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- Author or Editor: O. M. Phillips x

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## Abstract

Evidence has recently accumulated that stably stratified regions of the ocean and atmosphere often consist of a series of layers of nearly uniform density separated by steps in which the gradient is large. It is shown that the motion of this structure relative to a measuring instrument results in a spectral density proportional to (frequency)^{−2}, over a range which is not limited by the overall value of the stability frequency *N*. Similarly, the spectra obtained by transversing such a structure is found to be proportional to (wavenumber) ^{−2}. Spectral forms of this type cannot necessarily be associated with spectral densities of either internal gravity waves or turbulent eddies.

## Abstract

Evidence has recently accumulated that stably stratified regions of the ocean and atmosphere often consist of a series of layers of nearly uniform density separated by steps in which the gradient is large. It is shown that the motion of this structure relative to a measuring instrument results in a spectral density proportional to (frequency)^{−2}, over a range which is not limited by the overall value of the stability frequency *N*. Similarly, the spectra obtained by transversing such a structure is found to be proportional to (wavenumber) ^{−2}. Spectral forms of this type cannot necessarily be associated with spectral densities of either internal gravity waves or turbulent eddies.

## Abstract

This paper is concerned with the patterns in the degree of saturation of short wind-generated waves (at scales much smaller than those of the spectral peak but large compared with the capillary scales) that are produced by current variations in the presence of wind energy input and loss by breaking or by the formation of parasitic capillaries. It has two aims: the first is to provide a base for interpretation of patterns observed in synthetic aperture radar imagery in terms of current features. The second is to give analytical expressions for the magnitude of the variations in degree of saturation produced by given current fields so that, when appropriate quantitative measurements become available, better parametric representations of the energy loss rates can be developed.

Particular care is taken to provide physically based representations of wind input and loss by wave breaking and a relatively convenient equation (4.2) is derived that specifies the distribution of the degree of saturation in a current field, relative to its ambient (undisturbed) background in the absence of currents. The magnitude of the variations in *b* depends on two parameters, *U*
_{0}/*c*, where *U*
_{0} is the velocity scale of the current and *c* the phase speed of the surface waves at the (fixed) wavenumber considered or sampled by SAR, and *S* = (*L*/λ)(*u*
_{*}/*c*)^{2}, where *L* is the length scale of the current distribution, λ the wavelength of the surface waves and *u*
_{*} the friction velocity of the wind. When *S* is large (of order 10 or more) the distribution of *b* is insensitive to currents for which *U*
_{0}/*c* ∼ 1, but when *S* is of order unity or less, significant variations in *b* are produced. A convergence zone is associated with a maximum in *b* relative to its ambient levels ofwhere *m* ≈ 0.04 and *n* ∼ 3. This appears as a bright line in the SAR imagery against the ambient background. In general, changes of order unity in *b* (and the return SAR signal) should be observed if the local current strain-rate scaleA local divergence or upwelling reduces the relative degree of saturation; when *S* is small the reduction is by the factor (1 + 2*U*/*c*)^{−9/2} and continues until the waves grow back to the equilibrium level under the influence of the wind. A divergence line would be imaged as a line across which the return decreases relatively abruptly from the ambient level upwind, to a lower level downwind, gradually recovering to the ambient.

## Abstract

This paper is concerned with the patterns in the degree of saturation of short wind-generated waves (at scales much smaller than those of the spectral peak but large compared with the capillary scales) that are produced by current variations in the presence of wind energy input and loss by breaking or by the formation of parasitic capillaries. It has two aims: the first is to provide a base for interpretation of patterns observed in synthetic aperture radar imagery in terms of current features. The second is to give analytical expressions for the magnitude of the variations in degree of saturation produced by given current fields so that, when appropriate quantitative measurements become available, better parametric representations of the energy loss rates can be developed.

Particular care is taken to provide physically based representations of wind input and loss by wave breaking and a relatively convenient equation (4.2) is derived that specifies the distribution of the degree of saturation in a current field, relative to its ambient (undisturbed) background in the absence of currents. The magnitude of the variations in *b* depends on two parameters, *U*
_{0}/*c*, where *U*
_{0} is the velocity scale of the current and *c* the phase speed of the surface waves at the (fixed) wavenumber considered or sampled by SAR, and *S* = (*L*/λ)(*u*
_{*}/*c*)^{2}, where *L* is the length scale of the current distribution, λ the wavelength of the surface waves and *u*
_{*} the friction velocity of the wind. When *S* is large (of order 10 or more) the distribution of *b* is insensitive to currents for which *U*
_{0}/*c* ∼ 1, but when *S* is of order unity or less, significant variations in *b* are produced. A convergence zone is associated with a maximum in *b* relative to its ambient levels ofwhere *m* ≈ 0.04 and *n* ∼ 3. This appears as a bright line in the SAR imagery against the ambient background. In general, changes of order unity in *b* (and the return SAR signal) should be observed if the local current strain-rate scaleA local divergence or upwelling reduces the relative degree of saturation; when *S* is small the reduction is by the factor (1 + 2*U*/*c*)^{−9/2} and continues until the waves grow back to the equilibrium level under the influence of the wind. A divergence line would be imaged as a line across which the return decreases relatively abruptly from the ambient level upwind, to a lower level downwind, gradually recovering to the ambient.

