and XML)
Thereof 1,089 with geography defined
and 90 with unknown origin.
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
Cited
34 citations as recorded by crossref.
- Uncertainty quantification in watershed hydrology: Which method to use? A. Gupta & R. Govindaraju https://doi.org/10.1016/j.jhydrol.2022.128749
- Simulation of streamflow and instream loads of total suspended solids and nitrate in a large transboundary river basin using Source model and geospatial analysis K. Ly et al. https://doi.org/10.1016/j.scitotenv.2020.140656
- An error model for long-range ensemble forecasts of ephemeral rivers J. Bennett et al. https://doi.org/10.1016/j.advwatres.2021.103891
- Application of stochastic time dependent parameters to improve the characterization of uncertainty in conceptual hydrological models M. Bacci et al. https://doi.org/10.1016/j.jhydrol.2022.128057
- Pooled error variance and covariance estimation of sparse in situ soil moisture sensor measurements in agricultural fields in Flanders M. Hendrickx et al. https://doi.org/10.5194/soil-11-435-2025
- On the use of distribution-adaptive likelihood functions: Generalized and universal likelihood functions, scoring rules and multi-criteria ranking J. Vrugt et al. https://doi.org/10.1016/j.jhydrol.2022.128542
- Diagnosis of Model Errors With a Sliding Time‐Window Bayesian Analysis H. Hsueh et al. https://doi.org/10.1029/2021WR030590
- Estimating the parameters of a monthly hydrological model using hydrological signatures A. Matos et al. https://doi.org/10.1590/2318-0331.292420230121
- Design of stormwater bioretention systems for improved volume and peak runoff reduction U. Adhikari et al. https://doi.org/10.1016/j.jhydrol.2026.135248
- Performance comparison of green roof hydrological models for full-scale field sites I. Broekhuizen et al. https://doi.org/10.1016/j.hydroa.2021.100093
- Reliable hourly streamflow forecasting with emphasis on ephemeral rivers M. Li et al. https://doi.org/10.1016/j.jhydrol.2020.125739
- Identifying the possible driving mechanisms in Precipitation-Runoff relationships with nonstationary and nonlinear theory approaches T. Li et al. https://doi.org/10.1016/j.jhydrol.2024.131535
- A novel physical process-ensemble learning model framework with residual error decomposition to upskill daily runoff prediction Y. Kang et al. https://doi.org/10.1016/j.jhydrol.2024.132565
- Achieving high-quality probabilistic predictions from hydrological models calibrated with a wide range of objective functions J. Hunter et al. https://doi.org/10.1016/j.jhydrol.2021.126578
- Conceptual Stormwater Quality Models by Alternative Linear and Non-linear Formulations: an Event-Based Approach S. Sandoval et al. https://doi.org/10.1007/s10666-022-09838-1
- Expectile-based hydrological modelling for uncertainty estimation: Life after mean H. Tyralis et al. https://doi.org/10.1016/j.jhydrol.2022.128986
- Exploring a copula-based alternative to additive error models—for non-negative and autocorrelated time series in hydrology O. Wani et al. https://doi.org/10.1016/j.jhydrol.2019.06.006
- On constructing limits-of-acceptability in watershed hydrology using decision trees A. Gupta et al. https://doi.org/10.1016/j.advwatres.2023.104486
- Improving probabilistic streamflow predictions through a nonparametric residual error model J. Liang et al. https://doi.org/10.1016/j.envsoft.2024.105981
- Characterizing fast herbicide transport in a small agricultural catchment with conceptual models L. Ammann et al. https://doi.org/10.1016/j.jhydrol.2020.124812
- Residual-Oriented Optimization of Antecedent Precipitation Index and Its Impact on Flood Prediction Uncertainty J. Liang et al. https://doi.org/10.3390/w14203222
- A comparison of numerical approaches for statistical inference with stochastic models M. Bacci et al. https://doi.org/10.1007/s00477-023-02434-z
- Exploring the potential processes controlling changes in precipitation–runoff relationships in non-stationary environments T. Lan et al. https://doi.org/10.5194/hess-29-903-2025
- Hydrograph and recession flows simulations using deep learning: Watershed uniqueness and objective functions A. Gupta & S. McKenna https://doi.org/10.1016/j.hydroa.2024.100198
