ALBERT

Description: Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient-related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, 'roughness' and 'sparseness', respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from approximately 60 m to approximately 60 km. Finally, we define the 'mean multifractal plane' and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.

Description: A system has been developed to measure wideband electic field derivatives (dE/dt) at five ground stations in a 15 km x 15 km network at Kennedy Space Center. Individual station responses are normalized using digital filters. Pulse-timing resolution is improved to much less than 50-ns sample interval by interpolation using packing in the frequency domain. A time tag for each pulse is defined as the mean of the times of the rising-edge half peak, peak, and falling-edge half peak. The standard deviation in these times defines the timing error and is shown to be a function of noise and bandwidth rather than digitization rate. Each of the four unknowns for a pulse source location (x,y,z) and time of occurrence (t) is found from the five time-tag measurements using different weightings for all five combinations of the four-station hyperbolic equations. Weighting factors and errors in x,y,z and t are estimated using error propagation techniques.

Description: We present an analysis of a 'quasi-steady' cusp ion dispersion signature observed at low altitudes. We reconstruct the field-parallel part of the Cowley-D ion distribution function, injected into the open low-latitude boundary layer (LLBL) in the vicinity of the reconnection X-line. From this we find the field parallel magnetosheath flow at the X-line was only 20 +/- 60 km/s, placing the reconnection site close to the flow streamline which is perpendicular to the magnetosheath field. Using interplanetary data and assuming the subsolar magnetopause is in pressure balance, we derive a wealth of information about the X-line, including: the density, flow, magnetic field and Alfven speed of the magnetosheath; the magnetic shear across the X-line; the de-Hoffman Teller speed with which field lines emerge from the X-line; the magnetospheric field; and the ion transmission factor across the magnetopause. The results indicate that some heating takes place near the X-line as the ions cross the magnetopause, and that sheath densities may be reduced in a plasma depletion layer. We also compute the reconnection rate. Despite its quasi-steady appearance on an ion spectrogram, this cusp is found to reveal a large pulse of enhanced reconnection rate.

Description: Urban temperature bias, defined to be the difference between a shelter temperature reading of unknown but suspected urban influence and some appropriate rural reference temperature, is estimated through the use of polar-orbiting satellite data. Predicted rural temperatures, based on a method developed using sounding data, are shown to be of reasonable accuracy in many cases for urban bias assessments using minimum temperature data from selected urban regions in the United States in July 1989. Assessments of predicted urban bias were based on comparisons with observed bias, as well as independent measures of urban heat island influence, such as population statistics and urban-rural differences in a vegetation index. This technique provides a means of determining urban bias in regions where few if any rural reference stations are available, or where inhomogeneities exist in land surface characteristics or rural station locations.