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USGS2010

The problem of complex eigensystems in the semianalytical solution for advancement of time in solute transport simulations: a new method using real arithmetic

In the numerical modeling of groundwater solute transport, explicit solutions may be obtained for the concentration field at any future time without computing concentrations at intermediate times. The spatial variables are discretized and time is left continuous in the governing differential equation. These semianalytical solutions have been presented in the literature and involve the eigensystem of a coefficient matrix. This eigensystem may be complex (i.e., have imaginary components) due to the asymmetry created by the advection term in the governing advection-dispersion equation. Previous investigators have either used complex arithmetic to represent a complex eigensystem or chosen large dispersivity values for which the imaginary components of the complex eigenvalues may be ignored without significant error. It is shown here that the error due to ignoring the imaginary components of complex eigenvalues is large for small dispersivity values. A new algorithm that represents the complex eigensystem by converting it to a real eigensystem is presented. The method requires only real arithmetic.

Water Resources Research↗

USGS2010

A new formula for the analytical solution of the radial dispersion problem

A new formula is presented for the analytical solution of the radial dispersion problem, which analyzes the dispersive transport of a tracer in radial flow from a recharge well. This formula is simpler than a solution presented by previous investigators, but the two solutions are shown to be equivalent. Because the analytical solution consists of an integral of an oscillatory function, it is evaluated as an alternating series, the terms of which are the integrals over successive half cycles of the integrand. An efficient algorithm is used to accelerate convergence of the series. The accuracies of previous solutions obtained by finite difference, numerical Laplace transform, and perturbation methods are examined by comparison with the analytical solution. Numerical values of the solution are tabulated for readers interested in checking the accuracies of solute transport codes.

Water Resources Research↗

USGS1988

Cobalt in ferromanganese crusts as a monitor of hydrothermal discharge on the Pacific sea floor

Ferromanganese oxide crusts, which accumulate on unsedimented surfaces in the open ocean 1–6 , derive most of their metal content from dissolved and particulate matter in ambient bottom water 7,8 , in proportions modified by the variable scavenging efficiency of the oxide phase for susceptible ions 9 . They differ in this respect from abyssal nodules, much of whose metals are remobilized from host sediments. Here we present maps of cobalt concentration and inferred accumulation rate of ferromanganese crusts from the Pacific Ocean. We propose that depletion of cobalt in Pacific crusts measures the location and intensity of submarine hydrothermal discharge. Use of the 'cobalt chronometer', an algorithm inversely relating cobalt content and crust growth rate, permits mapping of the accumulation rate of ferromanganese crusts with only indirect recourse to radioactivity-based dating methods. These maps show that crusts in hydrothermal areas grow from two to more than four orders of magnitude faster than in the Central Pacific Ocean. Cobalt-enriched crusts are found where water masses are most isolated from continental-coastal and hydrothermal sources of metals, now and in the past. This relationship can resolve the problem of cobalt enrichment in crusts without recourse to hypotheses invoking special cobalt sources or enrichment mechanisms.

Nature↗

USGS2020

A rasterized building footprint dataset for the United States

Microsoft released a U.S.-wide vector building dataset in 2018. Although the vector building layers provide relatively accurate geometries, their use in large-extent geospatial analysis comes at a high computational cost. We used High-Performance Computing (HPC) to develop an algorithm that calculates six summary values for each cell in a raster representation of each U.S. state, excluding Alaska and Hawaii: (1) total footprint coverage, (2) number of unique buildings intersecting each cell, (3) number of building centroids falling inside each cell, and area of the (4) average, (5) smallest, and (6) largest area of buildings that intersect each cell. These values are represented as raster layers with 30 m cell size covering the 48 conterminous states. We also identify errors in the original building dataset. We evaluate precision and recall in the data for three large U.S. urban areas. Precision is high and comparable to results reported by Microsoft while recall is high for buildings with footprints larger than 200 m2 but lower for progressively smaller buildings.

