Model simulation of gravity waves triggered by a density current

Authors


Abstract

In this study, starting from an observational case of internal gravity waves (IGWs) generated at the top of a drainage flow during the SABLES2006 field campaign, we aim to reproduce the IGWs and their origin through mesoscale meteorological modelling. We used the Weather Research and Forecast (WRF) model with fine horizontal resolution (1 km), testing the model capabilities to simulate the IGWs through a WRF fixed physics package option but two different planetary boundary layer schemes, the Mellor-Yamada-Janjić (MYJ) and the Yonsei University (YSU). The comparison between model simulations and measurements from a 100 m meteorological tower reveals that the MYJ scheme simulation gives much better results, as it better represents the main features of the density current measured by the tower instruments, although the event is predicted to occur sooner than it is observed to occur. The study has also shown the capacity of this scheme to detect the oscillations in temperature and specific humidity generated by the arrival of the density current. In contrast, the YSU scheme captures the arrival of the current on time but it fails to correctly track its properties and therefore it does not reproduce the gravity waves with the current arrival. In addition, wave parameters calculated from model outputs (MYJ) using the wavelet method reveal waves with longer periods and longer wavelengths (T = 20–22 min and λ = 8–10 km) than those calculated from measurements (T = 9.2 min and λ = 3.5 km) using the same technique. Copyright © 2012 Royal Meteorological Society

1. Introduction

Gravity or density currents are flows created by differences in the density of two adjacent fluids (Adachi et al., 2004). They are important mesoscale phenomena, often originated and driven by topographical features that influence local weather. They are manifested as cold air, close to the ground, that flows under the influence of gravity (Stull, 1988), and they can arise from squalls, distant cold fronts, sea-breeze fronts or other atmospheric mesoscale disturbances (Simpson, 1997). In addition, on relatively flat plains adjacent to mountain slopes, gravity currents may be initiated by katabatic flows coming off the mountains at night (Adachi et al., 2004). Papadopoulos and Helmis (1999) found that the origin of a katabatic flow at the foot of a slope can be both local cooling and the arrival of a density current that enhances shallow surface inversions and produces sharp falls in temperature as well as changes in wind direction. The development of the different regimes depends on the distribution of cooling along the slope, the stratification at the bottom of the slope, and the ambient wind speed and direction (Mahrt et al., 2010).

In any case, the irruption of this flow with sudden variations in the above-mentioned magnitudes may result in vertical displacement of air parcels from their equilibrium position, which has been shown to be a common source of internal gravity waves (IGWs) (Chemel et al., 2009). These act as a modulator of the gravity current and may produce events of intermittent turbulence (Soler et al., 2002; Sun et al., 2002; Terradellas et al., 2005). IGWs are important atmospheric disturbances because they transport energy and momentum and they can be a source of turbulence. During breaking processes a transfer of momentum, heat and humidity is produced from the wave field to the main flow. The interaction between waves, turbulence and small-scale structures is complex in the boundary layer (Chimonas, 1999; Viana et al., 2009, 2012).

Waves are usually manifested as fluctuations in pressure, wind and temperature fields (Nappo, 2002). Many studies have dealt with the theory of IGWs (Rottman and Enaudi, 1993; Chimonas, 2002). Several authors have observed them in the nocturnal atmospheric boundary layer (NBL) (Sun et al., 2004), in katabatic flows (Gryning et al., 1985; Bastin and Drobinski, 2005) or within gravity currents (Adachi et al., 2004). Gravity waves can exist over a wide range of scales and periods. In the present study we deal with IGWs generated in the first few hundred metres of the NBL within a cold density current.

Experimental campaigns such as SABLES98 (Stable Atmospheric Boundary Layer Experiment in Spain—1998) (Cuxart et al., 2000), CASES99 (Cooperative Atmosphere–Surface Exchange Study—1999) (Poulos et al., 2002) and SABLES2006 (Yagüe et al., 2007) have dealt with typical processes in the stable boundary layer. It was often observed that mesoscale circulations were the origin of different phenomena such as: intermittent turbulence, IGWs, low-level jets (LLJs) and drainage winds. Some of these events have been analysed using the wavelet method and multi-resolution flux decomposition to study pressure perturbations related to IGWs (Cuxart et al., 2002; Terrradellas et al., 2005; Viana et al., 2007, 2009, 2010).

As Conangla and Cuxart (2006) indicate, high-resolution mesoscale simulations are needed to better determine the origins of IGWs and turbulent processes. Little effort has been made to model gravity waves around the range of the meso-gamma scale. Thus, starting from an observational study of IGWs generated at the top of a drainage flow (Viana et al., 2010) during the SABLES2006 field campaign, here we aim to simulate the event through mesoscale meteorological modelling. Since we deal with mesoscale motions, mesoscale meteorological simulations are a good tool for representing thermal circulations over complex terrain, such as sea-breezes, drainage flows and LLJs. Mesoscale models can solve the atmospheric equations with quite detailed horizontal and vertical resolution; however, the turbulent diffusion processes are subgrid-scale and therefore they have to be parametrized in the models. Different ways of representing subgrid-scale vertical mixing processes lead to differences in the turbulent fluxes predicted by the boundary-layer schemes (Alapaty et al., 1997).

