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Inverse modeling of groundwater flow in the semiarid evaporitic closed basin of Los Monegros, Spain F. J. Samper-Calvete 7 M. A. García-Vera

Abstract Only minor attention has been given in the past to the study of closed-basin hydrogeology in evaporitic environments, because these basins usually contain poor-quality groundwater. The motivation for hydrogeological research in the Los Monegros area in northeastern Spain was the approval in 1986 of a large irrigation project in the Ebre River basin. The irrigation of 60,000 ha is planned, partly in an evaporitic closed basin containing playa lakes. The project has given rise to environmental concerns. The evaluation of the hydrologic impacts of irrigation requires quantifying properly the hydrogeology of the area. With the available information, a conceptual hydrogeological model was formulated that identifies two main aquifers connected through a leaky aquitard. On the basis of the conceptual model, a numerical model was calibrated under steady-state conditions using the method of maximum-likelihood automatic parameter estimation (Carrera and Neuman, 1986a). The calibrated model reproduces the measured hydraulic heads fairly well and is consistent with independent information on groundwater discharge. By the solution of the inverse problem, reliable parameter estimates were obtained. It is concluded that anisotropy plays a major role in some parts of the lower aquifer. The geometric average of model conductivity is almost two orders of magnitude larger than the average conductivity derived from small-scale field tests. This scale effect in hydraulic conductivity is consistent with the findings of Neuman (1994) and Sánchez-Vila et al. (1996).

cherches hydrogéologiques dans la région de Los Monegros, dans le nord-est de l’Espagne est dû à l’approbation en 1986 d’un vaste projet d’irrigation dans le bassin de l’Ebre. L’irrigation de 60 000 ha a été programmée, en partie dans un bassin évaporitique fermé où existent des lacs de playa. Le projet a fait émergé des préoccupations environnementales. L’évaluation des impacts hydrologiques de l’irrigation implique de quantifier correctement l’hydrogéologie de cette région. A partir des informations disponibles, un modèle hydrogéologique conceptuel a été établi; il identifie deux aquifères principaux interconnectés par drainance au travers d’un imperméable. Un modèle numérique, établi sur la base de ce modèle conceptuel, a été calibré en conditions de régime permanent, en utilisant la méthode d’estimation automatique du maximum de vraisemblance des paramètres (Carrera and Neuman, 1986a). Le modèle calibré reproduit correctement la piézométrie mesurée et est en accord avec les informations concernant l’écoulement des nappes. La résolution du problème inverse a fourni des estimations acceptables des paramètres. On en a conclu que l’anisotropie joue un rôle essentiel dans certaines parties de l’aquifère inférieur. La moyenne géométrique de la conductivité hydraulique est d’environ deux ordres de grandeur plus élevée que la conductivité hydraulique moyenne obtenue par des essais de terrain à l’échelle locale. Cet effet d’échelle sur la conductivité hydraulique est conforme aux résultats obtenus par Neuman (1994) et Sánchez-Vila et al. (1996).

Résumé Dans le passé, on s’est peu intéressé à l’hydrogéologie des bassins fermés en milieu évaporitique, parce que ces bassins possèdent en général de l’eau souterraine de qualité médiocre. L’intérêt porté aux re-

Resumen La hidrogeología de zonas endorreicas en zonas evaporíticas ha recibido muy poca atención en el pasado debido fundamentalmente a que en estas zonas las aguas subterráneas tienen una elevada salinidad debido a la alta solubilidad de sus materiales. El interés por la hidrogeología de la zona de Los Monegros en el noreste de Espanã surgió a raiz de la aprobación en 1986 del proyecto de Los Monegros II en la zona central del valle del Ebro que contempla la puesta en regadío de 60,000 ha, algunas de las cuales se encuentran situadas en la zona endorreica de Los Monegros en la que existen toda una serie de lagunas salinas. La implantación del regadío en esta zona puede alterar el régimen hidrológico de las lagunas, provocar problemas de salinización de suelos y aguas y aumentar la salini-

Received, December 1997 Revised, December 1997 Accepted, January 1998 F. J. Samper-Calvete (Y) Escuela de Ingenieros de Caminos, Universidad de la Corunã, Campus de Elvinã, s/n, E-15192 La Corunã, Spain Fax: c34-8-110-2876 e-mail: samper6iccp.udc.es M. A. García-Vera P o Constitución 37, 30, E-50001 Zaragoza, Spain Hydrogeology Journal (1998) 6 : 33–49

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dad del río Ebro. Con el fin de evaluar estos efectos se construyó un modelo numérico del flujo subterráneo. Con la información disponible se pueden distinguir dos acuíferos que están conectados mediante un acuitardo. El modelo de flujo se calibró en régimen estacionario utilizando el procedimiento de calibración automática de Carrera y Neuman (1986a) basado en el método de la máxima verosimilitud. El modelo finalmente calibrado es capaz de reproducir los niveles piezométricos medidos y es coherente con los resultados de los balances hidrológicos en las lagunas. La conductividad hidráulica media del modelo es superior en casi dos órdenes de magnitud a la media de las conductividades hidráulicas obtenidas en ensayos de campo a escala local. Este efecto de escala en la conductividad hidráulica es coherente con los resultados de Neuman (1994) y Sánchez-Vila et al. (1996) y confirma que dicho efecto también se observa en medios evaporíticos. Key words inverse modeling 7 numerical modeling 7 Salinization 7 salt-water/fresh-water relations 7 Spain

Introduction Salt lakes in closed basins have been studied by hydrochemists and sedimentologists in many parts of the world (Eugster and Hardie 1978; Smoot and Lovenstein 1991). Some of the largest and best-known closed basins include those of Australia (Bowler 1986; Jacobson et al. 1988) and those in the southwestern parts of the U.S. (Lines 1979; Osterkamp and Wood 1987; Senger et al. 1987; Duffy and Al-Hassan 1988; Senger 1991; Scanlon and Goldsmith 1997). The role of groundwater discharge on the chemistry of salt lakes and the type and thickness of lake deposits has been studied by Sanford and Wood (1991). Closed-basin hydrogeology in evaporitic environments has traditionally received little attention because these basins usually contain poorquality groundwater (Lines 1979). This trend has changed recently. In some cases, such basins are being studied for their potential suitability to host hazardous wastes (Bath et al. 1985; Senger et al. 1987; Senger 1991; Wooding et al. 1997). In other cases such as that in Los Monegros, Spain, they contain unique ecological systems associated with salt lakes and playa lakes (Balsa et al. 1991). To some extent, closed-basin hydrogeology resembles groundwater flow in coastal aquifers (Herbert 1988; Duffy and Al-Hassan 1988). Many aspects of seawater intrusion also take place near salt lakes in closed basins (Samper and García-Vera 1993). Playa lakes are commonly considered to be groundwater discharge areas (Duffy and Al-Hassan 1988). However, the recent experimental observations of Scanlon and Goldsmith (1997) in some playas at a site in the Southern High Plains (U.S.) indicate that playa lakes focus groundwater recharge. According to Wooding et al. (1997), convective downward groundwater motion can be generated in aquifers beneath playas, depending Hydrogeology Journal (1998) 6 : 33–49