Scientific Data↗

USGS2020

Blind testing of shoreline evolution models

Beaches around the world continuously adjust to daily and seasonal changes in wave and tide conditions, which are themselves changing over longer time-scales. Different approaches to predict multi-year shoreline evolution have been implemented; however, robust and reliable predictions of shoreline evolution are still problematic even in short-term scenarios (shorter than decadal). Here we show results of a modelling competition, where 19 numerical models (a mix of established shoreline models and machine learning techniques) were tested using data collected for Tairua beach, New Zealand with 18 years of daily averaged alongshore shoreline position and beach rotation (orientation) data obtained from a camera system. In general, traditional shoreline models and machine learning techniques were able to reproduce shoreline changes during the calibration period (1999–2014) for normal conditions but some of the model struggled to predict extreme and fast oscillations. During the forecast period (unseen data, 2014–2017), both approaches showed a decrease in models’ capability to predict the shoreline position. This was more evident for some of the machine learning algorithms. A model ensemble performed better than individual models and enables assessment of uncertainties in model architecture. Research-coordinated approaches (e.g., modelling competitions) can fuel advances in predictive capabilities and provide a forum for the discussion about the advantages/disadvantages of available models.

Scientific Reports↗

USGS2025

Present-day vertical land motions (VLM) of the Chesapeake Bay region derived from robust network imaging of global navigation satellite system (GNSS) observations

The Chesapeake Bay region (defined as longitudes − 78° to -74° and latitudes 36.5° to 40°) experiences the highest rates of relative sea-level rise (RSLR) on the Atlantic Coast. Regional land subsidence influences RSLR, however quantified rates of vertical land motions (VLM) are inconsistent in published solutions. For 5 years from 2019 to 2023, new Global Navigation Satellite System (GNSS) campaign data were collected at over 60 sites across the Chesapeake Bay region annually. These data were processed and combined with continuous GNSS data (120 stations) from the region covering the same time-period using GAMIT-GLOBK to produce 3D velocities and their associated uncertainties. We use the Robust Network Imaging algorithm to interpolate GNSS-derived VLM to produce a new regional VLM solution of the Chesapeake Bay region. We find that land subsidence is ubiquitous throughout the region with rates varying from − 2.97 to -0.40 mm/yr. In major cities across the Chesapeake Bay region, VLM rates are − 1.1 ± 1.6 mm/yr (1-sigma) for Washington DC, -0.8 ± 1.4 mm/yr for Baltimore, MD, -2.4 ± 0.5 mm/yr for Ocean City, MD, and − 2.3 ± 1.0 mm/yr for Hampton, VA. When we compare our VLM rates with a geodetic-based solution from 1974, we observe meaningful shifts in the locations and rates of maximum subsidence. The results of this work underscore that regular monitoring of VLM and can be used to improve projections of relative sea-level changes as well as the associated coastal hazards for communities in the Chesapeake Bay region.

Delaware, Maryland, New Jeresy, Pennsylvania, Virg↗

USGS2014

Precise determination of δ 88 Sr in rocks, minerals, and waters by double-spike TIMS: A powerful tool in the study of chemical, geologic, hydrologic and biologic processes

We present strontium isotopic ( 88 Sr/ 86 Sr and 87 Sr/ 86 Sr) results obtained by 87 Sr– 84 Sr double spike thermal ionization mass-spectrometry (DS-TIMS) for several standards as well as natural water samples and mineral samples of abiogenic and biogenic origin. The detailed data reduction algorithm and a user-friendly Sr-specific stand-alone computer program used for the spike calibration and the data reduction are also presented. Accuracy and precision of our δ 88 Sr measurements, calculated as permil (‰) deviations from the NIST SRM-987 standard, were evaluated by analyzing the NASS-6 seawater standard, which yielded δ 88 Sr = 0.378 ± 0.009‰. The first DS-TIMS data for the NIST SRM-607 potassium feldspar standard and for several US Geological Survey carbonate, phosphate, and silicate standards (EN-1, MAPS-4, MAPS-5, G-3, BCR-2, and BHVO-2) are also reported. Data obtained during this work for Sr-bearing solids and natural waters show a range of δ 88 Sr values of about 2.4‰, the widest observed so far in terrestrial materials. This range is easily resolvable analytically because the demonstrated external error (±SD, standard deviation) for measured δ 88 Sr values is typically ≤0.02‰. It is shown that the “true” 87 Sr/ 86 Sr value obtained by the DS-TIMS or any other external normalization method combines radiogenic and mass-dependent mass-fractionation effects, which cannot be separated. Therefore, the “true” 87 Sr/ 86 Sr and the δ 87 Sr parameter derived from it are not useful isotope tracers. Data presented in this paper for a wide range of naturally occurring sample types demonstrate the potential of the δ 88 Sr isotope tracer in combination with the traditional radiogenic 87 Sr/ 86 Sr tracer for studying a variety of biological, hydrological, and geological processes.

