The Application of Proper Orthogonal Decomposition to Numerically Modeled and Measured Ocean Surface Wave Fields Remotely Sensed by Radar

Phase-resolved ocean surface wave elevation maps provide important information for many scientific research areas (e.g., rogue waves, wave-current interactions, and wave evolution/growth) as well as for commercial and defense applications (e.g., naval and shipping operations). To produce these maps, measurements in both time and space are necessary. While conventional wave sensing techniques are limited spatially, marine radar has proven to be a complex yet promising remote sensing tool capable of providing both temporal and spatial wave measurements. The radar return from the sea surface is complex because it contains contributions from many sources only part of which provide information about the ocean surface wave field. Most existing techniques used to extract ocean wave fields from radar measurements implement fast Fourier transforms (FFTs) and filter this energy spectrum using the linear dispersion relationship for ocean waves to remove non-wave field contributions to the radar signal. Inverse Fourier transforms (IFFTs) return the filtered spectrum to the spatial and temporal domain. However, nonlinear wave interactions can account for a non-negligible portion of ocean wave field energy (particularly in high sea states), which does not completely adhere to the linear dispersion relationship. Thus, some nonlinear wave energy is lost using these FFT dispersion-filtering techniques, which leads to inaccuracies in phase-resolved ocean surface wave field maps. This deficiency is significant because many of the aforementioned research areas and applications are most concerned with measurement and prediction of such anomalous wave conditions. Proper orthogonal decomposition (POD) is an empirical technique used in scientific fields such as fluid mechanics, image processing, and oceanography (Sirovich, 1987). This technique separates a signal into a series of basis functions, or modes, and time or spatial series coefficients. Combining a subset of the modes and coefficients can produce a reduced order representation of the measured signal; this process is referred to as a reconstruction. This research applies POD to radar Doppler velocity measurements of the sea surface and uses the leading modes as a filter to separate wave contributions to the radar measurement from non-wave contributions. In order to evaluate the robustness of this method, POD is applied to ocean wave radar measurements obtained using three different radar systems as well as to numerically modeled radar data for a variety of environmental conditions. Due to the empirical nature of the POD method, the basis functions have no innate physical significance, therefore the shape and content of leading POD modes is examined to evaluate the linkage between the mode functions and the wave field physics. POD reconstructions and FFT-based methods are used to compute wave field statistics that are compared with each other as well as to ground truth buoy measurements. Correlation coefficients and root mean squared error are used to evaluate phase-resolved wave orbital velocity time series reconstructions from POD and FFT-based methods relative to ground truth buoy velocity time series measurements. Results of this study show that when POD is applied to radar measurements of the sea surface: (i) the leading mode basis functions are oscillatory and linked to the physics of the measured wave field; (ii) POD performs comparably to FFT-based dispersion filtering methods when calculating wave statistics; and (iii) phase-resolved POD orbital velocity maps show higher correlations with buoy velocity time series relative to orbital velocity time series based on FFT dispersion filtering methods when high group line energy is present (i.e., in the presence of steep and breaking waves)

Occurrence and Energy Dissipation of Breaking Surface Waves in the Nearshore Studied with Coherent Marine Radar

