Climate models produce output over decades or longer at high spatial and temporal resolution. Starting values, boundary conditions, greenhouse gas emissions, and so forth make the climate model an uncertain representation of the climate system. A standard paradigm for assessing the quality of climate model simulations is to compare what these models produce for past and present time periods, to observations of the past and present. Many of these comparisons are based on simple summary statistics called metrics. In this article, we propose an alternative: evaluation of competing climate models through probabilities derived from tests of the hypothesis that climate-model-simulated and observed time sequences share common climate-scale signals. The probabilities are based on the behavior of summary statistics of climate model output and observational data over ensembles of pseudo-realizations. These are obtained by partitioning the original time sequences into signal and noise components, and using a parametric bootstrap to create pseudo-realizations of the noise sequences. The statistics we choose come from working in the space of decorrelated and dimension-reduced wavelet coefficients. Here, we compare monthly sequences of CMIP5 model output of average global near-surface temperature anomalies to similar sequences obtained from the well-known HadCRUT4 data set as an illustration.

We used cluster analysis on 200-year-old tree-ring chronologies to examine the patterns that emerge from self-organization, driven by environmental heterogeneity, that might drive diversification in ponderosa pine (Pinus ponderosa). We determined the natural patterns on the landscape and then tested these groups against historically separated varieties within this species that could be evidence of diversification. We used 178 previously collected tree-ring chronologies from the western United States that were archived in the International Tree-Ring Databank. We explored a variety of clustering techniques, settling on Ward’s clustering with Euclidian distance measures as the most reasonable clustering process. These techniques identified two (p = 0.005) to ten (p = 0.01) potential natural clusters in the ponderosa pine chronologies. No matter the number of clusters, we found that the ponderosa pine varieties ponderosa and benthamiana always cluster together. The variety scopulorum differentiates clearly on its own, but brachyptera is a mix of diverse groups, based on the environmental driving factors that control tree-ring chronology variability. Cluster analysis is a useful tool to examine natural grouping on the landscape using long-term tree-ring chronologies, enabling the researcher to examine the patterns of environmental heterogeneity that should lead to speciation. From this analysis, we suggest that the brachyptera variety should be more varied genetically.