Ensemble Kalman Filter Assimilation of ERT Data for Numerical Modeling of Seawater Intrusion in a Laboratory Experiment

Seawater intrusion in coastal aquifers is a worldwide problem exacerbated by aquifer overexploitation and climate changes. To limit the deterioration of water quality caused by saline intrusion, research studies are needed to identify and assess the performance of possible countermeasures, e.g., underground barriers. Within this context, numerical models are fundamental to fully understand the process and for evaluating the effectiveness of the proposed solutions to contain the saltwater wedge; on the other hand, they are typically affected by uncertainty on hydrogeological parameters, as well as initial and boundary conditions. Data assimilation methods such as the ensemble Kalman filter (EnKF) represent promising tools that can reduce such uncertainties. Here, we present an application of the EnKF to the numerical modeling of a laboratory experiment where seawater intrusion was reproduced in a specifically designed sandbox and continuously monitored with electrical resistivity tomography (ERT). Combining EnKF and the SUTRA model for the simulation of density-dependent flow and transport in porous media, we assimilated the collected ERT data by means of joint and sequential assimilation approaches. In the joint approach, raw ERT data (electrical resistances) are assimilated to update both salt concentration and soil parameters, without the need for an electrical inversion. In the sequential approach, we assimilated electrical conductivities computed from a previously performed electrical inversion. Within both approaches, we suggest dual-step update strategies to minimize the effects of spurious correlations in parameter estimation. The results show that, in both cases, ERT data assimilation can reduce the uncertainty not only on the system state in terms of salt concentration, but also on the most relevant soil parameters, i.e., saturated hydraulic conductivity and longitudinal dispersivity. However, the sequential approach is more prone to filter inbreeding due to the large number of observations assimilated compared to the ensemble size

Polarization of the recoil proton from π0 photoproduction in hydrogen

The D3/2 nature of the second resonance in neutral single pion photoproduction, γ+p→p+π0, suggested by Peierls, has been confirmed by additional experimental observations of the polarization of the recoil proton over a range of photon energies. The photon energy dependence of the polarization at 90° c.m. is in substantial disagreement with alternative models suggested by Stoppini and Pellegrini, and Landovitz and Marshall if the observed angular distributions are also considered. An experimental method using nuclear emulsion as scatterer-detector, in conjunction with a magnetic spectrometer, is shown to have both good energy resolution and reasonable counting rate

Design of anchored slabs in spillway stilling basins

This paper characterizes the temporal behavior of uplift force generated by turbulent pressure fluctuations in spillway stilling basins. Theoretical and experimental analyses are presented that define the magnitude and temporal evolution of the maximum uplift acting on the lining of such basins. Analyses for the dynamic behavior of anchored floor slabs are also investigated. It is concluded that the applicability of the equivalent thickness criterion based on the balance of the forces acting on the slabs in static condition is unsafe for anchored slabs, because this criterion yields an inadequate area for the anchor steel. The results lead to a recommendation to double the area of anchor steel as computed by the equivalent thickness criterion for the design of slabs in stilling basins

Numerical simulations of non-ergodic transport in natural formations

Tokio (Japan

Solute transport in highly heterogeneous aquifers

The paper deals with the transport of nonreactive solute in heterogeneous formations with prescribed statistical properties of the hydraulic log conductivity Y=ln K. Available solutions obtained from perturbation methods are limited to first- and second-order solutions, valid only for small values of the log conductivity variance \u3c32Y. Published numerical investigations give comparative results with finite values of \u3c32Y, but some discrepancies among the results generate doubts about the capability of numerical methods to capture high-order effects for media with large variance values. When these large \u3c32Y values are encountered in natural formations, the related nonlinear effects could be significant in the velocity statistics and in the overall dispersion process. The nonlinearity consequences are here investigated in two-dimensional isotropic porous media by the Monte Carlo technique coupled with a finite element analysis. The analysis includes \u3c32Y values from 0.05 to 4 enhancing the relevance of the nonlinear effects in the dispersion tensor solution. To dissipate the doubts related to the numerical approach, the accuracy of the solutions was defined by checking the influence of the factors which can affect the solution and by giving an estimation of the related errors. The numerical results confirm the validity of the first-order and second-order analyses when \u3c32Y \u2192 0; the second-order solution captures the nonlinear effects in a small range of log conductivity variance close to zero. The nonlinear terms neglected in the first-order formulation for higher \u3c32Y values give (1) late travel time longitudinal dispersion values greater than the linear solution, (2) notably non-Gaussian distribution of the Lagrangian velocity and particle displacements, and (3) travel times to approach the asymptotic Fickian regime longer than those obtained using the linear solution

