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

Inversion of multiconfiguration complex EMI data with minimum gradient support regularization: A case study

Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical for near-surface characterization in many fields of applications, for example, precision agriculture, pollution assessments, and shallow geological investigations. To this end, the inversion of either the real (in-phase) or the imaginary (quadrature) component of the signal has already been studied. Furthermore, in many situations, a regularization scheme retrieving smooth solutions is blindly applied, without taking into account the prior available knowledge. The present work discusses an algorithm for the inversion of the complex signal in its entirety, as well as a regularization method that promotes the sparsity of the reconstructed electrical conductivity distribution. This regularization strategy incorporates a minimum gradient support stabilizer into a truncated generalized singular value decomposition scheme. The results of the implementation of this sparsity-enhancing regularization at each step of a damped Gauss-Newton inversion algorithm (based on a nonlinear forward model) are compared with the solutions obtained via a standard smooth stabilizer. An approach for estimating the depth of investigation, that is, the maximum depth that can be investigated by a chosen instrument configuration in a particular experimental setting is also discussed. The effectiveness and limitations of the whole inversion algorithm are demonstrated on synthetic and real data sets

Final Report of the DAUFIN project

DAUFIN = Data Assimulation within Unifying Framework for Improved river basiN modeling (EC 5th framework Project

Geologically constrained joint inversion of hydraulic, tracer and ERT data for process visualization

Seawater intrusion (SWI) consists in the movement of seawater (SW) into freshwater (FW) aquifers, contaminating drinking water resources. SWI, along with the parallel reduction of Submarine Groundwater Discharge may lead to ecological impacts beyond the reduction of FW resources. Water salinity is the critical physical property to identify SWI. The salinity contrast between FW (~1g/L) and SW (35g/L) is high enough for salinity and, therefore, water electrical conductivity (ECw), to be indirectly measured using geophysical techniques such as geophysical logs (e.g. induction) or electrical and electromagnetic methods (e.g. electrical resistivity tomography, ERT). Although the context of SWI sounds ideal for the use of geophysics, ERT displays poor resolution in depth. We propose using cross-hole ERT (CHERT) to enhance resolution, placing the electrodes in depth along the boreholes. We tested it for the first time in a SWI context, at the Argentona experimental site, some 40 km NE of Barcelona. Results of the 2-years time-lapse CHERT monitoring showed that the use of CHERT and surface ERT increased the model resolution, and the bulk EC (ECb) values from CHERT were validated with induction logs from the site. We were able to image the seasonal fluctuations of groundwater flux that cause the SW-FW interface to move seawards during periods of high flux or landwards during periods of low flux; as well as the salinization of the aquifer due to an intense drought in the study area during the monitoring period. Two short-term events were also imaged: a decrease in ECb related to a heavy rain event, and an increase in ECb in the beach area related to storm surges. We built a hydrogeophysical model to characterize the Argentona site using all available data types. The model couples a density-dependent flow and transport simulator with a geoelectrical solver through a petrophysical relation. This model was calibrated by minimizing the misfit between observed and simulated hydraulic heads, salt concentrations and apparent ECb. The calibration was done on four time stages: a pseudo steady-state period, a model warm-up period for the introduction of time-varying boundary conditions, a calibration period covering the first year of the Argentona site monitoring, and a validation period covering the second year. The latter was used to assess the prediction capability of the models. The procedure allowed us to update the original conceptual model and demonstrate the importance of even the finest silt-rich layers. Then, three inverse problems were performed on the updated conceptual model: a) using the traditional point measurements of heads and salinity; b) adding the time variations of heads and the spatial differences of salinity to address common issues of using heads and salinity measurements taken from boreholes in coastal aquifers; and c) adding the apparent ECb from the time-lapse CHERT. We discuss the value of using time variations of heads, instead of only head absolute values; as well as on the use of spatial differences of salt concentrations. The model calibrated using all types of data (heads, salinity and ECb) had the best prediction capability and the model was able to reproduce the main events observed during the two years of monitoring of the Argentona site. Numerical dispersion prevents the model from simulating FW (0-1 g/L), which affects calibration. To tackle this issue, we propose to use an alternative conversion from water salinity to ECw that corrects for numerical dispersion when computing ECb. The methodology consists in applying and calibrating the error function to reduce salinity in the FW zone, and increase it in the SW zone. The error function calibration can also change the width of the FW-SW interface. This conversion improved the model prediction capability and led to a set of parameters less affected by numerical dispersion (e.g. estimated petrophysical parameters are within the expected range).La intrusión salina (SW) es el flujo de agua de mar (SW) hacia acuíferos de agua dulce (FW), contaminando las reservas de agua potable. La SWI, más la disminución de la Descarga de Agua Submarina, tiene impactos ecológicos más allá de la reducción del agua potable. La salinidad del agua es clave para identificar la SWI. El contraste entre el FW (~1g/L) y el SW (35g/L) es tan alto que la salinidad, y la conductividad eléctrica del agua (ECw), puede ser medida usando técnicas geofísicas como los sondeos (e.g. inducción) o los métodos eléctricos y electromagnéticos (e.g. tomografía de resistividad eléctrica, ERT). Aunque el contexto de la SWI suene ideal para el uso de la geofísica, la ERT tiene baja resolución en profundidad. Proponemos el uso de ERT entre pozos (CHERT) para mejorar la resolución, con los electrodos a lo largo de los piezómetros. Se ha testeado el CHERT por primera vez para la SWI en el sitio experimental de Argentona, a 40 km al noreste de Barcelona. Los resultados de los dos años de monitoreo muestran que el uso del CHERT y del ERT mejora la resolución del modelo, y los valores de la EC del medio (ECb) se validaron con los sondeos de inducción. Se logró visualizar las fluctuaciones temporales de los flujos de agua subterránea que causan que la interfaz FW-SW se mueva hacia el mar en periodos de alto flujo, o hacia el interior en periodos de bajo flujo; al igual que la salinización del acuífero debido a una sequía intensa en el área durante el periodo de monitoreo. Dos eventos de corta duración también se detectaron: una disminución en la ECb por un evento de lluvia intensa, y un aumento de la ECb en el área de la playa por las mareas de tormenta. Se construyó un modelo hidrogeofísico para caracterizar el sitio de Argentona usando todos los datos disponibles. El modelo acopla dos simuladores a través de una relación petrofísica: el de flujo y transporte con densidad variable y el de geoeléctrica. El modelo se calibró minimizando la distancia entre las medidas y las simulaciones de los niveles, las salinidades y las ECb aparentes. La calibración se hizo en cuatro periodos: uno pseudo-estacionario, uno de calentamiento que introduce las series temporales, uno de calibración que cubre el primer año de monitoreo, y uno de validación que cubre el segundo año. Este último fue usado para evaluar la capacidad de predicción de los modelos. El procedimiento nos permitió actualizar el modelo conceptual y demostrar la importancia de las capas de limo más finas. Luego, se resolvieron tres problemas inversos usando el modelo conceptual actualizado: a) usando las medidas tradicionales de niveles y de salinidad; b) añadiendo las variaciones temporales de nivel y la variación espacial de salinidad para hacer frente a la dificultad de usar los datos de nivel y salinidad tomados de pozos en acuíferos costeros; y c) añadiendo la ECb aparente del CHERT. Discutimos sobre el valor añadido de usar las variaciones temporales de nivel, en vez de únicamente los valores absolutos; así como sobre el uso de las diferencias espaciales de salinidad. El modelo calibrado usando todos los datos (niveles, salinidad y ECb) tuvo la mejor capacidad de predicción y es capaz de reproducir los principales eventos observados durante los dos años de monitoreo en el sitio de Argentona. La dispersión numérica evita que el modelo simule la zona de FW (0-1 g/L), afectando la calibración. Para esto, proponemos una conversión alternativa entre la salinidad y la ECw que corrige la dispersión numérica al calcular la ECb. El método consiste en aplicar y calibrar la función de error para reducir la salinidad del agua en la zona de FW, e incrementarla en la zona de SW. Esta calibración también puede cambiar el ancho de la interface FW-SW. La conversión mejoró la capacidad de predicción del modelo y llevó a obtener un conjunto de parámetros menos afectado por la dispersión numérica (e.g. parámetros petrofísicos estimados dentro del rango de valores esperados).Postprint (published version

