| Histograms of vortex intensity changes as measured from tropopause potential temperature amplitude changes. Data is from NCEP reanalysis data 1948-1999 of tropopause vortices lasting at least 2 days and spending more than 60 percent of their lifetimes north of 65N. The values on the x-axis are absolute values of the changes in 6-hour changes in vortex intensity. Potential temperature amplitude is as defined in Hakim and Canavan (2003). | ||
| TPV growth only | TPV decay only | TPV intensity changes (growth and decay; 1 K bins) | TPV intensity changes (growth and decay; 5 K bins) | TPV intensity changes (growth and decay; 10 K bins) | Same as above except bins centered at "5's" (for separating purposes later) |
| TPV intensity changes (growth and decay; 10 K bins) | ||
| This data set filtered out tracks in which there were vortex merger events. In those cases, there were separate tracks in the data file even though they were the same vortex after merging. Also filtered out are spikes in tropopause theta amplitude. Spikes here were defined as a sudden jump (of at least 10K) in tropopause potential temperature amplitude, immmediately followed by a reduction of amplitude by at least 75% of the original spike. These spikes were replaced with NaNs in the dataset. | ||
| TPV growth only | TPV decay only | TPV intensity changes (growth and decay; 1 K bins) | TPV intensity changes (growth and decay; 5 K bins) | TPV intensity changes (growth and decay; 10 K bins) | Same as above except bins centered at "5's" (for separating purposes later) |
| TPV intensity changes (growth and decay; 10 K bins) | ||
| Filter includes vortex mergers in which there was redundant 24-hour amplitude change data and spikes in which there was a spurious change of amplitude at one or two adjacent times. | ||
| TPV growth only | TPV decay only | TPV intensity changes (growth and decay; 1 K bins) | TPV intensity changes (growth and decay; 5 K bins) | TPV intensity changes (growth and decay; 10 K bins) | Same as above except bins centered at "5's" (for separating purposes later) |
| TPV intensity changes (growth and decay; 10 K bins) | ||
| Large amplitude change vortex density plots |
| Amplitude changes of 5K or more |
| Amplitude changes of 10K or more |
| Amplitude changes of 20K or more |
| Amplitude changes of 30K or more |
| Large amplitude change vortex density plots |
| Amplitude changes of 5K or more |
| Amplitude changes of 10K or more |
| Amplitude changes of 20K or more |
| Plots of TPV signficant growth and decay densities. For each vortex, the location in which the maximum growth and decay occurred was saved. Those vortices in which the growth and decay was more than two standard deviations from the mean were retained in the following plot. The plots show the number of vortices that had significant tropopause potential temperature amplitude changes within a 2.5 degree latitude by 7.5 degree longitude box (weighted by cos(latitude) to get equal areas) centered at each location on the map. | |
| Signficant amplitude change density plots | |
| Timeseries plots of cyclone and anticyclone tropopause theta amplitude for those vortices which had 6-hour tropopause theta amplitude changes of greater than 30K. | |
| Cyclone growth | Cyclone decay |
| Anticyclone growth | Anticyclone decay |
| The above timeseries plots revealed 2 problems with the data: (1) There were repeated vortex tracks, both in phase and out of phase and (2) there were tropopause theta "spikes." Both of these need to be filtered out. To combat (1), it is first worth noting the "repeats" appeared adjacent to each other, suggesting a bug in the original code that generated the data sets. To take care of this, I compared each vortex track with the adjacent vortex track in the data set, and if their correlations were unity, they were removed. For the out of phase ones, I took half of the first vortex track amplitude vector centered at the middle, then took the second one and shifted it the amplitudes backward and forward in time. If at one of these shifts the correlations were unity, then then the repeat was thrown out. Further, there had to be a minimum of 4 (24 hours since each step is 6 hours) "shifts" in which the unity correlation arose. To deal with (2), we can note that if there is a spike in the amplitude, then when looking at the amplitude changes, there will be a sudden increase in amplitude immediately followed by a sudden decrease in amplitude. Following this note, I tested to see first whether there was an amplitude increase of a treshold value (40 K here). If that was followed by a drop that was at least 90 percent of what the initial increase was, then I considered it a spike and replaced that amplitude with a NaN while keeping the rest of the vortex track. Here is a visual step through of the process, using cyclone growth as the example: | |
| After filtering out the repeats only | |
| After filtering out the spikes only | |
| Filtering out both the repeats and the spikes | |
| Table of results using the filtering techniques described above for vortices in which there were amplitude changes of at least 50K. | |||
| Cyclone growth at least 50K | Cyclone decay at least 50K | Anticyclone growth at least 50K | Anticyclone decay at least 50K |
| Unfiltered | Unfiltered | Unfiltered | Unfiltered |
| Repeated tracks removed | Repeated tracks removed | Repeated tracks removed | Repeated tracks removed |
| Amplitude spikes removed | Amplitude spikes removed | Amplitude spikes removed | Amplitude spikes removed |
| Full Filter: Repeated tracks + spikes | Full Filter: Repeated tracks + spikes | Full Filter: Repeated tracks + spikes | Full Filter: Repeated tracks + spikes |
| TPV density plots: Comparisons of filtered vs. unfiltered |
| Cyclones and anticyclones |
