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\appendix   \section{Appendix: Clustering evaluation}  Figure X \ref{fig:clustering_eval}  shows different ways of assigning ISCCP observations and ISCCP simulations to cloud regimes (clusters). We evaluate methods of assigning individual ISCCP-style histograms to cloud regimes (cluster centroids):   \begin{itemize}  \item Using the Euclidean distance between full (42-element) 42-element  CTP-$\tau$ joint histogram of cloud-top properties (HISTS)  \item Simplifying the CTP-$\tau$ histograms into histogram means: $\left(\overline{\alpha}, \overline{CTP}, TCC\right)$ (MEANS)  \end{itemize}  We observe: