deletions | additions       diff --git a/Clustering evaluation.tex b/Clustering evaluation.tex  index b743819..e431b44 100644  --- a/Clustering evaluation.tex  +++ b/Clustering evaluation.tex 
...
\begin{itemize}  \item Using the Euclidean distance between full 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)  \item The PDF of Euclidean distances is compared between the two methods of assigning histograms to cloud regimes: they aren't directly comparable due to the different number of dimensions in the vectors.  \end{itemize}  We observe:  \begin{itemize}  \item The observed clouds when applied using histogram means (OBS MEANS) have less coherence (more spread) in the range of cloud-top properties included. In some cases the frequency of occurrence of the cloud regimes is broadly similar to OBS HISTS (e.g. S4, S6, S7), while in others the regimes are strongly over- or under-represented (e.g. S1, S3, S8).   \item The simulated cloud when applied using the full histograms (SIM HISTS) sometimes generate comparable distributions of cloud-top properties (S2, S3, S8), but frequently---especially where mid-level cloud is observed by not modelled---there is a strong diagonal component to the distribution (e.g. S5, S6, S7).   \item The simulated cloud applied using histogram means (SIM MEANS) diverges significantly from both the observed histograms and the simulated histograms (SIM HISTS); the diagonal component is exaggerated even in optically thinner regimes (S2, S3), and some regimes are strongly under-represented (S6, S7).  \end{itemize}  Based on this comparison, assigning simulated ISCCP histograms to clusters based on the histogram mean properties \citep[as in][]{Williams_2009} is likely to introduce significant biases in both the properties and coherence of the resulting cloud regime members, as well as the frequencies of occurrence of those regimes.  It isn't clear how this approach can be avoided when making an intercomparison of GCMs, as in \citet{Williams_2009}, given the problems identified in \cite{Williams_2007}; hybrid cloud regimes for intercomparison may be possible, but this would require further investigation.