The Weather Research and Forecast (WRF) model is widely used to study mesoscale phenomena. Mesoscale disturbances are one of the sources of small-scale phenomena that most influence circulation patterns and the transport of any quantity (energy, heat, momentum, humidity etc.); it is therefore necessary for the model to capture them correctly. Recent evaluations and comparisons between different planetary boundary layer (PBL) schemes of the WRF model (Hu et al., 2010; Shin and Hong, 2011; Jiménez et al., 2012) show good performance in diurnal cycles but more discrepancies at night. Nocturnal flow regime studies reveal that boundary-layer fields are very sensitive to the boundary-layer scheme used (Mölders and Kramm, 2009). Here we examine the sensitivity of the model to two different PBL parametrizations: the Mellor–Yamada–Janjić (MYJ) scheme and the Yonsei University (YSU) scheme. In addition, fine horizontal resolution is used in the model (1 km), as recent studies (Seaman et al., 2009; Stauffer et al., 2009) have stressed the importance of using high horizontal and vertical resolutions to capture stable boundary-layer processes.

The WRF model has also been used to simulate convectively generated gravity waves (Lane and Knievel, 2005), associated with an upper-level jet system (Lu et al., 2006) or in stable conditions over Basen nunatak in Antarctica (Valkonen et al., 2010). Recently, Larsén et al. (2011) have used the WRF model to demonstrate the correspondence between the model and observed wind and temperature spectra, with and without the presence of gravity waves. Following on from previous studies, here we attempt to explore the capacity of WRF to: (i) simulate the presence of an IGW at the top of a gravity current with 1 km resolution; (ii) simulate the mesoscale flow structure that generated the gravity waves, as well as their origin; and (iii) analyse the characteristics of the gravity wave generated by the gravity current, using the wavelet transform (Torrence and Compo, 1998; Terradellas et al., 2001) applied to the WRF model data. The wavelet transform is a modern multiscale tool that permits the analysis of time series at very different scales in order to give the time evolution of the different frequencies that contribute in these time series (Terradellas et al., 2005). In this study the wavelet technique is applied to determine the characteristic parameters of the gravity waves in time series from one-minute model outputs of potential temperature.

The article is organised as follows: section 2 provides details of data collection and the study area, while the model experiment and the physical options used in the WRF model simulations are described in section 3. Evaluation of the model against tower measurements, a mesoscale circulation overview, as well as the modelled density current and wave characteristics are presented in section 4. Finally, a summary and our concluding remarks are in section 5.

2. Site and observational data

The study area and model domains are centred on the Research Centre for the Lower Atmosphere (CIBA in Spanish) situated at 41° 49'N, 4° 56'W, 840 m above sea level (ASL): about 30 km north-west of the city of Valladolid, in the upper Duero basin of northern Spain (San José et al., 1985). The area is surrounded by mountains, that over 100 km away rise to over 2500 m ASL: the Cantabrian Mountain Range to the north, the Central Mountain Range to the south and the Iberian Mountain Range to the east (Figure 1(a)). CIBA sits on a small plateau known as Montes Torozos, which is a nearly flat area of 800 km2, 840 m ASL and approximately 50 m above the surrounding flat lands (Figure 1(b)). The plateau has a gentle slope that accounts for a total increase in height of 30 m along 50 km from the north-east to the south-west, while the north-west and the south-east borders are slightly above the level of the inner plateau (Bravo et al., 2008). It is covered by grain crops and uniform vegetation with a roughness parameter of about 0.011 m (San José et al., 1985).

Figure 1.

Geographical location of the CIBA site: (a) topography and emplacement of 15 surface meteorological stations within the domain D3 (3 km resolution); (b) detailed topography of the inner domain D4 (1 km resolution) with 20 m contours. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

The area has been used for many atmospheric boundary layer experiments, such as SABLES98 and SABLES2006, whose objectives were to study the properties of the midlatitude stable boundary layer and the typical features of the nocturnal stably stratified boundary layer such as: intermittent turbulence, slope flows, down-valley winds, LLJs and gravity waves (Cuxart et al., 2000; Terradellas et al., 2001; Viana et al., 2007, 2009, 2012; Bravo et al., 2008; Conangla et al., 2008; Cuxart, 2008).

The laboratory's main facility is a 100 m mast equipped with fast-response sonic anemometers and a set of conventional sensors that measure wind speed and direction, air temperature and relative humidity at different heights (Table 1), as well as soil temperature and atmospheric pressure at the surface. In addition, six Paroscientific microbarometers were installed in 2006: three of them on the mast at 20, 50 and 100 m; and the remaining three at 1.5 m above ground level (AGL) on the vertices of a triangle of around 200 m to detect the IGWs (see Table 1 in Viana et al. (2010) for details). A Radio Acoustic Sounding System (RASS) sodar and tethered balloon soundings were used to collect additional data.

