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Synthetic aperture radar (SAR) data are affected by speckle noise, originated by the SAR system's coherent nature. The problem of speckle noise in one-dimensional (1-D) data is already solved, as speckle has a multiplicative characteristic. SAR polarimetry represents an extension to multidimensional data by the use of polarization wave diversity. As a consequence of the existence of a correlation degree between the SAR images, the 1-D speckle noise model cannot be extended to multidimensional SAR data. This paper is devoted to present a completely new speckle noise model for the complex covariance matrix describing polarimetric SAR data in the distributed scatterers case. As is shown, this new model is able to identify which are the noise mechanisms in all the covariance matrix elements. The speckle noise model is validated by using real L-band polarimetric data acquired with the German E-SAR sensor.