## Abstract

Recent ideas on the structure of the equilibrium range of wind-generated ocean waves are applied to the question of radar backscattered returns from the sea surface. It is shown that the backscattering cross section can be represented as the sum of separate contributions from Bragg-scattering and from individual breaking events:where θ is the angle of incidence, ϕ is the direction of observation relative to the wind, *u*
_{*} is the friction velocity and κ the radar wavelength; the Bragg-scattering contribution increases linearly with *u*
_{*} and the sea spike contribution cubically. The number of sea spikes per unit time per unit surface area for a given threshold of spike intensity or duration is proportional to *g*
^{−1}
*u*
_{*}
^{3}. Calibrated radar measurements of median values of σ_{0}, which tend to suppress sea spike contributions, have been made by Guinard et al. over a range of radar wavelengths from 70 to 3.4 cm. These scale consistently with the parameter (*u*
_{*}
^{2}κ/*g*)^{½} over angles of incidence greater than 30°, and are, overall, in accordance with a linear dependence. This suggests that the sea spike contribution to the median σ_{0} is generally small over the range of observations, though their influence on the mean is not established. The cubic dependence predicted for the *frequency of occurrence* of sea spikes on *u*
_{*} does, however, suggest a new and simpler method for the measurement of surface wind stress by remote sensing.

## Abstract

Recent ideas on the structure of the equilibrium range of wind-generated ocean waves are applied to the question of radar backscattered returns from the sea surface. It is shown that the backscattering cross section can be represented as the sum of separate contributions from Bragg-scattering and from individual breaking events:where θ is the angle of incidence, ϕ is the direction of observation relative to the wind, *u*
_{*} is the friction velocity and κ the radar wavelength; the Bragg-scattering contribution increases linearly with *u*
_{*} and the sea spike contribution cubically. The number of sea spikes per unit time per unit surface area for a given threshold of spike intensity or duration is proportional to *g*
^{−1}
*u*
_{*}
^{3}. Calibrated radar measurements of median values of σ_{0}, which tend to suppress sea spike contributions, have been made by Guinard et al. over a range of radar wavelengths from 70 to 3.4 cm. These scale consistently with the parameter (*u*
_{*}
^{2}κ/*g*)^{½} over angles of incidence greater than 30°, and are, overall, in accordance with a linear dependence. This suggests that the sea spike contribution to the median σ_{0} is generally small over the range of observations, though their influence on the mean is not established. The cubic dependence predicted for the *frequency of occurrence* of sea spikes on *u*
_{*} does, however, suggest a new and simpler method for the measurement of surface wind stress by remote sensing.

## Abstract

This paper is concerned with the expected configuration in space and time surrounding extremely high crests in a random wave field, or, equivalently, the mean configuration averaged over realizations of extreme events. A simple, approximate theory is presented that predicts that the mean configuration ζ¯(**x** + **r**, *t* + τ) surrounding a crest at (**x**, *t*) that is higher than γσ (where σ is the overall rms surface displacement and γ ≫ 1), when normalized by ζ¯(**x**,*t*) for ζ > γσ, is the space-time autocorrelation function ρ(**r**, *t*) = ¯ζ(**x**, *t*)ζ(**x** + **r**, *t* + τ)/ ζ¯^{2} for the entire wave field. This extends and simplifies an earlier result due to Boccotti and is consistent with a precise calculation of the one-dimensional case with **r** = 0, involving the time history of measurements at a single point. The results are compared with buoy data obtained during the Surface Wave Dynamics Experiment and the agreement is found to be remarkably good.

