idealised baroclinic channel simulations - Wiley Online Library

Quarterly Journal of the Royal Meteorological Society

Q. J. R. Meteorol. Soc. 138: 1297–1307, July 2012 A

Impact of different initial conditions on the growth of polar lows: idealised baroclinic channel simulations Muralidhar Adakudlu Uni Computing, Bergen, Norway Bjerknes Centre for Climate Research and Geophysical Institute, University of Bergen, Norway *Correspondence to: M. Adakudlu, Geophysical Institute, All´egaten-70, N-5007 Bergen, Norway. E-mail: [email protected]

The development of a polar low is simulated in an ideal baroclinic channel with the objective of studying the relative influence of different initial conditions on certain characteristics of the polar low. The basic state in the channel has a baroclinic jet at the tropopause level superposed by potential vorticity anomalies. The upperlevel perturbation leads to the genesis of a polar low through baroclinic instability. During its growth, the polar low is driven by a combination of baroclinic and convective processes as the vertical motion associated with the polar low is found to be forced simultaneously by the adiabatic and diabatic omega-forcing terms in the quasi-geostrophic omega equation. The degree of baroclinicity, surface heating and the scale of the upper-level anomaly were each reduced, and static stability increased separately in a series of sensitivity experiments. The results show that the pattern of the vertical motion, the growth rate and phase speed of the polar low are highly sensitive to the modifications in the background conditions. In particular, the surface temperature and baroclinicity appear to be crucial in determining the strength of the vertical motion associated with the polar low. The scale and structure of the polar low are more vulnerable to the scale of the upper-level anomaly and initial baroclinicity than to the rest of the parameters tested. In all the sensitivity experiments, the formation of the polar low gets delayed and its intensity, in terms of the surface pressure, reduced due to the modified initial conditions. The reduced intensity suppresses the tendency for a vertical coupling of upper- and lower-level c 2011 Royal Meteorological Society features of the polar low. Copyright Key Words:

baroclinic instability; omega equation

Received 4 April 2011; Revised 22 October 2011; Accepted 22 November 2011; Published online in Wiley Online Library 20 December 2011 Citation: Adakudlu M. 2012. Impact of different initial conditions on the growth of polar lows: idealised baroclinic channel simulations. Q. J. R. Meteorol. Soc. 138: 1297–1307. DOI:10.1002/qj.1867

Arctic PLs is the strong air–sea interaction triggered during the outbreak of a cold air mass from the Arctic ice-cap Polar lows (PLs) occur as a wide range of small-scale, over relatively warm ocean basins. PLs owe their mesoscale intense cyclonic systems that develop at high latitudes in nature to the shallowness of the cold air masses (∼ 1–2 km in both hemispheres mainly during winter. The major part of depth) advecting from the ice cover (Mansfield, 1974; WiinPL research has focused on the systems that develop in the Nielsen, 1989). Due to the lack of sufficient observational Northern Hemisphere due to a better observational coverage data, and the small temporal and spatial scale of PLs, accurate here than in the polar regions of the Southern Hemisphere forecasting of these storms has been a major challenge. As revealed by the imagery provided by polar-orbiting (Rasmussen and Turner, 2003, provide a comprehensive overview of PLs). A major cause for the development of weather satellites, PLs mainly occur either in the form of 1. Introduction

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comma-shaped clouds or spiraliform clouds (Rasmussen and Turner, 2003). While the theory of baroclinic instability has effectively explained the structure and energetics of comma-shaped PLs (Harrold and Browning, 1969; Mansfield, 1974; Duncan, 1977, 1978; Reed and Duncan, 1987), the theory of CISK (conditional instability of the second kind) was used by Økland (1977) and Rasmussen (1979) to account for the deep and organised convection associated with spiraliform PLs. The energy required for the growth of an instability was assumed to be supplied by a reservoir of convective available potential energy (CAPE; Charney and Eliassen, 1964; Ooyama, 1967). Emanuel and Rotunno (1989) argued that no such reservoir is present and the polar (and tropical) atmosphere is neutral to moist convection and challenged the application of CISK to the development of PLs (and tropical hurricanes). Emanuel and Rotunno attributed the deep cumulus convection in spiral clouds to air–sea interaction instability (ASII, later termed as WISHE or wind-induced surface heat exchange). In support of the view of WISHE being the main dynamical mechanism for spiraliform PLs, Craig and Gray (1996) showed that the process of WISHE predicts the observed dependency of PL intensification on surface properties whereas CISK does not. It has now been widely accepted that PLs may either develop as pure baroclinic systems or pure convective systems or a combination of both (Rasmussen and Turner, 2003). Several sensitivity experiments have been carried out in the past (e.g. Sardie and Warner, 1983, 1985; Roch et al., 1991; Albright et al., 1995; Pagowski and Moore, 2001) to understand the influence of different physical factors on PLs. These case-studies revealed the importance of an ice-free surface, heat and moisture fluxes from the surface, and condensational heating for the development of PLs. For example, Albright et al. (1995) performed certain experiments on a PL that formed over Hudson Bay during 8–9 December 1988. In one of the experiments, the sea surface temperature (SST) was raised by 8 K which led to a significant strengthening of the PL with the associated wind speed exceeding hurricane force. Recently, Adakudlu and Barstad (2011) showed an increase in the sea-level pressure anomaly by about –2 hPa K−1 for a PL subjected to SST variations. On the other hand, Linders et al. (2011) found a relatively weak response in sea-level pressure to SST variations of about –0.6 hPa K−1 . Apart from the differences in the model set-up, these widely varying results can be linked to the fact that several processes may operate simultaneously during the life cycle of a PL (Yanase and Niino, 2007). In the real atmosphere, the sensitivity of a PL to various conditions may vary from case to case depending on, for example, the dominating physical mechanism, geographical location, proximity of sea-ice, and so on. Sensitivity experiments in an idealised atmosphere have proven useful in studying the relative importance of individual physical processes in the development of PLs. By using a conceptual model, Montgomery and Farrel (1992) demonstrated that mobile upper-level troughs are important for initiating a PL development, but for the growth and maintenance of a PL, condensational heating is necessary. Craig (1995) found that radiative cooling is likely to increase the growth rate and maximum intensity of a convective PL. Using a three-dimensional non-hydrostatic model, Yanase and Niino (2007) investigated the way baroclinic and convective processes influence the development and energetics of PLs. The basic state for the study was c 2011 Royal Meteorological Society Copyright

