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  • View in gallery

    (a) Topography (m) at 12-km horizontal resolution and (b) geopotential height contours with the wind field overlain on the 925-hPa surface for the KMIN_1.0L simulation (see Table 1) at 0000 UTC 27 Jan 2003. The red box shows the nested 2-km simulation domain and crosses mark locations of two radiosondes used in this study. (c) Temporal evolution of the horizontally averaged vertical velocity profile. The horizontal average was obtained over the sea grid points of the 2-km domain. (d) PBLH (km) at 1200 UTC 27 Jan 2003 diagnosed by the top of the inversion determined by the temperature gradient (see section 3b for detailed description). White regions in (d) denote areas where the PBLH could not be diagnosed because of an insufficient gradient in temperature.

  • View in gallery

    (a)–(d) Maximum vertical temperature gradient found within the inversion, as diagnosed from the temperature profiles (see section 3b for details). (e)–(h) PBLH defined by the diagnosed inversion top. Sensitivity of inversion strength and height with respect to at 0000 UTC 27 Jan 2003 is shown. Black line in (d),(h) shows position of vertical potential temperature cross sections presented in Fig. 3.

  • View in gallery

    The θ cross sections (along black line shown in Figs. 2d,h) for simulations with different values at 0000 UTC 27 Jan 2003.

  • View in gallery

    (a) MODIS total CLC is compared against low CLC (below 800 hPa) at 0000 UTC 27 Jan 2003 for (b) KMIN_1.0L, (c) KMIN_0.4L, (d) KMIN_0.1L, and (e) KMIN_0.01L. The resolution of the MODIS retrieval has been reduced to 12 km to match the horizontal resolution of the simulations.

  • View in gallery

    RH, θ, and horizontal wind profiles from left to right for (a)–(c) 0000 and (d)–(f) 1200 UTC 27 Jan 2003 at Brest. The radiosonde soundings are denoted by black dashed lines in (a),(b),(d),(e) and are shown in the first column in (c) and (f). Simulated profiles at the nearest grid point on land to the radiosonde’s location are shown for the simulations with varied .

  • View in gallery

    As Fig. 5, but for the A Coruña radiosonde station.

  • View in gallery

    Evolution of TKE in the PBL at (a)–(d) Brest and (e)–(h) A Coruña for simulations with different values. Hatching denotes regions of grid-scale cloud.

  • View in gallery

    Sensitivity of the KMIN_0.01L simulation to different initial conditions. Initial conditions vary between 0000 UTC 24 Jan and 1200 UTC 26 Jan 2003 (see Table 1). The simulated profiles are shown at 0000 UTC 27 Jan with lead times of 12–72 h at (a)–(c) Brest and (d)–(f) A Coruña. The ERA-Interim is shown as a solid black line.

  • View in gallery

    Sensitivity of simulations to tur_len. Maximum temperature gradients simulated for (a) tur_len = 500 and (b) 60 m. Profiles shown at (c)–(e) Brest and (f)–(h) A Coruña for 0000 UTC 27 Jan 2003. The tur_len = 500 (TURL_500L), 60 (TURL_60L), and 150 m (KMIN_0.01L) parameters were investigated.

  • View in gallery

    Sensitivity of and simulations on horizontal resolution (see Table 1). Profiles shown at (a)–(c) Brest and (d)–(f) A Coruña for 0000 UTC 27 Jan 2003. (Note the height difference of the profiles near the surface is caused by the differently resolved topographies at 2- and 12-km horizontal resolution.)

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A Case Study in Modeling Low-Lying Inversions and Stratocumulus Cloud Cover in the Bay of Biscay

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  • 1 Institute for Atmospheric and Climate Science, ETH Zürich, Zurich, Switzerland
  • | 2 Federal Office of Meteorology and Climatology, MeteoSwiss, Zurich, Switzerland
  • | 3 Institute for Atmospheric and Climate Science, ETH Zürich, Zurich, Switzerland
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Abstract

Many regional forecasting models struggle to simulate low-lying strong temperature inversions. To understand this apparent deficit for forecast improvements, a case study of a strong inversion occurring in the Bay of Biscay on 27 January 2003 is conducted. The event was characterized by extensive stratocumulus cloud cover beneath an extensive high pressure system in combination with a particularly strong inversion of 10–12 K at an altitude of 500–800 m. Simulations were performed at 2- and 12-km horizontal resolutions, with 60 vertical levels (13 levels within the first 1000 m), and with lead times of 12–72 h. The simulations were validated using in situ radiosonde and satellite data. Besides large-scale subsidence, turbulent vertical mixing is a key dynamical process for the formation of nocturnal inversions. Sensitivities to parameters for vertical mixing (the minimum threshold for eddy diffusivity and the turbulence length scale) are investigated. Results presented herein show the planetary boundary layer (PBL) profiles to be very sensitive to the minimum threshold applied for eddy diffusivity, whereas little sensitivity with respect to the turbulence length-scale parameter was found. PBL moisture and potential temperature θ profiles for hindcasts between 24- and 72-h lead times at both resolutions were adequately simulated. In simulations with an adequate representation of the vertical turbulent exchange, realistic cloud cover was simulated, while too high values of the aforementioned threshold produced a strong underestimation of the cloud cover. These results indicate that a realistic simulation of strong inversions and their associated cloud cover is feasible, provided the vertical turbulent exchange is adequately represented.

