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Modeling hazardous mass flows Geoflows09: Mathematical and computational aspects of modeling hazardous geophysical mass flows; Seattle, Washington, 9–11 March 2009

A recent workshop at the University of Washington focused on mathematical and computational aspects of modeling the dynamics of dense, gravity-driven mass movements such as rock avalanches and debris flows. About 30 participants came from seven countries and brought diverse backgrounds in geophysics; geology; physics; applied and computational mathematics; and civil, mechanical, and geotechnical engineering. The workshop was cosponsored by the U.S. Geological Survey Volcano Hazards Program, by the U.S. National Science Foundation through a Vertical Integration of Research and Education (VIGRE) in the Mathematical Sciences grant to the University of Washington, and by the Pacific Institute for the Mathematical Sciences. It began with a day of lectures open to the academic community at large and concluded with 2 days of focused discussions and collaborative work among the participants.

Eos, Earth and Space Science News

USGS Spectral Library Version 7

We have assembled a library of spectra measured with laboratory, field, and airborne spectrometers. The instruments used cover wavelengths from the ultraviolet to the far infrared (0.2 to 200 microns [μm]). Laboratory samples of specific minerals, plants, chemical compounds, and manmade materials were measured. In many cases, samples were purified, so that unique spectral features of a material can be related to its chemical structure. These spectro-chemical links are important for interpreting remotely sensed data collected in the field or from an aircraft or spacecraft. This library also contains physically constructed as well as mathematically computed mixtures. Four different spectrometer types were used to measure spectra in the library: (1) Beckman™ 5270 covering the spectral range 0.2 to 3 µm, (2) standard, high resolution (hi-res), and high-resolution Next Generation (hi-resNG) models of Analytical Spectral Devices (ASD) field portable spectrometers covering the range from 0.35 to 2.5 µm, (3) Nicolet™ Fourier Transform Infra-Red (FTIR) interferometer spectrometers covering the range from about 1.12 to 216 µm, and (4) the NASA Airborne Visible/Infra-Red Imaging Spectrometer AVIRIS, covering the range 0.37 to 2.5 µm. Measurements of rocks, soils, and natural mixtures of minerals were made in laboratory and field settings. Spectra of plant components and vegetation plots, comprising many plant types and species with varying backgrounds, are also in this library. Measurements by airborne spectrometers are included for forested vegetation plots, in which the trees are too tall for measurement by a field spectrometer. This report describes the instruments used, the organization of materials into chapters, metadata descriptions of spectra and samples, and possible artifacts in the spectral measurements. To facilitate greater application of the spectra, the library has also been convolved to selected spectrometer and imaging spectrometers sampling and bandpasses, and resampled to selected broadband multispectral sensors. The native file format of the library is the SPECtrum Processing Routines (SPECPR) data format. This report describes how to access freely available software to read the SPECPR format. To facilitate broader access to the library, we produced generic formats of the spectra and metadata in text files. The library is provided on digital media and online at https://speclab.cr.usgs.gov/spectral-lib.html . A long-term archive of these data are stored on the USGS ScienceBase data server ( https://dx.doi.org/10.5066/F7RR1WDJ ).

