Stochastic-convective transport with nonlinear reaction and mixing: application to intermediate-scale experiments in aerobic biodegradation in saturated porous media

Aerobic biodegradation of benzoate by Pseudomonas cepacia sp. in a saturated heterogeneous porous medium was simulated using the stochastic-convective reaction (SCR) approach. A laboratory flow cell was randomly packed with low permeability silt-size inclusions in a high permeability sand matrix. In the SCR upscaling approach, the characteristics of the flow field are determined by the breakthrough of a conservative tracer. Spatial information on the actual location of the heterogeneities is not used. The mass balance equations governing the nonlinear and multicomponent reactive transport are recast in terms of reactive transports in each of a finite number of discrete streamtubes. The streamtube ensemble members represent transport via a steady constant average velocity per streamtube and a conventional Fickian dispersion term, and their contributions to the observed breakthroughs are determined by flux-averaging the streamtube solute concentrations. The resulting simulations were compared to those from a high-resolution deterministic simulation of the reactive transport, and to alternative ensemble representations involving (i) effective Fickian travel time distribution function, (ii) purely convective streamtube transport, and (iii) streamtube ensemble subset simulations. The results of the SCR simulation compare favorably to that of a sophisticated high-resolution deterministic approach.     

DNAPL source depletion: linking architecture and flux response

The relationship between dense non-aqueous phase liquid (DNAPL) mass reduction and contaminant mass flux was investigated experimentally in four model source zones. The flow cell design for the experiments featured a segmented extraction well that allowed for analysis of spatially resolved flux information. This flux information was coupled with image analysis of the NAPL spatial distribution to investigate the relationship between flux and the up-gradient NAPL architecture. Results indicate that in the systems studied, the relationship between DNAPL mass reduction and contaminant mass flux was primarily controlled by the NAPL architecture. A specific definition of NAPL architecture was employed where the source zone is resolved into a collection of streamtubes with spatial variability in NAPL saturation along each streamtube integrated and transformed into an effective NAPL content for each streamtube. The distribution of NAPL contents among the streamtubes (NAPL architecture) controlled dissolution dynamics. Two simplified models, a streamtube model and an effective Damkohler number model, were investigated for their ability to simulate dissolution dynamics.     

Upscaling heterogeneity in aquifer reactivity via exposure-time concept: forward model

Reactive properties of aquifer solid phase materials play an important role in solute fate and transport in the natural subsurface on time scales ranging from years in contaminant remediation to millennia in dynamics of aqueous geochemistry. Quantitative tools for dealing with the impact of natural heterogeneity in solid phase reactivity on solute fate and transport are limited. Here we describe the use of a structural variable to keep track of solute flux exposure to reactive surfaces. With this approach, we develop a non-reactive tracer model that is useful for determining the signature of multi-scale reactive solid heterogeneity in terms of solute flux distributions at the field scale, given realizations of three-dimensional reactive site density fields. First, a governing Eulerian equation for the non-reactive tracer model is determined by an upscaling technique in which it is found that the exposure time of solution to reactive surface areas evolves via both a macroscopic velocity and a macroscopic dispersion in the artificial dimension of exposure time. Second, we focus on the Lagrangian approach in the context of a streamtube ensemble and demonstrate the use of the distribution of solute flux over the exposure time dimension in modeling two-dimensional transport of a solute undergoing simplified linear reversible reactions, in hypothetical conditions following prior laboratory experiments. The distribution of solute flux over exposure time in a given case is a signature of the impact of heterogeneous aquifer reactivity coupled with a particular physical heterogeneity, boundary conditions, and hydraulic gradient. Rigorous application of this approach in a simulation sense is limited here to linear kinetically controlled reactions.     

