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Keywords:

  • roll convection;
  • cloud streets;
  • large eddy simulation

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Setup
  5. 3. Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[1] In this study we use large-eddy simulations (LES) to model roll convection within the convective atmospheric boundary-layer (CBL) during strong cold-air outbreaks (CAO). Previous LES were mostly unsuccessful in reproducing clear signals of roll convection, especially in case of strong surface heating and weak vertical wind shear in the CBL. In nature however, this phenomenon is very robust and roll convection can be observed as cloud streets in satellite pictures of almost any CAO. Previous LES studies assumed homogeneous sea-ice, unlike the current study, where under strong surface heating clear signals of rolls appear only when introducing sea-ice inhomogeneities in the marginal ice zone. For weaker surface heating, rolls also appear without sea-ice inhomogeneities. The results of this study suggest that in case of strong surface heating and weak vertical wind shear surface inhomogeneities increase the chance of roll formation.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Setup
  5. 3. Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[2] Roll convection is a common phenomenon in atmospheric CBLs with background wind. In case of cloudy CBLs the roll updrafts are apparent by cloud streets, as seen in numerous satellite pictures. Roll convection is observed both over land and over sea for different synoptic situations. As can be inferred from the review articles Etling and Brown [1993] and Young et al. [2002] there is still some debate about the different types of roll convection and their causes.

[3] The stability parameter ζ = −zi/L, with zi the boundary-layer height and L the Monin-Obukhov stability length, is widely used as a predictor for roll convection. In various observational studies dominant signals of roll convection only appeared for values of ζ < 10 [e.g., Grossman, 1982; Le Mone, 1973]. For 10 < ζ < 20 some roll structure coexists with cells although random cells dominate. For larger ζ, only cellular convection was observed. This coincides with theoretical findings that the shear in the flow has a supporting influence on roll development within thermal instability [e.g., Asai, 1970; Brown, 1972], as for large ζ turbulence generation due to shear is small compared to buoyancy. Gryschka and Raasch [2005] presented an LES of a moderate CAO with a water-ice temperature difference of ΔTs ≈ 6 K and ζ ≈ 7. In that simulation roll convection was accompanied by cloud streets. They showed typical characteristics such as increasing aspect ratios λ/zi with increasing distance from the ice edge (λ denotes the cloud street spacing). Furthermore, the roll axes were oriented in direction of the mean wind shear vector equation image = (equation image(zi)−equation image(zs))/(zizs), with equation image the wind vector and zs the top of the surface layer. This behavior was also observed in various field experiments [e.g., Lohou et al., 1998]. Accordingly, in later simulations with larger ζ (up to 20) we found only weak signals of roll convection while cellular convection dominated. In contrast to these findings Brümmer [1999] and Christian and Wakimoto [1989] and others report roll convection for even larger values (up to 250). In observational and numerical studies Kristovich et al. [1999] and Cooper et al. [2000] attributed roll formation at large ζ to strong low level wind shear (below 0.3 zi).

[4] To the authors' knowledge, there is no LES which could produce roll convection for strong CAOs (large ζ) so far. Müller et al. [1999] carried out a LES of a CAO with ΔTs ≈ 30 K as observed during the field experiment ARKTIS 1993. In this LES no rolls appeared although observations showed strong roll convection. Clear roll patterns developed only after they introduced an artificial wind shear in the upper half of the CBL [Müller et al., 1999, Figure 9]. In the measurements, however, such wind shear was only present above the inversion base.

[5] On the other hand, roll convection is very robust in nature. Brümmer and Pohlmann [2000] showed that organized convective patterns occur in more than 50% of the time over Greenland and the Barents Sea. Depending on the distance to the sea-ice, up to 100% of these organized convective patterns were cloud streets. Kristovich and Steve [1995] found similar results for the Great Lakes. The Labrador Sea is also an area with frequent cloud street formations [Renfrew and Moore, 1999].

[6] In contrast to previous LES, cloud streets have been simulated even for cases of strong surface heating by Cooper et al. [2000], Tripoli [2005], and Liu et al. [2004, 2006] but using cloud resolving models with a grid considerably coarser than used in LES (see Section 4).

[7] In the following we will show that one possible reason for the absence of roll convection under strong surface heating in previous LES is the omission of sea-ice inhomogeneities. Furthermore, we propose that the occasional roll occurrence at large ζ in different studies is due to two different types of roll convection caused by thermal instability.

2. Simulation Setup

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Setup
  5. 3. Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[8] As in a previous study [Gryschka and Raasch, 2005], we used the LES model PALM (Parallelized LES model) optimized for parallel computing [Raasch and Schröter, 2001]. The model is based on the filtered non-hydrostatic Boussinesq equations. Prognostic quantities are the three velocity components, liquid water potential temperature, total water content, and subgrid-scale turbulent kinetic energy as a 1.5 order closure is used. At the inflow, stationary vertical profiles are prescribed for all quantities, irrespective of the perturbation pressure, for which a zero gradient is used. At the outflow a radiation boundary condition is used for the velocities and a zero gradient is assumed for all other quantities. The two remaining lateral boundaries are periodic.

