Coupling surface flow and subsurface flow in complex soil structures using mimetic finite differences
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54 ENVIRONMENTAL SCIENCES↗
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Simulating coupled surface–subsurface flows with ParFlow v3.5.0: capabilities, applications, and ongoing development of an open-source, massively parallel, integrated hydrologic model
Surface flow and subsurface flow constitute a naturally linked hydrologic continuum that has not traditionally been simulated in an integrated fashion. Recognizing the interactions between these systems has encouraged the development of integrated hydrologic models (IHMs) capable of treating surface and subsurface systems as a single integrated resource. IHMs are dynamically evolving with improvements in technology, and the extent of their current capabilities are often only known to the developers and not general users. This article provides an overview of the core functionality, capability, applications, and ongoing development of one open-source IHM, ParFlow. ParFlow is a parallel, integrated, hydrologic model that simulates surface and subsurface flows. ParFlow solves the Richards equation for three-dimensional variably saturated groundwater flow and the two-dimensional kinematic wave approximation of the shallow water equations for overland flow. The model employs a conservative centered finite-difference scheme and a conservative finite-volume method for subsurface flow and transport, respectively. ParFlow uses multigrid-preconditioned Krylov and Newton–Krylov methods to solve the linear and nonlinear systems within each time step of the flow simulations. The code has demonstrated very efficient parallel solution capabilities. ParFlow has been coupled to geochemical reaction, land surface (e.g., the Common Land Model), and atmospheric models to study the interactions among the subsurface, land surface, and atmosphere systems across different spatial scales. This overview focuses on the current capabilities of the code, the core simulation engine, and the primary couplings of the subsurface model to other codes, taking a high-level perspective.
58 GEOSCIENCES↗
Deep Learning for Subsurface Flow: A Comparative Study of U‐Net, Fourier Neural Operators, and Transformers in Underground Hydrogen Storage
Subsurface flow research is essential for the sustainable management of natural resources and the environment. Deep learning (DL) has significantly advanced this field by developing efficient and accurate surrogate models to replace computationally expensive physics‐based simulations. These surrogate models are commonly used to predict the spatiotemporal evolution of state variables, such as gas saturation and reservoir pressure, in heterogeneous geological formations. Despite the various DL models applied to this task, there is a lack of studies systematically comparing their performance. This absence of comparative analysis leads to somewhat arbitrary DL model selection in subsurface flow research, resulting in suboptimal performance and potentially inaccurate predictions. To bridge this gap, we conduct a systematic comparison study of three popular DL architectures—U‐Net, Fourier Neural Operators (FNO), and Segmentation Transformer (SETR)—in surrogate modeling of underground hydrogen storage (UHS). We focus on UHS due to its promise of enhancing clean energy resilience and its cyclic operational conditions that represent common scenarios in various subsurface applications. We evaluate the models based on accuracy, training cost, and inference speed. The comparison shows that U‐Net achieves the highest accuracy, followed by SETR and FNO. Despite its lower accuracy, FNO has the highest inference speed. SETR offers competitive accuracy with the least training memory usage, demonstrating the potential of transformers in learning subsurface flow. Our results provide guidance for selecting DL models for surrogate modeling in a wide range of subsurface flow problems.
42 ENGINEERING↗
Forward and inverse modeling of fault transmissibility in subsurface flows
Characterizing physical properties of faults, such as their transmissibility, is crucial for performing predictive numerical simulation of subsurface flows, such as those encountered in petroleum engineering and remediation of subsurface contamination. Here, this paper provides a complete investigation of the inverse problem for fault transmissibility in subsurface flow models, under appropriate assumptions on fault structure. In particular, the following aspects are considered: 1) fault modeling and well-posedness of the forward problem; 2) finite element (FEM) discretizations of the forward problem and their rigorous a priori convergence analysis; 3) Well-posedness of the Bayesian inverse problem, FEM discretization of the infinite dimensional Bayesian inverse formulation, and its rigorous a priori analysis. Moreover, computation of the maximum a posteriori (MAP) point via fast inexact Newton-conjugate gradient optimization and a Laplace approximation of the Bayesian posterior are also presented. Numerical results illustrate the use of the proposed fault model in forward and inverse problems for subsurface flows in two dimensional domains with multiple faults.
