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LASER-GLINT MEASUREMENTS OF SEA-SURFACE ROUGHNESS by

Joseph Alan Shaw

A Dissertation Submitted to the Faculty of the

COMMITTEE ON OPTICAL SCIENCES (GRADUATE)

In Partial Fulfillment of the Requirements

For the Degree of

DOCTOR OF PHILOSOPHY hi the Graduate College

THE UNIVERSITY OF ARIZONA

1 9 9 6

UMI Number: 9720579 mvn Microform 9720579

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THE UNIVERSITY OF ARIZONA ®

GRADUATE COLLEGE

As members of the Final Examination Committee, we certify that we have read the dissertation prepared by Joseph Alan Shaw entitled Laser-Glint Measurements of Sea-Surface Roughness

2 and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy

John A. Reagan

KurtIS Thome

James H. Chumside

Dace

^ / f / 9 ^

Date

Date

Date

Date

7 A UI

Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the

Graduate College.

I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement.

John A. Reagan

Dissertation D Daxe

3

STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED:

ACKNOWLEDGMENTS

It is my pleasure to acknowledge the contributions of many to my education, and particularly to the creation of this dissertation. Support for my retum to graduate school was provided by a long-term training program of my employer, the Environmental

Technology Laboratory (then the Wave Propagation Laboratory) of the National Oceanic and Atmospheric Administration (NOAA). Dr. Ed Westwater, then my division chief, and Dr. Steven Clifford, our Laboratory Director, encouraged my participation and provided the necessary political support to make it happen. My supervisor. Dr. James

Chumside, helped me identify a project that fit our division's research objectives and my optical interests. His advice was crucial, and often led to more creative results than would have occurred without his input.

I express sincere gratitude to my advisor at The University of Arizona, Dr. John

Reagan, for agreeing to advise me on a research project that was not yet clearly identified and that was to be performed at work in Boulder, Colorado. His trust in my abilities, his willingness to meet with me when the opportunity arose (whether in Arizona, Alaska, or

Nebraska), and his support at critical examination times in Tucson is appreciated.

Similarly, I am grateful to the faculty and staff of the Optical Sciences Center at The

University of Arizona for providing an atmosphere where I could learn optics from the very best, and then for making my in absentia research arrangement succeed. I especially appreciate Dr. Kurt Thome for serving as a member of my dissertation committee, and

Didi Lawson for making each academic step at Optical Sciences so smooth. My fellow students deserve thanks as well, for contributing so much to the warm and friendly atmosphere that exists in all phases of Optical Sciences Center life.

I owe thanks also to my colleagues and friends at NOAA. Thanks to Dr. Mark

Jacobson, Dr. Richard Lataitis, Dr. Konstantin Naugolnykh, and Jim Wilson for many useful discussions; to Mark Jacobson for sharing the experience of life on the FLIP; to

Hector Bravo and Daniel Higgins for major contributions to the instrument hardware and software; to Peter Gauntt and Michael Fails for help building hardware, processing data, and creating figures; and to Sharon Kirby-Cole for taking care of many details while I was in Tucson and Boulder, and for helping to edit parts of this dissertation.

Finally, I express appreciation to my family, who by sharing every step of this undertaking with me, have made it infinitely more enjoyable. My wife Margaret has been my constant support, and my sons Aaron and Brian have cheerfiilly found joy living in two cities. My parents, Glenn and Gladys Shaw, encouraged and supported me in this and all previous endeavors. Most importantly, my family has always encouraged me to seek out and enjoy God's handiwork, much of which is manifested optically in nature.

DEDICATION

I dedicate this dissertation to my wife Margaret, and to my sons Aaron and Brian, for providing such brilliant light in my life.

TABLE OF CONTENTS

ABSTRACT

L INTRODUCTION

2. INSTRUMENT AND EXPERIMENT DESCRIPTION

2.1 Scanning-Laser Glint Meter

2.1.1 Hardware

2.1.2 Radiometry

2.2 Video Laser-Glint Imager

2.2.1 Hardware

2.2.2 Radiometry

2.3 Measurements in the Pacific Ocean

2.3.1 Deployment of the optical instruments

2.3.2 Sonic anemometer wind speeds

2.3.3 Radiometric air-sea temperature differences

2.3.4 Sonar long-wave heights

3. SEA-SURFACE SLOPE STATISTICS

3.1 Overview

3.2 Gram-Charlier Series

3.3 Mean-Square Slope

3.4Skewness

3.5 Peakedness

3.6 Discussion and Summary

4. FRACTAL ANALYSIS OF LASER GLINTS

4.1 Overview

4.2 Scanning-Laser Glint Counts

4.3 Video Laser-Glint Counts

4.4 Discussion and Summary

5. SPECTRAL ANALYSIS OF LASER-GLINT IMAGES

5.1 Overview

5.2 Measured Laser-Glint Images

5.3 Simulated Laser-Glint Images

5.4 Discussion and Summary

6. CONCLUSION

REFERENCES

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7

LIST OF ILLUSTRATIONS

FIGURE 2.1, Scanning-laser glint meter line drawing

FIGURE 2.2, Scarming-laser glint meter receiver schematic

FIGURE 2.3, Scanning-laser glint meter amplifier schematic

FIGURE 2.4, Scanning-laser glint meter motor-position sensors schematic

FIGURE 2.5, Geometry for radiometric calculations

FIGURE 2.6, Night-time signal-to-noise ratio for scanning-laser system

FIGURE 2.7, Video laser-glint imager line drawing

FIGURE 2.8, Schematic of the diode-laser bias electronics

FIGURE 2.9, Schematic of the diode-laser modulation electronics and timing

FIGURE 2.10, The FLoating Instrument Platform (FLIP)

FIGURE 2.11, Laser-glint instruments deployed on the FLIP

FIGURE 2.12, Wind speed and direction during the experiment

FIGURE 2.13, Air-water temperature difference during the experiment

FIGURE 2.14, Surface-height power spectrum measured by sonar

FIGURE 3.1, Measured along-wind slope probability density function (PDF)

FIGURE 3.2, Measured cross-wind slope PDF

FIGURE 3.3, Gram-Charlier series expansion of a measured PDF

FIGURE 3.4, Normalized error for the Gram-Charlier approximate PDF

FIGURE 3.5, Wind-speed dependence of my mean-square slope data

FIGURE 3.6, Wind-speed dependence of other mean-square slope data

FIGURE 3.7, Normalized mean-square slope vs. Ri (stability < 0)

FIGURE 3.8, Normalized mean-square slope vs. A(stability ^0)

68

70

71

FIGURE 3.9, Normalized mean-square slope vs. Ar^yi7,o (positive & negative) ... 72

FIGURE 3.10, Wind-speed dependence of PDF skewness 74

FIGURE 3.11, Stability dependence of PDF skewness

FIGURE 3.12, Wind-speed dependence of PDF peakedness

FIGURE 3.13, Stability dependence of PDF peakedness

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FIGURE 3.14, Dependence of skewness on the mean-square slope

FIGURE 3.15, Dependence ofpeakedness on the mean-square slope

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FIGURE 4.1, Scanning-laser glint-count time series

FIGURE 4.2, Scarming-laser glint-count histograms

FIGURE 4.3, Scanning-laser glint-count power spectrum

FIGURE 4.4, Video glint-count histogram

FIGURE 4.5, Cumulative probability distribution of glint counts

FIGURE 4.6, Video glint-count power spectrum

FIGURE 4.7, Scatter plot of spectral exponents for blob and pixel counting

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101

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50

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25

26

27

30

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40

44

FIGURE 5.1, Glint images for a smooth and a rough sea surface

FIGURE 5.2, Glint-image power spectrum for 1010 UTC, day 265

106

108

8

LIST OF ILLUSTRATIONS - Continued

FIGURE 5.3, Glint-image power spectrum for 1005 UTC, day 265

FIGURE 5.4, Glint-image power spectrum for 0700 UTC, day 265

FIGURE 5.5, Glint-image power spectrum for 0250 UTC, day 269

FIGURE 5.6, Glint-image power spectrum for 0546 UTC, day 266

FIGURE 5.7, Along-wind central slices of the measured glint-image spectra

FIGURE 5.8, Cross-wind central slices of the measured glint-image spectra

FIGURE 5.9, Power spectrum of a white dot on a black background

HGURE 5.10, Autocorrelation of the glint image at 1010 UTC, day 265

FIGURE 5.11, Autocorrelation of the glint image at 0546 UTC, day 266

FIGURE 5.12, Simulated sea-surface height and slope profiles

FIGURE 5.13, Simulated along-wind power spectra

FIGURE 5.14, Simulated cross-wind power spectra

109

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Ill

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125

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128

LIST OF TABLES

Table 2.1, Summary of the scanning-laser glint meter hardware

Table 2.2, Summary of the video laser-glint imager hardware

Table 3.1, Hermite polynomials of order n

Table 3.2, Scanning-laser data summary

Table 4.1, Summary of glint-count fractal dimensions

Table 5.1, Sunmiaiy of the video data analyzed in chapters 4 and 5

9

23

36

60

65

102

113

ABSTRACT

Optical glint patterns convey information about the roughness of the surface on which tliey are formed. This dissertation describes two new optical instruments that relate the variations of specular laser reflections (laser glints) from the sea surface in angular, temporal, and wavenumber space to the surface roughness. Measurements from these instruments are interpreted with the objective of improving the capabilities of remote-sensing instruments that view the ocean surface. Particular attention is paid to cm waves, which are resonant structures for microwave sensors and the most significant component of optical roughness.

The scanning-laser glint meter counts laser glints in 1" angular bins over a ± 75° nadir-angle range. The video laser-glint imager is a CQD video camera that images glints from an array of diode lasers. Both instruments were deployed on the research platform

FLIP in the Pacific Ocean near the Oregon coast for three weeks during September 1995.

Normalized histograms of angular glint counts are interpreted as the probability density fiinction (PDF) of sea-surface slope, a Gram-Charlier expansion of which facilitates studying the variation with wind speed and atmospheric stability of moments through order four. The PDF appears approximately Gaussian, but is skewed toward downwind slopes in the along-wind axis due to asymmetric wind waves. No skewness exists in the cross-wind axis. Slope PDFs also have positive peakedness, increasing the probability of very small and large slopes relative to a Gaussian.

Surface roughness is shown to depend strongly on atmospheric stability, which is proportional to the air-water temperamre difference. Both the mean-square slope and the

II

peakedness increase with negative stability (water warmer than air) relative to the neutralstability case (water and air temperatures equal). Increased surface roughness, due to increases in wind speed or negative stability, causes glint-count fractal dimensions to increase, glint-image power spectra to flatten, and glint-image autocorrelations to appear more wrinkled. Glint-image spectra are dominated by glint-size effects, which are related to surface curvature. New ways of modeling the interaction of electromagnetic waves with the ocean surface are suggested by the new fractal and spectral characterizations of surface roughness that are introduced here.

12

1. INTRODUCTION

Optical glints arc created by light reflecting from specular facets on a rough water surface. The changing surface produces twinkling glints m glitter patterns that are one of the many enjoyable visual phenomena of natural optics.'-^ Glitter pattems arise from both natural and man-made light sources, and in either case carry potentially useful information about their environment The size, shape, and brightness of a glitter pattem are related to a variety of environmental parameters, most notably wind speed. Watching glitter pattems appear and disappear on the water as wind gusts come and go, it is easy to conclude that measuring optical glitter pattems is a good way of learning about rough water surfaces.

To contribute to our knowledge about the ocean surface and its optical manifestations, thereby improving remote-sensing measurements of near-surface quantities, I have developed and applied several new optical techniques that use laser glints to measure sea-siuface roughness. The resulting knowledge will benefit a large variety of remote-sensing products, including sea-surface temperature, ocean color, atmospheric aerosols, and near-siuface wind vectors.

Remote-sensing measurements of sea-surface temperature have been formulated recently in a statistical fashion that incorporates surface roughness.^' Most imaging sensors, such as ocean color imagers, also rely on surface-roughness models for separating atmospheric from oceanic effects. Whereas early ocean-color and aerosolretrieval algorithms assumed a flat ocean surface,® the more sophisticated secondgeneration sensors require a more detailed treatment of the surface.*"'" Also, as lidars

become increasingly abundant, especially operating from aircraft or satellites, they too will require improved sea-surface models for interpretation of their data collected over the oceans''"'^and for assessment of eye-safety.'®

13

Remote sensing of near-surface winds over the ocean has depended historically on satellite-based radars, which measure enhanced backscatter from Bragg-matched wind waves on the ocean surface." Recently, the possibility has been recognized that passive polarimetric microwave radiometers can sense wind vectors with similar accuracy as radars, but with drastically reduced weight and power.'^^' In this case, the sensors measure thermal emission, the polarization state of which is made azimuthally anisotropic by wind waves that propagate preferentially along the wind vector. Reliable wind-vector retrievals from active or passive microwave measurements require better understanding of sea-surface roughness, particularly its dependence on local environmental parameters.

The capability of remotely sensing winds over the ocean is extremely important since most large-scale weather forecasts currently are limited by a lack of data over the majority of our planet that is covered by water.

This dissertation represents the results of one portion of a broad effort, directed by the Environmental Technology Laboratory (ETL) of the National Oceanic and

Atmospheric Administration (NOAA), that is part of a joint NOAA - Department of

Defense program to investigate radar and microwave polarization radiometry for remote sensing of ocean waves and near-surface wind vectors. As part of this program, in

September 1995, NOAA/ETL sponsored the Coastal Ocean Probing Experiment (COPE) on the Pacific coast of Oregon." My responsibility in COPE was to develop and deploy

14

optical techniques to provide surface-roughness information for improving basic understanding and for helping interpret radar and microwave radiometer measurements.

The ocean surface is rough with waves of various sources, sizes, and durations.^

These waves can be categorized generally as gravity waves or capillary waves. Gravity waves are large, long-lived waves whose restoring force is gravity, and capillary waves are small, short-lived waves whose restoring force is surface tension. Gravity waves have wavelengths on the order of 1-100 m, temporal periods on the order of 1—30 s, and they carry large amounts of mechanical energy. Swell waves are large gravity waves that are often formed by distant storms, propagate great distances, are the most unidirectional, and have the most sinusoidal profile of all ocean waves. Capillary waves have wavelengths s 2 cm, temporal periods 5 0.1 s, and carry very little mechanical energy. When the wind blows across the surface, they form in diamond-shaped patches with highly nonsinusoidal profiles. Waves between pure gravity and capillary waves are often referred to as capillary-gravity waves. These waves have characteristics of both types, but are very much like capillary waves in that they respond strongly to wind speed, wind direction, thermal stratification, and other local environmental parameters.

Waves of different types are not independent of each other. Nonlinear Wavewave interactions couple waves throughout the spectrum together, sloshing energy back and forth between long and short waves. This process begins at the onset of a wind, which forms capillary waves with lengths to a few cm and heights to a few mm. ff the wind ceases blowing, surface tension damps these tiny waves quickly. If the wind continues blowing, the capillary waves grow. When they become longer than about 2 cm.

15

they become capillary-gravity waves. Now if the wind stops blowing, the newly formed waves keep going until some other mechanism, such as turbulent water motion, drains their energy. Mechanisms of energy input from the wind to the waves include direct mechanical pushing on their upwind faces, frictional drag of the air on the ocean surface, and pressure differences in the air (turbulent exchange).

Because short wind waves are resonant structures for a large range of electromagnetic wavelengths, and because they have much steeper slopes than longer waves, they dominate the apparent surface roughness for most electromagnetic remote sensors. The need to resolve short capillary waves makes optical techniques desirable for sea-surface roughness measurements. Wave-slope measurements are often more sensitive than wave-height measurements because short waves have small heights but steep slopes.

