ALBERT

Description: We determine the time-dependent behavior of the dispersion coefficient for transport in formations with isotropic log-conductivity fields showing fractal behavior. We consider two different dispersion coefficients for point-like injection: (1) the ensemble dispersion coefficients, defined as half the rate of change of the second central moments of the ensemble-averaged concentration distribution and (2) the effective dispersion, which is half the rate of change of the expected second central moments. Our results show, that the two longitudinal macrodispersion coefficients steadily grow with time and remain different at all times in a fully fractal regime, indicating that no Fickian transport regime is ever reached. The resulting effective longitudinal transport model is consequently a fractional advection–dispersion equation. In the semi-fractal regime, a Gaussian transport regime is reached eventually. However, compared to the case of a classic non-fractal regime, the transient non-Gaussian regime lasts much longer. In the transverse direction, the two dispersion coefficients approach the same large-time limit also in fractal media highlighting the fundamental difference between longitudinal and transverse dispersion.

Description: Most of the current large scale hydrological models do not contain a physically-based groundwater flow component. The main difficulties in large-scale groundwater modeling include the efficient representation of unsaturated zone flow, the characterization of dynamic groundwater-surface water interaction and the numerical stability while preserving complex physical processes and high resolution. To address these problems, we propose a highly-scalable coupled hydrologic and groundwater model (mHM#OGS) based on the integration of two open-source modeling codes: the mesoscale hydrologic Model (mHM) and the finite element simulator OpenGeoSys (OGS). mHM#OGS is coupled using a boundary condition-based coupling scheme that dynamically links the surface and subsurface parts. Nested time stepping allows smaller time steps for typically faster surface runoff routing in mHM and larger time steps for slower subsurface flow in OGS. mHM#OGS features the coupling interface which can transfer the groundwater recharge and river baseflow rate between mHM and OpenGeoSys. Verification of the coupled model was conducted using the time-series of observed streamflow and groundwater levels. Moreover, we force the transient model using groundwater recharge in two scenarios: (1) spatially variable recharge based on the mHM simulations, and (2) spatially homogeneous groundwater recharge. The modeling result in first scenario has a slightly higher correlation with groundwater head time-series, which further validates the plausibility of spatial groundwater recharge distribution calculated by mHM in the mesocale. The statistical analysis of model predictions shows a promising prediction ability of the model. The offline coupling method implemented here can reproduce reasonable groundwater head time series while keep a desired level of detail in the subsurface model structure with little surplus in computational cost. Our exemplary calculations show that the coupled model mHM#OGS can be a valuable tool to assess the effects of variability in land surface heterogeneity, meteorological, topographical forces and geological zonation on the groundwater flow dynamics.

Description: Groundwater is the biggest single source of high-quality fresh water worldwide, which is also continuously threatened by the changing climate. This paper is designed to investigate the response of regional groundwater system to the climate change under three global warming levels (1.5, 2, and 3 °C) in a central German basin (Nägelstedt). This investigation is conducted by deploying an integrated modeling workflow that consists of a mesoscale Hydrologic Model (mHM) and a fully-distributed groundwater model OpenGeoSys (OGS). mHM is forced by five general circulation models under three representative concentration pathways. The diffuse recharges estimated by mHM are used as outer forcings of the OGS groundwater model to compute changes in groundwater levels and travel time distributions. Simulation results indicate that under future climate scenarios, groundwater recharges and levels are expected to increase slightly. Meanwhile, the mean travel time is expected to decrease compared to the historical average. However, the ensemble simulations do not all agree on the sign of relative change. The ensemble simulations do not show a systematic relationship between the predicted change and the warming level, but they indicate an increased variability in predicted changes with the enhanced warming level from 1.5 to 3 °C. This study indicates that a higher warming level may introduce more uncertain and extreme events for the studied regional groundwater system.

Description: This paper considers questions related to the adoption of stochastic methods in hydrogeology. It looks at factors affecting the adoption of stochastic methods including environmental regulations, financial incentives, higher education, and the collective feedback loop involving these factors. We begin by evaluating two previous paper series appearing in the stochastic hydrogeology literature, one in 2004 and one in 2016, and identifying the current thinking on the topic, including the perceived data needs of stochastic methods, the attitude in regulations and the court system regarding stochastic methods, education of the workforce and the availability of software tools needed for implementing stochastic methods in practice. Comparing the state of adoption in hydrogeology to petroleum reservoir engineering allowed us to identify quantitative metrics on which to base our analysis. For impediments to the adoption of stochastic hydrology, we identified external factors as well as self-inflicted wounds. What emerges is a picture much broader than current views. Financial incentives and regulations play a major role in stalling adoption. Stochastic Hydrology's blind spot is in confusing between risk and uncertainty and ignoring uncertainty. We show that stochastic hydrogeology comfortably focused on risk while ignoring uncertainty, to its own detriment and to the detriment of its potential clients. The imbalance between the treatment on risk on one hand and uncertainty on the other is shown to be common to multiple disciplines in hydrology that interface with risk and uncertainty.

