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A Modified Algorithm for Identifying and Tracking Extratropical Cyclones

doi: 10.1007/s00376-017-6231-2

  • In this study, a modified identification and tracking algorithm for extratropical cyclones is developed. This identification scheme is based on triangular-mesh contouring techniques combined with a connected-component labeling method in order to detect the outer boundaries and spatial domain characteristics of individual cyclones. A new tracking method allowing for the identification of cyclone merging and splitting events, as well as short-lived windstorms, is developed to reduce the uncertainty in the tracking of extratropical cyclones. I also show that this method excludes the tracks of open systems that would have been unnecessarily detected using conventional NCP methods. The climatological features of the distribution of cyclone frequencies are substantially larger over the traditional storm track regions compared to those seen in previous studies. Interestingly, a significant increase in the cyclone density in the Arctic occurs during all four seasons (up to 19% in summer) compared to that seen with a latitude-longitude gridded mesh analysis. I develop two new regional intensity indices (depth and vorticity) based on the cyclonic domain to better quantify the cyclonic activity in the Arctic region, and find that the interannual variabilities in these two indices are highly consistent. The results of this analysis may shed light on high-latitude cyclonic behavior studies via the newly detected 2D cyclone atlas derived from this cyclonic-domain-based algorithm.
    摘要: 建立了对于二维气旋的自动识别与追踪算法,有助于提高热带外地区的多中心气旋以及中尺度风暴识别的可靠性,并揭示了北极地区的气旋活动变化与北极涛动存在密切联系。
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Manuscript received: 05 September 2016
Manuscript revised: 02 March 2017
Manuscript accepted: 08 March 2017
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A Modified Algorithm for Identifying and Tracking Extratropical Cyclones

  • 1. Key Laboratory of Meteorological Disaster, Ministry of Education/Joint International Research Laboratory of Climate and Environment Change/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China

Abstract: In this study, a modified identification and tracking algorithm for extratropical cyclones is developed. This identification scheme is based on triangular-mesh contouring techniques combined with a connected-component labeling method in order to detect the outer boundaries and spatial domain characteristics of individual cyclones. A new tracking method allowing for the identification of cyclone merging and splitting events, as well as short-lived windstorms, is developed to reduce the uncertainty in the tracking of extratropical cyclones. I also show that this method excludes the tracks of open systems that would have been unnecessarily detected using conventional NCP methods. The climatological features of the distribution of cyclone frequencies are substantially larger over the traditional storm track regions compared to those seen in previous studies. Interestingly, a significant increase in the cyclone density in the Arctic occurs during all four seasons (up to 19% in summer) compared to that seen with a latitude-longitude gridded mesh analysis. I develop two new regional intensity indices (depth and vorticity) based on the cyclonic domain to better quantify the cyclonic activity in the Arctic region, and find that the interannual variabilities in these two indices are highly consistent. The results of this analysis may shed light on high-latitude cyclonic behavior studies via the newly detected 2D cyclone atlas derived from this cyclonic-domain-based algorithm.

摘要: 建立了对于二维气旋的自动识别与追踪算法,有助于提高热带外地区的多中心气旋以及中尺度风暴识别的可靠性,并揭示了北极地区的气旋活动变化与北极涛动存在密切联系。

1. Introduction
  • Studying and documenting the behavior of extratropical cyclones has great societal importance because these systems are typically accompanied by strong wind and intense precipitation. Cyclones are also a major transporter of meridional heat, energy and a contributor of air mass redistribution (Hu et al., 2014). On the climatic characteristics of extratropical cyclones in East Asia, new progress has been made in recent years based on automated identification and tracking methods. (Hu et al., 2010) studied the climatic characteristics of the cold vortex over Northeast China and suggested that sustained cold vortex activities could affect local and remote climatic anomalies and result in certain "climate effects". (Zhang et al., 2012b) reported that West Siberia, Mongolia and the coast of East Asia are the main formation areas for cyclones in East Asia; they noted that explosive cyclones rarely appear in the interior of East Asia. (Chen et al., 2014) found that the cyclone and anticyclone activities over China are apparent asymmetric, and their variabilities are closely linked with upper tropospheric jets over East Asia.

    There has been a remarkable renewal of interest in extratropical cyclone activity in recent years under global climate change. To objectively and efficiently measure cyclonic activity, a series of algorithms have been proposed to identify and track cyclones automatically (Murray and Simmonds, 1991; Hodges, 1994; Zhang et al., 2004; Wernli and Schwierz, 2006; Rudeva and Gulev, 2007; Wang et al., 2009). An intercomparison project referred to as IMILAST and involving 15 commonly used detection and tracking algorithms has been conducted to comprehensively assess the method-related uncertainty (Neu et al., 2013). However, because of the relatively ambiguous structure of extratropical cyclones, cyclone detection and tracking is highly complex (Neu et al., 2013).

