The decomposition of geophysical processes into relevant modes is a key issue for characterization, forecasting and reconstruction problems in environmental sciences. Moreover, the blind separation of contributions associated with different sources is a classical problem in signal and image processing. Recently, significant advances have been reported with the introduction of non-negative and sparse formulations. In this work, we address the blind decomposition of linear operators or transfer functions between variables of interest, with an emphasis on a non-negative setting. We illustrate the relevance of these decompositions for the analysis, prediction and reconstruction of geophysical dynamics.