To study the lake breeze effects in the Alqueva reservoir, the Meso-NH model was used. Meso-NH is a non-hydrostatic mesoscale atmospheric research model. It can simulate the evolution of the atmosphere on scales ranging from large (synoptic) to small (large eddy) and has a complete set of physical parametrizations. Meso-NH is coupled with the SURFEX (Surface Externalisée, ) platform of models for the representation of surface–atmosphere interactions by considering different surface types (vegetation, city, ocean, inland waters).

Meso-NH allows a multi-scale approach through a grid-nesting technique . In this work, three nesting domains were used: a 400×432 km2 domain with 4 km horizontal resolution to take into account the large-scale circulations, namely the influence of the sea breeze (Fig. a); an intermediate 96×72 km2 domain with 1 km horizontal resolution centred at the Alqueva reservoir (Fig. b); and a finer 40×40 km2 domain with 250 m spatial resolution to track the small-scale effects of the lake (Fig. c). Hereinafter we denote these three domains A–C correspondingly. The two-way nesting technique used in Meso-NH allows to conduct simulations on different horizontal resolutions at the same time. Domain A is the “father” domain for B, which means that simulation results in domain A are interpolated and used as initial and boundary conditions for domain B. The same scheme applies for domains B and C. European Centre for Medium-Range Weather Forecast (ECMWF) operational analyses, updated every 6 h, were used for Meso-NH initialization and domain A boundary forcing.

For surface and orography, ECOCLIMAP II and SRTM (Shuttle Radar Topography Mission, ) databases were used, respectively, both updated with the inclusion of the Alqueva reservoir by . All model domains had 68 vertical levels starting with 20 m up to 22 km, including 36 levels for the lower atmospheric level (2 km). The model configuration included a turbulent scheme based on a one-dimensional 1.5 closure , and a mixed-phase microphysical scheme for stratiform clouds and explicit precipitation , which distinguishes six classes of hydrometeors (water vapour, cloud water droplets, liquid water, ice, snow, and graupel), was used. Longwave and shortwave radiative transfer equations are solved for independent air columns . Atmosphere–surface exchanges are taken into account through physical parametrizations: the surface soil and vegetation are described by the Interface Soil Biosphere Atmosphere (ISBA) model ; the town energy balance was handled according to . Basic parameters for each model domain are shown in the Table . Deep and shallow convection parametrization schemes were activated in the coarser domain A. The 1 km and 250 m resolutions of domains B and C are fine enough for the deep and shallow convection to be represented explicitly. The following schemes were used (see Table ): KAFR , EDKF , WENO , and ICE3 .

To track the impact of the reservoir on the weather conditions, two numerical simulation were performed: one with the surface input files updated to include the Alqueva reservoir (ECOCLIMAP database version updated by ) and another with the previous version of this database where the reservoir is absent. In order to distinguish these simulations hereinafter we denote them LAKE1 and LAKE0, correspondingly. Both simulations covered the case study period, 22–24 July 2014, with 1 h output. To reproduce the atmospheric conditions more realistically the simulations included the previous 24 h (21 July), so the model was integrated for 96 h. The differences between these two simulations were then computed, with the aim of evaluating the direct influence of the lake on the atmosphere.

In order to better represent the evolution of the lake surface temperature and therefore the water–air heat fluxes, the FLake (Freshwater Lake) model was used. FLake is a bulk-type model capable of predicting the evolution of the lake water temperature at different depth on timescales from a few hours to many years. For an unfrozen lake it uses a two-layer approach: upper mixing layer, with a constant water temperature, and the thermocline beneath it where the temperature decreases with depth. Parametrization of the thermocline profile is based on the concept of self-similarity, assuming that such an approach could be applied to all natural and artificial freshwater lakes.

The FLake model requires at least the following sets of variables and parameters to run: four initial parameters to describe the lake temperature structure, six atmospheric input variables for each time step, and two parameters – lake depth and the attenuation coefficient of light in the water. This coefficient is used to compute the penetration of the solar radiation in the water body. In this work, the attenuation coefficient was set to 0.85 based on in situ measurements carried out in Alqueva by .

