The very stable boundary layer is a region of the atmosphere typified by large vertical gradients of temperature and momentum. Analysis of very stable atmospheric flows is complicated by the presence of nonlinear interactions among gravity waves, shear-driven overturning circulations, two-dimensional vortical modes and intermittent turbulence in various stages of development. This study examines the horizontal structure of a very stable atmospheric boundary layer, using data obtained primarily from terrain-following aircraft flights over central Oklahoma. Several diagnostic procedures are applied to the aircraft data, including classical and rotary spectral analysis, principal component analysis, and structure functions. Coherent structures with sharp boundaries are examined with a new conditional sampling technique which requires little a priori specification of sampling criteria. Because the flows involve sharp boundaries, spectral techniques do not provide as much useful information as other more localized procedures. The edges of the coherent structures are regions of significant vertical heat transport, a feature not often emphasized in studies of gravity waves and vortical modes in the stable boundary layer. The presence of significant turbulence even for large stability has implications for modelling of the very stable boundary layer. Forecasts of minimum temperature, boundary layer height, inversion characteristics, and pollutant dispersal are all significantly affected by turbulent mixing. Many models of the stable boundary layer artificially arrest the mixing under stable conditions, resulting in, for example, overestimates of nocturnal cooling. A new parameterization of the stable boundary layer is studied here by incorporating it into an existing model of the planetary boundary layer. The model is then run with one-dimensional sensitivity tests for an idealized atmosphere and with data from Wangara day 33. A simulation over snow cover is also examined. The tests substantiate the role of vertical mixing in ameliorating nocturnal cooling. An additional improvement is a more realistic boundary layer height for moderate wind speeds. / Graduation date: 1988

The influence of boundary layer pumping on an externally-forced synoptic-scale flow is examined. The results follow earlier theories of stratified incompressible Boussinesq flow. These theories state that the spin-down time scale and the penetration depth of the influence of boundary layer pumping are inversely proportional to the stratification and directly proportional to the horizontal length scale of the flow. However, the present development is performed in isentropic coordinates which allow estimates applicable to the atmosphere, and implicitly includes nonlinear influences due to tilting and vertical advection. This analysis indicates that boundary layer pumping could be important synoptically in the lower troposphere under conditions of significant surface stress and tropospheric stratification. The influence of stratification and accelerations on synoptic-scale, boundary layer production of vertical motion is examined for the case of oscillating boundary-layer flow driven by time-dependent, horizontally- periodic surface temperature perturbations. It is found that only very strong stratification can significantly reduce the boundary layer pumping through pressure adjustments within the boundary layer. As a step in understanding the complicated dynamics of the structure of accelerated stratified boundary layers, order-of-magnitude analyses of variables for each layer are examined. This structure depends on the relative magnitude of the non-dimensional forcing frequency and the product of the stratification parameter and Ekman number. Applications to both synoptic and diurnal atmospheric circulations are considered. / Graduation date: 1978

The numerical modeling of motions in the atmosphere's planetary boundary layer (PBL) is a challenging task. In general, the boundary layer interacts with both the overlying atmosphere and the underlying land or water surface in a complex manner. Random turbulence is also present in the PBL which precludes exact prediction by numerical models. Nonetheless, expensive three-dimensional numerical models have been developed which, with several parameterizations and assumptions, can give a good idea of the PBL structure in many situations. However, on certain occasions, there is strong mixing evident in the PBL which may enable one to describe the structure of the boundary layer in a much-simplified theoretical model. By eliminating the vertical dimension from consideration, this two-dimensional mixed-layer model can be applied to mesoscale phenomena (horizontal length scale < 100 km) at greatly-reduced costs. The equations for motion and mixed-layer height are derived for such a situation and methods appropriate to the numerical modeling of the atmospheric mixed layer are discussed. Using an energy-conserving finite-difference analog of the model equations, the model is integrated in time to simulate the motions which were associated with the atmospheric vortex street observed near Cheju-do, South Korea on 17 February 1975. Experiments were carried out which investigated the effects of lateral diffusion, horizontal resolution, and mixed-layer depth. It is concluded that, given proper representation of prognostic variables on a staggered finite-difference grid, only small, realistic values of eddy diffusivity need be utilized. It also appears evident from the numerical experiments and atmospheric observations that the vortex street will form only when the obstacle which triggers its formation protrudes above the mixed layer. Although the wind fields in the simulations sometimes lack clear, fully rotational cells well downstream of the island, the characteristic sinusoidal pattern observed in laboratory experiments and cloud photographs is explicitly resolved by the model. The simulated vortex street also compares favorably with the observed in that the dimensionless governing parameters of the simulated vortex street (the Reynolds number, Strouhal number, Lin's parameter, the spacing ratio, and the speed ratio) closely match the observed values. / Graduation date: 1981

