A global climatology of favourable conditions for polar lows

Transcription

1 Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: , October 2011 A A global climatology of favourable conditions for polar lows Erik W. Kolstad* Bjerknes Centre for Climate Research, Bergen, Norway *Correspondence to: E. W. Kolstad, StormGeo, Nordre Nøstekaien 1, 5011 Bergen, Norway. erik.kolstad@stormgeo.com Polar lows (PLs) are small-scale and intense low-pressure systems that form at high latitudes in both hemispheres. Due to their limited spatial scale and brief lifetimes, weather and climate models are often unable to resolve these systems. One way to overcome this problem is to define a suitable proxy for PLs, with which the likelihood of PL formation can be assessed even in coarse-resolution datasets. This study draws on previous studies and an empirical database of 63 PLs to quantify the respective influences of low-level static stability and upper-level forcing on PL formation, as both of these factors are known to favour PL development. Little redundancy between the two parameters is found. After defining threshold values for the two parameters, climatological properties of favourable conditions for PLs are computed for the North Atlantic, the North-West Pacific and the Southern Hemisphere. The low-level static stability, which is strongly modified during marine cold-air outbreaks, puts important constraints on where PLs can form, while the upper-level forcing determines whether or not they will form. As a result of the climatologically lower tropopause in the Labrador Sea region, favourable conditions for PLs occur more often there than in the Nordic Seas, which has long been believed to be the main PL region in the Northern Hemisphere (NH). In the Southern Hemisphere, favourable conditions for PLs occur substantially less often than in the NH. The PL index defined here is suitable for other climatological studies and PL forecasting. Copyright c 2011 Royal Meteorological Society Key Words: meteorology; Arctic Received 1 October 2010; Revised 15 February 2011; Accepted 24 June 2011; Published online in Wiley Online Library 11 August 2011 Citation: Kolstad, Erik W A global climatology of favourable conditions for polar lows. Q. J. R. Meteorol. Soc. 137: DOI: /qj Introduction Polar lows (PLs) are maritime, mesoscale cyclones at high latitudes (Rasmussen and Turner, 2003). While there exists no clear and all-encompassing definition of PLs, the term is usually reserved for cyclonic features that form in marine cold-air outbreaks (MCAOs), i.e. in cold air masses that are advected over a relatively warm, open ocean. The horizontal scale of PLs is normally less than 1000 km and the wind speeds are often 15 m s 1 or more. The overall objective of this study is to define an indicator that can be used to identify favourable conditions for PLs. Indices of this kind can be used to infer the probability of PLs even in datasets that do not have the resolution required to produce PLs, such as coupled climate models. Similar approaches have been used to analyse tropical cyclones (e.g. Camargo et al., 2007; Royer and Chauvin, 2009). If a reliable index can be identified, it allows for very fast computations of climatological properties of PLs in many different datasets. An alternative solution has been to dynamically downscale coarse datasets to a resolution that is high enough to simulate PLs, and then to track individual systems (Zahn and von Storch, 2008, 2010), but that method is significantly more computationally demanding than the one suggested in this paper. The most distinctive feature of MCAOs is their low static stability in the near-surface air masses, which is also the primary characteristic of PLs. In general terms, most Copyright c 2011 Royal Meteorological Society

2 1750 E. W. Kolstad PL developments go through two stages (Bracegirdle and Gray, 2009). The initial stage is typically characterised by low-level baroclinicity, which is often associated with large local temperature differences at the leading edges of, or inside, MCAOs in or near the marginal ice zone. Fuelled by baroclinic slantwise ascent (Browning, 1986), a comma cloud pattern (Carlson, 1980) may develop at this early stage. Many mesoscale features do not progress beyond the initial baroclinic stage, but if the incipient PL moves over warmer water, it may enter a new stage associated with more widespread low-level instability and convection than what is usually found in comma clouds. It is in this convective stage that the classical spiral-shaped PLs (e.g. Nordeng and Rasmussen, 1992) develop, and this is the kind of PL that is analysed here. A database of 63 such PLs is compiled with the aid of re-analysis data, satellite imagery and satellite-derived surface wind data. Comma clouds that do not move beyond the initial baroclinic stage are excluded from the database. Although low static stability near the surface appears to be a necessary condition for the development of PLs, the existence of upper-level forcing is also important. In the first major PL study (Harrold and Browning, 1969), it was noted that a high-level disturbance may be a factor contributing to the development of well developed polar lows. In recent years, the framework of upper-level potential vorticity (UPV) anomalies (Hoskins et al., 1985) has proved to be very useful in diagnosing cyclones in general, but also for PLs. For instance, the early development of a PL over the Norwegian Sea in October 1993 was found to be dominated by the arrival of a UPV anomaly over a low-level baroclinic zone (Claud et al., 2004; Bracegirdle and Gray, 2009). In a study of a pair of PLs that formed in an MCAO over the Labrador Sea, Pagowski and Moore (2001) found that their model was unable to realistically reproduce the cyclones, and attributed this to an incorrect representation of the UPV anomalies in the region. Many other studies have also found that UPV anomalies are an integral