A polar low named Vera: the use of potential vorticity diagnostics to assess its development

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1 Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: , October 11 A A polar low named Vera: the use of potential vorticity diagnostics to assess its development Thor Erik Nordeng a,b *and Bjørn Røsting a a Norwegian Meteorological Institute, Oslo, Norway b University of Oslo, Department of Geosciences, Oslo, Norway *Correspondence to: T. E. Nordeng, Norwegian Meteorological Institute, Research Department, PO Box 43 Blindern, NO-313 Oslo, Norway. thoren@met.no November 8 the Norwegian Meteorological Institute issued an extreme weather warning for Trøndelag County. A storm was expected in the afternoon. The storm, a polar low (PL), was named Vera. Vera was the second of two polar lows that developed along a wedge of warm air at the rear of a synoptic-scale low that moved northeastwards into northern Norway. The dynamical development may be explained by classic dynamical theory: low-level warm air seclusion and shallow secondary circulation in a frontal zone that couples to transient upper level disturbances. The study focuses on the potential vorticity (PV) perspective of the PL development and we have modified the initial PV field to study the effect of each individual PV perturbation. Two PV and two low-level temperature anomalies have been chosen. The PV anomalies retained their structure during the development while the temperature anomalies became less coherent and difficult to define by the end of the cyclogenesis period. By modifying the initial conditions in the upper troposphere over Greenland, it is shown that in this case the upper PV anomaly had the strongest effect on the development, and that this effect remained strong throughout the cyclogenesis until the polar low made landfall. The effect from the low level PV anomaly became large after onset of cyclogenesis, reflecting the positive feedback, although its impact on the development remained smaller than that of the upper PV anomaly. It is also shown that the topography of Greenland was important in determining the correct position of this polar low development. Copyright c 11 Royal Meteorological Society Key Words: polar low; potential vorticity diagnostics; potential vorticity modification Received December 1; Revised 11 May 11; Accepted 4 June 11; Published online in Wiley Online Library 11 August 11 Citation: Nordeng TE, Røsting B. 11. A polar low named Vera: the use of potential vorticity diagnostics to assess its development. Q. J. R. Meteorol. Soc. 137: DOI:1.1/qj Introduction Polar lows (PL) are mesoscale cyclones that form during cold air outbreaks when the Arctic air is advected over comparatively warm waters. If there are weak seasurface temperature (SST) gradients and (or) no upper tropospheric troughs associated with upper level positive potential vorticity (PV) anomalies, PL developments are unlikely to occur. There is further observational evidence that PL developments require a temperature difference between the sea surface and tropopause of at least 4 C (Rasmussen and Turner, 3). Such favourable conditions are observed in flow with low static stability below a region of lowered tropopause, forming the classical three-dimensional structure of an upper level positive PV anomaly and its associated cold cyclonic vortex. Several investigations have been carried out yielding insight into the dynamics of PL development, e.g. Bracegirdle Copyright c 11 Royal Meteorological Society

2 A Polar Low Named Vera 1791 and Gray (9), Rasmussen and Turner (3), Nielsen (1997), Nordeng (199) and Rasmussen (1979). Strong PL developments are frequently triggered by a positive upper level PV (UPV) anomaly that overruns a low-level baroclinic zone. The latter may be created by strong sea-surface heating adjacent to the polar ice edge, cold snow-covered land or in the rear of synoptic-scale cyclones. During the development latent heat release takes place through dynamically forced (stable) ascent or strong convection as heat is transferred to the PL through the WISHE (wind induced surface heat exchange; Emanuel and Rotunno, 1989) and CISK (conditional instability of the second kind; e.g. Rasmussen, 1979) effects. Diabatic heating creates low-level PV (LPV) anomalies that are important for rapid cyclogenesis. Some studies (e.g. Bracegirdle and Gray, 9) have revealed that the LPV anomaly becomes the dominant contributor to the development, while the UPV anomaly becomes weaker through stretching and deformation as well as dilution due to the diabatic heating. Nordeng and Rasmussen (199) argue that this dilution of UPV above the volume where strong latent heating takes place enhances the vertical velocity in the area further due to the weakened static stability, i.e. a positive feedback. Cyclogenesis is generally described as A and B cyclogenesis (after Petterssen and Smebye, 1971). Recently C developments have been defined by Deveson et al. (), which describe about one-third of all PL developments quite well (Bracegirdle and Gray, 8). C cyclogenesis starts as for B cyclogenesis, with a UPV anomaly overrunning a low-level baroclinic zone. The UPV and low-level temperature waves form in positions favourable for sustained development. In the rising air ahead of the UPV anomaly latent heat release takes place, from which positive LPV anomalies are created while upper level PV is diluted. Such a formation of a negative UPV anomaly prevents the positive UPV anomaly from catching up with the low-level warm wave, maintaining a phase lag favourable for prolonged development. The dilution of UPV also lowers the static stability and may therefore strengthen the vertical ascent, i.e. a positive feedback. Of course this diabatic effect is also present in A and B cyclogenic development, but it is particularly strong in the C development. In C cyclogenesis the low-level baroclinicity tends to weaken. The UPV anomaly eventually weakens as it is wrapped up and stretched in the upper level circulation. However the LPV anomaly remains strong and often becomes the largest contributor to the development, as demonstrated in the case study by Bracegirdle and Gray (9). As PV thinking appears to be important in understanding rapid cyclogenesis in general (e.g. Hoskins et al., 1985), we also want to apply this consideration to a polar-low case study. This involves quantitative determination of the contribution of selected PV and potential temperature anomalies to the central geopotential height (or central surface pressure) of the PL, as well as assessing the interaction of selected PV and temperature anomalies important for PL development. Novel to this paper is that we will not only identify potential vorticity anomalies that we believe are important for PV development, but we also modify the initial PV fields (and hence all the others dependent variables) to identify their relative contribution to the PL development by a rerun based on an analysis obtained from inverting the PV field. This is carried out in order to test the sensitivity of the polar low development to changes in the upper level PV anomaly field. A similar approach was applied by Verkley et al. (5), Røsting and Kristjansson (6, 8) and Manders et al. (7), to study how the initials fields could be