Decorrelation Distance Research Articles

Objective Maps of Near-Surface Flow States near Point Conception, California

Abstract Objective streamfunction and velocity potential maps of three commonly observed flow states near Point Conception, California, are derived from moored current-meter and drifter observations. The states are defined using current-meter data. Drifter data are sorted by flow state and averaged within spatial bins to resolve their spatial structures. Spatial correlations of drifter data show the along-shelf and cross-shelf decorrelation distances are approximately 45 and 25 km, respectively. This information is used to make the objective streamfunction and velocity potential maps. The total velocity is represented as the sum of the rotational, nondivergent streamfunction component and the irrotational, divergent velocity potential component. The velocity derived from the streamfunction is much stronger than that derived from the velocity potential. The streamfunction is sufficiently well resolved to make meaningful vorticity maps. The velocity potential indicates a source term in the western Santa Bar...

Spatial variability of shelf sediments in the STRATAFORM natural laboratory, Northern California

The “Correlation Length Experiment”, an intensive box coring effort on the Eel River shelf (Northern California) in the summer of 1997, endeavored to characterize the lateral variability of near-surface shelf sediments over scales of meters to kilometers. Coring focused on two sites, K60 and S60, separated by ∼15 km along the 60 m isobath. The sites are near the sand-to-mud transition, although K60 is sandier owing to its proximity to the Eel River mouth. Nearly 140 cores were collected on dip and strike lines with core intervals from <10 m to 1 km. Measurements on each core included bulk density computed from gamma-ray attenuation, porosity converted from resistivity measurements, and surficial grain size. Grain size was also measured over the full depth range within a select subset of cores. X-radiograph images were also examined. Semi-variograms were computed for strike, dip, and down-hole directions at each site. The sand-to-mud transition exerts a strong influence on all measurements: on average, bulk density increases and porosity decreases with regional increases in mean grain size. Analysis of bulk density measurements indicates very strong contrasts in the sediment variability at K60 and S60. No coherent bedding is seen at K60; in the strike direction, horizontal variability is “white” (fully uncorrelated) from the smallest scales examined (a few meters) to the largest (8 km), with a variance equal to that seen within the cores. In contrast, coherent bedding exists at S60 related to the preservation of the 1995 flood deposit. A correlatable structure is found in the strike direction with a decorrelation distance of ∼800 m, and can be related to long-wavelength undulations in the topography and/or thickness of the flood layer or overburden. We hypothesize that the high degree of bulk density variability at K60 is a result of more intense physical reworking of the seabed in the sandier environment. Without significant averaging, the resistivity-based porosity measurements are only marginally correlated to gamma-ray-bulk density measurements, and are largely independent of mean grain size. Furthermore, porosity displays a high degree of incoherent variability at both sites. Porosity, with a much smaller sample volume than bulk density, may therefore resolve small-scale biogenic variability which is filtered out in the bulk density measurement.

A monitoring network for erythemally-effective solar ultraviolet radiation in Austria: determination of the measuring sites and visualisation of the spatial distribution

With 3 FiguresReceived September 12, 1999Revised April 6, 2001SummaryIn 1997 the Austrian ultraviolet radiation monitoringnetwork was to built up to measure continuously erythe-mally-effective ultraviolet radiation. For this network thenecessary measuring sites had to be selected by an objectivemethod. Therefore a method was used, based on the de-correlation distances, calculated by the daily maximum ofthe global solar irradiance across the entire spectrum. For acorrelation coefficient of 0.90, de-correlation distances werefound to be in the order of 170km (East-West) and 40km(North-South). From this, 7 measuring sites were selected toderive a total coverage of Austria.For the visualisation of the measured erythemally-effective solar radiation an optimum interpolation methodwas used to calculate the spatial distribution. The topographyof Austria was used for height correction. The global solarradiation of 39 stations is also used to include the spatialdistribution of cloud cover and the resulting attenuation ofthe erythemally-effective radiation. The combination of thesetwo data sets provides an accuracy estimation of people’sexposure to erythemally-effective UV radiation within themountainous country of Austria.

Gauge-Radar network adjustment for the baltic sea experiment

The gauge adjustment technique used to produce 2 × 2 km 3- and 12-hour radar-based accumulated precipitation datasets for the Baltic Sea Experiment is presented. The gauge adjustment technique is based on the gauge-to-radar ratio. A distance-dependent adjustment factor is derived and it is weighted against a spatially analyzed adjustment factor according to the local observation density and estimated spatial decorrelation distance. A preliminary adjustment strategy is applied in order to normalize data from many radars to a common level and to minimize the bias with gauges. The final adjustment field applied to radar accumulations is shown, through validation against independent gauge data, to minimize the bias between radar and gauge sums while raising the explained variance, compared to unadjusted radar sums. Areas not covered by radar are subjected to an optimal interpolation of systematically corrected gauge sums, and this field is merged with the gauge adjusted radar field in order to cover the entire Baltic Sea Experiment region.

