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Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts

Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright ?? 2002 John Wiley and Sons, Ltd.

International Journal for Numerical Methods in Eng↗

Removing tidal-period variations from time-series data using low-pass digital filters

Several low-pass, digital filters are examined for their ability to remove tidal Period Variations from a time-series of water surface elevation for San Francisco Bay. The most efficient filter is the one which is applied to the Fourier coefficients of the transformed data, and the filtered data recovered through an inverse transform. The ability of the filters to remove the tidal components increased in the following order: 1) cosine-Lanczos filter, 2) cosine-Lanczos squared filter; 3) Godin filter; and 4) a transform fitter. The Godin fitter is not sufficiently sharp to prevent severe attenuation of 2–3 day variations in surface elevation resulting from weather events.

Journal of Physical Oceanography↗

Accounting for orphaned aftershocks in the earthquake background rate

Aftershocks often occur within cascades of triggered seismicity in which each generation of aftershocks triggers an additional generation, and so on. The rate of earthquakes in any particular generation follows Omori's law, going approximately as 1/ t . This function decays rapidly, but is heavy-tailed, and aftershock sequences may persist for long times at a rate that is difficult to discriminate from background. It is likely that some apparently spontaneous earthquakes in the observational catalogue are orphaned aftershocks of long-past main shocks. To assess the relative proportion of orphaned aftershocks in the apparent background rate, I develop an extension of the ETAS model that explicitly includes the expected contribution of orphaned aftershocks to the apparent background rate. Applying this model to California, I find that the apparent background rate can be almost entirely attributed to orphaned aftershocks, depending on the assumed duration of an aftershock sequence. This implies an earthquake cascade with a branching ratio (the average number of directly triggered aftershocks per main shock) of nearly unity. In physical terms, this implies that very few earthquakes are completely isolated from the perturbing effects of other earthquakes within the fault system. Accounting for orphaned aftershocks in the ETAS model gives more accurate estimates of the true background rate, and more realistic expectations for long-term seismicity patterns.

Geophysical Journal International↗

Characterization methods for fractured glacial tills

This paper provides a literature review of methods successfully employed to characterize finegrained and fractured or unfractured glacial deposits. Descriptions and examples are given for four major categories of characterization methods: physical, hydraulic, chemical, and indirect. Characterization methods have evolved significantly within the past ten years; however, there still exists uncertainty about the reliability of individual characterization methods applied to till deposits. Therefore, a combination of methods is best, the choice of which depends on the objectives of the work. Sampling methods, sampling scales, and reporting methods are extremely important and should be considered when interpreting and comparing results between sites. Recognition of these issues is necessary to ensure that decisions regarding the transport of fluids in fractured tills are not based on the assumption that poorly permeable tills are always an inhibitor of subsurface flow.

Ohio Journal of Science↗

Estimating the timing and location of shallow rainfall-induced landslides using a model for transient, unsaturated infiltration

Shallow rainfall-induced landslides commonly occur under conditions of transient infiltration into initially unsaturated soils. In an effort to predict the timing and location of such landslides, we developed a model of the infiltration process using a two-layer system that consists of an unsaturated zone above a saturated zone and implemented this model in a geographic information system (GIS) framework. The model links analytical solutions for transient, unsaturated, vertical infiltration above the water table to pressure-diffusion solutions for pressure changes below the water table. The solutions are coupled through a transient water table that rises as water accumulates at the base of the unsaturated zone. This scheme, though limited to simplified soil-water characteristics and moist initial conditions, greatly improves computational efficiency over numerical models in spatially distributed modeling applications. Pore pressures computed by these coupled models are subsequently used in one-dimensional slope-stability computations to estimate the timing and locations of slope failures. Applied over a digital landscape near Seattle, Washington, for an hourly rainfall history known to trigger shallow landslides, the model computes a factor of safety for each grid cell at any time during a rainstorm. The unsaturated layer attenuates and delays the rainfall-induced pore-pressure response of the model at depth, consistent with observations at an instrumented hillside near Edmonds, Washington. This attenuation results in realistic estimates of timing for the onset of slope instability (7 h earlier than observed landslides, on average). By considering the spatial distribution of physical properties, the model predicts the primary source areas of landslides.