factor in PL developments (e.g. Montgomery and Farrell, 1992; Mailhot et al., 1996; Moore et al., 1996; Bresch et al., 1997; Browning and Dicks, 2001; Moore and Vachon, 2002). If one supposes that low-level instability and the presence of UPV anomalies are both necessary conditions, the next question is how strong must these factors be for PLs to form? In a modelling study of four situations during which the synoptic conditions appeared favourable, Grønås and Kvamstø (1995) found that PLs formed in only two of the cases. Their diagnostic parameter was the distance between the top of the boundary layer and the tropopause. In the two cases in which PLs did not occur, this distance was found to exceed 2500 m. The authors concluded that this distance was too large to allow interaction between the surface and upper-level anomalies. By contrast, in the two cases where PLs did form, the distance between the top of the boundary layer and the tropopause was less than 1000 m, allowing the upper and lower levels to interact more easily. The present study is divided into two parts. The purpose of the first part (section 3) is to quantify the influence of lowlevel static stability and UPV anomalies on the formation of PLs. For all of the PLs in the database, two diagnostic parameters are computed: (i) an MCAO index, which is more or less equivalent to the scalar difference between the sea-surface temperature (SST) and the potential temperature at 700 hpa, and (ii) the pressure at the tropopause, which can be used as an indicator of upper-level disturbances (Grønås and Kvamstø, 1995). Drawing on the analysis of the influence of these parameters on PL formation, empirical threshold values are identified for both of them and used to construct a PL index. The second part of this paper (section 4) aims to compile a climatology of favourable conditions for the formation of PLs. A number of climatological studies of PLs, mesocyclones and MCAOs already exist. Using weather maps, Wilhelmsen (1985) found 71 PLs close to Norway in the period from 1972 to While PLs were found from September to April, the maximum number occurred from November to January. The majority of the PLs formed between Spitsbergen and the Norwegian mainland or over the Barents Sea and subsequently moved southwards. The high frequency of PLs over the Norwegian and Barents Seas is well known, but other regions of the Northern Hemisphere (NH), such as the Sea of Japan, the Sea of Okhotsk and the region between Iceland and Canada, including the Labrador Sea, have also been found to be prone to MCAOs and PLs (Harold et al., 1999; Kolstad, 2006; Blechschmidt, 2008; Bracegirdle and Gray, 2008; Zahn and von Storch, 2008; Kolstad et al., 2009). PLs have also been identified in the Southern Hemisphere (SH) (Carleton and Carpenter, 1990), and recent work indicates that MCAOs near the Antarctic sea ice edge can be as strong as in the NH (Bracegirdle and Kolstad, 2010). The multitude of techniques applied in previous climatological work on PLs makes it hard to perform comparisons across different studies and regions. Here a comprehensive global climatology of the favourable conditions for PLs is presented. 2. Data The following six-hourly fields from the ERA-Interim dataset (Berrisford et al., 2009) were used: the temperature at 700 hpa (T 700 ), the geopotential height at 700 hpa (Z 700 ), the skin temperature (T S ), the mean sea-level pressure (p SL ) and the pressure at the tropopause level (p TR ). The tropopause level was derived by the European Centre for Medium-range Weather Forecasts (ECMWF) by searching downwards for the 2 PVU (1 PVU = 10 6 m 2 s 1 kg 1 K) surface from the model level close to 96 hpa (Berrisford et al., 2009). Grid points with a skin temperature of less than 1.9 C were assumed to be covered by sea ice. Otherwise the skin temperature is the same as the SST. Sea ice and land grid points were excluded from the analysis. The horizontal resolution of the ERA-Interim data is T255, but the data used here were downloaded from the ECMWF web site, and are on a regular grid. As in Bracegirdle and Kolstad (2010), a dimensionless MCAO index is computed as M = L Z (ln θ S ln θ 700 ), where Z is the geopotential height, θ S = T S (p 0 /p SL ) R/c p, p 0 is 1000 hpa, R is the specific gas constant for dry air (287Jkg 1 K 1 ), c p is the specific heat at constant pressure (1004 J kg 1 K 1 )andl is a scaling height of m. This value for L was chosen so that M is about the same as the scalar vertical temperature difference T S θ 700 under typical conditions (Bracegirdle and Kolstad, 2010). For the manual inspection of the PLs, satellite imagery from the Advanced Very High Resolution Radiometer (AVHRR: quicklook images downloaded from the web pages of the Dundee Satellite Receiving Station) and QuikSCAT scatterometer-derived surface winds (quicklook images

3 Global Climatology of Favourable Conditions for Polar Lows 1751 Table I. The 63 polar lows in the database. Year Date Time (UTC) Latitude ( ) Longitude( ) December N 0E December N 18E January N 29E January N 5E March N 10E March N 10E March N 5W December N 50W February N 5W February N 3E March N 8E March N 10E November N 25E November N 0E November N 37W November N 55W December N 5W December N 0E January N 42E January N 18E January N 14E January N 2W January N 12E February N 34E February N 30W February N 7E March N 0E March N 35W December N 43E January N 7E January N 10E January N 5E March N 52W December N 10E December N 20E January N 12E February N 10W March N 38W November N 12E January N 35W November N 0E December N 55W February N 40E March N 0E January N 10E March N 35W January N 50W March N 38W March N 7E March N 35W March N 8E March N 0E November N 12E November N 0E December N 55W December N 36W December N 15W December N 50W January N 25E January N 50W February N 0E March N 32W March N 40W For each case, the columns give the year, the day/month, the time, and the reference latitude and longitude.