Modeling water resources management at the basin level: review and future directions

Water quality / Water resources development / Agricultural production / River basin development / Mathematical models / Simulation models / Water allocation / Policy / Economic aspects / Hydrology / Reservoir operation / Groundwater management / Drainage / Conjunctive use / Surface water / GIS / Decision support systems / Optimization methods / Water supply

Numerical solution of the Richards equation based catchment runoff model with dd-adaptivity algorithm and Boussinesq equation estimator

This paper presents a pseudo-deterministic catchment runoff model based on the Richards equation model - the governing equation for subsurface flow. The subsurface flow in a catchment is described here by two-dimensional variably saturated flow (unsaturated and saturated). The governing equation is the Richards equation with a slight modification of the time derivative term, as considered e.g. by Neuman. The nonlinear nature of this problem appears in the unsaturated zone only, so it was possible to make use of adaptive domain decomposition algorithm. However delineating of the saturated zone boundary is a nonlinear computationally expensive issue. The simple one-dimensional Boussinesq equation was used here as a rough estimator of the saturated zone boundary. With this estimate the adaptive domain decomposition could always start with an optimal subdomain split, and thus it is now possible to avoid solving huge systems of linear equations in the initial iteration level. With this measure it is possible to construct an efficient two-dimensional pseudodeterministic catchment runoff model. Finally, the model is tested against real data originating from the Modrava 2 experimental catchment, Czech Republic