Journal of Geophysical Research F: Earth Surface↗

Physics-based forecasts of eruptive vent locations at calderas

Constraining stresses in the Earth's crust in volcanic regions is critical for understanding many mechanical processes related to eruptive activity. Dike pathways, in particular, are shaped by the orientation of principal stress axes. Therefore, accurate models of dike trajectories and future vent locations rely on accurate estimates of stresses in the subsurface. This work presents a framework for probabilistic constraint of the stress state of calderas by combining three-dimensional physics-based dike pathway models with observed past vent locations using a Monte Carlo approach. The retrieved stress state is then used to produce probability maps of future vent opening across a caldera. We test our stress inversion and vent forecast approach on synthetic scenarios, and find it successful depending on the distribution of the available vents and the complexity of the volcano's structural history. We explore the potential and limitations of the approach, show how its performance is sensitive to the assumptions in the models and available prior information, and discuss how it may be applied to real calderas.

Journal of Geophysical Research: Solid Earth↗

Foreshocks during the nucleation of stick-slip instability

We report on laboratory experiments which investigate interactions between aseismic slip, stress changes, and seismicity on a critically stressed fault during the nucleation of stick-slip instability. We monitor quasi-static and dynamic changes in local shear stress and fault slip with arrays of gages deployed along a simulated strike-slip fault (2 m long and 0.4 m deep) in a saw cut sample of Sierra White granite. With 14 piezoelectric sensors, we simultaneously monitor seismic signals produced during the nucleation phase and subsequent dynamic rupture. We observe localized aseismic fault slip in an approximately meter-sized zone in the center of the fault, while the ends of the fault remain locked. Clusters of high-frequency foreshocks (M w ~ −6.5 to −5.0) can occur in this slowly slipping zone 5–50 ms prior to the initiation of dynamic rupture; their occurrence appears to be dependent on the rate at which local shear stress is applied to the fault. The meter-sized nucleation zone is generally consistent with theoretical estimates, but source radii of the foreshocks (2 to 70 mm) are 1 to 2 orders of magnitude smaller than the theoretical minimum length scale over which earthquake nucleation can occur. We propose that frictional stability and the transition between seismic and aseismic slip are modulated by local stressing rate and that fault sections, which would typically slip aseismically, may radiate seismic waves if they are rapidly stressed. Fault behavior of this type may provide physical insight into the mechanics of foreshocks, tremor, repeating earthquake sequences, and a minimum earthquake source dimension.

Journal of Geophysical Research B: Solid Earth↗

Incorporating antenna detections into abundance estimates of fish

Autonomous passive integrated transponder (PIT) tag antennas are commonly used to detect fish marked with PIT tags but cannot detect unmarked fish, creating challenges for abundance estimation. Here we describe an approach to estimate abundance from paired physical capture and antenna detection data in closed and open mark-recapture models. Additionally, for open models, we develop an approach that incorporates uncertainty in fish size, because fish size changes through time (as fish grow bigger) but is unknown if fish are not physically captured (e.g., only detected on antennas). Incorporation of size uncertainty allows for estimation of size-specific abundances and demonstrates a generally useful method for obtaining state-specific abundances estimates under state uncertainty. Simulation studies comparing models with and without antenna detections illustrate that the benefit of our approach increases as a larger proportion of the population is marked. When applied to two field data sets, our approach to incorporating antenna detections reduced uncertainty in abundance substantially. We conclude that PIT antennas hold great potential for improving abundance estimation, despite the challenges they present.