## Abstract

This paper is concerned with the expected configuration in space and time surrounding extremely high crests in a random wave field, or, equivalently, the mean configuration averaged over realizations of extreme events. A simple, approximate theory is presented that predicts that the mean configuration ζ¯(**x** + **r**, *t* + τ) surrounding a crest at (**x**, *t*) that is higher than γσ (where σ is the overall rms surface displacement and γ ≫ 1), when normalized by ζ¯(**x**,*t*) for ζ > γσ, is the space-time autocorrelation function ρ(**r**, *t*) = ¯ζ(**x**, *t*)ζ(**x** + **r**, *t* + τ)/ ζ¯^{2} for the entire wave field. This extends and simplifies an earlier result due to Boccotti and is consistent with a precise calculation of the one-dimensional case with **r** = 0, involving the time history of measurements at a single point. The results are compared with buoy data obtained during the Surface Wave Dynamics Experiment and the agreement is found to be remarkably good.

## Abstract

In a previous paper (Phillips et al.) an approximate theory was developed that predicted that the expected configuration of extreme waves in a random sea (or the average configuration of an ensemble of extreme waves) is proportional to the space-time autocorrelation function of the surface displacement of the wave field as a whole. This result is tested by examination of scanning radar altimeter measurements made during SWADE in four different sea states, including a unimodal mature wave field, a short fetch, a wind-generated sea crossing swell, a very broad directional spectrum, and a fetch-limited wind sea with opposing swell. In each of these, the spatial autocorrelation function was found directly from the SRA data. The highest waves in each dataset were selected and their configurations averaged with respect to the crest. These averaged configurations were in each case found to be consistent with the autocorrelation function.

## Abstract

In a previous paper (Phillips et al.) an approximate theory was developed that predicted that the expected configuration of extreme waves in a random sea (or the average configuration of an ensemble of extreme waves) is proportional to the space-time autocorrelation function of the surface displacement of the wave field as a whole. This result is tested by examination of scanning radar altimeter measurements made during SWADE in four different sea states, including a unimodal mature wave field, a short fetch, a wind-generated sea crossing swell, a very broad directional spectrum, and a fetch-limited wind sea with opposing swell. In each of these, the spatial autocorrelation function was found directly from the SRA data. The highest waves in each dataset were selected and their configurations averaged with respect to the crest. These averaged configurations were in each case found to be consistent with the autocorrelation function.

## Abstract

A set of X-band radar measurements, backscattered from the sea surface at near grazing incidence with very high spatial and temporal resolution (30 cm in range and 2000-Hz pulse repetition frequency) in moderate wind conditions, are dominated by moving discrete events (sea spikes). They have radar cross sections of up to about 1 m^{2} and are found to possess the characteristics of breaking wave fronts. Contributions from Bragg backscattering appear to be at least two orders of magnitude smaller. The number of events detected per unit area per unit time was of the same order as found by Ding and Farmer at almost the same wind speed, but the distribution of event speeds was narrower—the fastest breaking wave events observed had line-of-sight speeds of about 0.6 of the dominant wave speed. The measured histograms of number of events versus event speed *c* suggested that the smaller events with *c* < 3 m s^{−1} were only incompletely counted so that the characteristics of only the faster events (3–6 m s^{−1}) were analyzed in detail. With the use of independent data on the average shape of broken areas, for the first time the form of the function Λ(*c*), the distribution with respect to speed of the length of breaking front per unit area of surface and *c*Λ(*c*), and the fraction of surface turned over per unit time per speed increment were determined. These were found to decrease monotonically with increasing event speed, indicating that these quantities are dominated by the smaller, more frequent breaking events. By making use of the Duncan–Melville expression for the dissipation rate per unit length of a breaking front, the distributions of wave energy dissipation by breaking and of momentum flux to the water by breaking wave impulses are also found for the first time. These were found to be broadband over the whole range of breaker speeds that could be measured reliably, that is, those corresponding to scales of 50%–20% of the dominant wavelength. These results offer no support to the hypothesis of a “Kolmogorov cascade” in wind-generated waves analogous to that in turbulence, with energy input from the wind at large scales and dissipation from the waves at small scales. The measurements indicate that, in contrast, dissipation is significant at the largest scales of wave breaking and is distributed widely across that spectrum. If the results are interpreted in terms of equilibrium range wave theory, a value for the numerical constant in the Duncan–Melville expression is inferred that is smaller than the range given by Melville, but a simple expression for the total rate of energy loss from the wind-driven waves is quantitatively consistent with results of upper-ocean turbulence dissipation measurements reported by Terray et al.

