Canonical correlation analysis (CCA) maximizes correlation between two sets of multivariate data. We applied CCA to multivariate satellite data and univariate radar data in order to produce a subspace descriptive of heavily precipitating clouds. A misalignment, inherent to the nature of the two data sets, was observed, corrupting the subspace. A method for aligning the two data sets is proposed, in order 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 having caused heavy precipitation in Denmark. The three cases are analyzed with and without using the proposed method. In all cases, the use of pre-alignment shows significant improvements in the descriptive capabilities of the subspaces, thus supporting the posed hypothesis.