Erin E. Hackett

Effect of Finite Spatial Resolution on the Turbulent Energy Spectrum Measured in the Coastal Ocean Bottom Boundary Layer

The effect of finite spatial resolution on the measured energy spectrum is examined via a parametric study using in situ particle image velocimetry (PIV) measurements performed in the bottom boundary layer on the Atlantic continental shelf. Two-dimensional (2D) box spatial filters of various scales are applied to the data, and these filtered distributions are used to compute 1D energy spectra in both frequency and wavenumber domains. It is found that energy levels are attenuated by more than 15% at all length scales that are smaller than 10 times the scale of the filter. Filtering both in the direction of the spectrum as well as perpendicular to it contributes to the extent of attenuation, the latter via implicit integration over all wavenumbers. At scales larger than that of the filter, Gaussian, nonlinear Butterworth, and median filters attenuate less energy than the box filter. When frequency spectra are converted using Taylor’s hypothesis, wave energy appears in wavenumber space at a location different than its true physical scale, which is much larger than the filter sizes. Consequently, wave energy is not attenuated and dominates over the turbulence through this spectral range. Because wave energy and turbulence respond differently to the filtering, modified spectral slopes at the transition between wave- and turbulence-dominated regions occur, resulting in inordinately steep spectral slopes. Finally, removal of the pressure-coherent part of the velocity signal is not sufficient to reveal the turbulence within the wave peak spectral range. Remaining energy in this range is still dominated by much larger scales.

Evaluation of simplified evaporation duct refractivity models for inversion problems

To assess a radar systems instantaneous performance on any given day, detailed knowledge of the meteorological conditions is required due to the dependency of atmospheric refractivity on thermodynamic properties such as temperature, water vapor, and pressure. Because of the significant challenges involved in obtaining these data, recent efforts have focused on development of methods to obtain the refractivity structure inversely using radar measurements and radar wave propagation models. Such inversion techniques generally use simplified refractivity models in order to reduce the parameter space of the solution. Here the accuracy of three simple refractivity models is examined for the case of an evaporation duct. The models utilize the basic log linear shape classically associated with evaporation ducts, but each model depends on various parameters that affect different aspects of the profile, such as its shape and duct height. The model parameters are optimized using radiosonde data, and their performance is compared to these atmospheric measurements. The optimized models and data are also used to predict propagation using a parabolic equation code with the refractivity prescribed by the models and measured data, and the resulting propagation patterns are compared. The results of this study suggest that the best log linear model formulation for an inversion problem would be a two-layer model that contains at least three parameters: duct height, duct curvature, and mixed layer slope. This functional form permits a reasonably accurate fit to atmospheric measurements as well as embodies key features of the profile required for correct propagation prediction with as few parameters as possible.

Global sensitivity of parabolic equation radar wave propagation simulation to sea state and atmospheric refractivity structure

Inadequate representation of the environment is a limitation for prediction of radar system performance as well as for validation of propagation codes. To improve understanding of how different environmental effects/parameters compete and compare, this study examines the sensitivity of radar wave propagation to a suite of environmental parameters for low grazing angle near-surface radar systems at 3–15 GHz at horizontal and vertical polarizations. A global sensitivity analysis method is used, which accounts for parameter interactions, and propagation is modeled using the parabolic equation method. Environmental parameters examined include eight sea state parameters and eight parameters characterizing the vertical structure and character of range-independent refractivity profiles. The relative importance of parameters varies more with frequency than polarization, and parameter interactions are found to be significant. Atmospheric mixed layer parameters are found to be the most sensitive, particularly the thickness of the mixed layer. The most significant ocean surface parameter is swell period, although sea directionality is important at 3 GHz and sea surface roughness and salinity are important at 9 and 15 GHz. Because of the spatial variability of sensitivity throughout the domain, regional analysis is performed to determine the most important parameters in different regions of the domain (1000 m in altitude and 60 km in range). These regional sensitivity results, along with those for the whole domain, provide guidance on prioritization of environmental characterization in numerical weather prediction and inversion studies (e.g., refractivity from clutter studies), which are two common methods currently used to address environmental effects on propagation.