characterised by an axisymmetric vortex at the surface with a finite radius and a uniform vertical shear of the zonal wind. The experiments of Yanase and Niino revealed that the structure of the PL was highly sensitive to the degree of baroclinicity present in the troposphere. An inclusion of condensational heating and surface fluxes resulted in an enhancement of the growth rate of the PL. The work effectively demonstrated the impacts of different physical conditions on the growth rate, energetics and structure of PLs. However, the study does not account for the influence of upper-level forcing on the characteristics of PLs. Many studies have highlighted the importance of upperlevel forcing on the formation and growth of PLs (e.g. Reed, 1979; Mullen, 1979, 1983; Rasmussen, 1985; Businger, 1985; Shapiro et al., 1987; Nordeng, 1990). After Hoskins et al. (1985) elaborated the application of isentropic potential vorticity (PV) in the diagnosis of the upper-level forcing in the development of extratropical cyclones, the approach has been used in analysing PL dynamics (e.g. Montgomery and Farrel, 1992; Sunde et al., 1994; Grøn˚as and Kvamstø, 1995; Moore and Vachon, 2002; Røsting et al., 2003; Røsting and Kristjansson, 2006, Bracegirdle and Gray, 2009; Wu et al., 2011). Montgomery and Farrel (1992) proposed a two-stage development process for PLs in their idealised numerical study. While the upper-level PV anomalies dominated the first stage of the development, lower-level PV anomalies created by diabatic heating were important in the second stage. The relative influence of upper- and lower-level PV anomalies was studied by Bracegirdle and Gray (2009) using a piecewise PV approach. This study showed a three-stage development mechanism for PLs wherein the first two stages were similar to those illustrated by previous works (e.g. Montgomery and Farrel, 1992). The third stage was dominated by the WISHE mechanism. Wu et al. (2011) diagnosed a PL formed over the Sea of Japan using the piecewise PV approach. In contrast to the earlier studies, the work of Wu et al. (2011) revealed that the whole life-cycle of the PL was dominated primarily by an upper-level PV anomaly with the lower-level PV anomaly playing a supplementary role. Given the significant impacts of an upper-level PV anomaly on the life cycle of PLs, it becomes important to understand how the features such as the structure and intensity of a PL respond to the changes in the structure of an upper-level PV anomaly. This may have direct implications for the issue of PL forecasting in the sense that it might be possible to qualitatively predict the features of a PL if the distribution of upper-level potential vorticity is known. Moreover, many PLs are characterised by a downward penetration of the upper-level perturbation causing a coupling between upper- and lower-level features, leading to cyclone intensification (Rasmussen and Turner, 2003). The coupling process mainly depends on the magnitude of static stability, baroclinicity and surface heating. The relative influence of these physical parameters on the growth rate and phase speed of a PL, and the strength and evolution of vertical motion associated with a PL is not well understood. This article addresses the issue of the formation and growth of PLs forced by a finite-amplitude perturbation at upper levels in an ideal baroclinic channel. Only the forward-shear PL developments will be considered here. The purpose of the study is two-fold. First, to analyse the influence of the structure of the upper-level PV anomaly on the characteristics of a PL. Second, to understand the Q. J. R. Meteorol. Soc. 138: 1297–1307 (2012)

Impact of Initial Conditions on Polar Low Growth

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y (km)

