In this paper, we propose a multi-scale modeling approach for SoS architecture description. This study aims at mastering the complexity of such systems both at the human and automated processing levels by considering increasingly detailed modeling scales. Some high level properties can be expressed on informal descriptions with a high level of abstractions and checked on simple formal descriptions. Some other properties need more detailed descriptions to be expressed and formal specifications to be elaborated. We elaborate a set of coarse-grained and fine-grained models and we define the corresponding refinement rules to build correct by design Publish-Subscribe software architectures. The defined rules respect the principle of information dissemination guaranteeing that the produced information reaches all the subscribed consumers. In order to formalize the multi-scale characterization process and to use it in the design process, we have chosen to follow an iterative modeling methodology that captures diverse perspectives of the performance modeling of SoS. We discuss how our approach to modeling supports the specific characteristics of an SoS and illustrate this through a case study, based on the (Integrated Air Defense) IAD scenario, demonstrating how we may obtain correct models within a SoS with emergent properties.