Spatio-temporal distribution, along-channel transport, and post-riverflood recovery of salinity in the Guadalquivir estuary (SW Spain)

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 8, 67 78, doi:./jgrc.7, 3 Spatio-temporal distribution, along-channel transport, and post-riverflood recovery of salinity in the Guadalquivir estuary (SW Spain) M. Díez-Minguito, E. Contreras, M. J. Polo, and M. A. Losada Received August ; revised March 3; accepted March 3; published 3 May 3. [] This paper presents an experimental analysis of the salinity distribution, the salt balance, and the variation of the saline intrusion in comparison to the freshwater discharge in the Guadalquivir estuary, which is a mesotidal system regulated and normally subjected to extremely low river flows. In such low-flow conditions, it is positive, well-mixed, and tidally dominated. The estuary is also characterized by a nonstationary, effective longitudinal dispersion coefficient, whose probability density becomes increasingly narrower and whose mean value is higher further upstream. The tidal-averaged salt flux is controlled by the following mechanisms (in order of importance): the nontidal transport, the Stokes transport, and the tidal pumping induced by the covariance between the current and salinity. These three factors account for more than 98% of the flux variation. In high river-flow conditions, the subtidal response and recovery of the estuary to changes in the river flow is analyzed. The increase in the tidal-averaged salinity during the first weeks of the post-riverflood recovery in the middle and upper sections of the estuary is found to be linear in time. During that time, the celerity of the salt intrusion front was 4 cm/s. The psu isohaline salt intrusion X exhibits a complex dependence on the river flow Q d, including the effects of human interventions in the estuary. Three regimes are identified for the intrusion: X = 57.. km for discharges of less than m 3 /s, X proportional to Q.48.6 d between and m 3 /s, and X proportional to Q..5 d for larger discharges. Citation: Díez-Minguito, M., E. Contreras, M. J. Polo, and M. A. Losada (3), Spatio-temporal distribution, along-channel transport, and post-riverflood recovery of salinity in the Guadalquivir estuary (SW Spain), J. Geophys. Res. Oceans, 8, 67 78, doi:./jgrc.7.. Introduction [] The adjustment of the salt intrusion to changes in the freshwater discharge or to atmospheric conditions on the continental shelf is generally unsteady [Simpson et al., ; Banas et al., 4]. Theories of estuary circulation are mostly based on the tidally averaged balance between the river flow and tidal mixing. In other words, such theories assume steady state conditions [Hansen and Rattray Jr, 965; Oey, 984; Savenije, 993; Prandle, 4; MacCready and Geyer, ]. Frequently, a sufficiently Environmental Fluid Dynamics Group, Interuniversity Research Institute of Earth System in Andalusia University of Granada, Granada, Spain. Fluvial Dynamics and Hydrology Research Group, Interuniversity Research Institute of Earth System in Andalusia University of Córdoba, Córdoba, Spain. Corresponding author: M. Díez-Minguito, Environmental Fluid Dynamics Group, Interuniversity Research Institute of Earth System in Andalusia University of Granada. CEAMA, Avda. del Mediterráneo, s/n, E-86, Granada, Spain. (mdiezm@ugr.es) 3. American Geophysical Union. All Rights Reserved /3/./jgrc.7 67 long time scale is defined for such averaging in order to obtain a long-term tendency of the system without having to consider the transients. Current research reflects significant efforts to obtain analytical and numerical results in quasi-steady conditions [Chatwin, 976; Kranenburg, 986; McCarthy, 993; MacCready, 999] and, to a lesser extent, in unsteady conditions [Banas et al., 4; MacCready, 7]. However, when the focus is on transient dynamics and the goal is to evaluate recovery times after changes in tidal, river, or atmospheric forcings, analytical solutions are difficult to obtain, and an experimental or numerical approach seems to be necessary [Nichols, 977; Officer and Kester, 99; Geyer, 997; Simpson et al., ; Monismith et al., ; Hetland and Geyer, 4; Lerczak et al., 9]. Recovery after the breakdown of steady state conditions is in itself an unsteady process. Its study is useful to understand the dependency of the exchange flow and the relative equilibrium of river, tidal, and atmospheric forcings. Moreover, observations of estuary adjustments are also necessary for management purposes as well as for the testing of numerical transport models. [3] Within this context, the aims of this research were () to analyze the transient response that takes place after

2 Figure. Map of study area. The monitoring network is composed of current-meter profilers, ADCPs (circles, i), tidal gauges (squares, ˇi), and environmental-quality probes or CTDs (triangles, i ). The origin of the along-channel coordinate (km ) was established at monitoring station, at the mouth. The meteorological station (M.S.) was installed on the Salmedina beacon located over the continental shelf off Chipiona. The Alcalá del Río dam, which is upstream tidal limit, is situated at km from.the Port of Seville is separated from the main channel by a lock. The three stretches are separated by the solid lines. The dominant processes which characterize each stretch are also indicated. a major river discharge event; () to characterize the variation of the saline intrusion in comparison to the freshwater discharge; and (3) to unravel the mechanisms which drive the salt transport in a particular estuary, the Guadalquivir River estuary. This was conducted by separately analyzing the low river-flow conditions that persist most of the year from high river-flow conditions [Díez-Minguito et al., ]. The approach was experimental and based on the data collected at 9 stations in a 3 year comprehensive campaign (8 ) during which the estuary was continuously monitored [Navarro et al., ]. For the Guadalquivir estuary, high-resolution measurements of the spatio-temporal salt distribution are scarce and, in general, have not been quantitatively related to tidal, fluvial, or other baroclinic flows. Tidal-fluvial dispersion was modeled by Ortiz et al. [6] and Toscano-Jimenez et al. [] using, respectively, Eulerian and Lagrangian transport models and measured by Baonza et al. [979] by means of radioactive tracers. Nevertheless, since 978, the estuary has undergone many changes and morpho-hydrodynamic alterations, mainly stemming from the dredging of the navigation channel and the significant reduction of tidal flats. [4] This work is organized as follows. The following two sections describe the characteristics of the study site (section ) as well as the data sources and the methodology used (section 3). In low river-flow or tidally dominated conditions, a brief survey of the salinity structure is given, including the estimate of the effective longitudinal dispersion coefficients (section 4). Section 5 describes the evaluation of the salt fluxes to identify the dominant mechanisms causing tidal-averaged salt transport. Section 