Corresponding author address: Anna Possner, Institute for Atmospheric and Climate Science, ETH Zürich, Universitaetstrasse 16, 8092 Zurich, Switzerland. E-mail: anna.possner@env.ethz.ch

Abstract

Many regional forecasting models struggle to simulate low-lying strong temperature inversions. To understand this apparent deficit for forecast improvements, a case study of a strong inversion occurring in the Bay of Biscay on 27 January 2003 is conducted. The event was characterized by extensive stratocumulus cloud cover beneath an extensive high pressure system in combination with a particularly strong inversion of 10–12 K at an altitude of 500–800 m. Simulations were performed at 2- and 12-km horizontal resolutions, with 60 vertical levels (13 levels within the first 1000 m), and with lead times of 12–72 h. The simulations were validated using in situ radiosonde and satellite data. Besides large-scale subsidence, turbulent vertical mixing is a key dynamical process for the formation of nocturnal inversions. Sensitivities to parameters for vertical mixing (the minimum threshold for eddy diffusivity and the turbulence length scale) are investigated. Results presented herein show the planetary boundary layer (PBL) profiles to be very sensitive to the minimum threshold applied for eddy diffusivity, whereas little sensitivity with respect to the turbulence length-scale parameter was found. PBL moisture and potential temperature θ profiles for hindcasts between 24- and 72-h lead times at both resolutions were adequately simulated. In simulations with an adequate representation of the vertical turbulent exchange, realistic cloud cover was simulated, while too high values of the aforementioned threshold produced a strong underestimation of the cloud cover. These results indicate that a realistic simulation of strong inversions and their associated cloud cover is feasible, provided the vertical turbulent exchange is adequately represented.

Corresponding author address: Anna Possner, Institute for Atmospheric and Climate Science, ETH Zürich, Universitaetstrasse 16, 8092 Zurich, Switzerland. E-mail: anna.possner@env.ethz.ch

1. Introduction

The planetary boundary layer (PBL) is often capped by pronounced inversions, which in turn may strongly affect the associated dynamics as well as the cloud distribution, cloud thickness, and cloud type. In the case of stratus and stratocumulus clouds considered in this study, a shallow well-mixed boundary layer with a strong low-lying temperature inversion is common. However, it is known that many regional and global models struggle to capture stable boundary profiles and, in particular, sharp inversions (Stevens et al. 2003; Bretherton et al. 2004; Hannay et al. 2009; Wyant et al. 2010; Svensson and Holtslag 2009; Svensson et al. 2011; Holtslag et al. 2013; Sandu et al. 2013).

The vertical extent, height, and strength of the inversion are determined by a balance between the large-scale subsidence and the boundary layer turbulence (Neiburger et al. 1961, 42–55; Stevens 2005). In recent studies it has been suggested that the inability of global- and regional-scale models to simulate stable boundary layer profiles results from the overprediction of the turbulent mixing (Holtslag et al. 2013; Sandu et al. 2013). Parameterizing subgrid-scale mixing, or turbulence, is based on the Reynolds-averaged flow in combination with some closure assumptions for the subgrid-scale fluxes. A common approach is to have a one-dimensional scheme in combination with a flux-gradient approach based on eddy-diffusivity closure (e.g., Cuxart et al. 2006). However, the implementation of such schemes varies considerably between different models, leading to variability in the skill of predicting stable boundary layers (Holtslag et al. 2013). For instance, Sandu et al. (2013) addressed the issue of overprediction of the vertical mixing resulting from the implementation of unsuited (for stable boundary layers) stability functions within the European Centre for Medium-Range Weather Forecasts (ECMWF) model. By changing the profiles of the prescribed stability functions, Sandu et al. observed a significant improvement in the stable PBL profiles, as well as low-cloud cover. However, they also observed a degradation of the large-scale flow when using fixed stability functions.

Buzzi et al. (2011) performed a different study using the regional Consortium for Small Scale Modeling (COSMO) model (Doms and Schättler 2002; Steppeler et al. 2003). In this model the turbulent fluxes are parameterized using the downgradient flux approach with a local closure of eddy diffusivity. In this scheme the vertical profile of the stability functions is explicitly diagnosed for each column, and a minimum threshold on the diagnosed eddy diffusivity is imposed. Buzzi et al. (2011) showed in idealized single-column experiments that the stable PBL structure and inversion were largely sensitive to this prescribed minimal eddy diffusivity. In particular, they found an improved representation of the inversion when this limiter was reduced. Such a limiter on the vertical turbulent flux has been in use in mesoscale models such as the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) and the Regional Climate Model (RegCM3).

Another study (Vellore et al. 2007) has also raised the issue of boundary data for simulating marine stable boundary layers with regional models. Vellore et al. analyzed MM5 hindcasts of stable marine boundary layers near the west coast of California and validated them against a comprehensive dataset including buoy, aircraft, satellite, and large eddy simulation (LES) data. They found the simulated inversion strength was underestimated by about 50%, which they believed to be as a result of deficiencies in the prescribed initial conditions from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR; Kalnay et al. 1996) and ECMWF (Uppala et al. 2005) reanalyses, which themselves severely underestimated the inversion. However, the MM5 also imposes a minimum value on the eddy diffusivity of at least 1 m2 s−1, so their forecasts might also be subject to an overprediction of vertical mixing, which depletes their simulated inversion.