Fig. 1 Location of study area

on the value of the Rayleigh number, a dimensionless number mainly controlled by aquifer permeability and evaporation rate from the lake. The motivation for hydrogeological research in Los Monegros area in northeastern Spain was the approval in 1986 of a large irrigation plan. This plan envisions the irrigation of 60,000 ha, some of which are located in an evaporitic closed-basin area with a shallow water table and abundant playa lakes. Locations are shown in Figure 1. A large part of this area is presently a cereal dry farming zone. Possible adverse effects of irrigation include: (a) soil salinization caused by rising water table; (b) extensive flooding of playa lakes and surface depressions; and (c) a significant increase of the Ebre River salinity, which would produce considerable damage downstream. In order to evaluate these effects, several studies were undertaken by various Spanish agencies and organizations (see García-Vera 1996). Berga (1993) conducted a climatological and hydrological study in this area and analyzed the solubility of the sediments. A systematic hydrogeological program of field activities was conducted by IRYDA (“Instituto para la Reforma y Desarrollo Agrario”; unpublished data) which included: (a) drilling of research boreholes; (b) conducting various field tests; and (c) collecting water samples for chemical and isotopic analyses. Samper et al. (1992) proposed preliminary conceptual hydrogeological models for this closed-basin area. García-Vera (1996) compiled all the available data and conducted additional geological, hydrodynamic, chemical, and isotopic surveys during 1991–94. In his dissertation he interpreted all these data by means of numerical models. The work presented here is a summary of his inverse quasi three-dimensional groundwater flow model for the closed-basin evaporitic area of Los Monegros. A description of the study area is presented first. Then, the main hydrogeological, hydrochemical and isotopic aspects, which form the basis for the conceptual model, Q Springer-Verlag

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are also presented. The details of the numerical model and the calibration process are provided, and the calibrated models for both the isotropic and anisotropic cases are described.

Description of Study Area The study area is near the centre of the Ebre River basin, approximately 60 km east of Zaragoza in northeastern Spain (Fig. 1). The area covers 200 km 2. Originally, the area was vegetated by brush and trees called “monegros,” which, however, were cut down centuries ago for timber and heating. The closed-basin area of Los Monegros contains almost 100 topographic depressions, 33 of which are small playa lakes and dry salt lakes (Balsa et al. 1991). The largest playa lake, locally known as La Playa, occupies approximately 2 km 2 and has a drainage basin of 25 km 2. Some playa lakes contain water only during wet periods. The water table is shallow near the topographic lows of these lakes, thereby allowing water to evaporate from the capillary fringe. The area is underlain by evaporite-bearing sediments that contain lacustrine limestones alternating with marl and gypsum layers. The geology is shown in Figure 2. According to previous studies (Quirantes 1978; IRYDA, unpublished data), the origin of the depressions is related to gypsum karst dissolution fol-

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lowed by collapse. Dissolution of gypsum layers was favored by water infiltrating preferentially along a system of faults. Surface elevation ranges from 320 m.a.s.l. at the bottom of the lakes to 360 m at the highest point in the study area. The climate is semiarid with an average temperature of 14 7C. The average annual rainfall is 360 mm but shows large annual variations. Most rainfall takes place during early spring and in the fall. Strong winter winds, together with high summer temperatures, cause high evapotranspiration rates. Surface runoff is sporadic and is less than 10% of the rainfall. Crude groundwater recharge estimates based on daily soil–water balance methods range from 20–45 mm/year (Samper et al. 1992).

Fig. 2 Geological map of Los Monegros closed-basin area; 1 red lutite with sandstone paleochannels; 2 green and red lutite with intercalations of gypsum and limestone; 3 limestone and marly limestone with intercalations of lutite; 4 gypsum and limestone with intercalations of lutites; 5 red lutite with intercalations of limestone, gypsum, and sandstone; 6 gypsum and limestone with intercalations of lutite; 7 red lutite; 8 lutite and limestone with thin intercalations of gypsum; 9 lutite and gypsum with thin intercalations of limestone

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Hydrogeologic Framework Hydrogeology The closed-basin area of Los Monegros is part of the Ebre River basin, which is underlain by limestone, marl, gypsum, and lutites of late Oligocene and early Miocene age. Toward the east, the units thin out near the Valcuerna Valley (see Fig. 2). Hydrogeological sections are shown in Figure 3. On the west, the boundary coincides with the Retuerta Formation, which is composed of gypsum silts. Both the northern and the southern boundaries coincide with abrupt changes in topography. At the interfluves between the depressions, the water table rarely exceeds 10 m in depth. Groundwater discharges to lakes and depressions, where it evaporates, and along the eastern and southern boundaries in a manner that is not well understood. Valcuerna Creek shows increased flow and salinity in the area (GarcíaVera et al. 1991). Three lacustrine units were identified (lower, intermediate, and upper). In all three units the gypsum content increases toward the west (Fig. 2). The upper and intermediate lacustrine units are separated by a thin lutitic layer (5–10 m), which is continuous over much of the basin. It forms the bottom boundary of an upper aquifer that contains lutitic limestones with some interbedded gypsum layers. The latter contains only a few lakes in the north, near the village of Bujaraloz (Fig. 2). The intermediate lacustrine unit contains gypsum and limestone with intercalations of lutite. Its

thickness decreases progressively to the west, where most lakes associated with this unit are located. The unit is a leaky aquifer in the northern part and a watertable aquifer in the southern part where the upper lacustrine unit is absent (Fig. 3). The northern boundary of the leaky aquifer coincides with a set of narrow creeks. On the south, the aquifer crops out at the surface. Given a lack of data in the northwest, a no-flow boundary is imposed in the model along the water divide. Underlying the intermediate lacustrine unit is a low-permeability lutitic layer that confines the lower lacustrine unit. Hydrochemical and isotopic data from a deep borehole (see borehole 418 in section E in Fig. 3) indicates that, under natural conditions, leakage between the intermediate and lower units is negligible (García-Vera 1996). Most hydrogeological and hydrochemical data were collected in: (a) 24 shallow boreholes, which include 7 of 12 m depth (the so-called 300 series) and 17 of 18 m depth (400 series); (b) a deep borehole of 120 m depth; (c) 43 shallow dug wells of large diameter; (d) 13 shallow well points (of less than 2 m depth) located mostly near the bottom of depressions and playa lakes; and (e) 20 playa lakes. Data on hydrodynamic parameters were derived from pumping and slug tests carried out at boreholes of the so-called 300 and 400 series, most of which were drilled near the largest surface depression (Pozo Agustín) for the purpose of evaluating its potential to act as an evaporation lake for agricultural drai-

