Uncertainty visualization for variable associations analysis

Uncertainty is inevitable in scientific simulations. As the increase in computing power, ensemble data have been generated for multiple variables. Uncertainty has become a great challenge to the analysis of variable associations for multivariate ensemble data, as the variable associations are very complex and diverse among different ensemble members. In this paper, we propose a novel visualization method to present the uncertain associations between a reference variable and the associated variable for multivariate ensemble data. Considering the huge scale of original ensemble data, Gaussian mixture model (GMM) is exploited to quantify the uncertainty and represent the original data compactly. To reveal the spatial uncertainty of the reference variable, a GMM-based method for extracting uncertainty isosurface is proposed and shows the accuracy advantage over Gaussian-based method. Meanwhile, a data reduction method is proposed to enhance the performance of extracting uncertainty isosurface. By mapping the values of the associated variable onto the uncertainty isosurface of the reference variable, a syncretic rendering method is proposed to show the variable associations intuitively. Besides, the screen space accumulating strategy is introduced to present the uncertainties of the associations. Furthermore, we provide a switchable view for users to obtain the credibility of variable associations. The credible associations can assist users to make reliable decisions. For the regions with not credible associations, the detailed information of the associations in every ensemble member can be explored through animation for further analysis. The effectiveness of our method is demonstrated by synthetic, climate and combustion data sets.