Data Series

USGS Digital Spectral Library splib06a

Introduction We have assembled a digital reflectance spectral library that covers the wavelength range from the ultraviolet to far infrared along with sample documentation. The library includes samples of minerals, rocks, soils, physically constructed as well as mathematically computed mixtures, plants, vegetation communities, microorganisms, and man-made materials. The samples and spectra collected were assembled for the purpose of using spectral features for the remote detection of these and similar materials. Analysis of spectroscopic data from laboratory, aircraft, and spacecraft instrumentation requires a knowledge base. The spectral library discussed here forms a knowledge base for the spectroscopy of minerals and related materials of importance to a variety of research programs being conducted at the U.S. Geological Survey. Much of this library grew out of the need for spectra to support imaging spectroscopy studies of the Earth and planets. Imaging spectrometers, such as the National Aeronautics and Space Administration (NASA) Airborne Visible/Infra Red Imaging Spectrometer (AVIRIS) or the NASA Cassini Visual and Infrared Mapping Spectrometer (VIMS) which is currently orbiting Saturn, have narrow bandwidths in many contiguous spectral channels that permit accurate definition of absorption features in spectra from a variety of materials. Identification of materials from such data requires a comprehensive spectral library of minerals, vegetation, man-made materials, and other subjects in the scene. Our research involves the use of the spectral library to identify the components in a spectrum of an unknown. Therefore, the quality of the library must be very good. However, the quality required in a spectral library to successfully perform an investigation depends on the scientific questions to be answered and the type of algorithms to be used. For example, to map a mineral using imaging spectroscopy and the mapping algorithm of Clark and others (1990a, 2003b), one simply needs a diagnostic absorption band. The mapping system uses continuum-removed reference spectral features fitted to features in observed spectra. Spectral features for such algorithms can be obtained from a spectrum of a sample containing large amounts of contaminants, including those that add other spectral features, as long as the shape of the diagnostic feature of interest is not modified. If, however, the data are needed for radiative transfer models to derive mineral abundances from reflectance spectra, then completely uncontaminated spectra are required. This library contains spectra that span a range of quality, with purity indicators to flag spectra for (or against) particular uses. Acquiring spectral measurements and performing sample characterizations for this library has taken about 15 person-years of effort. Software to manage the library and provide scientific analysis capability is provided (Clark, 1980, 1993). A personal computer (PC) reader for the library is also available (Livo and others, 1993). The program reads specpr binary files (Clark, 1980, 1993) and plots spectra. Another program that reads the specpr format is written in IDL (Kokaly, 2005). In our view, an ideal spectral library consists of samples covering a very wide range of materials, has large wavelength range with very high precision, and has enough sample analyses and documentation to establish the quality of the spectra. Time and available resources limit what can be achieved. Ideally, for each mineral, the sample analysis would include X-ray diffraction (XRD), electron microprobe (EM) or X-ray fluorescence (XRF), and petrographic microscopic analyses. For some minerals, such as iron oxides, additional analyses such as Mossbauer would be helpful. We have found that to make the basic spectral measurements, provide XRD, EM or XRF analyses, and microscopic analyses, document the results, and complete an entry of one spectral library sample, all takes about

Data Series

USGS Digital Spectral Library splib05a

We have assembled a digital reflectance spectral library of spectra that covers wavelengths from the ultraviolet to near-infrared along with sample documentation. The library includes samples of minerals, rocks, soils, physically constructed as well as mathematically computed mixtures, vegetation, microorganisms, and man-made materials. The samples and spectra collected were assembled for the purpose of using spectral features for the remote detection of these and similar materials.

Open-File Report

Projected effects of proposed chloride-control projects on shallow ground water– Preliminary results for the Wichita River basin, Texas

The U.S. Army Corps of Engineers' plan to control the natural chloride pollution in the Wichita River basin includes the construction of Truscott Brine Lake on a tributary of the North Wichita River. In connection with the proposed brine lake, the U.S. Geological Survey was requested to: (1) Define the existing ground-water conditions in the shallow fresh-water system of the project area; and (2) project the post-construction effects of the proposed lake on the fresh-water aquifer, especially in relation to hydraulic-head changes but also with respect to possible changes in the chemical quality of the ground water. The fresh-water aquifer in the project area is a shallow water-table system with relatively fresh water (generally a calcium sulfate type) that contains approximately 500 to 5,000 milligrams per liter of dissolved solids. The aquifer consists of Permian rocks with very small values of hydraulic conductivity and overlies a brine system (sodium chloride type) that is even less permeable. A thin transition zone separates the fresh-water aquifer and the brine system. Small quantities of infiltration from precipitation throughout the area's watershed constitute the recharge to the aquifer. Discharge from the aquifer consists of the small base flow along creeks; well discharge is negligible. Two-dimensional mathematical computer models were developed for aquifer simulation of: (1) Steady-state conditions in a fresh-water system and (2) transient conditions in a brine- fresh-water system where the density effects of the brine are considered. The main results 'of projecting the effects of the proposed Truscott Brine Lake on the fresh-water aquifer are: (1) Hydraulic head rises of 5 to 40 feet would be confined to areas near the proposed dam and along the lake shoreline, and (2) migration of salt water downstream from the dam generally would be limited to less than 1 mile and apparently would not reach equilibrium during the 100-year duration of the project. The modeling efforts did not include possible effects related to hydrodynamic dispersion in the brine- fresh-water system. Possible changes in the hydraulic conductivity of the aquifer, due to physical and chemical interactions in the brine and fresh-water environments, also were not considered.

