Wavelet Lag Regression Analysis of Atlantic Tropical Cyclones

John Moore, Aslak Grinsted, and Svetlana Jevrejeva

Abstract We discuss a novel wavelet-lag coherence method to study of cause-and-effect relations over a large space of timescales, phase lags and periods. We use 135 years of observational records to demonstrate how sea-surface temperature, sea-level pressure and cyclone numbers are linked. We examine the statistical properties of the time series and test how departure from Normality affects results found using the method. We also examine how historical inaccuracy in counting tropical cyclone numbers could influence the findings. Robustly we find that SST and cyclones in a negative feedback loop, where rising SST causes increased numbers of cyclones, which reduce SST. This is statistically most significant at decadal and not at longer periods. Only at periods of about 30 years do significant differences arise in using recently proposed corrections to cyclone numbers, and forcing the empirical distribution of cyclone numbers to be Normal. This could be incorrectly interpreted as support for a long period Atlantic Multidecadal Oscillation, whereas it actually reflects the time-varying bias functions applied to the observations. There is evidence of some linkage between Northern hemisphere snow cover and cyclone numbers, however this seems to be due to a common causative relationship between the known tropical cyclone drivers of ENSO and decadal scale North Atlantic ocean-atmospheric circulation systems.


Increases in Atlantic tropical cyclone intensity have been related to increases in Atlantic sea surface temperature (SST), and Elsner (2007) has shown that it is likely to be rising global temperatures that drive the increases in both cyclone intensity and Atlantic SST. However, the nature of the climate relationships to tropical cyclones is likely to be complex, and certainly includes oceanic and atmospheric circulation patterns that operate on ocean basic scales. Significant but weak

J.B. Elsner and T.H. Jagger (eds.), Hurricanes and Climate Change, 139

doi: 10.1007/978-0-387-09410-6, © Springer Science + Business Media, LLC 2009

statistical correlations exist between the Atlantic hurricane source region and the northern Atlantic (Goldenberg et al., 2001) and tropical Pacific warm pools (Wang et al., 2006). Several authors have used these statistical relationships to produce predictive models of Atlantic hurricane season intensity and tropical storm numbers (e.g. Elsner and Jagger, 2006; Sabbatelli and Mann, 2007). In contrast with this kind of approach, here we attempt to understand relationships between the large scale driving mechanisms and Atlantic tropical storm activity by examining the behaviour of the various multi-year cycles that exist in the time series. Decadal cycles are fairly ubiquitous across the planet, and are therefore persuasive of a global-scale climate mechanism (Jevrejeva, Moore and Grinsted, 2004; Moron, Vautard and Ghil, 1998; Dijkstra and Ghil, 2005). The main features of the planet's climate are the ENSO and the polar annular modes, which is determined by the strength of the polar stratospheric vortex (Thompson and Wallace, 1998). An index of Atlantic climate variability that is often (but not always - Jevrejeva and Moore, 2001) closely related to the arctic annual mode (the Arctic Oscillation) is the North Atlantic Oscillation (NAO). Unlike the purely polar defined annular modes, the NAO is linked to the tropics via its interaction with the Atlantic thermohaline circulation, most particularly through the modulation of the Gulf Stream mean-derings at 7.8 year periods (Dijkstra and Ghil, 2005). This is significant as Elsner, Kara and Owens (1999), noticed a 7.8 year periodicity in hurricane frequency.

Moore, Grinsted and Jevrejeva (2008) showed that robust linkages that may imply causal relationships between global sea-surface temperature (SST), pressure fields and cyclones exist. However, challenging the identification of such linkages are both the uncertainties in long-term observational records and the robustness of the advanced statistical methods designed specifically to extract possibly causal relationships that may be non-stationary and develop over many years. Here we examine how the results from wavelet lag regression are to perturbation of 135-year observational record and demonstrate cyclone numbers are linked on different time scales with high latitude processes that also determine snow cover in the Northern Hemisphere.


In contrast with modern satellite-era observations of hurricane wind speeds and atmospheric physical variables, numbers of Atlantic tropical cyclones per year (TC), has been collected since at least 1851. They are defined simply as non-frontal, synoptic-scale cyclones over tropical or sub-tropical waters (Jarvinen, Neumann, and Davis, 2005). TC representing cyclone count and Power Dissipation Index (PDI) (Emanuel, 2005; Landsea, 2005), an index of hurricane destructive power available from 1944-2004 are correlated at 0.68. Recent modifications to TC have been suggested (Landsea, 2007; Mann et al., 2007), however testing our results with the proposed time-varying bias added to TC makes only very slight differences to our results. For example the correlation coefficient between PDI and TC changes from 0.68 to 0.69. While Landsea (2007) makes good arguments for the systematic undercounting of tropical cyclones in the past due to the their existence being unnoticed, Mann et al., (2007) suggest various difficulties with a simple correction under the assumption of stationary climate forcing, and point out that sparse observations can also lead to over-counting when a single event is counted as two or more events. Moore, Grinsted and Jevrejeva (2008) showed the correlation between PDI and TC has varied over time, but for much of the common period of data the correlation is significant at the 95% level; with only the period prior to 1955 showing consistently lower significance. Moore, Grinsted and Jevrejeva (2008) concluded that as the moving correlation between TC and PDI (Fig. 1) was generally high, that TC could be used as a surrogate with reasonable confidence. Here, however we will examine the revised TC in some detail. The long TC record allows more rigorous significance testing for long period variability than analyses that have focused on the instrumental records available only from 1940s or later (Emanuel, 2005; Michaels, Knappenberger and Davis, 2006).

We consider the set of SSTs for the Atlantic averaged over the area 6-18°N, 20-60°W, defined as the cyclone main development region (MDR), during the months of August, September, and October, (SSTC). We use the HadISST2 data (Rayner et al., 2003) which extends from 1870 to 2004. There is no theory that predicts the number of Atlantic tropical storms directly as a function of SST (or potential intensity). GCM simulations suggest that there is a link between rising SST and strength of hurricane maximum wind speed, such that a 1°C rise in SSTC leads to a 5% increase in maximum wind speed (Knutson and Tuleya, 2004).

1830 1900 1920 1940 1960 1980 2000


Fig. 1 Time series of TC (black), modified TC (grey dotted) and PDI (grey, multiplied by 10)

1830 1900 1920 1940 1960 1980 2000


Fig. 1 Time series of TC (black), modified TC (grey dotted) and PDI (grey, multiplied by 10)

However observations in the Atlantic region suggest that the PDI, which is dominated by the largest storms, has increased by about 20% per °C since 1980, and perhaps by 10% per °C over the Twentieth Century (Emanuel, 2005; Landsea, 2005).

We used the historical variation in Northern Hemisphere and Eurasian snow cover extent derived from reconstructed daily snow depth (1922-1971) and NOAA satellite data (1972-1997). The method for reconstructing snow cover extent is described in Brown (2000). The spatial distribution of historical in situ data meant that reconstruction of continental-scale snow cover extent was only possible in three months: October, March and April for Eurasia, while for the whole Northern Hemisphere it was only possible for March and April. We constructed 2 indices: one of spring Northern hemisphere snow cover as the mean of march and April coverage, and one Autumn coverage for Eurasia based on the October extent in Eurasia. It is worth pointing out that these records are far longer than the purely satellite derived snow over extent data which begins only in 1972, and hence is of virtually no utility in examining decadal or longer relationships with other times series.

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