In this paper, a generalized hierarchical multiscale approach for modeling coupled groundwater and surface water systems is demonstrated. Groundwater–lake interactions are simulated by coupling the groundwater equations with the lake’s continuity equation and by providing a two-way iterative feedback between models at multiple scales using specified head/flux boundary conditions. A hierarchical parameter estimation method that allows data and parameters at different scales to communicate between each other is also developed. These methods are applied to simulate a lake augmentation system for the Sister Lakes in southwest Michigan, which involves pumping a large amount of water from an irrigation well into the lakes. This problem requires resolution of time scales ranging from site-scale (hours) to local-scale (months) to watershed-scale (years) and spatial scales ranging from a few meters to a few kilometers. A hierarchical modeling framework consisting of five interlinked models was created, and model calibration was performed using drawdown data from a 72-h pumping test. The calibrated model was then used to simulate the entire lake augmentation system. The results indicate that the proposed modeling and parameter estimation approach can help improve the ability to model real-world complexities.
One of the challenges in groundwater modeling is the prediction of hydraulic head in close proximity to a pumping well using a regional-scale model. Typical applications of numerical models to field-scale problems generally require large grids that can seldom accommodate cells as small as the actual well diameter. In this paper, we apply a dynamically integrated "hierarchical patch dynamics paradigm (HPDP)" to model detailed near-well dynamics and interactions. The HPDP enables converting a large, complex problem into a network of hierarchically nested and dynamically coupled patch models that can be easily solved. The performance of the HPDP is verified against the analytical solution for a single well, against a superposition of analytical solutions for a wellfield, and against a numerical solution in a three-dimensional heterogeneous system. The results show that the HPDP is capable of providing an accurate and efficient representation of head in a wellfield in large-scale hydrogeologic systems.
Abstract Although ultrahigh‐pressure (UHP) metamorphic rocks are present in many collisional orogenic belts, almost all exposed UHP metamorphic rocks are subducted upper or felsic lower continental crust with minor mafic boudins. Eclogites formed by subduction of mafic lower continental crust have not been identified yet. Here an eclogite occurrence that formed during subduction of the mafic lower continental crust in the Dabie orogen, east‐central China is reported. At least four generations of metamorphic mineral assemblages can be discerned: (i) hypersthene + plagioclase ± garnet; (ii) omphacite + garnet + rutile + quartz; (iii) symplectite stage of garnet + diopside + hypersthene + ilmenite + plagioclase; (iv) amphibole + plagioclase + magnetite, which correspond to four metamorphic stages: (a) an early granulite facies, (b) eclogite facies, (c) retrograde metamorphism of high‐pressure granulite facies and (d) retrograde metamorphism of amphibolite facies. Mineral inclusion assemblages and cathodoluminescence images show that zircon is characterized by distinctive domains of core and a thin overgrowth rim. The zircon core domains are classified into two types: the first is igneous with clear oscillatory zonation ± apatite and quartz inclusions; and the second is metamorphic containing a granulite facies mineral assemblage of garnet, hypersthene and plagioclase (andesine). The zircon rims contain garnet, omphacite and rutile inclusions, indicating a metamorphic overgrowth at eclogite facies. The almost identical ages of the two types of core domains (magmatic = 791 ± 9 Ma and granulite facies metamorphic zircon = 794 ± 10 Ma), and the Triassic age (212 ± 10 Ma) of eclogitic facies metamorphic overgrowth zircon rim are interpreted as indicating that the protolith of the eclogite is mafic granulite that originated from underplating of mantle‐derived magma onto the base of continental crust during the Neoproterozoic ( c . 800 Ma) and then subducted during the Triassic, experiencing UHP eclogite facies metamorphism at mantle depths. The new finding has two‐fold significance: (i) voluminous mafic lower continental crust can increase the average density of subducted continental lithosphere, thus promoting its deep subduction; (ii) because of the current absence of mafic lower continental crust in the Dabie orogen, delamination or recycling of subducted mafic lower continental crust can be inferred as the geochemical cause for the mantle heterogeneity and the unusually evolved crustal composition.
The sources of water and corresponding delivery mechanisms to groundwater-fed fens are not well understood due to the multi-scale geo-morphologic variability of the glacial landscape in which they occur. This lack of understanding limits the ability to effectively conserve these systems and the ecosystem services they provide, including biodiversity and water provisioning. While fens tend to occur in clusters around regional groundwater mounds, Ives Road Fen in southern Michigan is an example of a geographically-isolated fen. In this paper, we apply a multi-scale groundwater modeling approach to understand the groundwater sources for Ives Road fen. We apply Transition Probability geo-statistics on more than 3000 well logs from a state-wide water well database to characterize the complex geology using conditional simulations. We subsequently implement a 3-dimensional reverse particle tracking to delineate groundwater contribution areas to the fen. The fen receives water from multiple sources: local recharge, regional recharge from an extensive till plain, a regional groundwater mound, and a nearby pond. The regional sources deliver water through a tortuous, 3-dimensional "pipeline" consisting of a confined aquifer lying beneath an extensive clay layer. Water in this pipeline reaches the fen by upwelling through openings in the clay layer. The pipeline connects the geographically-isolated fen to the same regional mound that provides water to other fen clusters in southern Michigan. The major implication of these findings is that fen conservation efforts must be expanded from focusing on individual fens and their immediate surroundings, to studying the much larger and inter-connected hydrologic network that sustains multiple fens.
In this paper, we present a stochastic-analytical approach for uncertainty modeling in two-dimensional, statistically nonuniform groundwater flows. In particular, we develop simple closed-form expressions that can be used to predict the variance of Darcy velocities caused by random small-scale heterogeneity in hydraulic conductivity. The approach takes advantage of the scale disparity between the nonstationary mean and fluctuation processes and invokes an order-of-magnitude analysis, enabling major simplifications and closed-form solutions of the nonstationary perturbation equations. We demonstrate the accuracy and robustness of the derived closed-form solutions by comparing them with the corresponding numerical solutions for a number of nonstationary flow examples involving unconfined conditions, transient conditions, complex trends in mean conductivity, sources and sinks, and bounded domains.
It is generally recognized that fens and the rare species they support can only be effectively managed and protected by treating them as part of a larger, connected groundwater system. However, this underlying groundwater system is often not well understood. In this research, a geographic information system (GIS)-enabled, hierarchical modeling approach was applied to simulate the multiscale groundwater flow systems for several critical habitat units of the endangered Hine’s emerald dragonfly (HED) in Michigan. In particular, models for six habitat units were developed and calibrated to static water level measurements. Reverse particle tracking was used to trace source water and delineate the groundwater contribution areas for the habitat units. The results reveal that the units obtain water from regional groundwater mounds through direct or cascading connections. The travel time for groundwater from the mounds to reach the habitat units varied between 25 days and almost 11 years. These findings suggest that the current approach to fen conservation must be reassessed, from the protection of individual fens to conservation of the broad recharge areas and the multiple fens they support.
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