Mechanistic models, grounded in the Richards and advection-dispersion equations, provide a comprehensive theoretical framework for describing hydrological processes and solute transport in the vadose zone. Due to the limited transferability of laboratory estimates to field conditions, model parameters are often inversely estimated from transient field observations, making calibration an increasingly common practice in vadose zone modeling. The inescapable necessity to include some form of uncertainty assessment has led to the rise of Bayesian inference as the preferred tool for probabilistic calibration. By combining prior information with observations and model predictions, Bayesian inference enables the estimation of parameter posterior distributions, verification of model adequacy, and assessment of the model’s predictive uncertainty (The Good). Nevertheless, its application to mechanistic vadose zone models poses multiple challenges, among which the curse of dimensionality is likely the most critical (The Bad). We demonstrate that the performance of state-of-the-art Markov Chain Monte Carlo (MCMC) methods deteriorates even for moderately high-dimensional inverse problems, due to the shrinking of the typical set and improper spatiotemporal discretizations of the vadose zone domain during Monte Carlo runs, with both issues being exacerbated under model misspecification. Although using the gradient of the posterior density could mitigate the former problem, it is often rendered impractical due to numerical challenges. While these issues are generally manageable in low-dimensional settings, Bayesian inference remains hindered when applied in combination with computationally intensive vadose zone models (e.g., 2D/3D models, reactive solute transport) (The Ugly). We demonstrate that surrogate-based models can alleviate this problem, though their training and validation are not without difficulties. Based on these findings, we draw some conclusions and propose possible future directions for uncertainty assessment in physically based vadose zone modeling. 

How to cite: Brunetti, G. and Šimůnek, J.: Bayesian Inference in Physically-based Vadose Zone Modeling: The Good, The Bad and The Ugly, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-2130, https://doi.org/10.5194/egusphere-egu25-2130, 2025.

Hydrogeological modeling is critical in effective water management, particularly in response to increasing water demands and climate variability. However, it is subject to significant uncertainty, especially in hydrological data-scarce regions such as mountainous areas. Reducing parameter and prediction uncertainty and efficiently quantifying and analyzing uncertainty are essential for optimizing water resource management. Time-lapse gravity (TLG) is an emerging hydrogeophysical technique that provides spatially-integrative information on water storage changes. It is a promising, non-invasive solution for filling hydrological data gaps, yet efficient assimilation into hydrogeological models has not yet been achieved.

To help address these challenges, we have developed a numerical framework for the coupled assimilation of TLG and traditional hydro(geo)logical data into groundwater models. The open-source, user-friendly python tool integrates coupled groundwater-gravity forward modelling and powerful inverse modeling procedures. It implements a highly accurate and computationally efficient forward 3-D gravity model. The framework accommodates varying levels of hydrological model complexity, as developed in FloPy (a python wrapper for MODFLOW-based models). Moreover, by integrating PyEMU (a python wrapper for PEST++), the framework employs First-Order, Second-Moment (FOSM)- based techniques, offering an efficient approach for estimating uncertainty. Our tool facilitates the assimilation of TLG data to constrain parameters, make predictions, and perform uncertainty analyses. Finally, we employ our framework to test the impacts of including TLG data in groundwater models. Our results show that TLG data can significantly reduce parameter and prediction uncertainty, as well as computational time.

How to cite: Mohammadi, N., Mohammadigheymasi, H., and J.S. Halloran, L.: Mitigating uncertainty in hydrogeological modeling by integrating time-lapse gravity data, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-7128, https://doi.org/10.5194/egusphere-egu25-7128, 2025.

Numerical groundwater models are essential tools for simulating and understanding subsurface hydrological processes, supporting water resource management and environmental decision-making. Global sensitivity analysis (GSA) and history matching (HM) are critical methods for evaluating the influence of uncertain model parameters and calibrating models to observed data. However, applying these methods to transient, computationally expensive, large-scale groundwater models presents significant challenges.