altered in sensitive regions in order to improve the simulation of a synoptic-scale low, but to our knowledge the approach has not been used previously in a PL analysis. Since boundary low-level warm (cold) temperature anomalies can be regarded as positive (negative) PV anomalies (e.g. Hoskins et al., 1985), and PV anomalies determine the static stability of the flow, consideration of PV ought to be useful for understanding PL developments. We adopt piecewise PV inversion as described by Davis and Emanuel (1991) and Davis (199). A thorough investigation of the dynamics of a polar low through the use of piecewise PV inversion has been performed by Bracegirdle and Gray (9). We will use standard model output routinely archived from the operational 8 and 1 km grid sizes (called HIRLAM8 and HIRLAM1) limited-area numerical weather prediction models used at the Norwegian Meteorological Institute at the time. The rerun with PV-based modified initial fields uses the same model (HIRLAM1), but these data were not available when the storm actually took place. The HIRLAM models are described in Unden et al. (). T. E. Nordeng (9) studied how the various operational models at Norwegian Meteorological Institute performed at the time of the PL event and found that even coarse resolution models (resolution larger than 8 km) were capable of forecasting the development of the precursor of the low as well as the polar low itself with a lead time of approximately 36 h. We therefore have confidence that output from the model may be used to study the development of the low.. The large-scale precursor Vera was the second of two polar lows which formed along a wedge of warm air combined with strong baroclinicity at the rear flank of a synoptic-scale low (sometimes described as a redevelopment on the trailing occlusion). As for all extreme weather events it was given a name by duty forecasters at the Norwegian Meteorological Institute. This synoptic-scale low ( the mother low ) came from the Denmark Strait, crossed the northern part of the Norwegian Sea heading towards Northern Norway and the Coast of Troms County (Figure 1). Of some interest is the small-scale low off the coast of Troms County (Figure 1(c) and (d)), which developed strongly during the evening of 18 November. This was the first of two polar lows (Vera was the second) and it formed at the boundary between the relatively calm inner part of the mother low and a much stronger northeasterly wind further west. This configuration sets up a strong differential temperature advection creating a reversed shear baroclinic zone. In a reversed shear flow, wind and thermal wind are in opposite directions and the flow weakens with height. The area will in addition have strong (shearing) vorticity. In some respect this initial phase is similar to the development of a most beautiful polar low as described by Nordeng and Rasmussen (199) and is frequently found for polar lows developing in the area. Blechschmidt et al. (9) investigated the large-scale atmospheric patterns during polar low events over the Nordic Seas and the synoptic situation found here classifies the developing polar low into their classification of storm track polar lows. They also say that On average, polar lows develop in northerly cold flows Copyright c 11 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: (11)

3 179 T. E. Nordeng and B. Røsting Troms Trøndelag (c) (d) Figure 1. Mean sea-level pressure at contour intervals of hpa (dashed contours) and geopotential height of 5 hpa (full contours at intervals of 8 m) 17 November UTC; 18 November UTC; (c) 19 November UTC; (d) 19 November 1 UTC. The plots are taken from the operational HIRLAM1 analyses. to the west of large-scale lows. Although interesting in its own right, we will concentrate on the development of Vera, the second of the two polar lows. After the decay of the first low a wedge of warm air, seen as a trough extending westward in Figure 1(d), remained and was advected southwards. Vera developed on this low-level structure similar in many ways to her older sister. Figure shows Vera in its mature stage off the coast somewhat further south as seen from satellite and simulated clouds from HIRLAM8. It is noteworthy that HIRLAM8 apparently did an excellent job in simulating the event, making it possible to understand the dynamics of the system by studying model output. There is a clear contrast between cold Arctic air in the western part of the Norwegian Sea and much warmer air along the Norwegian coast and over Scandinavia. The strongest relative vorticity is found as narrow vorticity filaments (bands) along the frontal zones (Figure 3) making the area prone to baroclinic/barotropic instability. A necessary condition for barotropic instability is that the vorticity has a maximum in the interior of the flow (The Rayleigh Fjørtoft criterion). The baroclinic counterpart to this is that the potential vorticity has a maximum in the interior (see e.g. Holton, 4, pp ). This is the case here. Friction and diabatic heating are sources for potential vorticity. Since frictional force works in the opposite direction to the motion, we notice that low-level potential vorticity is created (destroyed) if there is cold (warm) air to the right (left) of the flow. The former (cold air to the right) is found in reversed shear cases. We therefore note that potential vorticity is created at low levels where friction is large and also above the low-level circulation connected to the front where condensation occurs. A wedge of warm air extending from the Scandinavian peninsula into the Norwegian Sea is created due to strong cold air advection from the northwest at the southern side of the mother low. According to Hoskins et al. (1985) a warm (cold) temperature anomaly at the surface will have the same effect as a potential vorticity anomaly setting up a cyclonic (anticyclonic) circulation. Release of latent heat will in addition create potential vorticity below the heating maximum and reduce potential vorticity aloft (in reality within a material volume, potential vorticity is not created nor destroyed but rather redistributed). All in all, as for its older sister, a potential vorticity anomaly is formed at low levels due to release of latent heat connected to the secondary circulation along the frontal zone. The frontal zone developed due to cold air advection west of the mother low. In addition, the warm surface air in the centre of the mother low acts as an additional PV source. This configuration alone may spin up the cyclone, as shown by Montgomery and Farrel (199) who termed it self-induced development. In section 3 we investigate if the low-level dynamical structure acts on its own or whether it interacts with upper level transient disturbances. 3. The potential vorticity perspective of the polar low development We first explain briefly how the PV and temperature anomalies are constructed. The reader is referred to Davis Copyright c 11 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: (11)

