Abstract Hydrothermal plumes are turbulent structures of intense heat and mineral smoke that rise and disperse into the deep ocean. Existing models generally characterize these systems as a single axisymmetric plume originating from a point source. However, this assumption breaks down in weakly venting, spatially distributed systems, where low‐flux discharge and strong background currents produce faint and distorted plumes that traditional centerline‐based diagnostics fail to characterize. We present a topology‐based visual analysis framework that treats plumes as time‐varying three‐dimensional scalar fields and captures their full structural variability. Using merge trees, we cluster plume snapshots into representative morphologies and uncover a clear coupling between plume structure and phases of the tidal cycle. To support exploration, we introduce a radial merge tree visualization that arranges plume similarity on a tidal clock, revealing periodic behaviors not discernible with existing techniques. We further develop an extremum graph based workflow that identifies discrete surface venting regions within a reconstructed porous rock, and use streamline visualizations to link subsurface transport pathways to the overlying plume.

Topological structures such as the merge tree provide an abstract and succinct representation of scalar fields. They facilitate effective visualization and interactive exploration of feature-rich data. A merge tree captures the topology of sub-level and super-level sets in a scalar field. Estimating the similarity between merge trees is an important problem with applications to feature-directed visualization of time-varying data. We present an approach based on tree edit distance to compare merge trees. The comparison measure satisfies metric properties, it can be computed efficiently, and the cost model for the edit operations is both intuitive and captures well-known properties of merge trees. Experimental results on time-varying scalar fields, 3D cryo electron microscopy data, shape data, and various synthetic datasets show the utility of the edit distance towards a feature-driven analysis of scalar fields.