Texas

Can machine learning accelerate process understanding and decision-relevant predictions of river water quality?

The global decline of water quality in rivers and streams has resulted in a pressing need to design new watershed management strategies. Water quality can be affected by multiple stressors including population growth, land use change, global warming, and extreme events, with repercussions on human and ecosystem health. A scientific understanding of factors affecting riverine water quality and predictions at local to regional scales, and at sub-daily to decadal timescales are needed for optimal management of watersheds and river basins. Here, we discuss how machine learning (ML) can enable development of more accurate, computationally tractable, and scalable models for analysis and predictions of river water quality. We review relevant state-of-the art applications of ML for water quality models and discuss opportunities to improve the use of ML for emerging computational and mathematical methods for model selection, hyperparameter optimization, incorporating process knowledge into ML models, improving explainablity, uncertainty quantification, and model-data integration. We then present considerations for using ML to address water quality problems given their scale and complexity, available data and computational resources, and stakeholder needs. When combined with decades of process understanding, interdisciplinary advances in knowledge-guided ML, information theory, data integration, and analytics can help address fundamental science questions and enable decision-relevant predictions of riverine water quality.

Hydrological Processes

Ground-water models for water resource planning

In the past decade hydrogeologists have emphasized the development of computer-based mathematical models to aid in the understanding of flow, the transport of solutes, transport of heat, and deformation in the ground-water system. These models have been used to provide information and predictions for water managers. Too frequently, ground-water was neglected in water resource planning because managers believed that it could not be adequately evaluated in terms of availability, quality, and effect of development on surface-water supplies. Now, however, with newly developed digital ground-water models, effects of development can be predicted. Such models have been used to predict hydrologic and quality changes under different stresses. These models have grown in complexity over the last ten years from simple one-layer models to three-dimensional simulations of ground-water flow, which may include solute transport, heat transport, effects of land subsidence, and encroachment of saltwater. Case histories illustrate how predictive ground-water models have provided the information needed for the sound planning and management of water resources in the USA. ?? 1983 D. Reidel Publishing Company.

GeoJournal

Granular avalanches across irregular three-dimensional terrain: 2. Experimental tests

Scaling considerations indicate that miniature experiments can be used to test models of granular avalanches in which the effects of intergranular fluid and cohesion are negligible. To test predictions of a granular avalanche model described in a companion paper, we performed bench top experiments involving avalanches of dry sand across irregular basal topography that mimicked the complexity of natural terrain. The experiments employed a novel method of laser-assisted cartography to map the three-dimensional morphology of rapidly moving avalanches, thereby providing high-resolution data for comparison with model output. Model input consisted of two material properties (angles of internal and basal Coulomb friction of the sand), which were measured in independent tests, and of initial and boundary conditions that characterized the geometry of the experimental apparatus. Experimental results demonstrate that the model accurately predicts not only the gross behavior but also many details of avalanche motion, from initiation to deposition. We attribute this accuracy to a mathematical and computational formulation that conserves mass and momentum in three-dimensional physical space and satisfies the Coulomb equation in three-dimensional stress space. Our results support the hypothesis that a Coulomb proportionality between shear and normal stresses applies in moderately rapid granular flows and that complicated constitutive postulates are unnecessary if momentum conservation is strictly enforced in continuum avalanche models. Furthermore, predictions of our Coulomb continuum model contrast with those of a Coulomb point mass model, illustrating the importance of multidimensional modeling and model testing.

