Climate Conditioned Networks

It is interesting to consider how the hurricane network properties change with climate factors. Here we consider three variables that have been related to the frequency of U.S. hurricanes. The variables include an index of the North Atlantic Oscillation (NAO), an index of the El Nino-Southern Oscillation (ENSO), and North Atlantic ocean temperatures (SST). Ordered factors are created by consider whether a year is above or below the long term average based on seasonal averages of the variables. Six separate networks are constructed using only hurricanes from years that fall into the six factor groups.

NAO index values are calculated from sea level pressures at Gibraltar and at a station over southwest Iceland (Jones et al. 1997), and are obtained from the Climatic Research Unit. The values used here are an average over the pre- and early-hurricane season months of May and June and are available back to 1851. Units are standard deviations. These months are chosen as a compromise between signal strength and timing relative to the hurricane season. The signal-to-noise ratio in the NAO is largest during the boreal winter and spring (see Elsner et al. 2001), whereas the Atlantic hurricane season begins in June.

Values of the Southern Oscillation Index (SOI) are used as an indicator of ENSO. Although noisier than equatorial Pacific SSTs, values are available back to 1866. The SOI is defined as the normalized sea-level pressure difference between Tahiti and Darwin. The SOI is strongly anti-correlated with equatorial SSTs so that an El Nino warming event is associated with a negative SOI. Units are standard deviations. The relationship between ENSO and hurricane activity is strongest during the hurricane season, so we use an August through October average of the SOI for our covariate. The monthly SOI values are obtained from the Climatic Research Unit where they are calculated based on a method given in Ropelewski and Jones (1987).

The SST values are based on a blend of model values and interpolated observations, which are used to compute Atlantic SST anomalies north of the equator (Enfield et al. 2001). As with the SOI, we use August through October average of the SST anomalies as our covariate. The anomalies are computed by month using the climatological time period 1951-2000 and are available back to 1871. Units are degrees C. Values are obtained online from NOAA-CIRES Climate Diagnostics Center (CDC).

Table 3 summarizes the network properties conditional on each of the factors. We see that the hurricane network changes substantially between above and below phases of the ENSO. With below average values of the SOI characteristic of an El

Table 3 Network properties conditional on climate factors. The plus and minus indicate 1 standard error

Above

Below

Above

Below

Above

Below

Max Degree Mean Degree Max Betweenness Mean Betweenness Connectedness

Nino event in the tropical Pacific, the mean nodal connectivity is 4.8 ± 0.79. This value is significantly less than the value of 7.2 ± 0.98 for the La Nina network of U.S. hurricanes. We also see more connectivity during warm SST years compared with cool SST years. The mean betweenness value during below average NAO years is higher largely due to the fact that North Carolina has a betweenness value of 251 compared with 9 during above average NAO years. The largest betweenness value during above average NAO years is 141 for southwest Florida. The connectedness which measures the fraction of all possible links over all nodes is highest for the below normal NAO and above normal SST and smallest for the below normal SOI.

Summary

Hurricane activity can have profound affects on lives and property along the coast. The frequency and intensity of hurricanes is the topic of much of the current research. Much less work has been done to understand the relationship of hurricanes across different regions. Here we examine the data on hurricanes that have affected the U.S. coast from a relational perspective using network theory. The tone of the chapter is expository since the analysis of climate data using networks is relatively new. In fact, the basics of networks are introduced using a hypothetical network of citations in the hurricane climate literature.

The primary analysis centers on the network of U.S. hurricanes. The network is created by considering hurricanes that have affected more than one coastal region. The regions are based on individual States, but Texas and Florida are further subdivided. The chapter describes how the adjacency matrix is derived from the incidence matrix and how a network is a graphical representation of the adjacency matrix. Graphical representations show ways to highlight different characteristics of the network.

The topology of the network is examined using various local and global metrics including degree, closeness, betweenness, diameter, and clustering coefficient. The degree quantifies the number of links between each node where a link between two nodes is established if at least one hurricane affected both regions. Areas that are affected by hurricanes making multiple landfalls have high degree. Paths through the network are routes between nodes via the links. Closeness and betweenness quantify how many shortest paths go through each node. The diameter and clustering coefficient are global metrics and measure the maximum shortest path in the network and the probability that adjacent nodes are linked, respectively.

The question of how the topology changes with changing climate is considered by reconstructing networks based on three independent climate factors. It is found that the ENSO phenomenon in the equatorial Pacific has the most significant influence on the network. The present work represents a first step toward understanding relational aspects of hurricane activity using networks and how those relationships change under different climate scenarios. A next step might be to build prediction models of network structure based on pre-season climate conditions.

Acknowledgments Partial support for this study was provided by the National Science Foundation (ATM-0435628) and the Risk Prediction Initiative (RPI-05001). The views expressed within are those of the authors and do not reflect those of the funding agencies.

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