Table 1. Main instrumentation installed on the 100 m mast.
InstrumentHeights (m)Sampling rate (Hz)
Metek USA-13, 19.6, 96.620
 sonic anemometers  
Wind vanes9.6, 34.6, 74.6, 98.65
Cup anemometers2.3, 9.6, 34.6, 50.0, 74.6, 98.65
Platinum resistance2.3, 10.5, 20.5, 35.5, 97.51
 thermometers  
Microbarometers20, 50, 1002
Humidity sensors10, 975

3. Numerical model experiments

Simulations were run with the WRF modelling system: a state-of-the-art mesoscale numerical weather-prediction system, developed by a collaborative partnership in the USA. The version used was 3.1.1 and the dynamics solver used in this study was the Advanced Research WRF (ARW) designed for both research and operational applications (Skamarock et al., 2008). WRF is a fully compressible non-hydrostatic model, with a terrain-following vertical coordinate; the horizontal and vertical grid staggering is of Arakawa C-grid type. It has many physics options to choose from for the parametrization of the microphysics, cumulus, surface layer, land surface, boundary layer and radiation physics.

The model configuration (Table 2) consists of four domains centred on the location of the CIBA meteorological tower, with horizontal resolutions of 27, 9, 3 and 1 km (Figure 2). Domains 1 (27 km), 2 (9 km) and 3 (3 km) are run in two-way nesting from 0000 UTC 22 June to 0600 UTC 23 June 2006 with output files saved every hour. For these domains, the first 6 h are treated as spin-up and the next 24 h are used for evaluation. Domain 4 (154 × 100, 1-km cells) is nested from domain 3 in one-way nesting, with the study focusing on the night from 1800 UTC 22 June to 0600 UTC 23 June 2006. The reason for applying one-way nesting for the smaller domain is that in two-way nesting, all domains are run at the same time and interact fully. The inputs into a nest from the coarse domains are introduced through its boundary, while feedback to the coarse mesh occurs over the whole of the nest interior, as its values are replaced by a combination of fine domain values. This procedure requires model outputs for the same time interval in all the domains, which makes it difficult to obtain model outputs with a higher frequency in the smaller domain (1 minute) for spectral analysis. Thus, domains 3 and 4 are run in one-way nesting, and the output files are saved at 12-minute and 1-minute time intervals for mean values and spectral analysis respectively. In general, two-way nesting is believed to work better because it allows smaller-scale features to feed back and influence features at the larger scale. However, detractors of two-way nesting claim that the method somehow ‘pollutes’ results obtained in the outer domain (Soriano et al., 2002).

Figure 2.

Topography of the studied area, and nested model domains D1, D2, D3, D4 with 27, 9, 3 and 1 km resolution respectively. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

Table 2. Model configuration options used for WRF simulations.
  Domain 1Domain 2Domain 3Domain 4
Horizontal grid27 km9 km3 km1 km
Dimensions (x,y,z)65, 60, 4888, 82, 48139, 130, 48154, 100, 48
Initial and boundary conditionsNCEP CFSR 0.5 × 0.5°  WRF external
  every 6 h  domain (D3)
Simulated periodFrom 0000 UTC 22 June 2006 to 0600 UTC 23 June 2006From 1800 UTC
     22 June to 0600 UTC
     23 June 2006
RadiationDudhia scheme for short-wave radiation. RRTM for long-wave radiation
Land surfaceNOAH land-surface model (4 subsoil layers)
MicrophysicsNew Thompson et al. scheme
ConvectionGrell 3D scheme
PBL and Surface layerExp 1. YSUYonsei University scheme (YSU) for PBL; MM5 similarity surface layer
 Exp 2. MYJMellor–Yamada–Janjić scheme (MYJ) for PBL; Eta surface layer scheme

In this work, the study and the analysis are focused on domains 3 and 4 (Figure 2) since their high resolution (3 and 1 km respectively) allow the details of the flow over the Duero basin and Montes Torozos plateau to be captured. In the vertical, 48 sigma levels are used from the ground up to 100 hPa for all the domains with the first level 6 m above the surface, and the first 20 levels all within the first 250 m. Initial and boundary conditions are taken from the National Centers for Environmental Prediction (NCEP), in particular from the Climate Forecast System Reanalysis (CFSR) which has a horizontal resolution of 0.5°, and the boundary conditions are forced every 6 h.

The physics package includes the rapid radiative transfer model (RRTM) scheme for long-wave radiation (Mlawer et al., 1997), the Dudhia scheme for short-wave radiation (Dudhia, 1989), the new Thompson microphysics scheme (Thompson et al., 2004), the Grell 3D cumulus scheme (Grell and Dévényi, 2002) and the Noah land surface scheme (Chen and Dudhia, 2001). With this physics package, two simulations are run using two different parametrizations of surface layer and PBL. The first one includes the MM5 similarity for surface layer and the YSU scheme (Hong et al., 2006) for PBL, whilst the second uses the Eta surface layer scheme and the MYJ for PBL (Janjić, 1990, 1996, 2002).

