Marine top predators such as seabirds are useful indicators of the integrated response of the marine ecosystem to environmental variability at different scales. Large-scale physical gradients constrain seabird habitat. Birds however respond behaviourally to physical heterogeneity at much smaller scales. Here, we use, for the first time, three-dimensional GPS tracking of a seabird, the great frigatebird (Fregata minor), in the Mozambique Channel. These data, which provide at the same time high-resolution vertical and horizontal positions, allow us to relate the behaviour of frigatebirds to the physical environment at the (sub-)mesoscale (10-100 km, days-weeks). Behavioural patterns are classified based on the birds' vertical displacement (e.g. fast/slow ascents and descents), and are overlaid on maps of physical properties of the ocean-atmosphere interface, obtained by a nonlinear analysis of multi-satellite data. We find that frigatebirds modify their behaviours concurrently to transport and thermal fronts. Our results suggest that the birds' co-occurrence with these structures is a consequence of their search not only for food (preferentially searched over thermal fronts) but also for upward vertical wind. This is also supported by their relationship with mesoscale patterns of wind divergence. Our multi-disciplinary method can be applied to forthcoming high-resolution animal tracking data, and aims to provide a mechanistic understanding of animals' habitat choice and of marine ecosystem responses to environmental change.