In order to compare the predictions of the standard deviation of the H-index with observations, we construct the integrated tropical cyclone index, where n is the number of TCs with the Saffir-Simpson scale (Sj). The count, C, which is computed from data in the website, http://weather.unisys.com/hurricane/, weights the tropical cyclones according to their intensity. The monthly average (Vm) of the standard deviation of the H-index (V), versus the corresponding monthly average (Cm) of the count (C) for each region (Fig. 6) has a linear trend with a high regression coefficient (r). The statistics of the regressions (Table 3), where s is the slope of Cm versus Vm, and V0 is the intercept of Vm, at which no tropical cyclones occur (Cm = 0) have been used to simulate the inter-monthly variability of tropical cyclone occurrence (C) over the record period (1979-2005), from V in each region using the relation,

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Sept Sept Sept e-ewp July 0.05 Fig. 4 Hodographs of the average (over the period 1979-2005) mean monthly standard deviation versus the mean of H for WP, ATL, EP and SUBTROPICS k26 w 25 24 23 Fig. 5 Annual cycle of the average mean monthly standard deviation of H and the SST for WP, ATL, and EP k26 w 25 24 23 J F M A M J JASOND Month Fig. 5 Annual cycle of the average mean monthly standard deviation of H and the SST for WP, ATL, and EP Fig. 6 Regressions of the average mean monthly standard deviation of H versus the monthly averaged count for WP, ATL, and EP 0.6 Table 3 Regression coefficients for the monthly average count versus the monthly average standard deviation of H It is apparent from Fig. 7, that the simulated variability of C has a high skill. The correlation coefficients between the observed and simulated (modeled) monthly time series of C for the WP, ATL and EP are respectively, 0.62, 0.53 and 0.42. An inspection of Fig. 7 reveals some interesting features. In the WP, the relatively small TC activity in 1998 and 1999 followed by a subsequent increase in activity is very well represented as also is most of the inter-monthly variability in the early years, except for some high activity years which are under-simulated. In the ATL, the minimum in TC activity between 1990 and 1995 is well represented, as also is the inter-monthly signal in later years, except for 2004. In the EP, which has the poorest correlation, the variability prior to 1993 is very well simulated as also is that after 1998. Discrepancies, however, occur during the years 1992-1994, which are under-simulated. Time (years) Fig. 7 Time series of C for the period 1979-2005 from observations and from the H-index model for WP, ATL, and EP Time (years) Fig. 7 Time series of C for the period 1979-2005 from observations and from the H-index model for WP, ATL, and EP The field of H during each month can of course be displayed to show the structures which give rise to its standard deviation. This was done for the ATL in Bye and Keay (2008) to illustrate why 2005 was a prodigious hurricane season whereas during 1983 no major hurricanes were recorded. It was apparent that the spatial structure of both the SST and the evaporation fields contributed to the field of H, from which the standard deviation that is used as an index for TC initiation was computed. The patterns of H incorporated regions of more or less permanent sign, either positive or negative, which were interpreted in terms of the local climatology, and other regions in which the sign of H changed from month to month. In general terms, these two scenarios are analogous to stationary and transient eddies in a turbulent fluid. These conclusions are consistent with the results from global simulations with very high resolution in the Atlantic Ocean (Chauvin et al. 2006) which emphasized the importance of the SST anomaly distribution on hurricane activity. Climate Model Downscaling of Tropical Cyclone Occurrences Climate models are run with various resolutions, and many are unable to resolve the tropical cyclones, although a few with resolutions of <25 km can. This gives the opportunity to use the techniques of this paper in a predictive manner to downscale the results of the coarse resolution models to provide information on tropical cyclone occurrence, and to use the results of the fine resolution models to make an explicit comparison with the resolved tropical cyclone occurrences. In general it would be expected that the standard deviation of the H-index would differ from that derived from the reanalysis data owing to differences in the resolution scale, however, a comparison between epochs should show whether the likelihood of tropical cyclone initiation would be less or greater under global warming. Here, we present the results from the CSIRO Mk3 coupled climate model (Gordon et al. 2002) for two epochs, 1961-1990 and 2051-2080, and consider the mean monthly signals over these two periods. Figure 8 shows that the standard deviation of H, obtained from the model for the period, 1961-1990, is about one-half that from the reanalysis data (Fig. 5). In the WP, its seasonal signal is very similar to that of the reanalysis data, but in the ATL and EP it differs substantially. The seasonal SST signals from the model results (Fig. 8) are similar to those from the reanalysis data (Fig. 5) for each region, but the annual mean SSTs differ; the model being about 2°C less than the reanalysis, except for summer in the EP in which they are in agreement. These discrepancies, although significant, will not deter us from making a comparison between the two epochs from the model in order to gain some insight into likely changes in tropical cyclone activity under global warming. It is emphasized however that the methodology to be used in this comparison can also be k 0.4 30 28 26 24 22 20 ## MonthsFig. 8 Annual cycle of the average mean monthly standard deviation of H and SST obtained from the climate model for the periods 1961-1990 and 2051-2080 for the WP, ATL, and EP J FMAMJ JASOND J FMAMJ JASOND
J FMAMJ JASOND J FMAMJ JASOND applied to the results from other climate models which may represent the present day monthly climatology better. The SST signal shows a very similar mean annual increase in the WP, ATL and EP of 1.54, 1.43 and 1.44°C respectively, which is almost uniform across the seasons in each basin (Fig. 8). The mean annual standard deviation of H, however, shows only a very modest increase in each basin of 3%, but with a significant change in the seasonal signal. These results indicate that the most important agent of change which determines H is the large scale adjustment of the evaporation and SST fields, rather than simply an increase in SST. In order to see the predicted change in TC climatology more clearly, we have normalized the seasonal signal of the standard deviation of H in the model for the period, 1961-1990 by computing the factor, and then evaluating, Vm' = F (Vm)modei(2051-2080). Vm' is the mean monthly standard deviation of H that would be obtained during the period 2051-2080 if the monthly signal of the model for the period 1961-1990 and the reanalysis signal for 19792005 were identical, on the assumption that the proportional changes in monthly standard deviation of H between the two model periods are correct. Fig. 9 shows the monthly averaged counts obtained by substituting for (Vm) reanalysis and Vm' in (13); the increases in the mean annual counts in the WP, EP and ATL are 20%, 50% and 100% respectively. This surprising result, that the mean annual counts have increased much more than the increases in the mean annual standard deviation of H of 3%, is due to the ratio of the standard deviations between the two model periods (1961-1990 and 2051-2080) tending to be larger in summer than in winter. In both the WP and ATL the monthly average count in the period 2051-2080 has an early season maximum which is absent in the contemporary climatology. The TC season is essentially advanced in the WP and lengthened in the ATL. The EC TC season is also lengthened with a small increase in the maximum count. We emphasize that as the count (C) depends on the intensity, any increase may be due to an increase in intensity rather than an increase in numbers. |

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