Holographic Diffraction Image Velocimetry for Measurement of Three-Dimensional Velocity Fields

A new optical nonintrusive method for the gross-field measurement of three-dimensional (3-D) three-component (3-C) flows has been developed and tested. Termed Holographic Diffraction Image Velocimetry (HDIV), it is based on double-exposure dual-reference-beam holographic capture of particle-seeded flow fields and the subsequent processing of time-sequence image data obtained from a single observation direction. The technique uses variable-size transplacing-window cross-correlation (VS-TW-CC) together with an image cross-product (CP) method to extract inand out-of-plane particle displacements from the particle diffraction images. Preliminary experiments have shown that the method can resolve fine in-plane motions limited only by the finite pixel size of the image digitizer and the magnification of the imaging system used. For out-of-plane motions, resolutions measured with a relatively crude setup have been shown to be on the order of two tenths of the illumination wavelength divided by the square of the effective angular aperture of the system, which represents the image decorrelation distance. (Author)

Average received signal power after two‐way propagation through ionized turbulence

In this paper we consider propagation through a structured ionosphere separating a monostatic or bistatic radar and its target. A new analytic calculation of the correlation function of the received, demodulated signal is presented. This result is a function of the locations of the transmit and receive apertures and of time during the duration of the received pulse. Strong scattering is assumed where the one‐way scintillation index is unity; under this assumption the parabolic wave equation can be solved using the quadratic approximation for the phase structure‐function; this facilitates tractable expressions for the mutual coherence function (MCF) for both one‐ and two‐way propagation. A new expression is given for the two‐position, two‐time, two‐frequency MCF for spherical wave propagation that allows simultaneous description of all effects of the ionospheric propagation channel (or transmission medium) on a propagating radar signal. To obtain useful and tractable results, the transmitted signal is assumed to be a chirp (linear FM) pulse, a waveform used by most long‐range defense radars. The result for the correlation function of the received signal is a function of the basic parameters that describe wave propagation through the ionospheric structure, including the channel decorrelation distance, decorrelation time, and coherence bandwidth. Both the two‐way enhancement in average power and aperture averaging effects are explicitly included in this derivation, and new results are presented that relate these effects to the characteristics of the propagation channel. The results are useful for propagation under conditions of saturated scintillation, for example HF through UHF radar in the natural equatorial environment and HF through gigahertz‐band radars that are required to operate in a disturbed propagation environment (i.e., in chemical releases or nuclear detonations).

Class of fast methods for processing irregularly sampled or otherwise inhomogeneous one-dimensional data.

With the ansatz that a data set's correlation matrix has a certain parametrized from (one general enough, however, to allow the arbitrary specification of a slowly varying decorrelation distance and population variance), the general machinery of Wiener or optimal filtering can be reduced from $O({n}^{3})$ to $O(n)$ operations, where $n$ is the size of the data set. The implied vast increase in computational speed can allow many common suboptimal or heuristic data analysis methods to be replaced by fast, relatively sophisticated, statistical algorithms. Three examples are given: data rectification, high- or low-pass filtering, and linear least-squares fitting to a model with unaligned data points.

Spatial and frequency averaging techniques for a polarimetric scatterometer system

Radar scattering signals from distributed targets exhibit fading due to interference associated with coherent scattering from individual scatterers within the resolution volume. Uncertainty in radar measurements which arises as a result of fading is reduced by averaging independent samples. Independent samples are obtained by collecting the radar returns from nonoverlapping footprints (spatial averaging) and/or nonoverlapping frequencies (frequency agility techniques). An improved formulation of fading characteristics for the spatial averaging and frequency agility technique is derived by taking into account the rough surface scattering process. Kirchhoff's approximation is used to describe rough surface scattering. Expressions for fading decorrelation distance and decorrelation bandwidth are derived. Rough surface scattering measurements are performed between L and S bands. Measured frequency and spatial correlation coefficients show good agreement with theoretical results. >

Diffuser speckle model: application to multiple moving diffusers

A simple model for the scattering of coherent light through diffusers has been applied to a moving diffuser despeckler in order to estimate the scattering angles, speckle decorrelation length, and interaction between multiple diffusers. A Gaussian model for the diffuser thickness variations has been used to derive a relation between the scattering cone of a diffuser and its decorrelation properties. This model is equivalent to a randomized array of lenslets. The lenslet's thickness and diameter correspond to the characteristic heights and widths of the diffuser roughness. This model predicts that a decrease in the decorrelation distance for two closely spaced counterrotating diffusers is accompanied by an increase in their scattering cone. Simulation and experimental measurements have been used to verify the predictions of this model. Significant speckle decorrelation has been demonstrated for a nanosecondpulsed laser source by using moderate diffuser rotation speeds.