Canadian Journal of Fisheries and Aquatic Sciences↗

Casual instrument corrections for short-period and broadband seismometers

Of all the filters applied to recordings of seismic waves, which include source, path, and site effects, the one we know most precisely is the instrument filter. Therefore, it behooves seismologists to accurately remove the effect of the instrument from raw seismograms. Applying instrument corrections allows analysis of the seismogram in terms of physical units (e.g., displacement or particle velocity of the Earth’s surface) instead of the output of the instrument (e.g., digital counts). The instrument correction can be considered the most fundamental processing step in seismology since it relates the raw data to an observable quantity of interest to seismologists. Complicating matters is the fact that, in practice, the term “instrument correction” refers to more than simply the seismometer. The instrument correction compensates for the complete recording system including the seismometer, telemetry, digitizer, and any anti‐alias filters. Knowledge of all these components is necessary to perform an accurate instrument correction. The subject of instrument corrections has been covered extensively in the literature (Seidl, 1980; Scherbaum, 1996). However, the prospect of applying instrument corrections still evokes angst among many seismologists—the authors of this paper included. There may be several reasons for this. For instance, the seminal paper by Seidl (1980) exists in a journal that is not currently available in electronic format and cannot be accessed online. Also, a standard method for applying instrument corrections involves the programs TRANSFER and EVALRESP in the Seismic Analysis Code (SAC) package (Goldstein et al. , 2003). The exact mathematical methods implemented in these codes are not thoroughly described in the documentation accompanying SAC.

Seismological Research Letters↗

Evaluation of trap capture in a geographically closed population of brown treesnakes on Guam

1. Open population mark-recapture analysis of unbounded populations accommodates some types of closure violations (e.g. emigration, immigration). In contrast, closed population analysis of such populations readily allows estimation of capture heterogeneity and behavioural response, but requires crucial assumptions about closure (e.g. no permanent emigration) that are suspect and rarely tested empirically. 2. In 2003, we erected a double-sided barrier to prevent movement of snakes in or out of a 5-ha semi-forested study site in northern Guam. This geographically closed population of >100 snakes was monitored using a series of transects for visual searches and a 13 ?? 13 trapping array, with the aim of marking all snakes within the site. Forty-five marked snakes were also supplemented into the resident population to quantify the efficacy of our sampling methods. We used the program mark to analyse trap captures (101 occasions), referenced to census data from visual surveys, and quantified heterogeneity, behavioural response, and size bias in trappability. Analytical inclusion of untrapped individuals greatly improved precision in the estimation of some covariate effects. 3. A novel discovery was that trap captures for individual snakes consisted of asynchronous bouts of high capture probability lasting about 7 days (ephemeral behavioural effect). There was modest behavioural response (trap happiness) and significant latent (unexplained) heterogeneity, with small influences on capture success of date, gender, residency status (translocated or not), and body condition. 4. Trapping was shown to be an effective tool for eradicating large brown treesnakes Boiga irregularis (>900 mm snout-vent length, SVL). 5. Synthesis and applications. Mark-recapture modelling is commonly used by ecological managers to estimate populations. However, existing models involve making assumptions about either closure violations or response to capture. Physical closure of our population on a landscape scale allowed us to determine the relative importance of covariates influencing capture probability (body size, trappability periods, and latent heterogeneity). This information was used to develop models in which different segments of the population could be assigned different probabilities of capture, and suggests that modelling of open populations should incorporate easily measured, but potentially overlooked, parameters such as body size or condition. ?? 2008 The Authors.

Journal of Applied Ecology↗

Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models

We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.

Journal of Agricultural, Biological, and Environme↗

Evaluation of transmitter attachment techniques on growth of wild turkey poults

We compared the effects on growth of backpack-mounted and surgically implanted radiotransmitters used as marking techniques in studies of wild turkey ( Meleagris gallopavo ) poult survival. We applied repeated-measures analysis of variance (ANOVA) and Bayesian analysis to evaluate the null hypothesis that marking technique did not affect growth. Growth in body mass was similar among treatment groups. We did, however, find differences in wing-growth rates among treatment groups. The control group had the highest wing-growth rate, the backpack group had the lowest growth rate, and the surgical implant group was intermediate. Latex backpack harnesses also caused physical developmental problems that would have negatively biased wild poult survival estimates in the field. Surgically implanted transmitters affected wing growth less than the backpack harnesses and are therefore recommended for attaching transmitters to wild turkey poults.