The basic state deployed for the simulations is taken from Wernli et al. (1999). The original state in Wernli’s case was C of a horizontal resolution ∼ 75 km. In the present study, the resolution has been increased to 10 km in order to make the 3000 set-up suitable for addressing the development of PLs. The channel has a two-dimensional baroclinic jet-like feature 264 superposed by a finite-amplitude initial perturbation at the 6300 tropopause level. The tropopause is situated at a level of 6325 ∼ 6.5 km (∼ 380 hPa) above the surface which is normally 2500 the case during PL developments in the real atmosphere. 6375 Figure 1 portrays a horizontal cross-section of the baroclinic jet at the tropopause level superimposed by a positive potential vorticity anomaly of ∼ 2 PVU. The meridional 276 2000 temperature gradient (as potential temperature contours) at the surface is also shown. W The upper-level perturbation is specified as a positive anomaly in the quasi-geostrophic potential vorticity (PV) field. The anomaly is in Cartesian space (x, y, z) and is 3000 3500 4000 x (km) determined by applying a PV inversion tool of Fehlmann Figure 1. A horizontal section of the basic state showing the potential (1997). The upper-level PV anomaly is prescribed as vorticity perturbation at the tropopause level (∼ 6.5 km). Bold contours indicate potential vorticity, with a central contour of 2 PVU, encircled by the 1 PVU contour; closed contours to left and right have a magnitude of x 2 x +d 2 –0.5 PVU (1 PVU = 10−6 m s−1 K kg−1 ). Thin black lines denote isentropes q (x, y, z) = Ac exp − +Al exp − at the surface (6 K intervals) with warm to the south and cold to the north. Lx Lx Grey contours represent the geopotential height at the tropopause level 2 (25 m intervals). The axes show distances in kilometres. x −d +Ar exp − Lx relative influence of three key factors that play decisive y 2 z−z0 2 roles in the growth of a PL, namely static stability, × exp − exp − , (1) Ly Lz baroclinicity and surface heating. The existing literature dealing with the evolution of baroclinic disturbances in an ideal atmosphere (e.g. Farrel, 1982, 1985; Rotunno et al., where Ac , Al and Ar represent the magnitudes of the centre, 1994; Wernli et al., 1999) focused largely on synoptic-scale left and right anomalies with values 2, –1 and –1 PVU systems. The experiments described in this article were respectively. The centre anomaly is positioned at (0, 0, z0 ) carried out at a model resolution of 10 km so that the and the left and the right anomalies are shifted in the zonal processes important for mesoscale disturbances could be direction on either side of the central anomaly by a distance simulated realistically. d (km). In this article, d equals 400 km in all the experiments, The model configuration and set-up of the basic state, z0 is the height of the tropopause, and Lx and Ly are the including the details of the sensitivity experiments, are horizontal scales of the anomaly in the zonal and meridional described in the next section. The results are discussed direction respectively. Lz denotes the vertical decay scale of in section 3 followed by the summary and conclusions in the anomaly which equals ∼ 8 km in all the experiments. section 4. Table I lists the sensitivity experiments with different initial conditions. The control simulation is denoted as 2. Experimental set-up CTL, and experiments PV1 and PV2 denote the sensitivity experiments with a modified horizontal scale of the upperThe Weather Research and Forecasting model (Ska- level PV anomaly. The rest of the experiments focus on the marock et al., 2008) is used for the simulations in an idealised relative influence of static stability N (N1), baroclinicity B baroclinic channel. The horizontal grid length is 10 km and (B1), and surface potential temperature θs (θ 1) of the basic the model has 36 vertical levels ranging from 1000 hPa up to state on the formation and growth of a PL. Magnitudes of ∼ 80 hPa. Periodic boundary conditions have been applied N, B and θs prescribed for the CTL simulation are such that at the zonal boundaries whereas the meridional boundaries the conditions in the baroclinic channel are favourable for are symmetric. The simulation domain covers an area of the formation of a PL (Sardie and Warner, 1983; Yanase and Niino, 2007). The reduction in the baroclinicity was ∼ 6000×5000 km. Computation of surface fluxes of heat, moisture and achieved in the B1 simulation by weakening the vertical wind momentum are based on Monin–Obukhov similarity theory shear. The magnitudes of the centre, left and right anomalies using the stability functions from Paulson (1970), Dyer remain the same in all the experiments. The simulations were and Hicks (1970) and Webb (1970). Vertical transport stopped when the PL attained the maximum intensity (in and mixing in the boundary layer are accounted for terms of the surface pressure anomaly and the near-surface by using the YSU-PBL scheme (Hong and Lim, 2006). wind speed), and appeared to be steady at this stage. In order Subgrid-scale convective processes and cloud formation are to see if the PL remained steady in the channel for a long parametrised using the Kain–Fritsch scheme (Kain, 2004) duration, the CTL simulation was extended further and the and microphysical cloud properties are determined through PL was found to start to dissipate gradually after attaining the WSM-6-class scheme (Hong et al., 2004; Dudhia et al., its peak intensity. It is assumed here that the sensitivity 2008). simulations would also show the same behaviour. c 2011 Royal Meteorological Society Copyright

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Table I. List of the sensitivity experiments. Experiment CTL PV1 PV2 N1 θ1 B1

Lx (km)

Ly (km)

N (10−2 s−1 )

B (10−3 s−1 )

θs (K)

800 800 200 800 800 800

700 250 700 700 700 700

0.9 0.9 0.9 1.0 0.9 0.9

∼5 ∼5 ∼5 ∼5 ∼5 ∼ 2.5

270 270 270 270 260 270

Definitions of symbols are given in the text.