The Characteristic Spatial and Temporal Scales for SLP, SST, and Air Temperature in the Southern Hemisphere

Abstract This study summarizes results of an analysis of the TOGA drifting buoy observations in the Southern Hemisphere. The data were first quality controlled for gross errors and then screened against climatology and products from national weather centers. The characteristic space scales of the SLP, SST, and air temperature fields for the summer months of December, January, and February, and the winter months of June, July, and August were determined next. Typical decorrelation distances for all fields were between 1200–2800 km with the correlations being generally isotropic. This information suggests that roughly 30–40 fully functional buoys evenly distributed over the southern oceans from 15° to 60°S should be able to resolve the major scales of Southern Hemisphere climate change.

Statistical inference of weakly correlated subthermocline fields from satellite altimeter data

To initialize the barotropic and baroclinic modes, numerical ocean prediction models need information both above and below the main thermocline. Forecasts of upper ocean mesoscale variability using real and simulated data show high sensitivity to the Subthermocline pressure (STP) field. Results using simulated data indicate that the accuracy of this field may be the limiting factor on the time scale for mesoscale oceanic predictive skill. Satellite altimetry provides a potentially abundant source of sea surface height (SSH) data, but there is no comparable source of Subthermocline information on the horizon. We investigate statistical techniques to infer Subthermocline pressure anomalies from SSH data, a problem complicated by the weak correlation between the fields. This problem is addressed by using the degrees of freedom available in the data and by describing them in an efficient manner to suppress noise, eliminate unskilled or redundant estimators and to prevent ill‐conditioned matrix inversions. Multilinear regression, empirical orthogonal function (EOF) regression and principal estimator patterns are compared using data simulated by a numerical ocean model and error models. Numerous questions that need to be addressed for proper application of the statistical techniques are investigated. Topics include noise suppression and the impact of the noise on accuracy. These topics are studied as a function of decorrelation distance in the noise and the presence or absence of noise in dependent and independent data sets. In this context we also investigate dependent data set size requirements, the criteria for choosing estimators, the number, areal coverage, and spacing of sampling locations used in the estimators, the effect of the ocean dynamical regime on the results, the effects of ocean model imperfections or changes in population statistics on the results, SSH versus ΔSSH in an orbital repeat period as estimators, and the effect of orbital repeat period on Subthermocline estimates from ΔSSH data. In the presence of 40% rms noise the usual significance tests are much too conservative for this application. (However, we also found that EOFs calculated from spatially correlated, temporally uncorrelated noise can pass a popular EOF significance test based on uncorrelated noise.) Although more difficult to suppress than uncorrelated noise, correlated noise did not markedly increase the error in these tests. Spatial coverage of the estimators was found to be an important parameter, and four to five ascending‐or descending tracks per wavelength were sufficient for uniformly accurate estimates whether beneath or between altimeter tracks. In most of these tests, ΔSSH proved a better estimator than SSH, but for ΔSSH resolving the shortest major time scale is a necessity. High accuracy is not required for Subthermocline pressure anomalies to substantially enhance upper ocean forecast skill in a numerical ocean prediction model. In results to be reported elsewhere, a statistically inferred STP field substantially enhanced the skill of a Gulf Stream forecast model where the SSH was initialized from oceanic observations. The inferred STP field allowed the model to show forecast skill in comparison to persistence of the initial state.

Shadowing variability in an urban land mobile environment at 900 MHz

Field tests have been performed in a high density urban environment to evaluate two important aspects of shadowing variability in land mobile radio links. These factors are the magnitude of variability and the rate at which variations decorrelate with time and spatial movement. The former was found to be significantly influenced by the size of the field test area. 1/e decorrelation times of the order of 15 s and decorrelation distances on the order of 100 m appear common.

Improved random spatial phase modulation for speckle elimination

An improved version of the random spatial phase modulator (RSPM) reported recently by one of us is described. Using the improved RSPM, a theoretical value of the SNR of several thousand can be achieved. Experimental results are presented verifying that speckle can be completely eliminated using RSPM. The measured SNR exceeds 100, and there is no visually detectable difference between images obtained with RSPM laser light and those with white light even for an optical system of f/600. The effective decorrelation distances for different diffusers and their dependence on the aperture of the RSPM are investigated. An application of RSPM to coherent spatial filtering is demonstrated.

Statistical Analysis of Random Components of Speed of Sound

Experimental data on the speed of sound variation with depth off the Florida Coast was statistically analyzed in order to obtain its characteristics and then to calculate their effect on ray tracing in ocean. The typical exponential depth decay of the speed of sound was removed by curve fitting in order to separate its randomly varying components. The experimental data were taken for depths up to 550 ft with an accuracy of 0.5 m/sec. The results of this work show that the probability distribution of the random component of the speed of sound is multimodal rather than of the usually expected normal form. Furthermore, the variance of the random component varies from a few tenths to up to 4 m/sec. The decorrelation distance of this random variation varies from 25 to 70 m, indicating a gross size of volume where temperature changes are correlated. This may be due to a transient temperature front or due to a volume perturbation in a stationary temperature distribution. Thus the importance of the random variations in the measurement of the speed of sound must be taken into account.