Wave breaking influences air-sea interactions, wave induced forces on coastal structures, sediment transport and associated coastline changes. A good understanding of the process and a proper incorporation of wave breaking into earth system models is crucial for a solid assessment of the impacts of climate change and human influences on coastal dynamics. However, many aspects are still poorly understood which can be attributed to the fact that wave breaking is difficult to observe and study because it occurs randomly and involves multiple spatial and temporal scales. Within this doctoral work, a nearshore field experiment was planned and conducted on the island of Sylt in the North Sea to investigate the dynamics of wave breaking. The study combines in-situ observations, numerical simulations and remote sensing using shore-based coherent marine radar. The field measurements are used to investigate the coherent microwave backscatter from shoaling and breaking waves. Three major developments result from the study. The first one is a forward model to compute the backscatter intensity and Doppler velocity from known wave kinematics. The second development is a new classification algorithm to identify dominant breakers, whitecaps and radar imaging artifacts within the radar raw data. The algorithm is used to infer the fraction of breaking waves over a sub- and an inter-tidal sandbar as well as whitecap statistics and results are compared to different parameterizations available in literature. The third development is a new method to deduce the energy of the surface roller from the Doppler velocity measured by the radar. The roller energy is related to the dissipation of roller energy by the stress acting at the surface under the roller. From the spatial gradient of roller energy, the transformation of the significant wave height is computed along the entire cross-shore transect. Comparisons to in-situ measurements of the significant wave height from two bottom mounted pressure gauges and a wave rider buoy show a total root-mean-square-error of 0.20 m and a bias of −0.02 m. It is the first time that measurements of the spatio-temporal variation of the bulk wave energy dissipation together with the fraction of breaking waves are achieved in storm conditions over such a large distance of more than one kilometer. The largest dissipation rates (> 300 W/m² ) take place on a short distance of less than one wave length (≈ 50 m) at the inter-tidal sandbar. However, during storm conditions 50 % of the incoming wave energy flux is already dissipated at the sub-tidal sandbar. The simultaneous measurements of the occurrence frequency and the energy dissipation facilitate an assessment of the bulk dissipation of individual breaking waves. For the spilling-type breakers in this area, the observed dissipation rate is about 30 % smaller than the dissipation rate according to the generally used bore analogy. This must be considered within nearshore wave models if accurate predictions of the breaking probability are required

Earth resources: A continuing bibliography with indexes (issue 52)

This bibliography lists 454 reports, articles, and other documents introduced into the NASA scientific and technical information system between October 1 and December 31, 1986. Emphasis is placed on the use of remote sensing and geophysical instrumentation in spacecraft and aircraft to survey and inventory natural resources and urban areas. Subject matter is grouped according to agriculture and forestry, environmental changes and cultural resources, geodesy and cartography, geology and mineral resources, hydrology and water management, data processing and distribution systems, instrumentation and sensors, and economic analysis

Development of a dynamic underwater acoustic communication channel simulator with configurable sea surface parameters to explore time-varying signal distortion

A wide-band phase-coherent multi-path underwater acoustic channel simulation is developed using an approximate quantitative model of the acoustic wave response to a time-varying three-dimensional rough surface. It has been demonstrated over transmission ranges from 100 m to 8 km by experimental channel probing and comparable synthetic replication of the channel probing through the simulated channel, that the simulation is capable of reproducing fine-time-scale Doppler and delay distortions consistent with those generated in real shallow channels

Earth resources: A continuing bibliography with indexes (issue 62)

This bibliography lists 544 reports, articles, and other documents introduced into the NASA scientific and technical information system between April 1 and June 30, 1989. Emphasis is placed on the use of remote sensing and geophysical instrumentation in spacecraft and aircraft to survey and inventory natural resources and urban areas. Subject matter is grouped according to agriculture and forestry, environmental changes and cultural resources, geodesy and cartography, geology and mineral resources, hydrology and water management, data processing and distribution systems, instrumentation and sensors, and economic analysis

Rough surface reconstruction at grazing angles by an iterated marching method.

An iterated marching method is presented for the reconstruction of rough perfectly reflecting one-dimensional (1D) surfaces from scattered data arising from a scalar wave at grazing incidence. This is based on coupled integral equations adapted from an earlier approach using the parabolic equation, relating the scattered field at a plane to the unknown surface. Taking the flat surface as an initial guess, these are solved here using at most three iterations. The method is applied to scattered field data generated from the full Helmholtz equations. This approach improves stability and self-consistency. The reconstructed surface profiles are found to be in good agreement with the exact forms. The sensitivity with respect to random noise is also investigated, and the algorithm is found to exhibit a type of self-regularization

Scattering of Ocean Surfaces in Microwave Remote Sensing by Numerical Solutions of Maxwell Equations