Figure 2. 120 h forecast from the CTL simulation. Black contours represent surface pressure anomaly (4 hPa intervals) and grey contours the 500 hPa geopotential height (50 m intervals). Potential vorticity on the 290 K isentropic level is shaded. The centre of the polar low is marked as ‘L’. Vectors represent the 10 m winds.

Within the framework of the experimental set-up described above, this article uses a slightly modified version of the definition of PLs given in Rasmussen and Turner (2003) to identify PLs in the channel. The definition is: ‘A polar low is a small, but fairly intense maritime cyclone that forms in the vicinity of a deep baroclinic zone. The horizontal scale of the polar low is approximately between 200 and 1000 km and surface winds near or above gale force.’ 3. 3.1.

Results The control simulation

The evolution of the flow in the baroclinic channel for the CTL case was similar to the developments explained in Wernli et al. (1999) i.e. a number of cyclones, both up- and down-stream, developed in the channel. The only difference between the cyclones in this study and that by Wernli et al. (1999) is the scale of the cyclones. In the latter case, the scale of the cyclones ranged between 3000 and 4000 km horizontally and up to 8 km vertically. In this study, the cyclones hardly exceeded 1000 km horizontally and 5 km vertically as a result of the finer resolution prescribed in the baroclinic channel. Due to the mesoscale and shallow features of these cyclones, it is reasonable to term them as PLs. A discussion on the up- and down-stream developments is skipped in this article since they are similar to the developments shown by Wernli et al. (1999). Rather, the focus is shifted towards understanding the relative influence of different parameters on the growth of a PL. The PL considered for the study is shown in Figure 2. The reason for considering this PL is that, at a reference time (120 h), it appeared to be the strongest (in terms of surface pressure anomaly and near-surface wind speed as indicated by Figure 2) of all the PLs developed in the channel. Note that this PL and the other PLs have a corresponding positive c 2011 Royal Meteorological Society Copyright

PV anomaly at upper levels, implying an upper-level forcing for the growth of individual PLs. The PL development began in the channel at 78 h (not shown). The PL reached its peak intensity by 120 h, with the associated surface pressure anomaly reaching ∼ −24 hPa and the near-surface winds exceeding 27 m s−1 (Figure 2(b)). During the initial stages of the development, the upper-level flow was characterised by a wave with its trough positioned over the western flank of the PL, implying a westward tilt of the PL axis in the vertical (not shown). As the PL intensified, the horizontal distance of separation between the 500 hPa trough and the surface vortex reduced. At 120 h, no vertical tilt of the PL axis can be seen as the 500 hPa trough is positioned exactly above the surface low (Figure 2(b)). As the PL grew, the upper-level PV anomaly associated with the PL amplified to ∼ 3 PVU from its initial value of 2 PVU. The positive PV anomaly, which was present only at the upper levels initially, extended towards lower levels during the growth of the PL and became coupled with the lowerlevel features. The vertical coupling is depicted in Figure 3 which shows a vertical cross-section of the PL in its mature stage. The vertical cross-section runs through the PL from the west to the east covering the region of cold air advection on the western flank, the centre of the PL in the middle, and the region of warm air advection on the eastern flank. Apart from the vertical PV coupling, the figure also shows the pattern of vertical motion associated with the PL. Strong ascent can be seen on the eastern flank of the PL. The descent on the western flank is weaker. The vertical motion (ω) associated with a weather disturbance is a crucial dynamical and diagnostic field. In practice, ω is estimated through the quasi-geostrophic omega equation (Nordeng, 1990) which is given by f ∂v f 2 ∂2 ∇2 + ω = (2) · ∇(f + ζ ) −∇ 2 H, σ ∂p2 σ ∂p Q. J. R. Meteorol. Soc. 138: 1297–1307 (2012)


Figure 3. A west–east vertical cross-section of the polar low in the CTL case at 120 h, showing isentropes (solid black contours, 1 K intervals), circulation vectors (black arrows), and potential vorticity (shading).

where H represents the contribution to ω from diabatic effects, σ denotes the static stability parameter and ζ the relative vorticity. ∂v/∂p signifies the thermal wind, and f is the Coriolis parameter. The terms on the right-hand side respectively represent the ω forcing due to the advection of relative vorticity with the thermal wind (adiabatic forcing), and that due to diabatic effects. The advantage of assessing ω from the above relation is that it allows us to determine the relative role of the diabatic and adiabatic processes during the growth of a weather disturbance. Such an analysis is especially important as far as PLs are concerned since the structure and dynamics of PLs might differ depending on which process dominates during the growth. In one such study, Nordeng (1990) utilised the above relation to diagnose two PLs with similar initial developments but different characteristics during the mature phase. He noticed that, in one of the two developments, ω was forced by the advection of relative vorticity only, but in the second case diabatic processes also played a significant role that led to a prolonged phase of the PL. In this article, the sensitivity of the pattern of ω and ω forcings on various initial conditions prescribed in the baroclinic channel will be discussed. Further, the impacts of different initial conditions on the growth rate and phase speed of the PL will also be discussed. In the section below, we shall see how the structure of the PL varies when the initial conditions in the baroclinic channel are modified. The PL in different experiments will be referred to as PLCTL for the PL in the CTL simulation, PLPV1 for that in the PV1 simulation, and so on.