## Abstract

A set of X-band radar measurements, backscattered from the sea surface at near grazing incidence with very high spatial and temporal resolution (30 cm in range and 2000-Hz pulse repetition frequency) in moderate wind conditions, are dominated by moving discrete events (sea spikes). They have radar cross sections of up to about 1 m^{2} and are found to possess the characteristics of breaking wave fronts. Contributions from Bragg backscattering appear to be at least two orders of magnitude smaller. The number of events detected per unit area per unit time was of the same order as found by Ding and Farmer at almost the same wind speed, but the distribution of event speeds was narrower—the fastest breaking wave events observed had line-of-sight speeds of about 0.6 of the dominant wave speed. The measured histograms of number of events versus event speed *c* suggested that the smaller events with *c* < 3 m s^{−1} were only incompletely counted so that the characteristics of only the faster events (3–6 m s^{−1}) were analyzed in detail. With the use of independent data on the average shape of broken areas, for the first time the form of the function Λ(*c*), the distribution with respect to speed of the length of breaking front per unit area of surface and *c*Λ(*c*), and the fraction of surface turned over per unit time per speed increment were determined. These were found to decrease monotonically with increasing event speed, indicating that these quantities are dominated by the smaller, more frequent breaking events. By making use of the Duncan–Melville expression for the dissipation rate per unit length of a breaking front, the distributions of wave energy dissipation by breaking and of momentum flux to the water by breaking wave impulses are also found for the first time. These were found to be broadband over the whole range of breaker speeds that could be measured reliably, that is, those corresponding to scales of 50%–20% of the dominant wavelength. These results offer no support to the hypothesis of a “Kolmogorov cascade” in wind-generated waves analogous to that in turbulence, with energy input from the wind at large scales and dissipation from the waves at small scales. The measurements indicate that, in contrast, dissipation is significant at the largest scales of wave breaking and is distributed widely across that spectrum. If the results are interpreted in terms of equilibrium range wave theory, a value for the numerical constant in the Duncan–Melville expression is inferred that is smaller than the range given by Melville, but a simple expression for the total rate of energy loss from the wind-driven waves is quantitatively consistent with results of upper-ocean turbulence dissipation measurements reported by Terray et al.

## Abstract

The Innovative Strategies for Observations in the Arctic Atmospheric Boundary Layer Program (ISOBAR) is a research project investigating stable atmospheric boundary layer (SBL) processes, whose representation still poses significant challenges in state-of-the-art numerical weather prediction (NWP) models. In ISOBAR ground-based flux and profile observations are combined with boundary layer remote sensing methods and the extensive usage of different unmanned aircraft systems (UAS). During February 2017 and 2018 we carried out two major field campaigns over the sea ice of the northern Baltic Sea, close to the Finnish island of Hailuoto at 65°N. In total 14 intensive observational periods (IOPs) resulted in extensive SBL datasets with unprecedented spatiotemporal resolution, which will form the basis for various numerical modeling experiments. First results from the campaigns indicate numerous very stable boundary layer (VSBL) cases, characterized by strong stratification, weak winds, and clear skies, and give detailed insight in the temporal evolution and vertical structure of the entire SBL. The SBL is subject to rapid changes in its vertical structure, responding to a variety of different processes. In particular, we study cases involving a shear instability associated with a low-level jet, a rapid strong cooling event observed a few meters above ground, and a strong wave-breaking event that triggers intensive near-surface turbulence. Furthermore, we use observations from one IOP to validate three different atmospheric models. The unique finescale observations resulting from the ISOBAR observational approach will aid future research activities, focusing on a better understanding of the SBL and its implementation in numerical models.

## Abstract

The Innovative Strategies for Observations in the Arctic Atmospheric Boundary Layer Program (ISOBAR) is a research project investigating stable atmospheric boundary layer (SBL) processes, whose representation still poses significant challenges in state-of-the-art numerical weather prediction (NWP) models. In ISOBAR ground-based flux and profile observations are combined with boundary layer remote sensing methods and the extensive usage of different unmanned aircraft systems (UAS). During February 2017 and 2018 we carried out two major field campaigns over the sea ice of the northern Baltic Sea, close to the Finnish island of Hailuoto at 65°N. In total 14 intensive observational periods (IOPs) resulted in extensive SBL datasets with unprecedented spatiotemporal resolution, which will form the basis for various numerical modeling experiments. First results from the campaigns indicate numerous very stable boundary layer (VSBL) cases, characterized by strong stratification, weak winds, and clear skies, and give detailed insight in the temporal evolution and vertical structure of the entire SBL. The SBL is subject to rapid changes in its vertical structure, responding to a variety of different processes. In particular, we study cases involving a shear instability associated with a low-level jet, a rapid strong cooling event observed a few meters above ground, and a strong wave-breaking event that triggers intensive near-surface turbulence. Furthermore, we use observations from one IOP to validate three different atmospheric models. The unique finescale observations resulting from the ISOBAR observational approach will aid future research activities, focusing on a better understanding of the SBL and its implementation in numerical models.