Partitioning of \alpha and \beta diversity using hierarchical Bayesian modeling of species distribution and abundance

Diversity partitioning is becoming widely used to decompose the total number of species recorded in an area or region \((\gamma )\) into the average number of species within samples \((\alpha )\) and the average difference in species composition \((\beta )\) among samples. Single-value metrics of \(\alpha \) and \(\beta \) diversity are popular because they may be applied at multiple scales and because of their ease in computation and interpretation. Studies thus far, however, have emphasized observed diversity components or comparisons to randomized, null distributions. In addition, prediction of \(\alpha \) and \(\beta \) components using environmental or spatial variables has been limited to more extensive data sets because multiple samples are required to estimate single \(\alpha \) and \(\beta \) components. Lastly, observed diversity components do not incorporate variation in detection probabilities among species or samples. In this study, we used hierarchical Bayesian models of species abundances to provide predictions of \(\alpha \) and \(\beta \) components in species richness and composition using environmental and spatial variables. We illustrate our approach using butterfly data collected from 26 grassland remnants to predict spatially nested patterns of \(\alpha \) and \(\beta \) based on the predicted counts of butterflies. Diversity partitioning using a Bayesian hierarchical model incorporated variation in detection probabilities by butterfly species and habitat patches, and provided prediction intervals for \(\alpha \) and \(\beta \) components using environmental and spatial variables.     

A flexible spatio-temporal model for air pollution with spatial and spatio-temporal covariates

The development of models that provide accurate spatio-temporal predictions of ambient air pollution at small spatial scales is of great importance for the assessment of potential health effects of air pollution. Here we present a spatio-temporal framework that predicts ambient air pollution by combining data from several different monitoring networks and deterministic air pollution model(s) with geographic information system covariates. The model presented in this paper has been implemented in an R package, SpatioTemporal, available on CRAN. The model is used by the EPA funded Multi-Ethnic Study of Atherosclerosis and Air Pollution (MESA Air) to produce estimates of ambient air pollution; MESA Air uses the estimates to investigate the relationship between chronic exposure to air pollution and cardiovascular disease. In this paper we use the model to predict long-term average concentrations of \(\text {NO}_{x}\) in the Los Angeles area during a 10 year period. Predictions are based on measurements from the EPA Air Quality System, MESA Air specific monitoring, and output from a source dispersion model for traffic related air pollution (Caline3QHCR). Accuracy in predicting long-term average concentrations is evaluated using an elaborate cross-validation setup that accounts for a sparse spatio-temporal sampling pattern in the data, and adjusts for temporal effects. The predictive ability of the model is good with cross-validated \(R^2\) of approximately \(0.7\) at subject sites. Replacing four geographic covariate indicators of traffic density with the Caline3QHCR dispersion model output resulted in very similar prediction accuracy from a more parsimonious and more interpretable model. Adding traffic-related geographic covariates to the model that included Caline3QHCR did not further improve the prediction accuracy.     

Investigating the complex relationship between in situ Southern Ocean pCO_{2} and its ocean physics and biogeochemical drivers using a nonparametric regression approach

The objective in this paper is to investigate the use of a non-parametric approach to model the relationship between oceanic carbon dioxide \((pCO_2)\) and a range of ocean physics and biogeochemical in situ variables in the Southern Ocean, which influence its in situ variability. The need for this stems from the need to obtain reliable estimates of carbon dioxide concentrations in the Southern Ocean which plays an important role in the global carbon flux cycle. The main challenge involved in this objective is the spatial limitation and seasonal bias of the in situ data. Moreover, studies have also reported that the relationship between \(pCO_2\) and its drivers is complex. As such, in this paper, we use the non-parametric kernel regression approach since it is able to accurately capture the complex relationships between the response and predictor variables. In this analysis we use the in situ data obtained from the SANAE49 return leg journey between Antarctic to Cape Town. To the best of our knowledge, this is the first time this data set has been subjected to such analysis. The model variants were developed on a training data subset, and the ‘goodness’ of the models were assessed on an “unseen” test data subset. Results indicate that the nonparametric approach consistently captures the relationship more accurately in terms of mean square error, root mean square error and mean absolute error, over a standard parametric approach (multiple linear regression). These results provide a platform for using the developed nonparametric regression model based on in situ measurements to predict \(pCO_2\) for a larger spatial region in the Southern Ocean based on satellite biogeochemical measurements of predictor variables, given that satellites do not measure \(pCO_2\) .     