6 studies the behavior of the tidally averaged salinity after a high river discharge event. Finally, section 7 determines the power-law behavior of the salt intrusion in response to the flow. The article ends with the most relevant conclusions derived from the study (section 8).. Description of the Study Site [5] The Guadalquivir estuary (Figure ) is located in the southwest part of the Iberian Peninsula (36 ı 43 N 37 ı 3 N, 5 ı 56 W 6 ı 3 W), and its waters flow into the Gulf of 68 Cádiz (Atlantic Ocean). From its mouth, the estuary extends km upstream, the first 85 km of which are navigable. It is a convergent estuary with sections that decrease exponentially from 455 m at the Port of Bonanza, at the estuary mouth, to 58 m at the head. It has an average depth of 7. m and a minimum depth of 6.5 m in the thalweg, which is maintained by periodic dredging. [6] The tidal wave penetrates the estuary from its only mouth near Sanlúcar de Barrameda to the Alcalá del Río dam. The dam is the last control point of the river flow and constitutes a barrier for the tide, which arrives with sufficient energy to be reflected and interact with the incident wave. This interaction causes the tidal elevations to show hypersynchronous behavior and produces a quasi-standing wave tidal regime in the upper third of the estuary [Díez-Minguito et al., ]. The discharge regime is conditioned by the extensive upstream regulation of the drainage basin and is characterized by frequent impulsive events, such as the sudden increase in freshwater discharges in a short period of time. These discharges are associated with high river flows (compared with the storage capacity of the Alcalá del Río reservoir) or occur because of the need to irrigate land downstream [Contreras and Polo, ]. Díez-Minguito et al. [] established two flow regimes: () a low river-flow regime for freshwater discharges of less than 4 m 3 /s; ()a high river-flow regime for discharges of over 4 m 3 /s. [7] Because of head dam s regulation, the estuary is in a low river-flow regime for over 75% of the days of the year. In those conditions, the mesotidal range and shallow depths indicate that the estuary is tidally dominated and well-mixed. This is confirmed by the Estuary number, the densimetric Froude number, and the estuarine Richardson number obtained at locations where current meters were placed [Fischer, 976; Dyer, 997] (see Table ). [8] The degree of mixing depends on the tidal amplitude, on the freshwater discharge, and also on the present stratification. The Estuary number is perhaps the simplest dimensionless number that characterizes these processes. This number is expressed as N = Q d T M /P t, i.e., the ratio of river flow in a semidiurnal cycle to the tidal prism P t, which is calculated here assuming triangular cross-sections. Highly stratified estuaries exhibit values of N greater than,

3 Table. Tidal Prism P t, Estuary Number N, Densimetric Froude Number F m, and Estuarine Richardson Number N R km P t ( 7 m 3 ) N ( ) F m ( 3 ) N R ( ) and well-mixed estuaries typically exhibit flow ratios less than.. As shown in Table, the Estuary number for the Guadalquivir estuary during a mean tide ranges from.5 to 5. for normal, low river-flow regime. [9] The baroclinic circulation and the stratification can be represented, respectively, by the densimetric Froude Number, F m, and the estuarine Richardson Number, N R [Hansen and Rattray Jr, 966; Fischer, 976]. The former is defined as F m = u d / p gh /, whereu d is the fresh water discharge velocity, h the mean depth, and 5 kg/m 3 is the density difference between the ocean water, 5 kg/m 3, and fresh water. This number expresses the ratio of river flow to potential for gravitational circulation. The estuarine Richardson number, which is N R = ( /)gq d /(Wu 3 rms ),wherewis the estuary breadth and u rms is the root mean squared (r.m.s.) tidal velocity, expresses the ratio of freshwater-derived buoyancy per unit width to the tide s mixing capabilities. Observations of real estuaries suggest that for N R >.8, the estuary is highly stratified, and for.8 < N R, the estuary is well-mixed. These two parameters, N R and F m, were computed assuming Q d =4m 3 /s, i.e., the most unfavorable case for mixing under low river-flow conditions. The results obtained for N R indicates again that the estuary is well-mixed under normal conditions (Table ). The values obtained of N R and F m plotted on the Hansen and Rattray diagram show that the Guadalquivir estuary is a Type a estuary. These estuaries are well-mixed (or weakly stratified) and develop a gravitational circulation. Low stratification is evident even during neap tides, despite the higher estuarine Richardson number caused by a decrease in the turbulent tidal mixing [Haas, 977]. During neap tides, vertical variations in salinity are less than psu. 3. Materials and Methods 3.. Field Data [] In 8, a real-time remote monitoring network was installed as close as possible to the navigation channel to study the spatio-temporal variability of hydrodynamic and biogeochemical variables. A detailed account of the instruments in this network (see Figure ) is given in Navarro et al. [, ], and the hydrodynamic data obtained from the network were analyzed in Díez-Minguito et al. []. For this reason, this paper only gives a brief description of the equipment employed here. [] In this monitoring network, eight environmentalquality stations or sensors Conductivity-Temperature-Depth (CTD) record conductivity, among other data, every 3 min. These CTDs (denoted by in Figure ) take samples at four depths at m intervals from the free water surface. The origin of the along-channel coordinate x was monitoring station, installed at the mouth of the estuary. The coordinate x is 69 positive upstream, following the axis of the main channel. The elevation of the free water surface was recorded by an array of seven tidal gauges moored at various points between the estuary mouth and the city of Seville. The map of the study site (Figure ) shows their locations. The tidal gauges (ˇ) provide a level datum in millibar every min. Six Acoustic Doppler Current Profilers (ADCPs) ( i in Figure ) supply data regarding the current in the entire water column (see Figure ). They take measurements from the free water surface to the bottom, and provide one data set per meter every 5 min. This set of data provide relevant information of the physical-biogeochemical processes along the estuary, despite of the possible deviations due to the punctual character of the measurements. [] Average daily data records of the discharges from the Alcalá del Río dam were provided by the Agencia Andaluza del Agua. Rainfall data were also obtained from the Red de Información Agroclimática. [3] Standard harmonic analysis was applied to the salinity time series in low river-flow conditions [Foreman, 996; Pawlowicz et al., ]. This analysis provided the amplitude and phase of the resolved harmonics. The time interval for the harmonic analysis was selected attending the following criteria: () it should span 9 days (7 June 9 to 7 September 9) in order to separate the most important constituents, and () the exceedances over the 4 m 3 /s limit should be as few and small as possible. 