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due to the modified initial conditions. In particular, the impacts of the modifications in the structure of upperlevel PV anomaly (PV1 and PV2 simulations) and in the initial baroclinicity (B1 simulation) are substantial. Firstly, the horizontal scale of the PL in these three runs is in the range 500–600 km whereas the scale of PLCTL is of the order 1000 km. Secondly, PLPV1 , PLPV2 , and PLB1 appear to be shallower than PLCTL as the 500 hPa flow has a weak trough in the latter cases while for PLCTL , the 500 hPa flow is characterised by a vortex. PLN1 and PLθ1 are also shallower than PLCTL but slightly deeper than PLPV1 , PLPV2 , and PLB1 . Thirdly, the surface pressure anomalies corresponding to PLPV1 , PLPV2 , and PLB1 are less than −10 hPa when the corresponding PL was most intense. On the other hand, the surface pressure anomaly for PLCTL , when it was at its peak intensity, was ∼ −24 hPa, as evident from Figure 2(b). Concerning the N1 and the θ 1 simulations, the respective PLs are not very different from PLCTL regarding the scale and the shape of the PL. The only notable feature is the weakening of PLN1 and PLθ1 with respect to PLCTL , as the surface pressure anomaly corresponding to PLN1 and PLθ1 are of the order ∼ −20 hPa. Figure 5 shows the west–east vertical cross-sections of the PLs in each of the sensitivity experiments (Figure 3 shows the vertical cross-section of PLCTL ). The forecast times of individual cross-sections are displayed on top of the corresponding cross-section plot. Features such as the vertical PV coupling, strength of the ascent on the eastern flank of the PL and the strength of baroclinicity associated with the PL appear to have undergone drastic changes in the sensitivity runs. There are no indications of a vertical PV coupling in the PV1, PV2, and B1 simulations. Most likely, this is the reason for the intensity of PLPV1 , PLPV2 and PLB1 being very low (as indicated by Figure 4). A tendency for a vertical PV coupling is discernible in the cross-section of PLN1 and PLθ1 . However, no coupling is achieved in these cases, even when the PL attains its peak intensity; this is in contrast to the CTL simulation where the coupling took place when PLCTL attained peak intensity. The suppression of the vertical PV coupling in the N1 simulation can be attributed to the high static stability in the basic state of the channel. As indicated by Eq. (3) for the Rossby penetration depth, D, of an upper-level anomaly (Rasmussen and Turner, 2003, p 367, give the derivation), high static stability does not favour a deep penetration of an upper-level anomaly. Similarly, the suppression of the vertical coupling in the θ 1 simulation can also be linked to high static stability resulting from the surface cooling in that simulation. D≈

f (f + ζ θ )L , N

(3)

where ζ θ is the isentropic relative vorticity, and L is the horizontal scale of the PV anomaly. The Rossby penetration depths for the upper-level PV anomaly in different simulations were estimated and they turn out to be Figure 4 shows the 500 hPa and the surface flow ∼ 1.6 km for PLCTL , ∼ 500 m for PLPV1 and PLPV2 , ∼ 1 km characteristics of the PL in the different sensitivity for PLN1 and PLB1 , and ∼ 800 m for PLθ1 . In addition to the vertical coupling, the strength of experiments. The time when the PL attains its maximum intensity differs from case to case and hence the individual the upward motion taking place on the eastern flank of plots in Figure 4 correspond to different forecast times. the PL has also been affected by the modifications in the The figure clearly shows that the PL undergoes changes in initial conditions. In all the sensitivity simulations, the its scale, structure and intensity in each of the sensitivity upward motion appears to be weaker than that in the simulation with respect to PLCTL (shown in Figure 2(b)) CTL simulation (Figure 3). This is an obvious outcome of 3.2. Sensitivity of the structure of the PL to different background conditions


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(a) PV1:120h

(b) PV2:120h

3000

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2500 W

2000

E

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E

1500 1500

2000

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0

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(d) θ1:144h

(c) N1:144h 2750 2250

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W

2000 2000

2500

3000

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3000

(e) B1:168h 3000 2500

E

W

2000 3500

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Y (km) X (km)

Figure 4. Horizontal structures of the polar lows in different sensitivity simulations, showing the surface pressure anomaly (black contours, 4 hPa intervals), and the geopotential height at 500 hPa (grey contours, 50 m intervals). (a) PV1 at 120 h, (b) PV2 at 120 h, (c) N1 at 144 h, (d) θ 1 at 144 h, and (e) B1 at 168 h. The vertical structures along the west–east lines are shown in Figure 5.

