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In recent years, critical slowing down phenomenon has shown great potentials in the area of disclosing whether complex dynamic system tends to critical cataclysm. Based on the concepts of critical slowing down, the observed data of pacific decadal oscillation (PDO) index and the national average monthly temperature are processed in this article to study the precursory signals of abrupt climate change. Take the abrupt climate change in a period from the late1970s to the early 1980s for example, the variances and autocorrelation coefficients which can characterize critical slowing down are calculated separately. The results show that the PDO index and the national average monthly temperature both have obviously a critical slowing down phenomenon before the abrupt climate change takes place, which indicates that critical slowing down phenomenon is a possible early warning signal for abrupt climate change. The introduction of critical slowing down theory into abrupt climate change precursory signals and study on it have practical significance and important scientific value for thoroughly understanding the abrupt climate change and for catching the precursory signals of abrupt climate change.

Clutter suppression in heterogeneous environments is a serious challenge for airborne radar. To address this problem, a matrix-manifold-based clutter suppression method is proposed. First, the distributions of training data in heterogeneous environments are analyzed, while the received data are characterized on a Riemannian manifold of Hermitian positive definite matrices. It is indicated that the training data with different distributions with the same power are separated, whereas data with the same distribution are closer together. This implies that the underlying geometry of the data can be better revealed by manifolds than by Euclidean space. Based on these properties, homogeneous training data are selected by establishing a binary hypothesis test such that the negative effects of the use of heterogeneous samples are alleviated. Moreover, as exploiting a geometric metric on manifolds to reveal the underlying information of data, experimental results on both simulated and real data validate that the proposed method has a superior performance with small sample support.

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