Search USGS⌕ Search
Home/Archive/USGS

USGS · 70019875

Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer

Allen F. Moench
View original source ↗Export metadata ↓

Abstract

A Laplace transform solution is presented for the problem of flow to a partially penetrating well of finite diameter in a slightly compressible water table aquifer. The solution, which allows for evaluation of both pumped well and observation piezometer data, accounts for effects of well bore storage and skin and allows for the noninstantaneous release of water from the unsaturated zone. For instantaneous release of water from the unsaturated zone the solution approaches the line source solution derived by Neuman as the diameter of the pumped well approaches zero. Delayed piezometer response, which is significant during times of rapidly changing hydraulic head, is included in the theoretical treatment and shown to be an important factor in accurate evaluation of specific storage. By means of a hypothetical field example it is demonstrated that evaluations of specific storage ( S s ) using classical line source solutions may yield values of S s that are overestimated by a factor of 100 or more, depending upon the location of the observation piezometers and whether effects of delayed piezometer response are included in the analysis. Theoretical responses obtained with the proposed model are used to suggest methods for evaluating specific storage.

Explore related subjects

Water Resources ResearchArticle

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Allen F. Moench. 1997. Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer. https://doi.org/10.1029/97wr00651

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related USGS reports

USGS2026

Landscape controls river continuum dissolved organic carbon in northeastern Alaska

Rivers draining continuous permafrost landscapes on the North Slope of Alaska span from the mountains to the coast, integrating gradients in vegetation, soil organic matter, and hydrologic flow. We investigated how these landscape transitions influence dissolved organic carbon (DOC) concentrations, radiocarbon ages, and export along the river continuum over seasonal timeframes in northeastern Alaska. Water samples were collected from the Canning River and its tributaries from the spring freshet through late summer via multiple campaigns during 2011–2024. A simulation from the Permafrost Water Balance Model (PWBM) estimated terrain-specific contributions to freshwater and DOC export. River DOC concentrations peaked during the spring and declined in summer, with episodic increases linked to summer rainfall. Summer river DOC concentrations from the Brooks Range remained low (0.41–0.64 mg C L −1 ) but increased downstream (0.5–3.0 mg C L −1 ), becoming younger from the mountains (805 yBP) to the river delta (525 yBP) as flow from DOC-enriched streams draining the foothills (6–18 mg C L −1 ; Modern yBP) entered the Canning. The PWBM simulation revealed that while the mountains dominate the Canning's annual (90%) and spring-summer (88%–93%) freshwater export, the foothills disproportionately influence its annual (56%) and spring-summer (44%–58%) DOC export. DOC yields from the coastal plain were also high but had little influence due to its small contributing area. Our findings highlight the outsized role of the foothills in modulating river-integrated DOC export to coastal ecosystems. Considering the impact of these landscapes on carbon source and runoff will aid in anticipating future DOC fluxes from Arctic rivers.

Alaska↗
USGS2026

Predicting Minnesota lake ice phenology with deep learning, explainable methods, and a physically based benchmark, 1980-2018

Globally, lakes are losing ice cover, but our understanding of the rates and variability of change are biased toward few lakes with long-term records. Recent works have used remote sensing and predictive modeling to supplement the observational record, but these approaches produce large errors when estimating ice phenology for individual lakes. Accurate, lake-specific estimates of ice formation and breakup through time are important for estimating variability in ice loss across heterogenous lakes and for understanding broader implications. This work explores machine learning (ML) approaches for hindcasting ice phenology using observations from 1980 to 2018 across 625 Minnesota lakes, covering 4359 lake-years of record. We used daily weather and static lake attributes to develop 60 neural networks for hindcasting lake ice time series. We considered LSTMs and attention-based transformers of varying size and initial parameters. We found that the largest LSTM performed most accurately on withheld data, and on a test set of unseen years and lakes, it outperformed a state-of-the-art physically based model in daily accuracy (97% vs. 95%), year-level metrics (RMSE for ice formation = 6.9 vs. 13.2 days; ice breakup = 7.5 vs. 12.2 days; ice duration = 9.6 vs. 13.7 days), and estimating loss of ice cover from 1980 to 2018 (observed = 8.4 days, LSTM = 7.2 days, GLM = 3.4 days). This demonstrates that ML can estimate historical lake ice formation and breakup dates within a week of observed phenology across heterogeneous lakes and recreate broad scale trends in ice cover phenology with limited long-term ice records.

Minnesota↗
USGS2026

A roadmap for identifying and interpreting physical processes and national water model prediction bias associated with baseflow index regimes across the contiguous United States

Understanding how groundwater–surface water interactions shape streamflow variability is critical for diagnosing low flow behavior and prediction bias in continental scale hydrologic models. We present a process informed framework that links observed baseflow (BF) dynamics, watershed attributes, and National Water Model (NWM) performance across the contiguous United States. Using daily observed streamflow from 797 reference quality streamgages, we developed monthly baseflow index (BFI) signatures using a streamgage specific, calibrated digital filter. Hierarchical clustering of these signatures identified seven distinct BFI regimes capturing regional and seasonal variability. We evaluated NWM v3.0 retrospective streamflow performance within each regime using multiple hydrograph and flow duration curve-based metrics. Model skill varied systematically across regimes: mixed flow systems were simulated most accurately, while predominantly BF dominated and quickflow dominated regimes exhibited substantially poorer performance. Across nearly all regimes, the NWM underestimated observed BFI magnitude and frequently failed to reproduce seasonal BF patterns, indicating systematic biases in simulated low flow contributions. To relate these regimes to potential process controls, we trained a Random Forest classifier using static watershed attributes and applied Shapley Additive Explanations to identify features most strongly associated with each regime. Results highlight regionally varying influences, including the dominant role of snow fraction and seasonal runoff timing in snow dominated basins and the importance of evapotranspiration and aridity in quickflow dominated systems. Collectively, these findings demonstrate how hydrologic signatures combined with interpretable machine learning can diagnose regime specific model biases and generate process-based hypotheses about limitations in large scale hydrologic prediction systems.

contiguous United States↗