Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

Fluid infiltration during contact metamorphism of interbedded marble and calc-silicate hornfels, Twin Lakes area, central Sierra Nevada, California

Abstract In the Twin Lakes area, central Sierra Nevada, California, most contact metamorphosed marbles contain calcite + dolomite + forsterite ± diopside ± phlogopite ± tremolite, and most calc-silicate hornfelses contain calcite + diopside + wollastonite + quartz ± anorthite ± K-feldspar ± grossular ± titanite. Mineral-fluid equilibria involving calcite + dolomite + tremolite + diopside + forsterite in two marble samples and wollastonite + anorthite + quartz + grossular in three hornfels samples record P± 3 kbar and T± 630° C. Various isobaric univariant assemblages record CO₂-H₂O fluid compositions of χCO₂= 0.61–0.74 in the marbles and χCO₂= 0.11 in the hornfelses. Assuming a siliceous dolomitic limestone protolith consisting of dolomite + quartz ° Calcite ± K-feldspar ± muscovite ± rutile, all plausible prograde reaction pathways were deduced for marble and hornfels on isobaric T-XCO₂ diagrams in the model system K₂O-CaO-MgO-Al₂O₃-SiO₂-H₂O-CO₂. Progress of the prograde reactions was estimated from measured modes and mass-balance calculations. Time-integrated fluxes of reactive fluid which infiltrated samples were computed for a temperature gradient of 150 °C/km along the fluid flow path, calculated fluid compositions, and estimated reaction progress using the mass-continuity equation. Marbles and hornfelses record values in the range 0.1–3.6 × 10⁴ cm³/cm² and 4.8–12.9 × 10⁴ cm³/cm², respectively. For an estimated duration of metamorphism of 10⁵ years, average in situ metamorphic rock permeabilities, calculated from Darcy's Law, are 0.1–8 × 10^?6 D in the marbles and 10–27 × 10^?6 D in the hornfelses. Reactive metamorphic fluids flowed up-temperature, and were preferentially channellized in hornfelses relative to the marbles. These results appear to give a general characterization of hydrothermal activity during contact metamorphism of small pendants and screens (dimensions ± 1 km or less) associated with emplacement of the Sierra Nevada batholith.     

Hysteresis‐based analysis of overland metal transport

Introducing a concept of equivalent mass depth of flow, this study describes the phenomenon of non‐point source pollutant (metal) transport for pavement (or overland) flow in analogy with wave propagation in wide open channels. Hysteretic and normal mass rating curves are developed for runoff rate and mass of 12 dissolved and particulate‐bound metal elements (pollutants) using the rainfall‐runoff and water quality data of the 15 × 20 m² instrumented pavement in Cincinnati, USA. Normal mass rating curves developed for easy computation of pollutant load are found to be of a form similar to Manning's, which is valid for open channel flows. Based on the hysteresis analysis, wave types for dissolution and mixing of particulate‐bound metals are identified. The analysis finds that the second‐order partial‐differential equation normally used for metal transport does not have the efficacy to describe fully the strong non‐linear phenomena such as is described for various metal elements by dynamic waves. In addition, the proportionality concept of the popular SCS‐CN concept is extended for determining the potential maximum metal mass M_p of all the 12 elements transported by a rain storm and related to the antecedent dry period (ADP). For the primary metal zinc element, M_p is found to increase with the ADP and vice versa. Copyright © 2003 John Wiley & Sons, Ltd.     

Benthic photosynthesis in submerged Wadden Sea intertidal flats

In this study we compare benthic photosynthesis during inundation in coarse sand, fine sand, and mixed sediment (sand/mud) intertidal flats in the German Wadden Sea. In situ determinations of oxygen-, DIC- and nutrient fluxes in stirred benthic chamber incubations were combined with measurements of sedimentary chlorophyll, incident light intensity at the sediment surface and scalar irradiance within the sediment. During submergence, microphytobenthos was light limited at all study sites as indicated by rapid response of gross photosynthesis to increasing incident light at the sea floor. However, depth integrated scalar irradiance was 2 to 3 times higher in the sands than in the mud. Consequently, gross photosynthesis in the net autotrophic fine sand and coarse sand flats during inundation was on average 4 and 11 times higher than in the net heterotrophic mud flat, despite higher total chlorophyll concentration in mud. Benthic photosynthesis may be enhanced in intertidal sands during inundation due to: (1) higher light availability to the microphytobenthos in the sands compared to muds, (2) more efficient transport of photosynthesis-limiting solutes to the microalgae with pore water flows in the permeable sands, and (3) more active metabolic state and different life strategies of microphytobenthos inhabiting sands.     