4 A Polar Low Named Vera 1793 Figure. Satellite picture taken November 8, 13 UTC (left panel) and simulated mean sea-level pressure at contour intervals of hpa (right panel) together with medium and high clouds from the model HIRLAM8 (1 h forecast from November 8, UTC). Figure 3. Full lines in black are relative vorticity at 95 hpa (only positive values are plotted) at contour intervals of s 1. Grey contour lines (with shading) are potential temperature at contour intervals of K also at 95 hpa. Valid at 19 November 1 UTC. (199) or Kristjansson et al. (1999) for a more detailed presentation. For PV inversion we adopt Ertel PV and Charney s balance condition (Charney, 1955). (1) The total PV and temperature fields are decomposed into mean and perturbation terms. The mean fields are in this study temporal means, taken as an average over 6 h. The perturbation term may be decomposed into several anomalies. One may of course consider the entire positive (negative) part of the perturbation as one positive (negative) PV anomaly. We are, however, interested in specific PV anomalies that appear to have a large influence on the phenomena of interest. Such anomalies are usually clearly defined as temporally and spatially coherent PV and boundary temperature structures, e.g. the PV and temperature anomalies shown later in Figure 6 by enhanced contours. The PV and temperature anomalies that are far away from the region of interest or difficult to define temporally are collected in a residual term (examples of the latter are the perturbation features are shown later in light contours in Figure 6). () In the present study we use the inversion method presented by Davis (199). This method combines two inversion methods. obtained by subtracting the specific anomaly (e.g. the UPV anomaly shown later in Figure 6), yielding a modified geopotential field. Finally we take the difference between the total and modified geopotential fields that yields the geopotential field associated with the selected PV anomaly. Addition to the mean (AM), i.e. inversion of the mean PV field, yielding the mean associated geopotential field, followed by inversion of the modified PV field obtained by adding the specific PV anomaly, from which we obtain the modified geopotential. The geopotential associated with the selected PV anomaly is then obtained by the difference between the mean and modified geopotential fields. We finally take the average between the two methods, which is the required geopotential field associated with the selected PV perturbation. The procedure for obtaining the geopotential field associated with the boundary temperature anomalies is similar. (3) The vertical structure of the selected PV anomalies is in each case determined through inspection of the pressure levels given by the World Meteorological Organization (WMO) mandatory levels (i.e. 1, 9, 8, 7, 6, 5, 4, 3, 5,, 15, 1 hpa). We distinguish between upper level PV (UPV) anomalies, usually confined to pressure levels between 6 hpa and 5 3 hpa (e.g. see Figure 6 showing the PV anomalies at 4 hpa). The PV anomalies within the stratosphere are not considered as they have small influence on the tropospheric flow features. Stratospheric PV anomalies have small Rossby penetration depth due to the very strong static stability in the stratosphere. We regard lowlevel PV (LPV) anomalies (created by diabatic effects and friction) as anomalies confined between pressure levels 9 and 7 hpa (e.g. see Figure 6 showing the PV anomalies at 8 hpa). The distinction between UPV and LPV anomalies may occasionally seem arbitrary. During dry intrusions stratospheric air with comparatively high values of PV is occasionally advected along the isentropes down to about the 7 hpa level, while positive PV anomalies created by latent heating may be located at about 7 hpa in some cases, Subtraction from the total (ST), i.e. inversion of depending on the spatial distribution of diabatic heating. the total PV field that yields the total associated By comparing PV and relative humidity fields we believe geopotential field, then inversion of the PV field that the separation of PV anomalies between UPV and LPV c 11 Royal Meteorological Society Copyright Q. J. R. Meteorol. Soc. 137: (11)

5 1794 T. E. Nordeng and B. Røsting anomalies can be ascertained rather well, although positive low-level PV anomalies formed through diabatic heating may be advected into dry regions. The boundary temperature anomalies subject to inversion are located on the 95 and 1 hpa pressure surfaces. Temperature anomalies at 1 hpa have negligible influence on the tropospheric flow due to the small Rossby penetration height, hence only impacts from low-level boundary temperature anomalies are considered (e.g. see Figures 6(c) and 7(c) and (d)). Davis (199) has shown that the method of combining the ST and AM methods yields results that are almost similar to the full linear method presented by Davis and Emanuel (1991). In addition to Charney s balance condition, appropriate horizontal and lateral balance conditions are used in the PV inversion (e.g. Davis and Emanuel, 1991). This technique yields balanced three-dimensional fields of geopotential height (Z), wind components (u,v) and temperature. The balance condition implies that the wind in the new analysis obtained through PV inversion is non-divergent. Since cyclogenesis involves strong ageostrophic winds, the absence of divergent winds in the initial state of a numerical rerun may be thought to be detrimental to the simulation. However, divergence is rapidly restored during the model integration after 3 6 h simulation time. It is also possible of course to retrieve divergent winds at the time of analysis by solving the quasi-geostrophic omega equation or even higher order filtered systems of equations (Iversen and Nordeng, 1984), and then adopt the continuity equation in pressure coordinates to obtain divergent winds. We have not included this procedure in this study, assuming that divergent winds were restored in the model simulation before the PL development started. The PV inversion is performed by solving (numerically) a Laplacian-like operator, from which geopotential heights are obtained. The iteration fails to converge in the presence of negative PV. The problem is dealt with by performing locally the inversion for a coarse grid (increased by a factor of four), subsequently the inversion is carried out stepwise for higher resolutions until performing the procedure at 55 km horizontal resolution (Kristjansson et al., 1999). This procedure allows the iteration to converge, however the inverted fields tend to deviate from those observed, occasionally in the range 1 15 m. Such a deviation from the observed fields may present difficulties in quantitatively applying PV consideration to PL studies. However, we did not experience such difficulties in the present work. Relative humidity (RH) fields required for a new numerical analysis are retrieved from the operational HIRLAM simulation, and interpolated to the smaller integration area used for the experiments. It is also possible to modify the RH fields, but this is not done in this experiment. When PV anomalies are modified while keeping RH fields unchanged, discrepancies between the new PV and the RH features tend to occur. However, model runs appear to be rather non-sensitive to local RH features in the model analysis, as the dynamics of the flow in the model integration rapidly creates consistent RH fields. The original data retrieved for this investigation are the operational HIRLAM simulation with 1 km horizontal resolution and 6 vertical model levels. The integration area is shown