Multidimensional, multicomponent, subsurface reactive transport in nonuniform velocity fields: code verification using an advective reactive streamtube approach

High performance computing has made possible the development of high resolution, multidimensional, multicomponent reactive transport models that can be used to analyze complex geochemical environments. However, as increasingly complex processes are included in these models, the accuracy of the numerical formulation coupling the nonlinear processes becomes difficult to verify. Analytical solutions are not available for realistically complex problems and benchmark solutions are not generally available for specific problems. We present an advective reactive streamtube (ARS) transport technique that efficiently provides accurate solutions of nonlinear multicomponent reactive transport in nonuniform multidimensional velocity fields. These solutions can be compared with results from Eulerian-based advection-dispersion-reaction models to evaluate the accuracy of the numerical formulation used. The ARS technique includes mixed equilibrium and kinetic complexation and precipitation-dissolution reactions subject to the following assumptions: (1) transport is purely advective (i.e., no explicit diffusion or dispersion), and (2) chemistry is described by a canonical system of reactions that evolves with time and is unaffected by position in space. Results from the ARS technique are compared with results from the massively parallel, multicomponent reactive transport model MCTRACKER on a test problem involving irreversible oxidation of organic carbon and reaction of the oxidation products with two immobile mineral phases, gypsum and calcite, and fifteen aqueous complexes. Truncation error, operator splitting error, and the nonlinear transformation of these errors in the high-resolution reactive transport model are identified for this problem.     

Development of a nonlocal convective mixing scheme with varying upward mixing rates for use in air quality and chemical transport models

BACKGROUND, AIM, AND SCOPE: Asymmetrical convective non-local scheme (CON) with varying upward mixing rates is developed for simulation of vertical turbulent mixing in the convective boundary layer in air quality and chemical transport models. MATERIALS AND METHODS: The upward mixing rate form the surface layer is parameterized using the sensible heat flux and the friction and convective velocities. Upward mixing rates varying with height are scaled with an amount of turbulent kinetic energy in layer, while the downward mixing rates are derived from mass conservation. RESULTS: This scheme provides a less rapid mass transport out of surface layer into other layers than other asymmetrical convective mixing schemes. DISCUSSION: In this paper, we studied the performance of a nonlocal convective mixing scheme with varying upward mixing in the atmospheric boundary layer and its impact on the concentration of pollutants calculated with chemical and air-quality models. This scheme was additionally compared versus a local eddy-diffusivity scheme (KSC). Simulated concentrations of NO(2) and the nitrate wet deposition by the CON scheme are closer to the observations when compared to those obtained from using the KSC scheme. CONCLUSIONS: Concentrations calculated with the CON scheme are in general higher and closer to the observations than those obtained by the KSC scheme (of the order of 15-20%). Nitrate wet deposition calculated with the CON scheme are in general higher and closer to the observations than those obtained by the KSC scheme. RECOMMENDATIONS AND PERSPECTIVES: To examine the performance of the scheme, simulated and measured concentrations of a pollutant (NO(2)) and nitrate wet deposition was compared for the year 2002. The comparison was made for the whole domain used in simulations performed by the chemical European Monitoring and Evaluation Programme Unified model (version UNI-ACID, rv2.0) where schemes were incorporated.     

Numerical validation of a Eulerian hydrochemical code using a 1D multisolute mass transport system involving heterogeneous kinetically controlled reactions

It is demonstrated that at steady state, the 1D thermo-kinetic hydrochemical Eulerian mass balance equations in pure advective mode are indeed identical to the governing mass balance equations of a single reaction path (or geochemical) code in open system mode. Thus, both calculated reaction paths should be theoretically identical whatever the chemical complexity of the water-rock system (i.e., multicomponent, multireaction zones kinetically and equilibrium-controlled). We propose to use this property to numerically test the thermo-kinetic hydrochemical Eulerian codes and we employ it to verify the algorithm of the 1D finite difference code KIRMAT. Compared to the other methods to perform such numerical tests (i.e., comparisons with analytical, semi-analytical solutions, between two Eulerian hydrochemical codes), the advantage of this new method is the absence of constraints on the chemical complexity of the modelled water-rock systems. Moreover, the same thermo-kinetic databases and geochemical functions can be easily and mechanically used in both calculations, when the numerical reference comes from the Eulerian code with no transport terms (u and D = 0) and modify to be consistent with the definition of the open system mode in geochemical modelling. The ability of KIRMAT to treat multicomponent pure advective transport, subjected to several kinetically equilibrium-controlled dissolution and precipitation reactions, and to track their boundaries has been successfully verified with the property of interest. The required numerical validation of the reference calculations is bypassed in developing the Eulerian code from an already checked single reaction path code. A forward time-upstream weighting scheme (a mixing cell scheme) is used in this study. An appropriate choice of grid spacing allows to calculate within the grid size uncertainty the correct mineral reaction zone boundaries, despite the presence of numerical dispersion. Its correction enables us to improve the convergence and to extend the numerical test to mixed advective-dispersive mass transport. However, the skewness factor involves numerical oscillations that prevent to compute different grid spacing. The use of a different chemically controlled time step constraint in both calculations induces some inconsistencies into the validation tests. This numerical validation method may be applied as well as to check a thermo-kinetic hydrochemical finite element based code, from a 1D heterogeneous systems, and 2D-3D systems provided that they are designed so as to be 1D equivalent. A one-step algorithm and the use of a numerical reference coming from the Eulerian code to be tested ensure the potential success (accuracy) of the numerical validation method.     