The dimensions of sand ripples in full-scale oscillatory flows

New large-scale experiments have been carried out in two oscillatory flow tunnels to study ripple regime sand suspension and net sand transport processes in full-scale oscillatory flows. The paper focuses on ripple dimensions and the new data are combined with existing data to make a large dataset of ripple heights and lengths for flows with field-scale amplitudes and periods. A feature of the new experiments is a focus on the effect of flow irregularity. The combined dataset is analysed to examine the range of hydraulic conditions under which oscillatory flow ripples occur, to examine the effects of flow irregularity and ripple three-dimensionality on ripple dimensions and to test and improve existing methods for predicting ripple dimensions.The following are the main conclusions. (1) The highest velocities in a flow time-series play an important role in determining the type of bedform occurring in oscillatory flow. Bedform regime is well characterised by mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth peak velocities in the case of irregular flow. (2) For field-scale flows, sand size is the primary factor determining whether equilibrium ripples will be 2D or 3D. 2D ripples occur when the sand D₅₀ ≥ 0.30 mm and 3D ripples occur when D₅₀ ≤ 0.22 mm (except when the flow orbital diameter is low). (3) Ripple type (2D or 3D) is the same for regular and irregular flows and ripple dimensions produced by equivalent regular and irregular flows follow a similar functional dependence on mobility number, with mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth velocities in the case of irregular flow. For much of the ripple regime, ripple dimensions have weak dependency on mobility number and ripple dimensions are similar for regular and irregular flows with the same flow orbital amplitude. However, differences in ripples produced by equivalent regular and irregular flows become significant at the high mobility end of the ripple regime. (4) Ripple dimensions predicted using the Wiberg and Harris formulae are in poor agreement with measured ripple dimensions from the large-scale experiments. Predictions based on the Mogridge et al. and the Nielsen formulae show better overall agreement with the data but also show systematic differences in cases of 3D ripples and ripples generated by irregular flows. (5) Based on the combined large-scale data, modifications to the Nielsen ripple dimension equations are proposed for the heights and lengths of 2D ripples. The same equations apply to regular and irregular flows, but with mobility number appropriately defined. 3D ripples are generally smaller than 2D ripples and estimates of 3D ripple height and length may be obtained by applying multipliers of 0.55 and 0.73 respectively to the 2D formulae. The proposed modified Nielsen formulae provide an improved fit to the large-scale data, accounting for flow irregularity and ripple three-dimensionality.     

Cross-shelf distribution of copepods and the role of event-scale winds in a northern California upwelling zone

Cross-shelf distribution and abundance of copepod nauplii and copepodids were measured during three summer upwelling seasons (2000–2002) in a coastal upwelling zone off northern California. These 3 years varied considerably in the intensity of winds, abundance of chlorophyll, and water temperature. The cruises in 2000 were characterized by relaxation conditions, with generally high levels of chlorophyll and high water temperature. The cruises in 2001 and 2002 were dominated by strong and persistent upwelling events, leading to lower chlorophyll and water temperatures. The copepod assemblage was dominated by Oithona spp., Acartia spp. and Pseudocalanus spp., with Metridia pacifica (lucens), Microsetella rosea, Oncaea spp. and Tortanus discaudatus also common during all 3 years. The cross-shelf distribution of copepods was generally shifted offshore during upwelling and onshore during relaxation events, although some variability between species occurred. Abundance of all life stages generally exhibited a negative correlation with cross-shelf transport averaged over at least 1–4 days and lagged by 0–3 days, indicating lower abundances during and immediately after active upwelling. However, copepod nauplii seemed to respond positively to wind events lasting 1–5 days followed by a period of relaxation lasting 6 or 7 days. These rapid rates of change in abundance are probably too great to be due to in situ growth and reproduction alone; physical processes must also play a role. These results suggest a highly dynamic relationship between copepods and upwelling events off northern California, with species-specific responses to upwelling to be expected.     