Optical techniques of numerous varieties have been used to measure watersurface roughness, but only several have been used successfully in field measurements of a real ocean. Cox and Munk made the first significant optical measurements of seasurface roughness."-^ They used airborne cameras to take defocussed, photometric pictures of sun glitter on the Pacific Ocean near the Hawaiian Islands. Then, by relating photographic density with the probability of a specular reflection, they formulated surface-slope statistics as a function of wind speed and direction. The Cox and Munk model remains today the most widely recognized and applied model of sea-surface slope statistics.

Stilwell extended the Cox and Munk photographic technique by using coherent

optical processing to derive directional wavenumber spectra of slopes from photographs

16

of reflected sky radiance.^®-" The appealing aspect of this technique is that an optical diffraction pattern of a single photographic negative instantaneously produces simultaneous directional and spectral wave-slope information. Though this is one of the most interesting techniques from an optical point of view, its practicality is limited strongly by the requirement of uniform sky radiance.

Stereo photography is an appealing photographic technique for profiling the seasurface height. Field applications thus far have used natural sky light to produce waveheight wavenumber spectra.^^ However, the small wave heights have precluded stereophotographic measurements of short capillary waves. Though this technique is limited less by sky-radiance assumptions than Stilwell photography, it requires laborious crosscorrelation of image-pairs and careful high-pass filtering to yield short-wave measurements. Furthermore, the specular and fractal nature of light reflection from water makes it difficult to register surface features in the two images taken from different angles.

A recent technique relies on time-series analysis of the irradiance on a single video pixel looking at a near-grazing angle at the ocean siuface."'^^ The disadvantages of this simple technique are that it requires uniform sky radiance, and its output appears to be most strongly related to long-wave heights, with no clear connection to short waves.

After interest in sea-surface roughness measurements was renewed by space deployment of radar scatterometers approximately two decades ago, the most productive optical technique has been the refractive laser slope gauge.^^"^' This method determines

17

wave slopes from the refraction of a laser beam as it passes through the water-air interface. Because the receiver is looking downward, directly at the nearby laser source, these instruments enjoy a high signai-to-noise ratio, almost totally independent of skylight. However, the large immersed support structure and optics package can disturb the water surface, just as the nearby receiver in the air can distort air flow, thereby altering the fine-scale surface structure. The ultimate angular limit of this technique is the critical angle, near 50° for sea water, beyond which the light is totally internally reflected back into the water. Practical systems, however, are limited to around 30° maximum angle by the size of the receiver optics.

Most early refractive laser slope gauges were mounted on wave-followers, essentially large hydraulic jacks, either resting on the ocean floor or connected to an off­ shore tower, that raised and lowered the optics package in synchronization with the large, low-frequency waves. This was necessary to maintain a short source-to-receiver distance

(- 0.8 m), which in turn was required for a reasonably sized receiver lens to measure the steep slopes (hence large refraction angles) of the short waves. This limited their use to shallow water (~ 5-20 m), often close to the shore. Instruments in this form have been used to measure wave-slope frequency spectra,^^-'®-^' wave-slope wavenumber spectra," long-wave modulation of short waves,^"® wave-slope statistics,^® and the effects on wave slopes"" of swell and atmospheric stability (which can be characterized by the air-sea temperature difference, as discussed later in section 2.3.3).

A refractive laser slope gauge has also been suspended from a ship's bow in sheltered (free of swell) ocean waters to study wave-slope statistics^ and interaal-wave

modulation of short waves.^® Most recently, a smaller version was mounted on a catamaran and used to measure wavenumber-frequency spectra of short-wave slopes."*'

18

The potential surface disturbance and difficult deployments associated with refractive laser slope gauges make reflective laser-glint sensors attractive, but they have only seen minimal application in the past. A reflective laser-glint sensor developed for laboratory wave-tank studies was field-tested on a moonless night from a pier, producing cursory wave-slope statistics."*^ A similar system with limited angular range (± 8.6°) was deployed with a mechanically damped mount from the bow of a ship, and produced qualitative surface-roughness measurements and suggestions of fractal ocean waves.'*''*^

In the interest of providing new techniques that could be operated successfully in the field, especially for measuring the characteristics of cm-waves that are resonant seasurface features for microwave sensors, NOAA/ETL personnel tested several new techniques. Polarization imaging of backscattered light from a searchlight was successful in the laboratory for measuring slopes in artificially turbid water."*^ A searchlight source eliminated the troublesome dependence on background radiance distribution, and pixelby-pixel ratios of orthogonally polarized light eliminated uncertainties in the incident irradiance. However, initial night-time field tests were troubled by excessive glints from insects attracted to the bright searchlight.

Somewhat similar to moire fnnge projection, which has seen one application^ in a laboratory setting, L-k lidar'*'"^ is a new and interesting approach that could be especially useful for measuring the time and space evolution of a particular ocean wavenumber. This technique involves projecting two overlapping laser beams with

slightly different wavenumbers ( k ) onto the ocean surface. When the resulting interference fnnges match a surface wave, the backscattered power is modulated at a frequency determined by the optical frequency difference and the velocity of the ocean wave. The measured modulation frequency gives the wave's phase velocity, and the modulation depth yields the wave amplitude. By varying the size of the projected

19

interference fringes, measurements conceivably could be made over a range of ocean wavenumbers. Though recent progress at NOAA/ETL with a A-fc lidar design based on an acousto-optic modulator is promising,®' vibration sensitivity and numerous other engineering issues need to be resolved before field deployment will be practical.

A careful review of these references leads to the conclusion that ideal instruments for field measurements of short ocean waves under a variety of conditions should: 1) use artificial illumination to remove sky-radiance dependencies; 2) be mgged and compact; 3) avoid disturbing the surface (i.e., not be refractive), and 4) be affordable and reasonably simple, the latter being important to expedite reliable scientific results.

In accordance with these objectives, I have developed a reflective scaiming-laser glint meter and a video laser-glint imager, and deployed them on the Scripps Institute of

Oceanography's FLoating Instrument Platform (FLIP) in the Pacific Ocean, near the

Oregon coast during September 1995. The scanning-laser glint meter provided angular laser-glint counts, from which I have calculated sea-surface slope probability density functions (PDFs), and investigated fractal characteristics of sea-surface roughness. The video laser-glint imager recorded two-dimensional glint images, which provide new insights into the fractal characteristics of sea-surface roughness, and the encoding of

surface-roughness information in glint-image wavenumber spectra.

This dissertation is organized in the following manner. Chapter 2 describes the

20

instruments developed in this project and the experimental deployment on the FLIP, including a summary of the supporting measurements of wind vectors, air-water temperature differences, and long-wave heights. Chapter 3 summarizes the sea-surface slope statistics measured by the scaiming-laser glint meter. These results confirm the Cox and Munk model, and improve it by adding a dependence on atmospheric stability

(essentially air-water temperature difference). Chapters 4 and 5 address more speculative approaches to characterizing sea-surface roughness. Chapter 4 explores the fractal characteristics of laser glint counts, which could lead to fractal surface models containing realistic roughness. The glint-count histograms and power spectra contain evidence of nonlinear wave-wave interaction, and the glint-count fractal dimension appears to vary in a manner consistent with the stability-dependent mean-square slope. Chapter 5 examines glint-image power spectra and autocorrelations for surface-roughness information. The spectra are found to contain dominant information about glint sizes, leading to the conclusion that glint-image spectral techniques may be useful for retrieving surface curvature. Reasonable agreement between measured and simulated glint-image power spectra encourages further refinement of the simulation technique. Chapter 6 contains recommendations for future sea-surface roughness measurements, and summarizes the results.

21

2. INSTRUMENT AND EXPERIMENT DESCRIPTION

Measuring sea-surface roughness requires solving some interesting problems. In his classic book about wind waves on the ocean surface,"

Kinsman

described the problem well: "The measurement of waves at sea is notoriously difficult. They change rapidly, and it is hard to find a place to 'stand' while you measure." The purpose of this chapter is to describe two instruments that I built for measuring ocean-surface roughness, and to explain how I found 'a place to stand' while making those measurements.

Both instruments developed in this project detect laser glints from specular regions on the surface, but they do so in a different manner for different purposes.

Sections 2.1 and 2.2 describe the instruments and their estimated radiometric performance, and section 2.3 describes an experiment conducted with those instruments in the Pacific Ocean, near the Oregon coast, in September 1995. The latter section describes the deployment of the optical package and summarizes the supporting measurements of wind vectors, air-water temperature differences, and long-wave heights.

2.1 Scanning-Laser Glint Meter

2.1.1 Hardware

The laser glint meter technique develops slope statistics by counting laser glints from specular facets as a laser beam is scaimed over the ocean surface. Table 2.1 summarizes the key characteristics of the scanning-laser system, shown schematically in

Fig, 2.1. As indicated in this figure, a 10-mW HeNe laser beam is directed by a spinning mirror onto the ocean surface in a linear scan along an azimuth set by the user

22

azimuth motor roller bearing electronics box receiver cross-scan mirror primary scan mirror primary scan motor housing

Figure 2.1 Line drawing of the scanning-laser glint meter, showing the primary optical and mechanical components. The instrument is suspended from a boom with a system of two mounting plates connected with crossed aircraft cables; the azimuthal orientation of the optical package is set with a computer-controlled azimuth motor, coupled to the optics package with a 30-cm-diameter bearing.

23

with a computer-controlled stepping motor. The intermediate cross-scan mirror is driven by another computer-controlled stepping motor to compensate for cross-scan instrument tilts. Motion along the scan direction is compensated for by shifting the angular bin locations where glints are counted in the computer. Instrument tilts in both axes are measured by inclinometers with 2-Hz bandwidth.

Table 2.1 Summary of the Laser Glint Meter Hardware

Laser power

Laser wavelength

Laser far-field divergence

Detector

Detector [email protected] 1 kHz bandwidth

Entrance-pupil diameter

Receiver optical filter bandwidth

Receiver lens

Receiver optics transmission (

t

J

Receiver field of view

Mirror rotation rate

Glint sampling rate

10 mW

632.8 nm

1.18 mrad

UDT 455 photodiode

8 X 10-" W

23 mm

10 nm

F/4.3,100-mm focus

= 0.4

25.4 mrad

2 rev/sec, adjustable

0.1 "/sample (nadir ± 75 ")

Glints (specular reflections) from the surface are detected by a receiver consisting of an f/4.3 lens with a 100-mm focal length, a 10-tmi-bandpass interference filter, and an integrated photodiode-preamplifier combination. Mounting the receiver next to the laser

24

introduces parallax into the optical system, but in the prototype instrument this approach was used for simplicity, particularly to avoid complications related to using coated beam­ splitter optics in a marine environment. An amplifier following the preamplifier provides computer control of the system gain. Figures 2.2 and 2.3 are schematic diagrams of the receiver and the digitally controlled amplifier circuitry, respectively. The computer digitizes the output signal at a rate of 0.1 ° per sample, and compares each sample with a threshold value to classify it as "glint" or "no glint." The signal is sampled over a 150° range centered on nadir, but the scan mirror is mounted on the shaft of a DC motor and rotates continuously through 360°. To reduce data-storage requirements, glints are counted in 1 ° bins. Therefore, the data stored by the computer consists of glint counts in

1 ° bins for nadir ± 75 ".

Reflective markers of 1 ° angular extent near the beginning and end of the digitized scan facilitate angular calibration to account for motor speed variations, which I measured to be ^ 5% from scan to scan. Motor speed variations during a single scan produce errors that are smaller than the final 1 ° resolution of the glint histograms.

The azimuthal orientation of the optics module is controlled remotely with a computer-controlled stepper motor. Azimuth is measured with respect to a reference position which is recognized when an LED, mounted on the rotating portion of the instrument, is detected by a photodiode mounted on the stationary mounting plate. The cross-scan mirror finds a reference position in a similar manner. Figure 2.4 is a schematic diagram of the opto-electronic circuitry that provides reference positioning to the azimuth and cross-scan stepper motors.

UDT455

Detector

Output

Figure 2.2 Schematic of the scanning-laser glint meter receiver. The detector and preamplifier are an integrated package.

25

Odtctor

Signal

0.1 tt

•15 V-

X

Input

OHiit

Ad|.

•10K

-15 V-

-IN

.IN

QA2 ncr

•VS

•VS

AD524

Output

OHsit

Adi.

RGI

10

100

SEN

VOUl

10 K

39.2K i-AAAr

9.09K h-A^

2K

Gain « 2

-A/yv

.^vyvSiiL-s

Gain «10

6 i 4

Gain t

000

001

010 oil

100

101

110

111

Gaini

1

2

5

10

20

SO

100

200

Qain

Cantrai

Ofliit

Adj.

1 K

Naii-z

00

01

02

VIN.

VIN-

0 . S . AOJ

voin

FORCE

FOBK

-15 V-

SIQ. QNO

V-

V* J_ +15 V—-y—

I

0.1 u 0.1 tt

Output

.Signal

Figure 2.3 Schematic of the digitally controlled amplifier that follows the receiver preamplifier. This amplifier allows the user to set the system gain with the computer.

26

.047 U

'"78n.';

+15 V

VIN VOUl

GND

Cross-Scan Mirror

Reference Sensor

TIL33

-15 V

+15 V

TL074

.047 u

TIL33

+5 V

.5 Watts

Azimuth Reference

TIL33

-15 V

+15 V

TL074

3.9 K

-15 V

+15 V

TL074

3.9 K

-15 V

+15 V

TL074

27

Figure 2.4 Schematic of the opto-electronic position references for the azimuth and crossscan mirror stepper motors. The azimuth reference position is marked by an LED and sensed by a photodiode when the motor is in the correct position; the cross-scan mirror reference position is marked by a photodiode that detects the HeNe laser beam.

28

2.1.2 Radiometry

Radiometric analysis of the glint meter signal requires consideration of the surface curvature. In this section, I use geometrical optics to derive a first-order signal-to-noise equation for estimating the radiometric performance and design limitations of a laser-glint instrument. The model treats specular ocean-surface facets as anamorphic mirrors in the plane transverse to the optical axis, so that each facet has maximum curvature, C„ in the along-wind axis, and minimum curvature, Cj, in the cross-wind axis of the transverse plane. Cj is computed from C, using the wavenumber-independent form of the wavespectrum azimuthal (i|r) dependence,^'

0.25 C..

(2.1)

The result is preferential spreading of the laser beam in the along-wind axis. Concave and convex curvatures produce similar results because the curvature radii are much shorter than the instrument-to-surface distance.

This approach also assumes that the laser beam encounters at most one wave facet at any given angle. This assumption and the anamorphic-mirror model both are generally appropriate only for waves whose wavelength is larger than the laser beam spot size at the surface. When the instrument is at height H above the surface and pointed at nadir angle

0, the laser spot diameter at the surface is equal to the initial beam diameter plus the product of the laser far-field divergence angle o) and the range to the surface (height H divided by the cosine of the nadir angle 0),

29

<xiH

cos(0)

(2.2)

Thus, for = 6 m and (1^=1.5 mm, the laser spot size is 8.5 mm at 0 = 0°, 9.3 mm at 0 =

25°, 12.5 mm at 0 = 50°, and 28.8 mm at 0 = 75°. So, for the nadir-angle range of about

±25°, where the highest slope probabilities occur (see Chapter 3), the assumptions are valid for cm and larger waves.

For a surface with optical power <|) = -2C, the paraxial ray-trace equations predict the angle u' and transverse distance y' from the optical axis for a ray that has been reflected through distance t after being incident with angle u and transverse distance y

(see Fig. 2.5 for the geometry):

u' = u - y ^ .