High resolution data of moisture, temperature and wind velocity collected by aircraft during the 1975 Air Mass Transformation Experiment (ANTEX '75) provide information for detailed investigations of the phenomena occurring at the top of a cloud-topped mixed layer. Joint frequency diagrams of humidity and temperature reveal that for parts of the record the coldest temperatures occur in air near saturation while drier air or air with substantial liquid water is warmer. This suggests the possible occurrence of cloud-top entrainment instability (Deardorff, 1980). Using humidity as an indicator, the flight record is systematically searched for penetrative mixed layer elements and pockets of dry air penetrating into cloudy air (wisps). The separate phenomena are then composited to produce an "average" wisp and penetrating element. The composites show evidence of net cooling due to evaporation downstream from the penetrating element and upstream from the wisps. Sinking motion is associated with the cold temperatures. These results suggest the interaction of shear, penetrating elements and wisps, and the existence of cloud-top entrainment instability. / Graduation date: 1981

A baroclinic, convective mixed-layer was modeled, using water, in a laboratory convection tank identical to that used in the free convection study of Deardorff and Willis (1985). Baroclinicity and mean-flow shearing were achieved by tilting the tank by an angle of 1O⁰. The resulting mechanical-production rate of turbulence kinetic energy was comparable in magnitude to the buoyancy-production rate at mid-levels within the mixed-layer. Velocities were obtained by taking time-lapse photographs of neutrally-buoyant oil droplets suspended in the mixed-layer fluid. Variances and other statistical descriptors of the turbulence obtained from these velocities are presented in comparison to the free convection results of Deardorff and Willis (1985). The deviation of the present results from those of Deardorff and Willis (1985) are assumed to be related to the effects of mean-flow shearing and are explained wherever possible with the aid of an appropriate kinetic energy budget (kinetic energy, here, refers to the kinetic energy of the turbulence and is not to be confused with the kinetic energy of the mean-flow). The results indicate that a maximum in downstream horizontal kinetic energy at mid-levels within the mixed layer was generated by shear-production and, also, by conversion from vertical kinetic energy. In the lower mixed-layer, vertical kinetic energy was amplified by a mechanical-production term associated with the divergence of the mean vertical velocity. Total turbulence kinetic energy, normalized by the square of the convective velocity scale, was much larger at mid-levels than in Deardorff and Willis (1985) due to mechanical-production which is not accounted for by simple mixed-layer scaling. Horizontal turbulence structure was predominately controlled by convection while vertical turbulence structure was significantly altered by mean-flow shearing. / Graduation date: 1989

A two-scale approach for the turbulent mixing of momentum in an unstable stratified boundary layer is proposed in an attempt to eliminate existing inconsistencies between parameterized mixing of heat and momentum. The parameterization of the large eddy stress is suitable for simple boundary layer models where computational efficiency is important. We test the proposed formulation in a simple boundary layer model and compare predicted momentum profiles with Lidar mean momentum profiles from FIFE 1989. We examine the sensitivity of the proposed mixing scheme to baroclinicity. While the proposed two-scale approach is able to better predict observed conditions of well mixed momentum profiles, the complexity of momentum transport in baroclinic conditions is not well approximated. / Graduation date: 1994

A shallow convection scheme is derived from several data sets (BOMEX, GATE, AMTEX, BLX83) and developed for the OSU 1-D boundary layer model. Results of the model structure and characteristics of the saturation point (SP) profile are compared against the constant cloud diffusivity scheme of Tiedtke (1983) and the ECMWF boundary layer parameterization scheme. The results indicate that the primary mechanism that transports moisture away from the lower boundary layer is the boundary layer turbulent flux and that the boundary turbulent mixing alone is capable of maintaining an apparent moisture source near the inversion. While the sensible heat flux over ocean becomes quite small after a few hours of model simulation, the virtual heat flux remains positive and the boundary layer remains in the unstable regime. / Graduation date: 1987