    Cyclonic-center identification is the first fundamental step for cyclone detection and tracking. The local pressure minimum or the maximum of the Laplacian of the pressure or relative vorticity is commonly identified as the cyclonic center. Some studies have also conducted spatial truncations to remove the large-scale background conditions before identification (Hoskins and Hodges, 2002). Once a cyclonic center is noted, its location and intensity, represented by pressure or relative pressure (Simmonds and Wu, 1993; Zhang et al., 2012a), can be obtained. Other characteristics, such as the circulation, size, depth, and radius of the cyclone can be determined once the potential cyclone centers have been detected or following the tracking stage (Nielsen and Dole, 1992; Sinclair, 1997; Simmonds, 2000; Wernli and Schwierz, 2006; Rudeva and Gulev, 2007). The cyclonic extent is an arguably realistic and reliable quantification of the system strength. This characteristic can be used to study the local physical relationship between cyclones and extreme precipitation (Finnis et al., 2007; Raible et al., 2007; Hawcroft et al., 2012; Pfahl and Wernli, 2012). Although it is difficult to define the region of a cyclone with a complex shape, a few methods have been proposed to determine a cyclone's domain. (Sinclair, 1997) defined the outer boundary of a cyclone as the zero contour of the vorticity. (Simmonds, 2000) and (Simmonds and Keay, 2000) estimated the cyclone size using a radial search from the cyclone center to the point at which the radial derivative of the sea level pressure (SLP) falls to zero. (Wernli and Schwierz, 2006) proposed a new scheme for directly detecting the outermost closed SLP contour. Following (Wernli and Schwierz, 2006), (Hanley and Caballero, 2012) recently developed an objective scheme for multicenter-cyclone identification and tracking.

    The detection of feature areas of cyclones in two dimensions also simplifies the complicated circumstances involved in extratropical cyclone tracking methods. For example, the conventional neighbor center point (NCP) schemes, which associate two neighboring candidate cyclone centers across consecutive time steps, are simple and popular in IMLAST (10-13 in Table 1). However, the NCP-only schemes have difficulty recognizing the trajectory of cyclones accompanied by more than two NCPs. This is especially the case when two or more neighboring cyclones are enclosed by the same depression (cyclone merger) or when one depression is divided into several subsystems (cyclone split). In either of these cases, recognition of the cyclone trajectory becomes more difficult. Alternatively, connecting the overlaid feature area (COFA) schemes, which join two cyclone systems with shaded feature areas in successive charts, can effectively reduce the complexity of tracking cyclone-merging or -splitting events (e.g., Hewson, 2009; Inatsu, 2009; Hanley and Caballero, 2012). Moreover, a maximum displacement condition in the NCP schemes, which disconnects two associated centers when they are far enough apart, does not require COFA schemes. However, one potential problem is that fast-moving cyclones without overlaid areas could be ignored by COFA-only schemes.

    Thus far, the development of an outer cyclonic-boundary detection scheme has remained a challenge. First, it is difficult to identify a set of closed contours accurately. Second, even the outermost cyclonic contour is delimited, and there are uncertainties in defining the actual cyclone region. Additionally, a single atmospheric field may not depict the extrema of the cyclone's location well (Ulbrich et al., 2001), or the early stage of the system, even in the presence of a strong background flow with a strong pressure gradient. Therefore, (Rudeva and Gulev, 2007) argued that "a complete quantitative characterization of the cyclone size is quite a difficult task in both methodological and physical senses".

    Figure 1.  (a, b) An illustration of the cyclone center detection at Z850 (20-gpm interval) at 0000 UTC 30 July 2002 using the (a) latitude-longitude grid and (b) EASE grid. (c) The spatial distribution of the 100 km × 100 km version of the EASE grid at high latitudes. The gray dots show the locations of the detected cyclone-center candidates, and the black dots show the locations of the minimum cyclone centers with enclosed outer contours. The black line in (b) is the outermost enclosed contour for the cyclone in the eastern Arctic Ocean, with a value of 1270 gpm, as detected by my algorithm.

    To filter some of the local heat lows, many existing tracking schemes use a minimum lifecycle to omit short-life cyclones. For example, 61% of the schemes in (Neu et al., 2013) applied this criterion, despite a variety of minimum lifetimes, as shown in Table 1. Another potential reason for the exclusion of short-lived cyclones is to reduce the difficulty and uncertainty that are induced by the inclusion of open systems (local pressure minimum with no closed isobars) and heat lows within or near other closed cyclone centers during tracking. Therefore, a minimum lifetime at 24 hours was fixed for all methods in (Neu et al., 2013). However, short-lived cyclones, such as those at or below the cut-off low, can have large impacts on their local weather [e.g., the Xola windstorm in late December 2009 (Pinto and Silva, 2010)]. For example, (Hewson, 2009) reported that 29% of cyclonic features lasted less than one day in the North Atlantic, based on the Met Office's global model forecasts. Sub-synoptic cyclones are the most frequent cyclone systems (68.6%) in the Changjiang River-Huaihe River valleys in spring (Qin et al., 2017).