the weakening in the intensity of the PL in the sensitivity runs. Another notable feature in the vertical cross-sections shown in Figure 5 is the influence of various conditions on the low-level baroclinicity represented by the sloping isentropes on the western flank of the PL. The low-level temperature contrast created across the PL by the cold air advection on the western flank and warm air advection on the eastern flank of the PL (not shown) caused the isentropes to slope towards the surface on the western flank. In real cases of PL developments, this situation is analogous to Arctic fronts that often form in association with PLs (Shapiro et al., 1987). From Figure 5, it seems that the low-level baroclinicities in the N1 and θ 1 simulations are comparable with the CTL simulation (Figure 3). In the rest of the cases, particularly PV1 and B1, the low-level baroclinicity associated with the PL was very weak. In the B1 simulation, the initial baroclinicity was only half the magnitude of that in the CTL simulation, whereas in the case of PV1 simulation, the meridional temperature gradient at the surface was reduced due to the contraction of the scale of the upper-level PV anomaly (not shown), which led to a weaker vertical wind shear to maintain the thermal wind balance (and in turn reduced the baroclinicity). Further, the comparison between the vertical cross-sections of PLB1 and PLCTL suggests that the impacts of baroclinicity are more pronounced for the lower-level features associated with the PL than for the upper-level features. c 2011 Royal Meteorological Society Copyright

3.3. Sensitivity of the pattern of vertical motion associated with the PL to different background conditions Figure 6 shows the growth curves for the surface pressure, ω, and the ω forcing during the growth of PLCTL , PLPV1 and PLPV2 . In this article, the magnitude of the condensational heating has been considered to be representative of the diabatic ω forcing. It is apparent that, in the CTL, PV1 and PV2 simulations, ω increases initially and starts to decrease gradually some hours after the PL formation. Both the adiabatic and the diabatic ω forcing terms contribute simultaneously to the total ω, implying that the PL in these simulations is driven by a combination of baroclinic and convective processes. The curves of the surface pressure anomaly in Figure 6 indicate that PLPV1 and PLPV2 are weaker than PLCTL . The pattern of ω is similar in all the simulations, though its strength is slightly less in the PV2 simulation and is least in the PV1 simulation in comparison with the CTL simulation. The weak low-level baroclinicity associated with PLPV1 , as shown by Figure 5(a), is most likely the reason behind the remarkable weakening of ω in the PV1 simulation. As far as the PV2 simulation is concerned, it is interesting to see that magnitudes of ω and ω forcings tend to exceed that of the CTL simulation. The vertical motion in a cyclonic system tends to be stronger when there is a westward vertical tilt of the cyclone axis (Holton, 2004). Figure 4 shows the 500 hPa and the Q. J. R. Meteorol. Soc. 138: 1297–1307 (2012)


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Figure 5. West–east vertical cross-sections of the polar lows corresponding to the panels in Figure 4. The variables shown are as in Figure 3.

surface flow characteristics of the PL in different sensitivity simulations when the maximum intensity was attained; a vertical westward tilt of the PL axis exists only for the PV2 case. For the CTL (Figure 2(b)), PV1 and the remaining cases, the 500 hPa trough was positioned exactly above the PL. This explains why ω associated with PLPV2 was the strongest when the PL was at its maximum intensity. The evolution of surface pressure anomaly, ω, and the ω forcings during the growth of PLN1 , PLθ1 , and PLB1 is shown in Figure 7 along with the same details for PLCTL . Figure 7 indicates that the formation of PLN1 , PLθ1 , and PLB1 is delayed compared to PLCTL . The pattern of the evolution of vertical motion is similar in all the cases, with strong ω initially and a relatively weaker ω later. The period during which ω is stronger in individual cases corresponds c 2011 Royal Meteorological Society Copyright

to the period when the respective PL was characterised by a vertical westward tilt (not shown). As soon as the vertical tilt disappears, the strength of ω starts to decrease. As reflected by Figure 7, the duration over which ω is strongest, and the time when it starts to decrease, occur at different stages in different experiments. Interestingly, in θ 1 and B1 simulations, ω is forced only by the adiabatic term which means that PLθ1 and PLB1 are driven mostly by baroclinic instability. The absence of the diabatic ω forcing in the θ 1 simulation can be directly linked to the surface cooling, whereas that in the B1 simulation is perhaps an outcome of the weakening in the strength of the boundary-layer convergence associated with PLB1 (not shown). As shown by Carlson (1991, p 217), the convergence in the boundary layer is one of the major sources for Q. J. R. Meteorol. Soc. 138: 1297–1307 (2012)

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−30

(b) −30 CTL PV1 PV2

−25

−25 Omega (Pas−1)

Surface pressure anomaly (hPa)

(a)

−20 −15 −10 −5

−20 −15 −10 CTL PV1 PV2

−5

0 70

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0 70

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Forecast time (h) x 10−6

(d) Diabatic forcing (Ks−2)

Adiabatic forcing (s−2)

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120

Forecast time (h)

1.5

x 10−6

1

0.5 CTL PV1 PV2 0 70

80

90

100

Forecast time (h)

