Many new Earth remote-sensing instruments are embracing both the advantages and added complexity that result from interferometric or fully polarimetric operation. To increase instrument understanding and functionality, a model of the signals these instruments measure is presented. A stochastic model is used as it recognizes the nondeterministic nature of any real-world measurements, while also providing a tractable mathematical framework. A wide-sense stationary, ergodic, Gaussian-distributed model structure is proposed. Temporal and spectral correlation measures provide a statistical description of the physical properties of coherence and polarization-state. From this relationship, the model is mathematically defined. A method of realizing the model (necessary for applications such as synthetic calibration-signal generation) is given, and computer simulation results are presented. The signals are constructed using the output of a multi-input, multi-output linear filter system, driven with white noise.