Following the findings of Buzzi et al. (2011), we investigated the role of the eddy diffusivity limiter in real-case simulations of stable boundary layers in a real-case simulation. We investigated if a reduction of this limiter would lead to an improved representation of inversion strength, inversion height, and low-cloud cover, and whether it affects the generation and strength of the turbulent kinetic energy distribution within the PBL. Furthermore, we considered the findings of Vellore et al. (2007) and determined the sensitivity of our results to the initial conditions by generating an ensemble of simulations with increasing lead time.

For our simulations we set up a case study in the Bay of Biscay, where a strong inversion of 10–12 K at a height of 500–800 m was observed with widespread stratus and stratocumulus cloud cover. The simulations were validated against soundings from stations located at Brest, France, and A Coruña, Spain, as well as using the Moderate Resolution Imaging Spectroradiometer (MODIS) data.

This paper is structured as follows. In section 2 we provide an overview of the COSMO model and the simulation setup, as well as the observations used. The results are then presented in the following section, which includes a discussion of the large-scale flow and predominant subsidence (section 3a), the influence of the eddy-diffusivity limiter (section 3b), the initial conditions (section 3c), the turbulence length-scale parameter (section 3d), and the horizontal resolution (section 3e). In the final section our main results are summarized.

2 Numerical setup and data

a. Model description

For this study the state-of-the-art regional climate and weather prediction model COSMO (version 4.14) was used. The governing equations for the fully compressible flow are discretized in time using a standard third-order Runge–Kutta scheme (Wicker and Skamarock 2002; Foerstner and Doms 2004). The horizontal advection is computed by a fifth-order upstream-biased advection scheme, whereas a centered second-order scheme is applied in the vertical. Moisture variables are advected using a semi-Lagrangian scheme with a multiplicative filling approach to guarantee positive-definite advection. The radiative transfer scheme of Ritter and Geleyn (1992) is used in combination with a relative humidity criterion for determining subgrid-scale cloud cover (CLC).

Instead of a simplified one-moment cloud microphysics scheme, a two-moment approach (Seifert and Beheng 2006; Zubler et al. 2011) was used. This scheme parameterizes droplet nucleation (based on the vertical saturation gradient and vertical velocity), as well as the processes of accretion and autoconversion, self-collection, raindrop breakup, and rain sedimentation for the warm-phase cloud microphysics on the grid scale. A constant cloud condensation nuclei (CCN) concentration of 100 cm−3 was prescribed, which is characteristic of the marine environment (Kubar et al. 2009). Deep and shallow convection are parameterized by the Tiedtke (1989) scheme.

Turbulence parameterization

The COSMO turbulence scheme is a one-dimensional turbulence parameterization based on a 1.5-order turbulence closure after Mellor and Yamada (1974, 1982). In this scheme the subgrid-scale vertical turbulent mixing is parameterized to first order using the traditional K-closure approach with a prognostic equation for turbulent kinetic energy q2, which over sea includes the following terms:
e1
where denotes the grid-scale mean westerly (northerly) horizontal velocity component, u′ (υ′) corresponds to the respective subgrid-scale fluctuation from the mean, and θυ denotes the virtual potential temperature. Therefore, the turbulent kinetic energy includes shear production, buoyancy generation, and pressure and turbulent transport, as well as eddy dissipation. The vertical diffusion coefficients for heat (subscript H) and momentum (subscript M) are parameterized as
e2
where SM and SH denote the stability functions for momentum and heat and l is given by Blackadar (1962):
e3
Here, l denotes the assumed fundamental length scale of turbulence and k is the von Kármán constant, which is set to 0.4 in the COSMO model.

In the standard setting of the COSMO model, minimum values for and have been introduced in order to avoid a too low mixing in very stable situations and for assuring mostly always good numerical stability of the turbulence scheme (M. Raschendorfer 2012, personal communication). A more detailed description of the turbulence parameterization and the computation of the stability functions can be found in Buzzi et al. (2011).

b. Simulation setup

The one-way nested simulations performed at two horizontal resolutions are initialized and driven at the lateral boundaries with the Interim ECMWF Re-Analysis (ERA-Interim; Uppala et al. 2005; Simmons et al. 2007). The low-resolution simulations (0.11° or ~12 km) cover a region from the northeast Atlantic to the eastern boarders of Switzerland and Germany, whereas the high-resolution simulation (0.02° or ~2 km) is centered over the ocean, covering a domain area of 1160 × 800 km2. The computational domains are shown in Figs. 1a,b. For the vertical coordinates, a nonhomogeneous level spacing was used with 13 levels within the first kilometer and at a minimum spacing of 20 m. A time step of 90 s is used in the low-resolution simulation and is reduced to 20 s in the high-resolution simulation. The model setup follows the MeteoSwiss COSMO configuration that is used for the operational forecasting. Whereas both deep and shallow convections are parameterized in the coarse-grid simulation, only shallow convection is parameterized by the reduced Tiedtke scheme in the 2-km simulation, in order to represent convective structures smaller than 12 km (six grid points) in diameter.

Fig. 1.
Fig. 1.