Description: This paper considers questions related to the adoption of stochastic methods in hydrogeology. It looks at factors affecting the adoption of stochastic methods including environmental regulations, financial incentives, higher education, and the collective feedback loop involving these factors. We begin by evaluating two previous paper series appearing in the stochastic hydrogeology literature, one in 2004 and one in 2016, and identifying the current thinking on the topic, including the perceived data needs of stochastic methods, the attitude in regulations and the court system regarding stochastic methods, education of the workforce, and the availability of software tools needed for implementing stochastic methods in practice. Comparing the state of adoption in hydrogeology to petroleum reservoir engineering allowed us to identify quantitative metrics on which to base our analysis. For impediments to the adoption of stochastic hydrology, we identified external factors as well as self-inflicted wounds. What emerges is a picture much broader than current views. Financial incentives and regulations play a major role in stalling adoption. Stochastic hydrology's blind spot is in confusing between uncertainty with risk and ignoring uncertainty. We show that stochastic hydrogeology comfortably focused on risk while ignoring uncertainty, to its own detriment and to the detriment of its potential clients. The imbalance between the treatment on risk on one hand and uncertainty on the other is shown to be common to multiple disciplines in hydrology that interface with risk and uncertainty.

Description: Groundwater travel time distributions (TTDs) provide a robust description of the subsurface mixing behavior and hydrological response of a subsurface system. Lagrangian particle tracking is often used to derive the groundwater TTDs. The reliability of this approach is subjected to the uncertainty of external forcings, internal hydraulic properties, and the interplay between them. Here, we evaluate the uncertainty of catchment groundwater TTDs in an agricultural catchment using a 3-D groundwater model with an overall focus on revealing the relationship between external forcing, internal hydraulic property, and TTD predictions. A stratigraphic aquifer model is applied to represent the spatial structure of the aquifer. Several recharge realizations are sampled from a high-resolution dataset of land surface fluxes and states. Constrained to expert knowledge and groundwater head observations, many realizations of hydraulic conductivity fields are stochastically generated using null-space Monte Carlo (NSMC) method for each recharge realization. The random walk particle tracking (RWPT) method is used to track the pathways of particles and compute travel times. Moreover, an analytical model under the random sampling (RS) assumption is fitted against the numerical solutions, serving as a reference of the mixing behavior of the model domain. The StorAge Selection (SAS) function is used to interpret the results in terms of quantifying the systematic preference for young/old water. The simulation results reveal the primary effect of recharge on the predicted mean travel time (MTT). The different realizations of calibration-constrained hydraulic conductivity fields moderately magnify or attenuate the predicted MTTs, provided that most parameters can be well constrained to the observations. The analytical solution under a random sampling assumption does not properly replicate the numerical solution, and underestimates the mean travel time. The SAS functions of ensemble simulations indicate an overall preference for young water for all realizations. The spatial pattern of recharge also has a strong impact on the shape and breadth of simulated TTDs. In conclusion, overlooking the input (forcing) uncertainty will result in biased travel time predictions, and may underestimate the overall uncertainty of TTD predictions. We also highlight the worth of reliable observations in reducing predictive uncertainty, and the good interpretability of SAS function in terms of understanding catchment transport processes.

Description: Travel-time distributions are a comprehensive tool for the characterization of hydrological system dynamics. Unlike the streamflow hydrograph, they describe the movement and storage of water within and throughout the hydrological system. Until recently, studies using such travel-time distributions have generally either been applied to lumped models or to real-world catchments using available time series, e.g., stable isotopes. Whereas the former are limited in their realism and lack information on the spatial arrangements of the relevant quantities, the latter are limited in their use of available data sets. In our study, we employ the spatially distributed mesoscale Hydrological Model (mHM) and apply it to a catchment in central Germany. Being able to draw on multiple large data sets for calibration and verification, we generate a large array of spatially distributed states and fluxes. These hydrological outputs are then used to compute the travel-time distributions for every grid cell in the modeling domain. A statistical analysis indicates the general soundness of the upscaling scheme employed in mHM and reveals precipitation, saturated soil moisture and potential evapotranspiration as important predictors for explaining the spatial heterogeneity of mean travel times. In addition, we demonstrate and discuss the high information content of mean travel times for characterization of internal hydrological processes.

Description: Groundwater travel time distributions (TTDs) provide a robust description of the subsurface mixing behavior and hydrological response of a subsurface system. Lagrangian particle tracking is often used to derive the groundwater TTDs. The reliability of this approach is subjected to the uncertainty of external forcings, internal hydraulic properties, and the interplay between them. Here, we evaluate the uncertainty of catchment groundwater TTDs in an agricultural catchment using a 3-D groundwater model with an overall focus on revealing the relationship between external forcing, internal hydraulic properties, and TTD predictions. Eight recharge realizations are sampled from a high-resolution dataset of land surface fluxes and states. Calibration-constrained hydraulic conductivity fields (Ks fields) are stochastically generated using the null-space Monte Carlo (NSMC) method for each recharge realization. The random walk particle tracking (RWPT) method is used to track the pathways of particles and compute travel times. Moreover, an analytical model under the random sampling (RS) assumption is fit against the numerical solutions, serving as a reference for the mixing behavior of the model domain. The StorAge Selection (SAS) function is used to interpret the results in terms of quantifying the systematic preference for discharging young/old water. The simulation results reveal the primary effect of recharge on the predicted mean travel time (MTT). The different realizations of calibration-constrained Ks fields moderately magnify or attenuate the predicted MTTs. The analytical model does not properly replicate the numerical solution, and it underestimates the mean travel time. Simulated SAS functions indicate an overall preference for young water for all realizations. The spatial pattern of recharge controls the shape and breadth of simulated TTDs and SAS functions by changing the spatial distribution of particles' pathways. In conclusion, overlooking the spatial nonuniformity and uncertainty of input (forcing) will result in biased travel time predictions. We also highlight the worth of reliable observations in reducing predictive uncertainty and the good interpretability of SAS functions in terms of understanding catchment transport processes.