General Lake Model (version 3.1.8) (Hipsey et al., 2019) is a one-dimensional vertical model, freely available, and is designed to simulate the water balance and the vertical stratification of lacustrine systems. The model computes the vertical profiles of temperature, salinity and density by considering hydrological and meteorological forcing. GLM adopts a flexible Lagrangian layer structure (Imberger et al., 1978; Imberger and Patterson, 1981), which allows the layer thicknesses to change dynamically by contraction and expansion, according to density changes driven by surface heating, mixing, inflows and outflows. The number of layers is adapted throughout the simulation to maintain homogeneous properties within them, while the water volume in each layer is determined based on the site-specific hypsographic curve.

The thickness of the surface mixed layer is described in terms of a balance of turbulent kinetic energy, comparing the available energy with that required for vertical mixing. The available kinetic energy calculation considers surface wind stress, convective mixing, shear production between layers and Kelvin–Helmholtz billowing. Mixing in the deeper hypolimnion is modeled using a constant turbulent diffusivity or a derivation by Weinstock (1981), in which the diffusivity is calculated as a function of the strength of stratification (described by the Brunt–Väisälä frequency) and the dissipation rate of turbulent kinetic energy.

The general heat budget equation for the uppermost layer considers the balance of shortwave and longwave radiation fluxes and sensible and latent heat fluxes. The effect of heating or cooling by the sediment can additionally be included. The rate of temperature change in each layer is a function of the temperature gradient and of the relative area of the layer that is in contact with the bottom.

Inflows can be characterized by temperature, salinity and other scalar concentration data. Initial mixing is estimated by the inflow entrainment coefficient, which is calculated using a bottom drag coefficient and water column stability characterized by the Richardson number. The inflow Richardson number, in turn, is computed according to the channel geometry and assuming a typically small velocity and Froude number for the drag coefficient (Imberger and Patterson, 1981). Thereafter, the inflow is placed in a layer of neutral buoyancy along the water column. Thus, a new layer is created, with a thickness dependent on the inflow volume.

CE-QUAL-W2 (version 3.7) (Cole and Wells, 2006) is a laterally averaged (2DV) model, resulting from the integration in one horizontal direction of the differential equations of conservation of mass, momentum and energy. It is an open-source Eulerian model using a structured orthogonal grid that uses a bathymetric map as geometry input and shortwave radiation, cloud cover, air temperature, dew point temperature, wind speed, wind direction and precipitation as meteorological forcing. Hydrodynamic output data include water temperature and longitudinal flow velocity. Laterally averaged models are based on the shallow water equations (Reynolds-averaged Navier–Stokes equations using the hydrostatic pressure assumption in the vertical, thus neglecting vertical accelerations) and are used for modeling hydrodynamics, water quality, and density stratification in lakes and reservoirs for which the transversal gradients of those properties are small compared to gradients in the longitudinal and vertical directions. The assumption of lateral homogeneity can be well suited for describing long and narrow water bodies. The equations are applied in a finite difference grid.

The default turbulence closure model (W2) uses the layer thickness as the mixing length and a formulation for the turbulent viscosity derived by Cole and Buchak (1995). It is also possible to use Nikuradse, parabolic, RNG (renormalization group) and TKE (turbulent kinetic energy, k–ε model) closure schemes. The k–ε closure is frequently used and was chosen for the study.

Delft3D-FLOW (version 4.04.01) (Deltares, 2013), from now on referred to as Delft3D, is a 3D open-source software for simulating the flow and transport of constituents in water bodies. For the simulation of the hydrodynamics, the numerical algorithms behind Delft3D solve the shallow water equations (3D Reynolds-averaged Navier–Stokes equations with the hydrostatic approximation for the vertical direction). The simulation of the transport of matter and heat is achieved through the solution of the advection–diffusion equation. The mentioned equations are solved on a structured finite-difference grid using case-appropriate initial and boundary conditions. Delft3D considers user-defined (constant) background viscosities and diffusivities. They represent all forms of mixing that are not parameterized through the turbulence closure scheme. In order to calculate the heat exchange between the water surface and the air, five different heat flux models are implemented in Delft3D. Those models consider the short- and longwave radiation balances, evaporation and sensible heat fluxes.

