Generalizing ‘z‐less’ mixing length for stable boundary layers

We examine the dependence of several turbulence quantities on the wind speed and stability using nocturnal data from the Shallow Cold Pool Experiment. The turbulent quantities (velocities) are defined in terms of the standard deviation of the horizontal and vertical velocity fluctuations, two different calculations of the friction velocity, and two turbulent velocities based on the heat flux. The dependence of the turbulent velocities on the wind speed shows a transition between the weak-wind regime of small slope and the stronger wind regime of larger slope, as found in previous studies. This transition occurs for all of the turbulent velocities examined and occurs for a wide range of averaging times. Although this study concentrates primarily on data over a flat surface above the valley, the transition also occurs at the other 18 stations that have non-zero local slopes up to about 10 %. At the same time, the relationship between the turbulence and the wind speed cannot be universal because of the influence of stratification and site-dependent non-stationarity in the weak-wind regime. The wind speed of the transition increases with increasing stratification at a rate that is an order of magnitude slower than that predicted by a constant transition bulk Richardson number. For the weakest winds, the impact of stratification is unexpectedly small.

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“…Turbulence that does not directly interact with the ground can be referred to as a form of "z-less" turbulence (e.g. Grisogono 2010).…”

Section: Introductionmentioning

confidence: 99%

Dependence of Turbulent Velocities on Wind Speed and Stratification

Mahrt

Sun

Stauffer

2014

Boundary-Layer Meteorol

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“…The coefficient of proportionality is 138 the turbulent exchange coefficient, which is a function of the length scale, the velocity scale, 139 and stability functions. Formulations of these functions depend on the approach and closure 140 technique deployed (e.g., Mellor and Yamada 1982, Cuijpers and Holtslag 1998, Weng and 141 Taylor 2003, Grisogono 2010. A relatively new method that integrates both the local and 142 non-local approaches has been proposed by Siebesma and Teixiera (2000).…”

Section: Santanello Et Al 2017) Precipitation Can Be Influenced Dirmentioning

confidence: 99%

A New Research Approach for Observing and Characterizing Land–Atmosphere Feedback

Wulfmeyer

Turner

Baker

et al. 2018

Bulletin of the American Meteorological Society

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38Forecast errors with respect to wind, temperature, moisture, clouds, and precipitation largely 39 correspond to the limited capability of current earth system models to capture and simulate 40 land-atmosphere feedback. To facilitate its realistic simulation in next generation models, an 41 improved process understanding of the related complex interactions is essential. To this end, 42 accurate 3D observations of key variables in the land-atmosphere (L-A) system with high 43 vertical and temporal resolution from the surface to the free troposphere are indispensable. 44Recently, we developed a synergy of innovative ground-based, scanning active remote sens-45 ing systems for 2D to 3D measurements of wind, temperature, and water vapor from the sur-46 face to the lower troposphere that is able to provide comprehensive data sets for characteriz-47 Motivation 71The land-atmosphere (L-A) system includes the soil, the land cover such as vegetation, and 72 the overlying atmosphere. The interaction of variables, e.g. related to the water and energy 73 budgets, results in characteristic natural variabilities and regimes as well as their changes due 74 to anthropogenic influences. The planetary boundary layer (PBL) is part of the L-A system 75 and represents the interface between the land surface and the free troposphere. Through an 76 exchange of momentum, energy and water, the dynamics, the thermodynamic structure, and 77 the evolution of the PBL affect the formation of shallow and deep clouds, convection initia-78 tion, and thus precipitation (Sherwood et al. 2010, Behrendt et al. 2011, Santanello et al. 79 2011, van den Hurk et al. 2011. One of the most complex feedback 80 loops is between soil moisture and precipitation (Seneviratne et al. 2010, Guillod et al. 2015, 81 Santanello et al. 2017). Precipitation can be influenced directly by the surface fluxes (Ek and 82Holtslag 2004), and indirectly via PBL dynamics and mesoscale circulations (Taylor et al. 83 2012). 84The PBL state and its evolution are strongly influenced by non-linear feedbacks in the L-A 85 system. These are due to two-way interactions between radiation, soil, vegetation, and atmos-86 pheric variables, which result in the diurnal cycles of surface fluxes. The feedbacks are rele-87 vant from local to global scales (Mahmood et al. 2013, Stéfanon et al. 2014, and their 88 strength varies both regionally and seasonally in dependence of soil moisture, advection, and 89 climate regimes. In locations where these feedbacks play an important role, it is likely that 90 they will become even more important due to anthropogenic climate change (Dirmeyer et al. 91 2012). Thus, to improve our understanding of the state and the evolution of the L-A system as 92 well as the dynamics and thermodynamics of the PBL, it is critical that feedbacks and fluxes 93 between the different components, including entrainment at the top of the PBL, are well char-94 4 acterized and appropriately represented in weather, climate, and earth system models (e.g., 95 Se...