    In this paper, I focus on the objective and automated identification and tracking of extratropical cyclones from 2D cyclonic fields. Therefore, a modified identification scheme together with a new NCP-COFA combined tracking method is developed to detect the trajectory and regional domain of extratropical cyclones by following the path of the outermost cyclonic contour scheme of (Wernli and Schwierz, 2006). The performance of my algorithm is evaluated using the 35-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Interim) high-resolution dataset.

2. Data
  • This study uses the ERA-Interim dataset from 1 January 1979 to 31 December 2013 (Dee et al., 2011). This reanalysis dataset is globally available with a relatively high, six-hourly temporal resolution, and the circulation patterns (including cyclones) are well constrained by observations. I use the full T255 [512 (Lon) × 256 (lat)] Gaussian grid, which has a global horizontal resolution of approximately 0.7°×0.7°. This resolution is relatively high compared with most previous studies. To alleviate the effects of topography on my results, I choose the geopotential potential height field at the 850 hPa level (Z850) and filter out terrain of >1500 m and the Tibetan Plateau region (20°-45°N, 65°-110°E). The choice of Z850 also facilitates a comparison of the relative vorticity with depth in quantifying the intensity within a cyclone at the same pressure level, as reported in section 5. This study focuses on extratropical cyclones over the Northern Hemisphere. Accordingly, the study region is the domain poleward of 20°N. The mean monthly indices of the Arctic Oscillation (AO) are from

3. Identification and tracking
  • Detecting a cyclone's center is the first fundamental step towards identifying a cyclonic system. Similar to the criteria applied in previous studies, a cyclone-center candidate is determined as the Z850 grid point that is lower than all eight surrounding grid points on a latitude-longitude grid mesh. This local minimum condition is relatively broad and requires several iterations over an enclosed contour search stage, since the procedure needs to be conducted for each cyclone-center candidate. As an example, I show the cyclonic-center candidates identified for the 0000 UTC dataset on 30 June 2002 in Fig. 1a. There are many open system candidates without a clear cyclonic shape, as well as a low-pressure system, on this arbitrarily chosen date. A further limit can be applied to reduce the unenclosed candidates (Murray and Simmonds, 1991; Pinto et al., 2005; Wang et al., 2006). In this study, whether the first contour is enclosed serves as an intuitive way to effectively filter out open systems.

    In addition to the large number of open candidates, a strong low-pressure system with two centers is incorrectly detected over the interior Arctic Ocean (Fig. 1a). I find that there are two adjacent zonal grids with equal local minima values at both incorrectly detected centers, as shown in the above strong Arctic cyclone. This incorrect detection is due to the substantial decrease in the gridded area as it approaches the poles (i.e., the convergence of meridian lines), such that the value at a cyclonic-center candidate grid point may not be clearly distinguished from its neighboring eight grid points. In this situation, the nine-point local minima method will miss the candidate. This ambiguity is enhanced as the horizontal resolution increases. To alleviate such problems, a spatial smoother (Sinclair, 1997) or projection transformation (Simmonds and Murray, 1999; Serreze and Barrett, 2008; Hanley and Caballero, 2012) can be applied. However, only five methods in (Neu et al., 2013) applied data transformation in the Arctic (Table 1), while some of the other methods were originally designed for regional cyclone activity studies. Here, I re-grid the Z850 field north of 60°N to a 100 km × 100 km version of the National Snow and Ice Data Center North Polar Equal-Area Scalable Earth (EASE) grid (Armstrong and Brodzik, 1995), and combine this newly gridded area with the original Gaussian grids from 20°N to 60°N. Accordingly, a quasi-equal-area projection with a hybrid grid mesh is applied to the boreal extratropics. The spatial distribution of the grid in the Arctic region has a horizontal resolution that is comparable to that of the middle and lower latitudes (Fig. 1c).

    Identification of candidates in the high latitudes may be improved after projecting the Z850 field onto the above-modified grids. As shown in Fig. 1b, four open candidates near northern Russia and Baffin Bay are automatically eliminated. This result reflects the bias towards higher cyclone-center counts in the polar regions when using a regular latitude-longitude grid mesh (Sinclair, 1997), which can be alleviated using my approach. Additionally, the previously mentioned incorrectly detected Arctic cyclone in Fig. 1a exhibits two cyclonic-center candidates with the same enclosed contours. Improving the identification of Arctic cyclones is discussed in more depth in section 5.

  • In contrast to the (Wernli and Schwierz, 2006) scheme, a new triangular filled-contour method is introduced to detect the outermost contour of a cyclone and its domain from a Z850 field at every time step. The triangular filled-contour method is also called the triangular mesh contour and is widely used in computer graphics programming (Boissonat, 1984). This method contains two steps: contour searching and grid filling or "shading".

    3.2.1. Collection of cyclonic contours

    In the cyclone-related enclosed contour searching procedure, I introduce a triangular-mesh contouring technique during cyclone-associated contour searches. This approach is clearly different from those of previous studies. The value of the cutting point is linearly interpolated between any two vertices of the chosen triangle. If the contour value differs from the value of any of the triangular vertices, then the number of cutting points in this triangle must be less than two. In most cases, a contour only cuts the perimeter twice in each triangle. Therefore, the use of the triangular-mesh technique is to better depict the shape of a cyclone and decrease the uncertainty in this stage. Appendix B details how I construct the triangular mesh over the extratropical region in the Northern Hemisphere. A schematic for how to determine a contour is shown in Fig. 2, and the details for how to get the outermost enclosed cyclone contour sets are documented in (Qin et al., 2017). I use 4 gpm as the contour interval for enclosed contour searching because I find that the contours in this interval are quite dense when plotting Z850 in the boreal extratropical regions. The sensitivity of the analysis to the choice of contour intervals will be discussed in section 8.

    Figure 2.  A sketch of the enclosed-contour-searching algorithm, with the interpolated Z850 contour points (gray dots) based on the slopes at the vertices. The arrows denote the tracking direction, and the black dots represent the centers of cyclone candidates.

    3.2.2. Definition of a cyclonic domain

    The definition of the domain of a cyclonic system is based on the grid-filled or area-shaded technique and is helpful for depicting the circulation regimes induced by cyclones with different geometries. The "classical ordered edge" approach (Newman and Sproull, 1979), which fills the grids between two or more endpoints in a sequence at every common latitude or longitude, is frequently applied to the shaded area. This process leads to increasing complexities when there are more than two endpoints in each structure. Alternatively, an iterative method has been devised to automatically detect the domain within the outermost contour or "interface" of a cyclonic system. This method is based on the use of a quad-tree data structure and a seed-filling scheme; it is used in conjunction with a connected component labeling (CCL) technique [i.e., the separation of object points into distinct objects via labeling (Rosenfeld and Kak, 1976)] and was first applied to cyclone identification by (Hodges, 1994). Each iteration starts at the candidate's nearest triangle. This triangle is labeled the "qualified" triangle within the cyclonic domain when the values at all three vertices are lower than their corresponding outermost contour values. Because every triangle involves three adjacent triangles (except for the boundary triangles), this process is repeated for any of the adjacent and qualifying triangles. Eventually, the iteration stops when it reaches the outermost boundary or the regional boundary.

    Since a cyclonic system may contain several local extrema, it is difficult to determine a one-to-one relationship between temporally local minima to connect local minima across successive time steps in order to track the cyclones. Similar to the scheme used by (Hanley and Caballero, 2012), a common outermost contour is considered the boundary of a system, as shown in Fig. 1b. Notably, a shared outermost contour may cover a large area of a polar stereographic projection map, such as a dominant low pressure system in the polar region. To highlight a local cyclone system, I use the criterion area of 3.14× 106 km2, which has an equivalent circular "radius" of 1000 km, as the maximum size of a cyclonic system with either single or multiple centers. In particular, if a cyclonic contour (Ci) is the first contour to encompass a cyclonic domain area greater than 3.14× 106 km2 around the candidate center, then the contour Ci-1 with 4 gpm less than Ci is labeled the outermost contour; the area encompassed by this contour is defined as the cyclonic domain. Otherwise, if the total area is less than 3.14× 106 km2, the area surrounded by the last enclosed cyclonic contour is considered the cyclonic domain. Therefore, this criterion permits the detection of the major regions of closed cyclone, including most mature storms as well as other shallow low-pressure systems. To make the algorithm more transparent and replicable, a detailed flowchart of the cyclone center detection and cyclone system identification procedures is given in Appendix A.

  • A new cyclone tracking scheme is developed by considering both NCP (point-to-point) and COFA (field-to-field) schemes. The new scheme includes two automatic steps. First, if two cyclones share common feature areas in two consecutive time frames, these two cyclones are connected by the same cyclone trajectory. Second, to avoid losing the fast-moving cyclones without common feature areas, the nearest neighbor approach is also applied to cyclone centers, with the enclosed contours imposing thresholds on the maximum displacement distance at 600 km within 6 hours. Merging (splitting) events are noted once two or more previously (currently) identified cyclone systems overlap a current (previous) cyclone.

