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Roland B. Stull

Abstract

For a boundary layer in free convection where turbulent thermal structures communicate information between the surface and the interior of the mixed layer, it is hypothesized that the surface momentum flux can be parameterized by u * 2 = bDwBM ML, the heat flux by w′θ′s = bHwBskin−θML), and the moisture flux by wrs = bHwB(rskinrML). In these expressions u * is the friction velocity, M is mean wind speed, θ is potential temperature, r is mixing ratio, subscript ML denotes the interior of the mixed layer, and subscript skin denotes the characteristics of the underlying solid or liquid surface. A buoyancy velocity scale is defined by wB≈[(gv)zivskin−θvML)]½, where zi is mixed-layer depth, θv is virtual potential temperature, and g is gravitational acceleration.

Using data from the BLX83 field experiment in Oklahoma (roughness length: 0.05 m, latitude: 35.03°N, vegetation: mixed pasture and crops, season: spring), the convective transport coefficients are empirically found to be bH = 5.0×10−4 for heat and moisture, and bD=1.83 × 10−3 for momentum. These parameters worked well when tested against independent data from the Australian Koorin field experiment (roughness length: 0.4 m, latitude: 16.27°S, vegetation: uniform sparse trees, season: winter). If these parameterizations and coefficient values are validated for other sites, then convective transport theory could be considered as a candidate to replace the resistance law similarity theory based on profile matching, for conditions of free convection.

The theory is extended to include near-free convective conditions in which mechanical transport associated with. mean wind shear contributes to the still dominant buoyant transport. Scaling variables such as Obukhov length are rewritten using the convective transport relationships, which could potentially be used in similarity theories to compute other surface-layer and mixed-layer quantities.

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Roland B. Stull

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A mathematical model to describe the height changes and other characteristics of an inversion base under the influence of surface convection and general subsidence is developed. Inversion interface dynamics and entrainment rates are formulated based on an unstable boundary layer environment of well-organized, plume-like, penetrative convection. The use of unstable boundary layer scaling velocities in describing the convection leads to a natural inclusion of the relevant parameters associated with inversions into this model. It is found that the model does accurately predict realistic rates of inversion rise and of temperature changes for conditions where organized free convection is prevalent.

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Roland B. Stull

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Roland B. Stull

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Roland B. Stull

Abstract

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

Abstract

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

Abstract

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

Static stability should not be evaluated from the local lapse rate. There is a growing body of observations, such as within portions of mixed layers and forest canopies, showing that the whole sounding should be considered to evaluate stability. Air parcels can move across large vertical distances to create turbulence within regions that would otherwise have been considered stable or neutral according to classical local definitions. A nonlocal determination of static stability is presented that accounts for both the local lapse rate and for convective air parcels moving across finite distances. Such a method is necessary to properly estimate turbulence, dispersion, and vertical fluxes that affect our weather and climate forecasts. Teachers of introductory meteorology courses and textbook authors are encouraged to revise their static stability discussions to follow air parcel displacements from beginning to end.

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Roland B. Stull

Abstract

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

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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