Wavelet Analysis for Wind Fields Estimation

Wind field analysis from synthetic aperture radar images allows the estimation of wind direction and speed based on image descriptors. In this paper, we propose a framework to automate wind direction retrieval based on wavelet decomposition associated with spectral processing. We extend existing undecimated wavelet transform approaches, by including à trous with B3 spline scaling function, in addition to other wavelet bases as Gabor and Mexican-hat. The purpose is to extract more reliable directional information, when wind speed values range from 5 to 10 ms−1. Using C-band empirical models, associated with the estimated directional information, we calculate local wind speed values and compare our results with QuikSCAT scatterometer data. The proposed approach has potential application in the evaluation of oil spills and wind farms

Utilization of Fourier domain real zeros in the phase retrieval problem.

A problem encountered in a number of disciplines is the phase retrieval problem: given only the magnitude of the Fourier transform of some object and some constraints about the object, reconstruct the object. This is equivalent to reconstructing the phase of the Fourier transform, hence the name phase retrieval. Common object constraints are compact support, real-valued, and non-negativity. For objects with pact support, the phase retrieval problem has been successfully characterized by utilizing the zeros of the analytic extension of the Fourier transform into the complex plane. All possible solutions can be generated in theory from these zeros. In practice most phase retrieval algorithms instead utilize an iterative approach which iterates between the spatial and frequency domains, successively satisfying the constraints in both. Such algorithms are simple to implement, but have been shown empirically to suffer from stagnation problems where the program continues to iterate but does not get closer to a solution. In this thesis we show that utilizing a subset of the zeros of the Fourier transform analytic extension, referred to as real zeros since they are the intersections of these zeros with the real plane, can improve existing phase retrieval algorithms. This is possible because: (1) these real zeros locations can be estimated from the Fourier magnitude data and thus represent information that is known; and (2) these real zeros locations determine the endpoints of the so-called branch cuts in the Fourier phase (curves across which there is a 2$\pi$ ambiguity). We show that the constraints imposed on the Fourier phase by the real zeros can be utilized to recover from specific stagnation conditions that are caused by the iterative algorithms generating a reconstruction that has real zeros in erroneous locations. We also develop an algorithm for estimating the Fourier phase values using the real zero locations, and show that when this phase estimate is combined with the known Fourier magnitude data to generate an initial guess for the iterative algorithms, the final reconstruction is improved.Ph.D.Applied SciencesEngineeringMathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/129092/2/9319648.pd

Tropical cyclone winds retrieved from c-band cross-polarized synthetic aperture radar

This paper presents a geophysical model function (GMF) that has been developed to describe the relation of the ocean surface wind with the normalized radar cross section (NRCS) at C-band cross polarization (cross-pol). Synthetic aperture radar (SAR) images have been simultaneously collected at copolarization (co-pol) and cross-pol at moderate to high wind speeds. Using the SAR co-pol retrieved wind fields and an uncertainty estimate of the retrieved wind speeds, the cross-pol dependencies of the NRCS are investigated with respect to wind, incidence angle, and polarization pairs. For wind speeds above 10 m/s, there is a significant dependence of the NRCS on wind speed. However, the SAR cross-pol data are also significantly affected by the noise floor and crosstalk between the channels. Estimates of the noise floor are determined and removed from the NRCS. Three GMFs are developed: the first is for transmission at horizontal (H) polarization and the second at vertical (V) polarization. A third GMF accounts for wind direction dependence. Validation of the GMFs is conducted by comparison with collocated Stepped Frequency Microwave Radiometer (SFMR) data. The resulting bias of -0.7 m/s and standard deviation of 3.7 m/s demonstrate the excellent performance for these GMFs for wind speed retrieval between 10 and 35 m/s. Furthermore, comparisons show that SAR cross-pol retrieved wind speeds are of similar quality as those of SFMR and are significantly better in the moderate to high wind speed regime than SAR co-pol retrieved winds

Coastal ocean fronts and eddies imaged with ERS 1 synthetic aperture radar

ERS 1 C band synthetic aperture radar (SAR) data were collected during the Norwegian Continental Shelf Experiment (NORCSEX) both in November 1991 during the ERS 1 commissioning phase and at different seasons in 1992 and 1993. Characteristic SAR image expressions are observed in relation to perturbation of the surface current-short wave interaction across the Norwegian Coastal Current front for winds less than 10–12 m s−1. In situ measurements document the existence of alternating zones of convergence and divergence coexisting with a strong near-surface current shear of nearly 4f (where f is the Coriolis parameter) across a distance of a few kilometers. Under calm to moderate winds, i.e., 4–7 m s−1, characteristic expressions of upper ocean circulation features also include the manifestation of eddies through the presence of surface film, which damps the Bragg waves. Comparison of a near-coincident National Oceanic and Atmospheric Administration advanced very high resolution radiometer image and an ERS 1 SAR image supports the interpretation that surface current fronts are imaged by SAR. In combination with a SAR image simulation model, the relative quantitative importance of shear, convergence, and divergence along the front is examined. Although the model formulation is simple and the absolute magnitude of the perturbations is uncertain, the study shows that the SAR images can sometimes be used to interpret frontal dynamics, including growth and decay of meanders