by A in Figure 4. The original fields are first interpolated to a coarser grid of 5 km horizontal resolution and 1 pressure levels (region B in Figure 4) according to WMO mandatory levels. We then calculate Figure 4. Region A corresponds to the operational HIRLAM model with 1 km resolution and 4 model levels. Region B is that used for calculating the potential vorticity fields. Region C is that used for the control and rerun simulations. potential vorticity in region B on these pressure levels. The PV inversion is performed for a region smaller than region B, but somewhat larger than C in Figure 4, covering the North Atlantic, Greenland, the Norwegian Sea and western Europe. Both control and rerun simulations are then prepared for integration for region C in Figure 4, still at 5 km horizontal resolution and with 1 pressure levels. Finally, the control and rerun initial fields are subsequently interpolated back to the operational HIRLAM grid (resolution 1 km), but for subarea C with HIRLAM1 topography (resolution 1 km). Boundary fields for area C are from the Meteorological Archival and Retrieval System (MARS) archive at the European Centre for Medium range Weather Forecasts (ECMWF). It is worth noticing that real comparison between the operational full area simulation and the run with modified PV fields initially will be difficult due to the implicit smoothing introduced by introducing a coarser grid (horizontally as well as vertically) during the interpolation process and also due to a different integration area. However, the difference between the modified and the rerun run (control) should shed light on this. 4. Potential vorticity anomalies and their impact on polar low development 4.1. Selection of potential vorticity anomalies During 19 November the incipient PL was not clearly defined, being a trough extending from the first of the two polar lows close to the coast rather than a clearly defined region of minimum central surface pressure. Before the onset of rapid development at UTC on November, we refer to the region of maximum relative vorticity at 95 hpa within the trough as the incipient polar low (Figure 5). We now define the PV and boundary potential temperature anomalies shown in Figure 6. Two PV anomalies and two boundary potential temperature (TH) anomalies are specifically chosen. (1) A positive UPV anomaly. This anomaly appears to be the main upper level forcing, and is defined for pressure levels 6, 5, 4 and 3 hpa. The PV associated with stratospheric air may occasionally penetrate as far as 7 hpa in tropopause foldings Copyright c 11 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: (11)

6 A Polar Low Named Vera 1795 Figure 5. Relative vorticity (contour interval s 1 and shaded) and geopotential height in dashed contours at 95 hpa (contour interval 4 m) from the HIRLAM operational numerical analysis at UTC on 19 November 8. (e.g. Browning, 1997). However, PV values at 7 hpa are generally below PVU. In our case study PV values at 7 hpa are very low. () A positive LPV anomaly, created by diabatic heating. This anomaly is defined at levels 9, 8 and 7 hpa. (3) Positive (warm) low-level boundary temperature anomaly, TH1, defined at 95 hpa. (4) A negative (cold) low level boundary temperature anomaly, TH, also defined at 95 hpa. Figure 6 presents a 4 h numerical weather prediction (NWP) simulation of the PV and TH perturbation and anomaly fields at UTC on November 8 at the time when the polar low intensified. The dashed contours show the height of the 1 hpa surface in all panels of Figure 6, with contours every m. Figures 6 and 6 show the PV perturbation fields at 4 and 8 hpa respectively, with the selected PV anomalies highlighted with bold contours. The equidistance is 1 PVU for the UPV fields and. PVU for the LPV. The zero contours are omitted. The potential temperature perturbation fields at 95 hpa are presented in Figure 6(c), with selected positive and negative TH anomalies shown by bold contours. In Figure 6(c) the positive potential temperature anomaly is shown as the two shaded areas. Six hours prior to this the anomaly was a continuous area. The field is shown for each degree K and the zero contours are omitted. Several other PV and TH anomalies may be identified in Figure 6. They all contribute to the central pressure of the PL, although this effect becomes smaller with increasing distance from the PL. The selected PV anomalies are close to the PL and thus have the largest impact on the depth of the low. The contribution to the height of the 9 hpa surface from the four PV and TH anomalies are shown in Figure 7 for UTC on November 8, the geopotential height at 9 hpa is shown by dashed contours. Figures 7 and 7 show the contribution from the UPV and LPV anomaly respectively. The positive UPV anomaly gives the strongest contribution, i.e. more than 8 m, while the LPV anomaly contributes with approximately 5 m to the instantaneous depth of the polar low. Hence the LPV contribution is large, despite its comparatively small amplitude. Figures 7(c) and 7(d) present the height field at 9 hpa associated with the warm and cold low-level (95 hpa) temperature anomalies respectively. The warm anomaly has a small positive (strengthening) contribution (a bit more than m). The effect from the cold anomaly works in the opposite direction and amounts to +1 to +15 m at the location of the PL. There are many anomalies that have not been defined and studied specifically; they all comprise the remaining part of the perturbation field, referred to as the residual term. Figure 7(e) shows the contribution from the residual term to the geopotential height field. Its contribution at the polar low location is +4 to +5 m at UTC November. Table I shows the contribution to the 9 hpa geopotential height at the PL centre from the UPV, LPV and TH1, TH anomalies during the simulation, until it made landfall at +4 h simulation time. The contribution from the residal term is also shown. The data are based on the operational HIRLAM simulation with initial time UTC 19 November. After +4 h simulation time the PL could perhaps be tracked as an upper level disturbance, occasionally associated with a weak low-level trough (results from beyond +4 h are not shown). Contrary to many previous investigations, we find that the contribution from the UPV anomaly remained the most important in contributing to the polar low central height (central pressure). The contribution from the LPV anomaly became apparent after +1 h. In this case it remained less than the effect from UPV, but reached the same magnitude early in the development. The warm anomaly, TH1, had some impact on the central pressure of the polar low, reaching its peak value at +18 h simulation time, after which time the effect almost vanished. The effect increased beyond +4 h, but the polar low was then difficult to define, except as a mainly upper level disturbance, as mentioned above. Although the direct effect of the warm anomaly seemed modest (as seen through PV inversion) it may have contributed significantly by preparing the environments favourable for condensation to take place either dynamically or by convective processes and hence deepened the low (warm low-level air, reduced static stability). The impact from the cold anomaly, TH, was present mainly at an early stage of the PL development, when it contributes to a filling (weakening). The residual term contributes to a lower central pressure of the polar low early in the development; at initial time UTC 19 November the strongest deepening effect on the PL is due to the residual term. This can be ascribed to the proximity of an upper level positive PV anomaly between Svalbard and Greenland (see Figure 6). After +1 h the residual term exerted a filling effect as the polar low moved southward and the PV anomaly at Svalbard weakened (see Table I). 