This paper generalizes a previous formulation of signal separation problem for dynamic wind turbine clutter mitigation at weather radar systems. In this modified formulation, we use nonconvex regularizers together with multichannel overlapping group shrinkage (MOGS) to penalize weather signals and adopt multidimensional processing. We show the restored weather signals in plan position indicator (PPI) format and, to demonstrate the improvement, compare them with the ones produced by the previous method in reflectivity, spectral width, and Doppler velocity estimates of weather data. The improvement results from a better characterization of the sparsities of the weather radar returns. During the course of experiments, we observe that the proposed method successfully mitigates the wind turbine clutter and dramatically increases the signal-to-clutter ratio, even for different weather and wind turbine signatures. In addition, when the wind turbine clutter is weak in the mixture, our algorithm manages to attenuate the ground clutters and produces clutter-free weather signals favorable for further processing.@en