Journal of Geophysical Research Earth Surface

Predicting paleoclimate from compositional data using multivariate Gaussian process inverse prediction

Multivariate compositional count data arise in many applications including ecology, microbiology, genetics and paleoclimate. A frequent question in the analysis of multivariate compositional count data is what underlying values of a covariate(s) give rise to the observed composition. Learning the relationship between covariates and the compositional count allows for inverse prediction of unobserved covariates given compositional count observations. Gaussian processes provide a flexible framework for modeling functional responses with respect to a covariate without assuming a functional form. Many scientific disciplines use Gaussian process approximations to improve prediction and make inference on latent processes and parameters. When prediction is desired on unobserved covariates given realizations of the response variable, this is called inverse prediction. Because inverse prediction is often mathematically and computationally challenging, predicting unobserved covariates often requires fitting models that are different from the hypothesized generative model. We present a novel computational framework that allows for efficient inverse prediction using a Gaussian process approximation to generative models. Our framework enables scientific learning about how the latent processes co-vary with respect to covariates while simultaneously providing predictions of missing covariates. The proposed framework is capable of efficiently exploring the high dimensional, multi-modal latent spaces that arise in the inverse problem. To demonstrate flexibility, we apply our method in a generalized linear model framework to predict latent climate states given multivariate count data. Based on cross-validation, our model has predictive skill competitive with current methods while simultaneously providing formal, statistical inference on the underlying community dynamics of the biological system previously not available.

Annals of Applied Statistics

Determination of ultimate carbonaceous BOD and the specific rate constant (K1)

Ultimate carbonaceous biochemical oxygen demand (BODu) and the specific rate constant (K1) at which the demand is exerted are important parameters in designing biological wastewater treatment plants and in assessing the impact of wastewater on receiving streams. An analytical method is presented which uses time-series concentrations of BOD, defined as the calculated sum of dissolved oxygen (DO) losses at each time of measurement, for determining BODu and K1. Time-series DO measurements are obtained from a water sample that is incubated in darkness at 20 degrees Celsius in the presence of nitrapyrin, a chemical nitrification inhibitor. Time-series concentrations of BOD that approximate first order kinetics can be analyzed graphically or mathematically to compute BODu and K1.

Open-File Report

Suspended-sediment yields and stream-channel processes on Judy's Branch watershed in the St. Louis Metro East region in Illinois

Judy's Branch watershed, a small basin (8.64 square miles) in the St. Louis Metro East region in Illinois, was selected as a pilot site to determine suspended-sediment yields and stream-channel processes in the bluffs and American Bottoms (expansive low-lying valley floor in the region). Suspended-sediment and stream-chan-nel data collected and analyzed for Judy's Branch watershed are presented in this report to establish a baseline of data for water-resource managers to evaluate future stream rehabilitation and manage-ment alternatives. The sediment yield analysis determines the amount of sediment being delivered from the watershed and two subwatersheds: an urban tributary and an undeveloped headwater (pri-marily agricultural). The analysis of the subwater-sheds is used to compare the effects of urbanization on sediment yield to the river. The stream-channel contribution to sediment yield was determined by evaluation of the stream-channel processes operat-ing on the streambed and banks of Judy's Branch watershed. Bank stability was related to hydrologic events, bank stratigraphy, and channel geometry through model development and simulation. The average suspended-sediment yield from two upland subwatersheds (drainage areas of 0.23 and 0.40 sq.mi. was 1,163 tons per square mile per year (tons/sq.mi.-year) between July 2000 and June 2004. The suspended-sediment yield at the Route 157 station was 2,523 tons/sq.mi.-year, near the outlet of Judy's Branch watershed (drainage area = 8.33 sq.mi.). This is approximately 1,360 tons/sq.mi.-year greater than the average at the upland stations for the same time period. This result is unexpected in that, generally, the suspended-sediment yield decreases as the watershed area increases because of sediment stored in the channel and flood plain. The difference indicates a possible increase in yield from a source, such as bank retreat, and supports the concept that land-use changes increase stream-flows that may in turn result in higher rates of bank retreat. Utilizing both bank-rod data and resurveyed cross-section data, it was determined that approxi-mately half of the suspended- sediment yield at Route 157 during July 2000-June 2004 came from bank retreat. Given that bank retreat can be a substantial portion of the sediment yield, understanding bank stability processes is important. Bank stability can be assessed mathematically by computing the factor of safety, which is defined by the ratio of the shear strength (resisting force) along the failure surface and the shear stress (driving gravitational force). Once the factor of safety falls below one, the bank theoretically becomes unstable. Bank-stability conditions were related to hydrologic events, bank type, and channel geometry through model develop-ment and simulation. The most common type of bank in the watershed consists of cohesive alluvial soil deposits overlying a stiff glacial till. A stabil-ity chart for different bank types was developed using a bank-stability analysis. Banks steeper than 70 degrees and higher than from 10 to 11.5 feet (depending on bank type) become at risk for mass failure in the watershed under conditions that pro-mote saturation of the bank and a sudden drop in the river level.

