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Open Access Publications from the University of California

Slopes of the sea surface deduced from photographs of sun glitter


Part I: Experimental Method and Observations.-The distribution of brightness of sun glitter on the sea surface is interpreted in terms of the statistics of the sea-surface slope distribution. The method consists of two phases: (I) identifying, from the law of reflection, any point on the surface with the particular slope required to reflect the sun's rays toward the observer, and (2) interpreting the average brightness of the sea surface in the vicinity of this point in terms of the frequency with which this particular slope occurs. The computation of the probability of large (and infrequent) slopes is limited by the disappearance of the glitter into a background consisting of (1) sunlight scattered from particles beneath the sea surface, and (2) skylight reflected by the sea surface. The method has been applied to aerial photographs taken near the Hawaiian Islands. Winds were measured from a vessel at the time and place of the aerial photographs, and cover a range from 1 to 14 m. set.-I The logarithmic distribution of slopes has been tabulated for various wind speeds. A two-dimensional Gram-Charlier series is fitted to the data. As a first approximation the distribution is Gaussian and isotropic. The mean square slope (regardless of direction) increases linearly with the wind speed, reaching a value of (tan 16")* for a wind speed of 14 m. set.-I The ratio of the crosswind to the up/downwind mean square slope component varies depending on the steadiness of the wind from 1.0 to 0.5. There is some skewness which increases with increasing wind speed. As a result the most probable slope at high winds is not zero but a few degrees, with the azimuth of ascent pointing downwind. The measured peakedness is near the limit of observational error and is such as to make the probability of very large and very small slopes greater than Gaussian. The effect of oil slicks covering an area of one-quarter square mile is to reduce the mean square slopes by a factor of two or three, to eliminate skewness, but to leave peakedness unchanged.

Part II: Interpretation.-An attempt is made to interpret the results given in Part I in terms of models having simple wave spectra. The observed nearly Gaussian distribution of slopes is inconsistent with a spectrum consisting of a few discrete frequencies, but can be accounted for by a continuous spectrum of arbitrary width or a large number of discrete frequencies. The observed skewness may be a nonlinear effect, and is not treated. The observed ratio between cross- and up/ downwind slopes can be interpreted in terms of two wave "beams" intersecting at 70°, or a single wide beam subtending 130'. These values apply to the relatively short waves that contribute largely to the slope spectrum. The observed proportionality between mean square slope and wind speed follows from a spectrum proposed by Neumann on the basis of wave amplitude observations, but yields a constant of proportionality too small by a factor of three. A spectrum proposed by Darby- shire cannot be reconciled with the observed slope distribution. Measurements of curvature will provide a critical test of the high-frequency end of the spectrum. An extrapolation of the Neumann spectrum into the region of capillary waves predicts an r.m.s. by a slick may be accounted for by assuming that the slick forms an inextensible surface against which waves (Neumann spectrum) are dissipated by viscosity. Some difficulties of this interpretation are stated. The distribution of surface-particle acceleration is closely related to the distribution of slopes. The total mean square acceleration increases linearly with wind speed and reaches a value of (0.4 g.)= at a wind speed of 14 m, set.-I

Part III: Application.-Measurements of the probability distribution of sea-surface slopes have made accessible to numerical treatment problems involving the interaction of short-wave radiation with a roughened sea surface. It is found that the refracted sun's glitter (as seen from beneath the surface) is scattered into a smaller solid angle but is about one thousand times more luminous (neglecting absorption) than the reflected glitter, and that, unlike the reflected glitter, it expands and dims as the sun sets. The albedo of a rough surface to direct sunlight is slightly larger at high sun angles, and substantially smaller at low sun angles, than the albedo of a flat surface. Accordingly, more solar energy penetrates waters at high latitudes than had previously been estimated, and the amount of this additional energy depends upon wind speed. The luminosity of the sea surface due to skylight has been computed for various conditions. A rough surface is darker at the horizon than a smooth surface, thus enhancing the horizon contrast. The albedo of the sea surface to skylight varies from 5 to 10 per cent depending on the distribution of illumination from the sky; it is largest when the sea is flat calm. The roughening by a Beaufort 4 wind reduces the albedo by about 20 per cent. Finally, a discussion of the visibility of slicks is given. When illuminated with skylight, natural slicks, of a thickness small compared to a wave length of light, contrast with a clean sea surface most sharply when they are near the horizon. Freshly spread oil slicks, on the other hand, show more contrast directly beneath the observer.

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