(2.3) and

y' = y + u ' t .

(2.4)

Combining these two equations for a ray normally incident at distance y from the optical axis inclined at nadir angle 0, the transverse distance at which the ray will intersect the entrance-pupil plane at height H above the surface is given by

(2.5)

The reflected light beam is elliptical, due to the two different surface curvatures.

glint meter

30

Figure 2.5 The distances and angles used in the signal-to-noise calculation are shown here. The different along- and cross-wind surface curvatures cause the laser spot to spread out into an elliptical beam with dimensions d, and dj.

Representing the orthogonal beam diameters by J, and the irradiance of the reflected

31

laser beam (for surface reflectivity R ~ 0.02) at the entrance-pupil plane is

" 1^-

e.6)

The power detected by the receiver, Pj, is equal to the irradiance in Eq. (2.6) multiplied by the entrance-pupil area and the optics transmittance;

P = E X

° 4

= ^o^^laser^ep

'

(2.7)

To express this equation for detected power in terms of more elementary parameters, first J, and are each replaced by 2y' from Eq. (2.5) using Q and Cj, respectively, then 2y is replaced by from Eq. (2.2). The resulting equation for the detected laser power is

P .

=

.

( H H d^+

cos(0).

"••o ^ ^laser^ep

1 + -

I C M

COS(0);

1 +

2C^H

COS

(0)^

(2.8)

For uniform background radiance Lxt,, the surface curvature can be ignored because the same background is reflected into the field of view by waves of all slopes.

Thus, the di^se-background power detected in a solid angle Q^ through the entrancepupil area Agp with a spectral bandwidth A Ais

32

(2.9)

Expressing Aep and in terms of receiver parameters, and writing the radiance in terms of irradiance - En/u), Eq.(2.9) becomes

Pb = 16/2 ' for detector diameter D^, entrance-pupil diameter D^, and receiver-lens focal length /.

For a noncircular detector, is the detector area and a factor of 7t/4 is removed.

In terms of the detected laser and background powers and the detector noiseequivalent power (NEP), the signal-to-noise ratio is given by

SNR = \QLog

10

(

P,

NEP+P^

(2.11)

Figure 2.6 shows the night-time signal-to-noise ratio estimated in this fashion for the parameters listed in Table 2.1 and H = 6 m, plotted as a fimction of nadir angle for various typical curvature values.'^ A weak curvature of C = 10'^ m"' would be present at very low wind speeds 2 m s*'); C = 10 m"' is expected for wind speeds - 2-3 m s"';

C ~ ICP m*' is perhaps the most typical of these curvature values, being appropriate for wind speeds ~ 3-8 m s*'; C = 10^ m"' occurs for cm waves at higher wind speeds, ~ 8-10 m s '; C = 10^ m"' represents extreme curvature, significant only in the tiniest of capillary waves at wind speeds exceeding 10 m s '. Thus, Fig. 2.6 shows that the scanning-laser

33

CQ

X3

CE

Z

CO

C,= 103 ni-1

-20

-40

0

1 0

20

40

nadir angle (deg)

50

60

70

Figure 2.6 Signal-to-noise ratio for the scanning-laser glint meter operating 6 m above the surface at night. Each line is for the annotated value of surface curvature.

system can make night-time measurements of cm waves to greater than 40° slopes. As described in Chapter 3, this range easily captures the most significant slope statistics.

Day-time operation of the present system is impossible because direct or diffuse solar irradiance is stronger than a laser glint for nearly any combination of curvature and nadir angle. Fumre systems may be able to operate in a diffuse solar background through a combination of better optical shielding, a narrower receiver filter, a narrower detector field of view, higher laser power, and coherent detection. Both calculations and field experience show that moon glints are not a significant problem.

2.2 Video Laser-Glint Imager

2.2.1 Hardware

The video laser-glint imager records images of diode-laser glints on videotape at a standard 30-Hz rate. A small array of diode lasers illuminates the same region on the ocean surface that is viewed by a charge-coupled-device (CCD) camera. Each pixel of the imaging chip in the camera views a portion of the surface at a different angle; when a local surface element is perpendicular to the light propagation axis, the corresponding pixel receives a bright glint of backscattered laser light. Thus, an image consisting of a collection of glints on a dark background contains information about the surface structure in the area being viewed. The surface-height spectmm is related to the glint spectrum, as discussed in Chapter 5.

As summarized in Table 2.2 and Fig. 2.7, the system consists of a CCD camera, an array of diode lasers, an electronics package containing the power supplies and laser-

35

computer with frame grabber

CCD camera diode laseis

Electronics

Figure 2.7 Simplified line drawing of the video laser-glint imager system, consisting primarily of a diode-laser array, a CCD camera with a 10-nm-bandpass interference filter, video timing and laser-modulation electronics, and a frame grabber in a control computer.

The entire system is housed in a small metal box on the side of the optics package shown in Figs. 2.1 and 2.11.

modulation electronics, and a frame grabber in a control computer. Continuous video is also recorded on a Super-VHS video recorder. The Pulnix TM-745E camera has no

Automatic Gain Control (AGC), in order to maintain the glint-image contrast without attempting to balance the exposure between the bright glints and the dark background.

This camera also has a high gamma factor, which enhances the contrast between glint and non-glint image regions. The lens has a 50-nmi focal length and an f/1.8 maximum aperture.

Table 2.2 Summary of the Video Laser-Glint Imager Hardware

Laser power

Laser wavelength

Laser far-field divergence

Camera

Camera sensitivity

Camera field of view

Pixel field of view

Effective number of pixels

Pixel size

Entrance-pupil diameter

Camera lens

Optical filter bandwidth

Optics transmission (xj

Video rate

Laser operating modes

30 mW each (120 mW total)

830 ± 2 nm

- 525 mrad x 175 mrad each

Pulnix TM-745E CCD nominally 1 lux

150 mrad x 112 mrad

0.25 mrad x 0.25 mrad

768x493

11 (imx 13 ^m

23 mm

F/1.8,50-mm focal length

10 nm (830 ± 5 nm)

30 frames/sec

CW and 7.5-Hz modulated

37

The field of view of each image pixel from 6 m height covers an area on the surface with dimensions of approximately 1.5 mm. The full camera field of view is

150 mrad x 112 mrad, so from 6 m height the camera images a region approximately

0.90 m X 0.67 m. Though the imaging chip contains 768 x 493 pixels, the data analyzed in Chapters 4 and 5 were digitized at 320 x 240 resolution, yielding an effective square pixel resolution of 2.8 mm per side.

The light source is an array of four AlGaAs diode lasers radiating nominally at

830 nm with an elliptical beam that overfills the camera field of view. The lasers are mounted on a heat sink in a shielded container, maintaining their temperature to approximately 20 ± 10 °C. The resulting wavelength fluctuations are approximately

± 2 nm, well within the 10-nm filter bandpass. The diode lasers are arranged in a tight cluster such that, seen from the sea surface, the source subtends an angular width less than half that of the sun. This reduces the spatial smearing compared with previous imaging methods that use the sun as a light source. Additionally, as is shown in the laserbias schematic of Fig. 2.8, each laser in the array can be turned on and off individually to allow variations of the source brightness and spatial extent.

Each laser radiates 30 mW of optical power, providing a total array output of

120 mW. The video system enjoys the advantage of simple optics, since the uncollimated diode laser beams easily fill the camera field of view. Each laser has an elliptical beam with divergence angles of roughly 175 mrad and 525 mrad. hi the laboratory, I adjusted the bias current (Fig. 2.8) and orientation of each laser to create maximally uniform

+ 5 V

100

2 W

27

2 W

100

2 W

27

2 W

100

2 W

2 W

100

2 W

27

2 W

Laser ON/OFF

Control

LT015MDO 30-(nW

Laser Diodes

IRF630

38

Figure 2.8 Laser-diode bias electronics and modulation switch (power FET at bottom).

39

illumination throughout the camera's field of view.

To aid in assessing and removing the effects of background light, two modes of operation are available: lasers-on and lasers-modulated. In the first mode, all four lasers are on all the time. In the second mode, the lasers are modulated so that successive video frames see full laser illumination followed by no laser illumination. This mode is useful for determining the impact of background light and provides a convenient way of choosing a glint threshold in post-processing of the video images. A typical sequence during COPE was to record a few minutes of modulated-lasers video at the beginning of each tape, and then record the balance of the tape with the lasers full on if the background light level was sufficiently low.

Figure 2.9 shows a schematic of the laser-modulation electronics and a timing diagram for a frame sequence with the lasers on and then off. The first-level input to the modulation electronics is a train of vertical-sync pulses that the frame-grabber board strips from the camera's composite video signal. Each of these pulses marks the beginning of a new field, two of which make up one video frame. A video firame consists of an even field, containing the even-numbered rows of the video frame, and an odd field, containing the odd-numbered rows of the video frame. In this camera, both fields are illuminated for a complete frame time (33.33 ms), but staggered by a field time (16.66 ms). Thus, while an even field is receiving its second field-time of illumination, the previous odd field is being read out. The charges from one field are transferred out of the imaging chip into a shift register at each transfer-gate pulse. For this camera, the transfergate pulse occurs 0.476 ms after each vertical-sync pulse.

40

>cu

74HC76

>cuc

74HC76 74HC76

4047

74HC04

4047

VD

TX-GATE

LASERS

TRIGGER

D D D D LJ] D_

J I I I I I L

Even-Field Exposure

Odd-Field Exposure

Digitize Digitize Digitize Digitize

Even Field Odd IHeld Even Field Odd Field

(ON) (ON) (OFF) (OFF)

Figure 2.9 Schematic of the diode-laser modulation circuitry and timing diagram for a modulated-lasers frame sequence. The input to the electronics is a string of vertical-sync pulses from the camera, and the output is a pulse that turns the lasers on and triggers the frame grabber for a modulated-lasers frame sequence.

Each J-K flip-flop in Fig. 2.9 divides the pulse-train frequency (60 Hz) by two, producing a 7.5 Hz pulse train at the output of the third flip flop. This signal is delayed

0.6 ms by the first 4047 timer, whose output then triggers the second 4047 timer to produce a 15-ms pulse that begins after the transfer-gate pulse and ends before the next frame begins. The IS-ms pulse turns the lasers on for the pulse duration with a power

Field Effect Transistor (FET), and triggers the frame grabber. After the falling edge of the trigger pulse, the frame-grabber board begins digitizing the lasers-on frame at the next vertical-sync pulse. While that frame is being digitized, a lasers-off frame is being exposed without laser illumination. The second frame requires no trigger, but instead is digitized at the next even vertical-sync pulse following the end of the triggered frame.

2.2.2 Radiometry

The radiometric analysis developed in section 2.1.2 applies to the video laser-glint imager with minor adaptations. Most notably, the effective laser irradiance and the detector NEP are not as easily defined. The power output of each diode laser is nominally 30 mW, but the illuminated surface area varies significantly for each laser.

The best estimate is that about 50% of the light falls within the camera field of view.

The camera sensitivity is more difficult to quantify. The manufacturer's rating is

1 lux, determined by reducing the illumination until the l-V maximum video signal is reduced to 300 mV. A lux is defined as 1 lumen m"^, and by definition there are 680 lumens per watt at a wavelength of 555 nm, so at the entrance pupil the equivalent radiometric specification is noise-equivalent irradiance (NEI) = 1.5 mW m"^ (for

42

comparison, night-time illuminance with a full moon is about 0,27 lux = 0.4 mW

Photometric quantities such as lumens and lux are usually scaled by the human visual response at wavelengths other than 555 nm, but here I use no scaling to relate lumens and watts at 830 nm because the CCD spectral response is much flatter over this range than is human vision. This introduces another factor of 2 or 3 uncertainty into this estimate.

For diffuse light, the noise-equivalent radiance (NER) is NEI/TC = 0.47 mW m'^ srThe NEP for a single pixel is found by multiplying the NER by the pixel throughput, equal to the product of pixel area and the solid angle subtended by the entrance pupil at the detector. The solid angle, equal to the entrance-pupil area over the square of the lens focal length, is 0.049 sr, and the resulting pixel NEP is 7x10"'^ W. This agrees well with the results of laboratory experiments with diffuse light, in which the order of 10*'^ W per pixel produced barely discemable images, and the order of 10"® W saturated individual pixels. Thus, a desirable glint signal level is on the order of 1 nW per pixel.

Equation (2.8) from section 2.1.2 applies here as well, with ~ 60 mW, and (o given by the geometric mean of the two primary diode-laser divergence angles listed in

Table 2.2. Then the result of Eq. (2.11) for an f/1.8 lens, the parameters listed in Table

2.2, and the above per-pixel NEP, is a set of curves similar to those in Fig. 2.6 for 0 smaller than 9°. The video curves are equal to the central ± 9" of the scanning-laser curves within the uncertainty of the NEP estimate. The video system has been used primarily at night for recording laser glints, but also for recording sun glints during the day. It also has successfully recorded laser glints with overcast day-time skies, but with more difficulty.

43

Although the design assumed an £^1.8 aperture, in actual deployment the camera had to be stopped down to HA so that the laser glints would remain in focus as the surface height went up and down with the swell. This reduced the detected glint power by a factor of almost 5, making the image contrast less than hoped for, but still sufRcient. In order to better fill the camera's dynamic range at f^4, future systems will benefit from increased laser power, preferably on the order of 1W.

2.3 Measurements in the Pacific Ocean

2.3.1 Deployment of the optical instruments

The first field deployment of the laser-glint instrument package was during the

Coastal Ocean Probing Experiment (COPE) near the Oregon coast in September 1995.

The sensor was suspended from a boom on the FLoating Instrument Platform (FUP) operated by the Scripps Listitution of Oceanography. The FLIP is a research platform that looks like a baseball bat with a big arrowhead attached to the skinny end. After the FLIP is towed to its operating location, air chambers inside its 300-m-long tube are flooded.

The larger-diameter end sinks first, causing the arrow-head-shaped living section to flip

90° into a vertical position, where it resembles the bow of a sinking ship. Figure 2.10 is a photograph of the FLIP, taken from a blimp that was carrying radars and radiometers.

The FLIP was moored 20 km from the Oregon coast, west of Tillamook at coordinates 45° 45.22' N. latimde and 124° 16.9' W. longitude, in 150 m of water. The measurements considered here were taken with the laser-glint sensor roughly 10 m upwind from the FLIP, and are thus unaffected by the platform itself. The height

Fig. 2.10 The Floating Instrument Platform (FLIP) in its vertical position during the

Coastal Ocean Probing Experiment (COPE) near the Oregon coast. The FLIP was moored approximately 20 km West of Tillamook, Oregon in 150-m of water. The laserglint instruments are not shown in this photograph. Picture courtesy of Len Fedor,

NOAA/ETL.

44

45

of the optics module was approximately 5-6 m above the surface.

One of the challenging tasks of this deployment was to design a mounting system that would position the optics at a desired height of 5-6 m above the surface as far from the FLIP as possible, allow the instrument to be brought in and out for adjustments, and minimize wind-induced instrument motion. The resulting mount is shown in Fig. 2.11, consisting of a 1-m-square plate bolted to a boom trolley and another identical plate suspended about 1.5 m below on aircraft cables crossed between comers of the upper and lower plates. The azimuth motor was mounted in the center of the lower plate with the optics package coupled to it with a 30-cm-diameter bearing. This arrangement successfully limited the total instrument motion, including wind-induced and FLIP motion, to less than ± 5° at a rate usually slower than 2 Hz. The motion-compensating cross-scan mirror and along-scan bin adjustments described above successfully compensated for the remaining instrument motion. The final angular uncertainty due to instrument motion and motor speed variations is on the order of a pdf bin width (1 °).