Fig. 3 Hydrogeological sections across the Monegros closed-basin area. Lines of section shown in Figure 2


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nage waters. Hydraulic conductivity (K) ranges from 1.4!10 –6 to 10.4 m/d with a geometric average of 0.013 m/d. The lowest values may entail large estimation errors. In some cases variations in pumping rates and wellbore-storage effects complicated the interpretation of some field tests. In general, K is lower than 0.01 m/d at the interfluves. The largest K values were obtained in boreholes located at the bottoms of topographic depressions. This was attributed to the fact that depressions contain shallow unconsolidated detritic sediments. They additionally tend to coincide with fracture zones along which gypsum karst development has led to the formation of permeable pathways. A pumping test with multiple observation points was performed in borehole 413, located at the bottom of the largest dry depression, Pozo Agustín (see Fig. 3). The test indicated a transmissivity anisotropy ratio of 10 and a storage coefficient of 0.023. Additional field tests were carried out to better understand the observed increase in salinity with depth at some boreholes. At five of them, detailed pumping tests were carried out, during which drawdowns and electrical conductivity of pumped water were recorded. Electrical conductivity and temperature logs were performed during the recovery stage. From the interpretation of drawdown data, García-Vera (1996) obtained estimates of transmissivities for the whole saturated thickness. From the analysis of electrical-conductivity data, he concluded that almost 75% of the pumped water was provided by the upper aquifer.

Hydrochemistry, Isotopes, and Salinity Several chemical surveys were carried out from 1988 to 1993. Samples were collected at 50 large-diameter shallow dug wells, 23 shallow piezometers and also at a few lakes and well points located near the bottoms of lakes. The largest salinities occur near the bottoms of depressions. Groundwater is typically of the magnesium-sulfate or calcium-sulfate type with an average TDS (total dissolved solids) of 5 g/L. The mean ratio rCl/rNa (rpmeq/L) is about 1, whereas that of r(SO4cHCO3)/ rCa is greater than 1. The average magnesium content exceeds 40 meq/L. Wells collecting some surface runoff have fresher waters, in which calcium exceeds magnesium. Samples from wells near the lakes have much higher salinities (up to 30 g/L) and are of the magnesium–sodium–sulfate–chloride type. Groundwater is saturated with respect to calcite and generally also with respect to gypsum. Groundwater chemistry is controlled by dissolution of soluble sediments (mainly gypsum and limestone) and evaporation in areas of shallow water table. The salinities and chemical composition of the lakes depend on their size and hydrological regime and show large seasonal variations. The mean of 139 samples is approximately 118 g/L. Salinities as great as 200 g/L have been measured in waters of the sodium-chloride type, accompanied by significant quantities of magneHydrogeology Journal (1998) 6 : 33–49

sium and sulfate. Samples from shallow well points near the lakes have stable chemistry with time; their average salinity is similar to that of the lakes. In perennial and ephemeral lakes as well as in other depressions, surface and phreatic waters evaporate to cause high salinity, changes in chemical composition, and variations in fluid density. Samper et al. (1993) reported the results of the interpretation of environmental isotopic data ( 18O, 2H, and 3 H). The analysis of stable isotopes indicates that rainwater from intense storms infiltrates and produces runoff that collects at the bottoms of depressions, directly or through interflow. The scarce vegetative cover, large fraction of arable land without crops during rainfall events, and water ponding cause isotope fractionation through surface soil-water evaporation. No identifiable isotopic evolution of groundwater occurs along conjectured flow paths. This is due to large spatiotemporal variations in recharge. Water electrical-conductivity logs in eight boreholes show sharp increases in salinity with depth. Results are shown in Figure 4. Water at shallow depths usually contains magnesium-sulfate at an average salinity of 6 g/L, similar to that of shallow wells. Water at greater depths is more saline and of the sodium–magnesium–sulfate–chloride type; salinities range from 10–60 g/L. Isotopic analyses conducted at both sides of the interface indicate that water at shallow depths contains measurable quantities of tritium, and that tritium content at greater depths is nearly zero. The lack of significant isotope fractionation in the deeper samples indicates that the sharp increase in salinity is not attributable to evaporation (Samper et al. 1993). Three possible hypotheses have been postulated for this vertical salinity stratification. One hypothesis postulates the existence of a shallow layer of large permeability above 320 m.a.s.l., within which most groundwater flow takes place; permeability at greater depths is at least one order of magnitude smaller, according to the results of pumping tests. Slow groundwater movement at these depths leads to longer residence times, which is consistent with the lower observed tritium contents, and to dissolution of highly soluble salts. Another hypothesis postulates the existence of a fresh-salt water boundary near salt lakes. Numerical analyses of variable-density effects carried out by Samper et al. (1993) with the SUTRA code (Voss 1984) using the conceptual model of Duffy and Al-Hassan (1988) show that the length of the salt wedge around salt lakes is very sensitive to areal recharge, layering, and vertical variations in hydraulic conductivity. For plausible recharge and conductivity values, the wedge extends at most 1 km from the lake. Most of the chemical, isotopic, and salinity logs were collected in an area where surface depressions are mostly dry. These data indicate that the high salinities observed in deep zones are not caused by evaporation. No data on vertical salinity variations are available near the playas. Therefore, it is concluded that density-driven flow is a local effect that may be imQ Springer-Verlag

38 Fig. 4 Electrical-conductivity logs at three boreholes

portant in the vicinity of the playas, but cannot fully explain the observed regional salinity stratification. A third hypothesis postulates a nearly horizontal interface within the currently saturated zone, and this boundary separates (a) an upper part, from which highly soluble salts have been leached by an increased groundwater flow (caused by changes in the vegetation cover centuries ago, which could have induced an increase in areal recharge); from (b) a lower part, still not leached. Although appealing, this hypothesis is just a conjecture, because little is known about historical changes in land use. Modeling, discussed below, strongly supports the first hypothesis.

Numerical Model The evaluation of the environmental effects of irrigation in Los Monegros closed basin requires quantifying properly the hydrogeology of the area. Constructing a Hydrogeology Journal (1998) 6 : 33–49

numerical model for groundwater flow permitted an integration of all the available pieces of information. Once calibrated, the model was used to predict the main hydrological effects of irrigation for various crops and irrigation practices.

