We present a new technique for the simultaneous visualization of an arbitrary number of scalar fields defined on a surface. The technique is called Generalized Atmosphere Upper Bound Level (GAUBL), since it is an evolution of our previous AUBL technique, that allowed for the visualization of a single scalar field. The generalized AUBL can highlight the dependencies and interactions between many scalar fields, and can handle a multi-valued scalar field as a special case. We have implemented the GAUBL into a visualization tool that handles triangle-based surface models, and we show here some experimental results.