4 1752 E. W. Kolstad (a) 80 N Sea ice 40 E Norway 70 N Sea ice Greenland 20 E Iceland 60 N 60 W 40 W 20 W 0 (b) Figure 1. The locations of the polar lows in the database. The black curve marks the approximate boundary between the grid points that had open water one-third of the time during the analysis period and the ones that did not. downloaded from the web pages of Remote Sensing Systems) were used. As the QuikSCAT data are only available from June 1999 to November 2009, all of the PLs in the database were selected from this period. When constructing the climatology, ERA-Interim data from 1989 to 2010 were used. These data covered 21 boreal winters (November March) and 21 austral winters (May September). The Northern hemisphere Annular Mode (NAM) index used here was downloaded from Jim Hurrell s web page ( accessed on 24 September 2010). The NAM index is the first principal component of seasonal sea-level pressure anomalies north of 20 N. 3. The polar low database A set of 63 PLs in the northern North Atlantic was compiled by manual inspection of satellite imagery. The dates and locations of these PLs are listed in Table I. The locations are also shown in Figure 1. All of the cases occurred from November 1999 to March 2009, and many of them were taken from a list of PLs provided by forecasters at the Norwegian Meteorological Institute in Tromsø (Noer and Lien, 2010; Noer et al., 2011). Upon inspection of the satellite imagery, the approximate times and locations were noted for each PL, from which the ERA-Interim grid points inside a radius of 400 km (a heuristic threshold) were scanned for the highest value of M. The data were also scanned in time to find the stage in the PL development with the lowest static stability. Using the PL s location as a reference, a new region within a radius of 400 km was then scanned for the highest value of p TR, a value that will henceforth be referred to as π TR to distinguish it from p TR. Comma clouds that did not develop into mature PLs were not included in the database. Also excluded was the requirement for surface-level winds to be of gale force or more, partly because QuikSCAT wind speeds have been shown to be biased in some conditions (Brennan et al., 2009), but the cases for which the QuikSCAT data did not Figure 2. AVHRR (channel 4) satellite images of (a) the Nordic Seas at 1147 UTC on 5 December 2003, and (b) the region to the south-west of Iceland at 1209 UTC on 2 March Both images were kindly provided by the NERC Satellite Receiving Station, Dundee University, Scotland. show any indications of cyclonic circulation and strong wind speeds (about 15 m s 1 ) were excluded. To illustrate the procedure used to identify PLs, two cases are discussed briefly. On 5 December 2003 a low over the Barents Sea formed a pressure dipole together with a high in the Iceland region. The satellite image in Figure 2(a) shows that the northerly flow between these two features gave rise to an MCAO (as evidenced by the cloud streets) over the Nordic Seas, in which a PL formed. The cross in Figure 2(a) is located at 71 N, 10 E and marks the grid point with the highest values of M in the region of the development. In Figure 3(a) (c), the sea-level pressure (Figure 3(a)) and the values of M (Figure 3(b)) and p TR (Figure 3(c)) are shown for 1200 UTC on 5 December. M-values of about 8 were found in the location marked with a cross in Figure 3(b). The grid points within a radius of 400 km from the cross are marked with dots in Figure 3(c), and the maximum value for the tropopause pressure within these grid points (i.e. π TR ) was about 560 hpa. A satellite image for the second case, on 2 March 2009, is shown in Figure 2(b), with the cross marking the grid point with the highest M-values at 61 N, 32 W. There was a synoptic low-pressure centre just east of Iceland, and a PL formed in the MCAO between Iceland and Greenland. The sea-level pressure (Figure 3(d)), M (Figure 3(e)) and p TR (Figure 3(f)) are shown at 1200 UTC on the same day. Figure 4(a) shows a scatter plot of the values of M and π TR for each of the PLs in the database, along with the climatological mean values for the corresponding locations

5 Global Climatology of Favourable Conditions for Polar Lows (a) SLP (b) M (c) p TR (d) SLP (e) M (f) p TR Figure 3. Diagnostic parameters for manual PL detection. For 1200 UTC on 5 December 2003, the three panels show: (a) sea-level pressure, with a contour interval of 5 hpa; (b) the MCAO index M, with a contour interval of 2, starting at zero; and (c) the tropopause pressure p TR, with a contour interval of 50 hpa, starting at 400 hpa. The black crosses show the reference location of this particular case in the PL database. The black dots in (c) show the grid points within a radius of 400 km from the reference location. (d) (f) As (a) (c), but for 1200 UTC 2 March (a) (b) π TR (hpa) Cumulative probability (c) MCAO index Cumulative probability MCAO index π TR (hpa) Figure 4. (a) For each case in the PL database, M is plotted against π TR with filled black circles. The open grey circles show the climatological values for the same dates and locations as the PLs. (b) The empirical cumulative distribution function (ECDF) of M during PLs in black and the climatological ECDF of M for the same locations and the same dates in grey. The vertical line marks the 0.05 quantile of M during PLs. (c) As (b), but for π TR.