3.. Decomposition of the Net Transport [4] The main mechanisms that contribute to salt transport in low river-flow conditions were identified by analyzing the tidally averaged and depth-integrated salt flux [Fischer, 976; Dyer, 997] in the stations i during two neap tide cycles and one spring tide cycle. The vertically integrated salt flux, u s, per unit of width, neglecting turbulent effects, is Z f = usdz () h [5] Hereu is the along-channel velocity; s is the salinity; and h = h + is the water column depth, where h is the mean depth and is the elevation of the sea surface. Averaging the salt transport f over the semidiurnal M cycle, denoted by an overline f, gives the following [Lewis and Lewis, 983; Uncles et al., 985; Simpson et al., ; Banas et al., 4]: f = h u s ƒ T + s e eu ƒ T + h u v s v + e eu v es v ƒ ƒ T7 T8 + u e es ƒ T3 + h eu es ƒ T4 + e eu es + h eu v es v + ƒ ƒ T5 T6 where for a generic variable,, represents the depth average performed over the local mean depth, and v is the deviation at each depth in regards to the mean value, i.e., the variable can be decomposed as = + v. The origin of vertical z coordinate is on the free surface, positive downwards. Accordingly, time averages at a given z are performed over the semidiurnal M cycle, defined from one high-water slack to the next. The deviations with respect to the tidally averaged value are denoted by e, i.e., = + e. In particular, h = h +. Term T of the integrated flux (equation ()) represents the nontidal transport, which is the residual transport ()

4 of salt due to the (Eulerian) tidally and depth-averaged flow of water [Fischer, 976; Dyer, 997]. This term is not only controlled by the river discharge but also includes the downestuary compensation for the landward net transport of water induced by the tidal wave [Ianniello, 979], weather effects, and, in general, all the local influences in the mean flow (e.g., irrigation return flows). T is the term associated with the Stokes transport. Terms T3, T4, and T5 are tidal pumping terms associated with the correlations between tidal variations of depth and depth-averaged current and salinity. Term T6 is a tidal pumping term that arises from the changing forms of the vertical profiles of current and salinity. Term T7 accounts for the vertical gravitational circulation and other vertically sheared flows, and T8 is the term due to the triple correlation between elevation and tidally varying deviation of u and s from their depth-mean values. The analyzed time interval (from July 8 to 6 August 8) is limited by the simultaneous availability of sea water elevations and salinity and currents at different depths Effective Dispersion Model [6] The residual baroclinic flows and tidal dispersion transport salt upstream, whereas the river flow tends to cause the salt intrusion to move seawards towards the mouth. The balance between both mechanisms is usually expressed on a tidally and cross-sectionally averaged scale [Hansen and Rattray Jr, 965; Fischer, 976; Dyer, 997; MacCready, 4] with a one-dimensional advectiondispersion equation. This approach neglects the crossproduct terms associated with tidal fluctuations between the channel geometry, current, and salinity [see Dyer, 997]. Despite the drastic simplification and that the decomposition of the net salt transport (equation ()) provides a more detailed description of the transport mechanisms, the approach based on the advection-dispersion equation still provides valuable information about mixing, determines a characteristic transport time scale, allows a simple comparison between estuaries, and usually serves as a benchmark against which numerical models are evaluated. In the literature, many reports of observations and uses of effective longitudinal dispersion coefficients can be found [see Zimmerman, 976; Fischer, 976; Helder and Ruardij, 98; McCarthy, 993; Austin, 4; Ortiz et al., 6; Toscano-Jimenez et al.,, and references therein], which are useful for both scientific and engineering applications. [7] The balance between local salinity variation, advection, and along-channel dispersion can be @x = (3) where A denotes the tidally averaged section, and U and S are the tidally and sectionally averaged mean current and salinity in the section A, respectively. The averaged variables in the section and the tidal cycle are designated by capital letters. The effective along-channel dispersion coefficient K A includes the Reynolds stresses, the dispersion associated with the deviation from the tidal average, and the deviation of sectionally averaged variables in regards to their mean value [Zimmerman, 976; Helder and Ruardij, 98; Austin, 4]. The dispersion coefficient was obtained by numerically integrating the advection-dispersion equation by stretches (similarly 7 Figure. (top) Along-channel salinity profiles (maximum, minimum, and tidal average on the day specified in the figure) in a low river-flow regime. (bottom) Vertical distribution of salinity averaged in the same semidiurnal cycle along the estuary. The black line denotes the along-channel variation of the average depth (data provided by the Port Authority of Seville). to other segmented model approaches [Ippen, 966; Gay and O Donnell, 7, 9]). Equation (3) was discretized by means of finite differences (see Appendix A). A Lax- Friedrichs finite-difference scheme was used for the material derivative of S, and a centered finite-difference scheme was used for the dispersive part. The algorithm requires a simultaneous knowledge of the salinity in three consecutive sections ( i, i,and i+ ) and current in two sections ( i and i+ ) estimated by interpolation. The analysis was thus carried out between 3 April 8 and 7 October. The length of the stretch or interval is x i+ x i,wherex i is the kilometer point of monitoring station i. The spacing used is x = x i+ x i. The temporal spacing t corresponds to a period M. The dispersion coefficient can thus be considered representative of the estuary stretch (x i, x i+ ). The result of the numerical integration is a time-dependent, effective dispersion coefficient on a subtidal scale, K n A.The series of K n A were compared with those obtained with the approach devised by Gay and O Donnell [7], assuming an exponentially varying cross-section [Díez-Minguito et al., ]. 4. Saline Structure in Low River-flow Conditions [8] Figure shows how the averaged salinity in a semidiurnal cycle, as well as the maximum and minimum in the cycle, monotonically decreases from the estuary mouth to the head. Consequently, this is a positive estuary [Elliot and McLusky, ], in which the freshwater discharges from the basin are sufficient to compensate evaporation losses. The standard intrusion limit X, which is the distance from the estuary mouth to the psu isohaline, occurs at km 6. During the 3 years of observations, the salt intrusion never reached the dam (located km upstream the mouth). The maximum horizontal density gradient occurs between km 8 and km 6, where tidal wave diffusion is dominant (Figure ).