Radar Measurement of Ocean Waves

Over the past two decades a number of advances have been made in the use of radar systems for the measurement of ocean waves, building on early work at universities and the Naval Research Lab (NRL) to investigate the potential for extracting wave field measurements from the sea clutter seen in shipboard radar images. This early work was the foundation for modern wave radar systems, with hardware systems ranging from commercial off the shelf (COTS) incoherent navigation radar to specially developed, calibrated, coherent instrumentation radar and phased-array systems. Software algorithms and image analysis techniques have also been in constant development, which have evolved from 2D analysis of digitized images into modern techniques performing real-time 3D transformation of high resolution images. Most of these systems are being utilized to measure the directional wave spectra, with some systems also providing wave height estimates and sea surface elevation maps. More recently, the Naval Surface Warfare Center, Carderock Division (NSWCCD) and others have begun to utilize these techniques for shipboard measurement of open ocean waves. All these efforts have led to higher fidelity data, as well as data that were previously unobtainable. In this paper we provide an overview and history of the development of COTS incoherent wave radar systems, analysis techniques, and capabilities, from early characterization of sea clutter return to the latest developments in image inversion and sea surface topography. This review and summary provides a foundation on which to develop analysis techniques for the higher fidelity data, using lessons learned to improve future analysis. While not intending to be exhaustive, this paper seeks to highlight the insights gained from both historical and recent applications of these techniques, as well as the difficulties and issues associated with shipboard measurements such as ship motion, logistical constraints, and environmental factors.Copyright

Shipboard Measurement of Ocean Waves

Over the past several years a number of techniques have been utilized for the measurement of ocean waves from shipboard platforms. These systems have ranged from commercial off the shelf (COTS) navigation radar and Light Detection and Ranging (LIDAR) systems to specially developed in-house instrumentation systems. Most of these systems have been utilized to measure the directional wave spectra around the ship. More recently, the Naval Surface Warfare Center, Carderock Division (NSWCCD) and others have begun to utilize these techniques for shipboard measurement of individual ship generated waves as well as open ocean waves. NSWCCD has used a number of these methods on various Office of Naval Research (ONR) and Naval Sea Systems (NAVSEA) sponsored field tests. These field tests were performed on a variety of naval platforms over a range of sizes, including some fixed platforms, for various sea states. While each of these tests has had individual measurement goals and objectives, the series of tests has also provided an environment for testing and developing new instrumentation and exploring their capabilities. As a result of these efforts, instrumentation has grown in sophistication from qualitative video-based observations of the wave field around an underway vessel to laser and radar based imaging and ranging measurements of free surface dynamics. This work has led to higher fidelity data, as well as data that were previously unobtainable. In this paper we provide an overview of these systems and techniques and summarize the basic capabilities of each method by providing measurement examples/applications. These systems include a shipboard array of ultrasonic distance sensors for measuring directional wave spectra, a COTS wave radar system, and a COTS scanning LIDAR system. While not intending to be exhaustive, this paper seeks to highlight the insights gained from the recent applications of these techniques, as well as the difficulties and issues associated with shipboard measurements such as ship motion and logistical constraints.

Comparison of Incoherent and Coherent Wave Field Measurements Using Dual-Polarized Pulse-Doppler X-Band Radar

Radar-based remote sensing for measurement of ocean surface waves presents advantages over conventional point sensors such as wave buoys. As its use becomes more widespread, it is important to understand the sensitivity of the extracted wave parameters to the characteristics of the radar and the scatterers. To examine such issues, experiments were performed offshore of the Scripps Institution of Oceanography pier in July 2010. Radar measurements in low wind speeds were performed with a dual-polarized high-resolution X-band pulse-Doppler radar at low grazing angles along with two independent measurements of the surface waves using conventional sensors, a GPS-based buoy, and an ultrasonic array. Comparison between radar cross section (RCS) and Doppler modulations shows peak values occurring nearly in-phase, in contrast with tilt modulation theory. Spectral comparisons between Doppler-based and RCS-based spectra show that Doppler-based spectra demonstrate greater sensitivity to swell-induced modulations, whereas RCS-based spectra show greater sensitivity to small-scale modulations (or generally have more noise at high frequency), and they equally capture energy at the wind wave peak. Doppler estimates of peak period were consistent with the conventional sensors, whereas the RCS differed in assignment of peak period to wind seas rather than swell in a couple of cases. Higher order period statistics of both RCS and Doppler were consistent with the conventional sensors. Radar-based significant wave heights are lower than buoy-based values and contain nontrivial variability of ~33%. Comparisons between HH and VV polarization data show that VV data more accurately represent the wave field, particularly as the wind speeds decrease.

Flow Scales of Influence on the Settling Velocities of Particles with Varying Characteristics.