4. Examples of cyclone system identification and tracking
  • The first case study, Fig. 3, shows a dramatic storm across the Arctic region in August 2012. This storm is labeled "The Great Arctic Cyclone of August 2012" in (Simmonds and Rudeva, 2012), with a minimum center SLP of 963.91 hPa at 1800 UTC on 6 August. The cyclone formed over the Taymyr Peninsula on 31 July, passed through the Arctic, and died in the Canadian Archipelago on 13 August. As shown in Fig. 3, the trajectory (T1) and its evolution of intensity found using my algorithm agree well with the results from Simmonds and Rudeva (2012, their Fig. 1 and Fig. 2) after 1800 UTC on 5 August. Based on the 9-point local minima method, a potential cyclone track (T2) is reconstructed for the evolution of the location of the cyclone center in (Simmonds and Rudeva, 2012). However, a clear deviation between T1 and T2 is seen before 1800 UTC on 5 August. An animation of the evolution of this cyclone over its lifetime is provided in a supplemental file (see supplementary video). An open system (C2) is generated over Siberia at 1200 UTC on 2 August, seven time steps after the closed cyclone (C1) is detected by the new algorithm (Fig. 3a). C2 then moves east-northeast and becomes a closed cyclone over 30 hours later, with a notably weaker intensity and smaller area than those of C1 (Fig. 3b). C2 merges with C1 six hours later and then enters the East Siberian Sea (Fig. 3c), while C1 becomes deeper, with a broader scale. The centers of C1 and C2 join at 1800 UTC 5 August near (83°N, 187°E), and the whole system reaches its maximum intensity 24 hours later (Fig. 3d). The elaborate evolutions of the central SLPs of C1 and C2 are shown in Fig. 3e. The intensity of C2 is substantially weaker than C1 before merging into C1. The intensity of C2 also decreases dramatically as it approaches C1, while that of C1 decreases slowly before their merger, suggesting the impact of C1 on the intensification of C2. Therefore, I argue that my algorithm offers a more natural description of this dramatic Arctic storm's trajectory and evolution than the results published by (Simmonds and Rudeva, 2012).

    Figure 3.  The track of "The Great Arctic Cyclone of August 2012" from 1800 UTC 31 July 2012 to 1800 UTC 13 August 2012. The Z850 field (units: gpm) is shown at (a) 1200 UTC 2 August, (b) 1800 UTC 3 August, (c) 1800 UTC 4 August, and (d) 1800 UTC 6 August. The shading areas denote the detected cyclonic areas. The black dots show the center point of C1 with its outermost enclosed contour (i.e., the black lines with their corresponding values in gpm), while the green dots are C2 from Simmonds and Rudeva (2012). The red line is the trajectory of C1 during its lifetime using my algorithm, and the green line denotes the constructed trajectory. (e) The time series of the SLP in the corresponding center-point grid of C1 (red-circle line) and C2 (green-circle line). The interval of the contours in (a-d) is 20 gpm, and the units are hPa for the SLP in (e).

    Figure 4 shows a second case study illustrating a short-life mesoscale cyclone with substantial wind-related damage. The windstorm, named Xola, struck Portugal at midnight on 23 December 2009, with a maximum wind gust intensity of 39.4 m s-1 at 0450 UTC (Pinto and Silva, 2010). As documented in Fig. 4, Xola developed off the west coast of Portugal and landed in Portugal, with high wind speed zones (>10 m s-1) in its southern reaches. A clear southwest-northeast trajectory evolved with an outermost enclosed contour that increased and then decreased in size within 12 hours. My algorithm recognizes such a high-impact but short-lived windstorm due to its lack of lifetime-related criteria. In contrast, this case will be excluded by the application of the >18-h minimum lifetime condition that is often applied when considering synoptic-scale cyclone tracking (e.g., Neu et al., 2013).

    Finally, Fig. 5 shows an example of a cyclone in its mature phase embedded within a potential open system trajectory. An extratropical cyclone formed over the mid-lower reaches of the Yangtze River in China at 0000 UTC 19 April 2012. This cyclone then moved northeastwards, with a gradually deepening central Z850, and entered the Sea of Japan three days later. A single cyclone track with an enclosed outermost contour is clearly detected by my algorithm. However, a Z850 minimum develops near Vladivostok, 513 km from the cyclone center, and gradually heads towards North Japan over the next three time steps. According to the NCP schemes, an overlapping track of local minima can be detected, which should be manually filtered in the cyclone analysis. The automatic exclusion of such a potential track in my algorithm highlights the importance of the closed multicenter system identification scheme, although the 9-point local minima criteria alone are weak conditions. Further conditions, such as a search radius for the merging of nearby local minima or a threshold for minimum lifetimes, are applied in most NCP schemes.

5. Climatological cyclone frequencies
  • To characterize the climatological features of cyclone circulations, I determine the winter (December-February;DJF), spring (March-May; MAM), summer (June-August; JJA) and autumn (September-November; SON) climatological densities of "cyclonic grid points" (Fig. 6). Here, the value for seasonal density can be expressed as $$ \left.\left(\sum_{i=1}^{\rm NT}(4C_i)/{\rm NT}\right)\right/A_j , $$ where Ci (counts of cyclone; 0 or 1) indicates the number of times the jth grid point is affected by a cyclone system at the ith time step, the area of the grid is Aj (area of the jth grid), and NT is the total number of time steps in a given season. Meanwhile, to quantitatively compare the cyclone climatology in (Wernli and Schwierz, 2006), I also define the cyclone frequency (f c) as the percentage of time that the grid points experience cyclonic conditions. Compared to the f c, the density field allows for the convergence of the meridian lines and a diversity of spatial resolutions at different latitudes.