Journal of Wildlife Management↗

Modeling radium and radon transport through soil and vegetation

A one-dimensional flow and transport model was developed to describe the movement of two fluid phases, gas and water, within a porous medium and the transport of 226Ra and 222Rn within and between these two phases. Included in this model is the vegetative uptake of water and aqueous 226Ra and 222Rn that can be extracted from the soil via the transpiration stream. The mathematical model is formulated through a set of phase balance equations and a set of species balance equations. Mass exchange, sink terms and the dependence of physical properties upon phase composition couple the two sets of equations. Numerical solution of each set, with iteration between the sets, is carried out leading to a set-iterative compositional model. The Petrov-Galerkin finite element approach is used to allow for upstream weighting if required for a given simulation. Mass lumping improves solution convergence and stability behavior. The resulting numerical model was applied to four problems and was found to produce accurate, mass conservative solutions when compared to published experimental and numerical results and theoretical column experiments. Preliminary results suggest that the model can be used as an investigative tool to determine the feasibility of phytoremediating radium and radon-contaminated soil. ?? 2003 Elsevier Science B.V. All rights reserved.

Journal of Contaminant Hydrology↗

An efficient Bayesian framework for updating PAGER loss estimates

We introduce a Bayesian framework for incorporating time-varying noisy reported data on damage and loss information to update near real-time loss estimates/alerts for the U.S. Geological Survey’s Prompt Assessment of Global Earthquakes for Response (PAGER) system. Initial loss estimation by PAGER immediately following an earthquake includes several uncertainties. Historically, the PAGER’s alerting on fatality and economic losses has not incorporated location-specific reported data on physical damage or casualties for a given earthquake. The proposed framework provides the ability to include early reports on fatalities at any given time and improve the overall impact forecast for the earthquake. The reported data on fatalities or damage are generally incomplete and noisy, especially in the early hours of the disaster. To address these challenges, we develop a recursive Bayesian updating framework that takes into account the loss projection model and the measurement and model uncertainties. The framework is applied to loss data for three example earthquakes, and the results show that the proposed updating improves the loss estimates and alert level to the correct level within the first day of the earthquake.

Earthquake Spectra Journal↗

Influence of grain size and shape on volcanic ash electrical conductivity

Few studies have examined the electrical properties of volcanic ash or considered the effects of physical characteristics, such as grain size and shape on its electrification. This study measures the resistivity of eight volcanic ash samples, three milled-samples and five natural ashfall samples from Alaska, U.S.A., using a current amplifier and examines the influence of particle size and particle shape on calculated grain conductivity. Grain conductivities are calculated by applying spherical, oblate, and prolate ellipsoidal shape parameters within a general effective media equation. Volcanic ash is an electrically insulating material with average resistivity values ranging from 1.732E 7 to 1.606E 12 Ωm. Results show that grain size has a limited impact on resistivity. Calculated grain conductivities remained within the same order of magnitude between the three different shape calculations ranging between 1.367E − 7 and 2.196E − 12 S/m using the spherical shape parameter. Electrical measurements of heterogeneous powders are complex and challenging. This study aims to expand the community's dataset and understanding of the electrical properties of volcanic ash and the impact of different physical characteristics. This has implication for understanding ash hazards to electrical infrastructure and volcanic lightning.

