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Covariance Statistics of Polarimetric Brightness Temperature Measurements

All microwave radiometer measurements of brightness temperature (T B) include an additive noise component. With conventional linearly polarized radiometers, the variance of the noise is a well-understood function of the system temperature, the predetection bandwidth, and the integration time according to the so-called ldquoradiometer uncertainty equation.rdquo The noise has generally been considered to be uncorrelated between orthogonally polarized channels. The variance and the correlation statistics of the additive noise component of fully polarimetric radiometer measurements are derived from theoretical considerations, and the resulting relationships are experimentally verified. It is found that the noise can be correlated between polarimetric channels, and the correlation statistics will vary as a function of the polarization state of the scene under observation. For example, a strong correlation is typical between the noise in either vertically or horizontally polarized TB and the 45 deg slant linear polarizations that are often used to derive the third Stokes T B. A weak, but nonzero, correlation is also possible between the additive noise in the vertically and horizontally polarized T B's themselves. This is a correction to the common assumption that they are uncorrelated.