The spatial discretization in the horizontal plane can be performed using curvilinear or rectangular grids, with the former having variable cell size. In the vertical direction a Z- or σ-layer configuration can be employed. In the Z model, the number of layers is not constant over the basin and varies with local bathymetry.

Relative humidity, downwelling shortwave radiation, wind (speed and direction at 10 m height) and dew point temperature were measured at a meteorological station located 4 km east of the reservoir. This station is operated by the Technology Institute of Paraná (TECPAR) and measured every 1 min, here averaged to 1 h. The company operating the reservoir (Sanitation Company of Paraná, SANEPAR) measured precipitation nearby the dam, and starting from May 2018, they also measured air temperature at the same location (temporal resolution of 10 min, later averaged to 1 h). Starting from this date, the air temperature data were taken from this station. Cloud cover data were downloaded from the ERA5 database from Copernicus (Hersbach et al., 2018) with hourly resolution.

Air temperature varied seasonally with a lowest monthly-mean value of 14.0±4.3 ∘C (mean ± standard deviation of hourly time series) in August 2018 and the highest temperature in January 2019 (23.7±3.6 ∘C). Large diel temperature variations followed the daily cycle in shortwave radiation. Wind speed was generally low with a total mean value of 2.0±1.0 ms-1. A slight seasonal variation was observed where the lowest monthly averaged wind speed occurred during winter (in June 2018, 1.6±1.0 ms-1) and the largest during spring (November 2018, 2.5±1.0 ms-1). No seasonal pattern was observed for the remaining parameters (Fig. 2).

Daily-averaged discharge and temperature of the inflows were modeled using the Large Area Runoff Simulation Model (LARSIM-WT; Haag and Luce, 2008). The model was calibrated with data from four gauging stations (the two most downstream stations are shown on the map in Fig. 1) for the period 2010 to 2013 with a Nash–Sutcliffe efficiency of 0.77 (for further information see Ishikawa et al., 2021d). In 2018, the model underestimated the peaks of discharges but had good agreement during baseflow conditions. Simulated water temperature for the year of 2018 had a Nash–Sutcliffe efficiency of 0.96.

Starting from March 2018, a temperature logger was installed in the Passaúna River and measured inflow temperature was used instead of the simulated values (sampling resolution of 10 min, here averaged to 1 h). The measurement was made with an accuracy of ±0.1 ∘C and resolution of 0.01 ∘C using a temperature–oxygen sensor (miniDOT, Precision Measurement Engineering, Inc.).

Water abstraction rate at the intake facility was provided by SANEPAR, measured with an inductive flow meter, and provided at hourly resolution. The operator also provided reservoir water level measured by an ultrasonic probe in a 30 min temporal resolution. Outflow discharge at the ground outlet and the spillway were calculated based on standard hydraulic structure design equations, according to the structure's geometry. The discharge coefficients were adjusted using a few downstream discharge measurements (MuDak-WRM project; Fuchs et al., 2019) but also considering the overall water balance, where simulated inflows minus calculated outflows should correspond to the measured water level changes.

Close to the intake facility, where the water depth is about 12 m, a thermistor chain was deployed from 1 March 2018 to 6 February 2019. The chain was fixed at the bottom and had 11 temperature loggers with 1 m vertical spacing, starting from 1 m above the bed. The loggers (Minilog-II-T, Vemco) measured at a sampling interval of 1 min with a precision of ±0.1 ∘C and 0.01 ∘C resolution. An additional logger of the same type was placed under the Ferraria Bridge, with the same configuration from 2 March 2018 to 12 August 2018. In addition, temperature profiles were collected with a CTD (conductivity–temperature–depth profiler, SonTek CastAway) at five locations along the reservoir (Fig. 1) in February, April, May, June, August, November and December 2018, as well as February 2019.