- Assimilating Low‐Cost High‐Frequency Sensor Data in Watershed Water Quality Modeling: A Bayesian Approach F. Han et al. https://doi.org/10.1029/2022WR033673
- Exploring controls on precipitation-runoff dependencies: Implications for non-stationary and spatially heterogeneous analyses T. Lan et al. https://doi.org/10.1016/j.jhydrol.2025.133333
- Quantifying the Uncertainty of a Conceptual Herbicide Transport Model With Time‐Dependent, Stochastic Parameters L. Ammann et al. https://doi.org/10.1029/2020WR028311
- A Data Censoring Approach for Predictive Error Modeling of Flow in Ephemeral Rivers Q. Wang et al. https://doi.org/10.1029/2019WR026128
- Potential and Challenges of Investigating Intrinsic Uncertainty of Hydrological Models With Stochastic, Time‐Dependent Parameters P. Reichert et al. https://doi.org/10.1029/2020WR028400
- Confidence intervals of the Kling-Gupta efficiency J. Vrugt & D. de Oliveira https://doi.org/10.1016/j.jhydrol.2022.127968
- Probabilistic Predictions of Ecologically Relevant Hydrologic Indices Using a Hydrological Model J. Hernandez‐Suarez & A. Nejadhashemi https://doi.org/10.1029/2021WR031104
- Legacy pollutants in fractured aquifers: Analytical approximations for back diffusion to predict atrazine concentrations under uncertainty E. Petrova et al. https://doi.org/10.1016/j.jconhyd.2023.104161
- Reliability of SWMM for Predicting Performance of Field-Scale Bioretention Systems U. Adhikari et al. https://doi.org/10.1061/JIDEDH.IRENG-10589
- The influence of the correlation-covariance structure of measurement errors over uncertainties propagation in online monitoring: application to environmental indicators in SUDS F. Peña-Heredia et al. https://doi.org/10.1007/s10661-021-09097-9
34 citations as recorded by crossref.
- Uncertainty quantification in watershed hydrology: Which method to use? A. Gupta & R. Govindaraju https://doi.org/10.1016/j.jhydrol.2022.128749
- Simulation of streamflow and instream loads of total suspended solids and nitrate in a large transboundary river basin using Source model and geospatial analysis K. Ly et al. https://doi.org/10.1016/j.scitotenv.2020.140656
- An error model for long-range ensemble forecasts of ephemeral rivers J. Bennett et al. https://doi.org/10.1016/j.advwatres.2021.103891
- Application of stochastic time dependent parameters to improve the characterization of uncertainty in conceptual hydrological models M. Bacci et al. https://doi.org/10.1016/j.jhydrol.2022.128057
- Pooled error variance and covariance estimation of sparse in situ soil moisture sensor measurements in agricultural fields in Flanders M. Hendrickx et al. https://doi.org/10.5194/soil-11-435-2025
- On the use of distribution-adaptive likelihood functions: Generalized and universal likelihood functions, scoring rules and multi-criteria ranking J. Vrugt et al. https://doi.org/10.1016/j.jhydrol.2022.128542
- Diagnosis of Model Errors With a Sliding Time‐Window Bayesian Analysis H. Hsueh et al. https://doi.org/10.1029/2021WR030590
- Estimating the parameters of a monthly hydrological model using hydrological signatures A. Matos et al. https://doi.org/10.1590/2318-0331.292420230121
- Design of stormwater bioretention systems for improved volume and peak runoff reduction U. Adhikari et al. https://doi.org/10.1016/j.jhydrol.2026.135248
- Performance comparison of green roof hydrological models for full-scale field sites I. Broekhuizen et al. https://doi.org/10.1016/j.hydroa.2021.100093
- Reliable hourly streamflow forecasting with emphasis on ephemeral rivers M. Li et al. https://doi.org/10.1016/j.jhydrol.2020.125739
- Identifying the possible driving mechanisms in Precipitation-Runoff relationships with nonstationary and nonlinear theory approaches T. Li et al. https://doi.org/10.1016/j.jhydrol.2024.131535
- A novel physical process-ensemble learning model framework with residual error decomposition to upskill daily runoff prediction Y. Kang et al. https://doi.org/10.1016/j.jhydrol.2024.132565
- Achieving high-quality probabilistic predictions from hydrological models calibrated with a wide range of objective functions J. Hunter et al. https://doi.org/10.1016/j.jhydrol.2021.126578
