José E. Capilla

Joint simulation of transmissivity and storativity fields conditional to steady-state and transient hydraulic head data

Abstract The self-calibrated method has been extended for the generation of equally likely realizations of transmissivity and storativity conditional to transmissivity and storativity data and to steady-state and transient hydraulic head data. Conditioning to transmissivity and storativity data is achieved by means of standard geostatistical co-simulation algorithms, whereas conditioning to hydraulic head data, given its non-linear relation to transmissivity and storativity, is achieved through non-linear optimization, similar to standard inverse algorithms. The algorithm is demonstrated in a synthetic study based on data from the WIPP site in New Mexico. Seven alternative scenarios are investigated, generating 100 realizations for each of them. The differences among the scenarios range from the number of conditioning data, to their spatial configuration, to the pumping strategies at the pumping wells. In all scenarios, the self-calibrated algorithm is able to generate transmissivity–storativity realization couples conditional to all the sample data. For the specific case studied here the results are not surprising. Of the piezometric head data, the steady-state values are the most consequential for transmissivity characterization. Conditioning to transient head data only introduces local adjustments on the transmissivity fields and serves to improve the characterization of the storativity fields.

Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric head data—3. Application to the Culebra formation at the Waste Isolation Pilot Plan (WIPP), New Mexico, USA

The self-calibrated approach is applied to the stochastic analysis of groundwater flow and advective mass transport in the WIPP site. Multiple equally likely realizations of logtransmissivity fields are generated, followed by the solution of variable density groundwater flow and particle tracking. Five different cases have been analyzed. The first one regards the modeling of variable-density groundwater flow and the remaining four regard the generation of the logtransmissivity fields. Results show that (i) it is important to model variable-density flow as accurately as possible, (ii) conditioning to piezometric head data helps in reducing the uncertainty in flow and transport predictions, (iii) accounting for uncertainty in boundary conditions helps improving the match to measured heads, and (iv) the interpreted value at location P-18 is not consistent with the model of spatial variability inferred from the data.

Simulation of non-Gaussian transmissivity fields honoring piezometric data and integrating soft and secondary information

The conditional probabilities (CP) method implements a new procedure for the generation of transmissivity fields conditional to piezometric head data capable to sample nonmulti-Gaussian random functions and to integrate soft and secondary information. The CP method combines the advantages of the self-calibrated (SC) method with probability fields to circumvent some of the drawbacks of the SC method—namely, its difficulty to integrate soft and secondary information or to generate non-Gaussian fields. The SC method is based on the perturbation of a seed transmissivity field already conditional to transmissivity and secondary data, with the perturbation being function of the transmissivity variogram. The CP method is also based on the perturbation of a seed field; however, the perturbation is made function of the full transmissivity bivariate distribution and of the correlation to the secondary data. The two methods are applied to a sample of an exhaustive non-Gaussian data set of natural origin to demonstrate the interest of using a simulation method that is capable to model the spatial patterns of transmissivity variability beyond the variogram. A comparison of the probabilistic predictions of convective transport derived from a Monte Carlo exercise using both methods demonstrates the superiority of the CP method when the underlying spatial variability is non-Gaussian.

Significance of conditioning to piezometric head data for predictions of mass transport in groundwater modeling

Transmissivity and head data are sampled from an exhaustive synthetic reference field and used to predict the arrival positions and arrival times of a number of particles transported across the field, together with an uncertainty estimate. Different combinations of number of transmissivity data and number of head data used are considered in each one of a series of 64 Monte-Carlo analyses. In each analysis, 250 realizations of transmissivity fields conditioned to both transmissivity and head data are generated using a novel geostatistically based inverse method. Pooling the solutions of the flow and transport equations in all 250 realizations allows building conditional frequency distributions for particle arrival positions and arrival times. By comparing these fresquency distributions, we can assess the incremental gain that additional head data provide. The main conclusion is that the first few head data dramatically improve the quality of transport predictions.

