Identifying global patterns of stochasticity and nonlinearity in the Earth System

Abstract. We demonstrate that two simple measures of time series analysis are able to capture different dynamical and statistical properties of large-scale atmospheric phenomena. We consider two surface air temperature (SAT) datasets, covering a spatial grid of points over the Earth surface (NCEP CDAS1 and ERA Interim reanalysis). In each location we analyze i) the distance between the lagged SAT time series and the insolation (i.e., the local top-of-atmosphere incoming solar radiation), and ii) the Shannon entropy computed from the probability distribution function (pdf) of SAT values. The distance quantifies the similarity between the lagged SAT waveform and the isolation waveform, while the entropy, as defined in information theory, measures the degree of disorder or uncertainty of each time series, which we refer to as stochasticity: the entropy captures the shape of the SAT pdf and is maximum when the pdf is uniform. With the distance measure we uncover well-defined spatial patterns formed by regions with similar SAT response to solar forcing, while with the entropy measure, we uncover regions that have SAT pdf of similar shape. The entropy analysis also allows identifying the geographical regions in which SAT time series has extreme values (i.e., values which are extreme in the local statistics), because the long-tail shape of the pdf is captured as low entropy values. We uncover significant differences between the NCEP CDAS1 and ERA Interim datasets in specific geographical regions, which are due to the presence of extreme values in one dataset but not in the other. In this way, the entropy maps are a valuable tool for anomaly detection and model inter-comparisons.