5 s(psu) s (psu) s (psu) s (psu) s (psu) M S N Msf Mm K Q O M4 MS4 MN4 M6 MS6 MN Distance (km) Figure 3. Amplitudes obtained from the harmonic analysis of the depth-averaged salinity. The data represented in this figure correspond to those listed in Table. The error bars show a 95% confidence bound. The harmonic analysis accounts for 85.8% of the variance at station ; 9.4% at ; 86.6% at ; 94% at 3 ; 89.4% at 4 ; 69.6% at 5 ; 8% at 6 ; and finally 84.7% at 7. Assuming tidally averaged values for the cross-sections and uniform along-channel stretches, the tidally averaged salt mass in the estuary was estimated during the spring tide of 3 August 8 in.9 7 ton, whereas during the neap tide of August 8, it was. 7 ton. Accordingly, the difference in salt mass between the spring and neap tides was ton. 4.. Harmonic Analysis [9] The harmonic analysis was applied to the salinity time series with a view to compute how much does the tidal forcing account for the spatio-temporal variability of the salinity gradient. This analysis was performed during low river-flow conditions to minimize as much as possible the river contribution to the salt content variability. The results provided in Figure 3 and Table indicate that the tides account for most of the variance. The ratio of the predicted variance to the original variance ranges from 69.6% at 5 to 94% at 3, but most ratios are over 85% (see caption Figure 3). The remaining variance may be explained by other, nonharmonic factors, e.g., atmospheric forcing. The variance explained by the tides tends to increase downestuary. This is consistent with the intuitive picture of a lower estuary more exposed to the marine forcing and an upper estuary more sensible to the freshwater discharge fluctuations. The lowest values are obtained at stations 5 (69.6%)and 6 (8%). This might be partly due to the influence of irrigation, since these stations are located near where the most intense agricultural activities take place (Figure ). Despite the fact that this analysis ignores nonharmonic contributions to the salt flux, the high ratios obtained suggest that the harmonic analysis may be a valuable tool to predict locally the salt variability. Amplitudes and phases of each constituent may also be useful for analytical estimates of correlations between tidal fluctuations of velocity, salinity and depth, and, thus, of the residual transport of salt [Lewis and Lewis, 983; McCarthy, 993]. The most relevant constituents are those of the semidiurnal group, as expected. The next in magnitude are the subtidal harmonics, MS f and M m. All of the constituents decrease in value the further the location is from the mouth after km 7 (monitoring station ). This is inherited from the positive behavior of the estuary. Station at the mouth recorded the highest level of salinity. However, this is not apparently reflected in the low-frequency (semidiurnal and lower) harmonics (see Figure 3, first to third panels). This is because the salinity gradient is small at that point, and the maximum salinity (i.e., the salinity of the open sea) is attained during the entry level semicycle before the high-water slack is reached, Table. Data From the Harmonic Analysis of Salinity a - M S N K Q O M 4 MS 4 MN 4 M 6 MS 6 MN 6 MS f M m a The amplitudes (upper panel) are multiplied by. The phases (lower panel) are given in ı Greenwich. The amplitude and phase error have a 95% confidence bound. The subscripts indicate the error in the last significant figure. 7

6 Ocurrences (%) γ γ 4 γ 4 γ 6 DÍEZ-MINGUITO ET AL.: SALT BALANCE IN THE GUADALQUIVIR ESTUARY K A n (m /s) 5 /4/9 /4/9 /4/9 /3/ K n (m /s) A γ γ 4, with Eq.A γ γ 4, with Eq.A Figure 4. Distribution of the effective along-channel coefficient K n A between and 4 (black line) and between 4 and 6 (gray line). The bin size used for both is 88 m /s. (inset) Temporal evolution of K n A (black line) between sections and 4. The series obtained with equation (A) is also shown for comparison (gray line). which leads to a saturation of the salinity signal. In order to reproduce this signal, higher amplitudes were assigned to high-frequency constituents (overtides M 4, M 6, and higher), at the expense of the rest of the constituents. 4.. Effective Longitudinal Dispersion Coefficient [] Figure 4 shows the distribution of the tidally averaged effective dispersion coefficient, K n A, in the stretches defined by sections and 4 (black line) and by sections 4 and 6 (gray line). For the stretch nearest to the mouth, the most probable value is approximately 5 m /s even though K n A frequently oscillates between m /s and m /s. The inset in Figure 4 (black line), which depicts the temporal evolution of K n A and the estimate of its uncertainty, shows the short-period oscillations associated with daily inequality and the long-period oscillations induced by the neap-spring tide variability, as previously observed by other authors [Haas, 977;Geyer et al., 8]. Error bars are relatively large. This is due to the simplifications adopted to derive equation (3) and to the spatial and temporal sampling limitations. The weighted mean of the time series showed in Figure 4, determined as P n Kn A ( Kn A ) / P n ( Kn A ),is( 3) m /s. This value apparently describes the data series well, according to the result of the Chi-square test of goodness of fit [Press et al., 99; Gay and O Donnell, 7]. A sample value of / =.73 was obtained, where =3is the number of degrees of freedom of the distribution. Such a low value of results from the long correlation time in K n A, as expected in a time-dependent, tidally averaged dispersion coefficient. The autocorrelation analysis shows a decay of approximately 6 days. [] A greater dispersion is observed during spring tides. This suggests that dispersion tends to increase with tidal velocity amplitude (and possibly with elevations), which exhibits a marked spring-neap variation (current velocity in spring tides almost doubles the velocity in neap tides). A plausible and simple mechanism that may explain 7 this behavior is shear dispersion. The turbulence generated by friction at the bottom and margins interacts with cross-channel shear and mixing, producing along-channel dispersion. The effective longitudinal dispersion is, thus, influenced by the combination of a gradient of cross-channel velocity