(a) Topography (m) at 12-km horizontal resolution and (b) geopotential height contours with the wind field overlain on the 925-hPa surface for the KMIN_1.0L simulation (see Table 1) at 0000 UTC 27 Jan 2003. The red box shows the nested 2-km simulation domain and crosses mark locations of two radiosondes used in this study. (c) Temporal evolution of the horizontally averaged vertical velocity profile. The horizontal average was obtained over the sea grid points of the 2-km domain. (d) PBLH (km) at 1200 UTC 27 Jan 2003 diagnosed by the top of the inversion determined by the temperature gradient (see section 3b for detailed description). White regions in (d) denote areas where the PBLH could not be diagnosed because of an insufficient gradient in temperature.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00039.1

In this case study, the sensitivities of the boundary layer and inversion strength on the time of initialization as well as the vertical turbulent mixing were investigated. An overview of the performed simulations can be found in Table 1. In particular, the sensitivities with respect to different values of and l, defined as tur_len = l/k in the COSMO namelist, were analyzed. The sensitivities to values of tur_len = {500, 250, 150, 60} m were also investigated, where tur_len = 500 and 250 m correspond to the COSMO standard setups with 12- and 2-km horizontal resolutions, respectively.

Table 1.

List of all simulations performed with distinguishing characteristics (see section 2a for details). Columns are related to horizontal resolution, turbulence parameters [ and tur_len], and initialization time during 2003.

Table 1.

Table 1 shows the details of the simulations. Most simulations were initialized at 0000 UTC 26 January 2003. However, we also performed an ensemble of simulations with different initialization times between 0000 UTC 24 January and 1200 UTC 26 January 2003.

c. Observational data

The COSMO simulations were compared against two different types of observations. The total cloud cover, obtained by the MODIS satellite (Platnick et al. 2003) and archived at 1-km resolution, provided the horizontal overview. In addition, two radiosonde stations, at Brest and A Coruña, were used that were predominantly exposed to maritime conditions. Radiosonde profiles for θ, relative humidity (RH), and horizontal wind at 0000 and 1200 UTC 27 January 2003 were compared against the simulated profiles within the simulation domain.

3. Results

a. Synoptic conditions and mesoscale forcing

On 26–27 January 2003, the large-scale flow throughout the 12-km and the therein nested 2-km domain was characterized by a high pressure system. This high pressure system was centered to the southwest of the Bay of Biscay, as is shown by the geopotential height at 925 hPa in Fig. 1b. The position and magnitude of the geopotential height, as well as the associated subsidence (Fig. 1c), are to a large extent determined by the driving ERA-Interim.

The large-scale subsidence is strongest during the night where values between −1.5 and −2 cm−1 are seen on 26 and 27 January 2003. At 0900 UTC 27 January there is a synoptic regime change within the 2-km domain, transitioning from a high pressure subsidence to a moderate large-scale ascent (of the order of 0.5–1.5 cm−1). This ascent is caused by a cold front propagating into the domain from the northwest, weakening the influence of the high pressure system that is displaced to the southwest. The position of the cold front can be inferred from Fig. 1d, which shows the diagnosed PBL height (PBLH) at 1200 UTC 27 January 2003. North of about 50°N, one can see a bandlike structure around the geographical position of Ireland, where the PBLH could not be diagnosed because of an insufficient temperature gradient.

Throughout the simulated time period, a maritime northerly flow toward the European landmasses was observed. As can be seen by the wind field at 925 hPa (Fig. 1b), the wind flow is diverted along the Spanish coast resulting from the increase in topography from sea level to 1000 m over a region of 200 km (see Fig. 1a). This diversion of the wind field can be explained by shallow water theory, as we are dealing with a shallow PBL, which is topped by a strong temperature inversion in the maritime domain (see Fig. 2). According to the flow diagnostics of Houghton and Kasahara (1968) for shallow fluid flow incident upon a ridge, the present situation can be classified as a “total blocking” event (i.e., the flow does not overcome the ridge).

Fig. 2.
Fig. 2.

(a)–(d) Maximum vertical temperature gradient found within the inversion, as diagnosed from the temperature profiles (see section 3b for details). (e)–(h) PBLH defined by the diagnosed inversion top. Sensitivity of inversion strength and height with respect to at 0000 UTC 27 Jan 2003 is shown. Black line in (d),(h) shows position of vertical potential temperature cross sections presented in Fig. 3.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00039.1

This flow diagnostic is based on the values of two nondimensional parameters: the Froude number F0 and a scaled mountain height M. The Froude number is defined as , where u is the incident wind speed, h0 the depth of the PBL, and g* = gΔθe/θe. The scaled mountain height is given by M = H/h0, where H is the height of the mountain (in this case the height of the Spanish coast). Depending on the position in this two-dimensional parameter space spanned by values of F0 and M, one can define different flow regimes as depicted in Fig. 6 of Houghton and Kasahara (1968). For the flow in the Bay of Biscay on 27 January, we estimate u to be about 5 m s−1, H to be about 1000 m, h0 to be about 700 m, and g* to be about 0.3 m s−2 (Fig. 2). These values lead to F0 of approximately 0.3 and M of approximately 1.4. Following Houghton and Kasahara (1968), these values suggest that the flow falls within the “blocking regime.”