Evaluation of simplified mass transfer models to simulate the impacts of source zone architecture on nonaqueous phase liquid dissolution in heterogeneous porous media

Nonaqueous phase liquid (NAPL) dissolution was studied in three-dimensional (3D) heterogeneous experimental aquifers (25.5 cm x 9 cm x 8.5 cm) with two different longitudinal correlation lengths (2.1 cm and 1.1 cm) and initial spill volumes (22.5 ml and 10.5 ml). Spatial and temporal distributions of NAPL during dissolution were measured using magnetic resonance imaging (MRI). At high NAPL spill volume, average effluent concentrations initially increased during dissolution, as NAPL pools transitioned to NAPL ganglia, and then decreased as the total NAPL-water interfacial area decreased over time. Experimental results were used to test six dissolution models: (i and ii) a one-dimensional (1D) model using either specific NAPL-water interfacial area values estimated from MR images at each time step (i.e., 1D quasi-steady state model), or an empirical mass transfer (Sh') correlation (i.e., 1D transient model), (iii and iv) a multiple analytical source superposition technique (MASST) using either the NAPL distribution determined from MR images at each time step (i.e., MASST steady state model), or the NAPL distribution determined from mass balance calculations (i.e., MASST transient model), (v) an equilibrium streamtube model, and (vi) a 3D grid-scale pool dissolution model (PDM) with a dispersive mass flux term. The 1D quasi-steady state model and 3D PDM captured effluent concentration values most closely, including some concentration fluctuations due to changes in the extent of flow reduction. The 1D transient, MASST steady state and transient, and streamtube models all showed a monotonic decrease in effluent concentration values over time, and the streamtube model was the most computationally efficient. Changes during dissolution of the effective NAPL-water interfacial area estimated from imaging data are similar to changes in effluent concentration values. The 1D steady state model incorporates estimates of the effective NAPL-water interfacial area directly at each time point; the 3D PDM does so indirectly through mass balance and a relative permeability function, which causes reduced water flow through high saturation NAPL regions. Hence, when model accuracy is required, the results indicate that a surrogate of this effective interfacial area is required. Approaches to include this surrogate in the MASST and streamtube models are recommended.     

Choice of dispersion coefficients in reactive transport calculations on smoothed fields