Computer Code The numerical model is based on the quasi-three-dimensional finite-element TRANSIN-II code (A. Medina et al., unpublished data), which solves both direct and inverse groundwater problems using the maximum likelihood automatic parameter-estimation method of Carrera and Neuman (1986a). This code allows modeling groundwater flow in layered three-dimensional systems by assuming horizontal flow in aquifers and vertical flow through aquitards. As part of the solution of the inverse problem, the code computes the values of several model identification criteria (Akaike, modified Akaike, Hannan, and Kashyap), which were developed in the context of maximum likelihood estimation (deQ Springer-Verlag

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tails are in Carrera and Neuman 1986a). These criteria were developed in the context of time-series analysis, and they penalize one for increasing the number of estimated parameters. They were tested by Carrera and Neuman (1986b) to distinguish among alternative parameterizations of transmissivities in dealing with aquifer inverse problems, and by Samper and Neuman (1989) in the context of estimation of spatial covariance functions. Their results indicate that these criteria are able to identify the correct model structure and that Kashyap’s criterion is best among those mentioned, because it not only always identifies the correct model but is also the most sensitive to the quality of the data. These criteria were used in Los Monegros model to test the hypothesis about the anisotropic behavior of hydraulic conductivities.

Conceptual Model Extensive hydraulic-head surveys in the whole area and monthly head measurements at selected boreholes were conducted by Berga (1993) and García-Vera (1996). The analysis of hydrographs indicates that time variability in hydraulic heads (approximately a few metres) is small compared with spatial variations (approximately several tens of meters). For this reason, groundwater flow can be analyzed as steady state. Most

flow seems to occur in the upper and intermediate lacustrine units, which have average hydraulic properties of aquitards but contain permeable preferential flow channels that justify treating them as aquifers. The upper unit is a water-table aquifer (facies nos. 8 and 9 in Fig. 2); the intermediate lacustrine unit forms a leaky confined aquifer in the north and a phreatic aquifer in the south (Fig. 3). In the north, the two aquifers are separated by a lutitic aquitard (facies no. 7 in Fig. 2).

Discretization and Parameterization Flow in both aquifers is assumed to be predominantly horizontal and is represented by two-dimensional finite-element grids of 572 and 1787 triangles, respectively, as shown in Figure 5. Flow through the aquitard is simulated by means of 1038 vertical one-dimensional elements, which connect the nodes of the top and bottom aquifer grids. Following the approach proposed by Carrera and Neuman (1986a), which was applied to an alluvial aquifer by Samper et al. (1990), model parameters are assumed to be constant within contiguous sets of elements called zones. Initial zones were defined based on the available hydrogeological information. During calibration, the number and outline of zones were modified to minimize the residual sum of squared difference between computed and measured heads at observation

Fig. 5 Finite-element grids used for Los Monegros model. Top upper aquifer; bottom lower aquifer


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40 Fig. 6 Hydraulic-conductivity zones of the upper aquifer (top) and lower aquifer (bottom)

points. Parameters of relevance under steady-state flow conditions include hydraulic conductivity, K; areal recharge, r; hydraulic heads, H, specified along boundaries; a parameter, a, which relates flux across a boundary to the corresponding head differential; and associated external heads, He. The number of conductivity zones increased from five to ten during calibration. The distribution of zones is shown in Figure 6. Areal recharge was assumed to be uniform throughout the study area, except in some calibration and sensitivity runs in which three zones with different recharge values were defined by considering variations in topographic slopes. Model results for the two cases were similar. Shallow well points near the lakes indicate an average depth to water of 1 m below the surface. Accordingly, salt lakes and playas were treated as upper fixedhead boundaries. To keep the number of parameters as low as possible, only the 13 largest lakes were included in the model. Their elevations were estimated from available topographic maps with an error of up to 5 m. A no-flow lateral boundary condition was imposed along the western water divide. The remaining lateral boundaries were of the mixed Cauchy type with flux, q (L 2T –1), given as the product of a leakage factor, a (LT –1), and the difference between head in the aquifer and head, He, outside the boundary; He was set equal to the elevation of the bottom of the aquifer. The numHydrogeology Journal (1998) 6 : 33–49

ber of a zones increased from two to eight during calibration.

Model Calibration Model calibration as practiced here is a process by which the structure and parameters of a numerical model are progressively changed in an iterative manner so as to obtain an acceptable match between observed and computed hydraulic heads, while maintaining consistency with prior information concerning model parameters and departing as little as possible from the original conceptual model. Head measurements were assigned a prior estimate of their standard deviation, which was equal to 1 m for most of the head data. A larger value of 2 m was assigned to five measurements that were thought to be less accurate. In addition to fitting hydraulic heads, calibration was based on the following criteria: 1. Computed discharges to the lakes should be consistent with prior estimates derived from lake water budgets and evaporation studies. The total maximum evaporative discharge into the 13 lakes was estimated to be 22,100 m 3/d (García-Vera 1996). Model configurations that provided lake discharges much greater than this value were discarded. 2. Given the absence of springs along the periphery of the study area, groundwater discharge along mixedQ Springer-Verlag

41 Table 1 Model structure and calibration results obtained at different calibrations stages Calibration stage

Number of zones K

Preliminary Isotropic Anisotropic

5 10 10

a

2 8 8

He

10 13 13

No. of estimated parameters

3K; 2a 7K; 8a 8K; 8a

No. of head measurements

70 66 66

type boundaries should be within the range of maximum potential evapotranspiration rates. A crude estimate of discharge along these boundaries, which extend over 147 km, ranges from 6550–9050 m 3/d (Berga 1993; García-Vera 1996). 3. Computed water levels should always stand below the topographic surface. The available topographic map (1 : 50,000 scale) was digitized and used to assign elevation data to the nodes of the finite-element grid representing the water table. From computed heads and topographic elevation, contour maps of water-table depth were prepared for all calibration runs. Modifications in model structure and parameters were introduced whenever the computed water table was above the ground surface. 4. Estimated hydraulic conductivities should be consistent with conductivities derived from field tests. 5. The spatial patterns of parameters should be consistent with available geological information. 6. The anisotropic behavior of hydraulic conductivities, for which there is no direct evidence, was tested using the model identification criteria mentioned previously. Calibration proceeded in three stages. The purpose of the first stage was to: (a) de-bug input data errors: (b) check and verify pre- and post-processing procedures; (c) filter out unreliable head data; (d) adjust the values of specified heads; and (e) perform preliminary sensitivity analyses of hydraulic heads with respect to the most uncertain model parameters for which prior information was lacking, namely, conductivities of the lutitic layer and confined part of the lower aquifer. The structure of the model during this initial calibration stage was kept simple, with five K zones, two a zones, and ten He zones. Areal recharge was uniform and equal to 20 mm/y. The objective function (the weighted sum of squared residuals) was 4115 m 2. The root mean square error of 70 head measurements was approximately 7 m. Table 1 summarizes the main features of the structure of the model, as well as the values of the objective function and the four model-identification criteria. The resulting head residuals in the southern part of the lower aquifer were too large, indicating the need to rezone this area of the model, and computed heads and fluxes were very sensitive to the vertical conductivity of the lutitic layer, which controls the amount of vertical Hydrogeology Journal (1998) 6 : 33–49