4.. Dynamical impacts by the potential vorticity anomalies We now study the interaction between the PV anomalies and the PL. Figure 8 shows the potential temperature at 95 hpa (dashed contours), with contours every degree K at UTC November. The bold contours represent the positive (warm) temperature anomaly. The winds (shown by conventional symbols) are associated with the positive UPV anomaly (described above and shown at 4 hpa in Figure 6). We observe that the northeastern part of the warm anomaly is advected to the southwest by these winds, while cold advection takes place to the south of Copyright c 11 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: (11)

7 1796 T. E. Nordeng and B. Røsting 8N Troms Trøndelag 7N 1W B A 1E (c) Figure 6. Potential vorticity (PV) anomalies at 4 hpa in solid contours at every 1 PVU, selected UPV anomaly in bold contours. Geopotential height at 1 hpa in dashed contours (contour interval m). Simulated fields, +4 h, valid at UTC on November 8. Same as in, but PV anomalies at 8 hpa in solid contours at every.5 PVU, selected LPV anomaly is in bold contours at every. PVU. Position of cross-section for Figure 9 is indicated as line AB. (c) Boundary temperature anomalies at 95 hpa in solid contours at every C, selected temperature anomalies are highlighted in bold contours with shading. The two shaded anomalies are warm; the remainder cold. Geopotential height at 1 hpa in dashed contours (contour interval m). Simulated fields, +4 h, valid at UTC November 8, based on the operational HIRLAM run. Table I. Contribution to 9 hpa geopotential height at polar low centre. Time is relative to UTC 19 November 8. Variable Time (hours) UPV LPV TH TH RESIDUE TOTAL the temperature anomaly. The southwestern part of the warm anomaly is advected to the southeast. This part of the warm anomaly weakens and has essentially disappeared 6 h later (not shown). The associated winds far away from the positive UPV anomaly, e.g. close to Greenland (to the left in the figure) are very weak, with negligible contribution to temperature advection in that region. Figure 8 shows the contribution from the LPV on temperature advection and we focus on the northeastern segment of the warm anomaly. Although the LPV anomaly is comparatively weak compared with the UPV anomaly (Figure 6 and ), its advective effect by the associated winds is at least as large as for the UPV anomaly. The LPV anomaly contributes to the cold advection to the south of the warm anomaly. There is also a tendency for frontogenesis due to the LPV induced winds at the western boundary of the warm anomaly. Due to the cold advection to the south there is a tendency for the formation of a warm core. On the other hand the strong cold advection in the region of the warm anomaly leads to its destruction. This can be seen in Table I, which shows a substantial weakening of the impact from the warm boundary anomaly (TH1) after +4 h simulation. We find merely a negligible temperature advection due to the warm anomaly itself (self-advection). The same is true for the cold anomaly (not shown) The source of the low-level potential vorticity anomaly In general the formation of low-level PV anomalies is due mainly to diabatic heating. However, the effects from friction may locally contribute to the formation of low-level PV anomalies. Low-level PV anomalies produced in this way may reach amplitudes as large as those due to diabatic heating (e.g. Stoelinga, 1996). The low-level PV anomaly Copyright c 11 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: (11)

8 A Polar Low Named Vera (c) (d) 1797 (e) Figure 7. Full lines are geopotential height at 9 hpa in solid contours given for every 1 m associated with the UPV anomaly. The total geopotential height at 9 hpa is given in dashed contours shown for every 4 m. Simulated fields, +4 h, valid at UTC on November 8. As in but for the geopotential height contribution from the LPV anomaly. (c) As in but for the geopotential height contribution from the TH1 (warm) anomaly. (d) As in but for the geopotential height contribution from the TH (cold) anomaly. (e) As in but for the geopotential height contribution from the residual PV anomaly. and 6 h accumulated precipitation data at UTC on November are fairly well collocated (Figure 9). The maximum low-level PV is located somewhat outside the area of maximum precipitation, but this is most likely due to advective effects since precipitation is accumulated over 6 h. In order to try to resolve this issue we study the cross-section given in Figure 9 and trajectories provided in Figure 1. The fields in Figures 9 11 are taken from the operational HIRLAM1 simulation. The location of the cross-section is shown in Figures 6 and 9. Figure 9 shows PV in heavy contours and RH larger than 7% in grey shading. The vertical velocity field is indicated by the dashed contours that separate regions of ascent (+) and descent ( ). The ascending moist air in the southern frontal wall (around 7 N) is collocated with a strong, though small scale, low-level PV feature with a peak amplitude at 9 PVU at around the 9 hpa level. We also notice rather high PV values ( 4 PVU) in the descending air at the warm core centre of the polar low. This PV appears to be separated c 11 Royal Meteorological Society Copyright from the upper level PV anomaly observed at 55 hpa and above (not shown). Figure 1 shows the back-trajectory of an air parcel that ends up at the centre of the low-level PV anomaly at UTC November. The trajectory is calculated on the 8 K isentropic surface. The air parcel starts at 687 hpa at UTC on 19 November with a PV value of about.3 PVU, and moves to 735 hpa with a PV value above PVU at UTC November (not shown). Hence the parcel is generally descending from 687 hpa to 737 hpa (Table II). However, as the parcel is caught up in the PL vortex, shown by the counter-clockwise turn of the trajectory, it rises to 7 hpa before descending to 737 hpa by the end of the trajectory. It is in this case difficult to assess the change of the air parcels PV, because the PV contours intersect the lower model surface in the flow at the 8 K surface. However, PV values appear to increase from an initial.3 UPV at 687 hpa to above PVU at 737 hpa 4 h later. It appears that the increase of PV for the air parcel at least partly coincides with the ascent and Q. J. R. Meteorol. Soc. 137: (11)