Journal of Volcanology and Geothermal Research↗

Modeling CO2 degassing and pH in a stream-aquifer system

Pinal Creek, Arizona receives an inflow of ground water with high dissolved inorganic carbon (57-75 mg/l) and low pH (5.8-6.3). There is an observed increase of in-stream pH from approximately 6.0-7.8 over the 3 km downstream of the point of groundwater inflow. We hypothesized that CO2 gas-exchange was the most important factor causing the pH increase in this stream-aquifer system. An existing transport model, for coupled ground water-surface water systems (OTIS), was modified to include carbonate equilibria and CO2 degassing, used to simulate alkalinity, total dissolved inorganic carbon (C(T)), and pH in Pinal Creek. Because of the non-linear relation between pH and C(T), the modified transport model used the numerical iteration method to solve the non-linearity. The transport model parameters were determined by the injection of two tracers, bromide and propane. The resulting simulations of alkalinity, C(T) and pH reproduced, without fitting, the overall trends in downstream concentrations. A multi-parametric sensitivity analysis (MPSA) was used to identify the relative sensitivities of the predictions to six of the physical and chemical parameters used in the transport model. MPSA results implied that C(T) and pH in stream water were controlled by the mixing of ground water with stream water and CO2 degassing. The relative importance of these two processes varied spatially depending on the hydrologic conditions, such as stream flow velocity and whether a reach gained or lost stream water caused by the interaction with the ground water. The coupled transport model with CO2 degassing and generalized sensitivity analysis presented in this study can be applied to evaluate carbon transport and pH in other coupled stream-ground water systems.An existing transport model for coupled groundwater-surface water systems was modified to include carbonate equilibria and CO2 degassing. The modified model was used to simulate alkalinity, total dissolved inorganic carbon (CT) and pH in Pinal Creek. The model used the numerical iteration method to solve the nonlinear relation between pH and CT. A multi-parametric sensitivity analysis (MPSA) was used to identify the relative sensitivities of the predictions to six of the physical and chemical parameters used in the transport model. MPSA results implied that CT and pH in the stream water were controlled by the mixing of groundwater with stream water and CO2 degassing.

Journal of Hydrology↗

A semi-mechanistic model for partitioning evapotranspiration reveals transpiration dominates the water flux in drylands

Popular evapotranspiration (ET) partitioning methods make assumptions that might not be well-suited to dryland ecosystems, such as high sensitivity of plant water-use efficiency (WUE) to vapor pressure deficit (VPD). Our objectives were to (a) create an ET partitioning model that can produce fine-scale estimates of transpiration (T) in drylands, and (b) use this approach to evaluate how climate controls T and WUE across ecosystem types and timescales along a dryland aridity gradient. We developed a novel, semi-mechanistic ET partitioning method using a Bayesian approach that constrains abiotic evaporation using process-based models, and loosely constrains time-varying WUE within an autoregressive framework. We used this method to estimate daily T and weekly WUE across seven dryland ecosystem types and found that T dominates ET across the aridity gradient. Then, we applied cross-wavelet coherence analysis to evaluate the temporal coherence between focal response variables (WUE and T/ET) and environmental variables. At yearly scales, we found that WUE at less arid, higher elevation sites was primarily limited by atmospheric moisture demand, and WUE at more arid, lower elevation sites was primarily limited by moisture supply. At sub-yearly timescales, WUE and VPD were sporadically correlated. Hence, ecosystem-scale dryland WUE is not always sensitive to changes in VPD at short timescales, despite this being a common assumption in many ET partitioning models. This new ET partitioning method can be used in dryland ecosystems to better understand how climate influences physically and biologically driven water fluxes.

New Mexico↗

Tree-ring derived avalanche frequency and climate associations in a high-latitude, maritime climate

Snow avalanches are a natural hazard in mountainous areas worldwide with severe impacts that include fatalities, damage to infrastructure, disruption to commerce, and landscape disturbance. Understanding long-term avalanche frequency patterns, and associated climate and weather influences, improves our understanding of how climate change may affect avalanche activity. We used dendrochronological techniques to evaluate the historical frequency of large magnitude avalanches (LMAs) in the high-latitude climate of southeast Alaska, United States. We collected 434 cross sections throughout six avalanche paths near Juneau, Alaska. This resulted in 2706 identified avalanche growth disturbances between 1720 and 2018, which allowed us to reconstruct 82 years with LMA activity across three sub-regions. By combining this tree-ring-derived avalanche data set with a suite of climate and atmospheric variables and applying a generalized linear model to fit a binomial regression, we found that February and March precipitation and the Oceanic Niño Index (ONI) were significant predictors of LMA activity in the study area. Specifically, LMA activity occurred during winters with substantial February and March precipitation and neutral or negative (cold) ONI values, while years not characterized by LMAs occur more frequently during warm winters (positive ONI values). Our examination of the climate-avalanche relationship in southeast Alaska sheds light on important climate variables and physical processes associated with LMA years. These results can be used to inform long-term infrastructure planning and avalanche mitigation operations in an urban area, such as Juneau, where critical infrastructure is subject to substantial avalanche hazard.

Alaska↗