In the past we proposed a multidimensional speckle noise model to which we now include systematic phase variation effects. This extension makes it possible to define what is believed to be a novel coherence model able to identify the different sources of bias when coherence is estimated on multidimensionalsynthetic radar aperture (SAR) data. On the one hand, low coherence biases are basically due to the complex additive speckle noise component of the Hermitian product of two SAR images. On the other hand, the availability of the coherence model permits us to quantify the bias due to topography when multilook filtering is considered, permitting us to establish the conditions upon which information may be estimated independently of topography. Based on the coherence model, two coherence estimation approaches, aiming to reduce the different biases, are proposed. Results with simulated and experimental polarimetric and interferometric SAR data illustrate and validate both, the coherence model and the coherence estimation algorithms.