Wlodek Tych

In situ high resolution measurements of fluxes of Ni, Cu, Fe, and Mn and concentrations of Zn and Cd in porewaters by DGT

The technique of diffusion gradients in thin films (DGT) was used to measure in situ fluxes of metals at fine spatial resolution (1.25 mm) in the surface sediments (029 cm) and immediately overlying water of Esthwaite Water, UK. DGT measures labile metal species in situ by immobilizing them in a layer of Chelex resin after diffusion through a 0.4 mm polyacrylamide gel. The measured mass per unit area which accumulates in a known time can be used to calculate an in situ flux from the porewaters to the resin. This flux to the resin can be interpreted to provide porewater concentrations or in situ fluxes of metal from solid sediments to porewaters. Concentrations of Zn and Cd in the porewaters were well buffered by rapid (< min) equilibria with the solid phase, allowing them to be measured by DGT. Particulate Mn was so tightly bound that it was not released to the porewaters within a timescale of hours, supply to the DGT device being solely by diffusion. Nickel, Cu, and Fe represented intermediate cases where there was partial resupply from solid phase to porewaters. In these cases the results from DGT provided a direct measurement of the mean in situ flux (mol cm−2 s−1) from solid to solution phase during 24 h deployment: Nickel (0.5–1 × 10−15), Cu(0.5–2.5 × 10−16), Fe (1.5–2.5 × 10−8). The generally good in situ availability suggests that porewater concentrations are controlled by adsorption/desorption processes rather than solubility or coprecipitation. These first measurements of trace metals at mm resolution showed tightly defined (< 1.5 mm) maxima at the sediment water interface. Their location, 1.5–3.0 mm above the broader Fe and Mn maxima, supports previous evidence which indicated they are due to release of metals from rapidly decomposing organic material. Increased spatial resolution will be required to resolve fully the surface maxima to define the zone of metal release, the concentration gradients to overlying water, and underlying sediments and remobilization fluxes.

Dynamic harmonic regression.

This paper describes in detail a flexible approach to nonstationary time series analysis based on a Dynamic Harmonic Regression (DHR) model of the Unobserved Components (UC) type, formulated within a stochastic state space setting. The model is particularly useful for adaptive seasonal adjustment, signal extraction and interpolation over gaps, as well as forecasting or backcasting. The Kalman Filter and Fixed Interval Smoothing algorithms are exploited for estimating the various components, with the Noise Variance Ratio and other hyperparameters in the stochastic state space model estimated by a novel optimization method in the frequency domain. Unlike other approaches of this general type, which normally exploit Maximum Likelihood methods, this optimization procedure is based on a cost function defined in terms of the difference between the logarithmic pseudo-spectrum of the DHR model and the logarithmic autoregressive spectrum of the time series. The cost function not only seems to yield improved convergence characteristics when compared with the alternative ML cost function, but it also has much reduced numerical requirements.

Kinetics of metal exchange between solids and solutions in sediments and soils interpreted from DGT measured fluxes

Our understanding of geochemical processes in sediments and soils has been limited by a lack of simple procedures to measure the kinetics of transfer from solid phase to solution. Diffusive Gradients in Thin-films (DGT) is an in situ technique which can be used to measure porewater concentrations and remobilisation fluxes of trace-metals, in sediments and soils. The dynamics of the sediment/DGT system were investigated using two dimensional modelling to ensure the correct interpretation of DGT measured fluxes, investigate the kinetics of the resupply from metal sorbed to particles, and estimate the magnitude of the resupply from particles to porewater in volumetric terms. When porewater concentrations adjacent to the DGT device are maintained by fast resupply from a large reservoir of metal sorbed to the solid phase (the sustained case), DGT measurements can be interpreted directly as porewater concentrations. When there is significant resupply from the solid phase, DGT can be used to measure kinetic parameters. If porewater concentrations are measured independently by an alternative technique, DGT measurements can be expressed in terms of a ratio R of DGT estimated to actual porewater concentration (0 < R < 1). Our model predicts a relationship between R, the kinetics of the resupply process, and the available reservoir of sorbed metal (expressed as a Kd value). If, as found previously for Cd and Zn in sediments, R ≥ 0.95, the response time (Tc) of the (de)sorption process must be ≤0.8 s and Kd (the distribution coefficient between solid and dissolved metal) must be ≥1.1 × 105 cm3 g−1. For any measured value of R, Tc can be estimated either precisely or within limits, depending on what is known about Kd. Published DGT measurements for Cu and Fe lead us to estimate response times for the sorption process of 30 mins and 19 mins. If Kd is known precisely, the apparent 1st order rate constants for the sorption process can be determined. Multiple DGT deployments with varying diffusion layer thicknesses can be used to estimate porewater concentrations. The DGT device depletes the reservoir of available metal sorbed to the solid phase. This depletion decreases with distance from the device. A simple relationship was developed to estimate, from the DGT measured flux, the mass of metal released from unit volume of particles.