The YSU PBL scheme is a first-order non-local scheme, with a counter-gradient term in the eddy-diffusion equation. The YSU scheme is modified in WRF version 3 (Hong, 2010) from the Hong et al. (2006) formulation by using the exchange coefficient as a parabolic function of height in the mixed layer. In addition, the top of the stable boundary layer (SBL) is determined by the bulk Richardson number, RB, increasing its critical value from zero to 0.25 over land, thereby enhancing mixing in the stable boundary layer (Hong and Kim, 2008). The MYJ PBL scheme uses the 1.5-order (level 2.5) local turbulence closure model of Mellor and Yamada (1982) to represent turbulence above the surface layer.

The MYJ scheme determines eddy-diffusion coefficients from prognostically calculated turbulent kinetic energy (TKE). Mellor and Yamada (1982) argue that the scheme is appropriate for all stable and slightly unstable flows, but that errors are likely to occur when the flow approaches the free-convection limit. Several studies have compared different PBL parametrizations in the WRF model (Nolan et al., 2009; Hu et al., 2010) showing that under stable conditions there is no PBL scheme that satisfactorily simulates the stable boundary layer and upper inversion. However, local TKE closure schemes perform better than first-order approaches (Chiao, 2006; Shin and Hong, 2011).

Currently, each PBL parametrization is tied to particular surface-layer schemes in the WRF model. The MM5 surface-layer scheme coupled to the YSU model uses the stability functions from Paulson (1970), Dyer and Hicks (1970) and Webb (1970) to compute surface exchange coefficients for heat, moisture and momentum. Following Beljaars (1995), a convective velocity is used to enhance surface fluxes of heat and moisture. Thermal roughness parametrization included in the current version of this scheme is assumed the same as momentum roughness length. A Charnock relation relates roughness length to friction velocity over water. Following Zhang and Anthes (1982), there are four stability regimes. In contrast, the Eta surface layer scheme (Janjić, 1996, 2002) coupled to the MYJ model is based on similarity theory (Monin and Obukhov, 1954). The scheme includes parametrizations of a viscous sub-layer. Over water surfaces, the viscous sub-layer is parametrized explicitly following Janjić (1994). Over land, the effects of the viscous sub-layer are taken into account through variable roughness height for temperature and humidity as proposed by Zilitinkevich (1995). The Beljaars (1995) correction is applied in order to avoid singularities in the case of free convection and vanishing wind speed (and consequently u*). The surface fluxes are computed by an iterative method.

The role of surface-layer parametrizations in atmospheric numerical models is to calculate the surface exchange coefficients to compute the sensible and latent heat fluxes and momentum flux, consistent with the flux-profile relationships. Furthermore, they provide the lower boundary condition for the vertical transport in PBL schemes. This implies that correct parametrization of land surface processes is very important if it is to provide crucial and reliable information on the daily evolution of the PBL. Much work analyses the sensitivity of simulated variables to surface-layer parametrizations in order to assess the relative contributions of the surface-layer parametrizations to typical features of each PBL scheme. Shin and Hong (2011) show that, in the surface layer, temperature and moisture are more strongly influenced by surface-layer formulations than by PBL mixing algorithms in both PBL convective and stable regimes, while wind speed depends on vertical diffusion formulations in the convective regime. Regarding PBL structures, surface-layer formulations only contribute to near-surface variability and then PBL mean properties, whereas the shapes of the profiles are determined by PBL mixing algorithms. However, there are still many sources of error in the surface-layer schemes which are not easy to isolate, although these errors can affect the performance of PBL parametrizations (Shin and Hong, 2011).

4. Results

4.1. Brief description of the night studied and outbreak of the density current

The study focuses on a single night during the SABLES2006 field campaign (Yagüe et al., 2007). The night of the case-study is 22–23 June 2006 when the synoptic situation over the Iberian Peninsula was dominated by an area of high pressure with a weak horizontal pressure gradient. Under these conditions, a sudden shift in the wind has commonly been observed at the CIBA site (Yagüe et al., 2007). It usually occurs between several tens of minutes and a few hours after the establishment of the stable regime. During the night in this study, a rapid reorganisation of the dynamic and the mass fields occurred soon after sunset (which took place at 1958 UTC). The overview of the night using the values recorded at the different levels of the mast show a weak north-west wind during the late afternoon (Figure 3(a)). The wind gradually turned north-east from 1900 UTC to 2130 UTC, when there was a sudden intrusion by an easterly current of moderate speed (about 10 m s−1 at the highest level of the mast, around 98 m) (Figure 3(b)). Surface radiative cooling favoured a temperature inversion of nearly 5°C between the surface and the top of the 100 m mast (Viana et al., 2010) before the passage of the density current, but the sudden change in wind velocity was accompanied by a rapid fall in temperature, especially at the upper levels (Figure 3(c)), causing a reduction in the thermal inversion after the outbreak of the current at the lower levels. The specific humidity increased at all levels (Figure 3(d)), suggesting the arrival of a cold and moist gravity current from the north-east whose origin could have been a diurnal sea breeze coming from the Cantabrian Sea (southern Bay of Biscay), as the WRF mesoscale simulations will evince in section 4.3 where an analysis at the regional scale is done. At the top of the tower, upward vertical heat flux (calculated using the 5-minute Reynolds average) reveals the displacement of the parcels due to the arrival of the current, since the mean vertical velocity is positive (Viana et al., 2010), turning downward a few minutes later when the cold air surpasses the measuring level (Figure 3(e)).