The FLake prognostic variables that need to be initialized are water temperature at the bottom, temperature and depth of the mixing layer, and shape factor Cf – a parameter that describes the shape of the thermocline curve. In the parametrization proposed by for the normalized temperature profile it varies from 0.5 to 0.8. The initial values of the shape factor Cf, a water mixing layer temperature, and depth were determined using a fitting technique applied to the observed water temperature profile at a given time in Montante platform (Fig. a). Short-term FLake model runs are very sensitive to initial parameters. The fitting technique is based on the assumption that the bottom temperature is fixed and given by the value of the lowermost sensor. Thereby, the other three parameters could vary within some range until the best set is found. The initial conditions for our simulations were obtained following this technique: Cf=0.8, mixed layer temperature is 23.8 ∘C, and depth is 3.4 m. Test simulation with these set of inputs was carried out using a stand-alone version of the FLake model (not coupled to Meso-NH). The results of the comparison of water mixing layer temperature is shown in Fig. b. The maximum difference does not exceed 0.8 ∘C, which is a very good result for such a short-term simulation.

The observed daytime temperature profiles showed strong skin effects (higher temperatures in the first 10 cm) and could not be well fitted by a FLake type temperature profile, which assumes a constant temperature in the mixed layer. Thus, the midnight profile was used initially and the simulation started at midnight, 21 July 2014.

The required atmospheric variables were taken interactively from the Meso-NH simulation since FLake was implemented in the SURFEX model by .

The depth of artificial lakes decreases rapidly from the centre to the shore, because the bottom of the reservoirs used to be valleys. In case of Alqueva, when completely filled, the mean depth is of about 17 m (http://www.edia.pt/pt/, 28 September 2018). However, the local depth at Montante platform can reach 70 m. As a 1-D bulk model, FLake has only one depth value, which should be seen as an effective depth and is not easy to assess. Moreover, the FLake model is not capable of representing deep lakes; it works well for depths from 20 to 50 m with the sediments routine switched off. After a series of sensitivity tests of short-term (2–4 days) and long-term (2–4 months) simulation it was found that the best simulations results can be obtained with the bottom depth value of 20–30 m. Thus, since the deepest temperature probe was installed at the depth of 27 m, this value was chosen for the effective lake depth in this work. The comparison between measurements of water temperature near the surface (at 1 m depth) and FLake-simulated values of mixed layer temperature is shown in Fig. b. The sensor at 1 m depth was chosen because it always stays in the mixed layer and is not affected by surface “skin” effects. Modelled values are close to measurements, which indicates that the initial conditions were realistically imposed.

The ALEX IOP took place between 22 and 24 July 2014 at the Alqueva reservoir. It included the launch of 18 meteorological balloons every 3 h. The radiosondes took measurements of air temperature, humidity, pressure, and wind speed. As the balloons did not ascend vertically and flew several kilometres away from the launching point, a trajectory profile comparison was performed. Each balloon had a GPS tracker to register its coordinates every 2 s, which was used to build a corresponding numerical trajectory on the simulation domain. Radiosondes reached the altitude of the top of the model (about 22 km in about 2.5 h). Therefore in order to build the simulated profile, three consecutive hourly outputs from the model were used.

Figure a–c represent examples of the daytime profiles of air temperature, relative humidity, and horizontal wind speed. Examples of night profiles can be found in Fig. d–f. In general, the night-simulated profiles show slightly better accordance with model results.

Figure  shows the same profiles, but for the lower troposphere level (3000 m altitude). Simulations are in good accordance with observations. The simulation results are within the confidence interval of the measurements as given by the radiosonde accuracy – ±0.5 ∘C, ±5 % relative humidity, and ±0.15 m s-1 wind speed with 2σ confidence level (95.5 %).

The principal features of the profiles are well represented by the model. During daytime, air temperature and relative humidity curves indicate that the model tends to represent the height of the boundary layer at 2–2.5 km altitude well (around 2 km in Fig. a and b). Overall, Meso-NH reproduces the air temperature above the surface layer (over 500 m) very well. Near the surface, the Meso-NH tends to anticipate the development of the unstable boundary layer in the morning (09:00 and 12:00 UTC), simulating higher temperatures in the lower levels. In the late afternoon (18:00 and 21:00 UTC) the model also tends to anticipate the decrease in the temperature in the surface layer (see the Supplement, Fig. S1).

The vertical patterns of relative humidity and wind speed are good, as observed and modelled curves look similar; nevertheless simulations tend to be more conservative and their values do not represent all changes in altitude recorded by the radiosonde. Nocturnal low-level jets at the edge of the boundary layer are represented by the model, but their magnitude is slightly weaker than that observed. The complete set of observed versus simulated profiles can be found in the Supplement (Fig. S2). The moisture vertical profile in the boundary layer is well reproduced by the model, as can be seen in the graphs of the relative humidity (Figs. b, e, and S3). Above the boundary layer, the radiosondes show a dry layer, which is also well simulated. From 23 July the observations show the appearance of a moist layer close to the troposphere, the magnitude of which is overestimated by the model. At dawn on 24 July the radiosondes and the model indicate the existence of a very moist layer close to the surface, with the formation of low clouds that were not formed in the simulations.

