Search USGS⌕ Search
Home/Archive/USGS

USGS · 70015017

Convergent radial dispersion: A note on evaluation of the Laplace transform solution

Allen F. Moench
View original source ↗Export metadata ↓

Abstract

A numerical inversion algorithm for Laplace transforms that is capable of handling rapid changes in the computed function is applied to the Laplace transform solution to the problem of convergent radial dispersion in a homogeneous aquifer. Prior attempts by the author to invert this solution were unsuccessful for highly advective systems where the Peclet number was relatively large. The algorithm used in this note allows for rapid and accurate inversion of the solution for all Peclet numbers of practical interest, and beyond. Dimensionless breakthrough curves are illustrated for tracer input in the form of a step function, a Dirac impulse, or a rectangular input.

Explore related subjects

Water Resources ResearchArticle

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Allen F. Moench. 2008-01-08. Convergent radial dispersion: A note on evaluation of the Laplace transform solution. https://doi.org/10.1029/91wr02301

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

KEEP EXPLORING

Related USGS reports

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↗
USGS2026

Global performance of remote sensing-based and reanalysis-driven models to estimate open water evaporation

Evaporation plays an essential role in the water cycle, influencing local and regional climates while directly impacting water availability in lakes. However, directly measuring evaporation over water bodies remains challenging due to the high costs of installing and maintaining the required in situ instrumentation. Although several remote sensing algorithms have been providing evaporation estimates, the lack of a global validation hinders our understanding of their relative uncertainties and performances across different regions. Here, we analyze the performance of a suite of models that leverage satellite data and meteorological reanalysis to estimate evaporation over lakes worldwide. We compare 3 remote sensing-based models, 1 reanalysis-driven model and 1 ensemble approach, using in situ observations from 27 lakes representing a diverse range of geographic and climatic regions. Our results demonstrate that, overall, the ensemble outperformed any individual model in terms of accuracy, with a RMSE and a bias of 1.3 and 0.3 mm day −1 , respectively. These findings highlight the benefits of using an ensemble approach to estimate open water evaporation with satellite-based models at the global scale, leveraging the unique strengths of each model. For the individual models, differences in the representation of heat storage changes and advection effects led to lower values of RMSE and bias, depending on the location and depth of the lakes. This study sets the path for future improvement of open water evaporation algorithms globally, while remote sensing techniques are proven satisfactory to monitoring of water loss in lakes globally, an essential step toward effective large-scale water resources management.

Water Resources Research↗
USGS2026

Modeling legacy nitrogen transport under instantaneous, steady-state, and transient groundwater flow conditions

In hydrologic settings where groundwater discharge contributes substantially to surface waters, legacy nitrogen in groundwater can confound surface water nitrogen loads estimated exclusively from current terrestrial sources. Additionally, legacy nitrogen in groundwater can contribute to lagged responses to nitrogen management efforts. Some methods of estimating groundwater contributions to surface water nitrogen loads account for legacy nitrogen, while others do not. The resulting differences are rarely quantified. We used a numerical modeling framework to compare three methods of estimating time-varying annual groundwater nitrogen loads to surface water receptors on eastern Long Island, New York. The instantaneous load method used steady-state contributing areas and includes no temporal groundwater lag. The second method used numerical simulations of nitrogen loads under steady-state flow, which captures groundwater transport lags but omits the annual variability in transient hydrologic stresses. The third method numerically simulated both transient groundwater flow and nitrogen transport to explicitly capture the effects of legacy nitrogen in groundwater. Depending on antecedent nitrogen and hydrologic conditions, historical nitrogen loads estimated from the numerical simulations were sometimes similar (<10% difference) and other times substantially different (±100%) from the instantaneous load estimates. Additionally, simulated future surface water nitrogen loads responded asymptotically over several decades following reductions in terrestrial nitrogen sources, further highlighting the effect of groundwater transport lag times. The comparison of the three methods, quantification of historical interannual variability, and prediction of lagged responses to nitrogen source reductions provide important context for decision makers using estimated groundwater nitrogen loads to help evaluate nitrogen management efficacy.

New York↗