This paper discusses the results of numerical analysis of dispersion of passive solutes in twodimensional heterogeneous porous formations. Statistics of flow and transport variables, the accuracy and the role of approximations implicit in existing first-order theories, and the convergence of computational results are investigated. The results suggest that quite different rates of convergence with Monte Carlo runs hold for different spatial moments and that over 1000 realizations are required to stabilize second moments even for relatively mild heterogeneity (rr• < 1.6). This has implications for the extent of the spatial domain for single-realization numerical studies of the same type. A comparison of the variance of plumes with the results of linear theories (0.05 < rr•, < 1.6) shows an unexpectedly broad validity field for the theoretical solution obtained from a suitable linearization of flow and transport. Reformulation of the same problem linearizing in turn the flow or the transport Recent experimental evidence and theoretical results suggest that the transport of passive solutes in natural porous formations is dominated by the spatial variations in hydrau-!ic conductivity resulting in heterogeneous convection fields (see, for an exhaustive review, Dagan [1989]). A theory of flow and transport has been developing in recent years , 1990] which links the kinematics of the dispersion process to field measurable quantities, i.e., the spatial correlation structure and the variability of the log conductivity field Y(x) of porous formations viewed as a random space function. Fundamental experimental validations from accurate field analyses and critical elaborations of the data support the validity of linear theories at least for mildly heterogeneous aquifers [e.g.McLaughlin, 1991; Le Blanc et al., 1991, Garabedian et al., 1991; Rajaram and Gelhar, 1991]. Limits and validity of the theory of flow and transport in heterogeneous porous formations have recently been discussed IDagan, 1989]. It is accepted that the linear (denoted here as Dagan's) theory subsumes a number of previous results [Matheron and de Marsily, 1980; Dagan, 1984; Gelhar and Axness, 1983; Dagan, 1987] and captures the foremost features of the processes whenever the variance of log conductivity •r2r, a significant measure of heterogeneity, is small (cr• < 1) because a first-order perturbation is used as a consistent approximation involving such a parameter. Zhang, Y. K., and S. P. Neuman, A quasi-linear theory of non-Fickian and Fickian subsurface dispersion, 2, Application to anisotropic media and the Borden site, Water Resour. Res., 26(5), 903-913, 1990.

Riverine environments, such as streams and rivers, have been reported as sources of the potent greenhouse gas nitrous oxide (N 2 O) to the atmosphere mainly via microbially mediated denitrification. Our limited understanding of the relative roles of the nearsurface streambed sediment (hyporheic zone), benthic, and water column zones in controlling N 2 O production precludes predictions of N 2 O emissions along riverine networks. Here, we analyze N 2 O emissions from streams and rivers worldwide of different sizes, morphology, land cover, biomes, and climatic conditions. We show that the primary source of N 2 O emissions varies with stream and river size and shifts from the hyporheic-benthic zone in headwater streams to the benthic-water column zone in rivers. This analysis reveals that N 2 O production is bounded between two N 2 O emission potentials: the upper N 2 O emission potential results from production within the benthic-hyporheic zone, and the lower N 2 O emission potential reflects the production within the benthic-water column zone. By understanding the scaling nature of N 2 O production along riverine networks, our framework facilitates predictions of riverine N 2 O emissions globally using widely accessible chemical and hydromorphological datasets and thus, quantifies the effect of human activity and natural processes on N 2 O production.riverine networks | greenhouse gas | N 2 O | emission scaling law | N 2 O emission potentials R iverine environments, such as streams and rivers, have been identified as hotspots of microbially mediated denitrification, where nitrate (NO3) is converted to both nitrogen gas (N2), which constitutes the majority of Earth's atmosphere, and nitrous oxide (N 2 O), the potent greenhouse gas responsible for stratospheric ozone destruction (1). Denitrification has been observed to occur within both bulk-oxic (2) and anoxic environments (3-5) of both benthic (i.e., sediment-water interface) and hyporheic (i.e., near-subsurface) zones of streams and rivers. Whereas the benthic zone is the ecological region of the streambed, where both aquatic fauna and flora can be found (4, 6), the latter is the band of streambed material mainly saturated of stream water (7). The benthic zone is at the interface between water and sediment and the upper boundary of the fluvial hyporheic zone. Current understanding suggests that riverine N 2 O production occurs predominantly in these two environments, reflecting two distinct biogeochemical transformation zones (6), irrespective of system size from headwater streams to rivers. The produced N 2 O is then exchanged with the atmosphere through diffusive evasion, with dynamics that depend on N 2 O concentrations of the water in relation to atmospheric equilibrium (6, 8), stream hydrodynamics, temperature, and the air-water gas exchange rate (9). Although it is understood that microbially mediated denitrification is responsible for a large proportion of N 2 O production in riverine networks (6, 10, 11), quantifying these emissions is challenging becau...