Scientific Investigations Report

On regional geomagnetic charts

When regional geomagnetic charts for areas roughly the size of the United States were compiled by hand, some large local anomalies were displayed in the isomagnetic lines. Since the late nineteen sixties, when the compilation of charts using computers and mathematical models was started, most of the details available in the hand drawn regional charts have been lost. One exception to this is the Canadian magnetic declination chart for 1980. This chart was constructed using a 180 degree spherical harmonic model. It managed to show considerable detail, but even more detail might be useful. Suggestions are made about how more detail might be displayed in regional charts when adequate data are available.

Journal of Geomagnetism & Geoelectricity

The measurement of total sediment load in alluvial streams

The measurement of the total sediment load transported by streams that flow in alluvial channels has been a perplexing problem to engineers and geologists for over a century. Until the last decade the development of equipment to measure bed load and suspended load was carried on almost independently, and without primary consideration of the fundamental laws governing the transportation of fluvial sediments. French investigators during the nineteenth century described methods of measurement and a mathematical approach for computing the rate of bed-load movement. The comprehensive laboratory investigations by Gilbert early in this century provided data that are still being used for studies of sediment transport. Detailed laboratory investigations of bed-load movement conducted during the last two decades by a number of investigators have resulted in the development of additional mathematical formulas for computing rates of bed-load movement. Likewise, studies of turbulent flow have provided the turbulence suspension theory for suspended sediment as it is known today.

Conference Paper

Section 1. Simulation of surface-water integrated flow and transport in two-dimensions: SWIFT2D user's manual

A numerical model for simulation of surface-water integrated flow and transport in two (horizontal-space) dimensions is documented. The model solves vertically integrated forms of the equations of mass and momentum conservation and solute transport equations for heat, salt, and constituent fluxes. An equation of state for salt balance directly couples solution of the hydrodynamic and transport equations to account for the horizontal density gradient effects of salt concentrations on flow. The model can be used to simulate the hydrodynamics, transport, and water quality of well-mixed bodies of water, such as estuaries, coastal seas, harbors, lakes, rivers, and inland waterways. The finite-difference model can be applied to geographical areas bounded by any combination of closed land or open water boundaries. The simulation program accounts for sources of internal discharges (such as tributary rivers or hydraulic outfalls), tidal flats, islands, dams, and movable flow barriers or sluices. Water-quality computations can treat reactive and (or) conservative constituents simultaneously. Input requirements include bathymetric and topographic data defining land-surface elevations, time-varying water level or flow conditions at open boundaries, and hydraulic coefficients. Optional input includes the geometry of hydraulic barriers and constituent concentrations at open boundaries. Time-dependent water level, flow, and constituent-concentration data are required for model calibration and verification. Model output consists of printed reports and digital files of numerical results in forms suitable for postprocessing by graphical software programs and (or) scientific visualization packages. The model is compatible with most mainframe, workstation, mini- and micro-computer operating systems and FORTRAN compilers. This report defines the mathematical formulation and computational features of the model, explains the solution technique and related model constraints, describes the model framework, documents the type and format of inputs required, and identifies the type and format of output available.