6 1754 E. W. Kolstad and dates. It is clear that the typical values of both M and π TR in the vicinity of PLs are higher than normal. In Figure 4(b) and (c) the empirical cumulative distribution functions for M and π TR are shown for the PL cases and for the entire period for the same locations and times of the year. By using the empirical data shown in Figure 4, it is possible to define a simple, binary PL index P, which is defined to be 1 if both M and π TR exceed certain thresholds and is defined to be 0 otherwise. The following threshold values are chosen here: 3.4 for M and 470 hpa for π TR. (A number of different thresholds were tried, but this did not significantly alter the analysis below.) These values are the 5 th percentiles of the two parameters during the PLs in the database and are indicated by the vertical lines in Figure 4(b) and (c). The thresholds correspond to the overall 77 th percentile of M and the overall 64 th percentile of π TR, indicating that the threshold for M is exceeded less often than the threshold for π TR. As M consists of two fields, the SST and the 700 hpa temperature, it is of interest to find out which of these parameters contributes most to the high index values. Figure 5(a), which is a scatter plot of these fields during PLs, indicates that the two parameters are correlated. This is probably due to the geographical variations across the database in regions where the SSTs are low (high), air temperatures are also low (high). This is also reflected in the climatological means (the grey circles). Figure 5(b) shows that the SSTs during PLs are, if anything, lower than normal. This is surprising because one might have thought that instantaneous positive SST anomalies (with respect to climatology) would lead to an increase in the probability of PL formation in any given location. But, as shown in Figure 5(c), it is low air temperatures that are the driving force behind large values of M (which after all is an index of cold air outbreaks). The influence of the SSTs seems to be restricted to determining where the ocean surface is warm enough to produce large values of M, e.g. along the warm ocean currents in the North Atlantic. 4. Climatology Figure 4 shows that PLs occur when the values of both M and π TR are higher than normal, suggesting that the climatological extreme values of these parameters may give a first indication of where PLs are most likely to occur. Maps of M and p TR will therefore be shown for each region. Figure 4(a) gave an indication of a positive correlation between the MCAO index and the tropopause height. It is therefore of interest to consider the degree of redundancy associated with considering both M and π TR in a PL index. The co-variation between these parameters is also interesting because a high level of correlation would imply that the two parameters tend to have high values at the same time, thereby boosting the PL index. The correlation between the two parameters was therefore computed for each grid point. In order to exclude situations with high static stability, only the halves of the time series that had the highest values of M were retained for the correlation analysis. The correlation coefficients between these time series and the time-wise corresponding time series for π TR were computed and will be shown for each region. The hit rates of the PL index P, i.e. the percentage of the time for which both M and π TR exceed the empirical thresholds defined above at the same time (this percentage is simply the time-averaged value of P multiplied by 100), will also be shown. The hit rates for M and π TR, using the individual thresholds defined earlier, were also computed. Finally, area-averaged time series for sub-regions with the highest P hit rates will be shown in order to facilitate the assessment of the seasonal cycles and the interannual variability of P, M and π TR The Northern Hemisphere In Figure 6(a), the 90 th percentiles of M during the boreal winter (November March) are shown for the NH north of 30 N. Grid cells over land or cells with sea ice more than two-thirds of the time are shown in grey. As expected from previous studies, the largest values in the Atlantic region are found over the Norwegian and Barents Seas, the Labrador Sea and over the northward branch of the Gulf Stream off the east coast of North America. In the North-West Pacific, the highest values are found in the Sea of Okhotsk, in the Sea of Japan and in a band stretching eastward from Japan. The NH 90 th percentiles of p TR are shown in Figure 6(b). Some of the highest values are found along the jets downstream of North America and Asia. This is in agreement with the eastward-propagating tracks of UPV anomalies during winter, as shown by Kew et al. (2010; their Figure 7(b)), and would seem to favour PLs over the Labrador Sea region and over the North-West Pacific. Among the regions with large M values in Figure 6(a), the Nordic Seas stand out with relatively low p TR values, probably due to a climatologically higher tropopause associated with southwesterly airflow into that region. The correlation coefficients between M and π TR are shown in Figure 6(c). Generally speaking, this correlation is high where the extreme values of p TR are relatively modest, such as west of Europe and over the North-East Pacific (Figure 6(b)). Near Japan, the correlation is high, but in most of the typical PL regions, i.e. the Labrador Sea, the Nordic Seas and the Sea of Okhotsk, the correlation is fairly low The northern North Atlantic In Figure 7(a), the hit rates of P are shown for the northern North Atlantic, along with the boundaries of two regions that will be studied in more detail below. The highest frequency of favourable conditions for PLs, up to about 8% of the time during winter, is found over the Labrador Sea. Hit rates of up to 4% are found along the southeast coast of Greenland (south of the Denmark Strait). In the Norwegian/Barents Seas region, hit rates of about 3 4% are found, indicating that PL conditions in that region occur only about half as often as over the Labrador Sea. Figure 7(b) and (c) provide a means to attribute the P hit rates to the separate diagnostic parameters. Figure 7(b) indicates that the MCAO index M dictates the geographical distribution of P, while the tropopause pressure π TR (Figure 7(c)) puts restrictions on how often PLs can form. As a result, the low π TR hit rates over the Nordic Seas curb the P hit rates in spite of relatively high hit rates for M. Over the Labrador Sea, high hit rates for both M and π TR lead to a high frequency of favourable conditions for PLs. It is interesting to note that the relatively high hit rates for P south of the Denmark Strait a region with frequent PLs according to some studies (Bracegirdle and Gray, 2008; Zahn and von Storch, 2008, 2010) can at least partly be attributed to the high π TR hit rates. The hit rates for M in

7 Global Climatology of Favourable Conditions for Polar Lows 1755 (a) (b) (c) Figure 5. As Figure 4, but for 700 hpa temperature and skin temperature. (a) M (b) p TR (c) Correlation Figure 6. Northern Hemisphere climatology: (a) the 90 th percentile of M; (b)the90 th percentile of p TR ; and (c) the correlation coefficients between M and π TR. Six-hourly data during winter (November March) were used. In (a) and (c), only the grid points with open water more than one-third of the time are shown. (a) P hit rate (b) M hit rate (c) π TR hit rate Figure 7. North Atlantic climatological hit rates for (a) P,(b)M,and(c)π TR, all shown as the percentage of the time during winter (November March) for which the criteria defined in the text were satisfied. Six-hourly data were used and only the grid points with open water more than one-third of the time are shown.

