2.1. Site Description
 The Sau Reservoir (41°58′N, 2°22′E) is a eutrophic and monomictic canyon-shaped reservoir (Figure 1a) located in the central reach of the Ter River in northeastern Spain. It is the first in a series of reservoirs supplying water to approximately 3 million people in the metropolitan area of Barcelona. When full the reservoir stores up to 165 hm3 of water, and its average inflow rate is ∼11.4 m3 s−1. Stored volumes, inflow and outflow rates, though, undergo large changes at interannual, seasonal, and subseasonal scales due to the natural variability associated with the Mediterranean climate, and hydraulic management practices. The total length of the reservoir is 20 km. A 3.6 km long and 1.3 km wide lacustrine zone, as termed by Kimmel et al. , is located next to the dam, with a maximum depth of 60 m. Further upstream, the reservoir is narrower (maximum width of 100 m), and meandering (Figure 1a). The Ter River enters the reservoir near its western boundary. Outflows are regulated with three withdrawal outlets located at different elevations (Figure 1b). Withdrawal elevations in the Sau are selected so that the best water quality (in terms of particulate organic matter concentration and absence of reduced soluble substances) is released downstream into the Susqueda Reservoir, while water of poorer quality is retained.
Figure 1. Sau Reservoir (a) shape and dimensions and (b) withdrawal outlets at dam. Note that water level fluctuations typical in Mediterranean reservoirs may leave some of the withdrawal outlets emerged. m a.b., meters above bottom; m a.s.l., above sea level.
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2.2. Observational Data
 Meteorological and hydrological data were available for the Sau Reservoir during a 9 year period, from 1998 to 2006 (simulation period). Hourly wind speed, air temperature, precipitation, and incoming short-wave solar radiation were recorded near the dam, 70 m from the shoreline and 12 m above the maximum water surface elevation. Surface heat fluxes into the reservoir were calculated from meteorological data and simulated near surface water temperature using bulk-parameter methods, as byFischer et al. . Incoming solar radiation, air temperature, and surface heat fluxes varied strongly on a seasonal basis (Figures 2a, 2b, and 2d). For example, air temperatures (Figure 2b) ranged from 0 to 4°C in winter to >20°C in summer. In comparison, the variability between years was much smaller, seen by the thin range of the shaded area (<5°C). The warmest year was 2003 with annual mean temperature of 13.7°C (dark dashed line in Figure 2), while 2005 was the coldest, with an annual mean of 12.3°C (light dashed line). Wind speed exhibited moderate seasonal and interannual variations, as indicated by the flat heavy line and narrow shaded area in Figure 2c. Annual wind speeds ranged between 1.7 m s−1 during the windiest year (2001) and 1.4 m s−1 during the calmest (2005). The wind speeds from January through May were generally higher than during other months of the year.
Figure 2. 30 day moving averages of meteorological conditions at the Sau Reservoir 1998–2006: (a) Incoming solar radiation, (b) air temperature, (c) wind speeds at 10 m above surface, and (d) net surface heat fluxes. The gray corresponds to the range over the 9 year simulation period, representative of the interannual variability measured by equation (8), while the thick black line represents the mean for all years ( in equation (7)).
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 Daily inflow and outflow rates and stored volumes in the reservoir were available from the Catalan Water Agency (ACA) and Aigües Ter Llobregat (ATLL), the water supply company managing outflows from the Sau Reservoir. During the simulation period, annual inflows into the reservoir (Figure 3a, black columns) averaged 340 hm3 yr−1, with significant interannual variability (standard deviation = 120 hm3 yr−1). To further characterize the hydrological variability among years, the aridity index AI was calculated as the ratio of the mean potential evapotranspiration (water demand) to mean precipitation (water supply) for the entire watershed contributing to the reservoir, as by Arora . This index varied between 0.75 and 2 (dashed line in Figure 3a), which are typical values for subhumid regions. Only during wet years (2002 and 2003), when inflow rates were at their maximum values (Qin > 450 hm3 yr−1), did the annual supply of water exceed the demand (AI < 1). River inflows varied on seasonal and synoptic scales associated with episodic rainfall and snowmelt events during early winter and spring (Figure 3b). On average, the annual withdrawal volumes (Figure 3a, white columns) mimicked the inflow volumes (Figure 3a, black columns) within ±40 hm3. Note that during the two years with lowest inflows, 1998 and 2005, the withdrawals exceeded the inflows by 65 and 50 hm3, respectively. To account for the effects of variable inflows and withdrawals in replenishing and flushing the reservoir, and Qin ≠ Qwdr, the volumetric flow rate Q in equation (1)was taken as the average through-flow rate, defined asQ = (Qin + Qwdr)/2.
Figure 3. Hydrological conditions at the Sau Reservoir, 1998–2006: (a) Annual river inflow (black), withdrawal volume (white), and aridity index (dashed). (b) Inflow rates in the Ter River, filtered using a Butterworth filter with cutoff frequency of 1/7 days. Numbers indicate the eight largest inflow events during the study period.