An upward-looking acoustic Doppler current profiler (ADCP Signature 1000, Nortek AS) was deployed close to the thermistor chain (<50 m distance) at the bottom of the reservoir to measure vertical profiles of flow velocity. The device was deployed and recovered for data download and battery replacement several times from 23 February 2018 to 5 February 2019. Its configuration was modified between individual deployments (Table S1 in the Supplement) to improve the data quality and also to adjust power consumption (measurement duration) to the monitoring program. Mean values of the three-dimensional flow velocities were recorded along a vertical profile starting at 0.7 m above the bed up to 1.5 m below the water surface with vertical and temporal resolution of 0.5 m and 5 or 10 min, respectively. High-resolution profiles of vertical velocities were used for turbulence analysis. These profiles covered a depth range of 7.4 m, starting 0.6 m above the bed with a spatial (vertical) resolution of 4 cm and a sampling frequency of 1 or 4 Hz. High-resolution data are not available for the first ADCP deployment.

Parameters that could be used for calibration are related to the exchange of heat and momentum at the water surface and include coefficients for wind drag, light extinction, and sensible and latent heat transfer. Scaling factors were not considered in the calibration process. The light extinction coefficient was intended to have a fixed value for all models based on Secchi disk depth measurements (which the average along the longitudinal and over time was 2 m, resulting in a light extinction coefficient of 0.85 m-1). However, it was noticed that the results of the 2D model could be improved based on this coefficient; therefore, it was considered an additional calibration parameter.

Each model underwent a manual calibration procedure, in which the listed coefficients (see Table 1) were modified in order to reduce the mean absolute error (MAE) of the water temperature. Automatic calibration procedures are available for GLM but were not applied, and its calibration processes were similar to those of the 2D and 3D models. The specific choice of model parameters is presented in Table 1.

Each model used different time steps; nevertheless, the difference between 2D and 3D models was minor. For Delft3D, the time step was defined based on the estimation of Courant number in order to reach numerical stability. In GLM, the default time step of 1 h was used, which was applied in several other studies using the same model (e.g., Farrell et al., 2020; Gal et al., 2020; Ladwig et al., 2021). Due to the relatively large difference between the 1D and the other models, we ran the GLM model with time steps ranging from 1 to 86400 s and compared the simulations with measurements (Fig. S1 in the Supplement). The simulation results differed due to the variable number of vertical layers. The default time step had one of the smallest centered root-mean-square errors and was used for the model comparison. The usage of different time steps should not affect the comparison, once all models were stable and calibrated.

The same boundary conditions were used for all three models, with temporal resolutions according to the availability of data and model requirements. The boundary conditions are the following: air temperature, relative humidity, downwelling shortwave radiation, wind speed, wind direction, precipitation, cloud cover, outflow discharge (for water intake and continuous discharge of ground outlet), and inflow discharge and temperature. The water level at the spillway was used as a boundary condition as it represents an open boundary in the 3D model.

The model simulations were compared with observations in terms of mean absolute error (MAE), centered root-mean-square error (cRMSE), standard deviation (σ), correlation coefficient (R) and coefficient of determination (r). These parameters were calculated as follows: 3MAE=1n∑i=1n(si-mi),4cRMSE=1n∑i=1n(si-s‾)-(mi-m‾)2,5σ=1n-1∑i=1nai-a‾2, where n is the number of observations, ai is one observation and a‾ is the mean of all samples (measured or simulated). 6R=1n∑i=1nsi-s‾mi-m‾σsσm, where s denotes the simulated value and m the measured value. 7r2=1-SSresSStot, where SSres is the sum of the squared residuals, and SStot is the sum of squared data.

Taylor diagrams (Taylor, 2001) are used to assess the simulation results of the vertical temperature distribution. The diagram provides a concise overview of results through comparison with observations in terms of standard deviation (σ), correlation coefficient (R) and centered root-mean-square error (cRMSE) in one plot.

In addition, descriptive statistics (mean, standard deviation, percentiles and percentage differences) were calculated to compare simulated and observed values.