8 1756 E. W. Kolstad Figure 8. North Atlantic seasonal and interannual cycles: (a) hit rates for P for each winter month; (b) hit rates for M; (c) hit rates for π TR ; (d) average SSTs; (e) average 700 hpa temperatures; and (f) hit rates for P for each winter from to The black (grey) bars show area-averaged values for the Labrador Sea (Nordic Seas) region. that region are quite low compared to the Labrador Sea and the Nordic Seas. Figure 8(a) shows the seasonal cycles of P in the regions indicated in Figure 7, multiplied by 100 and averaged for each month. In other words, the quantity shown is the average area-wise percentage of the regions with P = 1, but this can also be interpreted as the percentage of the time for which the whole region experiences favourable conditions for PLs. It is important to emphasise that the numbers presented in Figure 8 are all sensitive to the size and shape of the regions. Grid points with sea ice were ignored in the calculations. In Figure 8(b) and (c) the seasonal cycles of the hit rates for M and π TR are shown, and the monthly mean SSTs and 700 hpa temperatures are shown in Figure 8(d) and (e). In the Labrador Sea region (black bars), there is a build-up toward a peak in February, with a rapid decline into March. The seasonal cycles of the hit rates for M and π TR match the one for P. The maxima in P and M occur in February despite low SSTs, probably because the average 700 hpa temperatures over the region reach their annual minimum in that month. The substantial drop in the hit rate for P in this region from February to March is probably caused by a temperature increase at 700 hpa. The π TR hit rate and the SSTs do not change much between these two months. In the Nordic Seas region (grey bars), the peak in P occurs in January/February and in this region there is also a sharp drop from February to March. There is no evidence of any February nadir in PL activity, which has been suggested for PLs in other studies (Wilhelmsen, 1985; Kolstad, 2006; Noer et al., 2011). The highest M hit rates occur in December (Figure 8(b)), probably due to relatively high SSTs (Figure 8(d)), but the higher π TR hit rates in January and February probably contribute to the higher hit rates for P during those months. It is also worth noting that the hit rate for M is as high over this region as over the Labrador Sea in early winter, but as indicated above, a higher tropopause acts to restrain the P hit rates in the Nordic Seas compared to the Labrador Sea. In Figure 8(f), the interannual variability of P in the two regions is shown as seasonal (November March) averages of the P hit rates that were shown in Figure 8(a). There is no significant correlation between the two time series. During most winters, the hit rate in the Labrador Sea region is higher than the one in the Nordic Seas. The time series are too short for an assessment of trends, but it is obvious that the Labrador Sea hit rates have declined in recent years. This downward tendency coincides with the observed decrease in the wintertime NAM index. As the NAM index is positively correlated with a strong Icelandic low and northerly winds over the Labrador Sea, high P values in that region often coincide with high-nam winters, such as the winters of and Conversely, the low-nam winter of 2010 was associated with the highest 700 hpa temperature in the period (not shown) and a distinct minimum in P. The correlation coefficient between P and the NAM index on the seasonal (DJFM) time-scale is Note that only 21 winters were used to compute this correlation. Perhaps due to the direct links to the Icelandic low part of the NAM (which is known for its vigorous interannual variability) the interannual variability of the mean 700 hpa temperatures over the Labrador Sea region is quite large (σ = 1.8 C). The variability of P is also large (σ/µ = 0.47). Over the Norwegian/Barents Seas, the links to NAM are less clear. Kolstad et al. (2009) found a weak negative correlation between the North Atlantic Oscillation (NAO) index the first principal component of pressure anomalies in the North Atlantic sector and highly related to the NAM index and MCAOs over the Barents Sea, and attributed that correlation to the link between high-pressure anomalies over Greenland during negative phases of the NAO and northerly flow over the Nordic Seas. However, there is no significant correlation between the time series for P in Figure 8(f) and the NAM index. The interannual variability of the air temperatures over this region is less pronounced than over the Labrador Sea (σ = 0.8 Cfor T 700 ), but the variability of P is comparable in magnitude (σ/µ = 0.44). The Norwegian/Barents Seas maximum in P occurred during the winter of , a winter that was heavily represented in the PL database (see Table I) The North-West Pacific The hit rates for P in the North-West Pacific are shown in Figure 9(a). The highest hit rates (>6% of the time during winter) are found in the northern part of the Sea of Japan.

