Variable Spectral Slope and Nonequilibrium Surface Wave Spectrum

TL;DR

This paper investigates how the spectral slope of ocean surface waves varies in the centimeter to decameter range, highlighting its nonequilibrium nature and its impact on wave property measurements and remote sensing.

Contribution

It introduces a spectrum model that accounts for variable spectral slopes, linking observed non-constant slopes to the spectral properties of ocean surface waves.

Findings

Variable spectral slopes indicate nonequilibrium wave conditions.

Surface slope measurements are more sensitive than elevation data.

The model connects observed slopes with wave spectral characteristics.

Abstract

The wave spectral properties in the centimeter to decameter (cmDm) wavelength range is of great interest to ocean remote sensing and studies of ocean surface processes including the surface roughness, air-sea energy and momentum exchanges, wave breaking, and whitecap coverage. For more than six decades, the cmDm wave components are generally considered to be in the equilibrium range, and its spectral function has a constant slope: -5 or -4 in the 1D frequency spectrum, and -3 or -2.5 in the 1D wavenumber spectrum. Some variations of the equilibrium spectrum models include varying the frequency spectral slope from 4 to 5 at some multiple of the spectral peak frequency, or incorporating a threshold velocity in the reference wind speed. Extensive efforts are then devoted to quantifying the spectral coefficient of the equilibrium spectrum function. The observed wind wave spectral slopes in the ocean environment, however, are rarely constant. The variable spectral slope is indicative of the nonequilibrium nature of surface wind waves in the field. As a result the wave properties in field observations are significantly different from those inferred from assuming a constant spectral slope. From signal-to-noise consideration the surface slope measurements are much more sensitive than the elevation data for the study of cmDm waves. Recently, several large datasets of low-pass-filtered mean square slope (LPMSS) have been reported in support of the Global Navigation Satellite System Reflectometry (GNSSR) tropical cyclone wind sensing effort. Combining the LPMSS observations with a spectrum model that accommodates a variable spectral slope, this paper seeks to quantify the connection between the variable spectral slope and the spectral properties of cmDm waves.