Gravity currents with double stratification: a numerical and analytical investigation

We consider high-Reynolds-number Boussinesq gravity current and intrusion systems in which both the ambient and the propagating “current” are linearly stratified. The main focus is on a current of fixed volume released from a rectangular lock; the height ratio of the fluids $H$ , the stratification parameter of the ambient $S$ , and the internal stratification parameter of the current, $\sigma $ , are quite general. We perform two-dimensional Navier–Stokes simulation and compare the results with those of a previously-published one-layer shallow-water model. The results provide insights into the behavior of the system and enhance the confidence in the approximate model while also revealing its limitations. The qualitative predictions of the model are confirmed, in particular: (1) there is an initial “slumping” stage of propagation with constant speed $u_N$ , after which $u_N$ decays with time; (2) for fixed $H$ and $S$ , the increase of $\sigma $ causes a slower propagation of the current; (3) for some combinations of the parameters $H,S, \sigma $ the fluid released from the lock lacks initially (or runs out quickly of) buoyancy “driving power” in the horizontal direction, and does not propagate like a gravity current. There is also a fair quantitative agreement between the predictions of the model and the simulations concerning the spread of the current.     

Numerical analysis on the Brisbane River plume in Moreton Bay due to Queensland floods 2010–2011

During the Queensland floods in the summer of 2010–2011, a flood-driven Brisbane River plume extended into Moreton Bay, Queensland, Australia, and then seaward, travelling in a northward direction. It covered approximately 500 km $^{2}$ . This paper presents a three- dimensional hydrodynamic numerical model investigation into the behaviour of the Brisbane River plume. The model was verified by using satellite observations and field measurement data. The present study concludes that the high river discharge was the primary factor determining the plume size and its seaward extensions. A notable finding was that the plume was a bottom-trapped type rather than a buoyant type. Further, the southerly winds were found to have moderately confined the alongshore extension of the plume, and had caused the plume to mix thoroughly with the ocean water.     

A zero-inflated Bayesian spatial model with near-locating measurements

Zero-inflated data arise in many contexts. In this paper, we develop a zero-inflated Bayesian hierarchical model which deals with spatial effects, correlation among near-locating measurements as well as excess zeros simultaneously. Inference, including the sampling from the posterior distributions, predictions at new locations, and model selection, is carried out by using computationally efficient Markov chain Monte Carlo techniques. The posterior distributions are simulated using a Gibbs sampler with the embedded ratio-of-uniform method and the slice sampling algorithm. The approach is illustrated via an application to herbaceous data collected in the Missouri Ozark Forest Ecosystem Project. The results from the proposed model are compared with those generated from a non-zero inflated model. The proposed model fully incorporates the information from data collection and provides more reliable inference. A predictive $p$ value is computed for model checking and it indicates that the proposed model fits the data well.     

Waves and turbulence in katabatic winds

The measurements taken during the Vertical Transport and Mixing Experiment (VTMX, October, 2000) on a northeastern slope of Salt Lake Valley, Utah, were used to calculate the statistics of velocity fluctuations in a katabatic gravity current in the absence of synoptic forcing. The data from ultrasonic anemometer-thermometers placed at elevations 4.5 and 13.9 m were used. The contributions of small-scale turbulence and waves were isolated by applying a high-pass digital (Elliptical) filter, whereupon the filtered quantities were identified as small-scale turbulence and the rest as internal gravity waves. Internal waves were found to play a role not only at canonical large gradient Richardson numbers $(\overline{\hbox {Ri}_\mathrm{g} } >1)$ , but sometimes at smaller values $(0.1 < \overline{\hbox {Ri}_\mathrm{g}}<1)$ , in contrast to typical observations in flat-terrain stable boundary layers. This may be attributed, at least partly, to (critical) internal waves on the slope, identified by Princevac et al. [1], which degenerate into turbulence and help maintain an active internal wave field. The applicability of both Monin-Obukhov (MO) similarity theory and local scaling to filtered and unfiltered data was tested by analyzing rms velocity fluctuations as a function of the stability parameter z/L, where L is the Obukhov length and z the height above the ground. For weaker stabilities, $\hbox {z/L}<1$ , the MO similarity and local scaling were valid for both filtered and unfiltered data. Conversely, when $\hbox {z/L}>1$ , the use of both scaling types is questionable, although filtered data showed a tendency to follow local scaling. A relationship between z/L and $\overline{\hbox {Ri}_\mathrm{g} }$ was identified. Eddy diffusivities of momentum $\hbox {K}_\mathrm{M}$ and heat $\hbox {K}_\mathrm{H}$ were dependent on wave activities, notably when $\overline{\hbox {Ri}_\mathrm{g} } > 1$ . The ratio $\hbox {K}_{\mathrm{H}}/\hbox {K}_{\mathrm{M}}$ dropped well below unity at high $\overline{\hbox {Ri}_\mathrm{g} }$ , in consonance with previous laboratory stratified shear layer measurements as well as other field observations.     

