Dispersion in doublet-type flows through highly anisotropic porous formations

Steady doublet-type flow takes place in a porous formation, where the log-transform $Y = \ln K$ of the spatially variable hydraulic conductivity $K$ is regarded as a stationary random field of two-point autocorrelation $\rho _Y$ . A passive solute is injected at the source in the porous formation and we aim to quantify the resulting dispersion process between the two lines by means of spatial moments. The latter depend on the distance $\ell$ between the lines, the variance $\sigma ^2_Y$ of $Y$ and the (anisotropy) ratio $\lambda$ between the vertical and the horizontal integral scales of $Y$ . A simple (analytical) solution to this difficult problem is obtained by adopting a few simplifying assumptions: (i) a perturbative solution, which regards $\sigma ^2_Y$ as a small parameter, of the velocity field is sought; (ii) pore-scale dispersion is neglected; and (iii) we deal with a highly anisotropic formation ( $\lambda \lesssim 0.1$ ). We focus on the longitudinal spatial moment, as it is of most importance for the dispersion mechanism. A general expression is derived in terms of a single quadrature, which can be straightforwardly carried out once the shape of $\rho _Y$ is specified. Results permit one to grasp the main features of the dispersion processes as well as to assess the difference with similar mechanisms observed in other non-uniform flows. In particular, the dispersion in a doublet-type flow is observed to be larger than that generated by a single line. This effect is explained by noting that the advective velocity in a doublet, unlike that in source/line flows, is rapidly increasing in the far field owing to the presence there of the singularity. From the standpoint of the applications, it is shown that the solution pertaining to $\lambda \to 0$ (stratified formation) provides an upper bound for the dispersion mechanism. Such a bound can be used as a conservative limit when, in a remediation procedure, one has to select the strength as well as the distance $\ell$ of the doublet. Finally, the present study lends itself as a valuable tool for aquifer tests and to validate more involved numerical codes accounting for complex boundary conditions.

Numerical and experimental study on solute transport through physical aquifer model

Environmental concerns have drawn much research interest in solute transport through porous media. Thus, contaminants of groundwater permeate through pores in the ground, and adsorption attenuates the pollution concentration as the pollutants adhere to the solid surface. Mathematical models based on certain simplifying assumptions have been used to predict solute transport. The transport of solutes in porous media is governed by a partial differential equation known as the advection-dispersion equation. In this study, a two-dimensional numerical model has been developed for solute transport through porous media. Results of spatial moments have been predicted and analysed in the presence of both constant and time-dependent dispersion coefficients. Afterward, a numerical model is used to simulate experimentally observed breakthrough curves for both conservative and non-conservative solutes. Thus, transport parameters are estimated through numerical simulation of observed breakthrough curves. Finally, this model gives the best simulation of observed breakthrough curves, and it can also be used in the field scale.

Evidence of Preferential Flow Activation in the Vadose Zone via Geophysical Monitoring

Preferential pathways allow rapid and non-uniform water movement in the subsurface due to strong heterogeneity of texture, composition, and hydraulic properties. Understanding the importance of preferential pathways is crucial, because they have strong impact on flow and transport hydrodynamics in the unsaturated zone. Particularly, improving knowledge of the water dynamics is essential for estimating travel time through soil to quantify hazards for groundwater, assess aquifer recharge rates, improve agricultural water management, and prevent surface stormflow and flooding hazards. Small scale field heterogeneities cannot be always captured by the limited number of point scale measurements collected. In order to overcome these limitations, noninvasive geophysical techniques have been widely used in the last decade to predict hydrodynamic processes, due to their capability to spatialize hydrogeophysical properties with high resolution. In the test site located in Bari, Southern Italy, the geophysical approach, based on electrical resistivity tomography (ERT) monitoring, has been implemented to detect preferential pathways triggered by an artificial rainfall event. ERT-derived soil moisture estimations were obtained in order to quantitatively predict the water storage (m3m−3), water velocity (ms−1), and spread (m2) through preferential pathways by using spatial moments analysis.

Generalized Empirical Likelihood-Based Kernel Estimation of Spatially Similar Densities

This study concerns the estimation of spatially similar densities, each with a small number of observations. To achieve flexibility and improved efficiency, we propose kernel-based estimators that are refined by generalized empirical likelihood probability weights associated with spatial moment conditions. We construct spatial moments based on spline basis functions that facilitate desirable local customization. Monte Carlo simulations demonstrate the good performance of the proposed method. To illustruate its usefulness, we apply this method to the estimation of crop yield distributions that are known to be spatically similar.

Role of stationary convective bands and antecedent conditions on the flood response to the Vaia storm (October 27-30, 2018) in the Eastern Italian Alps

<p>Between the morning of 27 October 2018 and the evening of 29 October 2018, heavy precipitation over the Eastern Italian Alps led to damaging flooding. The event, which occurred at the end of a climatic anomaly of prolonged drought, developed into two phases, with a first phase (October 27-28) dominated by more stratiform orographically-enhanced precipitation. After a short lull, a second and more intense phase of the event took place on the 29th, when a cold front from the Gulf of Lion entered the Mediterranean basin triggering explosive cyclogenesis. A characteristic of the second phase of the storm is the rainfall organization in well-defined convective bands, some of which persisted at the same location for up to 3 hours. The bands, aligned from southeast to northwest, were initially located downstream of the pre-alpine region.</p><p>The work aims to investigate the impact of the stationary convective bands and of the dry antecedent conditions on the flood response to the storm. The availability of high-resolution rainfall estimates from weather radar and of dense rain gauge network data, along with flood response observations from stream gauge data and post-event surveys, enables to study the hydrometeorological and hydrological mechanisms associated with this extreme storm and the consequent flood response.</p><p>Observational and model analyses of the hydrologic runoff in two areas heavily impacted by the storm (Noce river basin, in the Trentino Province, and upper Cordevole river basin, in the Veneto Region) illustrate how the structure and evolution of the stationary convective bands translate into scale dependent flood response. For the upper Cordevole river basin, the event envelope curve shows two peculiar behaviors: (a) basin scale ranging from 1 to 200 km<sup>2</sup>, with peak unit discharges decreasing from 10 to 4 m<sup>3</sup>s<sup>-1</sup>km<sup>-2</sup>; (b) basin scale ranging from 200 to 2000 km<sup>2</sup>, with smaller peak unit discharges. The spatial extent of the first region is controlled by the structure of the central convective band. Moreover, the spatial moments of catchment rainfall are exploited to identify the impact of the convective cells motion along the stationary band on the flood response.</p>

Spatial structure arising from chase-escape interactions with crowding

Movement of individuals, mediated by localised interactions, plays a key role in numerous processes including cell biology and ecology. In this work, we investigate an individual-based model accounting for various intraspecies and interspecies interactions in a community consisting of two distinct species. In this framework we consider one species to be chasers and the other species to be escapees, and we focus on chase-escape dynamics where the chasers are biased to move towards the escapees, and the escapees are biased to move away from the chasers. This framework allows us to explore how individual-level directional interactions scale up to influence spatial structure at the macroscale. To focus exclusively on the role of motility and directional bias in determining spatial structure, we consider conservative communities where the number of individuals in each species remains constant. To provide additional information about the individual-based model, we also present a mathematically tractable deterministic approximation based on describing the evolution of the spatial moments. We explore how different features of interactions including interaction strength, spatial extent of interaction, and relative density of species influence the formation of the macroscale spatial patterns.