Particle Density Estimation with Grid-Projected Adaptive Kernels

The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk particle tracking (RWPT) simulations, particle density is directly linked to solute concentrations, which is normally the main variable of interest, not just for visualization and post-processing of the results, but also for the computation of non-linear processes, such as chemical reactions. Previous works have shown the superiority of kernel density estimation (KDE) over other methods such as binning, in terms of its ability to accurately estimate the "true" particle density relying on a limited amount of information. Here, we develop a grid-projected KDE methodology to determine particle densities by applying kernel smoothing on a pilot binning; this may be seen as a "hybrid" approach between binning and KDE. The kernel bandwidth is optimized locally. Through simple implementation examples, we elucidate several appealing aspects of the proposed approach, including its computational efficiency and the possibility to account for typical boundary conditions, which would otherwise be cumbersome in conventional KDE

Data assimilation of in situ soil moisture measurements in hydrological models: first annual doctoral progress report, work plan and achievements

Water scarcity and the presence of water of good quality is a serious public concern since it determines the availability of water to society. Water scarcity especially in arid climates and due to extreme droughts related to climate change drive water use technologies such as irrigation to become more efficient and sustainable. Plant root water and nutrient uptake is one of the most important processes in subsurface unsaturated flow and transport modeling, as root uptake controls actual plant evapotranspiration, water recharge and nutrient leaching to the groundwater, and exerts a major influence on predictions of global climate models. To improve irrigation strategies, water flow needs to be accurately described using advanced monitoring and modeling. Our study focuses on the assimilation of hydrological data in hydrological models that predict water flow and solute (pollutants and salts) transport and water redistribution in agricultural soils under irrigation. Field plots of a potato farmer in a sandy region in Belgium were instrumented to continuously monitor soil moisture and water potential before, during and after irrigation in dry summer periods. The aim is to optimize the irrigation process by assimilating online sensor field data into process based models. Over the past year, we demonstrated the calibration and optimization of the Hydrus 1D model for an irrigated grassland on sandy soil. Direct and inverse calibration and optimization for both heterogeneous and homogeneous conceptualizations was applied. Results show that Hydrus 1D closely simulated soil water content at five depths as compared to water content measurements from soil moisture probes, by stepwise calibration and local sensivity analysis and optimization the Ks, n and α value in the calibration and optimization analysis. The errors of the model, expressed by deviations between observed and modeled soil water content were, however, different for each individual depth. The smallest differences between the observed value and soil-water content were attained when using an automated inverse optimization method. The choice of the initial parameter value can be optimized using a stepwise approach. Our results show that statistical evaluation coefficients (R2, Ce and RMSE) are suitable benchmarks to evaluate the performance of the model in reproducing the data. The degree of water stress simulated with Hydrus 1D suggested to increase irrigation at least one time, i.e. at the beginning of the simulation period and further distribute the amount of irrigation during the growing season, instead of using a huge amount of irrigation later in the season. In the next year, we will further look for to the best method (using soft data and methods for instance PTFs, EMI, Penetrometer) to derive and predict the spatial variability of soil hydraulic properties (saturated hydraulic conductivity) of the soil and link to crop yield at the field scale. Linear and non-linear pedotransfer functions (PTFs) have been assessed to predict penetrometer resistance of soils from their water status (matric potential, ψ and degree of saturation, S) and bulk density, ρb, and some other soil properties such as sand content, Ks etc. The geophysical EMI (electromagnetic induction) technique provides a versatile and robust field instrument for determining apparent soil electrical conductivity (ECa). ECa, a quick and reliable measurement, is one of ancillary properties (secondary information) of soil, can improve the spatial and temporal estimation of soil characteristics e.g., salinity, water content, texture, prosity and bulk density at different scales and depths. According to previous literature on penetrometer measurements, we determined the effective stress and used some models to find the relationships between soil properties, especially Ks, and penetrometer resistance as one of the prediction methods for Ks. The initial results obtained in the first yearshowed that a new data set would be necessary to validate the results of this part. In the third year, quasi 3D-modelling of water flow at the field scale will be conducted. In this modeling set -up, the field will be modeled as a collection of 1D-columns representing the different field conditions (combination of soil properties, groundwater depth, root zone depth). The measured soil properties are extrapolated over the entire field by linking them to the available spatially distributed data (such as the EMI-images). The data set of predicted Ks and other soil properties for the whole field constructed in the previous steps will be used for parameterising the model. Sensitivity analysis ‘SA’ is essential to the model optimization or parametrization process. To avoid overparameterization, the use of global sensitivity analysis (SA) will be investigated. In order to include multiple objectives (irrigation management parameters, costs, …) in the parameter optimization strategy, multi-objective techniques such as AMALGAM have been introduced. We will investigate multi-objective strategies in the irrigation optimization