Figure 6. The evolution of (a) surface pressure anomaly, (b) ω, (c) adiabatic forcing, and (d) diabatic forcing for CTL, PV1 and PV2 simulations. In (a), the values denote the central pressure anomaly. The values in (b)–(d) are taken from the eastern flank of the polar low, where they tend to be a maximum.

the condensational heating in the clouds accompanying a cyclone. The N1 case is similar to the CTL case regarding the driving mechanism of the PL, i.e. both adiabatic and diabatic processes contribute to the total ω. The strength of ω and ω forcings associated with PLN1 is between that of PLCTL and the remaining two cases (i.e. PLθ1 and PLB1 ). 3.4. Effects of the background conditions on the growth rate and phase speed of the PL From the evolution curves for the surface pressure perturbation associated with the PL in different simulations shown in Figures 6 and 7, it is apparent that the growth of the PL in each of the sensitivity cases differed from that in the CTL simulation. It thus becomes important to estimate the growth rate and phase speed of the PL in each of the cases to get a clear picture of the influence of the modified initial conditions on these features. Figure 8 displays the estimated values of the growth rate and phase speed of the PL in the different experiments. The growth rates were computed by noting the rate of change of the surface pressure anomaly with time for the period starting from the formation of the PL to up to the time when the maximum intensity was reached. While estimating the phase speed, the total distance covered by the PL for the same duration was considered. In general, growth rate and phase speeds are determined as the eigenvalues of different normal modes present and hence are functions of the wavelength corresponding to the individual modes. For a PL with a wavelength in the range 800–1000 km (like the PL in the CTL simulation), the growth rate and phase speed are of the order ∼ 10−5 s−1 and ∼ 10 m s−1 (Mansfield, 1974). The values for the CTL simulation shown c 2011 Royal Meteorological Society Copyright

in the figure suggest that the estimated values of the growth rate and phase speed in the present work are slightly higher, but still comparable with the theoretical values. It is clear from Figure 8 that the growth rate and phase speed of the PL in different sensitivity simulations are weaker, by a factor of two or more, than that in the CTL simulation. Further, a comparison between the sensitivity simulations shows that the relative influence of different factors on the growth rate and phase speed of the PL are different. It is known that the growth rate of an unstable baroclinic wave is directly proportional to (f /N)(∂θ/∂y) (Rasmussen and Turner, 2003). The variations in the growth rate of the PL in the sensitivity simulations can be explained on the basis of this relation. Firstly, for PLN1 and PLB1 , the reduction in the growth rates is obvious since the corresponding simulations were initialised respectively with a higher static stability, N, and a lower baroclinicity, ∂θ/∂y. For PLθ1 , the reduction in the growth rate can be attributed to the surface cooling since such a perturbation will in turn raise the static stability. It has been mentioned earlier that the south–north contraction of the scale of the upper-level PV anomaly in the PV1 simulation had caused a weakening in the meridional temperature gradient at the surface, leading to a reduction in the baroclinicity. Thus the weakening of the growth rate of PLPV1 must be an outcome of the low baroclinicity. In the case of PLPV2 , the weakening in the growth rate is most likely due to its smaller scale than PLCTL (Figures 4(b) and 2(b)) since the growth rate of a growing wave is proportional to its wavelength. However, the exact nature of the relation between the wavelength and the growth rate of a wave depends on several factors, such as surface friction, surface wind speed, eddy diffusivity coefficients and Q. J. R. Meteorol. Soc. 138: 1297–1307 (2012)


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Figure 8. (a) The growth rate and (b) the phase speed of the polar low in the different experiments.

other factors related to the boundary layer (Mansfield, 1974; Rasmussen, 1979). The smaller scales of PLPV1 and PLB1 (Figures 4(a) and 4(e)) must also have affected their growth rates in addition to the low baroclinicity in the respective simulations. The changes in the magnitude of the phase speed of the PL in the sensitivity simulations can be explained on the basis of c 2011 Royal Meteorological Society Copyright

the two-layer baroclinic model of Holton (2004). According to this model, a wave will amplify when its phase speed has an imaginary part. The expression for the phase speed of a growing wave, as given by Eq. 8.21 in Holton (2004), involves mainly the variation of the Coriolis parameter with latitude (the β effect), the magnitude of the thermal wind and the scale of the growing wave. Since the β effect has been Q. J. R. Meteorol. Soc. 138: 1297–1307 (2012)

