Friday, August 07, 2009

A New Way to Define Anomalous Years

Recently we used networks to examine year-to-year relationships in hurricane activity. This requires mapping the time series of hurricane counts onto a network. In this way the network is physically related to the variation of hurricanes from one year to the next. This idea is relatively new and was introduced by Lacasa et al. [2008]. By doing this we address the following two questions: How can the occurrence of hurricane landfalls over time be examined from the perspective of network analysis? And, what advantages are gained from this perspective? The intellectual merit of the work is an advance in our understanding of historical coastal hurricane activity and the broader impact is a new method for identifying anomalies from time series data. The paper will appear in a forthcoming issue of Geophysical Research Letters. It is coauthored with Thomas Jagger and Emily Fogarty.

The picture shows the visibility network based on the time series of U.S. hurricane counts over the period 1851--2008. The colors indicate the node degree (number of links); 2 or less (red), 3--5 (orange), 6--10 (yellow), 11--20 (green), 21--30 (blue), and more than 30 (dark blue). The network suggests a novel way to think about anomalies in a time series. Years are anomalous not in a statistical sense of violating a Poisson assumption, but in the sense that the temporal ordering of the counts identifies a year that is unique in that it has a large count but is surrounded in time by years with low counts. Thus we contend that node degree is a useful indicator of an anomalous year. That is, a year that stands above most of the other years, but particularly above its "neighboring" years represents more of an anomaly in physical terms than does a year that is simply well-above the average. Node degree captures information about the frequency of hurricanes for a given year and information about the relationship of that frequency to the frequencies over the given year's recent history and near future. With this definition 1985 stands out as the most anomalous of the hurricane years with 1933, 1886, and 1964 also unusual.

Lacasa, L., B. Luque, F. Ballesteros, J. Luque, and J.C. Nuno (2008), From time series to complex networks: The visibility graph. Proc. Nat. Acad. Sci., USA, 105, 4972--4875.


Cristine said...

great post. thanks for sharing

Shawn_Lewers said...

I would assume that looking at this data in different time scales would change it. How would this map look if the same methodology was employed with only extreme value events by year? How do you think it would change with paleo-record frequencies? Has this been attempted?

James Elsner said...

Yes, using a different time scale would change it as would using more years at the start or end of the record. The paleo records of hurricanes are not generally resolved on the annual time scale so it would be difficult to "stitch" them onto the observational record.