Inverse problems are ubiquitous in hydrological modelling for parameter estimation, system understanding, sustainable water resources management, and the operation of digital twins. While statistical inversion is especially popular, its sampling-based nature often inhibits the inversion of computationally costly models, which has compromised the use of the Generalized Likelihood Uncertainty Estimation (GLUE) methodology, e.g., for spatially distributed (partial) differential equation based models. In this study we introduce multilevel GLUE (MLGLUE), which alleviates the computational burden of statistical inversion by utilizing a hierarchy of model resolutions. Inspired by multilevel Monte Carlo, most parameter samples are evaluated on lower levels with computationally cheap low-resolution models and only samples associated with a likelihood above a certain threshold are subsequently passed to higher levels with costly high-resolution models for evaluation. Inferences are made at the level of the highest-resolution model but substantial computational savings are achieved by discarding samples with low likelihood already on levels with low resolution and low computational cost. Two test problems demonstrate the similarity of inferred parameter posteriors and uncertainty estimates of MLGLUE and GLUE as well as increased computational efficiency. Findings are furthermore compared to inversion results from Markov-chain Monte Carlo (MCMC) and from multilevel delayed acceptance MCMC. The computation time of inversion of a groundwater flow model was decreases by ≈45% and ≈57% when using MLGLUE instead of conventional formulations of GLUE and MCMC, respectively.

Inverse problems are ubiquitous in hydrological modelling for parameter estimation, system understanding, sustainable water resources management, and the operation of digital twins. While statistical inversion is especially popular, its sampling-based nature often inhibits its application to computationally costly models, which has compromised the use of the Generalized Likelihood Uncertainty Estimation (GLUE) methodology, e.g., for spatially distributed (partial) differential equation based models. In this study we introduce multilevel GLUE (MLGLUE), which alleviates the computational burden of statistical inversion by utilizing a hierarchy of model resolutions. Inspired by multilevel Monte Carlo, most parameter samples are evaluated on lower levels with computationally cheap low-resolution models and only samples associated with a likelihood above a certain threshold are subsequently passed to higher levels with costly high-resolution models for evaluation. Inferences are made at the level of the highest-resolution model but substantial computational savings are achieved by discarding samples with low likelihood already on levels with low resolution and low computational cost. Two example inverse problems, using a rainfall-runoff model and groundwater flow model, demonstrate the substantially increased computational efficiency of MLGLUE compared to GLUE as well as the similarity of inversion results. Findings are furthermore compared to inversion results from Markov-chain Monte Carlo (MCMC) and multilevel delayed acceptance MCMC, a corresponding multilevel variant, to compare the effects of the multilevel extension. All examples demonstrate the wide-range suitability of the approach and include guidelines for practical applications.

Elevated nitrate concentrations in groundwater are observed in regions of intensive agriculture worldwide, threatening the safety of drinking-water production. Aquifers may contain geogenic reduced constituents, such as natural organic matter (NOM), pyrite, or biotite, facilitating aerobic respiration and denitrification. Because these electron donors are not replenished, the breakthrough of nitrate (and eventually dissolved oxygen) in production wells is only delayed. Frameworks of modeling nitrate fate and transport that assume constant rate coefficients of nitrate elimination cannot address the reduction of the aquifer’s denitrification potential by the reaction itself. We have tested several approaches of modeling the fate of dissolved oxygen and nitrate in aquifers, including multi-dimensional bioreactive transport models with dynamic abundances of aerobic and denitrifying bacteria, approaches neglecting the dynamics of biomass and dispersive mixing, and simple models based on an electron balance. We found that the primary control on the timing of nitrate breakthrough is the ratio of the bioavailable electron-donor content in the aquifer material to the electron-acceptor load in the infiltrating water. Combined spatial variability of groundwater velocities and electron-donor content can explain most of the spread in nitrate breakthrough, whereas kinetics of the reaction plays a minor role under most conditions. Our modeling study highlights the need for field surveys on joined physical and chemical heterogeneity of aquifers under the stress of pollutants that can react with the aquifer material.