However, rather than being reflected backward, as is the case in Houghton and Kasahara (1968) for calculations for infinitely long ridges, the flow is deviated along the Spanish coast to lower mountain passes (Fig. 1b). The flow blocking also leads to a lifting of the PBLH in front of the Spanish coast, as can be seen in Fig. 1d.

b. Sensitivity to eddy diffusivity limiter

Here, the sensitivity of the simulated boundary layer structure and cloud formation to the prescribed minimum threshold of the eddy diffusivity for momentum and heat was investigated. Throughout the maritime domain a tendency of shallower boundary layer formation with stronger capping inversions for lower minimum values of eddy diffusivity can be observed in Fig. 2. The top panels in Fig. 2 show the maximum vertical temperature gradient within the inversion layer. The inversion layer, using the standard definition of a temperature inversion (Geer 1996), was diagnosed between the lowest level where a positive temperature gradient is seen, up to the next level where the temperature gradient switches to a negative sign. If the total temperature increase is larger than 0.5 K, an inversion was diagnosed and the maximum gradient within the inversion layer was determined. The PBLH (Figs. 2e–h) was diagnosed at the determined inversion top. This diagnostic is to some extent sensitive to the vertical resolution, as the accuracy of the diagnosed PBLH is limited by the vertical grid spacing around the inversion layer (between 0.5 and 1 km, the vertical grid spacing varies between 100 and 150 m).

Throughout much of the maritime domain, no inversion (see Fig. 2a) could be diagnosed in the KMIN_1.0L simulation (; see Table 1). If an inversion was diagnosed, the maximum gradient is of the order of 1–2 K (100 m)−1 only. For lower values of , stronger temperature inversions were simulated over larger regions in the maritime domain. The strongest inversion was simulated by the KMIN_0.01L simulation (see Table 1), where over large areas a maximum vertical temperature increase of 6 K (100 m)−1 was diagnosed (Figs. 2d,h). The PBLH in these regions was diagnosed between 600 and 800 m. In general one observes a lowering of the PBLH with stronger inversions, dependent on the eddy diffusivity limiter chosen. Considering that the large-scale subsidence and therefore the adiabatic heating are not affected by , this increase in inversion strength and decrease in inversion height is due to the changed turbulent mixing (discussed below) only. Furthermore, the influence of the surface fluxes on the inversion strength was found to be negligible. The vertical mixing profile (and hence the inversion) was found to be more sensitive to changes in than changes in surface fluxes. The sensible heat flux (~10 W m−2 within the maritime domain) remained invariant, while the latent heat flux at the surface increased from approximately 10 to approximately 40 W m−2 as was reduced.

The vertical structure of the inversion layer is shown in Fig. 3. In the KMIN_1.0L simulation the gradient in θ is smoothed considerably throughout the first 2 km of the atmosphere (Fig. 3a). One can observe a constant increase of potential temperature of about 1K (100 m)−1. Consistent with Fig. 2, the inversion gradient increases considerably with the reduction of the eddy diffusivity limiter and the extent of the inversion layer.

Fig. 3.
Fig. 3.

The θ cross sections (along black line shown in Figs. 2d,h) for simulations with different values at 0000 UTC 27 Jan 2003.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00039.1

At either end of the cross sections, the inversion layer is lifted. The cross sections are oriented perpendicularly to the cold front. The left-hand side of the cross sections passes through the cold front to the southwest of Ireland (see Figs. 2d,h) and the right-hand side crosses the Spanish mainland. On the right-hand side of the cross section, the lifting of the inversion layer is consistent with the diagnosed total blocking (section 3a) of the flow caused by the coastal topography. On the left-hand side it is caused by cold-air advection into the PBL attributed to a cold front, which also weakens the inversion considerably. In addition, one can observe (Fig. 3) that the occurrence of gravity waves triggered by the cold front seems to be affected by . Vertical disturbances of the θ contours are visible in Figs. 3c,d, and to a lesser extent in Fig. 3b, but are completely absent in Fig. 3a. The absence of the θ perturbations in the vertical shows that higher values of the eddy diffusivity limiter led to a smoothing of gravity waves. Furthermore, between 800 and 1300 km along the cross section, one notices the absence of a mixed layer (ML) in Fig. 3a. It appears that the turbulent fluxes, with high values of , are strong enough to destroy the inversion and the ML below.

Comparing the simulated CLC for KMIN_1.0L to the retrieved CLC from MODIS, throughout the domain of strong inversions at the PBLH, it is clear that cloud cover was generally severely underestimated (Figs. 4a,b). The polar-orbiting satellite MODIS, which passed over the Bay of Biscay at 1200 UTC 27 January, can be used for the evaluation of low-level cloud cover since no high-level clouds were present in these regions according to the observed cloud-top temperature. For a fair comparison of the retrieval with the four simulations with varied , as shown in Figs. 4b–e, the MODIS CLC resolution was reduced to 12 km. Cloud cover from simulations that used is in much better agreement with the MODIS retrieval. A continuous cloud deck is simulated within the Bay of Biscay as well as in the southwest of the domain in all three simulations (Figs. 4c–e).

Fig. 4.
Fig. 4.

(a) MODIS total CLC is compared against low CLC (below 800 hPa) at 0000 UTC 27 Jan 2003 for (b) KMIN_1.0L, (c) KMIN_0.4L, (d) KMIN_0.1L, and (e) KMIN_0.01L. The resolution of the MODIS retrieval has been reduced to 12 km to match the horizontal resolution of the simulations.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00039.1

However, there is a noticeable structure of cloud lines within an otherwise cloud-free region visible in the satellite retrieval, which is not captured by the simulations. These streaks can be identified as ship tracks, which have been shown to be an aerosol-induced phenomenon (Bowley 1967; Durkee et al. 2000). The current simulations were carried out with constant CCN concentrations, and time-varying aerosol effects were ignored. Hence, these ship emission effects could not be captured in these simulations, but will be addressed in future work.