with turbulent mixing [Taylor, 954; Bowden, 965; Okubo, 967]. As is shown in the inset in Figure 4, the agreement between our model (equations (A) and (A)), whose derivation is based on the work of Gay and O Donnell [7], is fair. There is a specially good agreement during neap tides. The greatest differences in magnitude are observed during spring tides, probably due to differences in the treatment of advective terms between both models. Nevertheless, in most cases there is considerable overlap of the error bars. [] To estimate the influence of the salt storage term, we also determined the dispersion coefficient that numerically resolves the time-independent equation (i.e., assuming steady conditions). For the same stretch ( 4 ), values between and m /s were obtained. These values are similar to those in other estuaries [Zimmerman, 976; Austin, 4; Banas et al., 4; Geyer et al., 8; Savenije, 8] and comparable to the instantaneous values previously obtained in the lower stretch of the Guadalquivir with radioactive tracers [Baonza et al., 979]. The difference with respect to the unsteady case is significant, which highlights the importance of the salt storage term even during low river-flow conditions. [3] Figure 4 also represents the distribution of data corresponding to 4 6, located upstream from the previous stretch. As can be observed, the mode attains a greater value, which in this case, is close to 4 m /s. This behavior has been observed in other estuaries. Austin [4] observed that the effective dispersion is inversely proportional to the crosssectional area in the Chesapeake Bay. This author attributes this behavior to the intensity of either the area-averaged along-estuary tidal currents or exchange flow. For different flow conditions, Helder and Ruardij [98] obtained values of the effective longitudinal dispersion coefficient which exhibit a significant spatial variability, probably due to the multi-channel character of the Ems-Dollard estuary. The agent responsible for such behavior in the Guadalquivir may be the secondary circulation. In the lower stretch closest to the mouth (Figure ), where the estuary widens and the radius of bend curvature decreases, the secondary flows are expected to play an important role in the mixing processes [Geyer et al., 8]. One of the effects of the secondary flow is to augment the transverse turbulent mixing. This would tend to reduce the density gradient across the channel and, thus, to reduce the longitudinal dispersion associated with the transverse shear in the primary flow. A cross-sectional density gradient due to differential advection of salt may also set up a secondary circulation which also increases the lateral mixing and reduces the longitudinal dispersion [Smith, 976]. On the contrary, the (along-channel) gravitational circulation tends to increase the effective dispersion coefficient [Ippen, 966]. The mean value of the effective longitudinal dispersion coefficient seems to depend on the relative importance of these effects. In the Guadalquivir estuary, the fact that the effective longitudinal dispersion coefficient decreases downstream indicates that the secondary flows exert a greater control over mixing in the stretch 4.The

7 f (kg/(m s)) f (kg/(m s)) T T T3 T4 Neap tide DÍEZ-MINGUITO ET AL.: SALT BALANCE IN THE GUADALQUIVIR ESTUARY Spring tide 7/6/8 7/3/8 8/5/8 8//8 Neap tide Figure 5. Decomposition of the salt transport in sections (upper panel) and 5 (lower panel). Terms T5 T8 are not shown. The dates of spring and neap tides are indicated by the vertical lines. Positive values are upstream. greater transverse variability in the currents, increased vertical stratification of the water column, and increased channel width (larger eddies can form) are reflected in the wider possible range of values of K n A in the stretch 4, i.e., in a distribution of data with a greater variance. In the second stretch, however, there are fewer possible deviations associated to these factors with regards to the sectionally homogeneous behavior. 5. Transport Mechanisms and Salt Balance in Low River-Flow Conditions [4] The temporal evolution of each of the terms in which the tidally averaged and depth-integrated salt flux (equation ()) is decomposed provides additional insights into the specific mechanisms responsible for the salt transport. This is shown in Figure 5. The stations (upper panel) and 5 (lower panel) were selected. Figure 6 shows the terms, with respect to the distance from the mouth, which were averaged in the time interval analyzed. The net salt transport is also shown f = P 7 i= T i (bottom row to the right). [5] In both sections of the estuary, the spring and neaptide variations are evident as well as the highest frequency oscillation associated with diurnal inequality (see Figure 5). In station, it can be observed that the two most important terms are T (nontidal transport) and T (Stokes transport). In this section, these two terms in themselves comprise 8% of the salt transport, and T+T changes its sign from positive (neap tide) to negative (spring tide). The maximum value (in its absolute value) for T was observed during spring tides. Apparently, a substantial part of the nontidal drift during spring tides is a downstream compensation for the inland transport induced by the Stokes drift. The direction of the nontidal flux, T, varies during neap tides (towards the head) even though its magnitude is not as great. At present, and with the available data, we can offer no satisfactory explanation of this phenomenon. Nevertheless, the positive value observed during neap tides suggests a differential local circulatory regime during spring and neap 73 tides, possibly due to eddies generated near the cusp of the bend. The next most important term is T4, associated with the correlation of tidal deviations of current and salinity. The tidal pumping term is predominantly negative at this location, though it frequently changes sign even at diurnal frequency. The rest of the terms, of which only T3 is shown, are lower and do not significantly contribute to the net salt transport. This is particularly the case for T5 and T8, which are the triple correlation terms. In total, terms T, T, and T4 account for 99% of the mean salt transport. [6] These terms are also the most relevant at monitoring