Parameterization of the Turbulent Energy Budget at the Top of the Daytime Atmospheric Boundary Layer

Otto Zeman Department of Aerospace Engineering, The Pennsylvania Stage University, University Park 16802

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H. Tennekes Department of Aerospace Engineering, The Pennsylvania Stage University, University Park 16802

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Abstract

The budget of turbulent kinetic energy at the base of the inversion which caps the daytime atmospheric boundary layer depends on the lapse rate of potential temperature in the air aloft. The principal gain term in the energy budget is turbulent transport of kinetic energy, the principal loss term is buoyant conversion of kinetic energy into potential energy. The contributions made by these and other terms in the energy budget need to be parameterized for applications to inversion-rise prediction schemes. This paper contains a detailed analysis of the effects of dissipation near the inversion base, which leads to reduced entrainment if the air aloft is very stable. The parameterized energy budget also includes the Zilitinkevich correction, the influence of mechanical energy production near the inversion base, and modifications needed to incorporate cases in which the surface heat flux is negligible. Extensive comparisons of the theoretical model with experimental data indicate that a simplified treatment of the energy budget is adequate for forecasts of the development of convective mixed layers. The parameterization scheme is also applicable to thermocline erosion in the ocean; in that case, however, some of the minor terms in the energy budget often play a major role.

Abstract

The budget of turbulent kinetic energy at the base of the inversion which caps the daytime atmospheric boundary layer depends on the lapse rate of potential temperature in the air aloft. The principal gain term in the energy budget is turbulent transport of kinetic energy, the principal loss term is buoyant conversion of kinetic energy into potential energy. The contributions made by these and other terms in the energy budget need to be parameterized for applications to inversion-rise prediction schemes. This paper contains a detailed analysis of the effects of dissipation near the inversion base, which leads to reduced entrainment if the air aloft is very stable. The parameterized energy budget also includes the Zilitinkevich correction, the influence of mechanical energy production near the inversion base, and modifications needed to incorporate cases in which the surface heat flux is negligible. Extensive comparisons of the theoretical model with experimental data indicate that a simplified treatment of the energy budget is adequate for forecasts of the development of convective mixed layers. The parameterization scheme is also applicable to thermocline erosion in the ocean; in that case, however, some of the minor terms in the energy budget often play a major role.

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