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Publication# A Simple Model for the Afternoon and Early-Evening Decay of Turbulence over Different Land Surfaces

Résumé

Recent years have seen an increasing interest in the late-afternoon transition between the convective and stable regimes of the atmospheric boundary layer. There are several differences between the two regimes. On one hand, the convective boundary layer is characterized by an unstable stratification, turbulent mixing of mass, momentum and heat and buoyancy-driven eddies. On the other hand, the stable boundary layer is associated with a strong stable stratification that tends to suppress vertical motions generated by mechanical turbulence. One of the key processes of this complex transition period is the forcing time scale associated with the surface heat flux. Unfortunately, very few modeling studies have used realistic decaying time scales for the sensible heat flux. Therefore, in the first part of this study, we present a new function that better represents the afternoon and early-evening transitions and validate it with eddy covariance measurements over different land surfaces. The objectives are to capture the buoyancy forcing time scales observed in nature and the influence of surface properties. In the second part of the study, we show preliminary results of large-eddy simulation of atmospheric flow over heterogeneous cooling stripes. We focus our attention on the temperature advection between the different stripes as a result of their different cooling rates. Overall, this study is one of the first to model the convective decay of turbulence using realistic time scales over heterogeneous terrain.

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Chad Higgins, Daniel Nadeau, Eric Richard Pardyjak, Marc Parlange

A simple model to study the decay of turbulent kinetic energy (TKE) in the convective surface layer is presented. In this model, the TKE is dependent upon two terms, the turbulent dissipation rate and the surface buoyancy fluctuations. The time evolution of the surface sensible heat flux is modelled based on fitting functions of actual measurements from the LITFASS-2003 field campaign. These fitting functions carry an amplitude and a time scale. With this approach, the sensible heat flux can be estimated without having to solve the entire surface energy balance. The period of interest covers two characteristic transition sub-periods involved in the decay of convective boundary-layer turbulence. The first sub-period is the afternoon transition, when the sensible heat flux starts to decrease in response to the reduction in solar radiation. It is typically associated with a decay rate of TKE of approximately t −2 (t is time following the start of the decay) after several convective eddy turnover times. The early evening transition is the second sub-period, typically just before sunset when the surface sensible heat flux becomes negative. This sub-period is characterized by an abrupt decay in TKE associated with the rapid collapse of turbulence. Overall, the results presented show a significant improvement of the modelled TKE decay when compared to the often applied assumption of a sensible heat flux decreasing instantaneously or with a very short forcing time scale. In addition, for atmospheric modelling studies, it is suggested that the afternoon and early evening decay of sensible heat flux be modelled as a complementary error function.

2011Chad Higgins, Daniel Nadeau, Eric Richard Pardyjak, Marc Parlange

Recent years have seen an increasing interest in the late-afternoon transition between the convective and stable regimes of the atmospheric boundary layer. There are several differences between the two regimes. On one hand, the convective boundary layer is characterized by an unstable stratification, turbulent mixing of mass, momentum and heat and buoyancy-driven eddies. On the other hand, the stable boundary layer is associated with a strong stable stratification that tends to suppress vertical motions generated by mechanical turbulence. One of the key processes of this complex transition period is the forcing time scale associated with the surface heat flux. Unfortunately, very few modeling studies have used realistic decaying time scales for the sensible heat flux. Therefore, in the first part of this study, we present a new function that better represents the afternoon and early-evening transitions and validate it with eddy covariance measurements over different land surfaces. The objectives are to capture the buoyancy forcing time scales observed in nature and the influence of surface properties. In the second part of the study, we show preliminary results of large-eddy simulation of atmospheric flow over heterogeneous cooling stripes. We focus our attention on the temperature advection between the different stripes as a result of their different cooling rates. Overall, this study is one of the first to model the convective decay of turbulence using realistic time scales over heterogeneous terrain.

2010Chad Higgins, Daniel Nadeau, Eric Richard Pardyjak, Marc Parlange

The parameterization of the atmospheric boundary layer is essential for accurate numerical weather predictions. The near-surface values of air temperature or wind speed for instance are highly dependent on the complex land – atmosphere interactions over heterogeneous terrain. Over such surfaces, several open challenges remain regarding the growth of internal boundary layers, the determination of mixing layer heights and the spatial distribution of heat and momentum fluxes. The large-eddy simulation (LES) code we apply is based on the robust Lagrangian scale-dependent dynamic subgrid-scale model (Bou-Zeid et al., 2005, Physics of Fluids). The flow is driven by a mean pressure gradient expressed in terms of horizontal geostrophic winds. The code is pseudo-spectral with spectral decomposition in the horizontal dimensions. Land surface heterogeneities take the form of spatially distributed patches of surface temperature and roughness derived from satellite imagery and land use analysis. The simulation of the complete diurnal cycle is possible but we restrict our discussion to fully convective conditions. Data from LITFASS – 2003 (Lindenberg Inhomogeneous Terrain Fluxes between Atmosphere and Surface: a long-term Study) are used to validate the simulation results. The LES domain covers a 99-m meteorological tower with turbulent measurements and five surface micrometeorological stations. We investigate the presence of large-scale turbulent structures that are typical for daytime conditions with a particular interest in the blending height. Overall, this study illustrates how important is the accurate parameterization of heterogeneous terrain in studies of the atmospheric boundary layer.

2009