    Figure 4.  The evolution of a short-lived windstorm (Xola) tracked from 0000 UTC 23 December 2009 to 1200 UTC 23 December 2009, with 6-h time intervals. The contours, black dots, black line and red line are the same as in Fig. 3. The 10-m wind speeds greater than 10 m s-1 are shaded.

    Figure 5.  The evolution of a cyclone tracked in East Asia from 0000 UTC 22 April 2009 to 1800 UTC 22 April 2009, with 6-h time intervals. The shaded areas, contours, black dots, black line and red line are the same as in Fig. 3. The green dots are the cyclone center candidates. The green line denotes an additional potential trajectory from an open system nearby using an NCP-only scheme.

    Figure 6.  The seasonal mean cyclone density (shaded; units: counts d-1 10-4 km2) and frequencies fc (contours; units: %) projected onto the EASE grid in the boreal extratropics for the ERA-Interim period (1979-2013): (a) DJF; (b) MAM; (c) JJA; (d) SON. The fields with elevations exceeding 1500 m are excluded.

    The cyclonic grid density clearly shows regional and seasonal dependences (Figs. 6a-d). In the winter, high values predominantly occur over the North Pacific and North Atlantic sectors. These values are due to two common storm tracks that span from Japan to the Gulf of Alaska in the North Pacific and from the Greenland Sea, the Iceland Sea or the Norwegian Sea to the Kara Seas in the North Atlantic. Baffin Island and the Mediterranean are also characterized by high cyclonic densities. In spring, the high-value areas expand into the Far East in the North Pacific and into the southern continental areas of the North Atlantic, with slightly lower counts around the corresponding local maxima. The values in the western Mediterranean are larger than those in winter. During summer, the high-value areas are mainly confined to latitudes north of 45°N. The local maxima over Baffin Island and the Greenland Sea/Iceland Sea notably increase, and the local maxima originally located in the Kara Sea shift towards the polar ice cap and increase. However, the oceanic storm tracks in the North Pacific are weaker. In autumn, the high cyclone-center counts remain in the same regions as observed in winter, except for small areas in the Mediterranean.

    Figure 7.  As in Fig. 6 but for differences in the cyclone density of my hybrid grid and the latitude-longitude grid seen in the cyclone center location procedure. The units are the same as in Fig. 6.

    The main structures and seasonal variations in f c agree well with the density patterns and are highly consistent with (Wernli and Schwierz, 2006) (see their Figs. 6a-d). This result also closely corresponds to the results of previous similar studies (Whittaker and Horn, 1984; Hoskins and Hodges, 2002; Paciorek et al., 2002). However, my f c values are substantially higher than the values of (Wernli and Schwierz, 2006). There are several possible reasons why higher f c values can be expected in my results. First, (Wernli and Schwierz, 2006) uses the ERA-40 datasets, with a coarser spatial resolution at some time periods, while I use Z850 instead of SLP, which may introduce a difference in the stable boundary layers for the polar region. Second, there are notable differences in the identification algorithms and the grid meshes used, although both my algorithm and (Wernli and Schwierz, 2006) are based on the detection of the outermost contour of the cyclone. Third, the area of the multicenter cyclone I detect is generally larger than the sum of each single-center component.

    Interestingly, the summer frequencies around the subpolar regions are more prominent than the f c field in (Wernli and Schwierz, 2006), with a cyclone maximum over the central Arctic Ocean. This result is consistent with those of (Serreze and Barrett, 2008) and (Simmonds et al., 2008). These authors described a summertime maximum in cyclonic activity in the same region via projecting the data onto an EASE or polar stereographic projection mesh. Further straightforward comparisons, such as (Neu et al., 2013), deserve more study in the future.

    Figure 8.  The climatological winter cyclone density (shaded; units: counts d-1 10-4 km2) projected onto the EASE grid in the boreal extratropical region: (a) merging; (b) splitting.

    As discussed in section 3, the combination of a spatial smoothing latitude-longitude grid and an EASE grid could potentially improve the ability of the fundamental positioning procedure for cyclone-center identification. Therefore, I also apply my algorithm to a raw latitude-longitude grid mesh and show the differences in climatological cyclone densities between my hybrid grid mesh and a Gaussian grid mesh in Fig. 7. A substantially higher density of cyclones over the high latitudes is displayed, with a large difference over the Arctic Ocean. The largest increase is in summer, with a maximum density value of 0.27 counts d-1 104 km-2 (up to 19% higher than in the original Gaussian grid mesh). In winter, the maximum increase is 0.15 counts d-1 104 km-2 in the same areas. Such seasonal variations support the seasonality of climatological cyclone densities and frequencies, as seen in Fig. 6. This finding suggests that more cyclones are incorrectly detected due to the unaddressed convergence of the meridian lines while cyclonic density increases at the high latitudes.

