Model Rate Constants

Journal of Geophysical Research, 1990

Generalized models of thorium and particle cycling, data from Station P, and an inversion technique are used to obtain rate estimates of important biological and chemical transformations occurring in the water column. We first verify the inversion technique using an idealized data set generated by a finite difference model, and then apply the inversion technique to data from Station P. With the Station P data, predicted rate constants for adsorption and release of thorium between the dissolved and small particle phases are consistent with the results from other workers. The predicted rate constants for the interaction between small and large particles are smaller than previous estimates. The predicted concentration of large rapidly sinking particles is greater than the concentration of suspended non-sinking particles, whereas the reverse is usually assumed to be the case. The calculated sinking rate for the large particles is 20 m d-1. This sinking rate is an order of magnitude smaller than the large particle sinking rate inferred from sediment trap mass fluxes at two levels in the water column. The reason we predict a high large particle concentration and slow settling velocity has not been uniquely determined. Possible modifications of the current model that could help to reconcile the differences between observations and model predictions include: 1) two classes of rapidly sinking particles or rate constants that change with depth, 2) direct interactions between the large particle and dissolved phases, and 3) incorporation of a continuous distribution of particle size and settling velocity. These authors proposed that particle-thorium interactions can be represented by a box model that involves: dissolved trace metals; adsorption of dissolved trace metals onto relatively abundant non-sinking fine particles; desorption Copyright 1990 by the American Geophysical Union. Paper number 90JC00753. 0148-0227/90/90JC-00753505.00 of trace metals from the fine particles; aggregation of fine particles into rapidly sinking large particles, which are considered to have a very low abundance in the water column; and disaggregation of large particles. Using two western Pacific 23øTh profiles and the above box model Nozaki et al. [1987] succeeded in obtaining rate constants for adsorption and desorption of thorium and for particle aggregation and disaggregation. They assumed that the observed linear relation between thorium activity and depth extended to the surface. We show how to calculate estimates of the box model rate constants for any profile by solving simultaneous equations detailing the exchange of mass and thorium activity between the dissolved and various particulate phases. A parallel model for particle cycling includes processes that are usually thought to be biologically mediated and relates the trace metal cycling model directly to sediment trap and other particle measurements. We use a finite difference model based on the thorium model described above to generate a synthetic data set that is free of sampling and analytical errors. We then alter individual elements from the synthetic data set to test the sensitivity of rate constants predicted using the inverse technique. Finally, we apply the inverse technique to thorium data from Station P. Results from the Station P data are inconsistent with the basic assumptions underlying the development of the model and with field observations. In particular, we find that small particles are much lower in abundance than large particles, and we find that the large particles sink with a velocity that is almost an order of magnitude slower than inferred from sediment trap data. These inconsistencies suggest that the model assumptions are wrong. We offer some additional interactions that could be included in future models. 16,195 16,196 MURNANE ET AL.: THORIUM ISOTOPES AND PARTICLE CYCLING MODEL DESCRIPTION We use a trace metal cycling model (Figure la) analogous to that proposed by Bacon et al. [1985]. In addition to the rate constants for inorganic adsorption and desorption there is a rate constant associated with biologic processes that represents the active release of trace metals to solution. A simple particle model can incorporate the same phases and similar interactions (Figure lb). The activity of a trace metal radioisotope is divided between the dissolved (Ad), small particle (As), and large particle (Aoe) phases. These definitions correspond to the operationally defined classes of dissolved material (material that passes through a filter), small particles (suspended material collected by filtration) and large particles (sinking material collected in sediment traps). Filtration collects large particles as well as small particles, but we assume that the amount of large particles collected by filtration is small enough to be ignored. A is the activity in dpm L-1. We use the symbol A' to represent the activity per unit mass of particles (dpm g-l), i.e., AL-A t PL. P• is the large particle concentration and Ps is the small particle concentration, both in units of g L-1. The quantities measured directly are Ad, As, A t , and the large particle flux, wPoe. The large particle sinking velocity is w.

Proceedings of the National Academy of Sciences of the United States of America, 2019

International Journal of Recent Technology and Engineering

Non-point source pollution of surface water is a major impediment to meet water quality objectives. Managing such pollution sources in a sustainable way is a key success factor in maintaining high water quality and to prevent eutrophication. Mathematical models are widely used to simulate ecological and water quality interactions in surface waters. Simulation errors may arise due to uncertainties of the structure, input data and the model parameters. In this study, an attempt has been made to estimate the rate constants for nutrient transformations in Kabini River located in Southern part of Karnataka state in India. The experimental results demonstrated both ammonia and nitrite oxidation. In the river water, DO concentration was 5.2 mg/L. After addition of pollutants it reduced to 3.9 mg/L. EC changed from 370 to 550 µS/cm. pH remained almost the same. At 320C, the rate constants for phosphate, nitrate, nitrite, potassium and ammonia were found to be 0.165, 0.21, 0.077, 0.0777 and ...