Sea-surface scattering has long been studied using various analytical methods. These analytical methods include the two scale method (TSM), the small-slope approximation (SSA), the small-perturbation method (SPM), the Advanced Integral Equation Method (AIEM), and the Geometrical/Physical Optics (GO/PO) method. These analytical methods rely on making approximations and assumptions in the modelling process. Some of these assumptions undermine their applicability in a wide range of situations. The input for analytical methods are usually the ocean spectrum. In real implementations, there are 2 sources of uncertainty in such approaches: (1) the analytical methods have a limited range of applicability to the surface scattering problem; the approximations made in these methods are questionable and (2) the various ocean spectra are another source of uncertainty. We earlier applied a numerical method in 3-dimensions (NMM3D) to the scattering problem of soil surfaces. Through comparison with measured data, we established the accuracy and applicability of NMM3D. We see a drastic increase of ocean remote sensing applications in recent years. It is thus feasible to extend NMM3D to the sea-surface scattering problem. Compared to soil, sea water has a much higher permittivity, e.g., 75+61i at L-band. The large permittivity dictates the need for using a much denser mesh for the sea surface. In addition, the root mean square (rms) height of the sea surface is large under moderate to high ocean wind speeds, which requires a large simulation area to account for the influence of long scale wave like gravity waves. Compared to the two-scale model commonly used for the ocean scattering problem, NMM3D does not need an ad-hoc split wavenumber in the ocean spectrum. Combined with a fast computational algorithm, it was shown that NMM3D can produce accurate results compared to measured data like the Aquarius missions. TSM could also match well with Aquarius provided with a pre-selected splitting wavenumber. But it was observed that the result of TSM changes with different splitting wavenumbers. It is seen that TSM is fairly heuristic while NMM3D can serve as an exact method for the scattering problem. On the other hand, through our study of NMM3D, we found that with a fine grid, the final impedance matrix converges slowly and also it becomes hard to perform simulations for a large surface. This has provoked us to (1) solve low convergence problem for a dense mesh and (2) resolve difficulties in simulations of large surfaces. Inspired by the existing impedance boundary condition (IBC) method, we proposed a neighborhood impedance boundary condition (NIBC) method to solve the slow convergence problem caused by the dense grid. Different from IBC where the surface electric field and the surface magnetic field are related locally, NIBC relates the surface electric field to the magnetic field within a preselected bandwidth BW. Through numerical simulations, we found that the condition number can be reduced using NIBC. Errors of NIBC are controllable through changing BW. We applied NIBC to various wind speeds and surface types and found NIBC to be quite accurate when surface currents only suffer an error norm of less than 1%.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145797/1/qiaot_1.pd

