Tropical Cyclones as a Critical Phenomenon

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Abstract

It has been proposed that the number of tropical cyclones as a function of the energy they release is a decreasing power-law function, up to a characteristic energy cutoff determined by the spatial size of the ocean basin in which the storm occurs. This means that no characteristic scale exists for the energy of tropical cyclones, except for the finite-size effects induced by the boundaries of the basins. This has important implications for the physics of tropical cyclones. We discuss up to what point tropical cyclones are related to critical phenomena (in the same way as earthquakes, rainfall, etc.), providing a consistent picture of the energy balance in the system. Moreover, this perspective allows one to visualize more clearly the effects of global warming on tropical-cyclone occurrence.

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Power-law distributions in empirical data

Cosma Rohilla Shalizi, Aaron Clauset, M. Newman (2007)

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.

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The increasing intensity of the strongest tropical cyclones.

James B. Elsner, James P Kossin, Thomas Jagger (2008)

Atlantic tropical cyclones are getting stronger on average, with a 30-year trend that has been related to an increase in ocean temperatures over the Atlantic Ocean and elsewhere. Over the rest of the tropics, however, possible trends in tropical cyclone intensity are less obvious, owing to the unreliability and incompleteness of the observational record and to a restricted focus, in previous trend analyses, on changes in average intensity. Here we overcome these two limitations by examining trends in the upper quantiles of per-cyclone maximum wind speeds (that is, the maximum intensities that cyclones achieve during their lifetimes), estimated from homogeneous data derived from an archive of satellite records. We find significant upward trends for wind speed quantiles above the 70th percentile, with trends as high as 0.3 +/- 0.09 m s(-1) yr(-1) (s.e.) for the strongest cyclones. We note separate upward trends in the estimated lifetime-maximum wind speeds of the very strongest tropical cyclones (99th percentile) over each ocean basin, with the largest increase at this quantile occurring over the North Atlantic, although not all basins show statistically significant increases. Our results are qualitatively consistent with the hypothesis that as the seas warm, the ocean has more energy to convert to tropical cyclone wind.