Turbulent dynamical systems, such as those governing weather and climate, are characterized by both a high-dimensional phase space and a large number of instabilities, which are ubiquitous among many complex systems in science and engineering, including climate, material, and neural science. Following a brief introduction of the reduced-order models for predicting the statistical responses and uncertainty quantification in complex turbulent dynamical systems, Dr. Di Qi and Dr. Lei Wang will discuss the relevance of reduced-order models with weather and climate.