  The monopnictides TaAs and TaP are well-established Weyl semimetals. Yet, a
precise assignment of Fermi arcs, accomodating the predicted chiral charge of
the bulk Weyl points, has been difficult in these systems, and the topological
character of different surface features in the Fermi surface is not fully
understood. Here, employing a joint analysis from linear dichroism in
angle-resolved photoemission and first-principles calculations, we unveil the
orbital texture on the full Fermi surface of TaP(001). We observe pronounced
switches in the orbital texture at the projectedWeyl nodes, and show how they
facilitate a topological classification of the surface band structure. Our
findings establish a critical role of the orbital degrees of freedom in
mediating the surface-bulk connectivity in Weyl semimetals.