Statistical results for them are the following: temperature average bias is -0.13 ∘C, RMSE is 1.49 ∘C, and the correlation coefficient is 0.99; relative humidity average bias is 0.59 %, RMSE is 11.26 %, and the correlation coefficient is 0.87; and for the wind speed average bias is 0.05 m s-1, RMSE is 2.07 m s-1, and the correlation coefficient is 0.90. These values testify that the simulation is in a good accordance with the observations, in line with similar studies of Meso-NH validation against radiosonde data e.g..

The model was also validated against 12 IPMA automatic meteorological stations. For this comparison the output of the bigger domain A was used. Geographical positions of the stations can be found in Fig. a. Scatter plots of air temperature, relative humidity, and wind speed are shown in Fig. . It should be mentioned that not all stations provided the same set of variables. The scatter plots show the intercomparison of the model data (x axis) and the measured values (y axis) over all stations in the simulated period. The model tends to overestimate lower values of air temperature (14–24 ∘C) and slightly underestimate higher values (>30 ∘C), as can be seen from Fig. a.

In some stations and for several times, the model simulates lower values of relative humidity within the range from 40 to 100 % (Fig. b). Figure c indicates that the wind speed is slightly underestimated by the model.

Statistical parameters (bias, mean absolute error, root mean square, and the correlation coefficient) for each station are shown in Table .

Simulated and observed air temperature are highly correlated (the correlation coefficient is higher that 0.91) with bias always less than 1∘. The worst results are observed in Portalegre (square points in relative humidity plot in Fig. b), and a possible reason for this relies on the location of the station, which is installed in a complex mountain area, possible not well represented in the model orography. Regarding wind speed, Meso-NH provides values for 10 m height while the measurements were made at 2 m. For proper comparison modelled values were interpolated to the height of the sensors using a known logarithmic approach and a roughness length (which was also obtained from the model). Table  shows small biases, in general lower than 1 m s-1, and relatively high correlation coefficients for wind simulations (0.68–0.92). The lowest correlation coefficient is also obtained for Portalegre data. Overall, simulation results are in good agreement with synoptic station data, and the statistical parameters are similar to other published works that use Meso-NH e.g..

In addition to the validation against the IPMA synoptic stations, comparisons were made with data obtained at ALEX meteorological stations (Barbosa, Cid Almeida, and Montante platform). Their coordinates were used to locate corresponding grid points on the C domain output. For land stations with grid points associated with water fraction, the nearest land grid point was chosen.

Figure  shows the time evolution of simulated and observed air temperature and wind speed at Cid Almeida, Barbosa, and Montante sites. Overall, the simulation results are slightly more conservative (except wind speed over the Montante platform), but in general, the patterns are well represented. The model could not represent the maximum and minimum temperatures well, especially in land stations where the temperature range is larger. Regarding wind speed, the model underestimates the maximum values at land stations (Fig. e and f) and, on the contrary, overestimates the values at Montante platform (Fig. d), but the principal features of the curves are represented. Statistical values for this validation are as follows. For Barbosa, air temperature average bias is 0.23 ∘C, RMSE is 1.37 ∘C and the correlation coefficient is 0.98; for wind speed these values are as follows: average bias is 0.55 m s-1, RMSE is 1.08 m s-1, and the correlation coefficient is 0.73. For Cid Almeida, temperature average bias is 0.5 ∘C, RMSE is 1.57 ∘C, and the correlation coefficient is 0.98, wind speed average bias is -0.36 m s-1, RMSE is 1.24 m s-1, and the correlation coefficient is 0.69. For the Montante platform, air temperature average bias is -0.1 ∘C, RMSE is 1.22 ∘C, correlation is 0.98, wind speed average bias is -0.97 m s-1, RMSE is 1.55 m s-1, and the correlation coefficient is 0.61.

The temporal evolution of simulated and observed latent and sensible heat fluxes at Montante platform is shown in Fig. a and b. Overall patterns of the curves are similar but the simulated one is more smooth. Comparison demonstrates that for latent heat the RMSE is 57.34 W m-2 with correlation coefficient of 0.47, and for sensible heat the RMSE is 13.39 W m-2 with the correlation of 0.82.