Figure 3.

(a) Wind direction, (b) wind speed, (c) temperature, (d) specific humidity, and (e) vertical heat flux, at different tower levels during the night of 22–23 June 2006 (all averaged over 5-minute periods).

4.2. Model evaluation at the CIBA site

The model results from the D4 domain output corresponding to the two experiments (MYJ and YSU experiments) are checked against observations from tower measurements at the CIBA site during night-time (from 1800 UTC to 0600 UTC) (Figure 4).

Figure 4.

Comparison between time series measurements from CIBA tower and model simulations (12-minute outputs) using two model experiments (MYJ and YSU): (a), (b) temperature at 10 and 100 m respectively; (c), (d) wind speed at 10 and 100 m; (e), (f) wind direction at 10 and 100 m; (g), (h) specific humidity at 10 and 100 m; (i), (j) friction velocity and heat flux evaluated at surface layer respectively. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

Overall, the YSU experiment tends to match the observations better in time but it does not capture the sharp shifts (i.e. in wind speed or specific humidity), so the YSU scheme seems to be too diffusive. In contrast, the MYJ experiment gives a better picture of the changes in magnitude for nearly all the variables, but predicts the gravity current outbreak around 90 minutes earlier.

The temperature drop at 10 m and 97 m is well captured by the MYJ experiment but it is predicted around 90 minutes in advance, whilst the YSU experiment simulates the drop in temperature at the right time, but more gradually than actually occurs at low levels (Figure 4(a)). At the upper levels, the YSU scheme captures the drop in temperature at 97 m well although the scheme underestimates the temperature after 2300 UTC (Figure 4(b)). The observational fall in temperature matches a sudden increase in wind speed, especially around 100 m AGL, where it rises from 3 to 10 m s−1 (Figure 4(d)). This is also captured by the MYJ scheme, which is able to forecast the increase in wind velocity but it is predicted earlier than it is actually observed, while the YSU scheme predicts the increase at 10 m but does not capture the sharp increase at 100 m (Figure 4(c) and (d)). The shift in wind direction from north to east at all levels is captured quite well by the simulations, although they tend to overestimate the easterly component during the outbreak (Figure 4(e) and (f)). Specific humidity rise is simulated by the MYJ scheme but is also ahead of observations while the YSU scheme forecasts it gradually, meaning that the cold flow has been stirred and has been losing its original properties during the preceding hours (Figure 4(g) and (h)). With the change in wind speed and direction, strong shear at the surface layer is generated (Figure 4(i)) and therefore high values of friction velocity (u) are measured, which are quite well captured by the MYJ scheme but also ahead of the observations. With the arrival of the density current, the YSU scheme forecasts an increase in u, but it prevails all night, therefore it simulates much stronger turbulence than is observed during the hours after the arrival of the current. This behaviour indicates that YSU introduces too much diffusivity as we will see in the next sections. Also with the onset of the density current, a negative sensible heat flux is established at the surface (Figure 4(j)). TKE output is only calculated by the MYJ simulation as it is a 1.5 closure TKE scheme. Comparing the TKE simulation with the tower observations we can see that the model underestimates its value, even in daytime (not shown). In addition, during the transition from daytime to night-time, the model establishes values of TKE that are too low as well, therefore producing less turbulence, forcing suitable conditions to anticipate nocturnal radiative cooling, the generation of katabatic flows over the slopes and the arrival of the density current.

To further evaluate the differences between observations and model outputs and to understand the differences between the two PBL schemes used, the vertical structure of the gravity current at the CIBA site was analysed. To this end, we compare time–height diagrams of wind speed and direction (Figure 5(a) and (b)) and temperature (Figure 6(a) and (b)) from model outputs at the CIBA site with the RASS-SODAR sodargrams of wind speed (Figure 5(c)) and temperature (Figure 6(c)). The sodargrams only reach a height of 200 m, while the model outputs allow us to complete the vertical structure further up (up to 500 m in the plots).

Figure 5.

Time–height diagrams of wind speed (shaded) and horizontal wind direction (vector) in the (a) MYJ and (b) YSU schemes (12-minute outputs) at the CIBA site; (c) RASS-SODAR sodargram of wind speed during the night of 22–23 June 2006 (10-minute averaged). This figure is available in colour online at wileyonlinelibrary.com/journal/qj

Figure 6.

