The growing availability of multi-source environmental data (remote sensing data, numerical simulations, in situ data, etc.) paves the way for the development of novel data-driven models and strategies for the characterization, reconstruction and forecasting of geophysical dynamics. In this context, the observation-driven identification and separation of contributions and operators associated with different geophysical sources or processes is a key issue. Following significant advances reported in signal processing with the introduction of non-negative and sparse formulations, we address this issue from the blind decomposition of linear operators or transfer functions between variables or processes of interest. The proposed scheme relies on multiple superimposing linear regressions and on their calibration from the observed data. We explore locally-adapted multi-modal regression models and investigate different dictionary-based decompositions, namely based on principal component analysis (PCA), sparse priors and non-negativity constraints. This is regarded as a key feature to improve model calibration robustness. We illustrate and demonstrate the relevance of such decompositions for the analysis and reconstruction of geophysical dynamics. We first address forecasting issues. Using Lorenz ‘96 dynamical system as case-study, we introduce the blind dictionary-based decomposition of local linear operators. Our numerical experiments resort to improved forecasting performance when dealing with small-sized and noisy observation datasets. A second application addresses the super-resolution of irregularly-sampled ocean remote sensing images. We focus on the reconstruction of high-resolution Sea Surface Height (SSH) from the synergy between along-track altimeter data, OI-interpolated SSH fields and satellite-derived high-resolution Sea Surface Temperature (SST) fields. The reported experiments, for a case study region in the Western Mediterranean Sea, demonstrate the relevance of the proposed model, specially of locally-adapted parametrizations with non-negativity constraints, to outperform optimally-interpolated reconstructions.