For a more detailed analysis of the effects of on the PBL profiles we considered profiles at the location of two radiosonde stations that were exposed to marine air (see Fig. 1b). At Brest and A Coruña, we compared θ, RH, and horizontal wind profiles to the soundings at 0000 and 1200 UTC 27 January (as shown in Figs. 5 and 6, respectively), and investigated the effect of on the turbulent kinetic energy (TKE) in Fig. 7. At Brest a particularly strong inversion of approximately 12 K (150 m)−1 at a height of 500 m was observed at 0000 UTC (Fig. 5b, dashed line). As the PBL is heated during the day, the inversion strength was decreased to approximately 5 K (150 m)−1 by 1200 UTC, while the inversion height remained unchanged. At A Coruña the inversion was considerably weaker, but displayed a double-gradient structure at 0000 UTC, which was dissolved by 1200 UTC (Figs. 6b,e). Strong gradients were also observed in the RH profiles. In line with the θ profiles, similarly strong gradients and equivalent structures were observed for relative humidity. The RH profile at Brest for 0000 UTC (Fig. 5a) shows a clear decoupling between a near-saturated PBL and a dry free troposphere, which is to be expected because of the inhibition of adiabatic exchange across the inversion. Looking at the vertical distributions of the horizontal wind at Brest and A Coruña, one notices a uniform northeasterly wind at Brest, whereas the wind veers significantly with height at A Coruña, both at 0000 and 1200 UTC (Figs. 5c,f and 6c,f). In both cases one observes weaker wind speeds within the PBL and stronger wind speeds above. This suggests a decoupling of the wind field across the PBLH, as anticipated.

Fig. 5.
Fig. 5.

RH, θ, and horizontal wind profiles from left to right for (a)–(c) 0000 and (d)–(f) 1200 UTC 27 Jan 2003 at Brest. The radiosonde soundings are denoted by black dashed lines in (a),(b),(d),(e) and are shown in the first column in (c) and (f). Simulated profiles at the nearest grid point on land to the radiosonde’s location are shown for the simulations with varied .

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00039.1

Fig. 6.
Fig. 6.

As Fig. 5, but for the A Coruña radiosonde station.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00039.1

Fig. 7.
Fig. 7.

Evolution of TKE in the PBL at (a)–(d) Brest and (e)–(h) A Coruña for simulations with different values. Hatching denotes regions of grid-scale cloud.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00039.1

The exceptionally strong inversion at Brest at 0000 UTC is strongly underestimated in both the KMIN_1.0L and KMIN_0.4L simulations, but well captured by the two simulations with reduced eddy diffusivity limiters of 0.1 and 0.01 m2 s−1. The deficiencies of the simulated θ profiles for the KMIN_1.0L and KMIN_0.4L simulations are also mirrored in the RH profiles, where one observes a too dry upper PBL (by ~15%) and a too moist free troposphere above (15%–30%). On the other hand, the KMIN_0.1L and KMIN_0.01L simulations better capture the moisture decoupling. The decoupling of the horizontal wind profile is equally well captured at Brest at 0000 UTC in all four simulations.

These results are consistent with the previous findings presented in Figs. 2 and 4 and reiterate the strong influence of on the inversion strength and extent, as well as the moisture distribution between the free troposphere and the PBL. However, the comparison of the simulated profiles to the observed soundings also highlights some persisting biases of the simulations. Although the inversion gradient is better captured in simulations with reduced , the decrease in inversion strength from 0000 to 1200 UTC at Brest is not reproduced well. In the KMIN_0.01L simulation the PBL is about 2 K too cold and the free troposphere is 2 K too warm in the first 300 m above the inversion, leading to an overestimation of the inversion gradient and a too moist PBL. On the other hand, the inversion gradient is captured well in the KMIN_0.1L simulation, but the simulated inversion height is too high by approximately 150 m.

The decoupled boundary layer structure observed at A Coruña at 0000 UTC is not captured in the simulations. Looking at the RH profile, the decoupling is probably as a result of underlying cumulus clouds feeding the stratocumulus cloud deck above, which is consistent with the findings of previous studies (e.g., Serpetzoglou et al. 2008). This indicates that the simulation of decoupled boundary layers remains as a difficult issue independent of the values chosen for . However, in principle the model is able to simulate such a decoupling for higher boundary layers (up to 3 km), as can be seen in the θ cross sections in Fig. 3 just ahead of the cold front.

Further understanding of the results on a process level can be obtained from the evolution of the vertical TKE profiles shown in Fig. 7. Here, clear differences between the strength of the TKE and the turbulence structure are observed for simulations of varied . In most simulations, one can observe TKE being generated at the cloud top and the surface (during the day). In either stratus- or stratocumulus-topped cloud layers the turbulence during nighttime is driven by entrainment of warm dry air from above the inversion and by longwave radiative cooling at the cloud top (de Roode 1999), which is locally as large as −29 K day−1 at Brest and −24 K day−1 at A Coruña in our simulations. Convective eddies form during the day that are driven from the surface.

Consistent with the prescribed high minimum value for eddy diffusivity, higher values of TKE are generated over a greater vertical extent in the KMIN_1.0L simulation (Figs. 7a,e). Furthermore, TKE is generated far above the grid-scale clouds shown in Fig. 7a. This is attributable to subgrid-scale clouds (not shown) that continue forming higher up in the troposphere. At Brest these clouds form up to a height of 2 km, where RH is still as high as 75%. Between the KMIN_0.4L (Figs. 7b,f) and KMIN_0.1L (Figs. 7c,g) simulations, minor differences in structure as well as magnitude of TKE are found. In both simulations one can observe a reduction of TKE between the regions of TKE generation at the surface and at cloud top. However for , the cloud-top generated TKE is significantly reduced compared to the other simulations.