Time–height diagrams of absolute temperature in the (a) MYJ and (b) YSU schemes at the CIBA site (12-minute outputs); (c) RASS-SODAR sodargram of temperature during the night of 22–23 June 2006 (10-minute averaged). This figure is available in colour online at wileyonlinelibrary.com/journal/qj

Before the outbreak, the MYJ scheme predicts light winds from the north-east and north-west, whilst after 2000 UTC, an easterly current about 300 m thick is established with an LLJ which has a peak wind speed of around 11 m s−1 at 100 m (Figure 5(a)). As the night progresses, the wind direction turns from east to south above 200 m and the wind velocity decreases considerably. In the YSU scheme (Figure 5(b)) the current arrives around 2130 UTC with a similar thickness as in the MYJ scheme, but more stirred and with lower wind speeds (7–8 m s−1) which departs more from observations. With the outbreak of the density current, the thermal vertical structure forecast by both schemes (MYJ in Figure 6(a) and YSU in Figure 6(b)) changes completely, showing in both schemes and the temperature sodargram (Figure 6(c)) a strong temperature inversion. The MYJ scheme confines the cold air to a thinner layer than the YSU or temperature sodargram do, thus enhancing vertical temperature gradients. This fact contributes to accelerating the air mass coming from the north-east over sloping terrain and could be the reason why MYJ forecasts the outbreak of the density current in advance. Although the YSU scheme is capable of forecasting the outbreak on time, it confines the cold air to a thicker layer because it enhances vertical mixing during night-time (as in Hu et al., 2010). Also, as shown in Figure 6 and after the entrance of the density current, above the LLJ we can see a warm layer located at around 200 m high, since as the cold current advances it pushes the warm air upwards, similarly to the advance of a cold front. This warm layer is forecast by both schemes but its persistence is better simulated by MYJ in accordance with the RASS-SODAR data. This could also be evidence that YSU is too diffusive. In short, the comparison between the model outputs and the RASS-SODAR data in the first 200 m shows that the MYJ scheme represents the wind structure of the density current better.

4.3. Overview on mesoscale fields

A mesoscale overview of the wind and temperature fields could be very useful for detailed study of the flow and the thermal circulation patterns that cannot be inferred from tower measurements at a specific site. However, before analysing the model outputs from domain D3, we will evaluate them with a comparative analysis against observations from 15 surface stations covering this third domain (Figure 1(a)). We use the third domain model because it is centred on the CIBA site and covers the area within a radius of 250 km, including the nearest mountain ranges. The statistics are calculated hourly over a 24-hour period (from 0600 UTC 22 June to 0600 UTC 23 June 2006), dividing them into two periods: (i) transition from night-time to daytime and daytime (from 0600 UTC to 1700 UTC), and (ii) transition to night-time and night-time (from 1800 UTC to 0500 UTC), to take into account the daytime and night-time evolutions separately. Temperature at 2 m and both wind speed and direction at 10 m were chosen to calculate the following statistics: mean bias (MB) and root-mean-square error (RMSE) for wind speed; and mean bias and mean absolute gross error (MAGE) for temperature and wind direction (Tesche et al., 2002). Their values are summarised in Table 3.

Table 3. Statistics for surface temperature, wind speed and wind direction.
 StatisticBenchmarkMYJYSU
   DaytimeNight-timeDaytimeNight-time
  1. Based on hourly values for 15 surface meteorological stations (locations in Figure 1(a)) from daytime (0600 UTC to 1700 UTC 22 June 2006), and night-time (1800 UTC 22 June to 0500 UTC 23 June 2006) including the transition to night-time. The benchmarks for the statistics are proposed by Tesche et al. (2002) to validate meteorological simulations.

Temperature (2 m)MAGE<2 K1.2011.7401.1441.263
 MB −0.101−1.2750.027−0.504
Wind speed (10 m)RMSE<2 m s−11.5371.6761.4232.496
 MB 1.0721.0710.6861.803
Wind direction (10 m)MAGE<30 deg42.54737.16251.07541.729
 MB 37.1626.625−10.4000.917

Temperature and wind-speed statistics are overall below the benchmarks, except for wind speed predicted by YSU during night-time, which means that this scheme does not match with the real data from surface stations. Wind direction is not well predicted by any of the schemes at the station points. The MAGE value for temperature is slightly higher for the MYJ scheme than for YSU, although both tend to underestimate temperature values as MB is negative. This trend is noticeable during night-time for the MYJ scheme, which underestimates the surface temperature at most of the surface stations. During night-time, wind speed and wind direction are better predicted by the MYJ scheme although both schemes overestimate wind speed values.

For a broader mesoscale overview, temperature and wind fields for the third domain are shown. The analysed model outputs correspond to the MYJ scheme, as it is the scheme that better captures the onset of the density current. At 1600 UTC, a cold moist mass of air from the Cantabrian Sea started moving south-westward far from the CIBA site (Figure 7(a)). Over the following hours, the flow accelerated as it passed over the mountain ranges, arriving at the centre of the domain a few minutes after 2000 UTC (Figure 7(b)). This occurred during the transition from day to night, with the beginning of the establishment of the NBL. From 1600 to 2000 UTC we can see how near-surface air temperature falls as the flow moves from north-east to south-west due to the movement of the density current itself but also affected by ground radiative cooling which enhances the movement of the current at the mountain slopes via the generation of a katabatic flow. At 100 m AGL, behaviour of the air mass is similar, reaching high wind speeds of around 10 m s−1 (Figure 7(c) and (d)).