9 Global Climatology of Favourable Conditions for Polar Lows 1757 (a) P hit rate (b) M hit rate (c) π TR hit rate Figure 9. As Figure 7, but for the North-West Pacific. Figure 10. As Figure 8, but for the North-West Pacific regions. The black (grey) bars show area-averaged values for the Sea of Japan (Sea of Okhotsk) region. There is also a tongue of high values stretching eastwards from Honshu (the main island of Japan) along the warm Kuroshio ocean surface current (Mizuno and White, 1983). Values of about 4% are found over the Sea of Okhotsk. As in the North Atlantic sector, the geographical distribution of the hit rates of P is almost identical to the one for M.Low tropopause heights contribute most towards high P hit rates in the northern Sea of Japan, but most of the low tropopause events occur to the northeast of Japan, away from the major PL regions. The seasonal cycles of P in the two regions indicated in Figure 9 are shown in Figure 10(a). In the Sea of Japan region (black bars), a pronounced maximum is found in January, and the seasonal cycle follows the ones for both M and π TR (Figure 10(b) and (c)). The SSTs in this region (Figure 10(d)) are much higher than in the two main North Atlantic PL regions (Figure 8(d)). The January maximum in M coincides with the lowest 700 hpa temperatures (Figure 10(e)), but the sharp decline in M from January to February cannot be explained by a similar sharp drop in air temperatures. In the Sea of Okhotsk region (grey bars), the SSTs are very low (Figure 10(d)), but the air temperatures are low enough (Figure 10(e)) to ensure that the hit rate for M is relatively high in midwinter (Figure 10(b)). The maximum in P occurs in January and February (Figure 10(a)). The hit rate for π TR is fairly constant throughout the winter (Figure 10(c)), although the highest values are found in the two months with the highest P hit rates. Figure 10(f) shows the interannual fluctuations of the PL index for the two regions. The variability is relatively modest relative to the North Atlantic regions (σ/µ = 0.31 in the Sea of Japan and σ/µ = 0.35 in the Sea of Okhotsk). In both regions, the interannual standard deviation in T 700 is about 0.9 C. As for the two Atlantic regions, the two time series in Figure 10(f) are not correlated. For the Sea of Japan region, the anti-correlation with the NAM (r = 0.70) is as strong as the positive correlation that was found for the Labrador Sea. This shows that the anomalously low temperatures over East Asia during negative phases of the NAM (Thompson and Wallace, 2001) are associated with frequent MCAOs over the Sea of Japan, and that PL activity in that region is higher than normal in these periods. The cold and negative-nam winter of 2010 came in second after 2005 in terms of P hit rates for this region. Although the winter of 2010 was the most active winter in the Sea of Okhotsk region, there is no significant correlation between the NAM index and the PL index in that region on the interannual time-scale.

10 1758 E. W. Kolstad (a) M (b) p TR (c) Correlation Figure 11. As Figure 6, but for the Southern Hemisphere. Figure 12. As Figures 7 and 9, but for the Southern Hemisphere The Southern Hemisphere In Figure 11(a), the 90th percentiles of the MCAO index M during the austral winter (May September) are shown for the SH south of 30 S. As indicated by Bracegirdle and Kolstad s (2010) study of MCAOs, these extreme values are clearly lower than in the main PL regions of the NH during the boreal winter (Figure 6(a)). The 90th percentiles of ptr (Figure 11(b)) are also substantially lower than over the Labrador Sea and the Sea of Japan (Figure 6(b)). North of Antarctica towards the Indian Ocean, the values are comparable to the ones found over the Nordic Seas. As in the NH, the correlation between πtr and M (Figure 11(c)) is generally low in the regions with high extreme values of tropopause pressure. In Figure 12(a), the hit rates of P for the SH during the austral winter are shown. Two sectors stand out with hit rates higher than 0.5%: the marginal ice zone to the south of New Zealand (the westernmost of the two reference regions on the maps) and near the sea ice just north of the Amundsen Sea further east. These two regions also have the highest M hit rates (Figure 12(b)), but as for the Norwegian/Barents Seas region in the NH, relatively low πtr hit rates (Figure 12(c)) act to suppress the PL index hit rates. The two reference regions have distinct intraseasonal signatures. Figure 13(a) shows that the seasonal peak south of New Zealand (black bars) occurs in June and July, while c 2011 Royal Meteorological Society Copyright the peak to the north of the Amundsen Sea (grey bars) comes in August. This seasonal cycle is dictated by M (Figure 13(b)). In both regions the highest hit rates for the tropopause pressure is found in May (Figure 13(c)). From Figure 13(d) and (e) it is clear that the 700 hpa air temperatures, for which the minima occur in the same months that the P hit rates peak, determine the seasonal cycle of M. Figure 13(f) shows the interannual variation of P for the two regions. Interestingly, although the regions are located quite close to each other, the two time series are essentially uncorrelated. The interannual variability of the 700 hpa temperatures is weaker than in the Labrador Sea in absolute terms (σ = 0.6 C south of New Zealand and σ = 0.9 C north of the Amundsen Sea), but the relative variability of the P hit rate is larger than in all the NH regions (σ/µ = 0.49 and 0.51, respectively). 5. Discussion One of the most important indicators of MCAOs and the potential for PL activity is the difference between the temperature at or near the sea surface and the temperature of the cold air that is being advected over the same sea surface. Here I have tried to assess if it would be beneficial to include an additional parameter, which in combination with the MCAO indicator used in previous studies (Kolstad Q. J. R. Meteorol. Soc. 137: (2011)

