Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Tidal effects on sea water intrusion in unconfined aquifers

A variable-density groundwater model is used to analyse the effects of tidal fluctuations on sea-water intrusion in an unconfined aquifer. It is shown that the tidal activity forces the sea-water to intrude further inland and it also creates a thicker interface than would occur without tidal effects. Moreover, the configuration of the interface is radically changed when the tidal fluctuations are included. This is because of the dramatic changes in the flow pattern and velocity of the groundwater near the shoreline. For aquifer depths much larger than tidal amplitudes, the tidal fluctuation does not have much effect on how far the sea-water intrudes into the aquifer; nevertheless, a significant change in the configuration of concentration contours because of the effect of tidal fluctuations is observed. This change is more noticeable at the top of the aquifer, near the water table, than at the bottom of the aquifer, and is caused by the infiltration of salt water into the top of the aquifer at higher tidal levels. A flatter beach slope, therefore, intensifies this phenomenon. The interface configurations do not change noticeably over the course of a tidal cycle. Neglecting tidal fluctuation effects results in an inaccurate evaluation of the water table elevation at the land end of the aquifer, although no distinguishable difference is seen between the water tables near the shoreline. Where the landward boundary condition is a constant head, the effects of tidal fluctuations on sea-water intrusion are more pronounced than for cases where the landward boundary condition is a specified flux. Also it is shown that the effects of tidal fluctuations are more significant for a sloping beach than for a vertical shoreline and the salt water intrudes further inland for the sloping case. (C) 1999 Elsevier Science B.V. All rights reserved.

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated-unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face. (C) 1999 Elsevier Science B.V. All rights reserved.

Solute transport by surface runoff from low-angle slopes: theory and application

The removal of chemicals in solution by overland how from agricultural land has the potential to be a significant source of chemical loss where chemicals are applied to the soil surface, as in zero tillage and surface-mulched farming systems. Currently, we lack detailed understanding of the transfer mechanism between the soil solution and overland flow, particularly under field conditions. A model of solute transfer from soil solution to overland flow was developed. The model is based on the hypothesis that a solute is initially distributed uniformly throughout the soil pore space in a thin layer at the soil surface. A fundamental assumption of the model is that at the time runoff commences, any solute at the soil surface that could be transported into the soil with the infiltrating water will already have been convected away from the area of potential exchange. Solute remaining at the soil surface is therefore not subject to further infiltration and may be approximated as a layer of tracer on a plane impermeable surface. The model fitted experimental data very well in all but one trial. The model in its present form focuses on the exchange of solute between the soil solution and surface water after the commencement of runoff. Future model development requires the relationship between the mass transfer parameters of the model and the time to runoff: to be defined. This would enable the model to be used for extrapolation beyond the specific experimental results of this study. The close agreement between experimental results and model simulations shows that the simple transfer equation proposed in this study has promise for estimating solute loss to surface runoff. Copyright (C) 2000 John Wiley & Sons, Ltd.

Experimental examination of solute transport by surface runoff from low-angle slopes

The removal of chemicals in solution, by overland flow from agricultural land has the potential to be a significant source of chemical loss from zero-till and surface mulched farming systems. The objective of this study was to determine the magnitude of solute loss by surface runoff from agricultural systems. Previous experiments have enhanced the understanding of the exchange process, but the initial soil conditions together with the tracer application method in these experiments have meant that in some cases the results have limited applicability to field situations. In this study, two different sets of experiments were carried out to determine the magnitude of solute loss by surface runoff. These experiments entailed the surface application of bromide to (1) field scale plots 18 m long by 2 m wide and (2) repacked soil cores 236 mm in diameter; followed by the application of simulated rainfall in both cases. The most substantial finding of the field experiments was that the quantities of solute in surface runoff varied greatly with soil type and structure (0.07-14.9% of the applied bromide). Also, on some soils, large quantities of tracer were measured in the surface runoff even after several hours of infiltration. The experiments on soil cores showed that soil structure plays an important role in the quantity of chemical that may be transported in the surface runoff. These field results showed that, in certain systems, solute movement by overland flow is an important transport mechanism, which should be considered when budgeting for chemical loss. (C) 2000 Elsevier Science B.V. All rights reserved.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.