Local dispersion dominates the mixing of compounds that are introduced separately into the subsurface and do not partition into any other than the aqueous phase. Thus, reactions between these compounds are controlled by dispersive mixing if they are not limited by kinetics. I quantify longitudinal dispersive mixing by the longitudinal effective dispersion coefficient of a conservative tracer introduced by a point-like injection [Water Resour. Res. 36 (12) (2000) 3591-3604]. In the upscaling of mixing-controlled reactive transport, I apply the mean velocity and the effective dispersion coefficient to the macroscopic transport calculations, whereas the reactive parameters on the macro-scale are identical to those on the local scale. The applicability of the approach is demonstrated for the transport of compounds undergoing a second-order irreversible bimolecular reaction. Ten realizations of a two-dimensional heterogeneous log-conductivity field are considered. Using the effective dispersion parameters, the overall mass balance is met in the ensemble average, whereas solute spreading is underestimated. I assess the lack of spreading by the difference between the expected macrodispersion and effective dispersion coefficients. I extend the approach to simulations on log-conductivity fields obtained by kriging of regularly spaced conductivity measurements. These fields contain the large-scale features of the true fields but do not resolve the small-scale variability. For the calculations on the kriged fields, the corresponding conditional covariance is substituted into the analytical expressions of effective dispersion, yielding a correction effective dispersion coefficient. The comparison between simulations on the fully resolved fields and on the kriged fields indicates that the approach is valid for wide plumes meeting the ergodicity condition. The high variability of mixing on small scales unresolved by kriging, however, leads to severe uncertainty when mixing-controlled reactions are predicted for narrow plumes.     

Modeling atmospheric mercury deposition in the vicinity of power plants

Two mathematical models of the atmospheric fate and transport of mercury (Hg), an Eulerian grid-based model and a Gaussian plume model, are used to calculate the atmospheric deposition of Hg in the vicinity (i.e., within 50 km) of five coal-fired power plants. The former is applied using two different horizontal resolutions: coarse (84 km) and fine (16.7 km). More than 96% of the power plant Hg emissions are calculated with the plume model to be transported beyond 50 km from the plants. The grid-based model predicts a lower fraction to be transported beyond 50 km: >91% with a coarse resolution and >95% with a fine resolution. The contribution of the power plant emissions to total Hg deposition within a radius of 50 km from the plants is calculated to be <8% with the plume model, <14% with the Eulerian model with a coarse resolution, and <10% with the Eulerian model with a fine resolution. The Eulerian grid-based model predicts greater local impacts than the plume model because of artificially enhanced vertical dispersion; the former predicts about twice as much Hg deposition as the latter when the area considered is commensurate with the resolution of the grid-based model. If one compares the local impacts for an area that is significantly less than the grid-based model resolution, then the grid-based model may predict lower local deposition than the plume model, because two compensating errors affect the results obtained with the grid-based model: initial dilution of the power plant emissions within one or more grid cells and enhanced vertical mixing to the ground.     

A parametric transfer function methodology for analyzing reactive transport in nonuniform flow

We analyze reactive transport during in-situ bioremediation in a nonuniform flow field, involving multiple extraction and injection wells, by the method of transfer functions. Gamma distributions are used as parametric models of the transfer functions. Apparent parameters of classical transport models may be estimated from those of the gamma distributions by matching temporal moments. We demonstrate the method by application to measured data taken at a field experiment on bioremediation conducted in a multiple-well system in Oak Ridge, TN. Breakthrough curves (BTCs) of a conservative tracer (bromide) and a reactive compound (ethanol) are measured at multi-level sampling (MLS) wells and in extraction wells. The BTCs of both compounds are jointly analyzed to estimate the first-order degradation rate of ethanol. To quantify the tracer loss, we compare the approaches of using a scaling factor and a first-order decay term. Results show that by including a scaling factor both gamma distributions and inverse-Gaussian distributions (transfer functions according to the advection-dispersion equation) are suitable to approximate the transfer functions and estimate the reactive rate coefficients for both MLS and extraction wells. However, using a first-order decay term for tracer loss fails to describe the BTCs at the extraction well, which is affected by the nonuniform distribution of travel paths.     