Quantifying a significance of sediment particle size to hyporheic sedimentary oxygen demand with a permeable stream bed

A mechanistic model of sedimentary oxygen demand (SOD) for hyporheic flow is presented. The permeable sediment bed, e.g. sand or fine gravel, is considered with hydraulic conductivity in the range $0.1 < K < 20$  cm/s. Hyporheic pore water flow is induced by pressure fluctuations at the sediment/water interface due to near-bed turbulent coherent motions. A 2-D advection–diffusion equation is linked to the pore water flow model to simulate the effect of advection–dispersion driven by interstitial flow on oxygen transfer through the permeable sediment. Microbial oxygen uptake in the sediment is expressed as a function of the microbial growth rate, and is related to the sediment properties, i.e. the grain diameter $(d_{s})$ and porosity $(\phi )$ . The model describes the significance of sediment particle size to oxygen transfer through the sediment and microbial oxygen uptake: With increasing grain diameter $(d_{s})$ , the hydraulic conductivity $(K)$ increases so does the oxygen transfer rate, while particle surface area per volume (the available surface area for colonization by biofilms) decreases reducing the microbial oxygen uptake rate. Simulation results show that SOD increases as the hydraulic conductivity $(K)$ increases before a threshold has been reached. After that, SOD diminishes with the increment of the hydraulic conductivity $(K)$ .     

Initial mixing of inclined dense jet in perpendicular crossflow

A comprehensive experimental investigation for an inclined ( $60^{\circ }$ to vertical) dense jet in perpendicular crossflow—with a three-dimensional trajectory—is reported. The detailed tracer concentration field in the vertical cross-section of the bent-over jet is measured by the laser-induced fluorescence technique for a wide range of jet densimetric Froude number $Fr$ and ambient to jet velocity ratios $U_r$ . The jet trajectory and dilution determined from a large number of cross-sectional scalar fields are interpreted by the Lagrangian model over the entire range of jet-dominated to crossflow-dominated regimes. The mixing during the ascent phase of the dense jet resembles that of an advected jet or line puff and changes to a negatively buoyant thermal on descent. It is found that the mixing behavior is governed by a crossflow Froude number $\mathbf{F} = U_r Fr$ . For $\mathbf{F} < 0.8$ , the mixing is jet-dominated and governed by shear entrainment; significant detrainment occurs and the maximum height of rise $Z_{max}$ is under-predicted as in the case of a dense jet in stagnant fluid. While the jet trajectory in the horizontal momentum plane is well-predicted, the measurements indicate a greater rise and slower descent. For $\mathbf{F} \ge 0.8$ the dense jet becomes significantly bent-over during its ascent phase; the jet mixing is dominated by vortex entrainment. For $\mathbf{F} \ge 2$ , the detrainment ceases to have any effect on the jet behavior. The jet trajectory in both the horizontal momentum and buoyancy planes are well predicted by the model. Despite the under-prediction of terminal rise, the jet dilution at a large number of cross-sections covering the ascent and descent of the dense jet are well-predicted. Both the terminal rise and the initial dilution for the inclined jet in perpendicular crossflow are smaller than those of a corresponding vertical jet. Both the maximum terminal rise $Z_{max}$ and horizontal lateral penetration $Y_{max}$ follow a $\mathbf{F}^{-1/2}$ dependence in the crossflow-dominated regime. The initial dilution at terminal rise follows a $S \sim \mathbf{F}^{1/3}$ dependence.     

