This paper studies big data streams with regional-temporal extreme event (REE) structures and solar flare detection. An autoregressive conditional Fr'echet model with time-varying parameters for regional and its adjacent regionals extremes (ACRAE) is proposed. The ACRAE model can quickly detect rare REEs (i.e., solar flares) in big data streams and predict solar activity. The ACRAE model, with some mild regularity conditions, is proved to be stationary and ergodic. The parameter estimators are derived through the conditional maximum likelihood method. The consistency and asymptotic normality of the estimators are established. Simulations are used to demonstrate the efficiency of the proposed parameter estimators. In real solar flare detection, with the new dynamic extreme value modeling, the occurrence and climax of solar activity can be detected earlier than existing algorithms. The empirical study shows that the ACRAE model outperforms the existing detection algorithms with sampling strategies. (Joint work with Steven Moen and Jili Wang).