Following Ishikawa et al. (2021a), the water column was classified as mixed or stratified based on a threshold of the Schmidt stability (ST). Days with daily-averaged Schmidt stability equal or lower than 10 % of the annual maximum Schmidt stability (calculated with the measured data as 16.3 Jm-2) were considered mixed, while days with higher ST were classified as stratified.

Schmidt stability was calculated using the software Lake Analyzer (Read et al., 2011) as 8ST=gAS∫0zD(z-zv)ρzAzdz, where g (ms-2) is the gravitational acceleration, AS is the reservoir surface area, Az is the area at depth z, ρz is the water density at depth z, zD is the maximum depth and zv is depth of the reservoir center of volume calculated as zv=∫0zDzAzdz/∫0zDAzdz.

The thickness of the upper mixed layer (UML) was also computed by Lake Analyzer using a threshold for the vertical density gradient, which depends on the density gradient of the entire water column (see Read et al., 2011, for details).

Due to the dynamic mixed layers of GLM, its results were linearly interpolated for each 0.5 m over depth. To calculate errors, the measured temperatures correspondent to the timestamp of simulation results were selected, and simulation results were linearly interpolated to match with the observations over depth. This procedure was followed for the three models.

CE-QUAL-W2 provided one horizontal velocity component (longitudinal velocity), being positive in the downstream direction and negative in the upstream direction. To compare flow velocities, the longitudinal component of Delft3D and the measurements were computed by aligning the flow in the same direction as the 2D model; thus, the transversal velocity component was not considered in our analysis.

Water from inflowing rivers can take different flow paths after entering the reservoir, which are affected by density stratification in the reservoir and inflow conditions. Density-driven inflows can be classified as underflows, interflows, or overflows, where the first is spreading along the reservoir bottom, the second at an intermediate water depth and the last at the reservoir surface.

Substance transport in models was analyzed by simulating the transport of a conservative tracer that was added continuously to the inflowing water. Tracer concentrations at the intake region were assessed to observe substance transport from the Passaúna River to the monitoring site through vertical profiles of the daily maximum value of tracer concentration. The GLM model was set up with a maximum water depth of 17 m, while the water depth at the point of analysis was ∼12 m. For this reason, we present model outputs up to a maximum depth of 12.5 m. If the maximum tracer concentration was below this depth, the inflow regime was categorized as underflow. For CE-QUAL-W2 and Delft3D, the closest cell to the station was selected, which represents the actual water depth at the monitoring site.

At the end of the simulation period, all three models presented a lower water level than the measured. The last measurement was 886.81 m a.s.l., and the closest value simulated was in Delft3D with 886.49 m a.s.l., which was also the one with the lowest error (MAE=7.4 cm). GLM simulated a final water level of 886.44 m a.s.l., and CE-QUAL-W2 estimated 886.36 m a.s.l., with respective MAE values of 10.5 and 10.8 cm (Fig. S2a in the Supplement). Additional statistical metrics are presented in the Supplement (Table S2).

The largest discrepancies in water level occurred when it raised over the spillway crest. GLM and Delft3D had water above the crest for a longer period than observed, and their levels kept being larger than the measurements until a sharp increase in October 2018, which none of the models reproduced. Total spillway discharge had its largest volume in CE-QUAL-W2: 2.93×107 m3, GLM had a spillway volume as the 2D model of 2.87×107 m3, and Delft3D simulated 3.7 % less spillway discharge than CE-QUAL-W2 (2.83×107 m3) (Fig. S2b).

Evaporation values in all models were in the same order of magnitude but significantly different (one-way ANOVA test with p value=5×10-17, with the null hypothesis that both pieces of data have the same mean). The 1D, 2D and 3D model estimated daily-mean evaporation rates were 2.9±1.3, 2.7±1.0 and 3.4±1.4 mmd-1, respectively. Comparing the volumes due to evaporation with the reservoir volume (7.0×107 m3), over the year GLM lost the equivalent of 12.0 % of the reservoir volume, CE-QUAL-W2 with the lowest evaporation rate lost 11.0 % and Delft3D lost 14.3 %.