Dispersion tensor evaluation in heterogeneous media for finite Peclet values

In natural formations the transport process at the local scale is characterized by the spatial heterogeneity of hydraulic conductivity and by the pore-scale dispersion. Usually, theoretical investigations consider only the effect due to the spatial variation of hydraulic conductivity, because the first prevails over the latter by some order of magnitude. Nevertheless, the pore-scale dispersion has a noteworthy impact on the concentration variance evaluation and on the ergodicity condition, so that its influence on the overall dispersion processes may be relevant. The note illustrates a theoretical procedure that allows one to define the global dispersion tensor at the local scale by taking into account the pore-scale effects as evaluated in laboratory columns. To reach this goal, the pore-scale and the local-scale velocity fluctuations are coupled via a rigorous analytical procedure in the three-dimensional (3-D) domain, and it is demonstrated that the porous media heterogeneity modifies the pore-scale dispersion effects as measured in laboratory columns. The impact of the hydraulic conductivity heterogeneity on the pore-scale dispersion at the local scale is due to (1) the path line sinuosity and (2) the module of the local velocity variation. A quantitative evaluation of these effects is made according to a first-order analysis, i.e., assuming that the spatial fluctuations of the hydraulic conductivity are small, and, in the 2-D case, a comparison with nonlinear results is made also. The results demonstrate that the only path line sinuosity coupled with the pore-scale anisotropy enhances the transversal mixing and reduces the longitudinal one, but the global heterogeneity effect, considering also the velocity module fluctuations, gives a generalized increase of the local dispersion tensor components

Studio dell'andamento temporale delle pressioni al fondo in un bacino di dissipazione a risalto

The paper deals with the statistical structure of temporal distribution of the turbulent pressure fluctuations at the bottom of the hydraulic jump, in order to define their influence on the stability of the linings in stilling basins. The researches into the statistical characteristic of the fluctuating pressure have been mainly limited to the study of the instantaneous spatial structure; recently, moving from these results, a design criterion for suitable floor slabs was presented. This criterion was made neglecting the inertia force in the instantaneous equilibrium of the forces acting on the slab. This assumption is corrected if the stability of the slab is assured by its weight only. In the case of slabs anchored with steel bars the inertial force must be considered in the instantaneous equilibrium of the slab since the force acting on the steel bars is proportional to the displacement of the slab. This force depends on the temporal distribution of the turbulent pressure also. Theoretical and experimental analyses are presented and the time of persistence of the pulsating pressure above a defined level and the maximum value of the pressure occurred in this time are defined. On the basin of these results, the limitations of the static criteria in the case of anchored structures are pointed out

Performance Assessment of Water Distribution Systems Subject to Leakage and Temporal Variability of Water Demand

A water distribution system (WDS) is designed and managed to provide a reliable water supply, that is, to properly respond towater user demand, particularly in critical operating conditions such as in times of peak demand. Therefore, the assessment of the influence ofwater demand characteristics is an essential requirement in the context of WDS reliability. In this paper the impact of the pattern of hourlydemand on WDS performance is analyzed for a system subject to aging processes and temporary pipe unavailability and affected by waterlosses with different leakage levels. The hydraulic deficit that can occur when the pressure falls below the minimum service value is used as aperformance index, and its relevance is analyzed without and with preventive maintenance. The case of the synthetic Anytown network isanalyzed, but the procedure has general validity and can be applied to any real WDS. Defined in a prescribed temporal horizon the pipereplacement prioritization without preventive maintenance, the effects of pipe substitutions are analysed as a function of different schedulingtimes to quantify the reduction of the hydraulic deficit. The results show the capability of the proposed approach to define a pipe replacementprioritization and the related scheduling time, in view of the relevance that these aspects could have in any economic analysis developed todefine a proper maintenance strategy