station 5 (second panel in Figure 5) despite the fact that they have a lower magnitude than those calculated in.the three represent 98% of the flow (T and T, 75%). In this section of the estuary, the mean current is negative in almost all the data windows analyzed, except in certain cases. More specifically, T4, the tidal pumping term, inverts its sign with respect to the observations at station, because of an additional phase lag between the oscillatory part of the salinity and the tidal current. [7] Figure 6 shows the time average performed for each term in equation () as functions of the distance to the mouth. The net salt transport, the result of adding all the contributions (rightmost panel) is positive in the entire estuary, and its behavior shows roughly exponential decay. The reduction in magnitude of the upstream estuary transport reflects somehow the positive nature of the spatial distribution of salinity. More investigations will be required to explain the relative increase near km 6 nonetheless. The nontidal current is the mechanism that most contributes to transport salt landwards in the first stretch of the estuary. The Stokes transport also contributes to landward transport though to a lesser extent. The highest values were obtained in the lowest section of the estuary, and they progressively decrease in magnitude in the upstream estuary sections. This behavior is most likely induced by the quasi-standing tidal propagation in the upper third of the estuary. [8] The T4 integrated flux, which is the tidal pumping term associated with the correlation of tidal deviations of current and salinity, is negative until around km 3, after which it becomes positive. Between station and station 3, the phase difference between the oscillatory part of the salinity and the tidal current increases. Specifically, a phase shift of almost 7 ı was observed in the tidal M component of the salinity (see Table ), whereas within the error bars, the along-channel phase variation of the tidal current remains almost constant [Díez-Minguito et al., ]. Obviating the different location of CTDs and current meters, a reasonable possibility is that the sign change of T4 may be due to local topographic features, such as bends, which may have considerable influence on the lateral mixing driven by secondary flows and hence on the salt transport [Smith, 976; Lewis, 979; Lewis and Lewis, 983]. [9] The other tidal pumping terms, T3, T5, and T6, are order of magnitude less than T4. The vertical gravitational circulation (as expressed by term T7) transports salt upstream, more significantly near the estuary mouth, but makes a minor contribution to the net salt transport. Overall, tidal pumping advects salt more efficiently than baroclinic circulation. The triple correlation term T8 is the least relevant throughout the whole estuary. In steady state conditions, there is no net transport of salt across a given section.

8 f (kg/(m s)) T T.4 T T Net f (kg/(m s)) x 3.6 T7.4.. T5 T6 T Distance (km) Distance (km) Distance (km) Distance (km) Distance (km) Figure 6. Variation with the distance to the mouth of the averaged salt fluxes in the entire time interval analyzed. Positive values are upstream. However, this was not observed in the time period analyzed in our study. The nonzero net upstream flux of salt may be due to a change in salt storage and lateral variations over the cross-section. On one hand, the saline intrusion did not show appreciable variations besides the spring-neap cycle (Figure 8), and the weather conditions in the inner shelf were good. Thus, the positive net flow, which decays with x approximately exponentially, suggests the presence of lateral variations over the cross-section and a net transport towards the mouth on the banks that may compensate this salt discharge. In fact, the salt balance described here is representative of the main channel section or the momentumconveying part. It is not representative of the storage part corresponding to the banks and tidal flats. On the other hand, the unsteadiness of the system cannot be dismissed since, prior and during the analysis time interval, fluctuations of up to 3 m 3 /s in freshwater discharge occurred, even when discharges were consistent with low-flow conditions. 6. Post-riverflood Recovery of Salinity [3] In high river-flow conditions, when discharges are greater than 4 m 3 /s, the freshwater discharge controls the transport of substances and causes the salt intrusion to move off to the mouth. This increases the stratification by forming a discharge plume on the continental shelf. River discharges are typically associated with the regulation of the basin and the passage of storms. Such storms generally last 7 days and occur several times a year. The number of storms per year in the Guadalquivir watershed has a periodicity of 3 years [Ávila, 7]. In rainy cycles, the North Atlantic Oscillation Index, n, is negative, and its absolute value is greater than. In dry cycles, n is positive and is between and 5. After a discharge, the estuary returns to a low-water regime and then begins a post-flood recovery or saline intrusion adjustment [Nichols, 977; Kranenburg, 986; MacCready, 999, 7; Lerczak et al., 9]. [3] The recovery time, t rec (i.e., the time interval between the occurrence of a discharge and the estuary s recovery of its previous depth-averaged salinity level) mainly depends on the spring-neap tidal cycle during which the discharge occurs, the magnitude of the freshwater discharge, and the atmospheric and oceanographic conditions at the mouth and the inner shelf. After a discharge of 53. m 3 /s, which took place on 7 February 9 after the passage of a storm with prevailing westerly winds (the predominant wind direction on the continental shelf), t rec was measured in the estuary sections studied. Only after 6 days did section at the mouth recover its previous salinity level. The salt intrusion front took another 6 days to reach km 7 in the inner part of the estuary. Once the first stretch of the estuary had once again attained its initial salinity, the propagation speed of the salt front increased. From station to station 6 (separated by a distance of 4 km), salinity took scarcely 4 days to return to prior levels. The estuary (until 6 ) thus took a total of 6.5 days, a little more than