A riser monitoring assembly is provided to monitor and manage a riser extending between subsea well equipment and a floating vessel. A riser measurement instrument module is connected adjacent a selected portion of the riser provides dynamic orientation data for the selected portion of the riser. A computer having a memory associated therewith and riser system analyzing management software stored thereon is in communication with the riser measurement module to process data received therefrom. The riser monitoring assembly can utilize real-time orientation data for the selected portion of the riser to analyze the riser dynamic behavior, to determine a model of the real-time structure of the riser, to determine and manage the existence of vortex induced vibration, to determine and manage riser stress levels, to manage riser inspection and riser maintenance, and to supplement determination and management of the position of the vessel.