GNSS-R as a source of opportunity for remote sensing of the cryosphere

This work evaluates the potential use of signals from the Global Navigation Satellite Systems (GNSS) that scatter off the Earth surface for the retrieval of geophysical information from the cryosphere. For this purpose, the present study is based on data collected with a dedicated reflectometry GNSS receiver during two field campaigns, which were focused on two types of characteristic surfaces of the cryosphere: thin sea ice covers and thick dry snow accumulations. During the first experiment, the complete process of formation, evolution and melting of sea ice was monitorized for more than seven months in a bay located in Greenland. This type of ice is typically characterized by its thickness, concentration and roughness. Different observables from GNSS reflections are analyzed to try to infer these properties. The ice thickness is linked to the free-board level, defined as the height of the sea ice surface. Accurate phase altimetry is achieved, showing good agreement with an Arctic tide model. In addition, the long term results of ellipsoidal height retrievals are consistent with the evolution of the ice surface temperature product given by MODIS, which is a key parameter in the rate of growth of sea ice. On the other hand, the presence of salinity in the sea ice modifies its dielectric properties, resulting in different amplitude and phase for the co- and cross-polar components of the complex Fresnel coefficients. The polarimetric measurements obtained show good agreement with visual inspections of ice concentration from an Arctic weather station. Finally, the shape of the reflected signals and its phase dispersion are tested as potential signatures of surface roughness. For comparison, ice charts of the experimental area are employed. In particular, maximums in roughness given by the GNSS observables coincide with fast ice events. Fast ice is defined as ice anchored to the coast, where the tidal movements contribute to the development of strange patterns, cracks, and fissures on its surface, thus consistent with the GNSS-R roughness retrievals. The second experiment took place on Antarctica, monitoring a pristine snow area which is well-known for the calibration of remote sensing instruments. Due to the relative stability of the snow layers, the data acquisition was limited to ten continuous days. Interferometric beats were found after a first analysis of the amplitude from the collected signals, which were consistent with a multipath model where the reflector lies below the surface level. Motivated by these results, a forward model is developed that reconstructs the complex received signal as a sum of a finite number of reflections, coming from different snow layers (a snow density profile obtained from in-situ measurements). The interferometric information is then retrieved from the spectral analysis applied to time series from both real and modeled signals (lag-holograms). We find that the frequency bands predicted by the model are in general consistent with the data and the lag-holograms show repeatability for different days. Then, we attempt a proper inversion of the collected data to determine the dominant layers of the dry snow profile that contribute to L-band reflections, which are related to significant gradients of snow density/permittivity.Aquest treball avalua el possible ús dels senyals dels sistemes mundials de navegació per satèl lit (GNSS) que es reflecteixen a la superfície terrestre, per a l’extracció de la informació geofísica de la criosfera. Amb aquest propòsit, el present estudi es basa en dades recollides amb un reflectòmetre GNSS durant dues campanyes experimentals, centrades en dos tipus de superfícies característiques de la criosfera: cobertes de gel marí i gruixudes acumulacions de neu seca. En el primer experiment, el procés complet de formació, evolució i fusió del gel marí va ser monitoritzat durant més de set mesos a una badia situada a Groenlàndia. Aquest tipus de gel es caracteritza típicament amb el seu gruix, concentració i rugositat. Diferents observables de les reflexions GNSS són analitzats per tractar de fer una estimació d’aquestes propietats. El gruix de gel està relacionat amb el nivell de francbord, que a la seva vegada està relacionat amb l’alçada de la superfície de gel marí. S’ha aconseguit altimetria de fase precisa, que mostra correlació amb un model de marea de l’Àrtic. A més, els resultats a llarg termini de l’alçada elipsoidal segueixen l’evolució de les mesures de temperatura de superfície de gel donades per MODIS. La temperatura és un paràmetre clau en el ritme de creixement del gel marí. Per altra banda, la presència de sal a aquest tipus de gel modifica les seves propietats dielèctriques, el que implica variacions d’amplitud i fase per als coeficients de Fresnel complexos amb polaritzacions oposades. Les mesures polarimètriques obtingudes mostren concordança amb els valors de concentració de gel obtinguts des d’una estació meteorològica propera. Finalment, la forma de la senyal reflectida i la dispersió de la seva fase s’evaluen com a potencials indicadors de la rugositat de superfície. Per a la seva comparació, es fan servir mapes del gel de la zona experimental. En concret, els valors màxims a la rugositat estimada a partir pels observables GNSS coincideixen amb el gel fixe, que es refereix a gel ancorat a la costa, on els moviments de les marees contribueixen al desenvolupament de patrons estranys, esquerdes i fissures en la seva superfície. El segon experiment es va dur a terme a l’Antàrtida, monitoritzant una àrea de neu pristina que és ben coneguda per al calibratge d’instruments de teledetecció. A causa de la relativa estabilitat de les capes de neu, l’adquisició de dades es va limitar a deu dies consecutius. Es van trobar pulsacions interferomètriques a partir d’un primer anàlisi de l’amplitud de les senyals recollides, les quals eren compatibles amb un model de propagació multicamí a on el reflector es troba per sota del nivell de superfície. Com a conseqüència d’aquests resultats, s’ha desenvolupat un model que reconstrueix el senyal complexe rebut com la suma d’un nombre finit de reflexions, procedents de diferents capes de neu (determinat per mesures locals). La informació interferomètrica es recupera després de l’anàlisi espectral aplicat a les sèries temporals tant de les senyals reals, com de les modelades (lag-hologrames). Trobem que les bandes de freqüències predites pel model són en general consistents amb les dades i que els lag-hologrames mostren repetibilitat per dies diferents. Posteriorment, es realitza un anàlisi de les dades recollides per determinar les capes dominants del perfil de neu seca que contribueixen a les reflexions en banda L, i que a la seva vegada, estan relacionades amb gradents significatius de densitat/permitivitat.Este trabajo evalúa el posible uso de las señales de los sistemas globales de navegación por satélite (GNSS) que se reflejan en la superficie terrestre para la extracción de información geofísica de la criosfera. Con este propósito, el presente estudio se basa en datos recogidos con un reflectómetro GNSS durante dos campañas experimentales, centradas en dos tipos de superficies características de la criosfera: capas de hielo marino y gruesas acumulaciones de nieve seca. Durante el primer experimento, el proceso completo de formación, evolución y fusión del hielo marino fue monitorizado durante más de siete meses en una bahía ubicada en Groenlandia. Este tipo de hielo se caracteriza típicamente por su grosor, concentración y rugosidad. Diferentes observables de las reflexiones GNSS son analizados para tratar de estimar dichas propiedades. El espesor de hielo está relacionado con el nivel de francobordo o borda libre, que a su vez está relacionado con la altura de la superficie de hielo marino. Se ha logrado altimetría de fase precisa, mostrando correlación con un modelo de marea del Ártico. Además, los resultados a largo plazo de la altura elipsoidal siguen la evolución de las mediciones de temperatura de superficie de hielo proporcionadas por MODIS. La temperatura es un parámetro clave en el ritmo de crecimiento del hielo marino. Por otro lado, la presencia de sal en este tipo de hielo modifica sus propiedades dieléctricas, lo que implica variaciones en las amplitudes y fases de los coeficientes complejos de Fresnel con polarizaciones opuestas. Los resultados polarimétricos concuerdan con los valores de concentración de hielo obtenidos mediante inspección visual desde una estación meteorológica cercana. Por último, la forma de la señal reflejada y la dispersión de su fase son evaluadas como potenciales indicadores de la rugosidad de superficie. Para su comparación, se emplean mapas del hielo de la zona experimental. En particular, valores máximos de rugosidad estimada por los observables GNSS coinciden con hielo fijo, que se refiere al hielo anclado a la costa, donde los movimientos de las mareas contribuyen al desarrollo de patrones extraños, grietas y fisuras en su superficie. El segundo experimento se llevó a cabo en la Antártida, monitorizando una área de nieve pristina que es bien conocida para la calibración de instrumentos de teledetección. Debido a la relativa estabilidad de las capas de nieve, la adquisición de datos se limitó a diez días consecutivos. Se encontraron pulsaciones interferométricas a partir de un primer análisis de la amplitud de las señales recibidas, las cuales eran compatibles con un modelo de propagación multicamino donde el reflector se encuentra por debajo del nivel de la superficie. Como consecuencia de estos resultados, se ha desarrollado un modelo que reconstruye la señal recibida como la suma de un número finito de reflexiones, procedentes de diferentes capas de nieve (caracterizados por mediciones locales). La información interferométrica se recupera después del análisis espectral aplicado a las series temporales tanto de las señales reales, como de las modeladas (lag-hologramas). Encontramos que las bandas de frecuencias predichas por el modelo son en general consistentes con los datos y que los lag-hologramas muestran repetibilidad para días diferentes. Posteriormente, se realiza un análisis de los datos recogidos para determinar las capas dominantes del perfil de nieve seca que contribuyen a las reflexiones en banda L, y que a su vez, están relacionadas con gradientes significativos de densidad/permitivida