    Recall that my hybrid grid system is designed to identify (remove) cyclone centers missed (open) due to the convergence of the meridian lines. Because of the regional increase in the frequency of cyclonic grid points due to the addition of open cyclone centers, the missed centers are responsive to a regional 2D-cyclone-field density increase. Consequently, the increasing density of Arctic cyclones indicates the potential skill of this algorithm in detecting high-latitude cyclone centers and their domains.

6. Cyclone merges and splits
  • Using a 2D-cylone system tracking algorithm, the climatology of the density of merging and splitting cyclone events is shown in Fig. 8. The density is defined as the seasonal mean of the daily mean count of merging or splitting events in the same manner as that described in section 5. The geographical distribution of high frequencies of merged cyclones agrees well with (Inatsu, 2009) in the mid-high latitudes of the North Pacific and the North Atlantic (Fig. 8a). The large number of merged cyclones seen in the Mediterranean is also noted in (Hanley and Caballero, 2012) but is absent in (Inatsu, 2009). The distribution of the large number of splitting events in Fig. 8b is generally similar to the density of the merging events, but with higher values in the mid-high latitudes of the North Pacific and the North Atlantic. This feature correlates well with those of (Inatsu, 2009). Overall, the results are more consistent with (Inatsu, 2009) than with (Hanley and Caballero, 2012). This finding may be due to the three-time-step (>12-h) minimum lifetime imposed on cyclone tracks in (Hanley and Caballero, 2012) as opposed to the lifetime-free tracking in this study and (Inatsu, 2009). Allowing for short lifetime tracks probably induces a higher number of split events, especially in the distortion stage of a cyclone.

    Figure 9.  The time series for the Arctic (a) winter, (b) spring, (c) summer and (d) autumn means for the regional integration of the depth (I depth, solid line) and vorticity (I vor, dash line) in the ERA-Interim dataset (the units for depth and vorticity are gpm and 10-6 s-1, respectively).

7. Interannual variability in the integrated cyclone intensity in the Arctic region
  • Because of the nature of the cyclone-domain identification in this algorithm, the intensity of an individual system plus the integrated cyclone deficits over a study region can be quantificationally measured. To illustrate the regional characteristics of cyclonic activity, I choose the Arctic as my study region and develop a synthesized index of depth (I depth) for describing the low-frequency variabilities in cyclone intensity. Compared to the central SLP, the overall cyclone depth is considered to be a more representative way to estimate cyclone strength (Simmonds and Keay, 2000). The depth of an individual cyclone can be expressed by integrating the difference between the Z850 value of the outermost contour (Z c) and the Z850 values of every grid within its domain. Therefore, the Arctic cyclone-depth index is given by \begin{eqnarray} I_{\rm depth}&=&\overline{\left[\dfrac{\iint[Z_{\rm c}-{\rm Z850,0}]dA}{\iint dA}\right]} ,\nonumber\\ \left[Z_{\rm c}-{\rm Z850,0}\right]&=&\left\{ \begin{array}{l@{\quad}l} Z_{\rm c}-{\rm Z850}, & \hbox{within a cyclone}\\ 0, & \hbox{outside a cyclone} \end{array} \right.\ \ (1)\end{eqnarray} Here, the overbar represents the averages for each season, respectively, and \(\iint dA\) denotes the area integration north of 65°N. This index represents the seasonally integrated strengths of the cyclones in the Arctic region. Note that a cyclone domain may spread across the boundary of the Arctic region; its central location could appear either within or outside of the region. My depth index accounts for the part of the cyclone inside the Arctic regardless of where the cyclone center is located. This definition is another key feature that distinguishes the present work from previous studies (Simmonds and Keay, 2000). Here, the depth is an integrated measure of the "deficit" among all the cyclones within the region at each time step, which may counteract the effect of the background circulation signals. In addition, since the vorticity field focuses on smaller spatial scales and allows for systems to be identified much earlier in their life cycles (Hoskins and Hodges, 2002), I also defined a regional integrated cyclone intensity index (I vor) in a similar manner by using the relative vorticity at the 850-hPa level ( vor850), which can be expressed as \begin{eqnarray} \label{eq1} I_{\rm vor}&=&\overline{\left[\dfrac{\iint[{\rm vor}_{850},0]dA}{\iint{dA}}\right]} ,\nonumber\\ \left[{\rm vor}_{850},0\right]&=&\left\{ \begin{array}{l@{\quad}l} {\rm vor}_{850}, & \hbox{within a cyclone}\\ 0, & \hbox{outside a cyclone} \end{array} \right..\ \ (2)\end{eqnarray} One should note that even when two cyclones have the same size, their interior depths or vorticities may differ significantly due to their different pressure gradients. Therefore, both the I depth and I vor are more realistic measurements for the integrated intensity of a regional cyclone compared to a measure of the cyclone's area.

    Figure 10.  As in Fig. 9 but for I vor using different contour searching intervals (1-7 gpm) in my detection algorithm (units: 10$-6 s-1$).