Objective functions (m 2)

4115 376.5 275.4

Model-identification criteria (Carrera and Neuman 1986a) Akaike

Modified Akaike

Hannan

Kashyap

523.5 396.8 375.6

535.1 432.7 414.1

528.1 411.2 391.1

551.2 446.6 428.9

leakage between aquifers. Leakage was inconsequential when this conductivity was smaller than 10 –5 m/d and was directed downward when the conductivity increased beyond 10 –4 m/d.

Isotropic Model Most of the modeling effort took place during the second calibration stage. Changes were introduced in a stepwise manner. In the first step, the following changes were considered: 1. Two additional K zones were defined. The upper aquifer was assigned a different K zone from that used for the unconfined part of the lower aquifer. The latter was split into two additional K zones. The westernmost zone (zone 3 in Fig. 6) corresponds to the area where most surface depressions are located. 2. The vertical conductivity of the lutitic layer was assigned a value of 10 –8 m/d to prevent large leakage between the two aquifers; leakage would not be consistent with the results of a dilution test carried out by García-Vera (1996) in borehole 415, in which no measurable vertical flow was observed. 3. Three additional small lakes were incorporated as internal fixed head boundaries. 4. The geometry of the external boundary of the upper aquifer was slightly modified along its western edge. 5. Head data from two wells were excluded and four others were assigned a greater standard deviation of 2 m, because they were affected by sporadic inflows of surface runoff into the wells. 6. Measured hydraulic heads at boreholes intersecting both aquifers provide an average potentiometric head in the two aquifers. To compare such measurements with computed heads, the two nodes coinciding with borehole locations (one in each aquifer) were connected by means of a dummy one-dimensional element to a dummy node. The vertical conductivity of such dummy elements was assigned an arbitrarily small value to prevent a significant flux along such dummy connections. Under these conditions, the computed head at the dummy node represents the average of the heads at the upper and lower aquifers. These connections were implemented in five boreholes. Q Springer-Verlag

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With these changes, the inverse problem was solved by estimating the values of five K zones and two a zones. For a total of 68 head data, the objective function was 2552 m 2. This significant reduction in head residuals was achieved mainly by an improvement in the geometry of parameter zones. The analysis of computed head maps and boundary fluxes indicated that computed discharges into some depressions (such as Benamud and Pozo Agustín in Fig. 3) were too large. In fact, these discharges were greater than that computed for the largest playa lake of the area (La Playa Lake). Those two depressions collected much of the discharge of the southern and eastern parts of the lower aquifer, where computed heads were systematically lower than expected, therefore leading to some unrealistic results, such as some salt lakes acting as recharge areas. Discrepancies were also detected in the northernmost salt lake of the upper aquifer, which collected much of the discharge of the upper aquifer. The analysis of head residuals revealed that three boreholes, which were thought to intersect the lower aquifer, in fact, tap mostly the upper aquifer. Their head measurements were subsequently assigned to the upper aquifer. To improve the model structure for the southern part of the lower aquifer, the unconfined part of this aquifer was split into three K zones (zones 3, 7, and 9 in Fig. 6). With these changes, the objective function decreased significantly to 1690 m 2. Although encouraging, the results of this run provided a poor representation of the water table at the southeastern corner of the study area. Available head data indicate that this area should be a discharge area, whereas in the model this area received noticeable water inflows. To ensure groundwater discharge in this area, three additional a zones were defined for the lower aquifer. The spatial distribution of head residuals also revealed the need to modify slightly the limits of some K zones. In the following calibration trial, an additional K zone was defined for the upper aquifer (zone 10 in Fig. 6). The definition of two conductivity zones in the upper aquifer was consistent with geological descriptions of the upper lacustrine unit, in which the gypsum content of the sediments increases toward the west (see Fig. 2). These changes in the structure of the model led to a significant improvement in the objective function, which decreased from 1690–1233 m 2. Based on the findings of the previous calibration trial, additional a zones were defined in both aquifers. A sensitivity analysis with respect to the conductivity of the confined part of the lower aquifer (fourth K zone) and the vertical conductivity of the lutitic layer (fifth K zone), both of which were not being estimated, indicated that both conductivities should be increased. For the final calibration step of the isotropic model, these conductivities adopted the following values: K4p10 –2 and K5p10 –5 m/d. The final model structure included: (a) ten K zones (Fig. 6), two in the upper aquifer (zones 6 and 10), five in the lower aquifer (zones 2, 3, 4, 7, and Hydrogeology Journal (1998) 6 : 33–49

Fig. 7 Relation between computed and measured hydraulic heads for the isotropic model. Values are in meters above sea level

9), two for depressions and lakes (zones 1 and 2), one for the aquitard (zone 5), and one for the vertical onedimensional dummy elements; (b) eight a zones, four at each aquifer, their length being consistent with the final geometry of K zones; (c) and 13 fixed internal head zones. Estimated parameters included seven conductivities and eight leakage factors. The final value of the objective function is equal to 376.5 m 2, which amounts to a square-root mean square error of 2.4 m. This is an excellent result, because this error is of the same magnitude as the estimation errors of specified heads at the lakes and reference heads along external boundaries. In the scattergram of computed and measured heads shown in Figure 7, most points are near the straight line of unit slope, indicating that computed values at the location of boreholes and wells mostly coincide with the measured values. Most of the head residuals, which in this graph are equal to the horizontal distance from the symbols to the straight line, have absolute values smaller than 3 m. They have a mean and a skewness near zero, a variance of 5.7 m 2, and a kurtosis near three, attesting that they follow a Gaussian distribution. As shown in Figure 8, the histogram and probability plot of the residuals fit those of a Gaussian variable, except for some small discrepancies at the tails of the distribution. Head residuals show small spatial correlation. Their sample semivariogram, a function that quantifies spatial correlation, indicates that residuals are correlated up to a distance of approximately 2 km, as shown in Figure 9. The fact that head residuals are small and lack spatial correlation means that the structure of the model is adequate. Model conductivities of the isotropic model are listed in Table 2. The overall spatial distribution of conductivities is consistent with available geological information and prior information on transmissivity field Q Springer-Verlag