DIFS—a modelling and simulation tool for DGT induced trace metal remobilisation in sediments and soils

The technique of Diffusive Gradients in Thin-films (DGT) can measure in situ fluxes of trace metals in sediments. Interpretation of these measurements requires a numerical model of trace metal reaction and transport in sediments. The DIFS (DGT Induced Fluxes in Sediments) model has permitted quantitative interpretation of DGT measurements in terms of fundamental kinetic and equilibrium resupply parameters. DIFS is here further refined and developed into a software tool which both simulates temporal and spatial changes in concentrations of trace metals in solid and solution phases in sediments during in situ DGT deployments, and estimates resupply parameters from experimental data. The basis of the DIFS model is a pair of linked parabolic PDEs describing dissolved and sorbed trace metal concentrations in the sediment and DGT device. These are solved by the Method of Lines using standard ODE solvers. The solutions are processed to obtain the DGT response. The use of the software, in particular the format of the text file containing input parameters, is described. Illustrative examples of the type of behaviour predicted for DGT by DIFS are provided.

Modelling and PIP control of a glasshouse micro-climate

The paper discusses the modelling and control of the climate in a horticultural glasshouse system. A linear, reduced order, control model is obtained using identification and estimation techniques applied to a multivariable, nonlinear simulation model of the glasshouse microclimate. This control model is then used as the basis for the design of Proportional-Integral-Plus (PIP) control systems which regulate the levels of the major climate variables in the glasshouse. Finally, full multivariable extensions of this glasshouse control system design methodology are discussed and evaluated.

An unobserved component model for multi-rate forecasting of telephone call demand : the design of a forecasting support system.

An Unobserved Components (UC) Model based on an enhanced version of the Dynamic Harmonic Regression model, including new multi-rate and modulated cycle procedures, is used to develop a customised package for forecasting and signal extraction applied to hourly telephone call numbers made to Barclaycard plc. service centres, with a forecasting horizon of up to several weeks in advance. The paper outlines both the methodological and algorithmic aspects of the modelling, forecasting and signal extraction procedures, including the design and implementation of forecasting support software with a specially designed Graphical User Interface within the Matlab® computing environment. The forecasting performance is evaluated comprehensively in comparison with the well-known seasonal ARIMA approach.

2D DGT induced fluxes in sediments and soils (2D DIFS).

Diffusive gradients in thin films (DGT) is an emerging, dynamic, measuring technique that can provide diverse information on the concentrations and behaviour of solutes, including chemical speciation and partitioning between solid phase and solution in waters, sediments and soils. The DGT device, which accumulates solute in a binding layer after transport through a well-defined diffusion layer, is simple to construct and use. However, complete interpretation of the dependence of mass accumulation with time requires a numerical model of the transport and reactions occurring within the device and its deployment medium. We have developed a software tool that models the temporal dependence of DGT induced fluxes from soils or sediments by considering diffusion of solutes in two dimensions (2D) and incorporating first order exchange of solute between solid phase and solution. Microniches of elevated concentrations, that emulate zones of high microbial activity, can be created in the soil or sediment. The solver uses an advanced 2D FEM method and a flexible and user-friendly Graphical User Interface, which incorporates essential model calibration tools, is provided. This solution in 2D is shown to substantially increase the accuracy of the simulation, compared to that achieved with the established DIFS software that provides only a 1D solution, and yet it still has short calculation times on modern PCs. The 2D model is shown to provide a good approximation to the full 3D solution, obtained using FEMLAB, when the supply from the solid phase is larger than supply by diffusion. Example simulations are provided for the three major solute supply situations, namely diffusion only, very rapid and sustained supply from the solid phase and two intermediate cases of partial resupply.

