The Distributions of H

Figure 3 shows that each of the three generation regions (WP, ATL and EP) demonstrate a clear annual cycle in the fields of H in which the standard deviation is relatively large in the active months and relatively small during the rest of the year. Each of the distributions is almost symmetrical and appears to be confined within the —3 < H < 3 K—1 range. The histograms for the SUBTROPICS (Fig. 3) are also almost symmetrical, but confined within the much smaller range, —0.5 < H < 0.5 K—1, with only a modest seasonal cycle which, as to be expected, is of opposite phase to that in the northern hemisphere generating regions. On the basis of the arguments presented in The Physical Meaning of the Hurricane Index, this is the basic reason for the absence of TCs in the subtropical latitudes. An inspection of the distributions indicates that they all have a steeper taper than the corresponding normal distributions, and more importantly that their standard deviations are all much

Table 2 The tropical cyclone generation regions and the subtropical reference region Western Pacific (WF) 10—25°N 100—180°E Eastern Pacific (EP) 10-25°N 140-90°W Atlantic (ATL) 10-25°N 90-30°W Subtropics (SUBTROPICS)_25-40°S_180-150°W

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Fig. 3 Histograms of the monthly mean H for WP, ATL, EP and SUBTROPICS for the period 1979-2005

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Fig. 3 (continued)

greater than their mean values. In addition, the approximate symmetry of the distributions of H points out that the spin-up and spin-down phases of the loop discussed in The Physical Meaning of the Hurricane Index, which characterizes the thermodynamic equilibrium, are complementary.

The hodographs of the standard deviation of H versus the mean of H show a negative annual mean H for each of the generation regions (WP, ATL and EP) and a positive annual mean H in the SUBTROPICS region, where H « 0 (Fig. 4). The negative annual mean H values in the three generation regions, and the near zero mean value in the subtropics are consistent with the zonal mean graphs of lnE versus T (Figs. 1 and 2). The standard deviations of H in each generation region have a maximum in September, whereas the minimum of H occurs in November in the WP and EP, and in August in the ATL. It is important to point out, however, that the mean and standard deviation values of H cannot be meaningfully compared between the three generation regions as they depend on the spatial specification adopted (Table 2), however, it would be expected that the structure of the hodo-graph would not be too sensitive to this choice.

These results suggest that the standard deviation of the H-index, rather than its mean value, should be used as a suitable index for the inter-monthly variability of the potential for TC development. We explore this proposal in Section 6.

The seasonal cycle of the standard deviation of the H index is compared with the SST cycle for each region in Fig. 5. The H-index signal tends to show two plateaux, which correspond respectively with the active and the inactive hurricane seasons, whereas the SST signal is sinusoidal in character.

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