Design Data Collection with Skylab Microwave Radiometer-Scatterometer S-193, Volume 1

The author has identified the following significant results. Observations with S-193 have provided radar design information for systems to be flown on spacecraft, but only at 13.9 GHz and for land areas over the United States and Brazil plus a few other areas of the world for which this kind of analysis was not made. Observations only extended out to about 50 deg angle of incidence. The value of a sensor with such a gross resolution for most overland resource and status monitoring systems seems marginal, with the possible exception of monitoring soil moisture and major vegetation variations. The complementary nature of the scatterometer and radiometer systems was demonstrated by the correlation analysis. Although radiometers must have spatial resolutions dictated by antenna size, radars can use synthetic aperture techniques to achieve much finer resolutions. Multiplicity of modes in the S-193 sensors complicated both the system development and its employment. An attempt was made in the design of the S-193 to arrange optimum integration times for each angle and type of measurement. This unnecessarily complicated the design of the instrument, since the gains in precision achieved in this way were marginal. Either a software-controllable integration time or a set of only two or three integration times would have been better

Earth resources: A continuing bibliography with indexes (issue 61)

This bibliography lists 606 reports, articles, and other documents introduced into the NASA scientific and technical information system between January 1 and March 31, 1989. Emphasis is placed on the use of remote sensing and geophysical instrumentation in spacecraft and aircraft to survey and inventory natural resources and urban areas. Subject matter is grouped according to agriculture and forestry, environmental changes and cultural resources, geodesy and cartography, geology and mineral resources, oceanography and marine resources, hydrology and water management, data processing and distribution systems, and instrumentation and sensors, and economic analysis