Proportional-integral-plus (PIP) design for delta (delta) operator systems Part 2. MIMO systems

The proportional-integral-plus (PIP) controller for single-input, single-output, linear systems described by delta (delta) operator models, as presented in a companion paper, is extended to linear, multi-input, multi-output systems. The resulting multivariable PIP control law exploits the full power of state variable feedback control within a non-minimum state-space setting. In this manner, it allows not only for closed-loop pole assignment or linear quadratic optimal control, but also for the simultaneous achievement of multiple objectives, such as the combination of rapid response, smooth input activation and full, or partial, dynamic decoupling. The effectiveness of the design procedure is illustrated by both simulation and practical examples.

Characterizing solute transport in undisturbed soil cores using electrical and X-ray tomographic methods

Solute transport in undisturbed soil is a complex process and detailed information on the transport characteristics is needed to provide fundamental understanding of the processes involved. X-ray computer tomography (CT) and electrical resistivity tomography (ERT) have been used to gain information on the transport characteristics. Both methods are non-intrusive and do not disturb the soil, in contrast to other methods. CT provides high resolution information on bulk density and macropores, while ERT provides a three-dimensional image of the internal resistivity structure. By adding a suitable solute under steady-state flow, the internal resistivity changes can be interpreted as a change in resident concentrations. In our experiment two cores from different field sites were investigated. The ERT measurements revealed two transport modes (one fast and one slow) in one of the cores and only one mode in the other. This was consistent with the results of transfer function modelling on the independently measured breakthrough curves (BTCs). The fast transport mode is perhaps a result of many connected macropores, detected by CT, but this could not be verified with the ERT measurements because of the coarser resolution. However, with ERT in both cases we were able to explain the observed BTC qualitatively.

Estimation of Pore Water Concentrations from DGT Profiles: A Modelling Approach

The technique of Diffusional Gradients in Thin-films (DGT) can be used in situ to obtain high resolution profiles of trace-metals in sediment pore waters. Substances sampled by DGT continuously diffuse through a ‘diffusion layer’ comprising a hydrogel prior to being immobilized by binding to a resin layer. DGT therefore measures a time averaged flux from the pore water to the resin. Interpretation of this flux as pore water concentration is problematic for two reasons. Firstly, the pore water concentration adjacent to the sampler may become depleted by the DGT induced flux. Secondly, if there are steep vertical chemical gradients in the pore waters, they may relax by diffusion along the gradient within the gel layer. The extent of relaxation depends on the diffusion coefficient, gradient steepness, and diffusion layer thickness. Two dimensional (2D) numerical models of DGT deployments in horizontally uniform sediments were used to investigate to what extent DGT measured profiles accurately reproduced (a) the shape of pore water concentration profiles, and (b) the magnitude of pore water concentrations. A method is developed which translates high resolution DGT measured flux profiles into reliable estimates of pore water concentrations. Linear relationships are given which estimate the minimum DGT measured peak width (as a function of diffusion layer thickness) that ensures accurate reproduction of the shape and the magnitude of peaks in pore water concentrations. Peaks in DGT profiles obtained from assemblies with diffusion layer thicknesses of 0.3 mm (0.5 mm) should be at least 1.2 mm (1.8 mm) wide for their shape to reflect accurately their true shape in the pore water, and at least 1.7 mm (2.7 mm) wide to ensure the peak concentration is accurately estimated.