11 Global Climatology of Favourable Conditions for Polar Lows 1759 Figure 13. As Figures 8 and 10, but for the Southern Hemisphere. The black (grey) bars show area-averaged values for the south of New Zealand (north of the Amundsen Sea) region. and Bracegirdle, 2008; Kolstad et al., 2009) could potentially yield a more reliable index for the potential for PLs to form. Almost all studies of PLs emphasise that a certain degree of upper-level forcing seems to be a necessary condition for PL formation. I therefore chose the height of the tropopause (or rather the pressure on the tropopause) as the additional parameter, and by studying a set of 63 confirmed PLs, I was able to quantify the individual influences of static stability and upper-level forcing on PL formation. The results indicate that the MCAO index M dictates where PLs occur, while the tropopause pressure π TR is an important constraint on how often PLs form. The same can be said of the two components of the static stability: high SSTs prescribe where PLs can form, but individual PLs form in outbreaks of cold air. The air temperature is therefore the parameter that decides when PLs form. There have been several other studies on the climatology of northern North Atlantic PLs (Kolstad, 2006; Blechschmidt, 2008; Bracegirdle and Gray, 2008; Zahn and von Storch, 2008). In qualitative terms, the present study agrees well with the regions previously identified as PL hot spots in these other studies: the Norwegian/Barents Seas, the region to the south-west of Iceland and the Labrador Sea. Zahn and von Storch (2008) is the only study that has previously counted the number of PLs in each sub-region of the northern North Atlantic over a long time period. Over the Norwegian/Barents Seas, an average of about 4 PLs were identified per year in each of their regions 2 and 3 (their Figure 2(a)). This agrees well with the P hit rates of about 3% of the time during winter found here (Figure 7(a)), which corresponds to 4 5 days from November to March. If one assumes that the lifetime of a PL is about 24 hours, this means that the index defined here predicts an average of about 4 5 PLs each winter. In the region to the southwest of Iceland (their region 5), where over 11 PLs were counted each year by Zahn and von Storch (2008), the hit rates computed here were only about 3 4% (corresponding to about 4 5 PLs per winter). It is difficult to identify a reason for this discrepancy, but that region is characterised by a high frequency of synoptic lows. One may speculate that some of the PLs detected by Zahn and von Storch (2008) were in the grey area between synoptic lows and PLs, and that this led to an artificially high PL count in the region. A thorough investigation of lows in this grey area is suggested as interesting future work. Discrepancies between the present study and Zahn and von Storch (2008) are also evident for the Labrador Sea region, where only about 5 PLs were counted each year by Zahn and von Storch (2008), but the hit rates of up to 7% found here indicates that up to 10 PLs could form there each winter. This is a region with lower SSTs than in the Norwegian/Barents Seas (Figure 8). It is possible that the likelihood of PLs decreases nonlinearly with decreasing SSTs, and that PLs therefore form less often than the index used here indicates. The PL index suggested here is different to earlier PL and MCAO indices in that it includes upper-level forcing in addition to static stability. It was therefore necessary to find out if these two parameters were correlated. Such a correlation would make sense, as UPV anomalies have an influence on the static stability below them. A relatively high level of correlation between the tropopause pressure and the MCAO index M was found over the subtropical North Atlantic, but in the typical PL regions the correlation coefficients were well below 0.5. This indicates that M and π TR yield complementary information about the potential for PLs. In other words, a PL index that incorporates both of these parameters will be more useful than an index that consists of only one of them. The scatter plot in Figure 5(a) shows that, when looking for favourable conditions for PLs, it is not possible to define a global threshold value for the air temperature aloft. Businger (1985) found that, on average, PLs occurred when the average 500 hpa temperature was 38 C, but the PLs in that study were all located over the Nordic Seas. In Tromsø, the forecasters use a threshold value of about 40 C at the same level as a bellwether of PL conditions (Gunnar Noer, personal communication). If the 500 hpa temperature is the only variable under consideration, different thresholds should be used in other regions with different SST distributions. However, the preferred and universally valid modus operandi for PL forecasters is to look for large values of SST minus the temperature in the lower or middle troposphere, typically at 700 or 500 hpa. This difference is more or less equivalent to the MCAO index M. At the same time, forecasters are looking out for incoming UPV anomalies. The results presented in this paper show that this quick method can yield valuable information about the likelihood of PL formation. But it is important to note that the threshold values presented here

12 1760 E. W. Kolstad were chosen at the time of maximum forcing PLs can form in conditions with weaker forcing as well. It is worth emphasising that different methods can be used to compute the tropopause height. In the ERA- Interim dataset, the tropopause was located by searching downwards for the first 2 PVU level. Although not shown here, the analysis that was used to produce the scatter plot in Figure 4(a) was repeated with the National Centers for Environment Prediction/National Center for Atmospheric Research (NCEP/NCAR) re-analysis (Kalnay et al., 1996) and yielded different results for π TR (but practically identical results for M). This is probably because the tropopause level is computed differently. According to their web pages, the tropopause in the NCEP/NCAR re-analysis is identified by the lowest level above 450 hpa where the temperature lapse rate becomes less than 2 K km 1. Ideally, when using a new dataset, the threshold value