9 1798 T. E. Nordeng and B. Røsting E 7N B 1W A A B Figure 8. The warm anomaly at the 95 hpa surface in solid bold contours shown for every degree C. The isotherms for the total potential temperature field are shown for every degree K. The winds at 9 hpa are associated with the UPV anomaly. Simulated fields, +4 h, shown at UTC on November 8. As in but for winds associated with the LPV anomaly. Table II. Development of low-level potential vorticity anomaly on 19 November 8. Time (UTC) Anomaly (PVU) Pressure (hpa) associated diabatic heating around 18 UTC. Finally the air parcel is advected along the isentropic surface, retaining its PV value. Throughout the trajectory the air parcel is located at around the 7 hpa level. Hence we may disregard friction as a source or sink of PV. Changes in the PV are then due to latent heat release. The vertical displacement of the particle every 6 h and the acquired PV are given in Table II. Since the air parcel is not following an isentropic surface during latent heat release, the trajectory shown in Figure 1 gives a qualitative picture of the propagation only. Figure 9. The LPV anomaly at 8 hpa shown in solid contours for every. PVU, simulated fields +4 h, valid at UTC November 8, from the operational HIRLAM run. The shaded area is 6 h accumulated precipitation at the same time. Cross-section through the LPV anomaly; location of the cross-section shown in Figures 6 and 9. The solid contours represent potential vorticity, contour interval PVU. The dashed contours separate regions of descent ( ) and ascent (+). The shaded regions show relative humidity at and above 7% Sensitivity study through initial potential vorticity modification The persistent large impact from the UPV anomaly is contrary to results from the case study by Bracegirdle and Gray (9), where the influence from the upper level forcing, i.e. positive advection of the positive UPV anomaly, becomes negligible as the polar low intensifies and enters its mature stage. However, if the PL had stayed over open water, a weakening of the UPV anomaly would most likely have taken place through the continued effects from diabatic heating and deformation. To verify the real importance of the UPV anomaly, back-trajectories from the time of peak intensity of the polar low at 1 UTC on November (+36 h simulation time) have been calculated at the 3 K isentropic surface. The result is shown in Figure 11 and. The air parcels within the UPV anomaly at 1 UTC November (Figure 11) appear to have originated over northern Greenland at initiation time (i.e. 36 h earlier, Figure 11). Figures 11 and 11 also show PV fields on the 3 K isentropic surface (at initiation time, Figure 11, and at +36 h simulation time, Figure 11). Before reaching the polar low, the upper level flow from northern Greenland is not involved in any interaction with the low-level flow, hence the upper level PV is essentially retained for the air Copyright c 11 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: (11)

10 A Polar Low Named Vera 1799 a 7N 1E Figure 1. Isentropic potential vorticity (PV) on the 8 K surface for every. PVU. Dashed contours show the pressure of the 8 K surface. The back-trajectory is shown in the middle part of the figure. The PV and pressure fields are valid at UTC 19 November 8. The trajectory spans a time of 4 h (from 11 UTC 19 to UTC November). Fields are taken from the operational HIRLAM1 simulation. parcels (near adiabatic flow), as confirmed by studying the PV values shown at the start and end of the trajectories in Figure 11. The extent to which the UPV anomaly is important for the PL development can be assessed by introducing changes in the flow features over northern Greenland at initiation time, i.e. UTC 19 November. These are accomplished by modifying the upper level PV field at initiation time in that region and then applying inversion of the PV field for a region that contains region C (not shown). Two numerical runs based on an initial state, obtained through PV inversion, are now performed. The simulations are performed using HIRLAM1. Therunsare: 1. (1) The control run. The numerical analysis for initializing this simulation is obtained through inversion of the original PV field at UTC 19 November. A HIRLAM1 simulation then produces the control runinregionc.. () The modified run. The PV is reduced at initiation time ( UTC 19 November), by 1.5 PVU, over northern Greenland, at levels 6, 5, 4 and 3 hpa. The modified analysis is obtained through inversion of the modified PV file at initiation time. The modified run is then performed with the HIRLAM1 model in region C. Figure 1 shows the initial difference between the modified and original PV field at 3 hpa (full contours) and the associated difference between the modified and original height field at 9 hpa level (broken contours). Figure 1 shows the original and modified PV fields in dashed and solid contours respectively. The fields are presented in the crosssection C D with orientation shown in Figure 1. The modification amounts to a reduction of PV in the mid- and upper troposphere, and lower stratosphere over northern Greenland. Inspection of the potential temperature field (not shown) shows that the PV modification also results in an elevated tropopause in the region, from about 55 hpa in the control to 45 5 hpa in the modified analysis (not shown). Results from the numerical simulations, at +36 h, i.e. at 1 UTC on November are shown in Figure 13. Figure 13 shows mean sea-level pressure (MSLP) from the operational run (solid contours) and the synoptic analysis (dashed contours). The operational run captures the PL development quite well, with only slightly lower central pressure compared with the synoptic analysis. Figure 13 shows MSLP from the control (dashed contours) and modified runs (solid contours). In the modified run the PL is making landfall at this time. The pronounced trough with strong winds branching off to the west of the PL centre is missing and the winds are weaker than in the control and operational simulations. The rerun PL has higher surface central pressure as well. Three hours later, at +39 h, the PL in the modified run had disappeared, leaving a uniform northerly wind field in its wake (not shown), while the PL in the control and operational runs was still situated off the coast, retaining the structure observed at +36 h simulation time. The PL made landfall just after 15 UTC. The event is captured by both the operational run and the control simulation (not shown). It should be emphasized that the PV modification is subjective, based on experience, and designed to study the impact on the numerical simulation. In terms of geopotential heights, the perturbation is larger than typical analysis errors. The impact on the PL development due to weakened upper level PV over northern Greenland at UTC on 19 November can be understood by studying the upper level PV features 4 h later, at UTC on November. Figure 14 shows the initial PV perturbation, i.e. the difference between the PV in the control and modified runs (shaded and contours for every.5 PVU). The perturbation is shown at the 95 K isentropic surface, corresponding to about 4 hpa over northern Greenland and adjacent regions to the east. Also shown in the figure is the MSLP from the synoptic analysis (dashed contours) valid at that time. Figure 14 presents the same fields at 95 K, 4 h later, at UTC November. The initial perturbation has increased. This implies a weakening of the rerun upper level PV west of and close to the incipient polar low, which is indicated by L in the figure, while it has strengthened further north. This northward shift of the upper level PV maximum in the rerun simulation prevents interaction of the upper level PV anomaly with the incipient surface PL and its