One particularly interesting, but fairly typical, deployment difficulty deserves brief mention. Aligning the receiver to the laser spot at the surface, even with the generous receiver field of view, was extremely challenging. With the instrument winched up close to the hull so that I could reach it, there was nothing near the proper range to use as an alignment target. The instmment could only see an inclined portion of the hull that was too close and too strongly tilted, and the other booms were out of view or at the wrong height. After several futile attempts with sea-spray flying around me in a cold wind as I tried not to drop any more wrenches into the Pacific, the problem was solved when Jim

Fig. 2.11 The laser-glint instrument package deployed during COPE on the port boom of the FLIP. The optics package is the black box attached to the bottom plate of the twoplate mounting structure.

Chumside called to suggest that I use the reflective FLIP life jackets. With the laser pointed straight down at the surface, a helper pulled a life-jacket-on-a-rope through the

47

laser beam while I used glints from the reflective tape to adjust the optical alignment.

2.3.2 Sonic anemometer wind speeds

A sonic anemometer measured wind speed and direction above the port boom at a nominal height of 17 m. For standardization, I adjusted these data to neutral 10-m-height wind speeds through the following relation, derived from a standard logarithmic profile,^

C/,0 = — In

0.4

1

17

OAU,,

(2.12) where

U

I Q

is the wind speed referred to 10 m, U17 is the wind speed measured at 17 m, and u, is the friction velocity measured by the sonic anemometer as the covariance of the stream and vertical air velocities. For the data considered here, wind speeds varied from about I to 10 m s"'.

Figiure 2.12 shows that the wind speeds varied over a large range, but the direction remained fairly constant during the period for which I have analyzed laser-glint data. For several days until September 22 (Julian day 265), winds were calm and warm, blowing from inland. Video data from the end of this particularly calm period, just before and during the gap on day 265 in Fig. 2.12, are analyzed in Chapters 4 and 5.

The rest of the data are with colder, southerly winds. Chapters 4 and 5 discuss

18

CO

—•

14

•a

(D

12

03 o.

CO

"O c

6

c

cc

<D

E

4

2

265 266 267 268 269

decimal days (1995 Julian)

270

360

-

M

271

48

.2 240 —

265 266 267 268 269

decimal days (1995 Julian)

270

271

Figure 2.12 Mean wind speed and direction measured by a sonic anemometer on the FLIP port boom during the days for which laser-glint data are analyzed.

video data from days 266.24 and 269.12 (Sept. 23 and 26), both with -5 ms*' winds.

The scanning-laser glints discussed in Chapters 3 and 4 are from three periods: days

268.33-268.47 (- 3.3 hours), 269.12-269.56 (~ 10.7 hours), and 270.24-270.50 (- 6.2 hours). My instruments ran continuously during the interesting period of steadily increasing wind speed on day 269 until the mean wind speed became so high (~ 12 m s ') that the instrument was in danger of being blown off the boom, the FLIP hatches were locked shut, and no people were allowed outside until the storm subsided. The experiment ended early on day 270 so that the instruments could be removed from the booms and the FLIP retumed to its horizontal position before the next storm arrived.

2.3.3 Radiometric air-sea temperature differences

An elevation-scanning mm-wave radiometer,^^ deployed on the port boom of the

FLIP, measured air-water temperature differences nearly continuously during COPE.

This radiometer uses the high absorption of the 60-GHz (5-mm wavelength) Oj band to measure air temperature in the vicinity of the radiometer and water temperature with a penetration depth of about 0.3 nmi. The advantages of this technique are that it measures the important skin temperature which is intimately coimected with air-sea interaction, and it provides a differential measurement that has higher accuracy and stability than two independent bulk or radiometric sensors can provide.

Figure 2.13 is a plot of the 5-mm radiometer air-water temperature measurements for the period of September 22-27, 1995 (Julian days 265-270), for which laser-glint measurements are analyzed in this dissertation. The period of warm, easterly winds that

4 —

3 —

2 — oi

<D

•a

1 —

as

I I I I I I I I I I I I I I I I I I I I I I I

50

- 2 —

-3 —

265

I I I I I I I I I I I

266 267 268 269

decimal Julian day (1995)

I ' I

270 271

Figure 2.13 Air-water temperature difference measured by an elevation-scanning mmwave radiometer on the FLIP port boom. Positive values correspond to positive stability, and negative values correspond to negative stability.

ended on day 265 produced strong positive air-water temperature differences, whereas during the other measurement times, the differences were mostly negative.

Only recently has the importance of atmospheric stability, characterized by the airwater temperature difference," been recognized for ocean-surface roughness. Shortly after the effects of stability were recognized in radar data,'® suppression of the meansquare slope by positive stability (air warmer than water) was identified in refractive laser-slope-gauge data.^ Enhancement of the mean-square slope by negative stability (air colder than water) was predicted,^-'' but not measured before now. Recently, similar effects of stability on microwave polarimetric radiometers have been noted.®

There are many different parameters used to represent stability." A common one is the Richardson number, which I use briefly to relate my results to previous work.'*" A reduced Richardson number is given as

" 7 - f , 2 • w z

( 2 . 1 3 ) where g is gravitational acceleration (9.8 m s'^), z is the height at which the mean wind speed, is measured (10 m), is the mean water temperature, and is the air-sea temperature difference. The stability parameter that I prefer is the ratio of air-water temperature difference to the mean 10-m wind speed It was proposed by

Wu" for describing stability of the air-sea interface and is adopted here for its simplicity and completeness. Wu^' applied this parameter to optical and microwave mean-square slope measurements and discussed its relation to other conunon parameters such as the

Monin-Obukhov length. Both Ri and neutral cases, and negative for unstable cases. are positive for stable cases, zero for

52

2.3.4 Sonar long-wave heights

An ultrasonic sonar mounted on the optics package at the entrance-pupil plane recorded the mean height above the surface for each scan. The sonar beamwidth is ± 5°, producing a spot diameter at the surface of about 1 m. These data are primarily for measuring swell height during the glint measurements, and investigating modulation of short waves by long waves. For the measurements discussed here, the swell had periods of about 12-16 s, heights between 1.5 and 3.5 m, and directions that were reasonably stable from the east-southeast.

Figure 2.14 is a surface-height power spectrum computed from a 1-hour time series of sonar data, smoothed with a 40-point moving average. The peak near -1.1

(0.08 Hz) indicates swell with a period near 13 s. Waves smaller than the swell follow the theoretically predicted f'^ power spectrum, shown as a dashed line, reasonably well.

53

slope = -3

- 2

- 1

log(f)

Figure 2.14 Power spectrum of surface heights measured by an ultrasonic sonar mounted on the side of the laser-glint instrument package. Swell, with a period of approximately

12.6 s, is indicated as a spectral peak near -1.1 (0.08 Hz). The dashed line indicates the theoretical -3 slope.

3. SEA-SURFACE SLOPE STATISTICS

3.1 Overview

Cox and Munk"-^ used sun-glitter photographs to derive the most comprehensive sea-surface slope statistics as a function of wind speed to date. Their measurements covered a wind-speed range of 1 to 14 m s ', with neutral and positive stability. By interpreting the optical density in sun-glitter photographs as the probability of a specular slope, Cox and Munk derived a slope probability density function (PDF) and studied the wind-speed dependence of its first four moments. They reported bulk air and water temperatures, but did not investigate the effects of atmospheric stability.

The Cox and Munk results are as follows: the mean-square slope depends linearly on wind speed; skewness has a slight tendency to increase with wind speed; and peakedness (excess kurtosis relative to a Gaussian PDF) shows no significant correlation with wind speed. The ratio of cross-wind to along-wind mean-square slope shows no wind-speed correlation, and varies from 0.54 to 1.00 with a mean value of 0.75. The variability is apparently due to wind fluctuations. PDF skewness occurs for along-wind slopes because wind waves lean downwind when the wind pushes on their upwind faces; however, no skewness exists for cross-wind slopes that experience no direct wind forcing.

Cox and Munk mentioned several uncertainties that are clarified by my measurements. First, they suggested that systematic errors in their background-light correction may have contributed significantly to the PDF peakedness. Second, uncertainties in their photographic grid alignment made it difficult to specify the skewness value and its dependence on wind speed. Third, shadowing of sunlight by steep

55

waves limited their measurements to slope angles less than 27°, leaving questions about the influence of steeper slopes on the PDF.

Not very many ocean measurements have been compared carefully with the Cox and Munk slope statistics. Refractive laser slope gauge (RLSG) measurements taken by

Hughes et al.^ in sheltered waters near Vancouver Island under calm, positive-stability conditions, agreed well with the Cox and Munk model. A subsequent set of RLSG data taken in the open ocean by Tang and Shemdin^' included mean-square slopes that were much larger than predicted by the Cox and Munk model. Haimbach and Wu"^ gave a cursory comparison using a reflective scanning-laser system mounted on a pier. They showed reasonable agreement with the Cox and Munk model, and mentioned the possibility of a stability effect. Hwang and Shemdin'" used a RLSG to show that the mean-square slope is suppressed by positive stability, and to provide hints that negative stability might increase the mean-square slope.

The scaiming-laser glint measurements reported in this chapter provide signifrcant validation and clarification of the Cox and Munk results, and also add a negative-stability dependence that is extremely important. Measurements of the mean-square slope agree with those of Cox and Munk at near-neutral stability, but exceed them by as much as a factor of two for negative stability. Skewness and peakedness also agree well, except that

I find a weak wind-speed dependence for peakedness. My results for the dependence of skevraess and peakedness on stability are original: skewness is very weakly correlated with stability, whereas peakedness is much more strongly correlated and tends to increase with negative stability (i.e., peakedness depends on stability in a fashion similar to that of

56

the mean-square slope). Finally, neither skewness nor peakedness exhibit more than very weak correlation with mean-square slope.

3.2 Gram-Charlier Series

Before I could calculate slope statistics from the measured PDFs, it was necessary to correct the data from each scan for motor-speed variations. This was an unintentional consequence of using a DC motor for the primary scan mirror, so future designs should consider other motor options (perhaps a stepper motor would work). The angle correction involved identifying the signature of each reflective marker near the ends of the scan, referencing these points to the known marker angles, and adjusting the remaining bin locations uniformly between the markers. I averaged 2200 sequential scans

(20 min) into glint-count histograms, and normalized them to obtain slope PDFs.

Figure 3.1 shows a typical along-wind slope PDF (solid line) plotted as a function of slope angle with respect to nadir; positive slopes are downwind, and negative slopes are upwind. Also shown is a Gaussian (dashed line) with the same mean and variance.

Despite the general Gaussian appearance of the measured PDF, significant deviations are apparent. These differences, which carry important information about the surface roughness, can be described by coefficients of skewness and peakedness (i.e., excess kurtosis relative to Gaussian).

Because wind-driven waves tend to lean downwind, the scanning laser encounters more large-angle glints when pointed at the steeper downwind faces of the waves. This results in a net negative skewness in the along-wind PDF toward downwind (leeward)

0.04

0.03 a>

•a

0.02 o.

0.01

(upwind)

(downwind)

0.00

-40 30

20

10

0

1 0 slope angle (deg)

20

30

40

Figure 3.1 Measured along-wind slope probability density function (solid line) and a

Gaussian with the same variance (dashed line). Skewness toward positive (downwind) slopes is evident, due to wave asymmetry.

57

58

slopes in comparison with a symmetrical Gaussian. No significant skewness is expected in a cross-wind PDF because there is no wind-driven asymmetry. Figure 3.2 shows a typical cross-wind PDF and its corresponding Gaussian. As expected, there is no obvious skewness, but there is a significant difference in peakedness. Because of deployment difficulties, I have only a small number of cross-wind measurements, so subsequent discussion is limited to the along-wind PDFs.

In an approach similar to that of Cox and Munk,^ I computed a Gram-Charlier series®' ®^ to obtain an analytical estimate of each measured PDF. To simplify the polynomials, I expanded the PDFs in terms of a normalized slope,

=

0 - 0

, (3.1) where 0 is the slope angle with respect to nadir, 0 is the mean slope angle, and a is the measured PDF standard deviation. The series representation of the slope PDF is then c_

PeCTl) = I^-7ff„(n)Gauss(Ti), n

=o n!

(3.2) where Gauss(r|) is a zero-mean, unit-variance Gaussian,

/ \

Gauss(T|) = —^exp

I 2 ) v/2ti

(3.3)

H„(r[) are the nth-order Hermite polynomials listed in Table 3.1, and c„ are expansion

0.05

0.04 w 0.03

c

0)

•O

>%

CO

o 0.02

Q.

0.01

0.00

-40 -30 -20 -10 0 10

slope angle (deg)

20 30 40

Figure 3.2 Measured cross-wind slope PDF (solid line) and a Gaussian with the same variance (dashed line). There is no apparent PDF skewness.

59

coefficients computed by the following summation of the measured slope-PDF values:

60

C. = EPDF(t|;ff,(li;. (3.4)

Given that

H

Q

= \ , E q . ( 3 . 2 ) t a k e s t h e f o r m o f a s u m m a t i o n o f a b e s t - f i t G a u s s i a n p l u s higher order terms that correct for skewness and kurtosis (odd terms are related to skewness, even terms are related to kurtosis).

3

4

1

2

5

6

7

8

n

0

Table 3.1 Hermite Polynoinials of Order n

Hnin)

1 n

Ti'-i ri'*-6Ti^ + 3

Ti^- 10TI^+ 15TI

Ti®- 15ti^ + 45Ti^- 15

V - 2111^+ 105TI^-10511

Ti» - 2811® + 210ii'» - 420TI^ + 105

Some of the measurements are not as clean as those shown in Figs. 3.1 and 3.2.

"Bumps" and "wiggles" on the PDF are caused by random count fluctuations, breaking waves, interfering background light, sea gulls flying or floating through the beam, or mooring lines blocking part of the beam. Especially when excessive bumps and wiggles

occur in the tails of the PDF (as they usually do), the mean-square slope is determined

61 adequately, but the higher order moments are not. fo these cases, the Gram-Charlier representation does not converge. For such measurements, the higher-order moments were not used.

Figure 3.3 shows an example of one of the better Gram-Charlier PDF expansions, with Fig. 3.4 showing the corresponding normalized error. This error is the difference between the estimated PDF and measured PDF, divided point-by-point by the measurement uncertainty of each PDF bin. By Poisson statistics, the latter uncertainty is simply the square root of the number of glints counted in that bin normalized by the total number of counts in the histogram. Thus, a normalized error with magnitude of the order one means that the residual differences between the measured PDF and estimated PDF are on the order of the statistical noise in the PDF measurement, and therefore further terms in the series are insignificant. The normalized error in Fig. 3.4 shows outstanding convergence, with nearly the entire angular range of the PDF being estimated by the

Gram-Charlier expansion to within one standard deviation of the glint-count process.

The series-expansion for the estimated PDF shown in Fig. 3.3 includes terms up to n=8, but roughly 90% of the correction is contained within the n=3 and n=4 terms. Note that these are the first nonzero correction terms, since c, and C2 are both zero because the mean and variance have been fixed to match the measured PDF. For nearly all wellbehaved measurements, expansion to n=4 brings the normalized error to within 2-4 glintcount standard deviations, expansion to n=6 brings the normalized error to within 2-3 glint-count standard deviations, and expansion to n=8 brings the normalized error to

62

0.00

-40 -30 -20 -10 0 10

slope angle (deg)

20 30 40

Figure 3.3 Measured along-wind slope PDF (solid line) and the corresponding PDF calculated with a Gram-Charlier series (dashed line).

63

2 —

1 H -

2 0

o

-1

..

