Polarization Rotation Correction in Radiometry: An Error Analysis

Yueh proposed a method of using the third Stokes parameter T
_U
to correct brightness temperatures such as T
_v
and T
_h
for polarization rotation. This paper presents an extended error analysis of the estimation of T
_v
, T
_h
, and T
_Q
equiv T
_v
- T
_h
by Yueh's method. In order to carry out the analysis, we first develop a forward model of polarization rotation that accounts for the random nature of thermal radiation, receiver noise, and (to first order) calibration. Analytic formulas are then derived for the bias, standard deviation (STD), and root-mean-square error (RMSE) of estimated T
_Q
, T
_v
, and T
_h
, as functions of scene and radiometer parameters. These formulas are validated through independent calculation via Monte Carlo simulation. Examination of the formulas reveals that: 1) natural T
_U
from planetary surface radiation, of the magnitude expected on Earth at L-band, has a negligible effect on correction for polarization rotation; 2) RMSE is a function of rotation angle Omega, but the value of Omega that minimizes RMSE is not known prior to instrument fabrication; and 3) if residual calibration errors can be sufficiently reduced via postlaunch calibration, then Yueh's method reduces the error incurred by polarization rotation to negligibility.