Rui Hugman

Computational demands for uncertainty quantification and optimization often exceed available resources for high‐fidelity environmental models. While surrogate modeling (or model emulation) offers a pragmatic solution, widespread adoption is hindered by a significant “implementation gap”: practitioners often lack standardized, robust tools to integrate emulation techniques directly into existing modeling workflows, relying instead on bespoke implementations. To bridge this gap, we present the Emulator module within the open‐source pyEMU package. This framework provides a “plug‐and‐play” architecture for deploying Gaussian Process Regression (GPR), Data‐Space Inversion (DSI) and other model emulation approaches. The framework automates the complex “plumbing” of emulation‐based workflows, including non‐Gaussian data transformation and the generation of PEST interface files, allowing trained surrogates to serve as drop‐in replacements for physics‐based models. We believe this one‐to‐one correspondence between physics‐based model and emulator‐based workflows will facilitate direct comparisons between the two so that the community in general can build up the knowledge of when and how to effectively and appropriately deploy emulation. We demonstrate the utility of these tools through a benchmarking optimization problem and a history‐matching application on a synthetic groundwater model.

This paper presents the results of the 2022 Groundwater Time Series Modelling Challenge, where 15 teams from different institutes applied various data-driven models to simulate hydraulic-head time series at four monitoring wells. Three of the wells were located in Europe and one was located in the USA in different hydrogeological settings in temperate, continental, or subarctic climates. Participants were provided with approximately 15 years of measured heads at (almost) regular time intervals and daily measurements of weather data starting some 10 years prior to the first head measurements and extending around 5 years after the last head measurement. The participants were asked to simulate the measured heads (the calibration period), to provide a prediction for around 5 years after the last measurement (the validation period for which weather data were provided but not head measurements), and to include an uncertainty estimate. Three different groups of models were identified among the submissions: lumped-parameter models (three teams), machine learning models (four teams), and deep learning models (eight teams). Lumped-parameter models apply relatively simple response functions with few parameters, while the artificial intelligence models used models of varying complexity, generally with more parameters and more input, including input engineered from the provided data (e.g. multi-day averages). The models were evaluated on their performance in simulating the heads in the calibration period and in predicting the heads in the validation period. Different metrics were used to assess performance, including metrics for average relative fit, average absolute fit, fit of extreme (high or low) heads, and the coverage of the uncertainty interval. For all wells, reasonable performance was obtained by at least one team from each of the three groups. However, the performance was not consistent across submissions within each group, which implies that the application of each method to individual sites requires significant effort and experience. In particular, estimates of the uncertainty interval varied widely between teams, although some teams submitted confidence intervals rather than prediction intervals. There was not one team, let alone one method, that performed best for all wells and all performance metrics. Four of the main takeaways from the model comparison are as follows: (1) lumped-parameter models generally performed as well as artificial intelligence models, which means they capture the fundamental behaviour of the system with only a few parameters. (2) Artificial intelligence models were able to simulate extremes beyond the observed conditions, which is contrary to some persistent beliefs about these methods. (3) No overfitting was observed in any of the models, including in the models with many parameters, as performance in the validation period was generally only a bit lower than in the calibration period, which is evidence of appropriate application of the different models. (4) The presented simulations are the combined results of the applied method and the choices made by the modeller(s), which was especially visible in the performance range of the deep learning methods; underperformance does not necessarily reflect deficiencies of any of the models. In conclusion, the challenge was a successful initiative to compare different models and learn from each other. Future challenges are needed to investigate, for example, the performance of models in more variable climatic settings to simulate head series with significant gaps or to estimate the effect of drought periods.

Collecting detailed hydrogeological data before, during, and after remediation campaigns is essential for effective management and monitoring of contaminated sites. As in-situ remediation injection treatment becomes more popular, recording the hydraulic response during these events offers an opportunity to collect detailed data on hydrogeological parameters. Often, multiple injections are performed in a grid pattern over an area targeted for treatment, essentially serving as spatially distributed and high-frequency inverse pumping tests. This information, which is often overlooked, can be assimilated into numerical models for enhanced site characterization and improved forecasts of management actions. However, the high pressures during injections often result in hydraulic fracturing. These events can represent temporary or permanent changes in aquifer properties and should be considered when assimilating injection response data into a model to reduce the risk of introducing parameter bias. Four groundwater models were developed for a contaminated site in Sweden, treated with in-situ injections in 2017. The models were designed to evaluate strategies for assimilating injection response data, including alternative weighting schemes and the use of time-varying parameters around injection points to account for hydraulic fracturing during injections. Results show that assigning a higher weight to observations recorded during injections, compared to records of ambient head, combined with the use of time-varying parameters, yielded the best results with the lowest risk of underestimating predictive uncertainty. A subsequent data worth analysis revealed that injection response data provided detailed insights into aquifer properties in the injection zone that were not available from ambient head data alone.