Modeling Atmospheric Mercury Deposition in the Vicinity of Power Plants

Abstract

Two mathematical models of the atmospheric fate and transport of mercury (Hg), an Eulerian grid–based model and a Gaussian plume model, are used to calculate the atmospheric deposition of Hg in the vicinity (i.e., within 50 km) of five coal–fired power plants. The former is applied using two different horizontal resolutions: coarse (84 km) and fine (16.7 km). More than 96% of the power plant Hg emissions are calculated with the plume model to be transported beyond 50 km from the plants. The grid–based model predicts a lower fraction to be transported beyond 50 km: >91% with a coarse resolution and >95% with a fine resolution. The contribution of the power plant emissions to total Hg deposition within a radius of 50 km from the plants is calculated to be <8% with the plume model, <14% with the Eulerian model with a coarse resolution, and <10% with the Eulerian model with a fine resolution. The Eulerian grid–based model predicts greater local impacts than the plume model because of artificially enhanced vertical dispersion; the former predicts about twice as much Hg deposition as the latter when the area considered is commensurate with the resolution of the grid–based model. If one compares the local impacts for an area that is significantly less than the grid–based model resolution, then the grid–based model may predict lower local deposition than the plume model, because two compensating errors affect the results obtained with the grid–based model: initial dilution of the power plant emissions within one or more grid cells and enhanced vertical mixing to the ground.     

Chemical transport models

Background, aim, and scope  Improving the parameterization of processes in the atmospheric boundary layer (ABL) and surface layer, in air quality and chemical transport models. To do so, an asymmetrical, convective, non-local scheme, with varying upward mixing rates is combined with the non-local, turbulent, kinetic energy scheme for vertical diffusion (COM). For designing it, a function depending on the dimensionless height to the power four in the ABL is suggested, which is empirically derived. Also, we suggested a new method for calculating the in-canopy resistance for dry deposition over a vegetated surface. Materials and methods  The upward mixing rate forming the surface layer is parameterized using the sensible heat flux and the friction and convective velocities. Upward mixing rates varying with height are scaled with an amount of turbulent kinetic energy in layer, while the downward mixing rates are derived from mass conservation. The vertical eddy diffusivity is parameterized using the mean turbulent velocity scale that is obtained by the vertical integration within the ABL. In-canopy resistance is calculated by integration of inverse turbulent transfer coefficient inside the canopy from the effective ground roughness length to the canopy source height and, further, from its the canopy height. Results  This combination of schemes provides a less rapid mass transport out of surface layer into other layers, during convective and non-convective periods, than other local and non-local schemes parameterizing mixing processes in the ABL. The suggested method for calculating the in-canopy resistance for calculating the dry deposition over a vegetated surface differs remarkably from the commonly used one, particularly over forest vegetation. Discussion  In this paper, we studied the performance of a non-local, turbulent, kinetic energy scheme for vertical diffusion combined with a non-local, convective mixing scheme with varying upward mixing in the atmospheric boundary layer (COM) and its impact on the concentration of pollutants calculated with chemical and air-quality models. In addition, this scheme was also compared with a commonly used, local, eddy-diffusivity scheme. Simulated concentrations of NO₂ by the COM scheme and new parameterization of the in-canopy resistance are closer to the observations when compared to those obtained from using the local eddy-diffusivity scheme. Conclusions  Concentrations calculated with the COM scheme and new parameterization of in-canopy resistance, are in general higher and closer to the observations than those obtained by the local, eddy-diffusivity scheme (on the order of 15–22%). Recommendations and perspectives  To examine the performance of the scheme, simulated and measured concentrations of a pollutant (NO₂) were compared for the years 1999 and 2002. The comparison was made for the entire domain used in simulations performed by the chemical European Monitoring and Evaluation Program Unified model (version UNI-ACID, rv2.0) where schemes were incorporated.     

The spatial scale of organic chemicals in multimedia fate modeling. Recent developments and significance for chemical assessment

In the last years, the spatial range (SR) or characteristic travel distance (CTD) of organic chemicals has found increasing scientific interest as an indicator of the long-range transport (LRT) potential and, in combination with persistence, as a kind of 'hazard' indicator on the exposure level. This development coincides with European debates about more effective and more preventive approaches to the chemicals assessment, and about an international, legally-binding instrument for the phase out of persistent organic pollutants (POPs). Persistence and LRT potential are important issues in these debates. Here, the development of the concept of assessing the spatial scale from early ideas in the 1970s and 1980s to recent studies in the field of multimedia fate and transport modeling is summarized. Different approaches to the modeling of environmental transport (advective and dispersive) and different methods for quantifying the SR or CTD are compared. Relationships between SR or CTD and different persistence measures are analyzed. Comparison of these relationships shows that conclusions for chemical assessment should be based on an evaluation of different persistence and spatial scale measures. The use of SR or CTD and persistence as hazard indicators in the chemicals assessment is illustrated.     