Figure 7.

D3 MYJ model outputs of: (a) 2 m air temperature (shaded) and 10 m horizontal wind vectors at 1600 UTC; (b) idem at 2000 UTC; (c) horizontal wind speed at 100 m (shaded) and 100 m horizontal wind vectors at 1600 UTC; (d) idem at 2000 UTC. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

To further analyse the circulation pattern, we use the WRF outputs through a cross-section in the north-east to south-west direction. In Figure 8(a) and (b) we can see, through the potential temperature cross-section, a strong temperature inversion established within the density current in the north-east part of the domain, although a daytime regime still remains at the south-west part. The wind vector projected over the northeast/southwest axis is shown in Figure 8(c) and (d), which correspond to 1600 and 2000 UTC respectively. Maximum wind speeds are found over sloping terrain leeward of the north-eastern mountain range at around 2000 UTC (Figure 8(d)).

Figure 8.

Northeast/southwest (dashed line in Figure 7) vertical cross-section of: potential temperature at (a) 1600 UTC and (b) 2000 UTC, and horizontal wind parallel to the cross-section at (c) 1600 UTC and (d) 2000 UTC. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

The flow reaching the CIBA site seems to have originated over the Cantabrian Sea, but it was strongly perturbed by topographical features when the air mass crossed the mountain range located in the north-east part of the third domain. Flows over sloping terrain were accelerated due to pressure and temperature gradients. So both the sea breeze entrance and the katabatic wind were the origin of the cold density current that moved fast, as the air surface cooling established by the MYJ scheme is over-predicted by the model (as shown by surface station statistics). The topographical effects become even more decisive and the air mass from the north-east is accelerated even more in the model. This would also explain the anticipation of the event produced by the MYJ experiment. So this cold and moist gravity current moved fast, enhanced turbulence and produced waves over the Torozos plateau. Similarly, Sun et al. (2002) analysed a wind surge and a temperature drop that revealed the passage of a density current associated with intermittent turbulence.

4.4. Oscillation features

In Viana et al. (2010) wavelet transforms applied to the data from microbarometers revealed traces of IGWs in pressure records after the outbreak of the gravity current, generating periodic pressure and temperature oscillations. In this section we test the capacity of the model to reproduce the oscillations generated after the arrival of the cold current. To this end, we analysed one-minute model outputs at the CIBA site from the two WRF experiments (MYJ and YSU). Results from the MYJ experiment indicate the presence of oscillations in temperature and specific humidity between 130 m and 300 m AGL at the CIBA site (Figure 9), and therefore they demonstrate that the WRF model using the MYJ scheme can reproduce the generation of gravity waves. They appear a few minutes after the onset of the density current as a consequence of the cold air intrusion, since the air parcels rise forming a warm layer and therefore a pressure disturbance is generated, as we can see in Figure 9(a). A few minutes later, at the warm layer at the top of the current, periodic oscillations of temperature and humidity at different levels are simulated by the model, as seen in Figure 9(b) and (c). Before the outbreak, above 130 m, temperature decreases with height, whilst after this event a thermal inversion is well established (Figure 9(b)). In contrast, the specific humidity rises after the outbreak (Figure 9(c)) and changes its profile structure. The well-mixed vertical structure before the outbreak is replaced by a decrease in the specific humidity with height after the onset of the current. Vertical velocity from the model output at 167 m increases suddenly to about 0.3 m s−1 and then falls to about −0.1 m s−1 in two minutes (not shown). This upward motion coincides with the large temperature fall and the large increase in specific humidity. At the time the current arrives, maximum values for the vertical velocity of around 0.7 m s−1 are seen at around 300 m AGL whilst in the YSU scheme the values are slightly lower, only reaching vertical velocities of 0.5 m s−1 at the same heights.

Figure 9.

One-minute output time series from: MYJ experiment of (a) ΔP100–167, (b) temperature and (c) specific humidity at different levels from 2000 to 2200 UTC, and from YSU experiment of (d) ΔP100–167, (e) temperature and (f) specific humidity at different levels from 2100 to 2300 UTC, at the CIBA site. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

The disturbances are only detected by the model in the MYJ experiment, whilst the YSU experiment (Figure 9(d), (e) and (f)) did not reveal any monochromatic oscillating behaviour after the arrival of the density current. Although YSU is able to forecast the outbreak of the gravity current, the small fluctuations of pressure, temperature and humidity show that the scheme is not able to generate waves with sufficient intensity (Figure 9(d)–(f)). The reason is that YSU provides more night-time mixing than MYJ, as mentioned above.