Techniques and Methods

Computing maximum-likelihood estimates for parameters of the National Descriptive Model of Mercury in Fish

This report presents the mathematical expressions and the computational techniques required to compute maximum-likelihood estimates for the parameters of the National Descriptive Model of Mercury in Fish (NDMMF), a statistical model used to predict the concentration of methylmercury in fish tissue. The expressions and techniques reported here were prepared to support the development of custom software capable of computing NDMMF parameter estimates more quickly and using less computer memory than is currently possible with available general-purpose statistical software. Computation of maximum-likelihood estimates for the NDMMF by numerical solution of a system of simultaneous equations through repeated Newton-Raphson iterations is described. This report explains the derivation of the mathematical expressions required for computational parameter estimation in sufficient detail to facilitate future derivations for any revised versions of the NDMMF that may be developed.

Open-File Report

Mass-conserving method of characteristics for streamflow modeling

A robust numerical model is presented for the computation of unsteady streamflow on steep river slopes. The one-dimensional model uses the method of characteristics on a specified space-time grid to solve the Saint-Venant equations. An additional continuity equation requirement on each space-time element provides greatly improved conservation of mass over traditional implementations of the method of characteristics on a fixed grid. The space-time geometry of the problem is described in a finite element setting. Hermite interpolation of channel parameters is used to avoid numerical difficulties that may occur with steep slopes due to discontinuities in the derivatives of data such as channel top width. Manning's equation for friction slope can be modified by a factor to make the slope more appropriate for steep rivers. The standard Manning's friction slope can also be used, if preferred. The computer model is not restricted to steep slopes, and applies as well to gently sloping streams. Two numerical examples support the mathematical approach and computational algorithm.

Water Supply Paper

Image analysis as a method for determining grain-size distributions in sandstones

A Quantimet 720 image analyzing computer is useful for A Quantimet 720 image analyzing computer is useful for determination of grain-size distributions of sand-size material. Results including histograms and statistical measures of size can be produced in approximately 5 to 10 minutes per sample. Comparison with sieve results shows only small differences in the mean grain-sizes obtained. Research into operating methods for the image analyzing computer and into mathematical methods for combining data is continuing so that material coarser and finer than sand can be measured. The instrument, which is attached to a microscope via a black and white television scanner, uses the gray shades of features in the field of view as the means of detecting those features. The image analyzing computer can then measure the features including area, perimeter, and several types of diameters. These data are then analyzed by a computer and the results are plotted. Sample preparation for this technique is conventional. Samples can be run as loose disaggregated grains, grain mounts, or thin sections.

Open-File Report

Geomorphometry-Diversity in quantitative surface analysis

A widening variety of applications is diversifying geomorphometry ( digital terrain modelling ), the quantitative study of topography. An amalgam of earth science, mathematics, engineering and computer science, the discipline has been revolutionized by the computer manipulation of gridded terrain heights, or digital elevation models (DEMs). Its rapid expansion continues. This article reviews the remarkable diversity of recent morphometric work in 15 selected topics and discusses their significance and prospects. The quantitative analysis of industrial microsurface topography is introduced to the earth science community. The 14 other topics are Internet access to geomorphometry; global DEMs; DEM modelling of channel networks; self-organized criticality; fractal and wavelet analysis; soil resources; landslide hazards; barchan dunes; harvesting wind energy; sea-ice surfaces; sea-floor abyssal hills; Japanese work in morphometry; and the emerging fields of landscape ecology and image understanding. Closing remarks note reasons for the diversity within geomorphometry, speculate on future trends and recommend creating a unified field of surface representation.

Progress in Physical Geography: Earth and Environm