Modification of the background flow by roll vortices

Use of observed wind profiles, such as those obtained from ascent or descent aircraft soundings, for the identification of the expected roll modes is hindered by the fact that these modes are able to modify the wind profiles. When such modified wind profiles are utilized to estimate the critical values of the dynamic and thermodynamic forcing rates, large errors in the preferred orientation angles and aspect ratios of the rolls may result. Nonlinear analysis of a 14 coefficient spectral model of roll circulations shows that the primary modification of the background wind is the addition of a linear component. When the linear profile having the correct amount of shear is subtracted from the observed cross-roll winds, then the pre-roll wind profile can be estimated. A preliminary test of this hypothesis is given for a case in which cloud streets were observed during FIRE

Mixed convective/dynamic roll vortices and their effects on initial wind and temperature profiles

The onset and development of both dynamically and convectively forced boundary layer rolls are studied with linear and nonlinear analyses of a truncated spectral model of shallow Boussinesq flow. Emphasis is given here on the energetics of the dominant roll modes, on the magnitudes of the roll-induced modifications of the initial basic state wind and temperature profiles, and on the sensitivity of the linear stability results to the use of modified profiles as basic states. It is demonstrated that the roll circulations can produce substantial changes to the cross-roll component of the initial wind profile and that significant changes in orientation angle estimates can result from use of a roll-modified profile in the stability analysis. These results demonstrate that roll contributions must be removed from observed background wind profiles before using them to investigate the mechanisms underlying actual secondary flows in the boundary layer. The model is developed quite generally to accept arbitrary basic state wind profiles as dynamic forcing. An Ekman profile is chosen here merely to provide a means for easy comparison with other theoretical boundary layer studies; the ultimate application of the model is to study observed boundary layer profiles. Results of the analytic stability analysis are validated by comparing them with results from a larger linear model. For an appropriate Ekman depth, a complete set of transition curves is given in forcing parameter space for roll modes driven both thermally and dynamically. Preferred orientation angles, horizontal wavelengths and propagation frequencies, as well as energetics and wind profile modifications, are all shown to agree rather well with results from studies on Ekman layers as well as with studies on near-neutral and convective atmospheric boundary layers

Boundary layer roll circulations during FIRE

The probable mechanism underlying the development of boundary layer roll circulations are studied using wind and temperature profiles measured by the National Center for Atmospheric Research (NCAR) Electra during the stratocumulus phase of the First ISCCP Regional Experiment (FIRE). The expected, or preferred, roll orientations, horizontal wavelengths, and propagation periods are determined by finding the minimum values of the dynamic and thermodynamic forcing parameters, which here are the eddy Reynolds number (Re) and moist Rayleigh number (Ra sub m). These minimum values depend on the height z sub T of the capping temperature inversion and on the values of the Fourier coefficients of the background height-dependent vector wind profile. As input to our nonlinear spectral model, descent and ascent runs by the Electra provide for initial estimates of the inversion height and the wind profiles. In the first phase of the investigation presented here, a mechanism is said to be a probable contributor to the development of roll circulations within the stratocumulus-topped boundary layer if the modeled roll orientation and wavelengths agree with their observed values. Preliminary results using the 14-coefficient model of Haack-Hirschberg (1988) are discussed for the 7 July 1987 Electra Mission 188-A (Flight 5). This mission was flown across a sharp cloud boundary that was within a LANDSAT/SPOT scene. The stratocumulus deck was relatively solid in the eastern part of the scene, while there was a rapid decrease in cloud cover to scattered cumulus clouds aligned in streets to the west. These cloud streets were oriented nearly parallel to the mean wind direction in the layer, which was approximately 340 degrees. The hypothesis that roll circulations occurred in both the relatively clear and the cloudy regions is investigated using as model input a descent profile obtained in the relatively clear air and an ascent profile obtained in the cloudy air. Initial results for the clear air case are that the pure inflection point mode is not possible and the pure thermal mode was oriented 35 degrees to the right of the mean wind direction. The origin of this unacceptably large discrepancy between the observed and modeled results will be investigated further and the conclusions reported at the next FIRE workshop