The range of TKE in all simulations where was found to be in good agreement with the literature (e.g., Moeng et al. 1996; de Roode and Duynkerke 1997; Stull 2009).

c. Sensitivity to initial conditions

Here, we consider an ensemble of simulations in order to assess the level of predictability, the dependency on the initial boundary conditions, and the associated uncertainties of our results. To this end, we considered six hindcasts with a resolution of 12 km that were initialized between 0000 UTC 24 January and 1200 UTC 26 January. While all simulations use the same lateral boundary conditions, this setup serves well in generating perturbations that might lead to mesoscale differences (Hohenegger and Schär 2007). Indeed, the large-scale subsidence was found to be reduced in simulations with longer lead times. In the KMIN_2400L simulation the subsidence (not shown) between 2100 UTC 26 January and 0900 UTC 27 January was reduced from a range of [−1.5, −2] to [−0.75, −1] cm s−1 in the upper troposphere.

In Brest, the simulated profiles at 0000 UTC (Figs. 8a,b) and 1200 UTC (not shown) agree well with each other, independently of their time of initialization. Very little variation is observed in the wind fields. In the θ profiles, one notices a slight vertical shift of the inversion of approximately 150 m between simulations started at 0000 and 1200 UTC 24 January and 0000 UTC 25 January, and simulations started thereafter. This upward shift of the earlier initialized simulations increased to about 300 m at 1200 UTC and seems to coincide with the weaker subsidence predicted in simulations initialized prior to 0000 UTC 25 January. The inversion gradient on the other hand is equally strong in all simulations.

Fig. 8.
Fig. 8.

Sensitivity of the KMIN_0.01L simulation to different initial conditions. Initial conditions vary between 0000 UTC 24 Jan and 1200 UTC 26 Jan 2003 (see Table 1). The simulated profiles are shown at 0000 UTC 27 Jan with lead times of 12–72 h at (a)–(c) Brest and (d)–(f) A Coruña. The ERA-Interim is shown as a solid black line.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00039.1

These results show that the model was able to form and maintain as strong an inversion as was observed at Brest for a variety of initial conditions and simulated subsidence. Nonetheless, the inversion might still be sensitive to some extent to the reanalysis used (Vellore et al. 2007). However, investigating the effect of a wider range of initialization PBL profiles from different reanalyzes is beyond the scope of this study. The panels in Fig. 8 show the PBL profiles according to the driving ERA-Interim. Hence, we can demonstrate in this study that the simulation of the inversion is successful despite its strong underestimation in the driving lateral boundary data.

The lifting of the PBLH can also be observed throughout the maritime domain depicted in the previous figure shown in section 3b. In both Figs. 2 and 3 one also sees a lifting of the boundary layer at 1200 UTC 27 January ahead of the cold front. Although the cold front itself progressed in the same manner in all simulations, the extent of the prefrontal lifting is seen to be increased with larger lead times. In the KMIN_2400L simulation this lifting of the PBLH to 1–1.4 km reaches as far as the northwestern tip of the Spanish coast, but does not affect the northern part of the Bay of Biscay as strongly. This suggests that the formation of a stronger transverse ageostrophic circulation pattern across the cold front (Holton 1992, 267–270) is seen in simulations with longer lead times, which is in agreement with the weaker simulated subsidence.

At A Coruña (Figs. 8d,e), there are significant differences at 0000 UTC 27 January between simulations with different initial conditions. Inversion strength, height, and the vertical wind profiles of the horizontal wind vary significantly between the simulations. The double inversion and the associated turbulent decoupling of the boundary layer are not captured by the simulations. Nonetheless, one could argue that all of the simulations apart from KMIN_2400L and KMIN_2412L are performing better with respect to inversion extent and vertical position than the driving ERA-Interim at 1200 UTC 27 January.

d. Sensitivity to the turbulence length scale

The sensitivity of the PBL structure to the fundamental turbulent length scale, which is set by the tur_len parameter, was analyzed for tur_len = {500, 150, 60} m. To assess the impact of this parameter on the development of the parameterized PBL turbulence and simulated boundary layer profiles, we chose the setting for these simulations. In this setting the parameterization operates with the least restriction by the eddy diffusivity limiter.

As can be seen in Fig. 9, little difference can be found between the TURL_60L simulation and the KMIN_0.01L simulation, where tur_len was set to 150 m. The maximum temperature gradient within the inversion over the maritime domain is almost identical in both simulations, as are the θ and RH profiles at Brest and A Coruña for 0000 UTC. In agreement to these findings, we also observe no significant changes in the TKE patterns at the radiosonde locations (not shown) as we reduced tur_len from 150 to 60 m. However, the magnitude of the TKE was reduced by about 30% because of the reduction of tur_len.

Fig. 9.
Fig. 9.

Sensitivity of simulations to tur_len. Maximum temperature gradients simulated for (a) tur_len = 500 and (b) 60 m. Profiles shown at (c)–(e) Brest and (f)–(h) A Coruña for 0000 UTC 27 Jan 2003. The tur_len = 500 (TURL_500L), 60 (TURL_60L), and 150 m (KMIN_0.01L) parameters were investigated.

