There are two popular ways to quantify extratropical cyclone activity (ECA): Eulerian variance/covariance statistics, and Lagragian cyclone tracking statistics (Chang et al., 2002; Hoskins and Hodges, 2002).
Eulerian statistics require time series at fixed locations, for example observations made at a weather station, or gridded analysis/reanalysis or model data at a grid point. Since cyclones/anticyclones that generate weather are usually mobile systems and have characteristic timescales of about 2-7 days, time filtering is generally employed to highlight this so-called synoptic timescale. One simple time filter that our group frequently uses is the 24-hr difference time filter, first suggested by Wallace et al. (1988). This filter highlights timescales with periods between 1.2 and 6 days. For example, given a time series of sea level pressure (SLP) observations at a weather station, ECA can be quantified by the 24-hr filtered variance of SLP (we call that ECApp) and is defined by:
In equation (1), the overbar denotes time average, usually over a month or a season. Physically, since the passage of cyclones usually produce significant pressure changes, more frequent passages of cyclones, or passages of stronger cyclones, will lead to larger values of ECApp. Fig. 1 shows the geographical distribution of this metric:
Fig. 1: Climatological distribution of winter (December-January-February, DJF) of ECApp (equation 1, unit hPa2), calculated using 6-hrly ERA-Interim reanalysis data, for the winter seasons of 1979/80 to 2014/15.
This metric highlights cyclone activity spreading from the western Pacific eastward across the Pacific (the Pacific storm track) across North America, into western Atlantic (the Atlantic storm track), where it tilts northeastward and extends into northern Europe. Our previous studies have shown that variations and projected change in ECA as quantified by this metric significantly modulate the variability and projected change in precipitation over California and other parts of the U.S. (Chang, 2013; Chang et al., 2015), and variations in ECApp also significantly modulates the frequency of extreme events over North America (Ma and Chang, 2017). Apart from it’s link to high impact weather, recent research by our group shows that ECApp can be predicted with significant skill by state-of-the-art climate prediction model over the subseasonal to seasonal timescale (Zheng et al., 2019).
The second popular way of quantifying ECA is Lagrangian cyclone track statistics. This requires tracking of cyclones, usually using automated objective feature tracking algorithms applied to identify and track features using gridded analysis/reanalysis or model data sets. Many different algorithms have been developed and used by different groups (e.g. Neu et al., 2013). Our group usually use the feature tracking algorithm developed by Kevin Hodges (Hodges, 1994, 1999; see also Hoskins and Hodges, 2002). The tracker provides the location and intensity of cyclones, thus providing more information than Eulerian statistics. An example of cyclone tracks for one winter season generated using this algorithm is shown in Fig. 2.
Fig. 2: Tracks of all cyclones that passed over the boxed area during the winter season of DJF 2001/02. Cyclones are defined as minima in spatially filtered (T5-T70) SLP. The amplitude (in hPa) is shown by the color.
Multiple Lagrangian track statistics can be derived based on the output of the tracker (see Hoskins and Hodges, 2002). For example, the cyclone track frequency (Fig. 3a) is defined as the number of cyclone tracks that passes within 555 km (5 great circle degrees) of a grid point each month, while the track amplitude (Fig. 3b) is the average of the amplitude of all cyclones that pass within 555 km of a grid point. Both track frequency and amplitude have peaks over the Pacific and Atlantic storm track regions, consistent with the spatial distribution of ECApp (Fig. 1). However, track frequency (Fig. 3a) shows a secondary maximum over the Mediterranean, highlighting the storm track over that region. However, Fig. 3b shows that storms over that region usually have low amplitudes, thus explaining why the Mediterranean storm track does not show up in ECApp.
Fig. 3: Climatological distribution of winter (DJF) (a) cyclone track frequency (number per month), and (b) track amplitude (hPa).
References:
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