Inverse Modeling of Groundwater Flow in a 3D Fractured Media

In order to quantify the uncertainty in the prediction of three-dimensional groundwater flow and mass transport in a fractured volcanic tuff, a Monte-Carlo approach is used. An ensemble of equally likely realizations of 3-D spatially variable hydraulic conductivity is generated and used as input to groundwater flow and advective transport model.To reduce the uncertainty in the model predictions, the hydraulic conductivity fields integrate different types of data. On one hand, they are conditioned to hydraulic conductivity measurements and soft information on hydraulic conductivities taken from a structural geology model. On the other hand, they are conditioned to piezometric head measurements. While conditioning to hard and soft hydraulic conductivity data can be achieved by standard geostatis-tical techniques, conditioning to hydraulic head measurements is non trivial because hydraulic conductivity and hydraulic head are non linearly related through the groundwater flow equation. Conditioning to hydraulic head measurements is accomplished by the self-calibrated method, a technique combining geostatistics and non-linear optimization. The methodology is demonstrated in a 3-D fractured site using data on conductivity and on transient heads from a pumping test. Ensembles of hydraulic conductivity realizations conditioned to different types of information are used as input to a groundwater flow and advective transport model; the resulting hydraulic head fields and particle arrival times are compared in terms of their variability to conclude that, for this case study, incorporating hydraulic head data reduces the uncertainty in the conductivity realizations, but it does not in particle arrival times and arrival locations.

Identification of Spatial Models of \(\updelta ^{18}\)O in Precipitation of the Wet Season Over Spain Using Genetic Algorithms

The isotopic content in precipitation is a function of climatological conditions at the site of occurrence and at the source of the water vapour. In hydrogeology, the spatial trend of \(\updelta ^{18}\mathrm{{O}}\) in precipitation allows to identify the areas of recharge and transit time. The explicative variables of the spatial trend of \(\updelta ^{18}\mathrm{{O}}\) in precipitation are geographical and climatological. A regression model to describe the spatial trend of \(\updelta ^{18}\mathrm{{O}}\) in precipitation can include these variables in a variety of terms: linear, quadratic, cubic, reciprocal or logarithm. The number of possible models is so large that it is impossible to apply traditional methods in order to select the best combination of variables. However, it is possible to apply soft-computing techniques (genetic algorithms) for stochastic optimization in regression problems with a large number of variables. A modified fitting function is used in order to account for the parsimony principle and the goodness of fitness. The optimal models identified will allow a mapping of the spatial trend of \(\updelta ^{18}\mathrm{{O}}\) in precipitation of the wet season and it will help to characterize the water resources.

LOS SISTEMAS SOPORTES DE DECISION EN LA PLANIFICACION Y GESTION RACIONALES DE LOS RECURSOS HIDRICOS

La utilizacion racional del agua implica una gestion eficiente, integral y sostenible del recurso. Los sistemas de recursos hidricos y las soluciones para aliviar sus problemas son cada vez mas complejos. Por consiguiente, a efectos de analizar los sistemas de forma integrada y de abordar incertidumbres clasicas relacionadas con los usos, demandas o recursos, asi como nuevos temas tales como impactos de posibles cambios climaticos, sera necesario utilizar herramientas tecnologicamente avanzadas. El desfase existente actualmente entre el estado del arte del analisis de sistemas de recursos hidraulicos y la practica cotidiana de la toma de decisiones en el mundo real puede y debe reducirse. La factibilidad y realidad de este proceso es demostrada en este articulo, en el que se describe un sistema soporte de decision para recursos hidricos, que esta siendo utilizado en la actualidad en la Confederacion Hidrografica del Segura para responder a cuestiones enfocadas al uso racional del agua. Despues de una breve descripcion de la problematica de la cuenca, se llega a la conclusion de que, en sistemas tan complejos, el uso de herramientas como la que se describe es, mas que algo conveniente, la unica posibilidad de analizar con exito la planificacion y las politicas de gestion del sistema, obteniendo una idea del rendimiento y de la fiabilidad del mismo. El sistema soporte incluye dos modulos principales: un modulo para la optimizacion de esquemas de sistemas de recursos, y un modulo para la simulacion de la gestion de dichos sistemas incluyendo el uso conjunto de aguas superficiales y subterraneas. La creacion de esquemas y la introduccion de datos, asi como el analisis de resultados, se ven facilitados por interfases y postprocesadores graficos interactivos. La aplicacion de estas herramientas en una cuenca tan compleja como la del Segura tiene a su vez un efecto de promocion de su uso en otras cuencas, confirmando que, bajo ciertas condiciones, herramientas tecnologicamente avanzadas pueden ser usadas y aceptadas en la practica cotidiana de la planificacion y gestion hidrologicas.