Continuity preserving modified maximum cross-correlation technique

The maximum cross-correlation (MCC) method reconstructs the surface advective velocity fields from the displacements of spatial patterns in pairs of sequential satellite (normally infrared) images. However, the performance of the conventional MCC method is not always satisfactory. One of the main reasons for this is the fact that the method can correctly estimate only the velocity component parallel to the gradient of the property depicted in the images, while any small displacement perpendicular to the gradient (i.e., directed along the isolines) essentially maps the spatial pattern onto itself and therefore can not be detected using the conventional MCC technique. In the present work we propose a modification of the MCC method that allows circumventing this basic deficiency and improving the performance of the MCC technique. In this approach, the "cross-isoline'' components of the velocity field are obtained as in the conventional MCC scheme; however, the "along-isoline'' components derived from the MCC are disregarded as unreliable. Instead, the "true'' along-isoline components are then reconstructed from the given cross-isoline velocity field based on the continuity requirement and on the condition of no normal flow at solid boundaries. This inverse problem is solved by constructing the two-dimensional stream function in the curvilinear coordinate frame associated with the image isolines. The method is illustrated using AVHRR images from the southwestern Atlantic Ocean and the Black Sea. The results are compared with some direct drifter and current meter measurements and geostrophic estimates.