Continuously variable thickness porous anodic aluminum oxide (PAAO) films were obtained using electrochemical oxidation of bulk aluminum sheet while both electrodes were simultaneously withdrawn from the electrolyte solution. The thickness gradient was controlled by the withdrawal rate (1-10 mm/min range) and thickness variation demonstrated from below 50 nm to above 1 micrometer. The thickness increased linearly with the sample lateral coordinate, whereas the nanopore structure (diameter and interpore distance) remained unchanged. Effects of the initial pore growth and capillary forces are discussed. The presented method can be used for tuning optimal PAAO thickness for optical and other applications as exemplified by finding maximum plasmonic scattering in structured Al-PAAO-Au multilayers. Enhanced scattering from porous gold film separated by a specific-thickness PAAO layer from aluminum mirror surface is demonstrated.