Freshening of the Intermediate Waters in the Northern South China Sea over the PastSix Decades

The properties of salinity in the South China Sea (SCS), a significant marginal sea connecting the Pacific andIndian Oceans, are greatly influenced by the transport of fresh water flux between the two oceans. However, the long-termchanges in the intermediate water in the SCS have not been thoroughly studied due to limited data, particularly in relationto its thermodynamic variations. This study utilized reanalysis data products to identify a 60-year trend of freshening in theintermediate waters of the northern South China Sea (NSCS), accompanied by an expansion of low-salinity water. Thestudy also constructed salinity budget terms, including advection and entrainment processes, and conducted an analysis ofthe salinity budget to understand the impacts of external and internal dynamic processes on the freshening trend of theintermediate water in the NSCS. The analysis revealed that the freshening in the northwest Pacific Ocean and theintensification of intrusion through the Luzon Strait at intermediate levels are the primary drivers of the salinity changes inthe NSCS. Additionally, a weakened trend in the intensity of vertical entrainment also contributes to the freshening in theNSCS. This study offers new insights into the understanding of regional deep sea changes in response to variations in boththermodynamics and oceanic dynamic processes.     

Semi-analytical solutions of a contaminant transport equation with nonlinear sorption in 1D

A new method to determine semi-analytical solutions of one-dimensional contaminant transport problem with nonlinear sorption is described. This method is based on operator splitting approach where the convective transport is solved exactly and the diffusive transport by finite volume method. The exact solutions for all sorption isotherms of Freundlich and Langmuir type are presented for the case of piecewise constant initial profile and zero diffusion. Very precise numerical results for transport with small diffusion can be obtained even for larger time steps (e.g., when the Courant-Friedrichs-Lewy (CFL) condition failed).     

Momentum transport of wave zero during March: A possible predictor for the Indian summer monsoon

Analysis of monthly momentum transport of zonal waves at 850 hPa for the period 1979 to 1993, between ‡S and ‡N for January to April, using zonal (u) and meridional (v) components of wind taken from the ECMWF reanalysis field, shows a positive correlation (.1% level of significance) between the Indian summer monsoon rainfall (June through September) and the momentum transport of wave zero TM(0) over latitudinal belt between 25‡S and 5‡N (LB) during March. Northward (Southward) TM(0) observed in March over LB subsequently leads to a good (drought) monsoon season over India which is found to be true even when the year is marked with the El-Nino event. Similarly a strong westerly zone in the Indian Ocean during March, indicates a good monsoon season for the country, even if the year is marked with El-Nino. The study thus suggests two predictors, TM(0) over LB and the strength of westerly zone in the Indian Ocean during March.     

Screening model for volatile pollutants in dual porosity soils

This paper develops mass fraction models for transport and fate of agricultural pollutants in structured two-region soils. Mass fraction index models, based on a semi-infinite domain solution, are derived that describe leaching at depth, vapor losses through soil surface, absorption, and degradation in the dynamic- and stagnant-water soil regions. The models predict that leaching is the result of the combined effect of the upward vapor-phase transport relative to downward advection, residence time relative to half-life, dispersion, and lateral diffusive mass transfer. Simulations show that leached fraction of volatile compounds does not always decrease monotonically with increased residence time relative to the pollutant half-life, as a result of complex interactions among the different physical and biochemical processes. The results show that leaching, volatilization, and degradation losses can be affected significantly by lateral diffusive mass transfer into immobile-water regions and advection relative to dispersion (i.e. Peclet number) in the mobile-water regions. It is shown that solute diffusion into the immobile phase and subsequent biochemical decay reduces leaching and vapor losses through soil surface. Potential use of the modified leaching index for the screening of selected pesticides is illustrated for different soil textures and infiltration rates. The analysis may be useful to the management of pesticides and the design of landfills.