Journal of Analytical Atomic Spectrometry↗

USGS2003

Post-seismic relaxation theory on laterally heterogeneous viscoelastic model

Investigation was carried out into the problem of relaxation of a laterally heterogeneous viscoelastic Earth following an impulsive moment release event. The formal solution utilizes a semi-analytic solution for post-seismic deformation on a laterally homogeneous Earth constructed from viscoelastic normal modes, followed by application of mode coupling theory to derive the response on the aspherical Earth. The solution is constructed in the Laplace transform domain using the correspondence principle and is valid for any linear constitutive relationship between stress and strain. The specific implementation described in this paper is a semi-analytic discretization method which assumes isotropic elastic structure and a Maxwell constitutive relation. It accounts for viscoelastic-gravitational coupling under lateral variations in elastic parameters and viscosity. For a given viscoelastic structure and minimum wavelength scale, the computational effort involved with the numerical algorithm is proportional to the volume of the laterally heterogeneous region. Examples are presented of the calculation of post-seismic relaxation with a shallow, laterally heterogeneous volume following synthetic impulsive seismic events, and they illustrate the potentially large effect of regional 3-D heterogeneities on regional deformation patterns.

Geophysical Journal International↗

USGS2002

Using simple environmental variables to estimate below-ground productivity in grasslands

In many temperate and annual grasslands, above-ground net primary productivity (NPP) can be estimated by measuring peak above-ground biomass. Estimates of below-ground net primary productivity and, consequently, total net primary productivity, are more difficult. We addressed one of the three main objectives of the Global Primary Productivity Data Initiative for grassland systems to develop simple models or algorithms to estimate missing components of total system NPP. Any estimate of below-ground NPP (BNPP) requires an accounting of total root biomass, the percentage of living biomass and annual turnover of live roots. We derived a relationship using above-ground peak biomass and mean annual temperature as predictors of below-ground biomass (r2 = 0.54; P = 0.01). The percentage of live material was 0.6, based on published values. We used three different functions to describe root turnover: constant, a direct function of above-ground biomass, or as a positive exponential relationship with mean annual temperature. We tested the various models against a large database of global grassland NPP and the constant turnover and direct function models were approximately equally descriptive (r2 = 0.31 and 0.37), while the exponential function had a stronger correlation with the measured values (r2 = 0.40) and had a better fit than the other two models at the productive end of the BNPP gradient. When applied to extensive data we assembled from two grassland sites with reliable estimates of total NPP, the direct function was most effective, especially at lower productivity sites. We provide some caveats for its use in systems that lie at the extremes of the grassland gradient and stress that there are large uncertainties associated with measured and modelled estimates of BNPP.

Global Ecology and Biogeography↗

USGS1994

Multicomponent-flow analyses by multimode method of characteristics

For unsteady open-channel flows having N interacting unknown variables, a system of N mutually independent, partial differential equations can be used to describe the flow-field. The system generally belongs to marching-type problems and permits transformation into characteristic equations that are associated with N distinct characteristics directions. Because characteristics can be considered 'wave' or 'disturbance' propagation, a fluvial system so described can be viewed as adequately definable using these N component waves. A numerical algorithm to solve the N families of characteristics can then be introduced for formulation of an N-component flow-simulation model. The multimode method of characteristics (MMOC), a new numerical scheme that has a combined capacity of several specified-time-interval (STI) schemes of the method of characteristics, makes numerical modeling of such N-component riverine flows feasible and attainable. Merging different STI schemes yields different kinds of MMOC schemes, for which two kinds are displayed herein. With the MMOC, each characteristics is dynamically treated by an appropriate numerical mode, which should lead to an effective and suitable global simulation, covering various types of unsteady flow. The scheme is always linearly stable and its numerical accuracy can be systematically analyzed. By increasing the N value, one can develop a progressively sophisticated model that addresses increasingly complex river-mechanics problems.