Both observed and simulated curves of Fig. a reveal that sensible heat flux has two different periods during the day, positive when air-water temperature difference is negative, and vice versa, showing that during daytime the water receives energy from the air and during nighttime the water warms the nearby air. The transition between the two regimes is well captured by the model. Figure b also shows that the magnitude of the sensible heat flux is relatively small when compared with the other terms of the energy balance. Daily maximum positive (negative) fluxes between 30 and 60 W m-2 (-15 and -30 W m-2) are well reproduced by the model. An apparently strange behaviour appears on the afternoon of 22 July, with the sensible heat flux being almost zero. This effect, unfortunately not documented due to the lack of data, will be discussed later and is linked to the fact that the wind is very weak during this period (see Fig. d).

More detailed analysis of Fig. a shows that the lowest heat flux values usually occur during the afternoon (12:00–18:00 UTC), under windless conditions, and high peaks in the early evening (20:00–21:00 UTC). The simulation reproduces these peaks with 1–2 h delays that are related to the delay on the simulated wind speed. The magnitude of the latent heat flux daily maximum (order of 200–250 W m-2) is well captured by the model. The delay in the simulation of the peaks reduces the value of the correlation coefficient and is a manifestation of the so-called double-penalty that penalize high-resolution model scores. As seen in Fig. b the simulated latent heat flux is almost zero between 14:00 and 16:00 UTC of 22 July. As pointed out before, there is a gap in the flux measurements during this period, but data from the day before indicate that the results are realistic. This effect of almost zero evaporation from water on a very hot day is contrary to common sense and will be discussed later.

Wind direction at ALEX stations is represented in Fig. . Different behaviour in wind direction between the two stations from 21 to 23 July is clearly seen from measurement data (green dots). In Barbosa station the wind changes from a north-west to a south regime during daytime while in Cid Almeida this effect is not observed. In the simulations this difference is not so clear, but is still visible during the afternoon on 22 July. Barbosa station, located on the north-west shore of the lake, indicates the presence of the lake breeze because its direction is the opposite to the dominant wind. At Cid Almeida station, on the south-east shore, the lake breeze is co-directed with the dominant wind.

The lower layers of air are the first to be affected by the presence of the water surface. Differences in air temperature at 2 m during 22 July are shown in Fig. , the warmest day of the IOP and thus with a stronger lake breeze. The positive anomaly (up to 3–4 ∘C) can be traced during the period from 1 h after the sunset (21:00 UTC) to 1 h after the sunrise (07:00 UTC). By positive and negative anomalies here we mean differences between LAKE1 and LAKE0 simulations. Examples of positive night anomalies are illustrated in Fig. a and b. Night north-west wind transports warm air from the lake to the south-east part of the reservoir for up to 2 km away from the shore. The daytime period is characterized by negative temperature anomalies up to 7 ∘C (Fig. c–f). Initially, the effect is essentially limited by the lake borders. When the large-scale sea breeze system arrives, temperature trace of the lake impact is advected by the wind and can be found in 10–12 km away from the south-east part of the reservoir (Fig. f).

Vertical cross sections help to illustrate the processes at different altitudes. Two different cross sections Cs1 and Cs2 are shown to provide a better visualization of the three-dimensional structure of air circulation above the lake. The first one crosses the lake near Montante platform and the second in the middle, exact locations are indicated in Fig. a. Cross sections Cs1 along 38.215∘ N (Fig. ) show the evolution of wind and potential temperature during 22 July in the experiment with Alqueva (simulation LAKE1). The highest impact on the air temperature can be observed in the early afternoon (12:00–14:00 UTC). The boundary layer is cooling down and its height decreases from more than 2 km above the land outside to values close to 1 km over the lake surface (Fig. a). The thermal anomaly induced by the presence of the reservoir seems to affect an area greater than what was identified at the surface, especially in the middle of the boundary layer. Later on, at 19:00–20:00 UTC the powerful ocean breeze system reaches the area and cools the lower (1 km) layer of air by 6–7 K. The progression of the sea breeze front is impressively well shown in Fig. d (20:00 UTC), when it reaches the border of the reservoir, and in Fig. e and f (21:00–22:00 UTC), when it is already beyond the east bank of the Alqueva reservoir. More cross sections of 22 July 2014 with potential temperature can be found in Fig. S4.

Alqueva causes a similar anomaly on 2 m relative humidity, which is shown in Fig. .

At night when the temperature impact is negative some small negative differences in relative humidity can be seen over the lake surface (Fig. a). There are also traces of daytime positive impact, essentially due to the decrease in air temperature, advected by the sea breeze in the south-east direction. In the morning, however, the difference of relative humidity cannot be detected because the thermal impact is not strong enough (Fig. b). Figure c–e show how relative humidity increases during the daytime over the water surface. The peak of the difference can reach 50 % in the afternoon (Fig. f). In general, lake impact on relative humidity is limited by the area of the reservoir and does not spread over the surrounding land.

