Computer-generated simulations and visualizations in digital planetariums have the potential to bridge the comprehension gap in astronomy education. Concepts involving three-dimensional spatial relationships can be difficult for the layperson to understand, since much of the traditional teaching materials used in astronomy education remain two-dimensional in nature. We study the student performance after viewing visualizations in an immersive theater and in non-immersive classrooms for the topic of seasons in an introductory undergraduate astronomy course. Using weekly multiple-choice quizzes to gauge student learning, comparison of curriculum tests taken immediately after instruction and pre-instruction quizzes show a significant difference in the results of students who viewed visualizations in the planetarium versus their counterparts who viewed non-immersive content in their classrooms, and those in the control group that saw no visualizations whatsoever. These results suggest that the immersive visuals help by freeing up cognitive resources that can be devoted to learning, while visualizations shown in the classroom may be an intrinsically inferior experience for students.
The optimal forcing patterns for El Niño-Southern Oscillation (ENSO) are examined for a hierarchy of hybrid coupled models using generalized stability theory. Specifically two cases are considered: one where the forcing is stochastic in time, and one where the forcing is time independent. The optimal forcing patterns in these two cases are described by the stochastic optimals and forcing singular vectors, respectively. The spectrum of stochastic optimals for each model was found to be dominated by a single pattern. In addition, the dominant stochastic optimal structure is remarkably similar to the forcing singular vector, and to the dominant singular vectors computed in a previous related study using a subset of the same models. This suggests that irrespective of whether the forcing is in the form of an impulse, is time invariant, or is stochastic in nature, the optimal excitation for the eigenmode that describes ENSO in each model is the same. The optimal forcing pattern, however, does vary from model to model, and depends on air-sea interaction processes.Estimates of the stochastic component of forcing were obtained from atmospheric analyses and the projection of the dominant optimal forcing pattern from each model onto this component of the forcing was computed. It was found that each of the optimal forcing patterns identified may be present in nature and all are equally likely. The existence of a dominant optimal forcing pattern is explored in terms of the effective dimension of the coupled system using the method of balanced truncation, and was found to be O(1) for the models used here. The implications of this important result for ENSO prediction and predictability are discussed.
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