On the dynamic and thermodynamic structures of marine stratocumulus

Latent heating effects on stratocumulus circulations were studied successfully with a nine-coefficient spectral model of two-dimensional shallow Boussinesq convection (Laufersweiler and Shirer, 1989). Further, more realistic investigations are being performed currently with a larger, 18-coefficient spectral model, in which the effects of cloud top radiational cooling and in-cloud radiational heating are also being represented. Because assuming a rigid lid at the inversion base may have affected previous results significantly, the domain top was raised to include the lower portion of the capping inversion. As in the previous model, a uniform cloud base is assumed and latent heating effects are included implicitly such that the motions in the sub- and above-cloud regions are dry adiabatic and the motions in the cloud region are moist adiabatic. The effects of forcing by radiational heating profiles that are tied to the cloud layer, such as the one used by Nicholls will be investigated, as will profiles measured during the FIRE experiment. One concern of using truncated spectral models is that the phenomena are so poorly represented that they can change dramatically as the number of spectral coefficients is increased. The efficacy of the nine-coefficient model results is checked by examining the steady state solutions of the 18-coefficient model for parameter values used by Laufersweiler and Shirer (1989), which corresponds to the case of a moderately deep cloud and no capping inversion. The horizontally asymmetric circulation patterns that have narrow downdraft areas and broad updraft areas are virtually the same as those found in the smaller spectral model. Also captured in the case of weaker heating is an elevated circulation centered at cloud base. Thus, the results of the smaller model are substantiated. Since one of the goals of studying the new model is to represent a more realistic domain, the second test of the model is to investigate whether the steady solutions are suppressed in the case of an inversion with no cloud

Stratiform clouds and their interaction with atmospheric motions

During the 1987 to 1988 academic year, three projects were finished and plans were made to redirect and focus work in a proposal now being reviewed. The completed work involves study of waves on an equatorial beta-plane in shear flow, investigation of the influence of orography on the index cycle, and analysis of a model of cloud street development in a thermally-forced, sheared environment. The proposed work involves study of boundary layer circulations supporting stratocumulus decks and investigation of how the radiative effects of these clouds modulate larger-scale flows such as those associated with the index oscillation

Nonlinear feedbacks between stratocumulus and synoptic-scale systems

The research progress for FY-91 is presented. Wintertime and springtime stratocumulus observations for a number of 5-day periods were collected. Close correlations between the mean 850 and 500 mb trough positions and cloud cover over marine areas were found. A linear study of the radiatively-driven interaction between stratocumulus and synoptic-scale waves was completed. Shallow surface-bound traveling waves are created that are strongly dependent on the phase relation between cloud and low-level flow. A nonlinear model is now under development that will permit a more detailed investigation of these interactions. Finally, a nonlinear study of the modifications of the background flow by boundary layer roll vortices was revised for submission for publication. The research plans for FY-92 are included

Stratiform clouds and their interaction with atmospheric motion

The spatial patterns of stratocumulus cloud frequency for the continental United States and adjacent oceans were routinely obtained from surface cloud observations every six hours. These frequencies were correlated with upper air patterns at 850, 700, and 500 mb. Significant frequency maxima were found near trough axes over marine areas during relatively stationary large-scale wave patterns. These maxima tended to occur to the east of trough axes. Over continental regions, there was little relationship between stratocumulus and synoptic-scale flows patterns, probably because of the short lifetime of cloud over land. A summary of these findings is included

Nonlinear Hydrodynamic Modeling A Mathematical Introduction

Bibliography: p. [517]-525.Includes index

Computational approaches to fMRI analysis

Analysis methods in cognitive neuroscience have not always matched the richness of fMRI data. Early methods focused on estimating neural activity within individual voxels or regions, averaged over trials or blocks and modeled separately in each participant. This approach mostly neglected the distributed nature of neural representations over voxels, the continuous dynamics of neural activity during tasks, the statistical benefits of performing joint inference over multiple participants and the value of using predictive models to constrain analysis. Several recent exploratory and theory-driven methods have begun to pursue these opportunities. These methods highlight the importance of computational techniques in fMRI analysis, especially machine learning, algorithmic optimization and parallel computing. Adoption of these techniques is enabling a new generation of experiments and analyses that could transform our understanding of some of the most complex - and distinctly human - signals in the brain: acts of cognition such as thoughts, intentions and memories