Regarding the water balance, all models had errors of comparable magnitude: 1D, 2D and 3D models had errors in stored water volume of -4.4 %, -4.9 % and -3.7 %. The error in terms of water level was similar for all models (∼10 cm) and is in the range of errors reported in the literature (e.g., Dai et al., 2013; Jeznach et al., 2014; Chen et al., 2016; Bueche et al., 2020). GLM had a constant water level from January to May 2018, corresponding to the maximum level defined by the hypsographic curve due to the spillway crest elevation. CE-QUAL-W2 had lower water levels and a larger discharge over the spillway. Both models calculated the discharge by empirical equations. Delft3D was forced by the measured water level as an open boundary at the spillway location. For water level elevations higher than the bathymetry at the outflow cells, water will leave the domain. For water level elevations lower than the bathymetry at the outfall cells, no water should flow at all. However, as the bathymetry at the outflowing cells could not reproduce the spillway geometry, periods of water flowing into the domain were observed, which is obviously an artifact. Despite similar results in terms of storage volume, discharges through the spillway and evaporation differed among models, with Delft3D having the largest evaporation loss and CE-QUAL-W2 the lowest. The differences can be attributed to the differences in how the models describe and implement the boundary conditions. We cannot affirm which model is most precise, because the modeled processes (e.g., evaporation or flow over spillway) were not directly measured. In addition, measured data are also associated with uncertainties. There is an underestimation of peaks of inflow discharge from LARSIM-WT and poor data accuracy on outflows of the bottom outlet at the dam and the spillway discharge, which were important parameters that contributed for the discrepancies of the water balance of the reservoir. Thus, care has to be taken when defining boundary conditions in all models, and the first step should always be to check water balance and flows at the boundaries.

All three models simulated the dynamics of temperature stratification in reasonable agreement with observations. Resulting errors are in the same order of magnitude as values reported in other model applications (e.g., Bruce et al., 2018; Weber et al., 2017; Kobler et al., 2018; Mi et al., 2020; Chanudet et al., 2012; Dissanayake et al., 2019).

Stratification is mostly driven by heat exchange associated with absorption of solar radiation, net longwave radiation, evaporation, precipitation and sensible heat transfer at the water–air interface. Despite the different parameterizations of the surface heat flux, which also included downwelling longwave radiation that was not measured, and the use of different coefficients (see Table 1); daily averages of net surface heat flux of the three models had no significant difference among each other. Other processes that influence the temperature stratification are inflows, surface runoff, groundwater inflow and heat exchange with the sediment (Wetzel, 2001). Out of those, only river inflow temperatures were known and implemented in all models. The others were considered to be negligible. Regarding the heat exchange with sediment, Stepanenko et al. (2013) showed that it did not have significant influence on simulations of bottom water temperature of a shallow lake for a comparable temperature range as observed in Passaúna Reservoir. Even though the errors were of comparable magnitude, the model simulations of thermal stability differed among the models, with underestimated temperature in the 2D simulations and overestimated temperature in the 3D simulations. We assume that the differences were related to model dimensionality and the parameterization of vertical mixing and inflows.

The 1D model imposes the largest simplification by neglecting horizontal variations in flow and water temperature, even though an initial mixing of inflows due to entrainment is parameterized in the model. It is important to point out that the continuous temperature measurements at a single sampling location are not ideal for comparison with 1D simulations, and spatially averaged temperature profiles are more representative for the horizontally homogenous conditions assumed by the 1D model. The lower temperatures in the deeper layers can be explained by the cold inflow temperatures combined with the inability of reproducing the enhanced heat exchange of the inflowing water with the atmosphere in the shallow forebay. In addition, the surface temperature was overestimated by GLM, which explains the larger number of stratified days and increased thermal stability. Another factor that can potentially contribute to errors is the selection of the first 12 m in depth for comparison with measurements, thus excluding the bottom boundary layer of the 1D vertical grid. On the other hand, the 2D and 3D models had a better representation of the strength of vertical density stratification, despite having overall divergent results – respectively colder and warmer temperatures than measured. These differences can be at least partially explained by the calibration process, which becomes more difficult for increased dimensionality. Due to the short computational time required for 1D models, it is possible to perform repeated runs with varying calibration parameters (e.g., light extinction coefficient) and to improve agreement with data during model calibration. Moreover, tools for automated model calibration are available (Bueche et al., 2020).