The analysis of drought onset and their potential relationship to drought severity (deficit volume) are critical for providing timely information for agricultural operations, such as cultivation planning and crop productivity monitoring. A coupling between drought timing and deficit volume can be used as a proxy for drought-related damage estimation and associated risks. Despite its high importance, so far little attention was paid to determine the timing of drought and its linkage with deficit volume for hydrological droughts. This study utilizes quality-controlled streamflow observations from 1965 to 2018 to unveil regional patterns of hydrological drought onset, trends in event-specific deficit volume, and nonlinear relationships between onset timing and deficit volume across 97 rain-dominated catchments in Peninsular India (8-24o N, 72-87o E). Our results show a shift towards earlier hydrological drought onset in conjunction with a decrease in deficit volume during the Indian monsoon (June-September) season, which is contrasted by a delayed onset in the pre-monsoon (March-May) and post-monsoon (October-February) seasons. Further, approximately one-third of the catchments show a significant nonlinear dependency between drought deficit volume and onset time. We find environmental controls, such as soil organic carbon, vertical distance to channel network, and soil wetness are dominant factors in influencing droughts. Our analysis provides new insights into the causal chain and physical processes linking climatic and physiographic controls on streamflow drought mechanisms, which can support drought forecasting and climate impact assessment studies.

Characterization of karst systems, especially the assessment of structure and geometry of conduits along with forecast of state-variables, are essential for groundwater quality/quantity management and implementation/rehabilitation of large-scale engineering projects in karst regions. These objectives can be fully met by utilizing process-based discrete-continuum models, such as MODFLOW-2005 CFPv2, as employed here. However, such tools should be used with the caveat of the potential non-uniqueness of results. This research focuses on the joint-inversion of discharge, water temperature, and solute concentration signatures of Freiheit Spring in Minnesota, USA, in response to a spatiotemporally small-scale hydraulic and transport experiment. Adopting the multi-model concept to address conceptual uncertainty, seven distinctive model variants were considered. Spring hydro-chemo-thermo-graphs for all variants were simultaneously simulated, employing joint-inversion by PEST. Subsequently, calibrated models were compared in terms of calibration performance, parameter uncertainties and reasonableness, as well as forecast capability. Overall, results reveal the reliability of the discrete-continuum flow and transport modeling, even at a spatiotemporally small-scale, on the order of meters and seconds. All conceptualized variants suggest almost identical conduit tracer passage sizes which are close to the flood-pulse method estimates. In addition, the significance of immobile conduit-associated-drainable storages in karst hydrodynamic modeling, which is uniquely provided in our model code, was highlighted. Moreover, it was demonstrated that the spring thermograph and hydrograph carry more information about the aquifer characteristics than the chemograph. However, this last result can be site-specific and depends on the scale of the experiment and the conceptualized variants of the respective hydrological state.

Understanding onset of droughts and its potential linkage to resulting responses like severity (deficit volume) is crucial for providing timely information related to drought sectors including the cultivation planning and monitoring crop productivity. Using high-quality daily observed streamflow records from 82 medium-to-large sized catchments over (tropical) peninsular India, we show that the variability in onset timing drives the severity of hydrological droughts. The strength of onset timing-severity relationships using observed records indicate seasonality of rainfall and catchment characteristics mainly modulate hydrological drought responses in peninsular India, which is not readily apparent from land-surface model simulations. The observed trend for mean onset of drought depicts delayed occurrence for more than half of the catchments. Around one-third of the catchments shows a stronger non-linear significant dependency (>0.7) between severity and onset of drought. The findings of the study highlight the need for accounting feedback between drought onset and severity and their concurrent changes for seasonal-to-sub-seasonal predictability of droughts; and contributes to discussions on building resilience to extreme droughts in a changing climate.