-2 —

-3

-40

-20 0

slope angle (deg)

20

-

40

Figure 3.4 Normalized error of the estimated PDF in Fig. 3.3, equal to the difference between the measured and estimated PDF values, divided by the statistical uncertainty of the measured PDF. A normalized error of ± I or less means that the Gram-Charlier series estimates the measured PDF to within the statistical uncertainty of the measurement.

64

within 1-2 glint-count standard deviations. Further terms carry no statistically significant information.

Because they carry the majority of the information, I use the third- and fourthorder Gram-Charlier coefficients (C3 and C4) to represent skewness and peakedness, respectively. Due to the form of the Hermite polynomials, C3 is a scaled third central moment and C4 a scaled fourth central moment of the PDF. Use of the normalized angle

rj produces the exact scaling required to equate to the coefficient of skewness," and C4 to the coefficient of kurtosis,"

. ^"4

"

W12

(3.6) where represents the xth-order central moment. Because £4 = 3 for a Gaussian, the peakedness with respect to a Gaussian is given by the coefficient of excess,®

Y = C4 - 3. (3.7)

Table 3.2 summarizes the scanning-laser results discussed in this chapter. It lists, when available, the key parameters associated with stability, the along-wind mean-square slope (Cg^), PDF skewness

(C3),

and PDF peakedness iy). Each measurement is a 20-min average, corresponding to 2,200 laser scans.

Table 3^ Scanning-Laser Data Summary (blanks indicate no available data)

Julian day 1995

268

269

270

Start time

OJTC)

0538

0558

0618

0638

0646

0706

0726

0742

0802

0822

0848

0908

0928

0959

0306

0326

0346

0403

0423

0443

0503

0518

0754

0814

0834

0854

0914

0934

0954

1014

1034

1054

0246

1019

1039

1102

1122

1142

1202

1222

1242

1308

0545

0648

0708

0916

1102

1122

1142

Ujo u«

Cms"') (ms"')

AU

(»C)

Tw C3

Y

5.76

5J4

0.21

0.19

-0.904

-0.951

17.06

17.00

0.039

0.035

1.967

2.117

5.20

5.11

0.18

0.16

-0.969

-0.929

16.99

16.99

0.032

0.031

-0.022

-0.151

1.885

2.075

4.69 0.15 -0.809 16.96 0.029 -0.027

4.91

5.05

4.71

0.12

0.18

0.22

-0.848

-0.827

-0.851

16.94

16.92

16.92

0.031

0.031

0.031

-0.005

-0.063

2.464

2.028

1.884

0.012 2.395

4.85 0.21 -0.878 16.91 0.034 -0.079

5.31 0.20 -0.817 16.95 0.025

-0.131

4.03 0.23

2J75

1.334

17.41 0.025 -0.017 0.752

4.38 0.26

4.68 0.28

4.04

0.24

4.91 0.20

17.37

17.39

17.39

17.34

0.024

0.023

0.030

0.024

-0.014

-0.003

0.121

-0.033

0.786

0.868

1.317

0.778

5.19

5.13

5.14

5.38

5.99

6.44

5.99

5.63

5.03

0.20

0.16

0.12

0.15

0.17

0.10

0.09

0.14

5.68 0.17

0.34 -0.581

17.31 0.025 -0.244 1.110

17.28 0.024 -0.084 0.711

17.29 0.024 -0.129

17.28 0.031 -0.154

1.215

1.689

17.24 0.030 -0.206

17.20 0.029 -0.019

1344

1.022

17.19 0.028 -0.148 1.113

17.12 0.029 -0.159 0.986

17.12

17.08

0.030

0.029 -0.053

4.66 051 -0.559 17.05 0.027 0.021

4.87 0.45 -0.820

17.08

0.029 -0.215

4.42

0.23 -0395

17.10

0.031 -0.121

4.63

0.17

-0.180

17.09 0.026 -0.250

4.51 0.20 -0.098

17.07

0.018

4.99

0.20 -0.215 17.06 0.027 -0.023

5.51 0.25 -0.343 17.09 0.028 -0.190

1.190

1.326

1.094

1.688

1.373

1.230

1.339

2.113

1.092

1.130

1.280

1.291

0.761

6.46 0.25 -0.415 17.12 0.02S -0.079

6.17 0.27 -0.491 17.12 0.031 -0.188

5.9 0.23 -0.473 16.99 0.032 -0.342

7.47 0.08 -0.757 17.02

0.039 -0.139

7.87 0,14 -0.833 17.02

0.037 -0.088

8.76 0.30 -0.871 16-99

0.038 -0.030

8.61 0.27 -0.864 17.01 0.043

-0.150

8.59 0.31 -1.036 16.92 0.038 -0.035

8.74 0.29 -1.065 16.91 0.042 -0.186

9.37 0,28 -1.120 17.00 0.046 -0.156

7.28

0.33

-0.045 16.14

0.034

8.38

0.34

-0.113

16.54 0.035

8.22 0.33

-0.0063 16.53 0.046

8.23 0.27

0.634 15.41 0.023

8.84 0.30

0.661 15.46 0.028

9.01

0.28

9.05 0.32

0.535 15.53 0.029

0.528 15.58 0.031

0.717

0.980

0.369

0.846

1.092

2.225

2.002

65

66

3.3 Mean-Square Slope

Figure 3.5 shows the measured along-wind mean-square slopes as a function of

C/,0. Statistical fluctuations of the mean-square slope measurements are within the size of the symbols on the plot; the dominant uncertainty is a 5-15% standard deviation of the wind speed over the 20-min measurement time. In Fig. 3.5 the squares correspond to near-neutral stability and the dots correspond to negative stability (air-sea temperature difference between -0.1 and -1.1 °C). The dotted line is the Cox and Munk linear regression for along-wind, clean-surface mean-square slope, measured with near-neutral stability; the solid line is a linear regression through my negative-stability data. The few laser-glint data points taken during near-neutral stability agree well with the Cox and

Munk regression, demonstrating the essential validity of the laser-glint technique. The more numerous points taken under negative stability are significantly higher than the Cox and Munk regression.

Figure 3.6 shows the wind-speed dependence of along-wind mean-square slopes measured by several techniques. Data from the laser glint meter are shown as dots; data from Hwang and Shemdin's'"' refractive laser slope gauge are shown as crosses; and data from Cox and Munk's^"-^ sun-glitter photographs are shown as triangles. The increased scatter in both of the later data sets compared to the Cox and Munk data is due largely to wider ranges of stability. This is illustrated in the next several figures, which plot the ratio of along-wind mean-square slope, and the Cox and Munk along-wind meansquare-slope regression value,o^^, vs. the two different stability parameters introduced in section 2.3.

67

0.05

0.04 —

CO

0.03 —

0.02 —

0.01 —

Cox-Munk

0.00

U,„(m s" )

Figure 3.5 Wind-speed dependence of the along-wind mean-square slope measured by the scanning-laser glint meter for negative (dots) and near-neutral (boxes) stability. The dashed line is the Cox and Munk along-wind mean-square slope regression line; the solid line is a regression through my data.

68

0.05 —

0.04 —

CO

0.03 —

0.02 —

0.01 —

0.00

0 2 4 6 8

-1,

Uio (m s )

10 12 14

Figure 3.6 Wind-speed dependence of the along-wind mean-square slope measured by my scanning-laser glint meter (dots), Hwang and Shemdin's refractive laser slope gauge

(crosses), and Cox and Munk's sun-glitter photographs (solid triangles).

Figures 3.7 and 3.8 are plots of the normalized mean-square slope, o^ta^, for my data vs. stability. Only the measurements for which air-sea temperature differences were available are included in these plots. The trend of increasing mean-square slope with increasing negative stability is clear in both of these figures. The linear regressions shown as solid lines through these figures are given by

= 1.31-3.54Ri, -0.22 sRi^ 0.060

(3.6) and

= 1.32-3.64

Ar

U

10 ;

Ar

-0.19^—^^0.077.

U,

(3.7)

Fig. 3.9, my data are combined with Hwang and Shemdin's^ data in a similar plot vs. the stability parameter

AT

^

JU

IQ

. The corresponding plot vs. Ri is similar, but has more scatter because of the increased uncertainty of bulk water-temperature measurements.

Figure 3.9 demonstrates the similarity, but opposite sign, of the effect that moderately positive and negative stability have on mean-square slope. For strong positive stability, the mean-square slope suppression becomes constant; such a saturation effect for negative stability was not observed within the range of my measurements.

The solid lines in Fig. 3.9 represent approximate best-fit lines that describe the ratio of along-wind mean-square slope to the Cox and Munk regression for along-wind mean-square slope (a^^^) as a function of stability. The corresponding equations are:

70

Figure 3.7 Stability dependence of the normalized along-wind mean-square slope, using a generalized Richardson number. The ratio on the ordinate is the scanning-laser glint measurement of the along-wind mean-square slope, divided by the Cox and Munk regression.

71 ca ca

CO

2.6

2.2

0.6

-0.20 -0.10

0.00

0.10

Figure 3.8 Stability dependence of the normalized along-wind mean-square slope, using the ratio of air-water temperature difference to the mean wind speed.

72

2.6

2.2

1.8 —

CVi

£ o

1.4 —

C\J

ea

1 . 0 — — — — — — —

0.6 —

0.2

-0.2 0.0 0.2

^^a-w / '-'lO

0.4 0.6

Figure 3.9 Stability dependence of the normalized along-wind mean-square slope from my scanning-laser glint meter (dots) and Hwang and Shemdin's refractive laser slope gauge (crosses), using the ratio of air-water temperature difference and mean wind speed.

— = 1.42-2.80

2

\

-0.19 <

at;

^<0.28

73

(3.8) and

a.

— = 0.65,

_2

(3.9)

Note that inclusion of Hwang and Shemdin's data results in a slightly larger intercept and moderately smaller slope than is obtained from my data alone. Also, Eq. (3.8) has a value larger than unity at neutral stability

IQ

= 0) because the Cox and Munk data were collected under primarily positive stability, so they have slightly smaller mean-square slopes than would occur under more neutral stability. In fact, after removing two curiously large values, the remaining clean-suiface Cox and Munk measurements have an average value of 0.16 for the stability parameter

(3.8) has a value of unity at agreement with this, Eq.

= 0.14, equal within experimental uncertainty to the average Cox and Munk stability.

3.4 Skewness

Figure 3.10 shows the weak wind-speed dependence of the skewness coefficient,

C3, for along-wind measurements. Only data for which the higher order moments are well behaved, as discussed in section 3.2, are plotted here. More of the measurements at high wind speeds had unstable higher moments than those at low wind speed. This suggests

Figure 3.10 The PDF skewness exhibits only weak correlation with wind speed.

74

that part of the problem could be either extraneous large-angle signals from breaking waves, inadequate sampling of extremely steep slopes that occur more frequently at high wind speeds, or simply a degradation of signal-to-noise ratio because of the higher surface curvamres that occur at higher wind speeds. The edited data cluster in the

4-6 m s"' wind speed range, with only a few points at higher wind speeds. All but three of the data points have negative skewness, as expected from the wave asymmetry discussed earlier, but there is wide scatter in the data plotted vs. wind speed. The resulting linear regression of Cj with wind speed is

C3 = 0.0101 - 0.0170 C/10 ± 0.087 (r=-0.21).

(3.10)

The small value of r, the intercept standard error of 0.0830, and especially the slope standard error of 0.0154, show that this trend is statistically very weak, but still signifrcant. Note that my result is 60% lower, but still within the statistical uncertainty of, the Cox and Munk result.

A similar result exists for the dependence of skewness on stability, shown in Fig.

3.11, which contains fewer data points than Fig. 3.10 because air-sea temperature differences were not available for every PDF. Again, wide scatter exists in the data, but a statistically significant trend does exist (the standard errors are 0.049 for the intercept and 0.365 for the slope):

C3 = -0.147 - 0.490 ± 0.079 (r=0.29).

(3.11)

0.1

1 1 1 1

1 1 1 1 1 1 r 1 1

1 ' '

TT"

-

-

CO

O

0.0

-

2

(D

O

O

CO

CO

<u c: a>

CO

-0.1

-

-

-0.2

-

-

_

• •

-

-

-

-

-

-0.3

1 1 1 1

-0.25

1 1 1 1 1 1 1 1 1 i 1 1 1 i 1 1 1 1 1

-0.20

-0.15

-0.10

-0.05 0.00

AT a-w

/ U i o

76

Figure 3.11 The PDF skewness is only weakly correlated with atmospheric stability.

Without assigning excessive value to these weak statistical correlations, it is fair to say

77

that stability is at least as important as wind speed in determining the value of skewness, but neither effect dominates in these measurements.

3.5 Peakedness

The peakedness (excess kurtosis), y. is positive for these measurements because each measured PDF has a higher peak value rhan the corresponding Gaussian. The plot of Y vs. UiQ in Fig. 3.12 shows that, similar to skewness, there is a weak but statistically significant linear correlation of peakedness with wind speed. Peakedness tends to decrease with increasing wind speed, which may be related to a general trend toward a broad, isotropic PDF at high wind speeds. The linear regression shown in Fig. 3.12 (with standard errors of 0.3391 for the intercept and 0.0559 for the slope) is given by

Y

= 1.8804-0.0834

f/jo

± 0.543 (r=0.23).

(3.12)

A much more significant correlation exists between peakedness and stability, as shown in Fig. 3.13. Both linear and exponential fits are shown in this figure. The linear fit, however, has a slightly larger correlation coefficient than the exponential fit. The corresponding regression equations are

0.2945 -9.199

/

AT. ,

\

I

± 0.032 (r=-0.70) (3.13) or

3.0

'

' 1 ' 1 ' 1

1

-

2.0

• •

1 . 0

• • •

• • •• •

• • •.

-

' M l

T

• •

-

0.0

1 1 1 1 1 1 1 1 1 1 1 1 1 -1

8

1 0

U i o ( m / s )

78

Figure 3.12 The PDF peakedness exhibits only weak correlation with wind speed.

3.0

I I 1 I I I I I I I I I I I I I I I I I I I

79

2.0 —

1.0 —

0.0

I I I I

-0.25

I I 1 I

-0.20

I I I I

-0.15

I I I I

-0.10

-0.05

• ' '

0.00

^^a-w ^ ^10

Figure 3.13 The PDF peakedness is strongly correlated with atmospheric stability.

ln(Y)

= -0.4631 -5.968

f \

a-w

± 0.367 (r=0.59). (3.14)

The standard errors of the regression intercept and slope, respectively, are 0.2576 and

1.902 for Eq. (3.13), and 0.2240 and 1.654 for Eq. (3.14). Regardless of which leastsquares curve is chosen, the point is clear that stability must be considered in order to define the peakedness adequately in a sea-surface slope PDF. Over the range of negative stability encountered during this measurement period, the peakedness coefficient varies by a factor of four, and the neutral-stability intercept (at = 0) of Eq. (3.13) suggests that y might vary by as much as a factor of seven over this range extended to neutral stability.

It is interesting that the neutral-stability intercept of Eq. (3.13) is y = 0.29 ± 0.26, very close to the Cox and Munk peakedness coefficient, = 0.23 ± 0.41 (found independent of wind speed but not analyzed as a function of stability). Recognizing that the Cox and Munk measurements were made under near-neutral (but slightly positive) stability, I propose that the Cox and Munk result is actually an average near-neutralstability peakedness value. It will be interesting to see what peakedness looks like as a function of positive stability in future data.

