Improving Simulation Efficiency of MCMC for Inverse Modeling of Hydrologic Systems with a Kalman-Inspired Proposal Distribution

Bayesian analysis is widely used in science and engineering for real-time forecasting, decision making, and to help unravel the processes that explain the observed data. These data are some deterministic and/or stochastic transformations of the underlying parameters. A key task is then to summarize the posterior distribution of these parameters. When models become too difficult to analyze analytically, Monte Carlo methods can be used to approximate the target distribution. Of these, Markov chain Monte Carlo (MCMC) methods are particularly powerful. Such methods generate a random walk through the parameter space and, under strict conditions of reversibility and ergodicity, will successively visit solutions with frequency proportional to the underlying target density. This requires a proposal distribution that generates candidate solutions starting from an arbitrary initial state. The speed of the sampled chains converging to the target distribution deteriorates rapidly, however, with increasing parameter dimensionality. In this paper, we introduce a new proposal distribution that enhances significantly the efficiency of MCMC simulation for highly parameterized models. This proposal distribution exploits the cross-covariance of model parameters, measurements and model outputs, and generates candidate states much alike the analysis step in the Kalman filter. We embed the Kalman-inspired proposal distribution in the DREAM algorithm during burn-in, and present several numerical experiments with complex, high-dimensional or multi-modal target distributions. Results demonstrate that this new proposal distribution can greatly improve simulation efficiency of MCMC. Specifically, we observe a speed-up on the order of 10-30 times for groundwater models with more than one-hundred parameters

Smog Nitrogen and the Rapid Acidification of Forest Soil, San Bernardino Mountains, Southern California

We report the rapid acidification of forest soils in the San Bernardino Mountains of southern California. After 30 years, soil to a depth of 25 cm has decreased from a pH (measured in 0.01 M CaCl2) of 4.8 to 3.1. At the 50-cm depth, it has changed from a pH of 4.8 to 4.2. We attribute this rapid change in soil reactivity to very high rates of anthropogenic atmospheric nitrogen (N) added to the soil surface (72 kg ha–1 year–1) from wet, dry, and fog deposition under a Mediterranean climate. Our research suggests that a soil textural discontinuity, related to a buried ancient landsurface, contributes to this rapid acidification by controlling the spatial and temporal movement of precipitation into the landsurface. As a result, the depth to which dissolved anthropogenic N as nitrate (NO3) is leached early in the winter wet season is limited to within the top ~130 cm of soil where it accumulates and increases soil acidity

LEACHABILITY OF SOME EMERGING CONTAMINANTS IN RECLAIMED MUNICIPAL WASTEWATER-IRRIGATED TURF GRASS FIELDS

Emerging pollutants inherent in reclaimed municipal wastewater, including endocrine-disrupting compounds (EDCs) and pharmaceutical and personal care products (PPCPs), often have cast uncertainties on the safety of water reuse. We examined the fate and transport behavior of several PPCP and EDC compounds through observations made at experimental turf fields irrigated with naproxen, clofibric acid, diclofenac sodium, ibuprofen, estrone, 4-tert-octylphenol, bisphenol A, 4-n-nonylphenol, and triclosan latent irrigation water. The potential of the compounds to contaminate underlying groundwater was assessed using three screening protocols that employed the attributes of soils, chemicals, and water fluxes as the estimators. No compound was detected in the leachate draining through the 89-cm profile of a loamy sand soil and a sandy loam soil turf grass field during four months of irrigation according to operations typical of golf courses in southern California (USA). Ibuprofen, naproxen, triclosan, bisphenol A, clofibric acid, and estrone were detected in the surface to 30-cm soil profiles. Higher irrigation rate and coarser textural soil enhanced the downward movement of chemicals in both soils. The pollution risk screenings identified the same six compounds as having the potential to contaminate groundwater, and under conditions of turf grass irrigation, clofibric acid and ibuprofen would be most prone to cause the pollution

Relationship between pore size, particle size, aggregate size and water characteristics