Hyporheic flows, which stem from the interaction between stream flow and bedform, transport solute‐laden surface waters into the streambed sediments, where reactive solutes undergo biogeochemical transformations. Despite the importance of hyporheic exchange on riverine ecosystem and biogeochemical cycles, research is limited on the effects of hyporheic fluxes on the fate of reactive solutes within the hyporheic zone. Consequently, we investigate the controls of hyporheic flowpaths, which we link to stream morphology and streamflow, on prevailing hyporheic redox conditions and on biogeochemical transformations occurring within streambeds. We focus on the dissolved inorganic reactive forms of nitrogen, ammonium and nitrate, because nitrogen is one of the most common reactive solutes and an essential nutrient found in stream waters. Our objectives are to explore the influence of stream morphology, hyporheic water temperature and relative abundance of ammonium and nitrate, on transformation of ammonium, removal of nitrates and production of nitrous oxide, a potent greenhouse gas. We address our objectives with analytical solutions of the Multispecies Reactive Advection‐Dispersion Equation coupled with linearized Monod's kinetics and analytical solutions of the hyporheic flow for alternate‐bar morphology. We introduce a new Damköhler number,Da, defined as the ratio between the median hyporheic residence time and the time scale of oxygen consumption, which we prove to be a good indicator of where aerobic or anaerobic conditions prevail. In addition, Dais a key index to quantify hyporheic nitrification and denitrification efficiencies and defines a new theoretical framework for scaling results at both the morphological‐unit and stream‐reach scales.

[1] We present a three-dimensional semianalytical process-based model of dissolved oxygen and dissolved inorganic nitrogen (DIN) transformation within the hyporheic zone of gravel bed rivers. Oxygen and multispecies solute transport is solved within a Lagrangian framework with transformation of DIN species modeled by linearized Monod's kinetics, with temperature-dependent reaction rate coefficients derived from field experiments. Our solutions, which are obtained under the assumptions of sediments with uniform hydraulic properties and negligible local dispersion, highlight the importance of morphological characteristics of the streambed on DIN transformations within the hyporheic zone. By means of this model we explore the effects of streambed topography and relative abundance of ammonium and nitrate in stream waters on the reactive nitrogen cycle in the hyporheic zone of gravel bed rivers with a pool and riffle morphology. Our model shows complex concentration dynamics within the hyporheic zone that may act as a source or a sink of nitrogen depending on the residence time distribution, which can be parameterized in terms of streambed morphology, and the ratio between the in-stream concentrations of ammonium and nitrate. Application of the model to seven natural streams shows good agreement between predicted and measured nitrous oxide emissions from their hyporheic zone.Citation: Marzadri, A., D. Tonina, and A. Bellin (2011), A semianalytical three-dimensional process-based model for hyporheic nitrogen dynamics in gravel bed rivers, Water Resour.

We present a new approach for modelling macrodispersivity in spatially variable velocity fields, such as exist in geologically heterogeneous formations. Considering a spectral representation of the velocity, it is recognized that numerical models usually capture low-wavenumber effects, while the large-wavenumber effects, associated with subgrid block variability, are suppressed. While this suppression is avoidable if the heterogeneity is captured at minute detail, that goal is impossible to achieve in all but the most trivial cases. Representing the effects of the suppressed variability in the models is made possible using the proposed concept of block-effective macrodispersivity. A tensor is developed, which we refer to as the block-effective macrodispersivity tensor, whose terms are functions of the characteristic length scales of heterogeneity, as well as the length scales of the model's homogenized areas, or numerical grid blocks. Closed-form expressions are developed for small variability in the log-conductivity and unidirectional mean flow, and are tested numerically. The use of the block-effective macrodispersivities allows conditioning of the velocity field on the measurements on the one hand, while accounting for the effects of unmodelled heterogeneity on the other, in a numerically reasonable set-up. It is shown that the effects of the grid scale are similar to those of the plume scale in terms of filtering out the effects of portions of the velocity spectrum. Hence it is easy to expand the concept of the block-effective dispersivity to account for the scale of the solute body and the pore-scale dispersion.