Embryonic development of the nervous system of the temnocephalid flatworm Craspedella pedum

The nervous system of temnocephalid flatworms consists of the brain and three pairs of longitudinal connectives extending into the trunk and tail. The connectives are crosslinked by an invariant number of regularly spaced commissures. Branches of the connectives innervate the tentacles of the head and the sucker organ in the tail. A set of nerve rings encircling the pharynx and connected to the brain and connectives constitute the pharyngeal nervous system. The nervous system is formed during early embryogenesis when the embryo represents a multilayered mesenchymal mass of cells. Gastrulation and the formation of separate epithelial germ layers that characterize most other animal groups are absent. The brain arises as a bilaterally symmetric condensation of postmitotic cells in the deep layers of the anterior region of the embryonic mesenchyme. The pattern of axon outgrowth, visualized by labeling with anti-acetylated tubulin (acTub) antibody, shows marked differences from the pattern observed in other flatworm taxa. in regard to the number of neurons that express the acTub epitope. Acetylated tubulin is only expressed in neurons that form long axon tracts. In other flatworm species, such as the typhloplanoid Mesostoma and the polyclad Imogine, which were investigated by us with the acTub antibody (Hartenstein and Ehlers [2000] Dev. Genes Evol. 210:399-415; Younossi-Hartenstein and Hartenstein [2000] Dev. Genes Evol. 210:383-398), only a small number of pioneer neurons become acTub positive during the embryonic period. By contrast, in temnocephalids, most, if not all, neurons express acTub and form long, large-diameter axons. Initially, the brain commissure, pharyngeal nerve ring, and the connectives are laid down. Commissural tracts and tentacle nerves branching off the connectives appear later. We speculate that the precocious differentiation of the nervous system may be related to the fact that temnocephalids move by muscle action, and possess a massive and complex muscular system when they hatch. In addition, they have muscular specializations such as the anterior tentacles and the posterior sucker that are used as soon as they hatch. By contrast, juveniles of Mesostoma and larvae of polyclads move predominantly by ciliary action that may not require a complex neural circuitry for coordination. (C) 2001 Wiley-Liss, Inc.

Tidal effects on groundwater dynamics in unconfined aquifers

The variation of seawater level resulting from tidal fluctuations is usually neglected in regional groundwater flow studies. Although the tidal oscillation is damped near the shoreline, there is a quasi-steady-slate rise in the mean water-table position, which may have an influence on regional groundwater flow. In this paper the effects of tidal fluctuations on groundwater hydraulics are investigated using a variably saturated numerical model that includes the effects of a realistic mild beach slope, seepage face and the unsaturated zone. In particular the impact of these factors on the velocity field in the aquifer is assessed. Simulations show that the tidal fluctuation has substantial consequences for the local velocity field in the vicinity of the exit face, which affects the nearshore migration of contaminant in coastal aquifers. An overheight in the water table as a result of the tidal fluctuation is observed anti this has a significant effect on groundwater discharge to the sea when the landward boundary condition is a constant water level. The effect of beach slope is very significant and simplifying the problem by considering a vertical beach face causes serious errors in predicting the water-table position and the groundwater flux. For media with a high effective capillary fringe, the moisture retained above the water table is important in determining the effects of the tidal fluctuations. Copyright (C) 2001 John Wiley & Sons, Ltd.

Influence of seaward boundary condition on contaminant transport in unconfined coastal aquifers

Contaminant transport in coastal aquifers is complicated partly due to the conditions at the seaward boundary including seawater intrusion and tidal variations of sea level. Their inclusion in modelling this system will be computationally expensive. Therefore, it will be instructive to investigate the consequence of simplifying the seaward boundary condition by neglecting the seawater density and tidal variations in numerical predictions of contaminant transport in this zone. This paper presents a comparison of numerical predictions for a simplified seaward boundary condition with experimental results for a corresponding realistic one including a saltwater interface and tidal variations. Different densities for contaminants are considered. The comparison suggests that the neglect of the seawater intrusion and tidal variations does not affect noticeably the overall migration rate of the plume before it reaches the saltwater interface. However, numerical prediction shows that a more dense contaminant travels further seaward and part of the solute mass exits under the sea if the seawater density is not included. This is not consistent with the experimental result, which shows that the contaminant travels upwards to the shoreline along the saltwater interface. Neglect of seawater density, therefore, will result in an underestimation of the exit rate of solute mass around the coastline and fictitious migration paths under the seabed. For a less dense contaminant, neglect of seawater density has little effect on numerical prediction of migration paths. (C) 2001 Elsevier Science B.V. All rights reserved.