43 Table 2 Hydraulic conductivity values for isotropic and anisotropic models. The eight K zone corresponds to the dummy onedimensional vertical elements connecting both aquifers. (*)pfixed values and thus not estimated. Kx and Ky denote the principal components of the conductivity tensor Zone

Isotropic model

Anisotropic model

1 2

K1p1.35 K2p13.2

3

K3p0.38

4

K4p10 P2 (*)

5 6 7 9

K5p10 P5 (*) K6p1.24 K7p1.67 K9p0.18

K1p316 K2xp6 K2yp0.23 K3xp0.2 K3yp0.68 K4xp3.2710 P2 (*) K4yp3.2710 P3 (*) K5p10 P5 (*) K6p1.49 K7p1.4 K9xp0.54 (*) K9yp0.054 (*) K10p0.27

10

Fig. 8 Frequency distributions of head residuals obtained with the isotropic model

data. Conductivities of the western K zones (zones 3 and 10) are smaller than those of the zones located at the eastern edge of the basin, where the sediments contain more limestone layers. Contrary to field test data, the conductivity of the deposits in the bottom of the depressions (first K zone) is one order of magnitude

Fig. 9 Semivariograms of head residuals of isotropic and anisotropic models Hydrogeology Journal (1998) 6 : 33–49

Hydraulic conductivity (m/d)

K10p0.27

smaller than the conductivity at the hillslopes (second K zone). Available conductivity data were derived from single-hole pumping and slug tests, which provide estimates of hydraulic conductivity at a local scale of less than a few meters. These data vary greatly (almost eight orders of magnitude) with a geometric mean of approximately 0.013 m/d, which is almost two orders of magnitude smaller than the geometric mean of the model conductivities (0.53). This discrepancy could be caused by an overestimation of infiltration recharge. However, the sensitivity analyses carried out by GarcíaVera (1996) indicate that recharge values smaller than the reference value of 20 mm/y lead to groundwater discharges to the lakes that are smaller than the lower limits estimated from water budgets in the lakes. The increase of the average conductivity with the scale of observation could be attributed to a scale effect that has been observed and reported for heterogeneous porous and fractured media (Neuman 1994; Sánchez-Vila et al. 1996). Figure 10 shows a log–log plot of conductivity values and scale of observation. This figure includes all the pumping and slug tests, except those carried out at boreholes at the bottoms of depressions. The scale of these data is assumed to be equal to the saturated thickness of the borehole. Model conductivities include all zones except those used for depressions (first and second K zones). The scale of these data was assumed equal to the average size of K zones. Figure 10 illustrates that the variability of K values decreases with the scale of observation, whereas the geometric mean increases. This result confirms that such scale effects are also present in evaporitic media. Computed hydraulic heads in both aquifers are shown in Figure 11. The overall picture of groundwater flow in the system can be gained from the potentiometric maps as well as from the graphs of computed disQ Springer-Verlag

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Fig. 10 Relation between hydraulic conductivity and scale of observation

charges along the boundaries, which are depicted in Figure 12. The main components of the groundwater balance are listed in Table 3. The potentiometric map of the lower aquifer reproduces the features of the initial conceptual model. Recharge takes place at the in-

terfluves and highlands, whereas groundwater discharges mostly to the lakes and into the bottom of surface depressions. The computed groundwater balance in this aquifer reflects that leakage from the upper aquifer amounts to only 5% of the total inflows to this aquifer (Table 3). Discharge across the outer boundary is approximately 40% of the total discharge. The average discharge rate along this boundary is approximately 20 m 3/y per meter (Fig. 12). The largest values (up to 150 m 3/y per meter) are observed in an area where there is historical evidence of intermittent springs (García-Vera 1996). The confined part of the lower aquifer receives some leakage through the leaky aquitard. The head difference between the two aquifers is almost negligible toward the west. In the eastern part, however, a downward hydraulic gradient exists. The model is able to represent groundwater discharge from the lower aquifer into the Salineta Lake, one of the few perennial salt lakes located just south of Bujaraloz (Fig. 2). The fact that this lake contains the thickest halite layers among all the lakes is consistent with the fact that this lake receives the discharge of groundwaters having long residence times and high chloride and sodium contents. In the upper aquifer, recharge takes place at the highlands and its steady-state value is 5822 m 3/y (Table 3). Downward leakage amounts to one tenth of the

Fig. 11 Distribution of hydraulic head computed with the isotropic model. Top upper aquifer; bottom lower aquifer. Values are in meters above sea level


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were assigned directly from available topographic maps.

Fig. 12 Groundwater discharge fluxes along the external boundaries of the upper aquifer (top) and lower aquifer (bottom)

total recharge. One third of total recharge discharges into the Salineta Lake, whereas the rest leaves the aquifer across the external boundaries in the manner shown in Figure 12. The fact that some minor recharge takes place at some of the nodes is just a numerical artifact caused by errors arising from assigning values of external heads at finite-element nodes. Such values

Anisotropic Model Previous geological studies in the closed-basin area of Los Monegros pointed out the existence of a system of quasi-vertical faults and fractures (Quirantes 1978; Salvany et al. 1996). Their main strike is 60 7W. These fractures played a major geomorphological role and, according to some authors (IRYDA, unpublished data; Samper et al. 1992), could have caused the development of most lakes and topographic depressions in the area. The orientation of the surface drainage system for the most part coincides with the orientation of either the main family of fractures or its conjugate. This would be consistent with major fractures acting as preferential groundwater pathways. However, little information exists from field observations on fracture spacing and apertures, and therefore it is difficult to ascertain their hydrogeological role. To investigate the effect of fracturing on groundwater flow, two orthogonal sets of perfectly parallel planes were considered. At the scale of the numerical model, in which the sides of the elements are tens of meters, a fractured medium behaving like an equivalent porous medium would exhibit anisotropy. The principal directions of the conductivity tensor should coincide with the orientation of the two main sets of fractures. In order to account for anisotropy, the coordinate system was rotated in such a way that the transformed x-coordinate coincides with the first principal component of the conductivity tensor. In the new coordinate system, the conductivity tensor becomes diagonal and is defined entirely by its two principal values, Kx and Ky. The third stage of the calibration of Los Monegros model involved the calibration of the numerical model by assuming conductivity to be anisotropic. The calibration of the anisotropic model was initiated with the same K- and a zones as those of the final isotropic model. Calibration of the anisotropic model involved more parameters for conductivity, because for each zone both Kx and Ky had to be estimated. Accounting for anisotropy in all the conductivity zones (except for the leaky aquitard and the confined part of the lower aquifer) led to a significant improvement in head fitting. The objective function decreased from 376.5 to

