Scientific modeling provides mathematical abstractions of real-world systems and builds software as implementations of these mathematical abstractions. Ocean science is a multidisciplinary discipline developing scientific models and simulations as ocean system models that are an essential research asset. In software engineering and information systems research, modeling is also an essential activity. In particular, business process modeling for business process management and systems engineering is the activity of representing processes of an enterprise, so that the current process may be analyzed, improved, and automated. In this paper, we employ process modeling for analyzing scientific software development in ocean science to advance the state in engineering of ocean system models and to better understand how ocean system models are developed and maintained in ocean science. We interviewed domain experts in semi-structured interviews, analyzed the results via thematic analysis, and modeled the results via the business process modeling notation BPMN. The processes modeled as a result describe an aspired state of software development in the domain, which are often not (yet) implemented. This enables existing processes in simulation-based system engineering to be improved with the help of these process models.