3.6 Discussion and Suimnary

Given that the mean-square slope depends on both wind speed and stability, it is reasonable to ask whether or not skewness or peakedness can be determined by the mean-

81

square slope alone. Figures 3.14 and 3.15 indicate that, in fact, skewness and peakedness are both only weakly correlated with the mean-square slope. The linear regression shown in Fig. 3.14 (with standard errors of 0.1392 for the intercept and 4.446 for the slope) is given by

C3 = -0.2349 + 4.8120^ ± 0.0809 (r=0.24), (3.15) and the linear regression in Fig. 3.15 (with standard errors of 0.6818 for the intercept and

20.31 for the slope) is given by

Y = 2.505-31.12 o, ± 0.566 (r=0.29). (3.16)

Since the mean-square slope alone is insufGcient to determine skewness or peakedness, it is possible that there is yet another important physical parameter. I have already shown that peakedness is significantly correlated with the stability of the air-water interface, but have not yet found a strong correlation of the skewness magnitude with any physical process.

These measurements from a scanning-laser glint meter of sea-surface slope statistics have provided new results regarding the dependence on wind speed and stability for sea-surface-slope probability density moments. These results agree with the classic work of Cox and Munk, with several important exceptions. First, my measurements show that negative stability strongly increases the mean-square slope. Second, my data have a weak linear correlation between peakedness and wind speed, whereas Cox and

Munk found no statistically significant correlation.

82

0.1

0.0 —

-0.1 —

-0.2 —

-0.3

0.024

J I L

J.

J I L

i

I L

0.028 0.032 0.036

' ' •

0.040

mean-square slope, 0^2

Figure 3.14 The PDF skewness is not determined by the mean-square slope alone.

3.0

2.0

'

'

t

1 -

1—

••

^ 1.0

0.0

0.02

t

0.03 i .. 1.

0.04

mean-square slope, <5^

1

0.05

Figure 3.15 The PDF peakedness is not determined by the mean-square slope alone.

84

Several uncertainties left by the Cox and Munk measurements have been clarified by my measurements. My PDF peakedness and skewness results are close enough to theirs to minimize concerns they had about removal of background light and alignment of the photographic grid. Similarly, my measurements at angles larger than 27° did not change their results significantly.

These are the first measurements of slope-PDF skewness and peakedness as a function of stability. In summary, these data show that skewness is only weakly correlated, but peakedness is strongly correlated with stability. Peakedness of the slope

PDF is affected by stability in a similar fashion as is the mean-square slope; peakedness increases as the stability becomes increasingly negative. Finally, neither skewness nor peakedness can be determined sufficiently by the mean-square slope alone.

85

4. FRACTAL ANALYSIS OF LASER GLINTS

4.1 Overview

Fractals, as first formalized by Mandelbrot,^ generally can be described as geometrical structures having similar characteristics over a range of scales. That is, a fractal process has no characteristic size (or time) scale, bstead, it is characterized by a fractal dimension, which describes how wiggly the structure is relative to its smooth

Euclidian counterpart. Essentially, the fractal dimension replaces the geometric length, which approaches infinity for a fractal that consists of wiggles upon wiggles on increasingly small scales, with a number that instead quantifies the degree of irregularity of the wiggly surface. The fractal dimension can be related to the spectral exponent (P) of an inverse-frequency power spectrum that varies with frequency if) according to/' ^ over some spectral range.®^ The fractal dimension of such a process in E Euclidian dimensions is related directly to the log-log power-spectrum slope by®®

D ^ E * i ± .

(4.:)

Thus, a (one-dimensional) time series has a fractal dimension of 2.5 for random "white" noise (P = 0); 2.0 for a l/^process (P = 1), and 1.5 for a Brownian process (P = 2).

The recent literature refers to an impressively large and varied collection of fractals in nature,®^'^ including coastlines, clouds, snowflakes, galaxies, and ocean waves.

Two approaches have been taken for smdying the fi^tal characteristics of ocean-wave

processes. The first approach is to calculate the fractal dimension of the dynamical attractor, which describes the evolution of the process in phase space.®'"® The second approach is to calculate a fractal dimension of the process itself.'""''^ I adopt the second approach, and calculate the fractal dimension of glint-count time series. These time series are related to sea-surface roughness, and are shown to contain useful information regarding nonlinear wave-wave interactions. Other workers have applied similar fractal approaches to wave heights,™" images of breaking-wave regions,^*'" and time series of laser glints from the ocean surface."*^ These processes have different fractal dimensions and scale ranges because they depend on different physical processes.

My scanning-laser data set provides an opportunity to confirm the fractal results obtained with a similar scanning-laser glint sensor by Zosimov and Naugolnykh;^ the glint video data set provides further insight into the glint-count process and its fractal characteristics. The number of glints is equivalent to an integral of the product of the surface curvature and the slope probability density function over the appropriate angular range. Thus, the glint-count variability can be considered to be a measure of the surfaceroughness variability, and therefore related to both wave-slope and short-wave variability.

I first examined the glint counts for low-frequency variability on scales longer than the wave correlation time. For well-developed waves, the correlation time is approximately equal to the period of the dominant wind-wave at wind speed C/,o,

g

87 with

g

representing the gravitational acceleration, 9.8 m s*^. Wind speeds for the measurements considered here ranged between I and 6 m s ', with both positive and negative atmospheric stability. Although one instrument provides a one-dimensional measurement, and the other a two-dimensional measurement, the low-frequency results from both instruments are surprisingly similar. For the video data, the faster sample rate allows investigation of an additional high-frequency variability. The separation of the low- and high-frequency variability regimes occurs in the vicinity of the dominant windwave frequency.

Zosimov and Naugolnykh^ analyzed low-frequency variability in time series of laser glint counts from a ship in the tropical and sub-tropical Atlantic under steady trade winds (8-10 m s"' wind speeds). With the ship steaming into the wind, they scanned a narrow HeNe laser beam ± 8.6° from nadir in the cross-wind direction, at a rate of 25 Hz, and counted the number of glints occurring per second over the entire angular range. The resulting glint-count time series, at scales longer than the wind-wave correlation length, maintained a similar variance when the averaging and counting times were increased by an order of magnitude. Therefore, the process did not conform to Gaussian or Poisson statistics, for which the variance is expected to reduce in proportion to the averaging time.

This apparent statistical self-similarity was manifested further in the glint-count power spectrum, which had a well-defined/" form between about 0.02 and 0.2 Hz. As has been pointed out by several authors,®^*®®*"'^ an/" ^ power spectrum is inherently selfsimilar, and is therefore a common indicator of a fractal process.

Zaslavskii and Sharkov'''counted the average number of breaking waves in areas

of various sizes, from the correlation length (40 m for their conditions) to about five or six times larger. Their results exhibited a power-law dependence on the linear dimension of the area, with an exponent of 0.5. The processes investigated in ref. 44 and ref. 74 are both related to large-scale variability of wind waves, and the similarity of their resulting spectral exponents is interesting. However, it is difficult to draw precise conclusions from this comparison because of the inexact correspondence of the processes; particularly because in one case the data were in the form of a one-dimensional time series, whereas in the other case the data were in the form of a two-dimensional count plotted against linear dimension.

The scarming-laser results reported here are sufficiently similar to those of

Zosimov and Naugolnykh''^ to validate the generality of their results for large-scale surface-roughness variability. I find much larger influence of swell on the shape of the glint-count power spectra, most likely due to larger swell in my experiment than theirs.

My laser-glint image data exhibit a nearly identical fractal dimension for large-scale variability (frequencies lower than the dominant wind wave), and also demonstrate a similar fractal behavior, with smaller fractal dimension, for small-scale variability

(frequencies higher than the dominant wind wave). My large-scale variability spectral exponents for both one-dimensional and two-dimensional glint counts are close to

Zaslavskii and Sharkov's'^ value of 0.5, but smaller than Zosimov and Naugolnykh's^ result of 0.86. Furthermore, the glint images produce nearly identical fractal results with either a pixel-counting or a blob-counting approach, implying a true fractal characteristic that is somewhat independent of counting technique.

89

An additional result that becomes mote apparent as the averaging time increases is that for both instruments, the glint-count histograms are approximately lognormal. The existence of a lognormal histogram is related to the glint-count process arising from a series of multiplicative, interdependent, sequential events, which in turn suggests a fractal, or self-similar, process.'^''

The following sections present fractal results for the scanning-laser glint meter and the video laser-glint imager. I conclude this chapter by summarizing the results and suggesting some future applications and extensions of this work.

4.2 Scanning-Laser Glint Counts

The scanning-laser glint meter records the number of glints above a threshold value in 1 ° angular bins for nadir angles out to ± 70°. However, for comparison with the previous work of Zosimov and Naugolnykh,"*^ the results in this section were processed by forming time series of the total number of glints ± 10° from nadir, and examining the behavior of the corresponding histograms and power spectra on various time scales.

There may be some difference between these data and those of Zosimov and Naugolnykh because these are along-wind scans, and theirs were cross-wind scans.

Figure 4.1 shows two ± 10° scaiming-laser glint-count time series. On scales larger than the dominant wind-wave period, these time series have variances that do not reduce significantly as the averaging scale and measurement time are increased by an order of magnimde. Figure 4. la contains 5 min of 1-s samples, and Fig. 4. lb contains 50 min of 10-s samples. This statistical self-similarity of the glint-count process, and

90

CO c

3

O

0

^ 60 K

O) k-

0}

CO iS 30 H

O)

CO o

CO

0 —

60 120 180 time (s)

240 300

90

- 300

6 0 0 1200 1800 time (s)

2400

3000

Figure 4.1 Scanning-laser glint-count time series that exhibit self-similarity: (a) 5 min of

1-s counts; (b) 50 min of lO-s counts.

therefore of the surface-roughness variability, is demonstrated further in Fig. 4.2, which

91

shows histograms for the two glint-count time series of Fig. 4.1. Whereas Gaussian statistics predict a variance of Fig. 4.2b that is smaller by a factor of 10''^ than that for

Fig. 4.2a, in fact, the difference is much smaller, less than a factor of two. This behavior occurs consistently in the entire data set, regardless of wind speed, atmospheric stability, or sea state.

As the averaging time increases, the apparently lognormal histogram shape becomes more and more skewed. Indeed, this is not surprising because longer averaging times allow the low-probability tail to be sampled more completely. The lognormal shape of the histograms is important because lognormal processes arise when completion of a task depends on prior completion of many steps." It is reasonable to think of the growth process of ocean waves as such a process, where energy is continuously exchanged between waves of different scales. The fact that this implies nonlinear wavewave interaction over a large range of waves is both interesting and important. An additional interesting possibility is that there is a scale time associated with the nonlinear wave-wave interactions, so the histograms become more lognormal as the averaging time approaches and exceeds that scale time. This, however, is purely speculative at present.

A power spectrum is shown in Fig. 4.3 for a 75-niin time series of 2-Hz laser scans, taken with C/,o = 5 m s"' and near-neutral stability. The peak near 0.07 Hz represents swell, and corresponds well to the 12-16 s swell periods measured by the collocated sonar system. The strength of the swell peak varies throughout these data, but

Fig. 4.3 is reasonably typical. Zosimov and Naugolnykh's^ power spectra show no

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c

<D w_ w.

3

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15 —

1 0 —

(D

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3

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5 —

0 —

ou

20 40

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glint count (s )

60

u

80

92

glint count (s' )

Figure 4.2 Histograms of the scanning-laser glint counts in Fig. 4.1: (a) 5 min of 1-s counts; (b) 50 min of 10-s counts.

2.8

I I I 1 I I I 1

I I I I I I I I I I

93 w

c

a>

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07

O.

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k.

(D

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^ slope = - 0.47

1.6

-2.0

I I I I

i ' ' ' ' i ' ' ' ' I ' ' ' '

•1.5 -1.0 -0.5

0.0

log(f)

Figure 4.3 Power spectrum of a scanning-laser glint-count time series containing 9000 samples. Each sample is the number of glints within ± 10° of nadir in a single scan. The peak near -1.15 (0.07 Hz) is due to swell. The dashed line shows the slope chosen (-0.47) for the low-frequency slope in this example.

94

obvious swell features, and they recall calm seas (IC Naugolnykh, personal communication). The fact that my power spectra do exhibit a swell peak suggests the important possibility that information about swell modulation of short waves is contained in these simple glint counts. An important consequence is that measurement of the fiill slope probability density function or mean-square slope may not be necessary for studying long-wave modulation of short waves.

In Fig. 4.3, an/' ^ type of spectrum exists between approximately 0.01 Hz and

0.20 Hz. The slope (P) chosen for this particular spectrum is 0.47, shown in Fig. 4.3 with a dotted line. The values of P for the full data set are 0.56 ± 0.05. This is nearly identical to Zaslavskii and Sharkov's result'* of 0.5, and is similar to Zosimov and Naugolnykh's result of 0.86 for approximately the same frequency range.''* Also similar to the results of

Zosimov and Naugolnykh, my glint-count power spectra tend to continue increasing at scales even longer than 100 s. Such behavior and the/" ^ spectral density both suggest surface-roughness variability over scales much larger than the wind-wave correlation length.

According to Eq. (4.1), my scanning-laser data produce a fractal dimension of the low-frequency glint-count process equal to 2.22 ± 0.11. A fractal dimension of 2.22 implies a highly wiggly curve for the scanning-laser time series, significantly less random than white noise (D = 2.5), but more random than a pure 1//process (D = 2.0). Zosimov and Naugolnykh's result"* of D = 2.05 (P = 0.86), while similar to mine, is closer to a pure l/|f behavior, and Zaslavskii and Sharkov's result'* of D = 2.25 (P = 0.5) is statistically equal to mine.

4.3 Video Laser-Glint Counts

The video fractal analysis is based on time series of frame-by-frame glint counts from the 30-Hz video records. Operating the video glint imager with flashing lasers, as was discussed in section 2.2.1, provided a convenient way to choose a glint threshold in post-processing of the video images. A few minutes of video with the lasers flashing at the start of several tapes provided sufficient statistics from which an appropriate threshold of 11 (on a scale of 0 to 255 digitization levels) was selected. Background light and noise fluctuations smaller than the threshold were set to zero, and any pixels with magnitude larger than 11 were set to one and counted as a "glint" pixel.

I used two different techniques to count video glints. In the first case, I counted the number of glint pixels in each video frame, while in the second case, I counted the number of blobs, or glint regions, in each frame. A blob is any grouping of glint pixels that are connected horizontally or vertically. From time series of these pixel or blob counts, I analyzed the behavior of the corresponding histograms and power spectra under a variety of conditions and temporal averaging periods.

As with the scanning-laser data, the video glint-count histogram variances reduce by no more than a factor of two for an order of magnitude change of averaging scale and measurement time. Because of the video data's higher temporal density, the lognormal histogram shape becomes apparent more rapidly than it does for the scanning-laser data.

However, the lognormal distributions firom both instruments are similar for an equal number of data points. Figure 4.4 shows a histogram for a 9000-point video glint count

(5 min of 30-Hz video). This curve is representative of all the histograms for long time

30

CO

(D

O c

<D

3

O

o o

20

(D

10

C

0

0 300 600

video pixel glint count

900

Figure 4.4 Glint-count histogram for 9000 frames (5 min) of video laser-glint images.

Each sample is the number of glints in the camera field of view (8.7° x 6.4°) for one video frame. The distribution is approximately lognormal.

96

averages of data from both instruments. The best-fit lognormal density function for glintcount rig in this example measurement is

P .

=

1

\/27c(1.2)n. exp

/ \

In

I 160/

2(1.2)

(4.3)

The lognormal characteristic of the histogram in Fig. 4.4 is demonstrated further in Fig. 4.5, which is a plot of the integral of the normalized histogram on a probability scale vs. the logarithm of glint count. The nearly linear behavior verifies that the glint counts are indeed lognormally distributed.