Modeling long term Enhanced in situ Biodenitrification and induced heterogeneity in column experiments under different feeding strategies

Enhanced In situ Biodenitrification (EIB) is a capable technology for nitrate removal in subsurface water resources. Optimizing the performance of EIB implies devising an appropriate feeding strategy involving two design parameters: carbon injection frequency and C:N ratio of the organic substrate nitrate mixture. Here we model data on the spatial and temporal evolution of nitrate (up to 1.2 mM), organic carbon (ethanol), and biomass measured during a 342 day-long laboratory column experiment (published in Vidal-Gavilan et al., 2014). Effective porosity was 3% lower and dispersivity had a sevenfold increase at the end of the experiment as compared to those at the beginning. These changes in transport parameters were attributed to the development of a biofilm. A reactive transport model explored the EIB performance in response to daily and weekly feeding strategies. The latter resulted in significant temporal variation in nitrate and ethanol concentrations at the outlet of the column. On the contrary, a daily feeding strategy resulted in quite stable and low concentrations at the outlet and complete denitrification. At intermediate times (six months of experiment), it was possible to reduce the carbon load and consequently the C:N ratio (from 2.5 to 1), partly because biomass decay acted as endogenous carbon to respiration, keeping the denitrification rates, and partly due to the induced dispersivity caused by the well developed biofilm, resulting in enhancement of mixing between the ethanol and nitrate and the corresponding improvement of denitrification rates. The inclusion of a dual-domain model improved the fit at the last days of the experiment as well as in the tracer test performed at day 342, demonstrating a potential transition to anomalous transport that may be caused by the development of biofilm. This modeling work is a step forward to devising optimal injection conditions and substrate rates to enhance EIB performance by minimizing the overall supply of electron donor, and thus the cost of the remediation strategy.Peer ReviewedPostprint (author's final draft

Hydrodynamic dispersion within porous biofilms

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport

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

Stochastic estimation of hydraulic transmissivity fields using flow connectivity indicator data

This is the peer reviewed version of the following article: [Freixas, G., D. Fernàndez-Garcia, and X. Sanchez-Vila (2017), Stochastic estimation of hydraulic transmissivity fields using flow connectivity indicator data, Water Resour. Res., 53, 602–618, doi:10.1002/2015WR018507], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/2015WR018507/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Most methods for hydraulic test interpretation rely on a number of simplified assumptions regarding the homogeneity and isotropy of the underlying porous media. This way, the actual heterogeneity of any natural parameter, such as transmissivity ( math formula), is transferred to the corresponding estimates in a way heavily dependent on the interpretation method used. An example is a long-term pumping test interpreted by means of the Cooper-Jacob method, which implicitly assumes a homogeneous isotropic confined aquifer. The estimates obtained from this method are not local values, but still have a clear physical meaning; the estimated math formula represents a regional-scale effective value, while the log-ratio of the normalized estimated storage coefficient, indicated by math formula, is an indicator of flow connectivity, representative of the scale given by the distance between the pumping and the observation wells. In this work we propose a methodology to use math formula, together with sampled local measurements of transmissivity at selected points, to map the expected value of local math formula values using a technique based on cokriging. Since the interpolation involves two variables measured at different support scales, a critical point is the estimation of the covariance and crosscovariance matrices. The method is applied to a synthetic field displaying statistical anisotropy, showing that the inclusion of connectivity indicators in the estimation method provide maps that effectively display preferential flow pathways, with direct consequences in solute transport.Peer ReviewedPostprint (published version