The settling velocities of natural, synthetic, and industrial particles were measured in a grid turbulence facility using optical measurement techniques. Particle image velocimetry and 2D particle tracking were used to measure the instantaneous velocities of the flow and the particles’ trajectories simultaneously. We find that for particles examined in this study (Rep = 0.4–123), settling velocity is either enhanced or unchanged relative to stagnant flow for the range of investigated turbulence conditions. The smallest particles’ normalized settling velocities exhibited the most consistent trends when plotted versus the Kolmogorov-based Stokes numbers suggesting that the dissipative scales influence their dynamics. In contrast, the mid-sized particles were better characterized with a Stokes number based on the integral time scale. The largest particles were largely unaffected by the flow conditions. Using proper orthogonal decomposition (POD), the flow pattern scales are compared to particle trajectory curvature to complement results obtained through dimensional analysis using Stokes numbers. The smallest particles are found to have trajectories with curvatures of similar scale as the small flow scales (higher POD modes) whilst mid-sized particle trajectories had curvatures that were similar to the larger flow patterns (lower POD modes). The curvature trajectories of the largest particles did not correspond to any particular flow pattern scale suggesting that their trajectories were more random. These results provide experimental evidence of the “fast tracking” theory of settling velocity enhancement in turbulence and demonstrate that particles align themselves with flow scales in proportion to their size.

Global sensitivity of radar wave propagation power to environmental variables for a parabolic equation numerical simulation in maritime regions

Numerous environmental factors impact radio wave propagation in the marine atmospheric boundary layer (MABL) through effects such as scattering and refraction. Furthermore, environmental parameters can interact with each other to either compound or reduce the impact of each individual parameter. Thus, in order to properly assess the sensitivity of radar wave propagation power to environmental variables a global sensitivity approach is needed. In this study, we examine the global sensitivity of propagation power to a number of environmental variables using a parabolic equation (PE) numerical simulation for maritime regions. The sensitivity analysis is performed using the Extended Fourier Amplitude Sensitivity Test, which is a global variance-based method that can account for multi-degree interaction effects. The method is ideal for complex nonlinear models and permits computation of both leading order and total order sensitivity for each parameter. The study examines 16 environmental parameters, 8 sea state and 8 atmospheric, that are used to generate inputs for the Variable Terrain Radiowave Parabolic Equation (VTRPE) numerical simulation. This model uses a split-step rotated Greens function parabolic wave equation solution to the scalar wave equation for transverse field components derived from Maxwells equations. The simulation accounts for effects of refraction (including ducting) as well as variable boundary conditions on water surfaces, such as wind seas, swell, and variable dielectric properties. Vertical profiles of atmospheric refractivity, which are assumed homogenous in range for this study, are generated using a simplified refractivity model that depends on the 8 atmospheric parameters and can generate linear refractivity profiles as well as evaporation, surface, and elevated ducts, including any combination of these ducts. Sea state parameters can be grouped into 3 general categories: surface dielectric properties, directionality, and surface roughness. Atmospheric parameters can be grouped into 4 general categories: evaporation layer, mixed layer, inversion layer, and upper layer parameters. We examine results in the context of these parameter groupings.

Use of Proper Orthogonal Decomposition for Extraction of Ocean Surface Wave Fields from X-Band Radar Measurements of the Sea Surface

Radar remote sensing of the sea surface for the extraction of ocean surface wave fields requires separating wave and non-wave contributions to the sea surface measurement. Conventional methods of extracting wave information from radar measurements of the sea surface rely on filtering the wavenumber-frequency spectrum using the linear dispersion relationship for ocean surface waves. However, this technique has limitations, e.g., it isn’t suited for the inclusion of non-linear wave features. This study evaluates an alternative method called proper orthogonal decomposition (POD) for the extraction of ocean surface wave fields remotely sensed by marine radar. POD is an empirical and optimal linear method for representing non-linear processes. The method was applied to Doppler velocity data of the sea surface collected using two different radar systems during two different experiments that spanned a variety of environmental conditions. During both experiments, GPS mini-buoys simultaneously collected wave data. The POD method was used to generate phase-resolved wave orbital velocity maps that are statistically evaluated by comparing wave statistics computed from the buoy data to those obtained from these maps. The results show that leading POD modes contain energy associated with the peak wavelength(s) of the measured wave field, and consequently, wave contributions to the radar measurement of the sea surface can be separated based on modes. Wave statistics calculated from optimized POD reconstructions are comparable to those calculated from GPS wave buoys. The accuracy of the wave statistics generated from POD-reconstructed orbital velocity maps was not sensitive to the radar configuration or environmental conditions examined. Further research is needed to determine a rigorous method for selecting modes a priori.

Similarity and dissimilarity measures for comparison of propagation patterns

This study examines several different similarity and dissimilarity measures for comparing propagation patterns. Typically used in image registration problems, we evaluate their utility here using propagation patterns simulated using a parabolic equation simulation. High correspondence between certain pairings of measures may indicate structural similarity or the absence of noise, and strong correspondence among all measures reduces ambiguity in the best-matching pattern. Incorporating multiple evaluation measures thereby improves the fidelity of the pattern comparison.