Illustration showing the pipelines of PCAA. We first project the PPV cubes along either of the spatial directions (panel 1), in which we would call the compressed PPV cubes “PV tires” (panel 2) in which the covariance matrix S of the PV tires (panel 3, Equation (15)) can be computed. The eigenvalues of the covariance matrix (panel 4) contain the velocity information along this particular PV tire, and the ﹩{e}^{-1}﹩ lag of the autocorrelation functions of the eigenvectors and eigen-projections (panel 5, Equation (21)) tells us the characteristic velocities ﹩\delta {v}_{x,y}﹩ and length scales ﹩{L}_{x,y}﹩, respectively.