a spring-neap cycle, to recover its previous salinity level. This represents a net celerity of the salt front inside the estuary of 4cm/s(3.5 km/day). However, the salinity front propagation velocity changes with distance along the estuary. The magnitude of the differences in t rec between consecutive stations is related to changes in their cross-sectional areas, or, more precisely, the celerity of the salt front, c rec = ( x/ t) rec, was found to be inversely proportional to the along-channel gradient of 74 cross-sectional area, i.e., c rec = A A/ x. Thisheuristic simple relation expresses the dependence of the salt front celerity on the channel geometry. The characteristic time scale =7.3. days was estimated by a least squares fitting of a straight line to the experimental data. The response time scale is thus comparable to the remote wind time scale and half an order of magnitude of the fortnightly timescale. Further assuming that the cross-sectional area between two stations varies exponentially as e x/,where is the local convergence parameter, this leads to a celerity of /. This seems to indicate that the more convergent the reach is (lower ) the slower (lower c rec ) the salt front propagates in that particular reach. This may be related to the relative importance of the bottom stress term in convergent channels [Friedrichs and Aubrey, 994]. [3] The behavior of the initial phases of the recovery of tidally averaged salinity just after the discharge was observed to be linear in time. In other t)/@t / p(x), wherep(x) is positive does not depend explicitly on t or s. This indicates that the relation between the river flow

9 S (psu) S (psu) DÍEZ-MINGUITO ET AL.: SALT BALANCE IN THE GUADALQUIVIR ESTUARY /8/9 //9 /6/9 //9 /6/9 //9 /6/9 //9 /6/9 Figure 7. Temporal evolution of the depth- and tidally averaged salinity after a discharge from the Alcalá del Río dam (7 February 9) as measured by the CTDs in the middle stretch of the estuary. (inset) Enlargement of the main figure. The slopes p are indicated in psu/day and were calculated by minimum squares as the best line of fit. The subscripts indicate the error in the last significant figure. and the upstream salt transport is rather independent of the local salinity. Despite fluctuations in the magnitude of freshwater discharge and in the tidal action, this behavior lasted weeks at the monitoring stations located furthest upstream. In subsequent stages, recovery is not uniform, and there are evident changes in the mixing properties associated with cycles of spring and neap tides. The computed values of p(x) are shown in Figure 7. They vary from.49.7 psu/day at station 3 to.64.7 psu/day at station 6. Thus, the function p(x) decreases with x, which is consistent with a more rapid recovery in the sections closest to the mouth. 7. Relation Between River Flow and Saline Intrusion [33] In a tidally dominated estuary, the spatio-temporal variability of the saline intrusion essentially depends on the transport and diffusion associated with tidal flows, freshwater discharges, and wind action [Garvine, 975; McCarthy, 993; Monismith et al., ; MacCready, 4; Banas et al., 4; Scully et al., 5]. Figure 8 depicts the extension of the psu isohaline saline intrusion X. Also shown is the curve of X 5 (distance from the estuary mouth to the 5 psu isohaline) as a reference that helps to better understand the along-channel salinity gradient. During the summer of 8, the estuary was in a low river-flow regime. In such conditions, the variability of the saline intrusion is mainly tidal in origin. From June 8 to 4 September 8, the intrusion point X oscillated around its mean value of 67 km. Maxima of X occurred during spring tides, reaching up to km 75 in the estuary. In contrast, the minima occurred during neap tides, which caused the intrusion point to recede to 65 km. This signifies that the net displacement of the psu isohaline in a spring-neap semicycle is thus of the order of km. At the study site and its basin, the saline intrusion undergoes a substantial regression in γ 3 γ 4 γ 5 γ 6 response to the passage of storms because of the freshwater contribution. The autumn rains from September 8 onwards reduce the tidal-mean intrusion about km (from X 67 km to 57 km), even when the discharges from the dam do not exceed 4 m 3 /s (Figure 8). In the high river-flow regime, elevated discharges keep the saline intrusion close to the mouth. [34] The response of the saline intrusion X to the river discharge Q d is one of the most important relations used to estimate the magnitude of estuarine circulation [Hansen and Rattray Jr, 965; Oey, 984; Garvine et al., 99; Monismith et al., ] as well as to optimize basin regulation and its management. Moreover, the dependence of X on Q d emerges as a valid criterion that provides in-depth knowledge regarding estuary classification and definition. Figure 9, which shows X as a function of Q d, suggests that the intrusion follows three regimes, depending on the volume of the discharge [Monismith et al., ]. The continuous lines indicate the better fit to the data by means of nonlinear least squares. Cross-over points are approximately located around the discharges m 3 /s and m 3 /s. These points are mainly determined by () human-controlled discharges to maintain minimum flows for environmental purposes; () maximum fluvial discharges associated to seasonal rainfall events during humid seasons; and (3) intermediate values ranging from high discharges associated to rainfall occurrence upstream of the dam, to medium values associated to controlled discharges to provide irrigation water for crops downstream of the dam and to control the salinity of water uptake for irrigation. Under the current regulation level, the regime can be described as controlled for discharges of less than m 3 /s. In this condition, the fitted saline intrusion response, with a value of X = 57.. km, 75 H (m) Q d (m 3 /s) P (mm) X S (km) X X 5 8/3/8 /9/8 /8/8 /7/9 3/8/9 5/7/9 Figure 8. From top to bottom: (a) Tidal range at the estuary mouth (station ˇ), (b) daily average discharges from the Alcalá del Río dam, (c) accumulated daily rainfall in Puebla del Río, town located at km 76 upstream at the site of monitoring station ˇ6, and (d) extension of the saline intrusion X (continuous line) and X 5 (dashed line).