Data depth for the uniform distribution

Given a set $X$ of $k$ points and a point $z$ in the $n$ -dimensional euclidean space, the Tukey depth of $z$ with respect to $X$ , is defined as $m/k$ , where $m$ is the minimum integer such that $z$ is not in the convex hull of some set of $k-m$ points of $X$ . If $z$ belongs to the closed region $B$ delimited by an ellipsoid, define the continuous depth of $z$ with respect to $B$ as the quotient $V(z)/\text{ Vol }(B)$ , where $V(z)$ is the minimum volume of the intersection of $B$ with the halfspaces defined by any hyperplane passing through $z$ , and $\text{ Vol }(B)$ is the volume of $B$ . We consider $z$ a random variable and prove that, if $z$ is uniformly distributed in $B$ , the continuous depth of $z$ with respect to $B$ has expected value $1/2^{n+1}$ . This result implies that if $z$ and $X$ are uniformly distributed in $B$ , the expected value of Tukey depth of $z$ with respect to $X$ converges to $1/2^{n+1}$ as the number of points $k$ goes to infinity. These findings have applications in ecology, namely within the niche theory, where it is useful to explore and characterize the distribution of points inside species niche.     

Gravity currents with tailwaters in Boussinesq and non-Boussinesq systems: two-layer shallow-water dam-break solutions and Navier–Stokes simulations

We consider the dam-break initial stage of propagation of a gravity current of density $\rho _{c}$ released from a lock (reservoir) of height $h_0$ in a channel of height $H$ . The channel contains two-layer stratified fluid. One layer, called the “tailwater,” is of the same density as the current and is of thickness $h_T (< h_0)$ , and the other layer, called the “ambient,” is of different density $\rho _{a}$ . Both Boussinesq ( $\rho _{c}/\rho _{a}\approx 1$ ) and non-Boussinesq systems are investigated. By assuming a large Reynolds number, we can model the flow with the two-layer shallow-water approximation. Due to the presence of the tailwater, the “jump conditions” at the front of the current are different from the classical Benjamin formula, and in some circumstances (clarified in the paper) the interface of the current matches smoothly with the horizontal interface of the tailwater. Using the method of characteristics, analytical solutions are derived for various combinations of the governing parameters. To corroborate the results, two-dimensional direct numerical Navier–Stokes simulations are used, and comparisons for about 80 combinations of parameters in the Boussinesq and non-Boussinesq domains are performed. The agreement of speed and height of the current is very close. We conclude that the model yields self-contained and fairly accurate analytical solutions for the dam-break problem under consideration. The results provide reliable insights into the influence of the tailwater on the propagation of the gravity current, for both heavy-into-light and light-into-heavy motions. This is a significant extension of the classical gravity-current theory from the particular $h_T=0$ point to the $h_T > 0$ domain.     

RNA-DNA ratio: an index of larval fish growth in the sea

Data on water temperature, RNA-DNA ratio, and growth of eight species of temperate marine fish larvae reared in the laboratory were fit to the equation: $$G_{pi} = 0.93{\text{ }}\operatorname{T} + 4.75{\text{ RNA - DNA}} - 18.18$$ where G_pi is the protein growth rate in % d^-1 and T is the water temperature. Water temperature and larval RNA-DNA ratio explained 92% of the variability in growth rate of laboratory-reared larvae. The model is useful over the entire range of feeding levels (starvation to excess), temperatures (2° to 20°C) and fish species studied. Estimates of recent growth of larval cod, haddock, and sand lance caught at sea based on water temperature and RNA-DNA ratio ranged from negative to 26% d^-1. These data demonstrate the importance of food availability in larval fish mortality and suggest that short-term growth under favorable conditions may be considerably higher than expected from long-term indicators. RNA-DNA ratio analysis offers new possibilities for understanding larval growth and mortality, and their relation to environmental variability.     

A note on a non-stationary point source spatial model

A point source, non-stationary covariance structure model is proposed, having only one additional parameter over a standard, stationary covariance structure, spatial model. Additionally, the proposed model is demonstrated to fit better than the three extra parameter, point source, non-stationary spatial model proposed by Ecker and De Oliveira (Commun Stat Theory Methods 37:2066–2078, 2008). The proposed model is fit from a Bayesian perspective and illustrated using a house sales dataset from Cedar Falls, Iowa.     