The Algarve region of Portugal is experiencing severe water scarcity with existing water supplies insufficient to meet demand, with limited resilience to drought. Managed aquifer recharge (MAR) can provide intermediate storage and bridge the gap between water availability and demand, with success depending on the water available and the aquifer capacity to accept and store the water. We present the results of a regional study quantifying both these aspects to estimate the regional potential for MAR. Our results demonstrate that MAR can comprise 10% of the total water demand of the region (24 Mm³/yr) using water that is not otherwise captured, with quality that meets the requirements of the Groundwater Directive. MAR can replace 15 Mm³/yr of surface water used in the public irrigation perimeters and 9 Mm³/yr can be used to develop and maintain a strategic groundwater resource in the aquifers of the Central Algarve. Although climate change is predicted to result in an 8–13% decrease in MAR recharge, this can be addressed by incrementally increasing MAR design capacity. MAR has similar water resource benefits to the planned major infrastructure projects (desalination and River Guadiana abstraction), with reduced environmental impacts and lower costs than almost all feasible alternatives. We conclude that MAR is an important measure to increase water supply security and drought resilience in the Algarve region.

This paper describes a methodology for undertaking probabilistic investigations into the locations at which contaminants have leaked into a groundwater system. The methodology is built with highly parameterized, stochastic history-matching in mind. It is able to reduce uncertainties associated with estimates of subsurface hydraulic properties at the same time as it reduces uncertainties associated with inferences of contaminant sources. Particles are used to simulate contaminant movement. This reduces simulator execution time while increasing simulator stability. Borehole measurements of groundwater chemistry are endowed with a binary classification that indicates the presence, or otherwise, of a contaminant plume. This classification is transferred to passing particles as a detect or nondetect status awarded to their trajectories. Because this status is continuous with respect to model parameters, the latter can be adjusted in order to ensure that the same trajectory cannot possess both a detect status and a nondetect status. Particle trajectory statuses can be assigned to model cells from which they are released. By calculating cell statistics using a large number of history-match-constrained, stochastic parameter fields, probability maps can be drawn. We illustrate two of these. The first maps the probability that a contaminant sourced at a particular location will go undetected by the current observation network. The second maps the probability that a contaminant source cannot exist at a particular location. The method is extended to examine the worth of supplementing an existing observation network with new wells.

The primary tasks of decision-support modelling are to quantify and reduce the uncertainties of decision-critical model predictions. Reduction of predictive uncertainty requires assimilation of information. Generally, this information resides in two places: 1) expert knowledge emerging from site characterization and 2) field measurements of present and historical system behavior. The former is uncertain and should therefore be expressed stochastically in a model. The range of parameter and predictive possibilities can then be constrained through history-matching. Implementation of these Bayesian principles places conflicting demands on the level of model structural complexity. A high level of structural complexity can facilitate expression of expert knowledge by establishing model details that are recognizable by site experts, and through supporting model parameters that bear a close relationship to real-world hydraulic properties. However, such models often run slowly and are numerically delicate; history-matching therefore becomes difficult or impossible. In contrast, if endowed with enough parameters, structurally simple models facilitate the achievement of a good fit between model outputs and field measurements. However, the values with which parameters are endowed may bear a looser relationship with real-world properties and are therefore less receptive to information born of expert knowledge. The model design process is therefore one of compromise. In this paper we describe a methodology that reduces the cost of compromise by allowing expert knowledge of system properties to inform the parameters of a structurally simple model. The methodology requires the use of a complementary model of strategic, but not excessive, structural complexity that is stochastic, fast-running and requires no history-matching. We demonstrate the approach using a real-world case in which modelling is used to support management of a stressed coastal aquifer. We empirically validate the approach using a synthetic model.