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 As part of a long-term water quality monitoring program funded by ATLL, inflow temperatures, light attenuation in the water column, and 1 m vertical resolution reservoir temperature profiles were collected monthly, at noon (local time), from 1998 to 2006. A total of 169 temperature profiles were available. A regression equation was developed to estimate river water temperatures (θin) on day i from average air temperatures (θa) measured on previous days as follows:
This equation is similar to that used by Rueda et al. , and incorporates a total number of 1167 data points in its derivation (R2 = 0.95, p < 0.0001, root mean square error RMSE = 1.44°C).
2.3. Model Simulations
 Daily estimates of river water residence time were obtained as by Rueda et al. , from a series of conservative pulse tracer release experiments simulated with the dynamic reservoir simulation model (DYRESM) [Imberger and Patterson, 1981]. A process-based one-dimensional model, DYRESM includes descriptions of mixing and transport processes associated with river inflow, natural or manmade outflows, vertical diffusion in the hypolimnion, and mixed-layer dynamics; it is also used to predict the variation of water temperature and salinity with depth and time. The lake is conceptualized as a stack of horizontal layers which are free to move vertically, and to contract and expand in response to hydrologic or meteorological forcing (e.g., layers can mix together, have inflows inserted, or outflows removed). Outflows are taken from horizontal withdrawal layers of limited vertical extent centered approximately at the level of the outlet. Inflow parcels, each corresponding to a single day's inflow, remain separate from the main layer structure until they reach their level of neutral buoyancy. Once at this level, they leave the river channel and become inserted in the layer stack, mixing with the water existing in the host layer, and forming over-, under-, or interflows depending on whether the insertion level is at the surface, at the bottom, or in between, respectively. The path of each inflow parcel traveling vertically from the inflow section toward the insertion layer, and entraining ambient fluid as it progresses, is explicitly simulated in the model. Intrusions and withdrawal layers are, in general, narrow, their vertical extent depending on the flow rate and the degree of density stratification [Fischer et al. 1979]. The model has been extensively described and applied with success in the literature to simulate the vertical thermal and salinity structure a wide range of lakes [see Perroud et al., 2009, and references therein], and, in particular, the Sau Reservoir [Han et al., 2000]. The success of DYRESM to reproduce the vertical density structure of lakes and reservoirs implies that the level of process description, including temporal and spatial scales in the model, is fundamentally correct [Hamilton and Schladow, 1997].
 The model was set to simulate the thermodynamics and transport processes in the Sau Reservoir during a 9 year period. The model was forced, using observed daily meteorological and hydrological variables (see Figures 2 and 3), and the temperature predictions were compared with the temperature profiles collected in the reservoir from 1998 to 2006. This was considered a first check to make sure that the vertical position of the inflow intrusions was predicted correctly.
 Tracer experiments consisted of injecting a pulse of one conservative tracer of mass M0 on each day i of the 8 year study period. The mass of that tracer leaving the reservoir thereafter, until the end of the 9 year simulation period (day n) was monitored. Hence, 2920 simulations were conducted, each one with the conservative tracer released on a different day. The average residence time of the river water entering reservoir during day i, Ti, was then calculated as follows [Rueda et al., 2006]:
Here Cwdr,k and Qwdr,k represent tracer concentration in water and flow rates withdrawn on day k. For all the experiments conducted from 1998 to 2005 (study period), 99% of the mass released M0 was recovered at the outlet at the end of the simulation.
 The elevation of the river water intrusion in the reservoir Zin was estimated as follows. The first day after the release with simulated tracer concentrations in the reservoir above zero was initially identified. The tracer profiles on that day were then inspected to determine the elevation where the concentration was maximal. This approach, though approximate, was a good estimate of the intrusion elevation, given the limited vertical extent of the intrusions under stratified conditions.
 The stability of the water column was characterized using lake numbers LN defined as the ratio between the stabilizing moments due to the stratification and the destabilizing moments associated with wind forcing, both of them referring to the center of volume. Low lake numbers (LN < 1) are indicative of unstable water columns. High lake numbers, in turn, are indicative of stable water columns. Lake number values were calculated from daily simulated reservoir temperatures and observed daily averaged winds following Stevens and Imberger . In these calculations, the elevation of the thermocline ZT was defined as the center of the metalimnion, taken as the layer where the buoyancy frequency exceeded a threshold value of 10−3 s−2 [Hoyer et al., 2009].
