  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.