associated sharp front. In both control and rerun simulations the PL developed somewhat to the east, closer to the pre-existing low off the coast, while the real development took place within the low-level trough extending westward from the eastern low (Figure 1(d)). This development was properly captured by the operational HIRLAM simulation (with 1 km horizontal resolution). Although the initial position of the polar low in both the control and rerun was too far to the east, the subsequent development in the simulation took the PL close to its observed position, as observed in Figure 13. The position error of the PL in the control simulation as compared with the operational run may be understood by studying Figure 15, which shows the initial difference of geopotential height (Z) at 85 hpa UTC on 19 January between control and operational simulations. Geopotential height is used rather than PV since the isentropic surfaces and PV features at low levels cut the ground west of the PL, rendering interpretation difficult. Figure 15 shows that interpolation from the control analysis, with 1 pressure levels and 5 km horizontal Copyright c 11 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: (11)

11 18 T. E. Nordeng and B. Røsting Figure 11. Isentropic potential vorticity (PV) and trajectories starting at +36 h, i.e. 1 UTC November, on the 3 K surface shown in solid contours for every 1 PVU. The PV field is valid at UTC 19 November 8. Isentropic PV shown for every 1 PVU and trajectories on the 3 K surface. The PV field is valid at 1 UTC November 8. The trajectories have been calculated backwards from the region of maximum PV (UPV anomaly) west of the Norwegian coast at 1 UTC November 8 to northern Greenland 36 h earlier as indicated by the crosses seen in the figure. Fields from the operational HIRLAM1 simulation are used. b a 1 C 1 1 C Figure 1. The change of upper level potential vorticity (PV), at 3 hpa, over northern Greenland in solid contours (reduction of PV) every 1 PVU. The dashed contours represent the associated change of the geopotential height field at 9 hpa, shown for every 1 m. The fields are shown at analysis time, UTC 19 November. Cross-section (location shown in Figure 1) showing the original initial and modified PV field in dashed and solid contours respectively, at UTC 19 November. resolution to the model levels required for the HIRLAM simulation (1 km horizontal resolution and 4 model levels), has produced a perturbation field. The perturbation is particularly large at low levels over Greenland, amounting to a peak value of 1 m at this level (85 hpa). Largest values are found at 1 hpa ( m) falling off to less than 5 m above 85 hpa (not shown). This perturbation is larger than the geopotential perturbation related to the PV modification, which is mainly in the range 3 4 m at 8 9 hpa levels (Figure 1), and reaches peak values of slightly more than 7 m at 4 5 hpa levels (not shown). At the position of the low-level trough branching off from the first polar low, there are only small differences in Z between the control and the operational runs D D Figure 15 shows the perturbation field, obtained as the difference at UTC on January between 85 hpa geopotential height (Z) of the control and the operational simulations. The perturbed height field over Greenland is now smaller. However, at this time there is a strong signal at the PL location, amounting to an increase of 6 m at the site of the incipient polar low and a reduction of Z further east of 5 m. The latter location is where the PL started to develop in both the control and rerun simulations. Based on these results we argue that Greenland s topography may have an influence on the location where the PL developed. However, we perceive that the changes of geopotential height Z as seen in Figure 15 may be ascribed to technical reasons since pressure surfaces in the analysis obtained through PV inversion intersect Greenland s topography. 5. Discussion and summary This study has focused on the PV perspective of the Vera PL development. The low had its most intense phase during th November 8. For the PV diagnostics we focused on UTC November 8 when the low started its rapid intensification. Two PV and two low-level temperature anomalies were chosen. The main reasons for selecting the four anomalies were that they could easily be identified, particularly prior to and in the early phase of rapid cyclogenesis, and they appear to have a well-defined impact on the development. However, the effects from the low-level boundary temperature anomalies weaken as the PL develops, suggesting that the PL development can be regarded as a C-type cyclogenic development. The PV anomalies retained their structure during the development while the temperature anomalies became less coherent and difficult to define by the end of the cyclogenesis period. In this case the UPV anomaly had the strongest effect on the development, and this effect remained strong throughout the cyclogenesis until the polar low made landfall. This is in contrast to results from other PL studies (e.g. Bracegirdle and Gray 9), where the upper level forcing becomes much weaker, while the contribution from the low-level diabatically produced PV anomaly becomes the main contributor to the deepening of the cyclone. In the present case the effect from the lowlevel PV anomaly became large after onset of cyclogenesis, reflecting the positive feedback, although its impact on the development remained smaller than that of the UPV Copyright c 11 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: (11)

12 A Polar Low Named Vera 181 L Figure 13. The 36 h simulation of mean sea-level pressure by the operational HIRLAM model in solid contours, every 5 hpa, valid at 1 UTC November. The synoptic surface analysis valid at the same time is shown by the dashed contours. Some synoptic observations are shown by their standard symbols. The 36 h simulation of mean sea-level pressure by the control simulation in dashed contours, every 5 hpa, valid at 1 UTC November. The 36 h simulation of mean sea-level pressure by the rerun simulation (with modified PV distribution initially) is shown by the solid contours, every 5 hpa. anomaly. A cross-section through the PL and the associated front revealed very high low-level PV values in the region of ascent, reaching 9 PVU in the operational run; although values were substantially lower in the control run obtained through PV inversion with 5 km horizontal resolution and 1 pressure levels. In the operational run there were high values of PV in the descending dry air at the PL centre as well. A back-trajectory revealed that flow with low values of PV was descending along its track towards the PL. However, the trajectory showed that on entering the PL circulation ascent took place, before the air parcels finally descended again in the PLs warm core. The air parcels appeared to retain their acquired PV during descent. Although the LPV was a smaller scale feature of the flow, the effect on the dynamics of the PL development was large, intensifying the low-level wind field and enhancing the cold advection to the south of the PL (Figure 8). The low-level warm anomaly occurred early in the period, before the cyclogenesis started, being located at the east coast of Greenland (not shown) and shifting eastwards, most likely