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00039.1

On the other hand, increasing tur_len to its operational value of 500 m reduces the inversion strength significantly. The maximum temperature gradient is reduced by up to 1 K (100 m)−1 (Fig. 9a). The simulated inversion is nevertheless strong enough for low-cloud formation, as the cloud cover (not shown) was not significantly changed by tur_len. Looking at the PBL profiles at Brest, one observes a weaker inversion at 0000 UTC as well as a corresponding weakened moisture decoupling. The θ and RH profiles at A Coruña are not strongly affected. Increasing tur_len to 500 m leads to a stronger production of TKE throughout the boundary layer. Particularly high values of over 5 m2 s−1 were reached in the TURL_500L simulation at the cloud top.

These results suggest that the inversion strength is sensitive to tur_len. In particular, one has to care not to choose high values for tur_len. In the case of a shallow boundary layer with a depth between 500 and 800 m within the maritime subsidence domain, it might not be surprising that a value of 500 m for tur_len leads to a degrading of the inversion. Finally, it should be noted that no sensitivity to tur_len was observed in the KMIN_1.0L simulation. Therefore, seems to dominate the evolution of TKE and, hence, the evolution of the PBL structure when set to 1.0 m2 s−1.

e. Sensitivity to horizontal resolution

We tested whether the simulated PBL structure and the influence of would change when applying a higher horizontal resolution. To do this, two 2-km-resolution simulations for and were performed (see Table 1). As can be seen in Fig. 10 no difference in PBL structure was found either between KMIN_1.0H and KMIN_1.0L or between KMIN_0.01H and KMIN_0.01L.

Fig. 10.
Fig. 10.

Sensitivity of and simulations on horizontal resolution (see Table 1). Profiles shown at (a)–(c) Brest and (d)–(f) A Coruña for 0000 UTC 27 Jan 2003. (Note the height difference of the profiles near the surface is caused by the differently resolved topographies at 2- and 12-km horizontal resolution.)

Citation: Weather and Forecasting 29, 2; 10.1175/WAF-D-13-00039.1

The strong inversion at Brest was equally well captured by KMIN_0.01H and KMIN_0.01L and strongly underestimated to the same extent by KMIN_1.0H and KMIN_1.0L. The equivalent simulated PBL structures of the 12- and 2-km simulations were also found at 1200 UTC at Brest (not shown), as well as in A Coruña. Considering that the key processes of stratocumulus formation are parameterized at both 2- and 12-km scales, this might not be surprising. One needs to access considerably higher horizontal and vertical resolutions in order to physically resolve turbulent and convective processes for stratified PBLs (Mason 1989; Stevens et al. 1998; Siebesma et al. 2003). Therefore, increasing the horizontal resolution has no impact on the model’s ability to simulate the observed decoupled boundary layer.

4. Conclusions

Forecasting shallow boundary layers with strong capping inversions has been a challenge for many regional and global models. To analyze this problem, we set up a case study, and based on process or subjective understanding, we isolated the problems that are commonly experienced by mesoscale models. Large-scale subsidence and turbulence have previously been identified as the main drivers of inversion formation. In this study we investigated whether the simulated inversion is sensitive to parameters used within the turbulence parameterization and if their modification within a range of physical limits would lead to an improved simulation of the inversion. In particular, we investigated the effect of two key turbulence parameters: minimum vertical diffusion and turbulence length scale (tur_len). In addition, we analyzed the uncertainty of our results by using an ensemble of simulations with different lead times. In this setup, we investigated whether the inversion was formed and maintained for simulations with lead times between 12 and 72 h.

We used the COSMO model in this study, which was set to run at two horizontal resolutions (2 and 12 km) and 13 vertical levels focused in the lowest kilometer. In particular, PBL profiles were verified with Brest and A Coruña soundings and horizontal cloud cover by using MODIS.

The key findings of this study are summarized as follow:

  • Turbulent vertical mixing is crucial for the thermodynamic PBL structure. One has to take extreme precaution when introducing flux limiters such as into the turbulence formulation, as the PBL profile is found to be largely sensitive to this parameter.
  • Despite the evident dependency on parameterizations, nocturnal inversions of 10–12 K were accurately predicted with lead times between 24 and 72 h, provided small values of were used.
  • The inversion height, inversion strength, and cloud distribution below the inversion were obtained with identical quality in simulations performed at the mesoscale (12 km) and cloud-resolving scale (2 km).
Inversions of the above-mentioned magnitude were simulated throughout vast portions of the maritime domain, and are in particularly good agreement with the observations at Brest at 0000 UTC 27 January. These findings are also in good agreement with other recent studies (Holtslag et al. 2013; Sandu et al. 2013), which suggest that the simulation of stable PBL characteristics can be improved by decreasing the simulated vertical mixing.

Although one seems to have improved the model’s ability to simulate inversions and to maintain sharp inversion gradients, the process of decoupling in a stable boundary layer remains a difficult issue. Our simulations show that the model in principle is capable of simulating such boundary layers, but not adequately enough to reproduce the shallow decoupled boundary layers.

Acknowledgments

We thank the COSMO consortium for access to the code, the German Weather Service (DWD) and MeteoSwiss for code maintenance and setup, C2SM for source code support, and the Swiss National Supercomputing Centre (CSCS) for providing a simulation platform. In particular, we thank Dr. Dani Lüthi for his help on data handling and Anne Roches for technical support. Finally, we thank the anonymous reviewers for their valuable suggestions and comments.

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