The influence of irregular terrain on the evolution of the daytime planetary boundary layer (PBL) and meso-β scale dry circulations is studied using two three-dimensional hydrostatic σ-coordinate models with different approaches for the PBL parameterizations; the 4-layer model uses the mixed-layer (bulk-layer) approach, while the 7-layer model adopts the eddy-diffusivity (multi-layer) approach. Numerical experiments are carried out under the conditions of a dry, sunny summer day with moderate prevailing westerly winds blowing over gently sloping idealized hills in a domain of 150 km on a side. The results from the two models are compared and their performances are evaluated. The behaviors of the mean PBL depth and inversion strength are analytically described using a simple one-point mixed-layer model. Counterclockwise rotation of the mean PBL winds with time observed in both model results can be explained only when the non-zero momentum flux at the PBL top is taken into account. However, stresses associated with entrainment at the PBL top are not sufficient to pull the cold air out of the valleys so as to result in breakup of the early morning stable layer, as is suggested in a previous study. The regions of weak winds that persist in the morning PBL are attributed largely to the baroclinic effect of horizontal variations of potential temperature θ in the PBL, while the effect of surface drag is quite small in these areas. Significant differences in the flow patterns near the surface in two results suggest the importance of the local pressure gradient force associated with terrain irregularities. The effect of horizontal θ advection is also significant in helping reduce the PBL θ anomalies and promote breakup of the stable layer. The well-mixed assumption generally applies quite well to the development of the θ profiles, while for momentum it seems valid only during the peak of convective mixing and the eddy-diffusivity approach is probably preferable for a better description of the low-level flows. The fields of the PBL top height obtained using different procedures in the two models are found to correspond fairly well to each other. Mass-flux convergence associated with terrain irregularities and resulting changes in the wind fields are shown to play a key role in the midday PBL height patterns. The development of the PBL structure as revealed by the θ cross sections obtained from either model corresponds favorably to that indicated by idealized cross sections previously constructed from observed data. The formation of a region of mass-flux convergence and accompanying updrafts near the surface on the leeward side of a mountain, processes which are likely to be important in terrain-induced cloud initiations, seem to be simulated. / Graduation date: 1985

The mixing layer (ML) heights inferred from radiosondes, wind profilers, airborne lidar, airborne microwave temperature profiler (MTP), and in-situ aircraft data were compared during the Texas 2000 Air Quality Study in the Houston area. The comparisons and resulting good agreement between the separate instruments allowed for the spatial and temporal evolution of the ML height distribution to be determined across the Houston area on September 1, 2000. A benchmark method was created for determining ML heights from radiosonde data. The ML heights determined using this method were compared to ML heights determined using wind profiler data. The airborne lidar and MTP heights were also compared to the wind profiler heights. This was the first time the MTP was used for estimating ML heights. Because of this, the MTP heights were also compared to the ML heights determined by in-situ aircraft data. There was good agreement between the ML estimates when the instruments were co-located. The comparisons between the benchmark method and the wind profilers were independent of the quality of the profiler heights. The statistics for lidar and the wind profilers were better for the inland profiler comparisons. Even so, the results for coastal profilers were similar to the other comparisons. The results between the MTP and the wind profilers were comparable with the results found between the other instruments, and better, in that the statistics were similar for the both the inland and coastal profilers. The results between the MTP and in-situ aircraft data provided additional support for the use of MTP for determining ML heights. The combination of the inland and coastal wind profilers with the airborne instruments provided adequate information for the spatial and temporal evolution of the ML height to be determined across the Houston area on September 1, 2000. By analyzing the ML height distribution, major features were evident. These features included the shallow ML heights associated with the marine air from Galveston Bay and the Gulf of Mexico, and the sharp gradient of increasing ML heights north of Houston associated with the variation in the inversion depth found on this day.

Simple models of transpiration, e.g., the Penman-Monteith equation, treat atmospheric conditions as driving variables. In fact, transpiration modifies temperature and humidity throughout the convective boundary layer, creating feedbacks that stabilize the water use of vegetation. This thesis concentrates on the new empirical relationships proposed by Monteith (1995), for developing simple models of feedback, and then applies these relationships to data from the Oregon Cascades. Monteith showed that there is strong laboratory evidence to support a linear relationship between leaf transpiration rate and leaf conductance. If this relationship holds for vegetation in the field, simple models to explain the diurnal variation of canopy conductance can be developed. When this model was applied to data from a Douglas fir forest, canopy conductance changed in response to transpiration rate, rather than to saturation deficit, as has been previously assumed. Monteith also reanalyzed data from McNaughton and Spriggs (1989) which explored the dependence of the Priestley-Taylor coefficient alpha on surface parameters. He showed that there is a linear relationship between alpha and surface conductance. By combining this "demand function" with the physiological "supply function" described earlier, the PMPT model is developed in which evaporation rate depends on physical feedbacks in the convective boundary layer and physiological feedbacks within plants. The thesis will focus on the results of the research done using this model. The PMPT model will then be compared with other simple models of transpiration in order to determine its applicability. / Graduation date: 1997