Compositionality is a property of natural language which is of prime importance: It enables humans to form and conceptualize potentially novel and complex ideas, by combining words. On the other hand, the symbol grounding problem examines the way meaning is anchored to entities external to language, such as sensory percepts and sensory-motor routines. In this paper we aim towards the exploration of the intersection of compositionality and symbol grounding. We thus propose a methodology for constructing empirically derived models of grounded meaning, which afford composition of grounded semantics. We illustrate our methodology for the case of adjectival modifiers. Grounded models of adjectively modified and unmodified colors are acquired through a specially designed procedure with 134 participants, and then computational models of the modifiers "dark" and "light" are derived. The generalization ability of these learnt models is quantitatively evaluated, and their usage is demonstrated in a real-world physical humanoid robot. We regard this as an important step towards extending empirical approaches for symbol grounding so that they can accommodate compositionality: a necessary step towards the deep understanding of natural language for situated embodied agents, such as sensor-enabled ambient intelligence and interactive robots.