Michael N. Fienen

There are often competing options for process representation when designing process‐based hydrologic models. Comparing candidate model configurations during model development can be computationally expensive and existing methods for evaluating prior‐data conflict often cannot distinguish between multiple models with low prior‐data conflict. Here, we demonstrate a workflow to efficiently identify better performing models by comparing prior model output distributions to observed data distributions using a metric referred to as Mahalanobis distance deviation (). The metric was developed to incorporate the notion of balancing model fit with model complexity into prior‐data conflict approaches. Ninety‐six different configurations of the Precipitation‐Runoff Modeling System were designed for the East River watershed, Colorado by considering uncertainty in representing spatial discretization, forcing data, potential evapotranspiration, soil zone flow, snow depletion curve, and transpiration period processes. The prior‐to‐calibration adequacy of each model was estimated by calculating for observed streamflow, areal runoff, actual evapotranspiration, groundwater recharge, soil moisture, and snow‐covered area. All 96 models were then calibrated using the PEST++ iterative ensemble smoother to quantify their performance and validate the results. The metrics calculated from prior parameter ensembles as small as 25 exhibited strong correlation with calibrated objective function values highlighting the substantial information on model performance that can be gained prior to calibration through the workflow. Spatial discretization and forcing data were most influential on model performance and their better performing representations were most easily identified. This work demonstrates an efficient approach to identify better performing model configurations and the processes driving those improvements.

Groundwater depletion for agricultural irrigation poses significant environmental and economic challenges. This study introduces a proof‐of‐concept that combines hydro‐economic modeling, scenario‐based modeling, and multi‐objective optimization to manage pumping curtailment in an over‐allocated basin in the western United States. Three optimization scenarios were evaluated, each offering different degrees of management flexibility. Results reveal that scenarios with finer spatial resolution achieved greater environmental benefits per unit profit loss. Additionally, strategies allowing fractional reductions in curtailed wells–rather than complete shutdowns based on water rights seniority–substantially improved efficiency, highlighting the value of increased decision‐making flexibility. Although scenario testing can aid stakeholder engagement and strategy exploration, multi‐objective optimization provides a systematic framework to quantify tradeoffs between competing objectives. This combined approach demonstrates promise for building consensus and supporting the design of sustainable water management strategies that balance agricultural livelihoods with ecosystem preservation.

History matching of large hydrologic models is challenging due to data sparsity and non‐unique process combinations (and associated parameters) that can produce similar model predictions. We develop an ensemble‐based history matching (and uncertainty quantification) approach using an iterative ensemble smoother (iES) method for three cutouts of the National Hydrologic Model (NHM) and qualitatively compare the results and performance to the stepwise history matching approach. In the latter approach, subsets of parameters and observations were sequentially calibrated to a diverse range of observations to mitigate non‐uniqueness and local minima. In iES, localization simulates the same causal connections between parameters and observations without the need (and computational cost) of sequential history matching steps. iES uses a weighted sum‐of‐squared‐errors objective function which allows differential weighting of multiple data sources. Formal adoption of range observation also pushes results to within ranges of observation values rather than discrete values. Overall, the ensemble approach performs similarly to the stepwise approach. Both approaches performed poorly for the cutout representing a snowmelt‐dominated watershed, indicating a structural issue in the process representation of the model. The main advantage of iES is quantification of uncertainty in both the history matching and the predictions of interest.

Regulatory agencies in humid temperate environments rely on timely evaluations of streamflow depletion and drawdown to protect aquatic ecosystems and existing water users. Numerical models offer detailed insights, but their complexity and time demands often preclude their practical use in rapid decision‐making. We present pycap‐dss, an open‐source Python package that implements a suite of analytical solutions for estimating streamflow depletion and drawdown. The tool supports superposition of multiple wells and time‐varying pumping, enabling cumulative impact assessments in situations with multiple wells and streams. The software is modular and extensible, allowing users to interchange solutions or add new analytical methods. A YAML‐based configuration supports batch processing of multiple wells, and an optional AnalysisProject class facilitates integration with regulatory workflows. Rigorous unit and regression testing ensures computational reliability, and continuous integration supports ongoing development. We demonstrate deterministic examples of drawdown where multiple solutions are readily compared and streamflow depletion with multiple wells in the Central Sands region of Wisconsin. We also show the value of Monte Carlo analyses of streamflow depletion in the same Central Sands example, leveraging computational efficiency to evaluate the uncertainty of individual and cumulative streamflow depletion calculations from over 200 high‐capacity wells.

Model criticism, discrimination, and selection methods often rely on calibrated model outputs. Because calibration can be computationally expensive, model criticism can first be undertaken by assessing model outputs obtained from limited prior parameter ensembles. However, such prior‐based methods are often heuristic and do not formalize the notion of balancing model consistency with data and model complexity (i.e., model adequacy). We present a new framework to discriminate among candidate models prior to calibration that formalizes prior‐to‐calibration model adequacy into a metric to implicitly balance prior model output data coverage with model complexity represented by prior output (co)variance. The prior model adequacy metric “Mahalanobis distance deviation” quantifies the deviation of (a) the set of squared Mahalanobis distances of data from a prior model output distribution from (b) the set of squared Mahalanobis distances of data from their own distribution. A new data worth metric “discernment value” is also presented which quantifies the value of data for screening less‐adequate models prior to calibration. Discernment value is calculated from the change in variance of a weighted average of prior model outputs from all candidate models due to less‐adequate model outputs receiving lower weight. The framework is demonstrated using a one‐dimensional groundwater flow model with eight possible configurations. A synthetic data network is used to test the framework. Results show the framework identifies the candidate models most similar to the true model used to create the synthetic data. Discernment values show variation in the value of different data types and locations for screening less‐adequate models.

PEST++IES (White 2018; White et al. 2020) is widely used in the groundwater modeling community for its ability to perform computationally efficient history matching and uncertainty analysis in a highly parameterized context. One primary advantage of using an iterative ensemble smoother is that the number of model runs required per iteration depends on the number of realizations in an ensemble, not the number of parameters in each realization. However, this raises the question: what is the optimal number of realizations and iterations to use for any one model before the point of diminishing returns? Using a modified version of the Freyberg model (Freyberg 1988; Hunt et al. 2020), different parameter and observation scenarios were evaluated for four iterations and ensembles of 10, 25, 50, 100, 250, 500, 1000, and 2000 realizations. To match observations, PEST++IES altered hydraulic conductivity ( k ), both globally across the model and locally at three different pilot point densities, as well as global recharge (via a single multiplier), global river conductance, and individual well flow rates. Risk‐based well capture zone results (Fienen et al. 2022a) and estimated hydraulic conductivity fields from each scenario were quantitatively and qualitatively compared against the “truth” model and its outputs. Across the cases examined, ensemble sizes of 100 to 250 realizations and two PEST++IES iterations were generally sufficient to achieve good results.

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.

The history-matching approach to parameter estimation with models enables a powerful offshoot analysis of data worth—using the uncertainty of a model forecast as a metric for the worth of data. Adding observation data will either have no impact on forecast uncertainty or will reduce it. Removing existing data will either have no impact on forecast uncertainty or will increase it. The history-matching framework makes it possible to perform this quantitative analysis leveraging the connections among observations, model parameters, and model forecasts. We show this behavior on a specific groundwater flow model of the Mississippi Alluvial Plain and show where the analysis can be informative for considering the potential design of an observation network based on existing or potential observations.