Table 3 Components of groundwater balance for the isotropic and anisotropic models Component

Value (m 3/d) Isotropic model

Infiltration recharge Leakage between aquifers Discharge to lakes Discharge through external boundaries


Anisotropic model

Upper Aquifer

Lower Aquifer

Upper Aquifer

Lower Aquifer

5822 P 583 P1905 P3334

11 303 583 P6807 P5079

5822 P 620 P1801 P3401

11 303 620 P7002 P4901

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255 m 2. Such an improvement, mostly caused by a significant increase in the number of parameters, revealed that measured hydraulic heads were consistent with the anisotropy in hydraulic conductivity. The results of the initial calibration run for the anisotropic model indicated also that: 1. The conductivities of the upper aquifer showed no significant anisotropy. A similar result was observed for the conductivity of zone 1 (bottoms of depressions). 2. The conductivities of the unconfined part of the lower aquifer showed noticeable anisotropy. The fact that the geological deposits of this unit contain less plastic sediments (lutites and marls) could explain why these materials contain more fractures. Most of the lakes and depressions are in this area. All the conductivity zones in this aquifer show anisotropy. The x component is greater than the y component, except for zone 3, where the anisotropy ratio (defined as Kx/Ky) is less than 1. 3. With the estimated anisotropy of the conductivity of zone 9, the water table in the unconfined region of the lower aquifer is too high; in some nodes, it is above the ground surface. Too large an anisotropy ratio for the ninth K zone led to a better matching of measured head data, but at the price of forcing too high a phreatic surface at locations where head data are not available. 4. Groundwater discharge rates for the anisotropic model were similar to those computed with the isotropic model. Only the computed discharge into the Benamud depression (Fig. 3) was greater than its estimated maximum evaporation. To prevent instabilities in the solution of the inverse problem, the number of estimated parameters was reduced. The conductivities of the upper aquifer were assumed isotropic as well as those of the first and seventh K zones. The anisotropy ratio of some conductivity zones was fixed. After testing several anisotropy ratios, a final optimum ratio of 10 was selected for K zones 4 and 9. In each them, Kx and Ky values were assigned in such a way that their geometric averages were approximately equal to the conductivities estimated for the isotropic model. For instance, the values adopted for zone 9, K9xp0.54 and K9yp0.054 m/d, are such that their geometric mean (0.17) is almost equal to the value of K9 estimated with the isotropic model (Table 2). The final objective function value was 275.4 m 2. As expected, the fit of the anisotropic model was better than that of the isotropic model (375.5 vs 275.4 m 2), due to the increase in the number of parameters. Accounting for anisotropy resulted in head residuals that have smaller variance (4.2 m 2) and correlation length than those of the isotropic model (Fig. 9). The scattergram of computed and measured heads in Figure 13 illustrates that heads computed with the anisotropic model match better the measured values (compare Figs. 7, 13). The residuals of the anisotropic, shown in Figure 14, model fit better to a Gaussian distribution Hydrogeology Journal (1998) 6 : 33–49

Fig. 13 Relation between computed and measured hydraulic heads for the anisotropic model. Values are in meters above sea level

Fig. 14 Frequency distribution of head residuals obtained with the anisotropic model

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than they do those of the isotropic model (compare Figs. 8, 14). The fact that head residuals have a Gaussian distribution with a mean near zero and a small variance and lack spatial correlation means that the structure of the anisotropic model is adequate. Table 2 indicates that no major differences exist in the conductivities of the two models, except for the first two K zones. The anisotropic model recognizes that the materials at the bottom of the depressions (first K zone) are more permeable than those at hillslopes (second K zone). This difference is consistent with available field data. Accounting for anisotropy leads to hydraulic-head contours, shown in Figure 15, that are more elongated than those of the isotropic model (compare Figs. 11, 15). The anisotropic numerical model leads to a better fit of measured heads while keeping a structure similar to that of the isotropic model. Thus, it is concluded that the anisotropic model is a more realistic representation of the hydrogeological conditions of Los Monegros closed-basin area. This conclusion is also supported by all model-identification criteria, which rate the anisotropic model as the best model (Table 1).

Sensitivity Analyses A sensitivity analysis was performed to (a) quantify the uncertainty in the estimated parameters and that of the Hydrogeology Journal (1998) 6 : 33–49

parameters that remained fixed during calibration, and (b) evaluate the effect of some hypotheses of the conceptual model. Sensitivity of the model was tested for (a) vertical conductivity of the aquitard (K5), (b) conductivity of the confined part of the lower aquifer (K4), (c) leakage coefficients, and (d) specified heads at the lakes. The sensitivity of the model with respect to a given parameter was evaluated by performing calibration runs in which this parameter was assigned a fixed value within a plausible interval while the rest of model parameters were estimated. Sensitivity analyses were carried out using the final structure of the anisotropic model. No field data were available for the vertical conductivity of the aquitard. Its value in the final calibrated model was 10 –5 m/d. When this conductivity was assigned a value of 10 –7 m/d, the resulting model was clearly inadequate, as indicated by (a) a significant worsening of hydraulic-head fit (the objective function increased from 275 to 329 m 2); (b) a large head difference between the two aquifers. which was not consistent with the lack of significant vertical flow in the boreholes connecting them; and (c) poor representation of groundwater flow in the eastern unconfined part of the lower aquifer. When the vertical conductivity of the aquitard was assigned a value of 10 –3 m/d, the objective function increased slightly (from 275 to 304 m 2), but the leakage from the upper to the lower aquifer inQ Springer-Verlag

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creased noticeably, from 620 to 2926 m 3/day, which caused a similar increase in boundary discharges. Under these conditions, the lower aquifer received much greater leakage and that in turn caused an increase in groundwater discharges to the lakes from 8803 (reference model) to 9901 m 3/d. Some of the lakes and depressions received discharges much above their maximum potential evaporation rates. Computed hydraulic heads were similar to those of the reference model, except for the upper aquifer, where the fit to measured data was poorer. Data are lacking for the conductivity of the confined portion of the lower aquifer. During calibration, this conductivity was assumed to be between 10 –2 and 10 –4 m/d. The final adopted value was 10 –2 m/d (Table 2). When this conductivity was decreased by two orders of magnitude, the objective function increased noticeably and leakage between the two aquifers decreased by a factor of 2. However, when this conductivity was taken to be ten times larger than the reference value, the overall head fit remained approximately the same, but leakage between aquifers doubled due to a sharp increase in the head difference. From these results, it is concluded that the conductivity of the lower aquifer in this zone must not differ from the calibrated value of 10 –2 m/d. The calibrated model was very sensitive to changes in leakage factors, meaning that the uncertainty in their calibrated values was small. On the other hand, model results were not very sensitive to small changes in the specified heads at the lakes. Therefore, the calibrated model was not sensitive to errors in the heads of the lakes.

