Modal analysis has been used to gain physical insight into unsteady flows in a data-driven and an operator-driven manner. Examples include proper orthogonal decomposition, dynamic mode decomposition, and resolvent analysis. However, their formulations often rely on the assumption of time-invariant mean flow, thereby encountering challenges in capturing the dominant characteristics about unsteady, aperiodic base flow. Since such flows with a time-varying base state emerge in a range of situations, including dynamic stall and unpredictable weather, of interest here is how modal analysis can be employed while accordingly extracting their transient characteristics. We discuss a data-driven snapshot decomposition, extracting time-varying modal structures that most contribute to a user-defined (target) variable in the future. This is achieved with a nonlinear, causal machine-learning approach that constrains the data-driven decomposition with the assistance of information theory, thereby extracting the causal relationship between a future variable and the current flow structures. Through the analysis with examples of unsteady aerodynamic flows across a range of Reynolds numbers, we show that it is possible to extract physically-interpretable, causal vortical structures with respect to a future aerodynamic response over time. We further argue the scalability of the current technique by employing two different learning approaches, i.e., local and global learning, enabling the selection of algorithms based on the spatiotemporal degree of freedom of flow fields considered. The present study provides causality-based insights into a range of unsteady aerodynamic flows.