Convex Estimation of Sparse-Smooth Power Spectral Densities From Mixtures of Realizations With Application to Weather Radar

In this paper, we propose a convex optimization-based estimation of sparse and smooth power spectral densities (PSDs) of complex-valued random processes from mixtures of realizations. While the PSDs are related to the magnitude of the frequency components of the realizations, it has been a major challenge to exploit the smoothness of the PSDs, because penalizing the difference of the magnitude of the frequency components results in a nonconvex optimization problem that is difficult to solve. To address this challenge, we design the proposed model that jointly estimates the complex-valued frequency components and the nonnegative PSDs, which are respectively regularized to be sparse and sparse-smooth. By penalizing the difference of the nonnegative variable that estimates the PSDs, the proposed model can enhance the smoothness of the PSDs via convex optimization. Numerical experiments on the phased array weather radar, an advanced weather radar system, demonstrate that the proposed model achieves superior estimation accuracy compared to existing sparse estimation models, regardless of whether they are combined with a smoothing technique as a post-processing step or not

Improvement of High-Resolution Satellite Rainfall Product for Typhoon Morakot (2009) over Taiwan

The authors improve the high-resolution Global Satellite Mapping of Precipitation (GSMaP) product for Typhoon Morakot (2009) over Taiwan by using an orographic/nonorographic rainfall classification scheme. For the estimation of the orographically forced upward motion used in the orographic/nonorographic rainfall classification scheme, the optimal horizontal length scale for averaging the elevation data is examined and found to be about 50 km. It is inferred that as the air ascends en masse on the horizontal scale, it becomes unstable and convection develops. The orographic/nonorographic rainfall classification scheme is extended to the GSMaP algorithm for all passive microwave radiometers in orbit, including not just microwave imagers but also microwave sounders. The retrieved rainfall rates, together with infrared images, are used for the high-resolution rainfall products, which leads to much better agreement with rain gauge observations