- Conceptual Stormwater Quality Models by Alternative Linear and Non-linear Formulations: an Event-Based Approach S. Sandoval et al. https://doi.org/10.1007/s10666-022-09838-1
- Expectile-based hydrological modelling for uncertainty estimation: Life after mean H. Tyralis et al. https://doi.org/10.1016/j.jhydrol.2022.128986
- Exploring a copula-based alternative to additive error models—for non-negative and autocorrelated time series in hydrology O. Wani et al. https://doi.org/10.1016/j.jhydrol.2019.06.006
- On constructing limits-of-acceptability in watershed hydrology using decision trees A. Gupta et al. https://doi.org/10.1016/j.advwatres.2023.104486
- Improving probabilistic streamflow predictions through a nonparametric residual error model J. Liang et al. https://doi.org/10.1016/j.envsoft.2024.105981
- Characterizing fast herbicide transport in a small agricultural catchment with conceptual models L. Ammann et al. https://doi.org/10.1016/j.jhydrol.2020.124812
- Residual-Oriented Optimization of Antecedent Precipitation Index and Its Impact on Flood Prediction Uncertainty J. Liang et al. https://doi.org/10.3390/w14203222
- A comparison of numerical approaches for statistical inference with stochastic models M. Bacci et al. https://doi.org/10.1007/s00477-023-02434-z
- Exploring the potential processes controlling changes in precipitation–runoff relationships in non-stationary environments T. Lan et al. https://doi.org/10.5194/hess-29-903-2025
- Hydrograph and recession flows simulations using deep learning: Watershed uniqueness and objective functions A. Gupta & S. McKenna https://doi.org/10.1016/j.hydroa.2024.100198
- Assimilating Low‐Cost High‐Frequency Sensor Data in Watershed Water Quality Modeling: A Bayesian Approach F. Han et al. https://doi.org/10.1029/2022WR033673
- Exploring controls on precipitation-runoff dependencies: Implications for non-stationary and spatially heterogeneous analyses T. Lan et al. https://doi.org/10.1016/j.jhydrol.2025.133333
- Quantifying the Uncertainty of a Conceptual Herbicide Transport Model With Time‐Dependent, Stochastic Parameters L. Ammann et al. https://doi.org/10.1029/2020WR028311
- A Data Censoring Approach for Predictive Error Modeling of Flow in Ephemeral Rivers Q. Wang et al. https://doi.org/10.1029/2019WR026128
- Potential and Challenges of Investigating Intrinsic Uncertainty of Hydrological Models With Stochastic, Time‐Dependent Parameters P. Reichert et al. https://doi.org/10.1029/2020WR028400
- Confidence intervals of the Kling-Gupta efficiency J. Vrugt & D. de Oliveira https://doi.org/10.1016/j.jhydrol.2022.127968
- Probabilistic Predictions of Ecologically Relevant Hydrologic Indices Using a Hydrological Model J. Hernandez‐Suarez & A. Nejadhashemi https://doi.org/10.1029/2021WR031104
- Legacy pollutants in fractured aquifers: Analytical approximations for back diffusion to predict atrazine concentrations under uncertainty E. Petrova et al. https://doi.org/10.1016/j.jconhyd.2023.104161
- Reliability of SWMM for Predicting Performance of Field-Scale Bioretention Systems U. Adhikari et al. https://doi.org/10.1061/JIDEDH.IRENG-10589
- The influence of the correlation-covariance structure of measurement errors over uncertainties propagation in online monitoring: application to environmental indicators in SUDS F. Peña-Heredia et al. https://doi.org/10.1007/s10661-021-09097-9
Saved (final revised paper)
Latest update: 03 Nov 2026
Short summary
The uncertainty of hydrological models can be substantial, and its quantification and realistic description are often difficult. We propose a new flexible probabilistic framework to describe and quantify this uncertainty. It is show that the correlation of the errors can be non-stationary, and that accounting for temporal changes in correlation can lead to strongly improved probabilistic predictions. This is a promising avenue for improving uncertainty estimation in hydrological modelling.
The uncertainty of hydrological models can be substantial, and its quantification and realistic...
Altmetrics
Final-revised paper
Preprint