    Figure 9 shows the time series of the seasonal mean Arctic cyclone intensity over the four seasons. Considerable interannual variability in both I depth and I vor are visually apparent in the plots, with no obvious low-frequency behaviors. In particular, the two intensity indices exhibit exceptionally large-amplitude interannual fluctuations in winter. The interannual oscillations of I depth and I vor are highly consistent throughout all four seasons, and they are significantly correlated above the 99% confidence level, as listed in Table 1. Their high correlation indicates that either of the two indices represents the regional cyclone intensity well, assuming a circular cyclone shape and a geostrophic balance. However, the correlation is slightly lower in summer than in the other seasons because less consistency exists before the mid-1990s in the summer. Additionally, the intensities are stronger in autumn, which has a climatological I depth value of 6.88 gpm as opposed to 5.75 gpm in spring. The open-water conditions in the Arctic Ocean may lead to an increasing baroclinicity and diabatic effects, as well as the intensification of cyclones in the warm season.

    As shown by many previous studies, the dominant mode of the Northern Hemisphere atmospheric variability is the AO. Although the behavior of a cyclone depends on the baroclinic structure of the synoptic-scale waves related to the static stability of the atmosphere and the surface friction, it may also be associated with the strength of the zonal flow. To explore the association between cyclonic activity in the Arctic region and the AO, I correlate the time series of I depth and I vor with the AO index in Table 2. Both I depth and I vor display significant positive correlations with the AO during the four seasons at a confidence above the 95% level. Therefore, the positive phase of the AO is closely associated with deeper storms in the Arctic region. The correlation of I vor with the AO is slightly higher than the correlation of I depth with the AO. This correlation suggests a dynamical contribution from synoptic cyclone activity to the variability of the AO. The above positive correlation is consistent with (Simmonds et al., 2008); however, my results display notably higher significance levels during 1979-2013. This difference may result from the different definitions for the index of the cyclone depth, the different reanalysis datasets used, and the study periods.

8. Conclusion
  • A modified detection algorithm is proposed to identify extratropical cyclones. This new algorithm combines triangular-mesh contouring techniques with a CCL method to detect the outer boundary and spatial domain characteristics of individual cyclones. Then, these cyclones are tracked using a new combined NCP-COFA tracking method that allows for the identification of cyclone merging and splitting events, as well as short-lived windstorms. I also show that this method naturally excludes tracks of open systems that would have been unnecessarily detected using NCP-only methods.

    The resulting climatological features of the distribution of the cyclone frequency are characterized by high cyclone densities, which correlate well with storm track maps. The spatial distribution of the cyclone frequency f c agrees well with (Wernli and Schwierz, 2006), but generally has higher values. Furthermore, a substantially increased density of cyclone counts occurs at high latitudes in my hybrid quasi-equal-area grid mesh with respect to those found with a latitude-longitude Gaussian grid, with an exceptionally large difference over the Arctic Ocean (0.27 counts d-1 104 km-2 in summer and 0.15 counts d-1 104 km-2 in winter).

    Cyclonic activity shows a considerable interannual variability in the Arctic region, as depicted by the new regional integrated intensity indices (depth and vorticity). Correlation analyses of these indices indicate that the interannual variations in these two indices are highly consistent and are closely associated with the AO. These findings reinforce the view that both the depth and vorticity represent valuable and representative measures of regional cyclonic behavior. Compared with the traditional point-to-point cyclone depth or center quantification, the depth and vorticity indices measure the overall integrated intensity within the Arctic region. The definitions of these two indices allow for a more realistic measurement of the regional general intensity, and these indices can be applied to study cyclonic activity in other regions.

    In recent decades, the Arctic climate has undergone significant variability and changes. The studies of the behavior of cyclones in the Arctic region alongside those of the accelerating retreat of sea ice and other parameters have been of increasing interest. The potential for detecting and tracking high-latitude cyclones using this algorithm combined with the new quantification of the integrated Arctic cyclone intensity presented in this study may shed light on the study of the Arctic climate.

    As mentioned above, I use 4 gpm as the interval for detecting enclosed contours. (Wernli and Schwierz, 2006) argued that the number of identified cyclones would significantly increase as the interval decreased. Here, I use 1-3 and 5-7 gpm as the interval values to examine the sensitivity of my results. These results agree with those of (Wernli and Schwierz, 2006) (figure not shown). The number of shallow or small cyclones is mostly sensitive to the choice of the interval. This result agrees with my experience in identifying cyclones from a synoptic chart. Clearly, when the contours become dense, relatively small-scale weather systems, which were originally ignored, will appear, whereas the original systems remain, despite the potential extensions of their original boundaries. However, as documented in Fig. 10, the interannual-scale (and longer) variations in the Arctic cyclonic vorticity index are highly consistent among the different intervals. Therefore, using 4 gpm and adjacent values for the contour interval for cyclone identification provides reasonable descriptions of the variations in cyclone intensity on an interannual scale (and longer) in the Arctic region.

    Electronic Supplementary material: Supplementary material is available in the online version of this article at 10.1007/s00376-017-6231-2.




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