Differences in near-surface sensible heat fluxes and contrast of the air temperature over the land and water surfaces during the daytime induce the formation of the lake breeze system. The development of the lake breeze is illustrated in Fig.  (arrows that correspond to the wind speed lesser than 0.5 m s-1 are not plotted). During the night, the large-scale circulation (Fig. a and b) is dominant in the area. After the sunrise (07:00–08:00 UTC) the air temperature over the water surface becomes lower than the air temperature over the surrounding areas, which induce a thermal circulation directed from the centre of the lake to its shores. The breeze intensifies during the afternoon reaching 6 m s-1 in some areas (Fig. d and e).

Daytime cross sections Cs1 in Fig. a–c indicate that the direct lake breeze can be found on altitudes up to 300 m above the lake, with a divergent flow over the water surface. The lake breeze intensity and pattern depends on the local orography, but usually the traces can be found 4–6 km away from the lake shores (Fig. c). In altitude, a return flow is visible in the eastward wind component over the west shore and a westward component in the east of the reservoir, which causes an upper-level convergence that can be seen in Fig. a–c. This will be discuss together with the effects of the reservoir on the moisture field, in which the structure of the lake breeze system is more visible.

In the late afternoon (18:00 UTC) the negative temperature anomaly due to the presence of the lake is getting weaker, and the breeze system starts to wane and dissipate. At 19:00–20:00 UTC the ocean breeze arrives to the area and overlaps the local circulations (Fig. d–f).

Cross sections Cs1 and Cs2 presented in Fig.  show that the lake breeze system includes a descending branch over the reservoir that carries dry air from a height of about 2–2.5 km and redistributes it over the lake surface. Additional cross sections illustrating this process can be found in the Supplement (Figs. S5 and S6).

This dry downstream is confirmed by the measurements of water vapour mixing ratio at the Montante platform. As can be seen in Fig.  the observed and the simulated mixing ratio of water vapour have a daily minimum with average values of about 8–8.5 g kg-1 around 14:00–16:00 UTC. During the afternoon of 22 July, the day with a strong lake breeze, the minimum reached a value lower than 6 g kg-1. Out of the period in which the air over the lake subsides, the water vapour mixing ratio returns back to 9–10.5 g kg-1. The presence of this dry downstream was proposed as a hypothesis by and is proved through the performed simulations. In the same figure it is clearly seen that the model tends to overestimate the mixing ratio, except during the afternoon of 22 July.

However, Fig.  also shows that outside the reservoir there are zones of low-level convergence and upward motion that increase the moisture of the boundary layer and form some kind of lake breeze fronts. The complex shape of the reservoir implies also an complex 3-D structure of the breeze system. Towards the southernmost part, near the dam, the low-level divergent breeze circulation is very clear, but the convergence upper-level return current is weaker (Fig. a–c). In contrast, near the middle of the reservoir (cross section Cs2 in Fig. d–f) where two water branches exist, the circulation near the surface is more complex due to the presence of a land area in between, but the subsidence motion is more prominent, inducing a decrease in mixing ratio through the boundary layer, which reaches a magnitude of about 4 g kg-1 at 16:00 UTC (Fig. f).

Figure  illustrates this process in a horizontal plane. At midnight (Fig. b) the reservoir does not directly affect vapour mixing ratio in the air. In the morning hours, when the sun rises, but the breeze system is not yet formed, a positive impact on the moisture over the lake can be seen due to the increase in the evaporation. This anomaly affects the air above the central and southern parts of the reservoir and is advected to nearby areas (Fig. c). Later in the afternoon, with the formation of the lake breeze, a negative impact can be traced over the water surface due to the descending branches of the local circulation (Fig. d and e). This explains the afternoon decrease in the water vapour mixing ratio observed at the Montante platform, as seen in Fig. . The localization of the area of this negative anomaly changes in time, but predominantly it is over the larger southern part of the reservoir. With the dissipation of the local lake breeze system and the arrival of the stronger large-scale north-western wind, the negative moisture anomaly over the reservoir disappears and a positive effect is visible in the downwind region (Fig. a and f), due to the increase in evaporation (note that Fig. a corresponds to the night of 21 to 22 July, when the effect was more noticeable).

During daytime, water temperature is lower than air temperature, which is associated with a very weak air circulation over the water surface, which leads to very low evaporation from the lake (refer to low latent heat flux values in Fig. a). This period of day is characterized by higher evaporation over the land than over water. By late afternoon when the dominant sea breeze system reaches the region, the north-western wind accelerates significantly when passing over the smooth surface of the lake. As result, evaporation from the lake becomes very intense.