Discovering Typical Canadian Cyclone Tracks
To develop our climatology, we used a well known cyclone-tracking algorithm from CMC and UQAM (Canadian Meteorological Centre and Université du Québec à Montréal, respectively). This algorithm was applied to gridded height, wind, and pressure fields from the NARR (North American Regional Reanalysis). The algorithm output consists of cyclone tracks over Canada from 1992-2011 (twenty years). Each cyclone track is a series of points (circulation centers) at three-hour intervals, which is the native resolution of the NARR data.
Before further analysis, cyclone tracks are divided into three-month seasons: winter (DJF), spring (MAM), summer (JJA), and winter (DJF). This decision was based on well known seasonal differences in cyclone strength and movement. (This also reduced the runtime of the subsequent clustering algorithm.)
For each season, original cyclone tracks were fed into a clustering algorithm, to reduce the number of original tracks (about 1000 per season) to a small number of typical cyclone tracks. Specifically, we used agglomerative hierarchical clustering (AHC), with longest common subsequence (LCSS) as the distance metric. To our knowledge, this is the first time that anyone has combined AHC and LCSS or attempted an objective climatology of cyclone tracks.
The two most similar cyclone tracks within a set are those with the longest sequence of common points (occurring within a certain distance of each other and in similar stages of their respective cyclones' life cycles). For each season, the clustering algorithm takes the set of original cyclone tracks and joins the two most similar tracks. If the number of original cyclones were 1000, there would now be 999 objects (where an “object” may be either a single track or a cluster of tracks). A cluster of cyclone tracks is represented by its “medoid,” which is the one track in the cluster that is most similar to all other tracks in the cluster. This process is repeated until there is one object left, containing all 1000 cyclone tracks. The overall clustering process is represented by a dendrogram, showing all linkages on the way from 1000 objects to one object.
* “Cyclone” in this case refers to a synoptic-scale low-pressure system.
However, a climatology with only one cluster is just as useless as one with the 1000 original tracks. Thus, we developed several error metrics to assess the clustering and determine the optimal number of clusters. Based on a consensus between these error metrics, we determined that the optimal number of clusters is about 20 per season. The medoid of each cluster is then considered a typical cyclone track.
Although maps of typical cyclone tracks were useful, they did not show the amount of variation within each cluster. Thus, our final deed was to develop an objective method to draw a swath around each typical cyclone track. Each swath has varying width along the typical cyclone track, showing where there is more or less spread between members in the cluster.
Environment Canada plans to publish this work in its upcoming Arctic Marine Weather Guide, which will provide climatological information for mariners and other people operating in Arctic waters.