Eulerian derivation of the fractional advection-dispersion equation

A fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the second-order derivative is replaced with a fractional-order derivative. In contrast to the classical ADE, the fractional ADE has solutions that resemble the highly skewed and heavy-tailed breakthrough curves observed in field and laboratory studies. These solutions, known as alpha-stable distributions, are the result of a generalized central limit theorem which describes the behavior of sums of finite or infinite-variance random variables. We use this limit theorem in a model which sums the length of particle jumps during their random walk through a heterogeneous porous medium. If the length of solute particle jumps is not constrained to a representative elementary volume (REV), dispersive flux is proportional to a fractional derivative. The nature of fractional derivatives is readily visualized and their parameters are based on physical properties that are measurable. When a fractional Fick's law replaces the classical Fick's law in an Eulerian evaluation of solute transport in a porous medium, the result is a fractional ADE. Fractional ADEs are ergodic equations since they occur when a generalized central limit theorem is employed.     

Fast method for simulation of radionuclide chain migration in dual porosity fracture rocks

In fractured rocks with a porous rock matrix such as granites, radionuclides will flow with the water in the fracture network. The nuclides will diffuse in and out the rock matrix where they can sorb and be considerably retarded compared to the water velocity. A water parcel entering the network will mix and split at the fracture intersections and parts of the original parcel will traverse a multitude of different fractures. The flowrates, velocities, sizes and apertures of the fractures can vary widely. Normally one must solve the transport equations for every fracture and use the effluent concentration as inlet condition to the next fracture and so on. It is shown that under some weakly simplified conditions it suffices to determine one single parameter group containing information on the flow wetted surface that a water parcel contacts along the entire path. It is also shown how this can be obtained. Then, solving the transport equations only once for time and location along the path gives the concentration and nuclide flux of every nuclide in the chain everywhere along a path. The same solution actually is valid for every path in the network. This dramatically reduces the computation effort. The same approach can be used for models based on streamtubes.     

Transport modeling of copper and cadmium with linear and nonlinear retardation factors

The predictive accuracy of using the one-dimensional advection–dispersion equation to evaluate the fate and transport of solute in a soil column is usually dependent on the proper determination of chemical retardation factors. Typically, the distribution coefficient (K_d) obtained by fitting the linear sorption isotherm has been extensively used to consider general geochemical reactions on solute transport in a low-concentration range. However, the linear distribution coefficient cannot be adequately utilized to describe the solute fate at a higher concentration level. This study employed the nonlinear equilibrium-controlled sorption parameters to determine the retardation factor used in column leaching experiments. Copper and cadmium transportation in a lateritic silty-clay soil column was examined. Through the explicit finite-difference calculations with a third-order total-variation-diminishing (TVD) numerical solution scheme, all results of the theoretical copper and cadmium breakthrough curves (BTCs) simulated by using the Freundlich nonlinear retardation factors revealed good agreement with the experimental observations.     

Evaluating the ability of a numerical weather prediction model to forecast tracer concentrations during ETEX 2

In this paper the meteorological processes responsible for transporting tracer during the second ETEX (European Tracer EXperiment) release are determined using the UK Met Office Unified Model (UM). The UM predicted distribution of tracer is also compared with observations from the ETEX campaign. The dominant meteorological process is a warm conveyor belt which transports large amounts of tracer away from the surface up to a height of 4 km over a 36 h period. Convection is also an important process, transporting tracer to heights of up to 8 km. Potential sources of error when using an operational numerical weather prediction model to forecast air quality are also investigated. These potential sources of error include model dynamics, model resolution and model physics. In the UM a semi-Lagrangian monotonic advection scheme is used with cubic polynomial interpolation. This can predict unrealistic negative values of tracer which are subsequently set to zero, and hence results in an overprediction of tracer concentrations. In order to conserve mass in the UM tracer simulations it was necessary to include a flux corrected transport method. Model resolution can also affect the accuracy of predicted tracer distributions. Low resolution simulations (50 km grid length) were unable to resolve a change in wind direction observed during ETEX 2, this led to an error in the transport direction and hence an error in tracer distribution. High resolution simulations (12 km grid length) captured the change in wind direction and hence produced a tracer distribution that compared better with the observations. The representation of convective mixing was found to have a large effect on the vertical transport of tracer. Turning off the convective mixing parameterisation in the UM significantly reduced the vertical transport of tracer. Finally, air quality forecasts were found to be sensitive to the timing of synoptic scale features. Errors in the position of the cold front relative to the tracer release location of only 1 h resulted in changes in the predicted tracer concentrations that were of the same order of magnitude as the absolute tracer concentrations.     