Hydrological Effects of Irrigation The main environmental effects of irrigation in the closed-basin area of Los Monegros were evaluated by Samper and García-Vera (1994). Estimates of an increase in groundwater recharge caused by irrigation returns were obtained by IRYDA (unpublished data) using soil–water balance methods. These estimates depend largely on the types of crops and irrigation practices. Using the calibrated model presented above, García-Vera (1996) evaluated the effects of an increase in areal recharge. The most noticeable effect of the increase in groundwater recharge from 20–50 mm/y is that the water table would rise to the land surface. This result confirms that in such a low-permeability medium an increase in areal recharge causes a remarkable water-table rise. The total groundwater discharge to the lakes increases from 8800 to 22,045 m 3/d, a value almost equal to the estimated maximum evaporative capacity of all the lakes. This means that a moderate increase in areal recharge would cause an increase in the flooded area of the lakes, and that might affect some of the cultivated lands located near the lakes. Groundwater discharges along the outer boundaries would also inHydrogeology Journal (1998) 6 : 33–49

crease and would result in the appearance of springs. Greater irrigation returns would cause more severe effects. As indicated by Samper and García-Vera (1994), a highly dense subsurface drainage system would be needed in order to lower the water table below the root zone.

Conclusions In order to evaluate the potential environmental effects of the large irrigation project of Los Monegros II, a numerical groundwater flow model was constructed. Firstly, a conceptual hydrogeological model was formulated based on the available geological, water-level, chemical, isotopic, and field-test data. This model was the basis for the formulation of a numerical model, which was calibrated under steady-state conditions using a maximum-likelihood method for solving the deterministic inverse groundwater-flow problem. Both the conceptual and numerical models were updated during calibration. The final model reproduces fairly well the measured hydraulic heads, the estimated parameters are consistent with their prior estimates, and the computed fluxes are within the range of values derived from independent information. Even though prior information for some key parameters, such as anisotropy, was poor, the solution of the inverse problem resulted in reliable parameter estimates and a conclusion that a numerical model incorporating anisotropy in some hydraulic conductivities is more consistent with measured heads and thus more realistic. This conclusion is supported also by a set of model identification criteria, developed in the context of maximum likelihood estimation, which penalize one for increasing the number of estimated parameters. The modeling results suggest a scale effect in hydraulic conductivity. Hydraulic conductivities at the scale of the numerical model are almost two orders of magnitude greater than the conductivities derived from local-scale field tests. This result agrees with previous findings of Neuman (1994) and Sánchez-Vila et al. (1996), and confirms that such scale effects are also present in evaporitic media. Acknowledgments This work was carried out at “Universidad Politécnica de Catalunã” (UPC), Spain, within research projects funded by IRYDA and the Spanish Commission for Science and Technology (CICYT) through the National Program on Agriculture Research (Project AGR-89-0146-C02-02). The latter was a joint project in collaboration with “Servicio de Investigación Agraria in Zaragoza” (R. Aragüés and J. Samper, principal investigators). The work of the second author was carried out through a Scholarship from “Generalitat de Catalunya.” We thank E. Custodio for his contributions on isotopic, chemical and hydrogeological aspects; J. M. Salvany for updating the geology of Los Monegros, and the UPC researchers who participated in various field and modelling works (P. Badiella, A. Bayó, J. Guimerà, M. Manzano, R. Poncela and L. Vives). Thanks are also given to S. Neuman and M. Campana for their valuable comments and suggestions editing the final draft of this paper.

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Samper FJ, García-Vera MA (1993) A groundwater salinity model for the closed-basin area of Los Monegros, Spain. In: 12th Salt Water Intrusion Meeting, Barcelona, Spain. Proc Int Center for Numerical Methods in Engineering, pp 99–117 Samper FJ, García-Vera MA (1994) Hydrological aspects and environmental effects of irrigation in the closed-basin area of Bujaraloz-Sástago (Zaragoza-Huesca). In: Proc Spanish Conf on Water and Environment, Zaragoza, Spain, 1 : 66–74 (in Spanish) Samper FJ, Neuman SP (1989) Estimation of spatial covariance structures by adjoint state maximum likelihood cross-validation. 2. Synthetic experiments. Water Resour Res 3 : 363–372 Samper FJ, Carrera J, Galarza G, Medina A (1990) Application of an automatic calibration technique to modeling an alluvial aquifer. In: Int Conf on Calibration and Reliability in Groundwater Modeling. International Association of Hydrological Sciences, The Hague, The Netherlands, publication 195, pp 87–95 Samper J, Custodio E, Bayó A, Badiella P, Poncela R, Manzano M, García-Vera MA (1992) Hydrogeological study and preliminary evaluation of the environmental effects of irrigation in sectors VIII, IX and XI of Los Monegros II. Hidrogeol Recursos Hidráulicos 17 : 215–228 (in Spanish) Samper FJ, Custodio E, García-Vera MA (1993) Preliminary isotopic study of groundwater salinity variations in the closed basin semiarid area of Los Monegros, Spain. In: Int Symp on Isotopic Techniques in the Study of Past and Current Environmental Changes in the Hydrosphere and the Atmosphere. Proc Int Atomic Energy Agency, publication IAEA-SM-329/ 32, Vienna, pp 213–228 Sánchez-Vila X, Carrera J, Girardi P (1996) Scale effects in transmissivity. J Hydrol 183 : 1–22 Sanford WE, Wood WW (1991) Brine evolution and mineral deposition in hydrologically open evaporite basins. Am J Sci 291 : 687–710 Scanlon BR, Goldsmith RS (1997) Field study of variability in unsaturated flow beneath and adjacent to playas. Water Resour Res 33 : 2239–2252 Senger RK (1991) Regional hydrodynamics of variable-density flow systems, Palo Duro basin, Texas. University of Texas at Austin, Bureau of Economic Geology, Report of Investigation, 202 pp Senger RK, Kreitler CW, Fogg GE (1987) Regional underpressuring in deep brine aquifers, Palo Duro basin, Texas. 1. The effect of Cenozoic basin development. Water Resour Res 23 : 1494–1504 Smoot JP, Lowenstein TK (1991) Depositional environments of non-marine evaporites. Dev Sedimentol 50 : 189–347 Voss CI (1984) SUTRA: a finite element simulation model for saturated unsaturated density dependent groundwater flow. US Geol Surv National Center, Reston, Virginia, 409 pp Wooding RA, Tyler SW, White I (1997) Convection in groundwater below an evaporating salt lake. 1. Onset of instability. Water Resour Res 33 : 1199–1217

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