97 MATHEMATICS AND COMPUTING↗
Data used in manuscript "Quantifying Subsurface Flow and Solute Transport in a Snowmelt-recharged Hillslope with Multiyear Water Balance", submitted to Water Resources Research on 5-26-2022
Data in this package were used to calculate subsurface flow and solute (specifically dissolved nitrogen) transport in the Pumphouse Lower Montane (PLM) hillslope. These data are included in separate CSV files associated with each figure presented in the manuscript. The files describe site locations and elevations, weather data (air temperatures and precipitation), modeled evapotranspiration, time dependent groundwater elevations, calculated annual subsurface flow, hydraulic conductivity values, time trends in subsurface flow within different zones, pore water concentrations of total dissolve nitrogen (TDN), rates of TDN transport, soil water matric potentials following snowmelt, soil water contents during drainage, and evapotranspiration calculated by soil water mass balance versus by CLM4 model.
54 ENVIRONMENTAL SCIENCES↗
DART-PFLOTRAN: An ensemble-based data assimilation system for estimating subsurface flow and transport model parameters
Ensemble-based Data Assimilation (EDA), based on the Monte Carlo approach, has been effectively applied to estimate model parameters through inverse modeling in subsurface flow and transport problems. However, implementation of EDA approach involves a complicated workflow that include setting up and executing ensemble forward model simulations, processing observations and model simulation results for parameter updates, and repeat for sequential or iterative EDA. To facilitate the management of such workflow and lower the barriers for adopting EDA-based parameter estimation in subsurface science, we develop a generic software frame-work linking the Data Assimilation Research Testbed (DART) with a massively parallel subsurface FLOw and TRANsport code PFLOTRAN. The new DART-PFLOTRAN leverages both the core data assimilation engines in DART and the computational power afforded by PFLOTRAN. In addition to the standard smoother and filtering options, DART-PFLOTRAN enables an iterative EDA workflow based on the Ensemble Smoother for Multiple Data Assimilation method (ES-MDA) to improve estimation accuracy for nonlinear forward problems. Here, we verify the implementation of ES-MDA in DART-PFLOTRAN using two synthetic cases designed to estimate static permeability and dynamic exchange fluxes across the riverbed, respectively, from continuous temperature measurements made across a depth profile. One-dimensional hydro-thermal simulations are performed in both cases to relate temperature responses with the parameters of interest. In the case of estimating dynamic parameters, we demonstrate the flexibility of DART-PFLOTRAN in automating sequential ES-MDA workflow, which will significantly reduce the time researchers spend on managing complex workflows in similar applications. Both studies yield accurate estimations of the parameters compared to their synthetic truth, while ES-MDA leads to more accurate estimation when a high level of nonlinearity exist between observed responses and unknown parameters. With a code base in Python and Fortran, DART-PFLOTRAN paves the way for applications in large-scale subsurface inverse modeling by automating the complex workflow of sequential ES-MDA that can be executed on various computing platforms.
97 MATHEMATICS AND COMPUTING↗
Geophysical and Environmental Monitoring Data, and Subsurface Flow Modelling Results for Chicken Bone Meadow, Mt. Snodgrass, Crested Butte, CO
This dataset includes geoelectrical monitoring data acquired between October 2021 and November 2022, soil moisture and temperature data, groundwater data obtained from borehole SNIB covering the period from June 2021 to September 2022, and hydrological modelling results. The data were acquired to investigate how variations in bedrock type and topography, and vegetation cover control subsurface flow dynamics. To provide insights into the subsurface flow dynamics and their controls, a monitoring transect was installed at the Chicken Bone Meadow, Mt. Snodgrass, Crested Butte, CO, measuring the spatio-temporal variations of soil moisture, soil and snow temperature, subsurface electrical resistivity variations, and groundwater dynamics. Field data are organized in a folder structure, with Electrical Resistivity Tomography (ERT) data being provided as one file per measurement, and data of the soil moisture and temperature sensors being provided as text files covering the entire monitoring period. The ‘Locations.csv’ file contains the location of all sensors, given in NAD83 – UTM Zone 13N. ERT monitoring data has been processed to filter data based on reciprocal errors (data with errors > 30% were removed), a linear error model was fitted to each survey, and to ensure a constant set of measurements for time-lapse inversion, filtered data were interpolated and assigned a 100% measurement error. Soil moisture and temperature data were acquired at 15 min intervals, and averaged to provide 1h data. Weather data and borehole data (groundwater depth, conductivity and temperature) were acquired at 30 min intervals, and are provided as daily measurements; all measurements are averaged, except of precipitation values, which are given as daily accumulation. The hydrological model was set up along the ERT monitoring transect, and net infiltration was used as surface boundary condition and derived from the weather data. Four different results are provided, (1) results for a parameterization using hydraulic permeability and porosity as derived from the ERT data through petrophysical relationships, and (2) three simplified model results, using 1 to 3 geological layers above the bedrock. Modelling was performed using PFLOTRAN, and for each model the PFLOTRAN input files are provided. The result files include weekly hydrological modelling results (e.g., saturation, velocities, pressures), as well as the model parameterization. The dataset additionally includes a file-level metadata (flmd.csv) file that lists each file contained in the dataset with associated metadata; and a data dictionary (dd.csv) file that contains column/row headers used throughout the files along with a definition, units, and data type.