Upscaling heterogeneity in aquifer reactivity via the exposure-time concept: inverse model

A novel inverse technique is proposed to quantitatively characterize macroscopic variability in aquifer reactivity in a Lagrangian representation. Reactivity heterogeneity is expressed in terms of distributions of flux over cumulative time of exposure of the solution to reactive surface area, termed here 'cumulative reactivity'. In cases involving single aqueous species the combined effects of physical and reactivity heterogeneity on reactive solute transport can often be established and further investigated through joint distributions of flux over travel time and cumulative reactivity. The inverse technique requires the breakthrough curve of a passive tracer to determine the distribution of flux over travel time, and additional breakthrough curves of reactive tracers provide additional moments of the distribution of flux over cumulative reactivity given travel time. Thus breakthroughs of one passive and two reactive tracers can provide the mean and variance of the distribution of flux over cumulative reactivity. This Lagrangian characterization is achieved with knowledge of the types of reactive surfaces present, but not their spatial locations. The distributions can subsequently be applied via forward modeling using the same technique to predict breakthrough curves of other solutes undergoing first-order reactions in similar physically and chemically heterogeneous configurations.     

Boundary layer photochemistry simulated with a two-stream convection scheme

We explore the sensitivity of the simulation of photochemical smog to the turbulent mixing scheme, using two diffusion schemes and an original two-stream model (TSM) scheme, assuming in the column an updraft and a downdraft. In this latter scheme both updraft and downdraft concentrations are prognostic variables, unlike in previously proposed schemes. The comparisons are made using a one-dimensional column model, in a Eulerian or a Lagrangian mode. The diffusion schemes produce tilted concentration profiles for primary species, with higher concentrations near the surface and lower values at the top of the boundary layer, while TSM profiles yield more homogeneous concentrations in the planetary boundary layer (PBL). Ozone concentrations are also more homogeneous in the TSM PBL than in the diffusive PBL. Only deposition makes ozone concentrations slightly lower near the surface, while in diffusive case ozone is lower also due to titration by higher nitrogen oxide concentrations. The overall differences between the schemes remain small for ozone.Also, the development time and amplitude of an ozone city plume is not very sensitive to the choice of the mixing scheme. In the urban framework ozone build-up is slightly delayed by higher nitrogen oxide concentrations near the surface in the diffusive cases, but the plume development is similar to that of the TSM once the plume travels away from the emission area. Results also show that the sensitivity of ozone to nitrogen oxide and non-methane volatile organic compounds is itself not very sensitive to the mixing scheme.     

The energy balance of central Mexico City during the dry season

The first measurements of the energy balance fluxes of a dry, densely built-up, central city site are presented. Direct observation of the net radiation, sensible and latent heat flux densities above roof-top in the old city district of Mexico City allow the heat storage flux density to be found by residual. The most important finding is that during daytime, when evaporation is very small (<4% of net radiation), and therefore sensible heat uses dominate (Bowen ratio >8), the uptake of heat by the buildings and substrate is so large (58%) that convective heating of the atmosphere is reduced to a smaller role than expected (38%). The nocturnal release of heat from storage is equal to or larger than the net radiation and sufficient to maintain an upward convective heat flux throughout most nights. It is important to see if this pattern is repeated at other central city, or dry urban sites, or whether it is only found in districts dominated by massive stone structures. These findings have implications for the height of the urban mixing layer and the magnitude of the urban heat island.