On the periodicity of atmospheric von Kármán vortex streets

For over 100 years, laboratory-scale von Kármán vortex streets (VKVSs) have been one of the most studied phenomena within the field of fluid dynamics. During this period, countless publications have highlighted a number of interesting underpinnings of VKVSs; nevertheless, a universal equation for the vortex shedding frequency ( \(N\) ) has yet to be identified. In this study, we have investigated \(N\) for mesoscale atmospheric VKVSs and some of its dependencies through the use of realistic numerical simulations. We find that vortex shedding frequency associated with mountainous islands, generally demonstrates an inverse relationship to cross-stream obstacle length ( \(L\) ) at the thermal inversion height of the atmospheric boundary layer. As a secondary motive, we attempt to quantify the relationship between \(N\) and \(L\) for atmospheric VKVSs in the context of the popular Strouhal number ( \(Sr\) )–Reynolds number ( \(Re\) ) similarity theory developed through laboratory experimentation. By employing numerical simulation to document the \(Sr{-}Re\) relationship of mesoscale atmospheric VKVSs (i.e., in the extremely high \(Re\) regime) we present insight into an extended regime of the similarity theory which has been neglected in the past. In essence, we observe mesoscale VKVSs demonstrating a consistent \(Sr\) range of 0.15–0.22 while varying \(L\) (i.e, effectively varying \(Re\) ).     

Accounting for matching uncertainty in two stage capture–recapture experiments using photographic measurements of natural marks

We propose a Bayesian hierarchical modeling approach for estimating the size of a closed population from data obtained by identifying individuals through photographs of natural markings. We assume that noisy measurements of a set of distinctive features are available for each individual present in a photographic catalogue. To estimate the population size from two catalogues obtained during two different sampling occasions, we embed the standard two-stage $M_t$ capture–recapture model for closed population into a multivariate normal data matching model that identifies the common individuals across the catalogues. In addition to estimating the population size while accounting for the matching process uncertainty, this hierarchical modelling approach allows to identify the common individuals by using the information provided by the capture–recapture model. This way, our model also represents a novel and reliable tool able to reduce the amount of effort researchers have to expend in matching individuals. We illustrate and motivate the proposed approach via a real data set of photo-identification of narwhals. Moreover, we compare our method with a set of possible alternative approaches by using both the empirical data set and a simulation study.     

The effect of export to the deep sea on the long-range transport potential of persistent organic pollutants

Background

Export to the deep sea has been found to be a relevant pathway for highly hydrophobic chemicals. The objective of this study is to investigate the influence of this process on the potential for long-range transport (LRT) of such chemicals.

Methods

The spatial range as a measure of potential for LRT is calculated for seven PCB congeners with the multimedia fate and transport model ChemRange. Spatial ranges for cases with and without deep sea export are compared.

Results and Discussion

Export to the deep sea leads to increased transfer from the air to the surface ocean and, thereby, to lower spatial ranges for PCB congeners whose net deposition rate constant is similar to or greater than the atmospheric degradation rate constant. This is fulfilled for the PCB congeners 101, 153, 180, and 194. The spatial ranges of the congeners 8, 28, and 52, in contrast, are not affected by deep sea export. With export to the deep sea included in the model, the spatial ranges of the heavier congener are similar to those of the lighter ones, while the intermediate congeners 101 and 153 have the highest potential for long-range transport.

Conclusions

Transfer to the deep ocean affects the mass balance and the potential for LRT of highly hydrophobic chemicals and should be included in multimedia fate models containing a compartment for ocean water.     

On the effective hydraulic conductivity and macrodispersivity for density-dependent groundwater flow

In this paper, semi-analytical expressions of the effective hydraulic conductivity ( $K^{E})$ and macrodispersivity ( $\alpha ^{E})$ for 3D steady-state density-dependent groundwater flow are derived using a stationary spectral method. Based on the derived expressions, we present the dependence of $K^{E}$ and $\alpha ^{E}$ on the density of fluid under different dispersivity and spatial correlation scale of hydraulic conductivity. The results show that the horizontal $K^{E}$ and $\alpha ^{E}$ are not affected by density-induced flow. However, due to gravitational instability of the fluid induced by density contrasts, both vertical $K^{E}$ and $\alpha ^{E}$ are found to be reduced slightly when the density factor ( $\gamma $ ) is less than 0.01, whereas significant decreases occur when $\gamma $ exceeds 0.01. Of note, the variation of $K^{E}$ and $\alpha ^{E}$ is more significant when local dispersivity is small and the correlation scale of hydraulic conductivity is large.     