Journal of Marine Systems, 2006

A modelling system for coupled physical-biogeochemical simulations in the water column is presented here. The physical model component allows for a number of different statistical turbulence closure schemes, ranging from simple algebraic closures to two-equation turbulence models with algebraic second-moment closures. The biogeochemical module consists of models which are based on a number of state variables represented by their ensemble averaged concentrations. Specific biogeochemical models may range from simple NPZ (nutrient-phytoplankton-zooplankton) to complex ecosystem models. Recently developed modified Patankar solvers for ordinary differential equations allow for stable discretisations of the production and destruction terms guaranteeing conservative and non-negative solutions. The increased stability of these new solvers over explicit solvers is demonstrated for a plankton spring bloom simulation. The model system is applied to marine ecosystem dynamics the Northern North Sea and the Central Gotland Sea. Two different biogeochemical models are applied, a conservative nitrogen-based model to the North Sea, and a more complex model including an oxygen equation to the Baltic Sea, allowing for the reproduction of chemical processes under anoxic conditions. For both applications, earlier model results obtained with slightly different model setups could be basically reproduced. It became however clear that the choice for ecosystem model parameters such as maximum phytoplankton growth rates does strongly depend on the physical model parameters (such as turbulence closure models or external forcing).

Analytica Chimica Acta, 1994

The graphical method and the iterative method for analysing kinetic data for metal speciation in waters are described. The graphical method involves successive subtractions of one component from the total concentration of the metal remaining, beginning with the slowest component. The iterative method uses nonlinear regression of the experimental data assuming different numbers of components to obtain the weighted residuals. The number of components which gives a minimum to the sum of squares of the weighted residuals represents the number of kinetically distinguishable components. The weighted residuals should also have a normal distribution throughout the course of the reaction. These methods were applied to simulated data for systems containing three components whose rate constants differed by a factor of two and for some cases by a factor of three. When the concentrations of each component were equal and the ratio of the rate constants equal to two, the values of the rate constants obtained by these analyses ranged from 2 to 19% of the assigned values, but the values for the initial concentrations were as much as 40% different from the assigned values. When the concentration of one component was altered the reliability of its recovered rate constant and initial concentration decreased. The advantage of the iterative method is that no prior knowledge of the number of components, rate constants and initial concentrations is required. It is demonstrated that both of these methods provide simple, reliable ways of analysing kinetic data for characterization of metal species in waters.

1999

Marine Chemistry, 2006

Over the past few decades, the radioisotope pair of 238 U / 234 Th has been widely and increasingly used to describe particle dynamics and particle export fluxes in a variety of aquatic systems. The present paper is one of five review articles dedicated to 234 Th. It is focused on the models associated with 234 Th whereas the companion papers same issue) are focused on present and future methodologies and techniques (Rutgers van der Loeff et al.), C / 234 Th ratios (Buesseler et al.), 234 Th speciation (Santschi et al.) and present and future applications of 234 Th [Waples, J.T., Benitez-Nelson, C.R., Savoye, N., Rutgers van der Loeff, M., Baskaran, M., Gustafsson, Ö , this issue. An Introduction to the application and future use of 234 Th in aquatic systems. Marine Chemistry, FATE special issue].

Advances in Environmental Research, 2001

This paper intends to layout a foundation of protocols for planning and analyzing biogeochemical experiments. It presents critical theoretical issues that must be considered for proper application of reaction-based biogeochemical models. The selection of chemical components is not unique and a decomposition of the reaction matrix should be used for formal selection. The decomposition reduces the set of ordinary differential equations governing the production᎐consumption of chemical species into three subsets of equations: mass action; kinetic-variable; and mass conservation. The consistency of mass conservation equations must be assessed with experimental data before kinetic modeling is initiated. Assumptions regarding equilibrium reactions should also be assessed. For a system with M chemical species involved in N reactions with N linearly-independent reactions and N linearly-independent

2014

1] Enterococci are the U.S. Environmental Protection Agency recommended fecal indicator bacteria for assessing recreational marine water quality. Traditional methods of enterococci analyses are time consuming, resulting in delays in issuing beach closures. Models can potentially circumvent these delays by forecasting times when beaches should be closed. The objective of this study is to develop an innovative coupled microbehydrodynamic-morphological model. The unique feature of this model is its capability of simulating the release of microbes attached to coastal beach sands as a result of combined wave and tidal forcing. A nearshore process model (XBeach) was coupled with a microbe transport-decay equation. This equation included source functions that accounted for microbial release from mobilized sand, groundwater flow, entrainment through pore water diffusion, rainfall-runoff loading, and a fate function that accounted for solar inactivation effects. The model successfully simulated observed spatial and temporal patterns of enterococci in the beach water, including the reproduction of diel and tidal fluctuations and the rapid decrease of enterococci levels from the waterline to offshore. Primary processes for enterococci loading to the water column included wave-induced sediment resuspension and tidal washing for the entrainment of enterococci from the pore water in the intertidal zone. Diffusion was the major mechanism to transport enterococci from the intertidal zone to offshore. Sunlight inactivation was a key process to reduce enterococci levels during the day and to produce the diurnal cycles. Rainfall runoff was found to be an intermittent source of enterococci to beach water, whereas groundwater exchange was of secondary importance. Sensitivity analyses suggested that the processes and coefficients related to enterococci loading have quasi-linear characteristics, whereas model results of enterococci levels were sensitive to both diffusion and sunlight inactivation coefficients, showing high nonlinearity and spatial and temporal dependence. Citation: Feng, Z., A. Reniers, B. K. Haus, and H. M. Solo-Gabriele (2013), Modeling sediment-related enterococci loading, transport, and inactivation at an embayed nonpoint source beach, Water Resour. Res., 49,