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“…The SCM with BL89 overestimates the altitude of the LLJ and the slope of the wind profile in the lower part of the boundary layer (Figure 7). Overmixing is also associated with a more curved potential temperature profile (Grisogono, 2010) compared to that of the LES (Figure 6). The modified mixing length is in better agreement with that of the LES, with a less curved temperature profile, as well as a more realistic slope of the wind profile and altitude of the jet in all cases.…”

Section: Stable Boundary Layersmentioning

confidence: 98%

“…The additional shear length scale allowed to reduce the over-mixing of a buoyancy-based formulation in the z-less regime of the VSBL compared to an improved Prandtl model for a katabatic flow (Grisogono and Belušić, 2008;Grisogono, 2010). Although the representation of the length scales were improved recently for the SBL, a unifying formulation suitable for all stratification range is missing.…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…Associated with stability functions, different types of mixing lengths are used in TKE-l schemes with either local or nonlocal characteristics (Lenderink and Holtslag, 2004). Local formulations can be based on (i) the distance to the boundaries, l = κz (Prandtl, 1925), (ii) the local static stability (Deardorff, 1980), or (iii), more recently, the local vertical wind shear (Hunt, 1988;Tjernström, 1993;Schumann and Gerz, 1995;Grisogono and Enger, 2004;Grisogono and Belušić, 2008;Grisogono, 2010;Venayagamoorthy and Stretch, 2010). Non-local mixing lengths (Bougeault and Lacarrere, 1989;Holtslag and Boville, 1993;Lenderink and Holtslag, 2004) have been introduced for convective conditions when the mixing length depends on the size of the largest eddies and the coherent structures.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation of a Buoyancy and Shear Based Mixing Length for a Turbulence Scheme

et al. 2017

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We present a new diagnostic mixing length for a turbulence scheme based on a prognostic equation for the turbulence kinetic energy. The formulation adds a local vertical wind shear term to the non-local buoyancy-based mixing length currently used in the research mesoscale model Meso-NH. The combined effects better represent local mixing for stably stratified flows where the wind shear plays a major role. The proposed formulation is directly evaluated in large-eddy simulations of stable, neutral, and unstable atmospheres. It is tested in single-column simulations with different length scale formulations and compared to large-eddy simulations. Idealized cases with varying surface cooling rates and different prescribed geostrophic winds are used to evaluate the impact of the new model on the stable boundary layer. The model reduces the over-diffusion typically occuring in modeling the stable boundary layer and shows better performance in terms of the turbulent mixing, the temperature inversion, and the boundary-layer and low-level jet heights compared to large-eddy simulations. A slight improvement of the turbulence intensity is shown for convective boundary layers.

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Generalizing ‘z‐less’ mixing length for stable boundary layers

Cited by 32 publications

References 59 publications

Dependence of Turbulent Velocities on Wind Speed and Stratification

Dependence of Turbulent Velocities on Wind Speed and Stratification

A New Research Approach for Observing and Characterizing Land–Atmosphere Feedback

Evaluation of a Buoyancy and Shear Based Mixing Length for a Turbulence Scheme

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