54 ENVIRONMENTAL SCIENCES↗
Coupled Time-Lapse Full-Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation
We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion (FWI), subsurface flow processes, and rock physics models. For the inverse modeling, we handle the back propagation of gradients by an intrusive automatic differentiation strategy that offers three levels of user control: (1) At the wave physics level, we adopted the discrete adjoint method in order to use our existing high-performance FWI code; (2) at the rock physics level, we used built-in automatic differentiation operators from the TensorFlow backend; (3) at the flow physics level, we implemented customized partial differential equation (PDE) operators for the multiphase flow equations. The three-level coupled inversion strategy strikes a good balance between computational efficiency and programming efforts, and when the gradients are chained together, it constitutes a coupled inverse system. Our numerical experiments demonstrate that the three-level coupled inverse problem is superior in terms of accuracy to a traditional decoupled inversion strategy. Additionally, our method is able to simultaneously invert for parameters in empirical relationships such as the rock physics models. Our proposed inverted model can be used for reservoir performance prediction and reservoir management/optimization purposes.
54 ENVIRONMENTAL SCIENCES↗
Electrical monitoring of saline tracers to reveal subsurface flow pathways in a flat ditch-drained field
Time-lapse electrical resistivity imaging (ERI) combined with salt tracers can enhance our understanding of subsurface flow and transport in ditch-drained agroecosystems. In a nearly level field adjacent to a drainage ditch, we installed 192 electrodes in a 72-m2 plot along with five hydrometric stations to enable time-lapse ERI monitoring during storms. Immediately prior to a wintertime rainstorm, we applied 5 kg of KBr to a shallow trench located roughly 11 m upgradient from the ditch. Antecedent conditions prior to the storm were wet, assuring a hydrologically connected state that favored tracer dissolution and movement in the subsurface. We monitored the evolution of the tracer plume with ERI over a seven-day period. Four-dimensional (4D) delineation of precipitation and tracer transport using time-lapse ERI showed that the tracer plume moved preferentially downward through a discontinuity in the argillic horizon within the first 57 hrs. Over the following 79 hrs, the tracer plume exhibited steady, lateral movement towards the drainage ditch within a more permeable sandy horizon situated just below the argillic. A spatial moment analysis of logarithmic changes in conductivity in the sand layer revealed seepage velocities ranging from 0.0027 to 0.0482 m d-1; these values were positively correlated with hydraulic gradients, suggesting laminar flow processes typical of sandy aquifers. Increasing groundwater velocities with hydraulic gradients suggest that solute transfers from groundwater to ditch are likely to be faster in storms, especially during wet periods. Even so, predominantly slow lateral transport within the sandy horizon, even during storms, indicates that critical source areas of pollutant loss are likely within a few meters of the ditch.
Robinson, Judith L.↗
Characterization of Subsurface Flow Dynamics for Forecasting of Solar Activity
Evolution of large-scale magnetic field structures in the solar photosphere and corona is controlled by motions beneath the visible surface of the Sun. Subsurface plasma flows play a critical role in formation and evolution of active regions and their activity. We analyze subsurface flow maps provided by the local helioseismology pipeline from the Helioseismic and Magnetic Imager (HMI) data on board the Solar Dynamics Observatory, and investigate links between flow characteristics and magnetic activity. The primary goal is to determine flow descriptors, which can improve solar activity forecasts. In particular, by employing machine learning classifiers, we test how the flow helicity and velocity shear descriptors can improve the prediction of initiation of flares and CME eruptions.
