Automated Invariant Alignment to Improve Canonical Variates in Image Fusion of Satellite and Weather Radar Data

Abstract

anonical correlation analysis (CCA) maximizes the correlation between two sets of multivariate data. CCA is applied to multivariate satellite data and univariate radar data to produce a subspace descriptive of heavily precipitating clouds. A misalignment, inherent to the nature of the two datasets, was observed, corrupting the subspace. A method for aligning the two datasets is proposed to overcome this issue and render a useful subspace projection. The observed corruption of the subspace gives rise to the hypothesis that the optimal correspondence between a heavily precipitating cloud in the radar data and the associated cloud top registered in the satellite data is found by a scale, rotation, and translation invariant transformation together with a temporal displacement. The method starts by determining a conformal transformation of the radar data at the time of maximum precipitation for optimal correspondence with the satellite data at the same time. This optimization is repeated for an increasing temporal lag until no further improvement can be found. The method is applied to three meteorological events that caused heavy precipitation in Denmark. The three cases are analyzed with and without using the proposed method. In all cases, the use of prealignment shows significant improvements in the descriptive capabilities of the subspaces, thus supporting the posed hypothesis.