Studying temporal dynamics of topics in social media is very useful to understand online user behaviors. Most of the existing work on this subject usually monitors the global trends, ignoring variation among communities. Since users from different communities tend to have varying tastes and interests, capturing community-level temporal change can improve the understanding and management of social content. Additionally, it can further facilitate the applications such as community discovery, temporal prediction and online marketing. However, this kind of extraction becomes challenging due to the intricate interactions between community and topic, and intractable computational complexity. In this paper, we take a unified solution towards the community-level topic dynamic extraction. A probabilistic model, CosTot (Community Specific Topics-over-Time) is proposed to uncover the hidden topics and communities, as well as capture community-specific temporal dynamics. Specifically, CosTot considers text, time, and network information simultaneously, and well discovers the interactions between community and topic over time. We then discuss the approximate inference implementation to enable scalable computation of model parameters, especially for large social data. Based on this, the application layer support for multi-scale temporal analysis and community exploration is also investigated. We conduct extensive experimental studies on a large real microblog dataset, and demonstrate the superiority of proposed model on tasks of time stamp prediction, link prediction and topic perplexity.