A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence the spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribution, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolation experiments. The model does not require knowledge of the soil structure. A homogeneous or uniform distribution of a solute and/or soil-water is indicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mean. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 and heterogeneity is indicated by HI > 1. A large value for this index may indicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experiments and is, therefore, easily calculated. The index may also be used to describe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several different leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserved.

Assessment of intracellular water by whole body bioelectrical impedance and total body potassium in HIV-positive patients

.:Abstract-Objective: Bioelectrical impedance analysis (BIA) is widely used as bedside assessment of body composition. Body cell mass (BCM) and intracellular water (ICW) are clinically important body compartments. Estimates of ICW obtained from BIA by different calculation approaches were compared to a reference method in male HIV-infected patients. Patients: Representative subsample of clinically stable HIV-infected outpatients, consisting of 42 men with a body mass index of 22.4 +/- 3.8 kg/m(2) (range, 13-31 kg/m(2)). Methods: Total body potassium was assessed in a whole body counter, and compared to 50 kHz mono-frequency BIA and multifrequency bioelectrical impedance spectroscopy. Six different prediction equations for ICW from BIA data were applied. Methods were compared by the Bland-Altman method. Results: BIA-derived ICW estimates explained 58% to 73% of the observed variance in ICW (TBK), but limits of confidence were wide (-16.6 to +18.2% for the best method). BIA overestimated low ICW (TBK) and underestimated high ICW (TBK) when normalized for weight or height. Mono- and multifrequency BIA were not different in precision but population-specific equations tended to narrower confidence limits. Conclusion: BIA is an unreliable method to estimate ICW in this population, in contrast to the better established estimation of total body water and extracellular water. Potassium depletion in severe malnutrition may contribute to this finding but a major part of the residual between methods remains unexplained. (C) 2000 Harcourt Publishers Ltd.

Modelling basin level allocation of water in the Murray-Darling Basin in a world of uncertainty, Murray-Darling Program Working Papers WPM05-1, Risk and Sustainable Management Group, 8 February 2005

Abstract: The Murray-Darling Basin comprises over 1 million km2; it lies within four states and one territory; and over 12, 800 GL of irrigation water is used to produce over 40% of the nation's gross value of agricultural production. This production is used by a diverse collection of some-times mutually exclusive commodities (e.g. pasture; stone fruit; grapes; cotton and field crops). The supply of water for irrigation is subject to climatic and policy uncertainty. Variable inflows mean that water property rights do not provide a guaranteed supply. With increasing public scrutiny and environmental issues facing irrigators, greater pressure is being placed on this finite resource. The uncertainty of the water supply, water quality (salinity), combined with where water is utilised, while attempting to maximising return for investment makes for an interesting research field. The utilisation and comparison of a GAMS and Excel based modelling approach has been used to ask: where should we allocate water?; amongst what commodities?; and how does this affect both the quantity of water and the quality of water along the Murray-Darling river system?

Air-water flows down stepped chutes: turbulence and flow structure observations

Interactions between turbulent waters and atmosphere may lead to strong air-water mixing. This experimental study is focused on the flow down a staircase channel characterised by very strong flow aeration and turbulence. Interfacial aeration is characterised by strong air-water mixing extending down to the invert. The size of entrained bubbles and droplets extends over several orders of magnitude, and a significant number of bubble/droplet clusters was observed. Velocity and turbulence intensity measurements suggest high levels of turbulence across the entire air-water flow. The increase in turbulence levels, compared to single-phase flow situations, is proportional to the number of entrained particles. (C) 2002 Elsevier Science Ltd. All rights reserved.

The interaction of water flow and nutrients on aquatic plant growth

A long-term experiment was conducted to compare the effects of flowing and still water on growth, and the relationship between water flow and nutrients, in Aponogeton elongatus, a submerged aquatic macrophyte. A. elongatus plants were grown for 23 weeks with three levels of nutrition (0, 0.5 and 1g Osmocote Plus(R) fertiliser pot(-1)) in aquaria containing stirred or unstirred water. Fertilized plants grew much better than non-fertilized. The highest fertilizer level produced 29% wider leaves and 58% higher total dry weight in stirred water. Stirred water increased leaf area by 40% and tuber size by 81%, but only with the highest level of nutrition. These results suggest that this plant depends on its roots for mineral uptake, rather than from the open water, and the major limitation to growth in still water is the supply of dissolved inorganic carbon. It was the combined effects of nutrient availability and stirring that produced the strongest response in plant growth, morphology and composition. This study provides some explanation for the observations of others that these plants grow best in creeks or river systems with permanently flowing water.

Water table waves in an unconfined aquifer: Experiments and modeling

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.

Ground water model calibration using pilot points and regularization

Use of nonlinear parameter estimation techniques is now commonplace in ground water model calibration. However, there is still ample room for further development of these techniques in order to enable them to extract more information from calibration datasets, to more thoroughly explore the uncertainty associated with model predictions, and to make them easier to implement in various modeling contexts. This paper describes the use of pilot points as a methodology for spatial hydraulic property characterization. When used in conjunction with nonlinear parameter estimation software that incorporates advanced regularization functionality (such as PEST), use of pilot points can add a great deal of flexibility to the calibration process at the same time as it makes this process easier to implement. Pilot points can be used either as a substitute for zones of piecewise parameter uniformity, or in conjunction with such zones. In either case, they allow the disposition of areas of high and low hydraulic property value to be inferred through the calibration process, without the need for the modeler to guess the geometry of such areas prior to estimating the parameters that pertain to them. Pilot points and regularization can also be used as an adjunct to geostatistically based stochastic parameterization methods. Using the techniques described herein, a series of hydraulic property fields can be generated, all of which recognize the stochastic characterization of an area at the same time that they satisfy the constraints imposed on hydraulic property values by the need to ensure that model outputs match field measurements. Model predictions can then be made using all of these fields as a mechanism for exploring predictive uncertainty.

The plasticisation effect of glycerol and water on the gelatinisation of wheat starch

In the extrusion manufacture of starch-based thermoplastics, such as biodegradable packaging materials, glycerol is an effective additive as a plasticiser, that is, to diminish the brittle nature of the product and provide the desired extent of flexibility. However, the addition of glycerol may also affect the gelatinisation behaviour of the starch-water mixture, and hence the required processing conditions for producing a homogeneously gelatinised starch-based material. The effect of glycerol on the gelatinisation of wheat starch was studied using differential scanning calorimetry (DSC). Mixtures of starch, water and glycerol were investigated with a water content ranging from 12 - 40% and a glycerol concentration up to 75%. Dependent on composition, the enthalpy of gelatinisation ranged from 1.7 - 12.6 J/g (on a dry starch basis), while the onset and peak temperatures varied from 54 to 86 degreesC and 60 to 90 degreesC, respectively. As expected, water acted as a plasticiser in that the onset temperature for gelatinisation (TO) decreased with increasing moisture content. Glycerol, however, increased To. It is shown that the T-0 of starch-glycerol-water mixtures may be predicted on the basis of the effective moisture content of the starch fraction of these mixtures resulting from the relative speed of moisture absorption by glycerol and starch, respectively. Moisture sorption kinetics of wheat starch and glycerol in 100% relative humidity were determined and used to predict the preferential water absorption by glycerol in starch-glycerol-water mixtures and hence the resulting T-0 of the system.