Soil pore size distribution and water characteristics are important for water storage, water movement, and soil-plant interaction studies. Laboratory determinations of water characteristics and pore size distribution are time consuming and costly. Investigators have proposed many models to predict them from routinely available data. Most of the models are related to soil particle size distribution. However, they do not fit experiments well under different conditions. The objectives of this study are to determine whether some relationship between pore size distribution and particle size distribution exists for soils with different soil properties and to evaluate the influence of aggregation on the soil pore size distribution and water characteristics. After proper adjustment, the particle size, aggregate size, pore size distribution curves and the water characteristic curves were drawn on the same graph for each soil. Comparisons between pore size and particle size, aggregate size, and water characteristics were then made. A linearly transformed logistic response function was used to evaluate the equation d[subscript pore]= R[subscript x]d[subscript x], where R [subscript x] is the ratio coefficient of pore diameter to the diameter of component x, x = particle, aggregate, pore from water characteristics. Soil aggregation was quantitively related to pore size in this study. The calculated R[subscript aggregate] values are from 0.06 to 0.18; R [subscript particle] values are 0.87 to 3.20; and R[subscript water] values are 0.87 to 1.75. The R [subscript aggregate] values are much more consistent than the R [subscript particle] . This suggests that the aggregate size may be a better index for predicting pore size distribution, especially for swelling and high clay content soils. For soils with non-swelling clay, low clay content, and low aggregation, the shape of the pore size distribution, particle size distribution, and aggregate size distribution curves and their density function curves are very similar. The predicted pore size distribution curves fit the experimental curves very well. For soils with high swelling, high clay content and good structure, pore size distribution and aggregate size distribution have a better relation than the pore size and particle size. Water characteristic curves and pore size distribution curves did not coincide because of the different behaviors of particles and aggregates in water and in mercury. A systematic model was suggested to predict pore size distribution from particle size or aggregate size. This model divides the pore size distribution curve into six regions. After a computer program is completed, this model will be able to calculate the packing density and pore size distribution. The input variables are bulk density, particle density, and particle or aggregate size distribution data

Safe Application of Reclaimed Water Reuse in the Southwestern United States

Farmers in the arid Southwest are looking at new water use strategies, including conservation and reuse, as increasing human populations in the area compete with agricultural uses. Find out what methods are available and what legal restrictions apply

Kinetics of cation adsorption on charged soil mineral as strong electrostatic force presence or absence

The purposes of this research were to: (1) establish new analytical kinetic equation for describing the effect of strong electrostatic force on adsorption; (2) experimentally determine if it is a strong or weak electrostatic force adsorption process; and (3) evaluate the adsorption energies of the strong and weak force adsorptions based on the proposed new theory of cation adsorption kinetics. The constantly charged material-montmorillonite was used in the experiment. The montmorillonite was saturated with two Cation species: K+ and Ca2+, respectively, using KNO3 or Ca(NO3)2 before it was used for the experiment. The miscible displacement technique under a steady flow condition was adopted to the kinetic studies of Mg2+ (Mg(NO3)2) adsorption. In the experiment, 0.5000 g of K+- or Ca2+-saturated montmorillonite was layered on the exchange column, the thickness of sample layer was approximately 0.2–0.3 mm, the cross-sectional area of the column (sample area) was 15 cm2. The concentration of Mg2+ in the flowing liquid was 10−4 mol L−1. The flow velocity of the flowing liquid was 1.0 mL·min−1. Effluent was collected at 10-min intervals. Firstly, new and exact rate models for describing ion adsorption have been advanced. Secondly, based on the experiments of Mg2+/K+ and Mg2+/Ca2+ exchange in K+ and Ca2+-saturated montmorillonites, Mg2+ adsorption in K+-saturated sample appeared zero-order kinetic process in the initial stage of the strong force adsorption for t = 0–405 min, and then the adsorption process converted to the first-order kinetics of the weak force adsorption, which agrees with the theoretical prediction. However, for the Ca2+-saturated sample, merely first-order kinetic process appeared for Mg2+ adsorption. Either for Mg2+/K+ exchange or Mg2+/Ca2+ exchange, the quantities of Mg2+ by weak force adsorption at equilibrium were almost the same. Thirdly, several important dynamic and thermodynamic parameters can be theoretically calculated based on the new theory in describing cation adsorption. For Mg2+/K+ exchange, both strong and weak electrostatic force adsorptions exist, but for Mg2+/Ca2+ exchange only the weak electrostatic force adsorption occurs. The strong and weak force adsorption processes can be quantitatively described by the new analytical kinetic equations of the zero- and the first-order kinetics, respectively. Because each parameter in the analytical kinetic equations has its definitive physical meaning, several important dynamic and thermodynamic parameters in cation exchange can be theoretically estimated

Safe Application of Reclaimed Water Reuse in the Southwestern United States

Farmers in the arid Southwest are looking at new water use strategies, including conservation and reuse, as increasing human populations in the area compete with agricultural uses. Find out what methods are available and what legal restrictions apply