Once the storms are selected, the next step is to track them. A discussion of different tracking methods can be found in Section 2.5.4. The storm tracking used in this work is based on the group of methods, whereby a maximum or minimum in a meteorological parameter is identified as a cyclone centre, and connections between those at subsequent timesteps are made based on forming a coherent track (Murray and Simmonds, 1991; Pinto et al., 2005, e.g.). This is the most appropriate method to use, given that the aim of this work is to track particular storms, and this method yields the track of an individual storm most readily.
The tracking method, developed by Tomasz Trzeciak for the project in which this work is con- tained, uses MATLAB version 2012b. It was necessary to develop a tracking method for this project, because of the unique approach it takes; too many storms are included for tracking to occur by hand, but the selected storms must be easily identifiable in the tracker’s output. The al- gorithm identifies minima in mean sea-level pressure and then searches for an associated maxima in vorticity at 850hPa. Therefore, only cyclones with both of these features are located, which tend to be intense systems. The vorticity is first smoothed to T63 resolution, following the work of Hodges (1994), because the vorticity is a noisy field as it is a second derivative. Hodges smoothed to T42 resolution, whereas T63 was selected for this work because it retains more of the extremes than T42. Therefore, the vorticity field still bears a strong resemblance to the pressure field, which facilitates the matching of pressure minima and vorticity maxima. Once smoothed, the vorticity maximum must be over a limiting value, and only one vorticity maximum can be identified within a set radius of the pressure minimum; this returns the largest value of vorticity in that area. In terms of joining the points at consecutive timesteps, the first limit applied here is that the two points at consecutive timesteps must be less than a certain distance apart. The distance is measured as the shortest distance between the two points on a spherical surface, in degrees. Once two points closer than the threshold distance have been identified, then the contribution that each would have to the track’s overall smoothness is considered. This is done because broadly, cyclones’ tracks are a smooth curve, and only involve large changes to direction when they are dissipating, splitting, merging, or meet an obstacle (e.g. orography, high pressure). Another reason tracks can contain
sudden changes is if a secondary cyclone develops from the main centre, the tracker can pick it up and join it to the track of the primary cyclone. None of these situations are desirable, and so the smoothing criterion is included. When the storm is moving quickly, the smoothing criterion is calculated as the distance from the midpoint between the first and third points to the second point considered (Figure 3.2), illustrated by the red arrow. This distance is smaller for smoother tracks, and so it penalises sudden changes in direction or speed. The distance is divided the distance between P1 and P3 (Figure 3.2), and the fraction has a limit placed on it. When the storm is
moving slowly, the absolute distance between the points is used, so large deviations in the later stages in the track are less likely. By allowing each point on the track to have a number of possible next points, a situation is avoided where the point that scores best for smoothness subsequently has a large diversion on its track. However, this could easily become computationally cumbersome, so there is a limit on the number of future points kept for each point, and once the tracking is complete only the smoothest overall permutation is kept.
F 3.2: Diagram illustrating how the smoothing criterion is assessed. P1, P2and P3are the
first, second and third points on the track under consideration, and Pmis the midpoint between P1
and P3. The red arrow indicates the distance calculated as part of the smoothing calculation.
Next, the correlation is calculated on the pressure field at the two consecutive timesteps, for a spec- ified area centred around the pressure minima, so that the same storm is more likely to be followed, as any sudden change in the magnitude or shape of the pressure field would be discouraged. In particular, this criteria is intended to suppress joining a secondary cyclone to the primary storm, as the pressure field of the secondary storm is unlikely to yield a high correlation with that of the primary cyclone. Connections between consecutive points with high correlations in the pressure field score higher.
The tracks are given a total weighted score, calculated using:
trackscore = Ws n X i =1 Ss+Wc n X i =1 Sc− Wl× Sl (3.2)
Chapter 3. Data and Methods 57
where W refers to weighting, S to the score, n to the total number of points along the track length, and in the subscripts, s refers to smoothness, c to correlation and l to track length. It shows that the total score for the track is related to the smoothness and correlation between each connection, summed over each point on the track, with an additional component to encourage tracks with large total length. Long tracks are encouraged because the storms of interest are intense, so tend to have long, coherent tracks, and so short tracks are unlikely to yield useful results. To this end and in line with the work of Pinto et al. (2005) and Hoskins and Hodges (2002), a minimum on the cyclone lifetime of 24 hours is set. The relative weighting of the three components in the scoring can be altered, but during this work they are kept constant.
Finally, the tracks are output. Output is either done in the order of the total score for the track, or how well they compare with a reference track. The ranking by score is particularly useful in the work with NWP data, where it is necessary to match the track in forecast data to that in analysis data, so the analysis track can be given as a reference. Track matching will be discussed more in Section 3.6.
In summary, the thresholds that are applied to the track are:
• lifetime (24hours),
• vorticity value (1 × 10−5s−1), • vorticity radius of influence (3.75o),
• degree of direction change between successive points (0.75o),
• maximum distance between successive points (4.5o latitude, 15o longitude), • length scale for near-stationary cyclones (2.25o),
• number of future points kept for each point on track (2),
• area for correlation between pressure fields (3.75o latitude, 7.5o longitude),
• relative weighting of track length (0.3), track shape (0.5) and pressure field correlation (0.5) used to calculate track scores.