CE-QUAL-W2 estimated 92 d with mixed conditions, which is in closest agreement with the observations (95 d), but their temporal dynamics differed from observations especially during winter. The intermittency between mixing and stratification was more frequent; mixed periods were longer from June to August and the last mixing event shorter. In the Delft3D simulations, the shorter mixed periods are missing, which reduced the total duration of mixed conditions to 78 % of the observed.

Both 2D and 3D simulations of temperature distributions along the longitudinal cross-section of the reservoir were in good agreement with observed temperature distributions. The 1D simulations reproduced the horizontally averaged temperature distributions, with better results when the reservoir was relatively homogeneous. The close agreement between the 2D and 3D simulations with measurements indicates that transversal gradients are of minor importance for the stratification in Passaúna Reservoir. This is further supported by the good agreement between both models for the simulated tracer transport from the river inflow to the water intake station. Nevertheless, the tracer analysis showed how the differences in temperature simulated by each model also affected the inflow pathways.

These results highlight the advantages of CE-QUAL-W2 and Delft3D, as they are capable of representing the observed longitudinal gradient, especially considering the inflow region, where colder river water flows downwards as an underflow. This underflow is responsible for transporting not only cold water but also dissolved nutrients and suspended sediment over long distances into the deeper parts of the reservoir. Those dynamics are represented in GLM only in a very simplified manner, explaining the weaker performance of GLM with respect to water temperatures at higher depths (Fig. 5).

Tracer dynamics observed with GLM complies with the hypothesis that the lower temperature at the bottom was caused by inflow pathways of mostly underflows because of the absence of the forebay. Fenocchi et al. (2017) demonstrated that, in order to reproduce the thermal response to inflows in a subalpine lake with GLM, it was necessary to use an impractical coefficient of light extinction. The general colder temperatures simulated by CE-QUAL-W2 placed the inflow at deeper depths and confined them in layers. This behavior was observed because the longitudinal flows were located below the UML, thus showing the higher concentrations of tracer especially after September (Fig. 13). For Delft3D, the opposite was observed: the density currents were within the UML, which diluted the tracer concentration, and the depth of its maximum was strongly variable over the last 6 months. The travel times of the tracer was evaluated by identifying the first time that the tracer concentration was larger than 10-3 kgm-3 at the intake after the release of the tracer at Passaúna River. The transport in CE-QUAL-W2 was faster with travel times of 2.2 and 3.5 d in Delft3D, which can be associated with the higher tracer concentrations of the 2D model. This information is important for management of reservoirs during spilling accidents (e.g., Jeznach et al., 2014); for GLM it is not possible to estimate time travel, since inflows are directly placed at defined layers. Studies assessing the inflow pathways through modeling demonstrated a good agreement between simulations and observations, e.g., Marti et al. (2011) and Zamani et al. (2020) with 3D models and Jeznach et al. (2014) with CE-QUAL-W2.

Despite similar seasonality of stratification and mixing predicted by the three models, the tracer analysis demonstrated how the spatial simplification affects the transport of substances. This was clear especially for the 1D model that differed considerably from the 2D and 3D models. CE-QUAL-W2 and Delft3D presented similar seasonal patterns for density currents, which influenced the stratification in the reservoir mainly by underflows that added a layer of colder water at the bottom and were strongly present in the simulations during winter. Ishikawa et al. (2021a) analyzed the distribution of density currents, categorized as underflows, interflows and overflows, based on the comparison of the measured temperature between the forebay region and the main reservoir (only available for the first half of the total period) with the temperature profile at the intake. Overflows were assigned when the forebay temperature was larger than the surface of the measured profile, and underflows were assigned when lower than the bottom; otherwise, they were interflows. A similar classification of density currents was made using the location of the maximum tracer concentration of the models (Fig. S4). Processes such as entrainment, mixing, diffusion and dilution of inflow are neglected in this approach; therefore, overflows were frequent in March and April 2018, while of minor importance in the simulations. However, the underflow season that was expected in the prior analysis was at some extension reproduced by CE-QUAL-W2 and Delft3D. It was mainly present during the winter, with shifts of 1 month among analyses made based on observations and simulations, matching with the period where the process is relevant for stratification.

