The Climatic Temporal Feature Space: Continuous and Discrete

Climatic zones, representing seasonal variations in temperature (T) and precipitation (P), are generally mapped geographically using discrete classifications with distinct boundaries. However, it is well known that global T and P vary continuously in space and time with steep gradients occurring infrequently. The objective of this analysis is to use complementary forms of dimensionality reduction to quantify the spatiotemporal dimensionality of the climate system and to produce a continuous representation of global climate based on the temporal feature space of historical T and P alone. We characterize the continuous global feature space using principal components (PCs) to identify a parsimonious set of temporal endmember T and P patterns bounding the feature space of all observed T and P patterns. These endmember T and P patterns provide the basis for a linear temporal mixture model that can represent decadal T and P patterns of any geographic location as fractions of the endmember T and P patterns. Inverting this linear mixture model for each geographic T+P time series gives an estimate of the fractional contribution of each endmember to the observed time series. The resulting temporal endmember fraction maps provide a continuous representation of the Euclidean proximity of T and P observations at every geographic location to each of the temporal endmember climates bounding the space. The spatiotemporal dimensionality implied by the variance partition of T + P time series for 67,420 land-based observations suggests that the T + P temporal feature space is effectively 3D, accounting for 92% of total variance. From the topology of the feature space, we identify 4 bounding temporal endmembers upon which to base the linear temporal mixture model. Inversion of the model for each normalized observed time series yields endmember fraction estimates and a model misfit distribution with 99% of misfit < 0.21. For comparison, we also render temporal feature spaces from ensembles of 2D manifolds within the T + P space derived from suites of t-distributed Stochastic Neighbor Embeddings (t-SNE) to identify discontinuities in the feature space. Comparison of spatial PC(t-SNE) across hyperparameter settings reveals consistent structure and little hyperparameter sensitivity to temporal feature spaces rendered by t-SNE. Combining the physically interpretable continuous global structure resolved by the PC feature space with the finer scale manifold structure resolved by the t-SNE feature space provides a continuous alternative to discrete classifications of climate that cannot represent the continuous character of its temporal feature space.