Kosovichev, Alexander↗
Calibration and Uncertainty Estimation Using the Ensemble Kalman Filter with a Large Subsurface Flow and Transport Model - 20321
At routinely monitored groundwater contamination sites, periodically measured environmental conditions such as groundwater levels and contaminant concentrations are used to inform and confirm a conceptual site model (CSM) and guide the development and calibration of a numerical groundwater flow and transport model. The calibration of groundwater flow and transport models after each measurement (sampling) event can illuminate deficiencies in a CSM, identify areas where additional monitoring is warranted, and predict the behavior of the system to guide decision making. However, manual and automated (e.g. PEST) model calibration tools can be time-consuming and computationally expensive to implement after each sampling event. Perhaps as a result, such calibration tools generally utilize all available monitoring data simultaneously rather than sequentially assimilating monitoring data one sampling event at a time as the results from sampling become available. A more real-time data assimilation approach may reduce parameter uncertainty, quantify the value of additional monitoring data, and produce a usable model more quickly and with less effort. To mitigate the potential time-consuming aspects of manual and widely applied automated calibration techniques, a data assimilation algorithm called the ensemble Kalman filter (EnKF) was evaluated as a relatively efficient method of model calibration and uncertainty assessment via the sequential integration of monitoring data into a model. The EnKF was able to successfully and efficiently assimilate monitoring and modeling data to calibrate a complex flow and transport model at a real-world site with significant subsurface heterogeneity, uncertainty, and 12 years of monitoring data (over 4,000 individual measurements of groundwater levels and over 2,500 measurements of contaminant concentrations). Starting with an uncalibrated model data from annual sampling events were sequentially assimilated, and the resultant predication errors and estimated parameter uncertainties were tracked. After all monitoring data were assimilated, both flow and transport residuals at the end of the EnKF process were comparable to those produced via a concurrent PEST calibration effort but required fewer model simulations. Both uncertainty and prediction errors decreased over time. In a real-time application, the adequacy of the model could be assessed after each sampling event. The benefits of such a real-time approach to utilizing monitoring data include reduced costs (in the form of model updates or site characterization efforts), early flagging of possible errors in the CSM, and a reduced risk of overfitting and corresponding increased confidence in model predictions. This tool may be particularly useful compared to other calibration techniques (e.g. manual, PEST) when model runtimes are long, calibration parameters are many, or parameter uncertainty is large. (authors)
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Quantifying Subsurface Flow and Solute Transport in a Snowmelt‐Recharged Hillslope With Multiyear Water Balance
Abstract Quantifying flow and transport from hillslopes is vital for understanding water quantity and quality in rivers, but remains obscure because of limited subsurface measurements. Using measured hydraulic conductivity K profiles and water balance over a single year to calibrate a transmissivity feedback model for a hillslope in the East River watershed (Colorado) proved unsatisfactory for predicting flow over the subsequent years. Well‐constrained field‐scale K were obtained by optimizing subsurface flux predictions over years having large differences in recharge, and by including estimates of interannual transfer of excess snowmelt recharge. Water and solute exports during high snowmelt recharge occur predominantly via shallow groundwater flow through weathered rock and soil because of their enlarged transmissivities under saturated conditions. Conversely, these shallow pathways are less active in snow drought years when the water table remains deeper within the weathering zone. Hillslope soil water monitoring showed that rainfall does not infiltrate deeply during summer and fall months, and revealed water losses consistent with model ET predictions. By combining water table‐dependent fluxes with pore water chemistry in different zones, time‐dependent rates of solute exports become predictable. As an example, calibrated K were combined with dissolved nitrogen concentrations in pore waters to show the snowmelt‐dependence of reactive nitrogen exported from the hillslope, further supporting the recent finding that the weathering zone is the dominant source of reactive nitrogen at this site. Subsurface export predictions can now be obtained for wide ranges of recharge based on measurements of water table elevation and profiles of pore water chemistry.
54 ENVIRONMENTAL SCIENCES↗
Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media
Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.
54 ENVIRONMENTAL SCIENCES↗
Solving Coupled Surface and Subsurface Flow with Multirate Time Integration [Slides]
This report details an end of summer internship. The report lists the objective, "Add more multirate time integration methods to Amanzi" and concludes that, "Multirate methods can be used to speed up simulations and to get higher orders of accuracy", and "Coupled surface and subsurface simulations could benefit from using multirate schemes".
