High accuracy simulation of compressor surge origin and growth is an important challenge for designers of systems using compressors likely to develop that severe instability. Indeed, understanding its driving phenomena, which can be system dependent, is necessary to build an adequate strategy to avoid or control surge emergence. Computational fluid dynamics (CFD) simulations, commonly used to explore flow in the compressor, need then to be extended beyond the compressor as surge is a system scale instability. To get an insight on the path to surge and through surge cycles, a reliable alternative to full three-dimensional (3D) system modeling is used for a turbocharger compressor inserted in an experimental test rig. The air flow in the whole circuit, is modeled with a one-dimensional (1D) Navier Stokes approach which is coupled with a 3D unsteady RANS modeling of the 360 deg air flow in the centrifugal compressor including the volute. Starting from an initial stable flow solution in the system, the back-pressure valve is progressively closed to reduce the massflow and trigger the instability. An entire deep surge loop is simulated and compared with good agreement with the experimental data. The existence of a system-induced convective wave is revealed, and its major role on surge inception at diffuser inlet demonstrated.