10 X (km) Ocurrences (%) Q d DÍEZ-MINGUITO ET AL.: SALT BALANCE IN THE GUADALQUIVIR ESTUARY X (km) 3 4 Q d (m 3 /s) Q d.48 Q d Figure 9. Length of the saline intrusion X compared to the discharge Q d. For flows lower than m 3 /s, the intrusion length is X = Between m 3 /s and m 3 /s, the line of fit is X = bq a d,wherea =.48.6 and b = km. Finally for higher flows, a =..5 and b = 4 km. The coefficients are within 95% confidence bounds. (inset) Distribution of X. The bin size used is 3.6 km. was found to be almost insensitive to the river flow. This behavior, exemplified with a very low Estuary number N (the ratio between the volume of fresh and saline water at a given section during a tidal period), can be interpreted in terms of nonsignificant inflows of freshwater when compared to the seawater volume present in the estuary and thus with nonsignificant changes in the spatial limit of saltwater influence. A wide range of variability in X is observed near the first cross-over point (inset Figure 9). This variability apparently reflects the interplay between weather conditions and springneap and river-flow variations. For larger discharges of up to m 3 /s, Figure 9 shows the typical power-law behavior with X / Q a d, whose exponent is a = This may be a transitional regime between low and high discharges due to fast fluctuations in Q d over relatively short periods. This regime, which depends on rainfall characteristics and current storage in the reservoir network upstream, roughly corresponds to the intermediate regime between the tidally dominated and the fluvially dominated regime, i.e., between 4 m 3 /s and 4 m 3 /s, established by Díez-Minguito et al. [] for the tidal wave propagation. As can be observed in Figure 9, the behavior of X again changes for more abundant river flows over m 3 /s with an exponent of a =..5. These values associated to rainfall-flood events, although scarce in occurrence compared with those in normal conditions (inset Figure 9), reduce the area where significant changes in water salinity can be observed to the surroundings of the mouth. The saline intrusion X transits smoothly between these regimes, and there may be additional regimes (e.g., around the second cross-over point between, approximately 4 m 3 /s and m 3 /s). [35] The exponents obtained for moderate and high flows are greater than the theoretical scaling exponent /3 [Hansen and Rattray Jr, 965], obtained assuming rectangular cross-sections, and turbulent coefficients (vertical turbulent 76 viscosity and vertical and horizontal turbulent diffusivity) which are independent of depth and local properties of the mean flow. These values also differ from those obtained in other estuaries. Our observations show that the higher the discharge, the higher the sensitivity of the intrusion on the flow. The exponent the Guadalquivir exhibits at low discharges is lower than the observed in other estuaries, which ranges from.4 in the Northern San Francisco Bay [Monismith et al., ] to.38 in the Hudson River estuary [Abood, 974]. When freshwater discharges are greater than m 3 /s, the Guadalquivir estuary behaves like a salt-wedge estuary at the lower stretch near the mouth. The fitted exponent is, larger than the observed in the other partially mixed and salt-wedge estuaries, except perhaps for the Hudson. Abood [974] obtained an exponent close to.9 for X. for the highest flows in the Hudson, and Ralston et al. [] modeled the equilibrium saline intrusion X in the Merrimack, classified as salt-wedge estuary, with a power law Q.57 d. Exponents.5 and.49 were obtained by computer simulations in the Skagit River and Mondaomen estuaries, respectively [Yang et al.,9;gong et al., ]. The disparity of exponents and methods used to estimate them makes it difficult to draw general conclusions regarding the sensitivity to the flow. Nevertheless, this set of exponents obtained in different study sites seems to suggest that in well-mixed estuaries, saline intrusion depends more markedly on the river flow than in partially stratified estuaries and salt-wedged estuaries. 8. Conclusions [36] Hydrological, meteorological, and hydrodynamic data records collected at 9 stations over a 3 year period were used to quantify the dependence of the salt intrusion on the river flow in a well-mixed regulated estuary, which is subject to extremely low flows and whose dynamics is partially controlled by tidal reflection on the head dam [Díez-Minguito et al., ]. The usually low riverflow regime signifies in the estuary that mixing is mainly caused by the tides. The time-dependent, tidally averaged effective dispersion coefficients vary depending on the estuary stretch under consideration. Between kilometer points 5 and 35, approximately, the most probable value of the distribution of coefficients is around 5 m /s. Nevertheless, the distribution obtained in our study is rather wide since values between m /s and m /s were often observed. Upstream between 35 km and 6 km, the distribution of effective dispersion coefficient values is narrower. Its variance is reduced, and its mean value increases to 4 m /s. In such conditions, the main transport mechanisms are (in this order) non-oscillatory salt fluxes, the Stokes transport, and the tidal pumping associated with the correlation between tidal variations of salinity and current. These three terms account for almost all the salt transport variance. The high degree of mixing signifies that the fluxes associated with vertical variability are much lower than the rest. Tidalinduced terms should be thus retained to model adequately transport in well-mixed estuaries [McCarthy, 993]. [37] Occasionally, the estuary suffers high river-flow conditions that are concentrated in short time periods that have an important impact on the dynamics of the estuary. Among other effects, these discharges move the saline intrusion to