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Abstract Estimating and predicting the state of the atmosphere is a probabilistic problem for which an ensemble modeling approach often is taken to represent uncertainty in the system. Common methods for examining uncertainty and assessing performance for ensembles emphasize pointwise statistics or marginal distributions. However, these methods lose specific information about individual ensemble members. This paper explores contour band depth (cBD), a method of analyzing uncertainty in terms of contours of scalar fields. cBD is fully nonparametric and induces an ordering on ensemble members that leads to box-and-whisker-plot-type visualizations of uncertainty for two-dimensional data. By applying cBD to synthetic ensembles, we demonstrate that it provides enhanced information about the spatial structure of ensemble uncertainty. We also find that the usefulness of the cBD analysis depends on the presence of multiple modes and multiple scales in the ensemble of contours. Finally, we apply cBD to compare various convection-permitting forecasts from different ensemble prediction systems and find that the value it provides in real-world applications compared to standard analysis methods exhibits clear limitations. In some cases, contour boxplots can provide deeper insight into differences in spatial characteristics between the different ensemble forecasts. Nevertheless, identification of outliers using cBD is not always intuitive, and the method can be especially challenging to implement for flow that exhibits multiple spatial scales (e.g., discrete convective cells embedded within a mesoscale weather system). Significance StatementPredictions of Earth’s atmosphere inherently come with some degree of uncertainty owing to incomplete observations and the chaotic nature of the system. Understanding that uncertainty is critical when drawing scientific conclusions or making policy decisions from model predictions. In this study, we explore a method for describing model uncertainty when the quantities of interest are well represented by contours. The method yields a quantitative visualization of uncertainty in both the location and the shape of contours to an extent that is not possible with standard uncertainty quantification methods and may eventually prove useful for the development of more robust techniques for evaluating and validating numerical weather models.