due to the stronger advection of cold air into the region west of the incipient PL. Although the influence from the warm Figure 14. Potential vorticity (PV) difference at 95 K (approximately 4 hpa over northern Greenland) between the control and rerun numerical analyses showing the initial PV perturbation indicated by the.5 PVU contour in bold. The dashed contours, ever 5 hpa, represent the synoptic surface analysis of mean sea-level pressure; fields valid at UTC 19 November 8. As in, but for +4 h, valid at UTC November 8. The L indicates the location of the incipient polar low. anomaly became rather small in terms of its contribution to the central pressure of the polar low (Figure 7(c)), it was related to a very sharp low-level front. This front was as an integral part of the PL, important for modulating the ascending and descending flow and hence the production and distribution of low-level PV. The cold temperature anomaly had a dampening effect on the PL (see Table I and Figure 7(c)). The cold anomaly gradually became difficult to define, but the cold air mass was a crucial component of the cyclogenesis as it was advected east and northward, wrapping around the cyclone to produce a warm core and intensifying the front. The cross-section (Figure 9) reveals features of such a seclusion process, i.e. the pronounced warm core. Eventually the warm core was destroyed by the ambient strong cold advection. In order to gain understanding of the importance of the UPV anomaly we modified the upper level PV anomaly (UPV). The PV modification was performed at UTC 19 November based on back-trajectories from 1 UTC November, in order to observe the relative importance of the various PV anomalies identified at UTC November. By running back-trajectories along potential temperature surfaces, starting at the centre of the UPV anomaly close to the PL at its peak intensity, we could identify a region at upper levels over northern Greenland where modification of PV was expected to have an impact on the PL development. Upper level PV was reduced by 1.5 PVU in that region for every 1 hpa level between 6 and Copyright c 11 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: (11)

13 18 T. E. Nordeng and B. Røsting Figure 15. The difference between the geopotential heights at 85 hpa between the control and the operational numerical analysis. Contour interval every 1 m valid at UTC 19 November 8. As in, but for +4 h, valid at UTC November 8. 3 hpa (Figure 1), hence an analysis error was deliberately introduced. Inversion of PV was then performed, yielding fields of Z and horizontal wind components u, v. Relative humidity (RH) fields were retrieved from the operational HIRLAM model. This procedure yielded fields (Z, u, v, RH) that are required for a numerical analysis, which in this study is referred to as the rerun analysis. In addition to the rerun analysis, a similar procedure based on the unmodified PV field produced another analysis, referred to as the control run. The control run is produced for a proper assessment of the effects from the UPV anomaly (i.e. to isolate the impact of the UPV perturbation from perturbations introduced by numerical formulation and interpolation from coarser to larger resolution). In the rerun simulation the PL was weaker than in the control run and made landfall earlier than in control. The control simulation produced a simulation that was almost as good as the operational run regarding central surface pressure and location at the time of peak intensity, i.e. 1 UTC November. Since the control analysis is obtained through inversion of PV fields calculated for a coarser resolution than the original numerical analysis (a possible added detrimental effect being the lack of divergent winds), the result is encouraging. The control run captures central pressure of the PL at 1 UTC November quite well and the position error is not much larger than observed in the operational simulation (Figure 13). Figure 14 shows that the perturbation over northern Greenland has a strong influence on the PL development and we may for that reason identify the conditions of that region as being important. The structure and growth of the PV perturbation shown in Figure 14 resemble those of optimal perturbations (e.g. growing singular vectors) and suggest a dualism between singular vector dynamics and the development of PV anomalies (e.g. Morgan, ). However, the amplification of the PV disturbance in this case is smaller than that observed for the leading singular vectors. It is noteworthy that at the time when the strong development started (at about UTC November) the PL in the control and rerun simulations was located somewhat too far to the east, closer to the first PL off the coast. The difference between the control and operational analyses produced a perturbation field that was particularly pronounced over Greenland at lower levels as well as in the upper troposphere and stratosphere. This perturbation field was much larger than the perturbation obtained from the difference between control and rerun analyses. Inspection of the development of this perturbation field (in 85 hpa geopotential heights) revealed a dipole configuration of the 85 hpa geopotential height perturbation at +4 h, at the time when the PL started to intensify. The perturbation indicated a filling in the western part and intensification in the eastern part of the surface trough oriented along 7 N (e.g. Figures 1 and 6), i.e. moving the PL to the east. A tentative conclusion is that the position error of the incipient PL is due to the adjustment of the control analysis to Greenland s topography. Possible future studies of this case and other PL cases may involve identification of sensitive regions in the atmosphere. Such a study will involve targeted singular vectors (e.g. Buizza and Montani, 1999; Montani et al., 1999) and/or other methods, e.g. the ensemble transform filter (ETKF; Bishop et al.1, Majumdar et al., Petersen et al.7), designed to reduce the forecast uncertainty in a specific region. An interesting study is to what extent Greenland s topography may influence PL propagation paths and developments over the Norwegian Sea. Such a study may technically be performed by removing Greenland s topography in the model formulation (Kristjansson and McInnes, 1999). 6. Conclusions This work has dealt with the development of the Vera PL that affected central Norway November 8. It has been demonstrated that consideration of PV is highly useful in understanding the dynamics of the PL development. As expected, the effect from the release of latent heat from condensation was important as low-level PV was produced. The role of the diabatic heating in delaying the upper level PV anomaly in catching up with the low-level disturbance is implied by the strong and persistent contribution of the upper level PV anomaly to the deepening of the PL. In fact the upper level PV anomaly remained the most important contributor to the central surface pressure of the cyclone throughout the development. This study has also shown that PV inversion was successful as a tool in PL research, in spite of the possible presence of regions with negative PV. The sensitivity study based on initially perturbing the PV field confirmed the importance Copyright c 11 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: (11)