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M. Adakudlu

This study has focused only on PLs developing under the ignored in the simulations here, the phase speed c of the PL would become a function of the remaining two factors only, forward-shear conditions, i.e. when the thermal wind and the mean wind are along the same direction. The opposite as given by situation, wherein the thermal wind and the mean wind 2 blow in opposite directions, called a ‘reversed-shear flow’ is 2 1/2 k − 2λ commonly seen in the Arctic area during the advection of , (4) c ∝ UT 2 k + 2λ2 cold air from the ice cap over relatively warm Nordic seas (Duncan, 1978). Development of PLs under such conditions where UT is the magnitude of the thermal wind, λ is the has been investigated in a number of articles (e.g. Duncan, wavelength of the growing wave and k is its wavenumber. 1978; Haugen, 1986; Reed and Duncan, 1987). It would be While the phase speed is directly proportional to the interesting to see how applicable the results shown in this magnitude of the thermal wind, and hence to baroclinicity, article are to the reverse-shear PLs. its dependency on the scale of the wave appears to be quite The PL in the control simulation lives for at least two complicated. Consequently, the reduction in phase speed of days once the development begins in the channel before the PLPV1 and PLB1 with respect to PLCTL must be the outcome dissipation sets in. In reality, the life cycle of PLs hardly of the low baroclinicity in the PV1 and B1 simulations. exceeds a day, though there have been a few instances where As the static stability tends to suppress vertical motion PLs lived for about three days (e.g. Claud et al., 2004). The associated with a disturbance, thereby stabilising its growth, unusually long lifetime of the idealised PL is most likely due the relatively low value of the phase speed of PLN1 can be to two major constraints of the model set-up: the absence attributed to the high static stability in the N1 simulation. of the β effect and a homogeneous water surface. A more The same argument is valid for the θ 1 case as well, since the realistic set-up involving the β effect and the inclusion surface cooling results in an increase of static stability of the of ice cover would bring the results closer to the reality. atmosphere. Concerning the PV2 simulation, the reason for Additionally, the impacts of varied initial conditions on the a low phase speed is uncertain. However, it is possibly due surface fluxes associated with the PL remains to be seen. to the low intensity and the small scale of PLPV2 . The issue of the development of a PL in an ideal baroclinic channel has been approached as an initial value problem in 4. Summary and conclusions this study. A number of PLs, with different intensities and scales, grew in the channel. The PL considered for further The development of a polar low (PL) and its sensitivity analysis was the most intense at a reference time of 120 h. to different background conditions have been described Another way of dealing with such issues is by applying the in this paper. The experiments were carried out in an normal mode technique. In the normal mode approach, only ideal baroclinic channel which has a baroclinic jet at the fastest growing or the most unstable mode dominates the tropopause level superposed by a finite-amplitude the rest of the modes in the channel after some hours. As perturbation in the form of potential vorticity (PV) shown by Mansfield (1974) and Rasmussen (1979), the scale anomalies. A series of sensitivity experiments were carried of an unstable wave depends on the initial conditions. Given out wherein the scale of the upper-level PV anomaly, this fact, it might not be appropriate to consider a same magnitude of the baroclinicity and that of the surface wavelength for the analysis of the growth rate when the potential temperature were reduced, and that of the static initial conditions are changing, as is done in this article. stability was raised in the basic state of the channel. Each Nevertheless, taking into account the nonlinearity of the experiment has only one of the above variations with respect problem, the initial value approach used in this paper is to the control simulation. The results show that features superior to the normal mode technique which is a linearised such as the scale, structure and intensity of the PL are more approach. sensitive to the baroclinicity and the structure of upper-level PV anomaly than to the rest of the parameters. Due to the Acknowledgements reduction in the baroclinicity and the scale of the upper-level PV anomaly in the initial conditions, the scale of the PL and This is publication no. A 381 from the Bjerknes Centre the associated surface pressure anomaly get reduced roughly for Climate Research. The research was funded by the by a factor of two with respect to the control simulation. The Norwegian Research Council’s Arc-Change project which vertical PV coupling which occurs in the control simulation is a part of the International Polar Year (IPY) programme. does not take place in any of the sensitivity simulations, The author is indebted to Dr Heini Wernli for providing the though the suppression of the coupling is more prominent code which was implemented in WRF for the experiments. in the simulations with modifications to the baroclinicity Discussions with Dr Idar Barstad, Dr Haraldur Olafsson and and the scale of the upper-level PV anomaly. Dr Nils Gunnar Kvamstø are appreciated. The pattern of the vertical motion associated with the PL and the degree to which individual ω forcing terms References contribute to the total vertical motion is shown to be highly sensitive to the background conditions tested here, Adakudlu M, Barstad I. 2011. Impacts of the ice-cover and sea-surface temperature on a polar low over the Nordic seas: A numerical particularly to the baroclinicity and surface temperature. In case-study. Q. J. R. Meteorol. Soc. 137: 1716–1730. the low baroclinicity and low surface temperature cases, the Albright MD, Reed RJ, Ovens DW. 1995. Origin and structure of diabatic ω forcing has negligible values, implying that, when a numerically simulated polar low over Hudson Bay. Tellus 47A: 834–848. the rest of the conditions favour the development of a PL, it TJ, Gray SL. 2009. The dynamics of a polar low assessed using is more likely to manifest as a pure baroclinic system if the Bracegirdle potential vorticity inversion. Q. J. R. Meteorol. Soc. 135: 880–893. baroclinicity and/or the surface temperature are relatively Businger S. 1985. The synoptic climatology of polar-low outbreaks. low. Tellus 37A: 419–432. c 2011 Royal Meteorological Society Copyright

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