For the second half of the simulated annual cycle, the flow paths of 2D and 3D models differed the most with respect to the occurrence of overflows, which is explained by the location of the density currents in relation to the UML depth (Figs. 13 and S4). All models had poor results for UML depth estimated from measurements. For this reason, the 2D model presented a smoothed error along the depth (Fig. 5), while the 1D and 3D models simulated consistently shallower UML depths, causing the peak in the error and correlation profiles. The predictions of thickness of the mixed layer and the slope of the thermoclines are generally challenging for models, as reported for other model applications (Perroud et al., 2009; Huang et al., 2010).

Simulation of flow velocities showed less agreement with measurements than temperature, although errors were in the same range of other work with Delft3D (Chanudet et al., 2012; Dissanayake et al., 2019). The magnitudes of simulated longitudinal flow velocities were generally lower than observations, but Delft3D was capable of reproducing the overall characteristic of larger magnitudes of longitudinal flow velocities during stratification and larger relative occurrence of currents (>90th percentile), while flow velocities simulated by CE-QUAL-W2 showed no agreement in magnitude or dynamics with observations. For a fair comparison with the 2D model, laterally averaged flow velocity observations would be required, which are not accessible from longer-term observations. However, the transversal flow velocity component of observations and simulations of Delft3D were disregarded in the comparison (0.96±0.98 and 0.54±0.64 cms-1, respectively). The ratios of mean transversal and longitudinal velocity components are 0.7 for measurements and 0.5 for Delft3D, which indicates that potential transversal flow processes are not resolved by CE-QUAL-W2.

The poor results regarding magnitude and direction of flow velocities in both models can be associated with the fact that flow velocities in Passaúna Reservoir were generally small, internal seiches were not observed and circulation patterns are absent. In studies where those properties are relevant, better agreement between observations and 3D simulations were reported (Huang et al., 2010; Chanudet et al., 2012; Dissanayake et al., 2019), and a simulation in Lake Erie with CE-QUAL-W2 reproduced the oscillation frequency of basin-scale seiches but not their amplitudes (Boegman et al., 2001). Further, the direction of flow velocities is highly affected by the inaccuracy of wind direction measurements, and weak wind intensities are expected to have lower correlation with flow velocities, since they potentially change direction more frequently (Dissanayake et al., 2019), which is the case in Passaúna. Moreover, the correlation between observed and simulated flow velocities increased towards the bottom, probably because the bottom is a better represented boundary for the process, whereas it is the opposite is the case for temperature.

The turbulent closure models are relevant for the vertical mixing, thus the different approaches implemented in the models can be considered to contribute to the variation among simulated UML thicknesses. GLM is the one with the thinner UML and poorest correlation; its simplification in dimensionality and the structure of the model in mixed layers can be the cause for lower mixing. CE-QUAL-W2 neglects transversal flows, which may contribute to the shear profile and cause errors in turbulence production. Lastly, Delft3D resolved all three dimensions, but dissipation rates simulated by the model differ from those estimated from measurements of flow velocities. The log-averaged profiles of dissipation rates computed by the 3D model follow an expected profile with a turbulent surface boundary layer, a low energetic interior and increasing dissipation rates towards the bottom (Wüest and Lorke, 2003). Only few studies in the literature reported comparisons of measured and simulated dissipation rates. In general they presented good agreement, but all of them were performed in high energetic environments such as ocean regions with the presence of breaking waves, near to the surface, and large lakes (Stips et al., 2005; Jones and Monismith, 2008; Paskyabi and Fer, 2014; Moghimi et al., 2016). In spite of all uncertainties regarding the estimated dissipation rates, in our study the results from the 3D simulations revealed that the model has limitations in reproducing all processes contributing to energy dissipation in a medium-sized reservoir.