 To explore the impact of management practices and natural meteorological and hydrological variability on daily residence time in the Sau Reservoir, a range of synthetic scenarios were simulated (see Table 1). We refer to the base case run as scenario 0, in which the simulations were forced with observations. In scenario 1, withdrawals were presumed to occur exclusively through the bottom outlet. In scenario 2, in addition, water level fluctuations were limited by setting the withdrawal rates from the bottom outlet equal to the observed inflow rates. Four additional subscenarios (2a–2d) were simulated with equal inflow and outflow rates to address the impact of varying withdrawal elevations (see Table 1). The tracers in these additional subscenarios were released every 5 days, and not daily as for the other scenarios. In scenario 3, the inflow and withdrawal rates were assumed constant. In the last scenario (scenario 4), river temperatures θin (equation (2)) were low-pass filtered (cutoff frequency of 1/60 days), leaving meteorological factors (Figure 2) as the sole source for short-term (daily and synoptic) variability.
Table 1. Description of Scenarios Modeled With DYRESM, Showing Mean (Min, Max) of Daily Input Parameters During 8 Year Study Period (1998–2005)
| ||Scenario||Zwdr (m a.s.l.)||Qwdr (hm3 day−1)||Qin (hm3 day−1)||V (hm3)||Suppressed Variability|
|0||Full natural variability and hydraulic management (base case)||(384.6, 399.1)||0.96||0.94||82||None|
|(0, 17)||(0, 25)||(24, 152)|
|1||Partial hydraulic management||384.6||0.96||0.94||82||Withdrawal elevation|
|(0, 17)||(0, 25)||(24, 152)|
|2||Limited hydraulic management||384.6||Qin||0.94||78||Withdrawal volumes|
|2a||388.6||(0, 25)||78||(Qwdr = Qin)|
|3||No natural hydrologic variability||384.6||Qin||0.93a||120b||Hydrological inputs and outputs|
|(Q = constant)|
|4||Limited river temperature variability (full natural meteorological variability)||384.6||Qin||0.93a||120b||Short-term river temperature (and hence intrusion depth)|
2.4. Model Simulations Quality Checks
 Even though longitudinal transport is not explicitly simulated in DYRESM [Hocking and Patterson, 1991], the daily estimates of mean residence times T are still expected to be valid, as long as the travel times of intrusions across the length of the reservoir TL are short compared to the vertical travel times of the insertion layers in the reservoir from their initial position to the withdrawal depth, hence, if TL ≪ T. Only when the intrusion forms at the withdrawal elevation can it be expected that T ∼ TL. But even in that case, our estimates of Tare reasonable given that the insertion layer will behave as a continuous reactor, in which the mean residence times do not depend on whether mixing is assumed to be infinitely fast as in DYRESM (or in other one-dimensional models), or if the motion is purely advective, as represented in higher-dimensional models.
 Longitudinal travel times were calculated, a posteriori, and compared to T as a form of quality check. These estimates of TLdiffer depending on whether river inflows form over-, inter-, or underflows when entering the reservoir. An overflowing parcel can travel to the dam in approximatelyTL∼ 9 days based on average wind-driven surface currents of 0.025 m s−1 estimated in the top 5 m of the Sau Reservoir [Marcé et al., 2007]. An interflowing parcel travels longitudinally as a result of a balance between inertial and buoyancy forces [Ford and Johnson, 1986], at a speed uL which can be estimated as follows [Fischer et al., 1979]:
Here Bi, Qi, and Ni represent the width of the lake, the flow rate, and the buoyancy frequency at the level of the insertion. Travel times as intrusions were calculated based on average dimensions of the reservoir, observed inflow rates, and simulated buoyancy frequencies at the level of insertion. Finally, underflowing parcels will reach the dam wall as gravity currents, and their travel time from the inflow sections to the dam is explicitly resolved in DYRESM.
2.5. Analysis of Variability
 The variability of residence times (and that of all other variables used in this work) were assessed on three different time scales (interannual, seasonal, and short-term) using the following approach, which is based on the method originally proposed byFeng and Qingcun  to characterize interannual variability and seasonality of wind fields. The value of the variable X at a given time is identified as Xij, where the index j identifies the year, and i the day of the year. The average value of Xij during the year j, X•j, is calculated as
Here nj is the number of days in year j. The mean of the variable during the study period was estimated by averaging equation (5) for all years N in the study period, as
 To analyze time variability of the variable Xij, a 30 day moving average was first calculated, and is denoted as . These filtered values were then averaged among years to get the interannual average of smoothed values (Figure 2, heavy lines), as follows:
These averaged values represent the evolution of variable X in a typical year. The interannual variability is referred to as ΔXy and was characterized as the averaged standard deviation of filtered values from their interannual mean in equation (7), i.e.,
Note that this approach quantifies the magnitude of interannual variability and not differences between years. Hence it does not establish whether some years have high values or low values.
 Seasonality, δXs, was defined by Feng and Qingcun  as the mean difference between summer (June–August) and winter (December–February) months:
Seasonality, as evaluated in equation (9), can be either positive or negative, depending upon whether the summer values were higher or lower, respectively, than winter values. Building upon this approach, seasonal variability was characterized as the average deviation between summer and winter, i.e.,
The benefit of this definition over, for example, that for the standard deviation of the interannual mean , is that it considers only the variability between summer and winter and discards any random monthly variability.