A numerical model for polarimetric thermal emission from penetrable ocean s
urfaces rough in two directions is presented, The numerical model is based
on Monte Carlo simulation with an iterative version of the method of moment
s (MOM) known as the sparse matrix flat surface iterative approach (SMF-SIA
), extended to the penetrable surface case through a numerical impedance bo
undary condition (NIBC) method, Since the small U-B brightnesses obtained f
rom ocean surfaces (usually less than 1.5 K, or 0.5% of a 300-K physical te
mperature) require extremely accurate simulations to avoid large errors, a
parallel version of the algorithm is developed to allow matrix elements to
be integrated accurately and stored, The high accuracy required also limits
simulations to near Bat surface profiles, so that only high-frequency comp
onents of the ocean spectrum are modeled, Variations in nadir polarimetric
brightness temperatures with spectrum low- and high-frequency cutoffs show
the Bragg (or shortwave) portion of the spectrum to contribute significantl
y to emission azimuthal signatures, as predicted by the small perturbation
or composite surface approximate theories, Quantitative comparisons with ap
proximate methods show perturbation theory to slightly overestimate linear
brightness temperatures, but accurately predict their azimuthal variations,
while physical optics (PO) significantly underestimates both linear bright
ness temperatures and their azimuthal variations, Further simulations with
the numerical model allow sensitivities to ocean spectrum models to be inve
stigated and demonstrate the importance of an accurate azimuthal descriptio
n for the ocean spectrum.