Video glint-count power spectra differ from the scanning-laser glint power spectra in two notable ways; first, the higher video sampling rate extends the video spectrum to higher frequencies; and second, the video power spectra tend to roll off instead of continuing to increase in magnitude at the lowest frequencies (below about 0.001 Hz).

This second difference may not be significant, though, since the extremely low-fi:equency tails can be affected by slow changes in the electronics, and they indeed seem to rise less rapidly for shorter scaiming-laser time averages. As shown in Fig. 4.6 for a typical video g l i n t - c o u n t p o w e r s p e c t r u m a t l o w w i n d s p e e d ( i / m = 1 m s" ' ) , t h e s a m e t y p e o f f ^ behavior that I found in the scanning-laser spectra exists over a similar frequency range

(= 0.01-0.3 Hz), and an additional region with obvious/'^ form is also evident in the higher-frequency region of approximately 1.5-15 Hz. The slopes chosen for the two regions are shown in Fig. 4.6 with offset dotted lines.

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3

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0.10 —

0.05 —

0.01 —

10

« I I I I I I I

100

I I I I I M i l

1000

glint counts (s'^)

Figure 4.5 Cumulative probability distribution plotted on a probability scale against the glint-count logarithm. The resulting nearly linear shape indicates that the glint counts obey an approximately lognormal probability density.

98

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99

Figure 4.6 Power spectrum of a 9000-sample (5 min) video glint-count time series. The slopes chosen for the low- and high-frequency spectral exponents are shown by dashed lines. The multi-peak feature from -0.30 (0.5 JIz) to 0.04 (1.1 Hz) is the signature of dominant wind waves for a wind speed fluctuating between 1.5 and 3 ms''.

100

Wind-speed fluctuations between 1.5 and 3 m s"' also are indicated clearly in the power spectrum of Fig. 4.6. The feamre covering the range of approximately 0.5-1.1 Hz contains multiple peaks that correspond to dominant wind waves for several wind-speed values between 1.5 and 3 ra s"'. No strong swell feature is apparent in Fig. 4.6, though my logbook indicates the presence of 1—1.5 m swell. Video glint power spectra at other times contain obvious swell peaks near 0.07 Hz. However, these other data contain a combination of higher wind speeds (= 6 m s"') and larger swell (= 2-3 m), which makes it difficult to separate out the two effects.

The video glint-count results are surprisingly similar for both pixel and blob counting, which is yet another manifestation of glint-count self-similarity. Fig. 4.7 is a scatter-plot that compares the spectral exponents derived by pixel and blob counting. The crosses indicate low-frequency (0.01-0.3 Hz) spectral exponents, and the circles represent high-frequency (1.5-15 Hz) spectral exponents.

There are two distinct clusters of high-frequency exponents, and two less-distinct clusters of low-frequency exponents in Fig. 4.7. This appears to be evidence of stability or wind-speed dependence. The measurements in the smaller-exponent clusters have the highest wind speeds (~ 6 m s"'), and also have the strongest negative stability (determined by the air-sea temperamre difference) of all the measurements. For those three points, the air-sea temperamre difference was -2.5 "C, whereas for the other measurements it was between +3.2°C and -O-e'C. The stability is apparently the most significant factor here because of two reasons: 1) from the results of section 3.3, such strong negative stability increases the surface roughness by nearly a factor of three over the neutral-stability

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0.5

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pixel-count spectral exponent

2.0

Figure 4.7 Scatter plot of spectral exponents resulting from blob and pixel counting.

Crosses are for the low-frequency spectral region; dots are for the high-frequency spectral region. The data for the three points that have the smallest exponents in both frequency regions are from measurements under extremely strong negative stability. This suggests that the spectral exponent depends on surface roughness variations due to stability.

102 roughness at the same wind speed, and 2) other measurements, with 5 m s"' wind speeds but near-neutral stability, produced exponents very close (although at the smaller end) to the higher cluster of data points. The fractal dimensions calculated from Eq. I are summarized in Table 1 for the different cases of low- and high-frequency exponents with strongly negative and near-neutral-to-positive stability.

Table 4.1 Summary of Glint-Count Fractal Dimensions

scanning laser video pixels: stability « 0 video pixels; stability ^ 0 video blobs: stability « 0 video blobs: stability ^ 0 low-f dimension

2.22 ±0.11

2.43 ±0.07

2.20 ±0.07

2.42 ±0.09

2.25 ±0.10 high-f dimension

NA

2.21 ±0.08

1.80 ±0.07

2.13 ±0.02

1.70 ±0.05

It seems reasonable for the spectral-exponent magnitudes to become smaller with increasing surface roughness (which occurs for both higher wind speeds and increasingly negative stability) because the smaller exponent denotes an increasingly random process.

In the limit of a zero-value spectral exponent, the process is purely random "white-noise."

Visually, the glint video records at the highest wind speeds are dramatically more random, with much weaker glints, than the highly organized patterns that appear at the lowest wind speeds. At wind speeds near 1 m s ', for example, the glint patterns form bright loops that slowly open and close in rather mesmerizing fashion (see Fig. 5.1).

103

Such circular patterns have been described theoretically and experimentally for sun glitter by Longuet-Higgins/® and aesthetically for reflections of street lights and moonlight by

Minnaert' and Lynch and Livingston.^

4.4 Discussion and Summary

More work is needed to quantify the relationship between the fi^tal dimension of the glint-count process and a quantitative measure of surface-roughness. However, an interesting comparison arises from noticing that the surface-height power spectrum in

Fig. 2.14 also shows fractal behavior in its long/ high-frequency tail. For this value of

P = 3, the time-series fractal dimension is D = 1.0, corresponding to a Brownian process.

A surface with an/'^ height spectrum should have an/"^ slope spectrum, producing D = 1.5. Except for the extremely strong negative-stability cases, the highfrequency part of the glint-count spectrum has an average slope of P = 1.4 for pixel counting and p = L6 for blob counting — about 25% smaller than the expected slopespectrum value. The corresponding fr^tal dimensions are D = 1.8 for pixels and D » 1.7 for blobs, just larger than that for the theoretical surface-slope fractal dimension.

The fact that the glint-count process has a similar fractal dimension as the surface slope, over essentially the same frequency range, confirms that the high-frequency portion of the glint-count spectrum contains wind-wave information that is similar to that obtained by measuring slope statistics. The low-frequency region is more closely related to large-scale variability of short waves, and hence, surface roughness. It therefore provides information beyond that contained in the theoretical surface spectrum.

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The fractal process formed by counting laser glints from ocean waves is a robust one that allows repeatable detection with a variety of measurement techniques. The fractal evidence found along the trail of glint-count time-series analysis provides new ways of thinking about and modelling the glint process, and hence, surface-roughness.

For example, if a reliable connection can be found between the fractal dimension and usefril physical observables such as wind speed or stability, this type of simple glint counting could be used to provide useful new data from compact and robust instruments.

Furthermore, a fractal surface model possibly could provide the geometric input to calculations of electromagnetic-wave interactions with a realistically rough ocean surface.

Repeating such calculations while systematically varying the input variables could yield valuable new insight into radar scattering, microwave polarimetric emission, and other ocean-sensing techniques.

In summary, the results of this chapter verify that the fractal behavior of the glintcount process, first pointed out by Zosimov and Naugolnykh,^ appears to be quite general. The low-frequency variability of glints, beyond the correlation scale of the dominant wind waves, shows that traditional slope statistics do not entirely characterize the surface roughness. The additional evidence of long-wave modulation and nonlinear wave-wave interaction that exists in the glint-count histograms and power spectra provides further practical motivation for pursuing this topic. In the video data, I have identifled a similar high-frequency fractal process at scales smaller than the dominant wind wave. For both scale ranges, but more obviously for high-frequency variability, the glint-count fractal dimensions appear to be sensitive to stability and wind speed.

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5. SPECTRAL ANALYSIS OF LASER-GLINT IMAGES

5.1 Overview

One motivation for developing the video laser-glint imager was to determine how glint-image spectra are affected by siirface roughness, with the hope of ultimately learning how to retrieve surface spectra from glint-image spectra. In this chapter I identify spectral characteristics of laser-glint images that are related to surface roughness, and show that autocorrelations might be useful in future studies. Finally, I show onedimensional spectra that are simulated using a surface-height-spectram approach augmented with my stability-dependent model of mean-square slope. This method produces results that are similar to the measured spectra.

5.2 Measured Laser-Glint Images

Video glint images recorded with a rough surface look fundamentally different than images recorded with a calm surface. At low wind speeds the glints tend to be relatively large and bright; at high wind speeds they become smaller and weaker because of the larger surface curvature. The spacing between glints generally becomes smaller with higher wind speeds because of the increased density of steep, short waves. Indeed, the glint spacing produces most of the surface-slope information in the glint-image power spectra discussed in this chapter.

Figure 5.1 illustrates the visual differences in laser-glint images: the top image is from an extremely calm surface {U ~ I m s ', positive stability), and the bottom one is from a much rougher surface (C/ = 6 m s'^ negative stability). These images are averages

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Figure 5.1 Time-exposed laser-glint images for a calm (top) and rough (bottom) sea surface. Each image is an average of 9 frames. The smooth surface generates glints that are large, bright loops, whereas the rough surface produces smaller and weaker glints.

107 of 9 video frames, to {^proximate what the eye sees on a video monitor. Furthermore, for printing clarity, the images are presented as negative images. The smooth-surface image on the top of Fig. 5.1 is an excellent example of the closed-loop glint patterns mentioned in section 4.3, which were predicted theoretically by Longuet-Higgins.™ The roughsurface image on the bottom of Fig. 5.1 demonstrates the dramatic difference that occurs in glint size and spacing when the surface roughness increases.

Glint-image power spectra are affected mainly by three glint characteristics. First, the sizes of individual glints determine the overall high-frequency spectral shape, and arc related primarily to surface curvature. Second, the variations of glint brightness contribute spurious fluctuations across a wide spectral range, and depend primarily on surface curvature. Third, the spacings between glints contribute spectral variations within the range considered here, dependent on the surface-slope distribution. The first effect is always present, the second is undesirable in most applications and can be removed by thresholding the glint images before spectral processing, and the third produces a slopedependent signal.

Figures 5.2-5.6 show average power spectra for the five video data segments analyzed in Chapters 4 and 5. The spectra in these figures are averages of 7200 singleframe power spectra from each data sequence. Each single-frame spectrum was calculated from a square (256-pixel x 256-pixel) image that was obtained from the thresholded glint image by truncating it in the x axis and zero-padding it in the y axis, and multiplying it by a Hanning window function. Li thresholding, I set any image pixel with a value greater than 11 (on a scale of 0-256) to one, and set all pixels with lower values

108

Figure 5.2 Power spectrum of the smoothest-surface glint image measured on Julian day

265 at 1010 UTC (see Table 5.1). The axis is along-wind, and ky is cross-wind.

109

Figure 5.3 Power spectrum of the glint image measured on Julian day 265 at 1005 UTC

(see Table 5.1). The fc, axis is along-wind, and ky is cross-wind.

110

Figure 5.4 Power spectrum of the glint image measured on Julian day 265 at 0700 UTC

(see Table 5.1). The axis is along-wind, and ky is cross-wind.

I l l

Figure 5.5 Power spectrum of the glint image measured on Julian day 269 at 0250 UTC

(see Table 5.1). The axis is along-wind, and ky is cross-wind.

Figure 5.6 Power spectrum of the roughest-surface glint image measured on Julian day

266 at 0546 UTC (see Table 5.1). The axis is along-wind, and ky is cross-wind.

112

to zero. The figures are presented in order of increasing surface roughness, as summarized in Table 5.1. Recall that surface roughness increases linearly with wind speed (C/), increases additionally with negative atmospheric stability (- AT^), and decreases with positive atmospheric stability. In all of these spectra, fc, is the wavenumber in the along-wind axis, and ky is the wavenumber in the cross-wind axis.

113

Table 5.1 Summary of the Video Data Analyzed in Chapters 4 and 5

Julian day time (UTC) :/(ms-')

265

1010-1015 0.9

265

265

1005-1010

0700-0705

1.5

2.2

269 0250-0255

266 0546-0551

5.2

6.0

3.56

2.13

1.36

-0.13

-0.42

0.00185

0.00308

0.00452

0.02925

0.04930

Oy'

0.00138

0.00231

0.00339

0.02193

0.03697

A comparison of these spectra illuminates systematic variations with surface roughness. Most notably, increased surface roughness generally causes energy to be moved from low to higher spatial frequencies, in agreement with the observation that a rougher surface creates glints with closer spacing. Figures 5,7 and 5.8, which show central and Ay slices through the three-dimensional spectra, help identify several other features. The slices are numbered in order of increasing surface roughness. Curves 1,2, and 3 have similar conditions of low wind speeds (- 1-2 m s"') and negative stability, whereas curves 4 and 5 are for higher wind speeds (~ 5-6 m s ') and positive stability.

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Figure 5.7 Along-wind central slices through the measured glint-image power spectra shown in Figures 5.2-5.6. The curves are labeled from 1 to 5 in order of increasing surface roughness.

114

0

-200

' '

-100

' '

0

ky

(m-1)

' I

100

I

200

Figure 5.8 Cross-wind central slices through the measured glint-image power spectra shown in Figures 5.2-5.6. The curves are labeled from 1 to 5 in order of increasing surface roughness.

In these measured spectra, the total energy of the thresholded glint images first

116

increases with surface roughness (curves 1 and 2), and then decreases (curves 3-5).

There are two causes of the total energy reducing as roughness increases. First, the rougher surface has higher curvature, which causes more of the glints to fall below the threshold, reducing the fractional glint coverage in the thresholded image. Second, the rougher surface produces smaller glints, which also reduces the fractional pixel coverage.

Notice also that the spectral densities in Figs. 5.2-5.8 are approximately three times larger at the high-frequency ends of the ky slice than the slice. This factor increases monotonically from 2.5 in Fig. 5.2 (curve 1 in Figs. 5.7 and 5.8) to almost 4 in

Fig. 5.6 (curve 5 in Figs. 5.7 and 5.8). This asymmetry is too large to be caused by the upwind-crosswind asymmetry of surface roughness, but instead is caused by taking the transform of a glint streak instead of a glint spot. The glints illuminate a line of pixels as they move along the wind direction during a single frame exposure time. The velocity required to move a glint through three pixels during a frame exposure time is approximately 0.2 m s"', which is almost exactly the dominant glitter-point velocity reported in the literature recently."

Because each frame of the glint-image video contains glints that tend to be rectangular, about one pixel wide in the cross-wind axis and three pixels long in the along-wind axis, the resulting spectra have the "pup-tent" spectral shape that is evident in

Figs. 5.2-5.6. The circular synmietry in Fig. 5.9, which is the power spectmm of a white dot on a black background, verifies that the azimuthal asynunetry is not a processing artifact.

Figure 5.9 Power spectrum of a white dot in the middle of a black background. The processing in this canonical test is the same as for the glint images.

117

118

From this argument, it becomes clear that the overall spectral shape is dominated by the glint size, which is related most strongly to surface curvature. Glint spacing, which is related mainly to surface slope, contributes energy to the middle of the spectral range in no easily identifiable manner. Because of this domination of the glint-image spectra by the glint sizes, this instrument that was designed to look at surface slopes appears better suited to smdying surface curvature. However, in order to do so, the instrument needs to have higher spatial resolution to resolve presently unresolved glints, and would benefit also fr^om higher laser power to make the thresholding process cleaner.

Glint-image autocorrelations verify these spectral interpretations. By the Wiener-

Khinchine theorem, the autocorrelation can be found as the inverse Fourier transform of the power spectram. Specifically, I removed the DC spike from each power spectram, applied a Hanning window, and calculated the inverse Fourier transform. Because the spectrum then has zero value at DC, the central peak of the autocorrelation is the variance of the glint size; the width of the central peak is the elementary glint size.