for π TR should be calibrated against a PL database (or the ERA-Interim data) before the PL index P is computed. The most reliable method would be to compute the tropopause height using the same algorithm for all datasets, but this requires a very high vertical resolution and huge amounts of data if long time periods are to be considered. For most climate model data, this is not a practicable approach. The index proposed here takes the static stability and upper-level forcing into account. Are these the most important factors for PL development, or should a PL index have included other parameters as well? It has been shown that many PLs form in reverse-shear conditions (Duncan, 1978; Kolstad, 2006), i.e. when the thermal wind is antiparallel to the winds at the steering level. However, although reverseshear PLs are an important subgroup of PLs, one study has indicated that they comprise only about one-fourth of all PLs (Blechschmidt, 2008). Sea ice and SSTs are also important factors for PLs. As mentioned earlier when discussing the high P hit rates in the Labrador Sea region, it would be interesting to find out if the likelihood of PL formation is nonlinearly related to the SSTs. For instance, are the SSTs in the Sea of Okhotsk region in winter (about 0 C, Figure 10) high enough to sustain PLs? Another factor that might be important for PLs, at least in the early stages, is the baroclinicity. This can be expressed through the Eady growth rate, which is proportional to the vertical wind shear v/ z and the Coriolis parameter f, and inversely proportional to the Brunt Väisälä frequencyn (Lindzen and Farrell, 1980; Hoskins and Valdes, 1990). Quantitative investigations of the importance of these and other parameters are suggested as future, important work on the study of PLs. One of the primary motivations for using an index for favourable conditions for PLs rather than detecting them directly is that coarse-resolution data model simulations and re-analyses are often unable to reproduce PLs. As mentioned earlier, a similar method to the one used here has been applied to detect favourable conditions for tropical cyclones (e.g. Camargo et al., 2007; Royer and Chauvin, 2009). The same method can probably be used to devise indicators of favourable conditions for other features as well, such as tip jets and barrier flow near topographic features (Moore and Renfrew, 2005), mesocyclones, and Arctic or boundary-layer fronts (Fett, 1989; Grønås and Skeie, 1999; Drüe and Heinemann, 2001). An interesting application would be to use the index defined here to parametrize the surface structure of PLs in a numerical model. This method was used by Condron et al. (2008) in a promising attempt to bogus the impact of polar mesocyclones on the ocean circulation. In a similar way, the index defined here can be used to improve the representations of surface winds and heat fluxes in numerical model simulations, and especially when the resolution of the model is too coarse to represent PLs directly. The application of such a scheme to re-analysis data or other model data is suggested as important future work. Acknowledgements I would like to thank Matthias Zahn, one anonymous reviewer and Tom Bracegirdle for their highly useful comments, which led to a much improved paper. My work was funded by the Norwegian Research Council through its International Polar Year programme and the project IPY-THORPEX (grant number /S30). References Berrisford P, Dee D, Fielding K, Fuentes M, Kållberg PW, Kobayashi S, Uppala SM The ERA-Interim archive. ERA Report Series 1. ECMWF: Reading, UK. Blechschmidt A-M A 2-year climatology of polar low events over the Nordic Seas from satellite remote sensing. Geophys. Res. Lett. 35: L09815, DOI: /2008GL Bracegirdle TJ, Gray SL An objective climatology of the dynamical forcing of polar lows in the Nordic seas. Int. J. Climatol. 28: Bracegirdle TJ, Gray SL The dynamics of a polar low assessed using potential vorticity inversion. Q. J. R. Meteorol. Soc. 135: Bracegirdle TJ, Kolstad EW Climatology and variability of Southern Hemisphere marine cold-air outbreaks. Tellus 62A: Brennan MJ, Hennon CC, Knabb RD The operational use of QuikSCAT ocean surface vector winds at the National Hurricane Center. Weather and Forecasting 24: Bresch JF, Reed RJ, Albright MD A polar-low development over the Bering Sea: Analysis, numerical simulation, and sensitivity experiments. Mon. Weather Rev. 125: Browning KA Conceptual models of precipitation systems. Weather and Forecasting 1: Browning KA, Dicks EM Mesoscale structure of a polar low with strong upper-level forcing. Q. J. R. Meteorol. Soc. 127: Businger S The synoptic climatology of polar low outbreaks. Tellus 37A: Camargo SJ, Sobel AH, Barnston AG, Emanuel KA Tropical cyclone genesis potential index in climate models. Tellus 59A: Carleton AM, Carpenter DA Satellite climatology of polar lows and broadscale climatic associations for the Southern Hemisphere. Int. J. Climatol. 10: Carlson TN Airflow through midlatitude cyclones and the comma cloud pattern. Mon. Weather Rev. 108: Claud C, Heinemann G, Raustein E, McMurdie L Polar low le Cygne: Satellite observations and numerical simulations. Q. J. R. Meteorol. Soc. 130: Condron A, Bigg GR, Renfrew IA Modeling the impact of polar mesocyclones on ocean circulation.j. Geophys. Res. 113: C10005, DOI: /2007JC Drüe C, Heinemann G Airborne investigation of Arctic boundarylayer fronts over the marginal ice zone of the Davis Strait. Boundary- Layer Meteorol. 101: Duncan CN Baroclinic instability in a reversed shear flow. Meteorol. Mag. 107: Fett RW Polar low development associated with boundary-layer fronts in the Greenland, Norwegian and Barents Seas. Pp in Polar and Arctic Lows, Deepak A (ed). A. Deepak Publishing: Hampton, VA. Grønås S, Kvamstø NG Numerical simulations of the synoptic conditions and development of Arctic outbreak polar lows. Tellus 47A: Grønås S, Skeie P A case study of strong winds at an Arctic front. Tellus 51A: Harold JM, Bigg GR, Turner J Mesocyclone activity over the North-East Atlantic. Part 1: Vortex distribution and variability. Int. J. Climatol. 19: