Theoretical study of the small slope approximation for ocean polarimetric thermal emission

Abstract

Analytical models for ocean surface polarimetric thermal emission based on the small perturbation method (SPM) have shown success in matching brightness temperature azimuthal variations from aircraft based measurements. It has also been shown that use of the small perturbation method for calculation of surface emissivity results in a series in surface slope, not surface height, so that the method remains accurate for large height surface emission even when it fails for the corresponding scattering calculations. This paper presents a detailed analysis of the SPM/small slope approximation (SPM/SSA) for ocean surface polarimetric thermal emission, and investigates the extent to which varying ocean surface length scales contribute to brightness temperature zeroth and second azimuthal harmonics. It is found that ocean waves of lengths both comparable to and much greater than the electromagnetic wavelength can contribute to these harmonics, depending on the extent to which the ocean surface spectral model places asymmetry in these length scales. In addition, the SPM/SSA is approximated for the contributions of both very long and very short ocean length scales compared to the electromagnetic wavelength, and it is found that both long and short wave contributions can be expressed in simple equations involving either standard or modified ocean surface slope variances.Index Terms-Microwave readiometry, passive remote sensing.

Active‐passive synergy for interpreting ocean L‐band emissivity: Results from the CAROLS airborne campaigns

“…The roughness contribution T A;rough is derived from the integration of these curvature spectra on logðk=k 0 Þ [Johnson and Zhang, 1999]. Figures 2b and 2c point out that T A;rough is sensitive to roughness wavelengths from 100 m to about 1 cm.…”

“…Using the same decomposition as in Johnson and Zhang [1999], we can derive an omnidirectional mss weighting function. We remark that this weighting function integrates homogeneously (in logarithmic scale) wave spectrum from largest wave scale up to 12 cm (Figure 2a in magenta).…”

“…using same notations as in Johnson and Zhang [1999], with h the incidence angle; b5k=k 0 the wavenumber k normalized by the electromagnetic wave number k 0 ; c the H or V polarization; g 0 c;0 the nonintegrated weighting function; G the antenna gain pattern; H534 the CAROLS pointing incidence angle and ½H2p=2; H1p=2 the front pattern of the antenna.…”

“…Four roughness models are compared here: three models used in various versions of SMOS data processing and one model used in Aquarius data processing. Two of these are new models derived from satellite measurements, called here ''Aquarius CAP'' [Yueh et al, 2013] and "SMOS M1v5" [Yin et al, 2012] (used in ESA processor version 5) and two are SMOS prelaunch models, called ''SMOS M1v3'' [Dinnat et al, 2003] and ''SMOS M2v3'' [Johnson and Zhang, 1999;Kudryavtsev et al, 2003] (used in ESA processor up to version 3). The main characteristics of these four models are summarized in Table 2.…”

“…Two main physical roughness models are used in L-band radiometry: a small perturbation method, small slope approximation (SPM/SSA), called here SSA [Johnson and Zhang, 1999], and a two-scale model. parameterization) and add a hydrodynamic modulation of the waves [Yueh, 1997;Dinnat et al, 2003].…”