Journal of Hydraulic Engineering↗

USGS2007

Application of acoustic doppler velocimeters for streamflow measurements

The U.S. Geological Survey (USGS) principally has used Price AA and Price pygmy mechanical current meters for measurement of discharge. New technologies have resulted in the introduction of alternatives to the Price meters. One alternative, the FlowTracker acoustic Doppler velocimeter, was designed by SonTek/YSI to make streamflow measurements in wadeable conditions. The device measures a point velocity and can be used with standard midsection method algorithms to compute streamflow. The USGS collected 55 quality-assurance measurements with the FlowTracker at 43 different USGS streamflow-gaging stations across the United States, with mean depths from 0.05to0.67m, mean velocities from 13 to 60 cm/s, and discharges from 0.02 to 12.4m3/s. These measurements were compared with Price mechanical current meter measurements. Analysis of the comparisons shows that the FlowTracker discharges were not statistically different from the Price meter discharges at a 95% confidence level. ?? 2007 ASCE.

Journal of Hydraulic Engineering↗

USGS1996

Hydrologic impact of Great Flood of 1993 in south-central Kansas

The writers analyze the hydrologic budget and quantify the ground-water recharge impact of the Great Flood of 1993 on the Great Bend Prairie aquifer of south-central Kansas. During the summer of 1993, rainfall totals exceeded normal levels by 200% in the northern portion of the study area, while air temperature and evapotranspiration were below normal levels. This extreme event provided the opportunity to revisit previously developed recharge-estimation algorithms. Average ground-water recharge for 1993 at four index sites was estimated at 178 mm using the hybrid water-fluctuation method of Sophocleous. Employing the recharge-estimation multiple-regression methodology of Sophocleous for the area, the writers estimated the 1993 recharge to be 145 mm. Both estimates are higher than the maximum annual recharge observed at the index sites during the 1985–1992 period. A January–July 1993 hydrologic balance analysis resulted in 130 mm of recharge. The recharge caused by the flood was three to more than four times the average annual recharge of the previous eight years. The regression-based recharge-estimation methodology proved to be generally reliable, even under extreme conditions.

Journal of Irrigation and Drainage Engineering↗

USGS1991

Seismic response of transamerica building. II. System identification

A detailed analysis of the recorded seismic response of the Transamerica Building during the October 17, 1989 Loma Prieta earthquake is presented. The system identification algorithm used for the analysis is based on the discrete-time linear filtering approach with least-squares approximation, and assumes a multi-input, single-output model for the building. Fifteen modes in the north-south direction, and 18 modes in the east-west direction are identified from the records. The analysis shows that the building's response to the earthquake was dominated by a coupled mode of vibration at 0.28 Hz in the southwest-northeast direction, which is almost parallel to one of the diagonals in the building's square cross section. The reason for this behavior is the symmetry of the building's structural characteristics, as well as the strong polarization of the S-waves of the earthquake. Several higher modes of the building were excited during the strong-motion part of the earthquake. The results also show a significant amount of rocking in the building at a frequency of 2.15 Hz.

Journal of Structural Engineering↗

USGS2004

Use of qualitative and quantitative information in neural networks for assessing agricultural chemical contamination of domestic wells

A neural network analysis of agrichemical occurrence in groundwater was conducted using data from a pilot study of 192 small-diameter drilled and driven wells and 115 dug and bored wells in Illinois, a regional reconnaissance network of 303 wells across 12 Midwestern states, and a study of 687 domestic wells across Iowa. Potential factors contributing to well contamination (e.g., depth to aquifer material, well depth, and distance to cropland) were investigated. These contributing factors were available in either numeric (actual or categorical) or descriptive (yes or no) format. A method was devised to use the numeric and descriptive values simultaneously. Training of the network was conducted using a standard backpropagation algorithm. Approximately 15% of the data was used for testing. Analysis indicated that training error was quite low for most data. Testing results indicated that it was possible to predict the contamination potential of a well with pesticides. However, predicting the actual level of contamination was more difficult. For pesticide occurrence in drilled and driven wells, the network predictions were good. The performance of the network was poorer for predicting nitrate occurrence in dug and bored wells. Although the data set for Iowa was large, the prediction ability of the trained network was poor, due to descriptive or categorical input parameters, compared with smaller data sets such as that for Illinois, which contained more numeric information.