ENCORE: The effect of nutrient enrichment on coral reefs. Synthesis of results and conclusions

Coral reef degradation resulting from nutrient enrichment of coastal waters is of increasing global concern. Although effects of nutrients on coral reef organisms have been demonstrated in the laboratory, there is little direct evidence of nutrient effects on coral reef biota in situ. The ENCORE experiment investigated responses of coral reef organisms and processes to controlled additions of dissolved inorganic nitrogen (N) and/or phosphorus (P) on an offshore reef(One Tree Island) at the southern end of the Great Barrier Reef, Australia. A multi-disciplinary team assessed a variety of factors focusing on nutrient dynamics and biotic responses. A controlled and replicated experiment was conducted over two years using twelve small patch reefs ponded at low tide by a coral rim. Treatments included three control reefs (no nutrient addition) and three + N reefs (NH4Cl added), three + P reefs (KH2PO4 added), and three + N + P reefs. Nutrients were added as pulses at each low tide (ca twice per day) by remotely operated units. There were two phases of nutrient additions. During the initial, low-loading phase of the experiment nutrient pulses (mean dose = 11.5 muM NH4+; 2.3 muM PO4-3) rapidly declined, reaching near-background levels (mean = 0.9 muM NH4+; 0.5 muM PO4-3) within 2-3 h. A variety of biotic processes, assessed over a year during this initial nutrient loading phase, were not significantly affected, with the exception of coral reproduction, which was affected in all nutrient treatments. In Acropora longicyathus and A. aspera, fewer successfully developed embryos were formed, and in A. longicyathus fertilization rates and lipid levels decreased. In the second, high-loading, phase of ENCORE an increased nutrient dosage (mean dose = 36.2 muM NH4+; 5.1 muM PO4-3 declining to means of 11.3 muM NH4+ and 2.4 muM PO4-3 at the end of low tide) was used for a further year, and a variety of significant biotic responses occurred. Encrusting algae incorporated virtually none of the added nutrients. Organisms containing endosymbiotic zooxanthellae (corals and giant clams) assimilated dissolved nutrients rapidly and were responsive to added nutrients. Coral mortality, not detected during the initial low-loading phase, became evident with increased nutrient dosage, particularly in Pocillopora damicornis. Nitrogen additions stunted coral growth, and phosphorus additions had a variable effect. Coral calcification rate and linear extension increased in the presence of added phosphorus but skeletal density was reduced, making corals more susceptible to breakage. Settlement of all coral larvae was reduced in nitrogen treatments, yet settlement of larvae from brooded species was enhanced in phosphorus treatments. Recruitment of stomatopods, benthic crustaceans living in coral rubble, was reduced in nitrogen and nitrogen plus phosphorus treatments. Grazing rates and reproductive effort of various fish species were not affected by the nutrient treatments. Microbial nitrogen transformations in sediments,were responsive to nutrient loading with nitrogen fixation significantly increased in phosphorus treatments and denitrification increased in all treatments to which nitrogen had been added. Rates of bioerosion and grazing showed no significant effects of added nutrients, ENCORE has shown that reef organisms and processes investigated ill situ were impacted by elevated nutrients. Impacts mere dependent on dose level, whether nitrogen and/or phosphorus mere elevated and were often species-specific. The impacts were generally sub-lethal and subtle and the treated reefs at the end of the experiment mere visually similar to control reefs. Rapid nutrient uptake indicates that nutrient concentrations alone are not adequate to assess nutrient condition of reefs. Sensitive and quantifiable biological indicators need to be developed for coral reef ecosystems. The potential bioindicators identified in ENCORE should be tested in future research on coral reef/nutrient interactions. Synergistic and cumulative effects of elevated nutrients and other environmental parameters, comparative studies of intact vs. disturbed reefs, offshore vs, inshore reefs, or the ability of a nutrient-stressed reef to respond to natural disturbances require elucidation. An expanded understanding of coral reef responses to anthropogenic impacts is necessary, particularly regarding the subtle, sub-lethal effects detected in the ENCORE studies. (C) 2001 Published by Elsevier Science Ltd.