A key obstacle arises from the requirement to adapt initial conditions for every model input parameter set during GSA and HM. Unlike steady-state models, transient groundwater systems often lack equilibrium, requiring initialization that reflects the dynamic nature of the system. Traditional approaches, such as performing a warmup simulation for each parameter set, ensure accurate initialization but are computationally infeasible for highly parameterized models.

To address this limitation, we propose a novel method to approximate suitable initial conditions for each parameter set without the need for costly warmup simulations. Our approach utilizes the fact that, after a system-specific relaxation time, the simulation becomes independent of the initial condition. Using a toy model as a test case, we demonstrate that the approximated initial conditions are sufficiently accurate for practical applications, with minimal impact on the outcomes of GSA and HM. The computational savings achieved through this method are substantial, making it particularly advantageous for large-scale systems with many parameters.

We also provide an analysis of the trade-offs between accuracy and efficiency and show that the inaccuracy introduced by the approximation is negligible. Finally, we outline a roadmap for extending this method to real-world groundwater models, addressing the computational barriers that may currently limit the application of GSA and HM in transient systems.

How to cite: Jupe, T. and Class, H.: Efficient Approximation of Initial Conditions for Global Sensitivity Analysis and History Matching of Transient Numerical Groundwater Models, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-11364, https://doi.org/10.5194/egusphere-egu25-11364, 2025.

Hydrological studies often depend on model simulations to analyze flood occurrences and frequency. A major challenge in this domain is quantifying and reducing uncertainty in simulations, particularly when dealing with complex models like WRF-Hydro, which involve extensive parameterization. To address this, we present a novel parameter estimation approach using Iterative Ensemble Smoothers (iES). While iES has been widely applied in calibrating parameters for general circulation models and groundwater models, its potential in improving surface water predictions remains underexplored. This study leverages iES to efficiently estimate and refine parameters, generating ensembles of equally plausible parameter sets. These ensembles yield streamflow predictions that incorporate parameter uncertainty. Unlike traditional sequential simulation methods, iES reduces computational costs by running ensembles of simulations (e.g., 100 members) parallelly refining the parameter space iteratively. Typically, only 3–4 iterations are sufficient to achieve convergence, resulting in reliable parameter sets with low wall clock times. We applied the iES-based calibration framework to the Carson River watershed in the mountainous western United States, focusing on 16 parameters spanning the land surface model, terrain routing, and channel routing components of WRF-Hydro. These parameters capture soil properties, runoff characteristics, groundwater dynamics, vegetation attributes, and snow processes. By refining these parameters, our approach improved the simulation of high-flow events, particularly by better representing snowmelt dynamics critical for flood modeling. Enhanced simulation of snow accumulation and melt processes led to more accurate streamflow predictions, providing valuable insights for flood risk management and water resource planning in snow-dominated regions. Specifically, the iES algorithm demonstrated convergence by the third iteration, with the KGE value improving from 0 in the initial run to 0.41 in the first iteration, 0.65 in the second, and 0.71 in the third Our results highlight significant advancements in computational efficiency, parameter precision, and uncertainty quantification.

How to cite: Pradhan, A., Wright, D., Peng, K., Fienen, M., and Alexander, G. A.: Iterative Ensemble Calibration of WRF-Hydro for Improved Hydrological Modeling, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-16292, https://doi.org/10.5194/egusphere-egu25-16292, 2025.

This paper applies recent results of risk bounds for time series forecasting to identify optimal complexity of conceptual models and complexity regularised streamflow predictions based on Vapnik-Chervonenkis generalization theory. Earlier reported similar study with SAC-SMA and SIXPAR conceptual models but on two large regions from CAMELS data set is extended to more basins in CONUS to demonstrate the effect of regularizing hydrological model calibration on streamflow prediction over unseen data. SAC-SMA and SIXPAR (conceptual simplification of SAC-SMA) are used as model examples. Results show that the effect of complexity regularization more visible on SIXPAR than SAC-SMA. Results further suggest that when basins itself are complex, regularizing complexity of models does not help and depends on hydrological characteristics of the basins. The benefits of complexity regularization are more evident when assessed based on variance based performance metrices such as correlation coefficient and the slope of observed vs predicted fit than bias and mean absolute error metrices. The paper therefore offers a novel, though computationally intense, method to calibrate conceptual models while controlling for their model complexity.

