Hampton N. Shirer

Estimating Convective Atmospheric Boundary Layer Depth from Microwave Radar Imagery of the Sea Surface

Abstract Kilometer-scale mottling seen on real and synthetic aperture radar imagery of the sea surface can be linked to the presence of microscale cellular convection (thermals) spanning the marine atmospheric boundary layer. In the current study, it is hypothesized that the typical scale of the mottling, found via standard Fourier spectral analysis, can be used to estimate the depth of the convective marine atmospheric boundary layer (zi) using a modified form of traditional mixed-layer similarity theory for these thermals’ aspect ratio. The hypothesis linking the typical scale of mottling to zi is substantiated using previously published boundary layer results and supporting meteorological and oceanographic data from a number of case studies.

Mathematical structure of the singularities at the transitions between steady states in hydrodynamic systems

to contact catastrophe theory.- Rayleigh-Benard convection.- Quasi-Geostrophic flow in a channel.- Rotating axisymmetric flow.- Stability and unfoldings.

Development of Boundary Layer Rolls from Dynamic Instabilities

Abstract The development of atmospheric boundary layer rolls from the inflection point and parallel instabilities is examined analytically using several three-dimensional linear models of flow in a neutral, rotational fluid. These models are formulated so that either arbitrary or observed background wind profiles can be examined easily to see which roll modes would likely occur. Necessary and sufficient conditions for the development of particular atmospheric modes are determined. These conditions are expressed as polynomials in the critical (eddy) Reynolds number Rec and depend on Fourier coefficients of a given height-dependent background wind profile. The preferred values of orientation angle θ and aspect ratio A, which describe the expected roll geometry, are assumed to be those that produce the smallest values of Rec. The ability of the models to successfully reproduce the modes arising from the inflection point and parallel instability mechanisms is tested by using idealized wind profiles to approxi...

Evaluating the Quality of Ground-Based Microwave Radiometer Measurements and Retrievals Using Detrended Fluctuation and Spectral Analysis Methods

Abstract Time series both of microwave radiometer brightness temperature measurements at 23.8 and 31.4 GHz and of retrievals of water vapor and liquid water path from these brightness temperatures are evaluated using the detrended fluctuation analysis method. As quantified by the parameter α, this method (i) enables identification of the timescales over which noise dominates the time series and (ii) characterizes the temporal range of correlations in the time series. The more common spectral analysis method is also used to assess the data, and its results are compared with those from the detrended fluctuation analysis method. The assumption that measurements should have certain scaling properties allows the quality of the measurements to be characterized. The additional assumption that the scaling properties of the measurements of an atmospheric quantity are preserved in a useful retrieval provides a means for evaluating the retrieval itself. Applying these two assumptions to microwave radiometer measurem...

A case study of stratus cloud base height multifractal fluctuations

The complex structure of a typical stratus cloud base height (or profile) time series is analyzed with respect to the variability of its fluctuations and their correlations at all experimentally observed temporal scales. Due to the underlying processes that create these time series, they are expected to have multiscaling properties. For obtaining reliable measures of these scaling properties, different methods of statistical analysis are used herein: power spectral density, detrended fluctuation analysis, and multifractal analysis. This broad set of diagnostic techniques is applied to a typical stratus cloud base height (CBH) data set; data were obtained from the Southern Great Plains site of the Atmospheric Radiation Measurement Program of the Department of Energy from a Belfort Laser Ceilometer. First, we demonstrate that this CBH time series is a nonstationary signal with stationary increments. Further, two scaling regimes are found, although the characteristic laws are quite similar ones. Next, the multi-affine scaling properties are confirmed. The scaling properties of the cloud base height profile of such a continental stratus are found to be similar to those of the marine cloud base height profiles studied by us previously. Some physical interpretation in terms of anomalous diffusion (or fractional random walk) is given for the continental case.

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

Abstract 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 arbit...

Transitions in Shallow Convection: An Explanation for Lateral Cell Expansion

Abstract A generalized seven-coefficient model of two-dimensional Rayleigh-Benard convection is presented. The model simulates successfully one means by which lateral cell expansion can occur as the value of the imposed vertical temperature difference is changed. Such changes in the horizontal wavelengths of the convective rolls are accomplished by the nonlinear transfer of energy from cells to other cells with smaller wavenumbers. The crucial effect is one represented by the advective term v˙∇v in the equation of motion, and as a consequence an interacting triad of harmonics must be included in the spectral model. Thus, the generalized model has basically the same form as that used by Saltzman or Shirer and Dutton, but in the generalized model the triad of interacting wavenumbers is varied as the vertical heating rate is varied. Actual values of the horizontal wavenumbers are determined by assuming that the first unstable wave will have the largest growth rate, or equivalently that the bifurcation point ...

The Branching Hierarchy of Multiple Solutions in a Model of Moist Convection

Abstract The dynamics of two-dimensional, shallow moist convection is examined with the use of a six-component spectral model. Latent heating effects are incorporated by assuming that upward motion is moist adiabatic and that downward motion is dry adiabatic. The resulting nondimensional system of equations has the same form as that for Benard convection, with the moist effects included by replacing the Rayleigh number with a modified form. The six-coefficient model contains a wide variety of multiple solutions with as many as 12 time-independent convective states and one conductive state occurring simultaneously. Temporally periodic solutions are also indicated, and some are found numerically that branch from stationary solutions at critical values of the external parameters. Only some of the solutions are linearly stable and hence observable, and we give a summary of the possible branching orders of these solutions. We find that the development of moist convection proceeds in the model via one of severa...

Estimating the Correlation Dimension of Atmospheric Time Series

Abstract The correlation dimension D is commonly used to quantify the chaotic structure of atmospheric time series. The standard algorithm for estimating the value of D is based on finding the slope of the curve obtained by plotting ln C(r) versus ln r, where C(r) is the correlation integral and r is the distance between points on the attractor. An alternative, probabilistic method proposed by Takens is extended and tested here. This method is based on finding the sample means of the random variable (r/ρ)p[ln(r/ρ)]k, expressed as the conditional expected value E((r/ρ)p[ln(r/ρ)]k : r < ρ), for p and k nonnegative numbers. The sensitivity of the slope method and of the extended estimators Dpk(ρ) for approximating D is studied in detail for three ad hoc correlation integrals and for integer values of p and k. The first two integrals represent the effects of noise or undersampling at small distances and the third captures periodic lacunarity, which occurs by definition when the ratio C(xρ)/C(ρ) fails to conve...

Compact Spatial Differencing Techniques in Numerical Modeling

Abstract The accuracies of the usual centered differencing, compact differencing and finite element methods are compared linearly with a geostrophic adjustment problem and nonlinearly with a vorticity advection problem. The finite element method provides the best approximation in the geostrophic adjustment problem on either a staggered or an unstaggered grid. The compact scheme provides the most accurate representation of the wavenumber distribution for the vorticity advection when the Arakawa Jacobian J7 is used.