Visual data analysis often requires grouping of data objects based on their similarity. In many application domains researchers use algorithms and techniques like clustering and multidimensional scaling to extract groupings from data. While extracting these groups using a single similarity criteria is relatively straightforward, comparing alternative criteria poses additional challenges. In this paper we define visual reconciliation as the problem of reconciling multiple alternative similarity spaces through visualization and interaction. We derive this problem from our work on model comparison in climate science where climate modelers are faced with the challenge of making sense of alternative ways to describe their models: one through the output they generate, another through the large set of properties that describe them. Ideally, they want to understand whether groups of models with similar spatio-temporal behaviors share similar sets of criteria or, conversely, whether similar criteria lead to similar behaviors. We propose a visual analytics solution based on linked views, that addresses this problem by allowing the user to dynamically create, modify and observe the interaction among groupings, thereby making the potential explanations apparent. We present case studies that demonstrate the usefulness of our technique in the area of climate science.