Journal of Hydrologic Engineering↗

USGS2009

Evaluation of a moderate resolution, satellite-based impervious surface map using an independent, high-resolution validation data set

Given the relatively high cost of mapping impervious surfaces at regional scales, substantial effort is being expended in the development of moderate-resolution, satellite-based methods for estimating impervious surface area (ISA). To rigorously assess the accuracy of these data products high quality, independently derived validation data are needed. High-resolution data were collected across a gradient of development within the Mid-Atlantic region to assess the accuracy of National Land Cover Data (NLCD) Landsat-based ISA estimates. Absolute error (satellite predicted area - "reference area") and relative error [satellite (predicted area - "reference area")/ "reference area"] were calculated for each of 240 sample regions that are each more than 15 Landsat pixels on a side. The ability to compile and examine ancillary data in a geographic information system environment provided for evaluation of both validation and NLCD data and afforded efficient exploration of observed errors. In a minority of cases, errors could be explained by temporal discontinuities between the date of satellite image capture and validation source data in rapidly changing places. In others, errors were created by vegetation cover over impervious surfaces and by other factors that bias the satellite processing algorithms. On average in the Mid-Atlantic region, the NLCD product underestimates ISA by approximately 5%. While the error range varies between 2 and 8%, this underestimation occurs regardless of development intensity. Through such analyses the errors, strengths, and weaknesses of particular satellite products can be explored to suggest appropriate uses for regional, satellite-based data in rapidly developing areas of environmental significance. ?? 2009 ASCE.

Journal of Hydrologic Engineering↗

USGS2011

Finite volume model for two-dimensional shallow environmental flow

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

Journal of Hydraulic Engineering↗

USGS2012

Using "big data" to optimally model hydrology and water quality across expansive regions

This paper describes a new divide and conquer approach that leverages big environmental data, utilizing all available categorical and time-series data without subjectivity, to empirically model hydrologic and water-quality behaviors across expansive regions. The approach decomposes large, intractable problems into smaller ones that are optimally solved; decomposes complex signals into behavioral components that are easier to model with "sub- models"; and employs a sequence of numerically optimizing algorithms that include time-series clustering, nonlinear, multivariate sensitivity analysis and predictive modeling using multi-layer perceptron artificial neural networks, and classification for selecting the best sub-models to make predictions at new sites. This approach has many advantages over traditional modeling approaches, including being faster and less expensive, more comprehensive in its use of available data, and more accurate in representing a system's physical processes. This paper describes the application of the approach to model groundwater levels in Florida, stream temperatures across Western Oregon and Wisconsin, and water depths in the Florida Everglades. ?? 2009 ASCE.

Conference Paper↗

USGS2012

Bayesian WLS/GLS regression for regional skewness analysis for regions with large crest stage gage networks

This paper summarizes methodological advances in regional log-space skewness analyses that support flood-frequency analysis with the log Pearson Type III (LP3) distribution. A Bayesian Weighted Least Squares/Generalized Least Squares (B-WLS/B-GLS) methodology that relates observed skewness coefficient estimators to basin characteristics in conjunction with diagnostic statistics represents an extension of the previously developed B-GLS methodology. B-WLS/B-GLS has been shown to be effective in two California studies. B-WLS/B-GLS uses B-WLS to generate stable estimators of model parameters and B-GLS to estimate the precision of those B-WLS regression parameters, as well as the precision of the model. The study described here employs this methodology to develop a regional skewness model for the State of Iowa. To provide cost effective peak-flow data for smaller drainage basins in Iowa, the U.S. Geological Survey operates a large network of crest stage gages (CSGs) that only record flow values above an identified recording threshold (thus producing a censored data record). CSGs are different from continuous-record gages, which record almost all flow values and have been used in previous B-GLS and B-WLS/B-GLS regional skewness studies. The complexity of analyzing a large CSG network is addressed by using the B-WLS/B-GLS framework along with the Expected Moments Algorithm (EMA). Because EMA allows for the censoring of low outliers, as well as the use of estimated interval discharges for missing, censored, and historic data, it complicates the calculations of effective record length (and effective concurrent record length) used to describe the precision of sample estimators because the peak discharges are no longer solely represented by single values. Thus new record length calculations were developed. The regional skewness analysis for the State of Iowa illustrates the value of the new B-WLS/BGLS methodology with these new extensions.

Conference Paper↗