47 OTHER INSTRUMENTATION↗
The Role of Subsurface Flow on Evapotranspiration: A Global Sensitivity Analysis
Abstract Water resources are impacted by water‐energy balance fluxes at the land surface, most notably evapotranspiration ( ET ), the largest component of surface energy balance. While integrated hydrologic models show promise in quantifying the nonlinear dynamics at this interface, the model results are plagued by parametric uncertainties. Given the high computational demand of running multiple parameter spaces of these models, little is known about how these uncertainties propagate into land surface processes. In this work, we perform a global sensitivity analysis by computing Sobol and AMAE indices using a surrogate model constructed with a polynomial chaos expansion to assess the impacts of the subsurface physical properties on ET . We do so by modeling a semisynthetic test case. Our results show that the effects of vertical hydraulic conductivity, porosity, and the water retention curve parameter Van Genuchten α mainly control ET . However, we note that while evaporation ( E ) shows behavior similar to the ET with high sensitivity to the parameters controlling the flow in the unsaturated zone, transpiration ( T ) is very sensitive to the saturated zone parameters and groundwater flow, especially during periods without rain. Our results also show that heterogeneities in land cover impact the flow in the saturated zone. Furthermore, our work demonstrates that reduced‐order models can be developed to make integrated models more accessible for rigorous sensitivity analyses and calibration purposes.
Maina, Fadji Zaouna↗
Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems
In this paper, we present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) models. We use PDEs in addition to measurements to train DNNs to approximate unknown parameters and constitutive relationships as well as states. The proposed approach increases the accuracy of DNN approximations of partially known functions when a limited number of measurements is available and allows for training DNNs when no direct measurements of the functions of interest are available. We employ physics informed DNNs to estimate the unknown space-dependent diffusion coefficient in a linear diffusion equation and an unknown constitutive relationship in a non-linear diffusion equation. For the parameter estimation problem, we assume that partial measurements of the coefficient and states are available and demonstrate that under these conditions, the proposed method is more accurate than state-of-the-art methods. For the non-linear diffusion PDE model with a fully unknown constitutive relationship (i.e., no measurements of constitutive relationship are available), the physics informed DNN method can accurately estimate the non-linear constitutive relationship based on state measurements only. Finally, we demonstrate that the proposed method remains accurate in the presence of measurement noise.
42 ENGINEERING↗
Understanding the Hydrogeochemical Response of a Mountainous Watershed Using Integrated Surface‐Subsurface Flow and Reactive Transport Modeling
Abstract Climate change and other disturbances significantly impact hydrogeochemical exports from mountainous headwater catchments such as the Upper Colorado River Basin. Developing a mechanistic understanding of how the physical and chemical processes interact in time and space in an integrated manner is key to quantifying the future impacts of such disturbances. The hydrogeochemical response of a mountainous catchment in the 2010–2019 period is evaluated quantitatively using a high‐resolution model that simulates integrated hydrology, and transport and reactions for selected solutes and minerals. The model assumes that pyrite is present only at depth while calcite is distributed uniformly, and captures the observed C‐Q reasonably well. Distinct C‐Q dynamics are observed in an average (WY16), a wet (WY17), and a dry (WY18) water year. The model also quantifies the water fraction from surface, shallow and deep groundwater compartments using tracers, and suggests greater groundwater contributions to peak stream discharge in the dry WY18. Results demonstrate that calcium concentrations do not change significantly from year to year, while sulfate shows significant temporal variability. Pyrite dissolution is affected by the changing hydrological drivers where it is enhanced in the dry WY18; calcite dissolution supplements calcium dilution under high flow conditions. The model simulates the reaction hotspots controlled by hydrological conditions, and the spatially‐resolved results show that higher soil saturation and less snowpack occur earlier on the south‐facing side than on the north‐facing side. This is a first‐of‐its‐kind demonstration of a model that integrates hydrologic processes, including evapotranspiration, and reactive transport to enable a predictive understanding of hydrogeochemical exports.
54 ENVIRONMENTAL SCIENCES↗
Calibrating Fractional-Order Models for Anomalous Subsurface Flow through Fractures.
Abstract not provided.
Gulian, Mamikon↗