To evaluate search result diversification, which is supposed to meet different needs behind a same query, a number of evaluation frameworks are proposed. Although most of these frameworks take the probability distribution of information needs(usually called subtopics) underlying a query topic into account, they usually do not consider the subtopic taxonomy information. In this paper, the decay function is first introduced to take the subtopic taxonomy information into account. And then based on the decay function, a novel framework called the subtopic taxonomy-aware(STA) framework is proposed to define the structure that the taxonomy-aware diversity evaluation metrics would have. The decay functions used for the informational and navigational subtopics are also discussed. Experiments based on TREC and NTCIR test collections show the effectiveness of the proposed method.