Figure 5.10 is the autocorrelation for the smoothest surface, and Fig. 5.11 is the autocorrelation for the roughest surface (the first and last data periods in Table S. 1). The central peak half-width at half-maximum is approximately one pixel wide in each direction, which says that the size of the smallest glint is one pixel. This central peak being one pixel wide for all three of the roughest video segments tells me that in reality the smallest glints in those images are smaller than a single pixel can resolve with the present system. Near the base of the central cone, the shape becomes more elliptical, verifying the existence of glint streaks that are longer in x than in y. The overall

119

09

0.14

0.07

0.00

-0.07

-0.14 -0.14

-0.07

0.00

0.07

0.14

Figure 5.10 Autocorrelation of the glint image measured on Julian day 265 at 1010 UTC

(the smoothest surface). The autocorrelation was computed as an inverse Fourier transform of the power spectrum in Fig. 5.2.

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cs

0.14

0.07

0.00

-0.07

-0.07

0.00

0.07

0.14

Figure 5.11 Autocorrelation of the glint image measured on Julian day 266 at 0546 UTC

(the roughest surface). The autocorrelation was computed as an inverse Fourier transform of the power spectrum in Fig. 5.6.

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"parachute" shape is the transform of the Harming window. Apparently, the wrinkles at medium and large x and y contain some information about surface roughness. Notice that the wrinkles in Fig. 5.11 are rougher than the wrinkles in Fig. 5.10 in a manner that resembles the differences in the glint images shown in Fig. 5.1. However, making use of these autocorrelation wrinkles for quantitative recovery of surface roughness may be difficult because of their small magnitude compared with the rest of the function.

Putting these pieces together, the main result is that glint-image spectra are dominated by glint-size effects, making the spectra more useful for studying surface curvature than surface slopes. However, this prototype instrument was designed with slope measurements in mind, and has insufficient spatial resolution to allow further curvature analysis to be performed on the present data.

5.3 Simulated Laser-Glint linages

In this section I show that a reasonably simple simulation technique generally can reproduce the spectral features found in the measured glint-image spectra. I simulated the surface-height profile with a 64-term Fourier series.

^ , .

(

nicx)

(5.1) where L is half the image dimension in the x direction on the surface (i.e., x goes from -L to +L). The slope profile was obtained by differentiating the height profile;

64

aW = 5]

«=i

L

L j

L

\ L j.

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(5.2)

I constrained the Fourier coefficient amplitudes to match a simple k surfaceheight spectrum model,®^

2 , 2

(5.3) where ^ is a constant of proportionality related to the surface roughness. In reality, this

k ' model is only valid for the equilibrium range of gravity waves (intermediate waves).

Recall that the surface-height measurements in Fig. 2.14 agreed with this model for wave frequencies between about 0.2 Hz and 0.8 Hz. The corresponding

minimum

wavenumber is found by rearranging a few basic equations. The phase velocity of deep-water waves with wavenumber k and wavelength A is given by

Therefore, using the fundamental relationship

S = the wavelength is

2nf

(5.5)

(5.6)

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The minimum wavenumber for which my sonar measurements agree with the k '^ height spectrum is the reciprocal of the wavelength at/= 0.2 Hz (A = 39 m), or = 0.026 m"'.

Returning to the derivation of the surface-height model, Eq. (5.3) can be combined with the definition of the phase angle (j), tan(<|)„) =

b

<2.

(5.7) and the trigonometric identity tan2((j)^) + l =cos-2((i)„) (5.8) to produce the following equations for the Fourier coefficients: a„ = and

(5.9) b„ = 2 sin((|)„), in which (j) is a uniform random variable from

-TZ

to

TZ

.

The value of ^ was determined by running an unsealed simulation, and then adjusting ^ to obtain the mean-square slope determined from the conditions at the time of the glint measurements. Specifically, I first determined the along-wind mean-square slope from the measured wind speed and stability using the formulation in section 3.3.

Then I estimated the cross-wind value by multiplying the along-wind measurement by the

average Cox and Munk ratio of cross-wind to along-wind mean-squaie slopes (0.75).

The glint profile for each surface realization is found by approximating the angular impulse response of the receiver telescope with a one-dimensional Gaussian,

124

/(x) = exp

2^/

(5.11) where a(x) is the surface tilt at location x, is a mean instrument tilt (set to zero for the nadir-looking video system), and Og is the geometrical optics telescope angular resolution

(the maximum surface-tilt angle for which a ray specularly reflected from a point at nadir is just captured by the telescope). For the current system at a height of 6 m, = 1 mrad.

This modeling approach is reasonably simple, but still captures the effects of slope and curvature variations on the surface. For example, a modestly tilted surface facet with large curvature will produce a glint that is smaller and weaker than a glint from a nearly flat surface area with the same mean tilt.

Figure 5.12 shows typical profiles of surface height (a) and slope (b) obtained with this method. This particular profile pair was generated for the case with the roughest surface (the last entry in Table 5.1, and the bottom image in Fig. 5.1). Profiles with lower mean-square slope look similar but with correspondingly smaller wave height and slope.

In this figure, the horizontal dimension has been scaled to match the camera along-wind field of view at an average height of 5.6 m. This simulates an image taken from a fixed height, whereas the actual images were taken with a variable height due to swell, thus smearing the spatial resolution by approximately 10%.

125

40

••

_ (b)

-2 0

• r

X (cm)

1

- T • -

/ \ -

-40

1 1

20

1

1

40

X ( c m )

1

60

1

80

Figure 5.12 Simulated profiles of (a) surface height and (b) surface slope for the roughestsurface case listed in Table 5.1.

126

Rgurc 5.13 shows along-wind simulated spectra for the five data periods summarized in Table 5.1. Each simulation represents the average of 1000 surface realizations. Figure 5.14 shows the corresponding cross-wind simulated spectra. The curves are numbered from 1 to 5 in order of increasing surface roughness. The observations made in section 5.2 are evident here: as the surface gets rougher, energy tends to move from low to higher frequencies, and the total spectral energy reduces monotonically as the roughness increases. The total energy in the simulated-spectra sequence does not first increase before decreasing, as occurred for the measured spectra.

This is because the threshold used in the simulated spectra was high enough to cause weak glints to drop out of the simulated images at lower roughness than in the measured images. This points out the need to carefully consider the threshold value used in these simulations.

5.4 Discussion and Summary

Laser-glint images visually convey information about surface roughness, so it is reasonable to believe that their spectra should as well. Indeed, in this chapter I have identified the source of several spectral features that are related to surface roughness. The main result is that the spectra are dominated by the glint size, making the spectra more useful for studying surface curvature. However, the prototype instrument does not have sufficient spatial resolution for quantitative surface-curvature investigations. Future versions of the video laser-glint imager should be designed with more laser power and higher spatial resolution so that surface curvature can be studied.

127

1.0 o o

0.8 —

CO c

0)

•o

15

w.

O

(D

Q.

(A

k—

<D

O

0 . 6

0.4 —

O)

o

0.2 —

0.0

-200

200

K

( m - ^ )

Figure 5.13 Simulated along-wind power spectra with the zero-frequency peak removed.

Curves are numbered from 1 to 5 in order of increasing surface roughness.

128

1.0

T—I—I—I I I—I—I I I—I I I I I I

O

o o

0.8 — c 0.6

<D

T3

"cO

•*—>

o o

CO 0.4 o

$

o

O)

o

— 0.2

(3)

0.0

-200

•100

k„ (m-i)

(4)

100

(5)

I—I—L

200

Figure 5.14 Simulated cross-wind power spectra with the zero-frequency peak removed.

Curves are numbered from 1 to 5 in order of increasing surface roughness.

129

Working with glint-image autocorrelations might be a useftil approach in future attempts to retrieve surface roughness information. The examples in this ch£^ter show that mid-range wiggles in the autocorrelation are correlated with sea-surface roughness, though they are small. A recently published paper®" suggests that sea-surface height spectra can be retrieved from sun-glitter photographs, using an image-autocorrelation approach. This is in fact similar to a technique published by Chumside" for determining speckle correlation from thresholded light intensities. These types of autocorrelation approaches might prove useful for retrieving surface curvature from the next-generation video laser-glint imager.

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6. CONCLUSION

The experiment described here represents the first successful deployment of laserglint instruments in an open-ocean environment for measuring sea-surface roughness.

Because there are so few practical ways of measuring surface roughness in an actual ocean environment, this instrument development and demonstration is worthwhile by itself. However, the value of the technique is made most apparent by the variety of new scientific knowledge that has resulted from its use.

My measurements of sea-surface slope statistics have verified the popular Cox and Munk model and improved it by adding a quantitative dependence on atmospheric stability, which can be characterized by the ratio of air-water temperature difference to the mean wind speed. Additionally, the laser-glint data have provided the first steps toward development of new fractal and spectral approaches to understanding sea-surface roughness. These new approaches are likely to lead to improved surface models for use in anayzing the interaction of electromagnetic waves with the ocean surface.

The theme that runs throughout this dissertation and represents one of its most signiticant scientific contributions is that sea-surface roughness depends strongly on atmospheric stability. Because most of the measurements reported here are for negative stability, what I have actually shown is that surface roughness is enhanced significantly by negative stability. Particularly, this dissertation has identified a stability dependence for the surface mean-square slope, slope-PDF peakedness, glint-count fractal dimension

(which is related to the fractal dimension of short-wave density), and the shape of glintimage power spectra. The variation with stability of all of these surface-roughness

131

manifestations implies that remote-sensing products must be derived from them in a stability-dependent manner. It also implies that each of these is in itself a measure of stability of the air-sea interface. For the purpose of developing improved instrumentation for measuring sea-surface roughness, it makes the inclusion of a reliable measurement of air-water temperature difference mandatory. The scanning mm-wave radiometer reported here is an ideal instrument for this purpose.

The second theme that appears several times is tha» surface roughness appears to vary on scales larger than that of the dominant wind waves. In the process of verifying that glint counts form a fractal process and showing that the resultant fractal dimension depends on surface roughness, evidence of large-scale variability of surface roughness appeared in several forms. Glint-count time series, histograms, and power spectra all contributed to this evidence. The importance of this is two-fold: first, it shows that further research needs to be directed at understanding this large-scale variability and its source, and second, it shows that fractal surface models are capable of incorporating the essential physical influences of wind speed and stability on surface roughness.

The results of Chapter 5 also contribute evidence of possible large-scale surfaceroughness variability. Some of the differences between simulated and measured spectra might be caused by ignoring long waves in the simulation. This would be important because the short waves contribute nearly all of the surface roughness, so it is tempting

(even quite conunon) to ignore long waves in surface-roughness simulations.

All of these findings have implications for how surface roughness should be measured in the future. The scanning-laser glint meter in a modified form will be an ideal

132

instrument for investigating long-wave modulation of short waves, while also providing valuable measurements of slope statistics and fractal glint counts.

The scanning-laser glint meter has several advantages. It is smaller and less invasive than a refractive laser slope gauge, and it provides the potential of measuring slopes over a large angular range. If modified to perform two-dimensional scanning faster than about 10 Hz (compared with 2 Hz now), it could also reproduce the same type of fractal and spectral results that I obtained here from the video glint imager. The twodimensional scanning capability would also represent a significant improvement for measuring slope statistics and long-wave modulation of surface roughness.

The scanning-laser system also has several disadvantages. It is much larger than the video laser-glint imager, and therefore more difficult to deploy. It has difficulty with daytime measurements, which is actually a disadvantage of the laser-glint technique in general. It has moving parts that make the angular calibration more difficult and the system less mechanically reliable. And, it is always harder to obtain high-resolution temporal-spatial data with a scanning system than with an imaging system.

The video laser-glint imager has its own set of trade-offs. Its advantages include its small size and ease of deployment, and that it has no moving parts and simple optics.

It can easily record great amounts of data at high spatial and temporal resolution.

Furthermore, data storage on videotape is easy and efficient. But the system is most promising because every component represents rapidly developing technologies: solidstate cameras, diode lasers, and image-processing hardware and software.

Such a nice, compact system comes at a price. That price primarily is computer-

133

intensive data processing, which especially may make image-spectral approaches less attractive than glint counting, fa its present form, the laser-glint imager only measures a small angular range encompassing the center of the slope-PDF peak. Thus, it is nearly useless for slope statistics. It will be difficult to get enough power to extend the angular range enough to allow measurement of slope PDFs. However, as diode-laser technology is rapidly advancing, it is worth considering this promising system even for slope statistics. As with the scanning-laser glint meter, the video system has difficulty making measurements in daylight. But again, higher laser power could improve this capability.

With the experience gained during this project, I recommend two parallel instrumental approaches. The first approach is to use an improved scanning-laser glint meter as the primary optical tool for advancing sea-surface science. Improvements include faster two-dimensional scanning, better optical shielding, higher laser power, increased receiver sensitivity through coherent detection, a smaller detector field of view

(to reduce background light seen by the detector), and a more accurate scan motor.

Stepper motors and synchronous motors are both candidates for this application.

The second approach is to consider glint imaging as a developmental approach that has great promise, but which is not quite ready for routine field work where the intensive data processing might be a problem. It will be wise to incorporate new technology into these systems as it becomes available, and to continue investigating fast and efficient glint-image processing techniques. A related approach that is worthy of investigation is infi^d polarization imaging. It would solve the problem of insects being attracted to a searchlight, and maintain most of the other advantages of polarization

134

imaging. No source is necessary, and day or night operation is equally feasible in the 10-

^m thermal region.

Regardless of what specific form the optical surface-roughness instrument takes, future systems must adopt a reliable measurement of air-water temperature difference.

The scaiming mm-wave radiometer used in this experiment represents an ideal new tool for this application. It is interesting to consider also the possibility of making a similar measurement using a scatming infrared radiometer tuned to the edge of the COj band near

14 Jim. The same basic approach could be used, with the possible advantage that the infrared system would measure the temperature in a much shallower skin layer (skin depth on the order of 10 |im) than the mm-wave system (skin depth on the order of several mm). A combined nun-wave and infrared system could possibly even measure heat fluxes through the air-sea interface.

The other measurement made in this experiment that is also important for future measurements is long-wave height. Wave wires can be used for this application, but I recommend continued use of an ultrasonic sonar to continue with a noninvasive measurement approach. The sonar deployed in COPE worked reliably, but had numerous missing points, hi the future, more attention needs to be paid to improving the alignment and sensitivity of this system.

Some of the more important scientific objectives recommended for future work in this area have already been indicated. First, long-wave modulation of short waves should be investigated. The current scanning-laser data set offers a good opportunity to begin this study. Second, the improved understanding of surface slope statistics should be

135

incorporated into the analysis of data firom polarimetric microwave radiometers, radars, and lidars that view the ocean surface.

Third, a larger variety of fractal glint-count data should be analyzed to develop a fractal siuface model that incorporates wind-speed and stability effects. This model should then be used with electromagnetic modeling techniques (such as flnite-difference, time-domain, or FDTD) to provide a new way of studying electromagnetic-wave interaction with the ocean surface that requires fewer assumptions than current methods.

Fourth, the use of a video laser-glint imager with higher spatial resolution should be explored for retrieving surface-curvature spectra from glint-image spectra.

Finally, the increased understanding and awareness of optical effects on rough water surfaces should provide aesthetic intrigue. Whether the source is a laser, an overhead street lamp, the sun, or the moon, it will produce glitter patterns on a water surface. The pleasure found in viewing such glitter patterns is enhanced by understanding more of what they say about the environment in which they are formed.

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