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Roland B. Stull

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Roland B. Stull

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Roland B. Stull

Abstract

In Part I, external forcings such as pressure gradient, terrain roughness and imposed cooling were used to forecast the thickness and strength of an exponentially-shaped (ES) nocturnal boundary layer (NBL) temperature profile. In Part II, it is suggested that the evolution of the ES temperature profile can be explained by simple models for background radiative, surface-induced radiative, and turbulence contributions to the total cooling. One partitioning model sets the ratio of turbulent to surface-induced radiative components to be a constant (∼3.35). The exponentially-shaped heat-flux profile implied by that ratio agrees favorably with the Minnesota field experiment profile of Caughey et al. Differences between an ES and a mixed-layer (ML) model for the NBL am presented using potential energy (PE) arguments, where a thinner ML yields the same PE change as a thicker ES. Differences are also apparent using eddy diffusivity (K) theory, where the bulging K-profile for a ML is dissimilar to the linear K-profile found for an ES. The implications of using velocity scales from Part I with the PE calculations done here are that over 90% of the turbulence kinetic energy is dissipated by viscosity, as opposed to smaller percentages suggested by others.

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Roland B. Stull

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Mixed layer depths are predicted using an entrainment equation with conservation equations. The entrainment equation is based on the turbulent kinetic energy equation for the mixed layer. The atmosphere is idealized as having temperatures, humidities and winds constant with height in the boundary layer with a step discontinuity marking the top of the mixed layer. This model is tested with mixed layer depth observations made during the 1953 Great Plains experiment, the 1967 Australian Wangara experiment, and the 1972 Puerto Rican tropical experiment. Model calculations of inversion rise and mixed layer depth offer good agreement with the observations. It is found that none of the turbulence generation and loss mechanisms for the mixed layer (such as buoyancy, wind shear and gravity waves) should be neglected a priori.

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Roland B. Stull

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Penetrative convection is modeled by a series of idealized disturbances at the base of an atmospheric temperature inversion. Internal gravity waves excited in the inversion by the disturbances are theoretically found to drain away a fraction of the initial energy of the disturbances. The portion of energy lost upward is significant when the temperature inversion is weak. Vertical energy fluxes due to internal gravity waves are mathematically described using wave group approaches.

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Roland B. Stull

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Even though a continuum of mixing parameters γ(t, z, ζ) is used in transilient turbulence theory to describe the effects of many superimposed eddy sizes (ζ) on the mean field at height z, the overall bulk dispersive rate at any height can be measured by one number, N 2(z). By utilizing second moment measures of dispersion, it is shown theoretically, for various special cases that the variance of tract position, σs 2, is given by σz 2(z, t = N 2(z)t, where N 2(z) = ∫ ζ2γ(z, ζ)dζ. An analogous expression for N 2(z) is derived for the discrete version of transilient theory, as can be used for grid point models. These bulk dispersive rates can easily be compared to eddy diffusivity, K(z), because the variance of tracer position for K theory is known to be σs 2(z, t) = 2K(z)t.

The discrete version of transilient turbulence theory is shown to be absolutely numerically stable, regardless of the timestep size or the grid point spacing. In addition, it is shown how the values of the discrete transilient coefficients are determined by two factors: 1) the physics governing the turbulence mixing, and 2) the nature of the discretization (i.e., size of timestep and grid spacing. Thus, it is possible to employ transilient turbulence theory for both the diffusive and boundary layer parameterizations in a large-scale numerical forecast model that, by operational necessity, has coarse grid spacing and large timesteps.

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Roland B. Stull

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A first-order turbulence theory is developed that describes eddy-like mixing. Named transilient theory after a Latin word meaning “leap across” this approach models the turbulent mixing between arrays of points separated in space. It differs from eddy-diffusivity theory in that it is not restricted to turbulent transfer between adjacent points. By explicitly including “large eddy” effects it can handle mixing across zero-gradient and counter-gradient situations such as found in convective mixed layers. Applications might include pollutant dispersion, boundary layer modeling and cloud entrainment studies.

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Roland B. Stull

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The stable-layer thickness h and near-surface potential temperature strength Δθs, of the nocturnal boundary layer (NBL) are shown to have a “background” square-root of time dependence. Superimposed upon this background are other time variations caused by changes in bulk turbulence parameter B and average surface heat flux H: h = 5(−HtB)&frac12 and &minusΔθs = (−HtB −1)&frac12). As an intentionally different approach to the NBL problem B is modeled in terms of forcings external to the NBL rather than in terms of internal variables such as friction velocity or Obukhov length. Nocturnal boundary layer observations from the Wangara and Koorin field experiments in Australia are used to guide some dimensional arguments to yield B − (ŪG UG −1)(|fUG|Zs)3/2/(−QHg), where UG is the geostrophic wind vector, f the Coriolis parameter, g the acceleration due to gravity, Zs is a site and wind-direction-dependent empirical parameter and the overbear indicates time-average since transition (near sunset). Apparently, Zs is a measure of the influence of terrain features such as roughness and slope on NBL development. The resulting model is shown to be adaptable to frost-warning and air-quality applications.

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Roland B. Stull

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Cover hours are defined as the cloud-cover fraction times the number of hours those clouds are observed. Case study statistics of cover hours during 1990 for nonprecipitating low clouds at Madison, Wisconsin, indicate the potential for climatic impact by boundary-layer clouds. A total of 1476.6 cover hours by all low clouds are observed, of which the subset of scattered boundary-layer clouds contributes 33%. The subset of low clouds that are turbulently coupled to the ground contributes 1199.1 cover hours, which is 81% of the total observed and 13.7% of the total possible 8760 hours per year.

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Roland B. Stull

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Not all cumulus clouds can vent mixed-layer air into the free atmosphere. Therefore, three subtypes of fair-weather cumulus clouds are identified based on the nature of their interaction with the mixed layer: forced, active and passive clouds. Forced clouds, the visible tracers within the tops of some mixed-layer thermals, are totally embedded within the mixed layer. Active clouds reach above their level of free convection and are responsible for inhibiting mixed-layer growth and for venting pollutants from the mixed layer. Passive clouds are the decaying remnants of formerly active clouds, and are disconnected from the mixed layer.

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