Passive scalar roughness lengths for atmospheric boundary layer flow over complex, fractal topographies

When modeling atmospheric boundary layer flow over rough landscapes, surface fluxes of flow quantities (momentum, temperature, etc.) can be described with equilibrium logarithmic law expressions, all of which require specification of a roughness length that is, physically, the elevation at which the flow quantity equals its surface value. In high Reynolds number flows, such as the atmospheric boundary layer, inertial forces associated with turbulent eddy motions are responsible for surface momentum fluxes (form, or pressure drag). Surface scalar fluxes, on the other hand, occur exclusively via diffusion in the immediate vicinity of the topography—the interfacial region—before being advected by turbulent eddy motions into the bulk of the flow. Owing to this difference in surface transfer mechanism, the passive scalar roughness length, $z_{0S}$ , is known to be less than the momentum roughness length, $z_0$ . In this work, classical relations are used to specify $z_{0S}$ during large-eddy simulation of atmospheric boundary layer flow over aerodynamically rough, synthetic, fractal topographies which exhibit power-law height energy spectrum, $E_h (k) \sim k^{\beta _s}$ , where $\beta _s$ is a (predefined) spectral exponent. These topographies are convenient since they resemble natural landscapes and $\beta _s$ can be varied to change the topography’s aerodynamic roughness (the study considers a suite of topographies with $-2.4 \le \beta _s \le -1.2$ , where $-2.4$ and $-1.2$ are the “most smooth” and “most rough” cases, respectively, corresponding with roughness Reynolds number, $Re_0 \approx 10$ and $300$ ). It is often assumed that $z_{0S}/z_{0} \approx 10^{-1}$ for all $Re_0$ . But results from this work show that the roughness length ratio, $z_{0S}/z_{0}$ , depends strongly on $Re_0$ , ranging between $10^{-3}$ and $10^{-1}$ .     

Large eddy simulation of dispersion around an isolated cubic building: evaluation of localized dynamic k_\mathrm{SGS}-equation sub-grid scale model

In the present study, the prediction accuracy of a dynamic one-equation sub-grid scale model for the large eddy simulation of dispersion around an isolated cubic building is investigated. For this purpose, the localized dynamic $k_\mathrm{SGS} $ -equation model (LDKM) is employed and the results are compared with the available experimental data and two other classic sub-grid scale models, namely, standard Smagorinsky–Lilly model (SSLM) and dynamic Smagorinsky–Lilly model (DSLM). It is shown that the three SGS models give results in good agreement with experiment. However, near the ground level of the leeward wall, dimensionless time-averaged concentration, $\langle K\rangle $ , profile is not quite similar to the experimental data. It is also demonstrated that the LDKM predicts the values of $\langle K\rangle $ on the roof, leeward and side walls more acceptably than the SSLM and DSLM. Whereas, the streamwise elongation of time-averaged structures of the plume shape is more over-estimated with the LDKM than with the other two SGS models. In terms of numerical difficulty, the LDKM is found to be stable and computationally reasonable. In addition, it does not suffer from a flow dependent constant such as the Smagorinsky coefficient employed in the SSLM model.     

Three-way compositional analysis of water quality monitoring data

Water quality monitoring data typically consist of \(J\) parameters and constituents measured at \(I\) number of static locations at \(K\) sets of seasonal occurrences. The resulting \(I \times J \times K\) three-way array can be difficult to interpret. Additionally, the constituent portion of the dataset (e.g., major ion and trace element concentration, pH, etc.) is compositional in that it sums to a constant (e.g., 1 kg/L) and is mathematically confined to the simplex, the sample space for compositional data. Here we apply a Tucker3 model on centered log-ratio data to find low dimensional representation of latent variables as a means to simplify data processing and interpretation of three years of seasonal compositional groundwater chemistry data for 14 wells at a study site in Wyoming, USA. The study site has been amended with treated coalbed methane produced water, using a subsurface drip irrigation system, to allow for irrigation of forage crops. Results from three-way compositional data analysis indicate that primary controls on water quality at the study site include: solutes concentration by evapotranspiration, cation exchange, and dissolution of native salts. These findings agree well with results from more detailed investigations of the site. In addition, the model identified Ba uptake during gypsum precipitation in some portions of the site during the final 6–9 months of investigation, a process for which the timing and extent had not previously been identified. These results suggest that multi-way compositional analyses hold promise as a means to more easily interpret water quality monitoring data.