How to cite: Pande, S., Moayeri, M., and Ponce-Pacheco, M.: Regularized calibration of conceptual hydrological models , EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-18346, https://doi.org/10.5194/egusphere-egu25-18346, 2025.

Global sensitivity analysis (GSA) is a crucial tool for identifying influential parameters in hydrologic models. GSA methods can guide the selection of calibration parameters, thereby reducing the dimensionality of the parameter space by discarding less influential parameters. This study will explore the use of Random Forest as a GSA method. In particular, feature importance in Random Forest can be interpreted as sensitivity measures of input parameters once the regression task is performed with respect to the output variable of interest. This work will be focused on a large-sample application of the Variable Infiltration Capacity (VIC) model across Europe. A substantial number of Monte Carlo simulations will be carried out for each catchment in order to explore the parameter space and generate a large dataset for the Random Forest regression. Parameters sensitivities will be quantified for the Kling-Gupta Efficiency (KGE) of daily streamflow based on feature importance, and results will be compared against traditional GSA techniques such as the Standardized Regression Coefficients (SRC) and the Regional Sensitivity Analysis (RSA) methods.

Acknowledgments: This study has been funded by a Humboldt Research Fellowship for Postdoctoral Researchers from the Alexander von Humboldt Foundation.

How to cite: Yeste, P. and Bronstert, A.: On the use of Random Forest as a Global Sensitivity Analysis method: a large-sample application across Europe, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-10333, https://doi.org/10.5194/egusphere-egu25-10333, 2025.

Information-theoretical evaluation of probabilistic hydrological forecasts has several advantages. Firstly, forecasts in terms of probability put the onus for correct expression of uncertainty on the forecaster, as opposed to the recipient of the forecast. Secondly, formulating the evaluation of forecast quality in terms of information-measures enables consistency with the principle of minimum description length. 

When applying the information-theoretical evaluation framework to forecasts of mixed-type variables, such as streamflow in rivers with intermittent flow regimes, subjectivity is introduced through the choice of units in which streamflow is measured. This can lead to preference reversals between forecasts when using certain information measures.  

At the hand of some examples, we explore the origins of this subjectivity, possible interpretations, as well as avenues for its resolution. Among others, the role of observation uncertainty and the physical meaning of zero flow are discussed. 

How to cite: Weijs, S.: Subjectivity in evaluation of forecasts for intermittent streamflow - an information-theoretical perpective, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-15081, https://doi.org/10.5194/egusphere-egu25-15081, 2025.

Global Water Models (GWMs) are essential for understanding and projecting global hydrological fluxes under changing climate conditions, yet their outputs often diverge from each other, limiting their utility for robust decision-making. We can evaluate GWM using functional relationships that capture the spatial co-variability of over 100 forcing variables, model parameters and key output variables (such as groundwater recharge). Uncovering and identifying relationships and interactions embedded in the high-dimensional and complex input-output datasets created by these simulation models requires measures of dependence that can capture a wide range of functional behaviors. In this study, we test the Maximal Information Coefficient (MIC), an information theory based, non-parametric measure of dependence, to systematically explore and characterize input-output relationships in the Community Water Model (CWatM) forced with ISIMIP3a observed climate data. Our results demonstrate that MIC not only recovers expected hydrological controls but also reveals previously unnoticed functional relationships that Pearson and Spearman correlation coefficients would have overlooked. Additional analysis steps enable us to isolate key explanatory factors from the model’s internal structure and domain-specific factors. This information theory based approach provides a systematic methodology to improve model diagnostic capabilities, guide targeted research directions, and ultimately strengthen the credibility and interpretability of large-scale hydrological simulations.

How to cite: Wagener, T., Serra Lasierra, M.-M., Wiesner, K., Höhne, M., Herbinger, J., Tang, T., and Wada, Y.: Using information theory to understand process controls in Global Water Models, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-14758, https://doi.org/10.5194/egusphere-egu25-14758, 2025.