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Secondary eyewalls occur in 70% of major tropical cyclones (TCs), and are associated with rapid changes in storm intensity and rapid broadening of strong winds. While mechanisms of secondary eyewall formation have been investigated from various perspectives, the explicit conditions on which secondary eyewalls occur in TCs remain veiled, leaving substantial uncertainties in TC intensity forecast, especially for the most extreme events. In this study, we present a simple diagnostic, in form of a singularity, for secondary eyewall occurrence in TCs. The diagnostic is solely dependent on three basic storm characteristics (the maximum wind speed, the radius of maximum wind, and the latitude) and shown to compare well with satellite observations. It provides a valuable tool to improve the understanding, modeling and risk assessment of secondary eyewall storms., Comment: 20 pages, 6 figures

Since the 1920s, when the three oscillations ENSO, NAO and NPO were found and defined, the theory of ocean-atmosphere coupling is particularly important in explaining the phenomena of atmospheric physics, then defined more than ten climate indexes, such as SOI, AO, AAO and Nino monitoring area and so on, the indexes usually adopt standardized sea level pressure (SLP) difference or standardized sea surface temperature anomaly (SSTA) difference definitions. The survey is carried out with seventy stations runoff of major rivers in the world shows that the correlation coefficient between these indexes and runoff is very low, most of which is between 0.1-0.2, the impact of the index on the hydrologic climate cannot be truly reflected, which has led to doubts about the clear physical mechanism and even questions of teleological authenticity. This is due to the fact that standardization is a nonlinear process, which changes the structure of the original data, causing the correlation coefficient to be low. Using sea surface temperature difference (SSTD) to define these climate indexes, the correlation coefficient is significantly improved, the Hankou station of Yangtze river, Darband station of Ind, Hope station of Fraser, Bangui station of Oubangui generally exceeds 0.8 strong degree, which prove that these relevant elements have a high resonance effect, there must be a common driving physical quantity. We find that the sun-earth distance has a very strong resonance effect, it is the earth's rotational orbit that determines their common activity intensity and cycle characteristics. The sun-earth distance can accurately calculate the tens and hundreds years of SST and SSTD, if using the SST or SSTD as the climate indicators, which express physical process of various ocean-atmosphere coupling, we can thoroughly solve long-term ultra-long-term forecast of international difficulty problems.