In order to obtain information about wave parameters such as period, wavelength, phase velocity and direction, the wavelet method described by Terradellas et al. (2005), never before applied to simulated data, is applied to the model results of the MYJ experiment with a frequency of 0.0166 Hz corresponding to the one-minute output. This method provides the horizontal components (kx, ky) of the wave-number vector, from the phase differences of the wavelet transforms from different time series of a given magnitude at different points at the ground or at a certain height. From kx and ky, the rest of the relevant wave parameters can be derived. In this case, the method is applied to potential temperature data at 167 m AGL from three-point triangulation around the CIBA tower. Theoretical polarisation relationships (Gossard and Hooke, 1975) between pressure, temperature and specific humidity over the tower are well accomplished by one-minute model outputs. That is why wavelet analysis has been applied to potential temperature rather than pressure. The theoretical polarisation relation is especially well fulfilled between temperature and specific humidity, so one-minute model outputs of potential temperature at 167 m AGL are chosen because they show the most monochromatic behaviour. The wavelet method establishes a wave period of around 20–22 minutes, a phase velocity about 6–9 m s−1, a wavelength of around 8–10 km and a direction of 240–260° (coming from the northeast and heading southwest). These wave parameters are quite different from those found in Viana et al. (2010) where they showed evidence of gravity waves from temperature measurements around 100 m above the ground and from pressure time series in the layer between 50 and 100 m. The main parameters of these waves were derived from wavelet cross-correlation of high-resolution pressure time series recorded by a 200 m array of microbarometers with a frequency of 2 Hz deployed at surface level (recall that pressure is a non-local flow variable that can be affected by events taking place in the whole overlying atmospheric layer). They found a wave with a period of around 10 minutes, propagating roughly from the north (20°) with a phase velocity of 6.2 m s−1 and a wavelength of nearly 3.5 km, propagating mainly around 50–100 m above the surface (as they could determine by a set of microbarometers deployed up the 100 m mast).

The estimated Brunt–Väisälä frequency during the event was N = 0.03 s−1 at 167 m AGL which is higher than the frequency of the wave (0.0052 s−1), which indicates that the modelled wave was compatible with an IGW (Stull, 1988; Sun et al., 2004). From these results, we can summarize that: (i) the model generates the waves propagating at higher levels from where they were produced according to observations, but not at lower levels; (ii) the oscillations generated by the density current in the model have some parameters that are different from those observed, since during its downward vertical propagation the modelled wave was damped and below 130 m the oscillation is almost imperceptible.

5. Summary and conclusions

Starting from an observational study of IGWs generated by a density current during a single night (Viana et al., 2010), in this study we try to simulate the presence of IGWs generated by a density current using the WRF model. Furthermore, we analyse the flow structure that generated these gravity waves, and its origin.

Our results show that WRF mesoscale meteorological modelling is an efficient tool for studying the origin and development of a density current and the generation of gravity waves. We show that the origin of the IGWs observed and modelled at the CIBA site was a cold-air density current coming from the north-east, which was modulated by the topography of the area studied. Specifically, the flow originated in the Cantabrian Sea; several mountain slopes then cross through its trajectory, which were the main cause of its strong acceleration.

High-resolution (1 km) simulations are also useful in the sensitivity analysis of two boundary-layer schemes (MYJ and YSU) that have been used extensively by the scientific community. A comparison of these schemes shows that the MYJ scheme simulation gives better results, as it better represents the main features of the density current measured by the tower instruments and by the RASS-SODAR, although the event is predicted to occur earlier than it is observed to occur. The study has also shown the capacity of this scheme to detect the oscillations in temperature and specific humidity generated by the arrival of the density current. However, although the YSU scheme captures the arrival of the current on time, it fails to correctly track its properties and predicts a less sharp change in magnitudes than is observed, because it provides more night-time mixing than MYJ. This is also why the YSU scheme does not reproduce the gravity waves due to the arrival of the cold current.

According to the model, with the intrusion of the cold air mass at the CIBA site, the ambient air is pushed upwards (the intrusion thus acts as a cold front) forming a warm layer above the maximum wind at the top of the density current where, a few minutes later, disturbances in pressure, temperature and humidity occur at these levels. It is also shown that the area where the waves are generated coincides with the warm layer at the top of the current. The comparison between measurements and simulations reveals some other discrepancies, in addition to the time gap. Measurements of oscillations from the tower sensors show that the waves were produced mainly at around 100 m, while model simulation results show waves above this level. Furthermore, the wave parameters calculated from the measurements reveal waves with shorter periods and shorter wavelengths than those calculated from the model outputs. Thus, the model seems to reproduce waves in the warm layers, where vertical temperature gradients are smoother and less than those found at lower levels. Therefore, at lower levels, the simulated propagated wave may arrive as a damped and smoothed perturbation, so the predicted parameters may be different from those calculated from observations. Moreover, the 1 km resolution of the model could be too coarse to solve a wave of 3.5 km wavelength. Other reasons for the discrepancies may include the application of the wavelet technique to different variables which, moreover, were sampled with different frequencies.

To achieve conclusive results regarding the capacity of the models to simulate IGWs, it is necessary to perform further studies to clarify the importance of the model parametrizations, especially in the surface layer and in the PBL.

Acknowledgements

This research was funded by the Spanish Government through projects CGL 2009-12797-C03-02 and CGL 2009-12797-C03-03.

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