[9] For the present study we carried out three simulations: two simulations (S1 and S2) with idealized sea-ice distributions to investigate the influence of sea-ice inhomogeneities on roll convection and a third simulation (S3) with realistic sea-ice distribution data to obtain a realistic representation of a CAO and cloud streets. The initial and boundary conditions for all simulations were derived from a strong CAO with roll convection and cloud streets observed during the ARTIST experiment on 5 April 1998 in the Fram Strait [Hartmann et al., 1999]. A grid size of Δx = Δy = 50 m (horizontally) and Δz = 25 m (vertically) was used.

[10] In all three simulations the model is driven with a geostrophic wind of 16.5 m/s. The inflow profiles of potential temperature and humidity are taken from aircraft soundings over the sea-ice (>95% fraction). The inflow wind profile is the result of a one dimensional pre-run using the given geostrophic wind and the inflow profiles of humidity and temperature assumed to be constant in time. At beginning of the simulation, the inflow profiles are set for the whole model domain. The water-temperature was set to Tw = 271.35 K at the marginal ice-zone with a linear increase of 2.3 K per 100 km downstream starting from 100 km distance from the inflow. The ice temperature was set to Ti = 247.6 K. The surface temperature at the horizontal grid cell (i, j) is defined by the sea-ice fraction A(i, j) as Ts(i, j) = A(i, j) Ti + [1−A(i, j)]Tw(j).

2.1. Sensitivity Study (S1 and S2)

[11] The model domain of S1 and S2 has a length of 102.4 km (y-direction), a width of 32.0 km (x-direction) and a height of 2.3 km (z-direction). S1 and S2 differ only in the distribution of the ice. In S2, the sea-ice fraction AS2 contains grid cells that are either completely ice covered (AS2(i, j) = 1) or free of ice (AS2(i, j) = 0). AS2 varies in both horizontal directions. In contrast, in S1 the sea-ice fraction AS1 contains grid cells that are partially ice covered (0 ≤ AS1(i, j) ≤ 1) and uniformly in x-direction. AS1 and AS2 are defined to have the same lateral (x-direction) mean: AS1(i, j) = equation imageAS2(i, j)/Nx with Nx the grid size in x-direction. Thus, possible differences in the CBL development between S1 and S2 cannot be caused by differences in the surface temperature averaged along x (lateral to the geostrophic wind). The sea-ice fraction used in both simulations is shown in Figure 1a in terms of Ts (partly overlayed by the cloud field). The roughness length is set to z0 = 1.8 mm for the whole model domain independent of the sea-ice cover to focus on the effect of inhomogeneities in surface temperatures onto roll convection.

image

Figure 1. (a) Horizontal cross sections of liquid water path and surface temperature and lateral mean of ζ for simulations (left) S1 and (right) S2 after 2 hours. (b) Enlarged view of the sea-ice distribution for S2 (white: ice, dark blue: water) with areas of positive vertical motion at z = 150 m superimposed (transparent grey), averaged over 10 timesteps after 2 hours. (c) The x-z-cross section of the secondary flow (curly vectors) at y = −50 km and y = −100 km averaged over 10 timesteps in the stationary state of S2. Light orange marks updrafts; light blue marks downdrafts. Grey shading marks liquid water content of greater than 0.05 g/kg.

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2.2. Full Simulation (S3)

[12] The third simulation S3 is carried out with a large model domain of 400 km length, 64 km width, and a height of 5 km. Here we apply an sea-ice mask AS3 ε {0, 1} obtained from infrared satellite images as described below. Unlike to S1 and S2, the roughness length is determined according to Lüpkes and Birnbaum [2005] and Charnock [1955] as a function z0 = image Abox) where image = 0.018 u*g−1 with g the gravitational constant, u* the friction velocity, and Abox(i, j) = equation imageAS3(n, m)/(NxNy) the ice fraction average over a 1000 × 1000 m2 box around the grid point (i, j).

2.3. Sea-Ice Data (S3)

[13] The sea-ice mask used in S3 is derived from MODIS (Moderate Resolution Imaging Spectroradiometer) infrared images taken on March 25, 2007 between 1000 and 1400 UTC. We used the MODIS potential open water algorithm (MPA) by Drüe and Heinemann [2004] to retrieve a sea-ice map of 1 km. The 64 km by 150 km area was rotated to align its long side perpendicular to the large-scale ice edge. The greyscale sea-ice map was transformed into a binary (ice-water) bitmap at 50 m resolution by Floid-Steinberg dithering. This bitmap preserves the same 1 km-averaged sea-ice fraction values as the original map.

3. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Setup
  5. 3. Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[14] The flow reaches a stationary state in the whole model domain after 2 hours in S1 and S2 and 8 hours in S3. The sensible and latent surface heat fluxes reach values of up to 650 W/m2 and 250 W/m2, respectively, with downstream variations similar to Liu et al. [2006]. The boundary-layer height increases from 300 m at the inflow up to 900 m in S1 (y = −100 km), 990 m in S2 (y = −100 km), and 2090 m at the outflow (y = −400 km) in S3.

3.1. Sensitivity Study: S1 and S2

[15] In Figure 1a the liquid water path (LWP), representative for the cloud field as seen in satellite images, is shown for S1 and S2: LWP = equation image dzqlϱ, with ql the liquid water and ϱ the density of air. Whereas in S1 the cloud field appears as an irregular cellular pattern, clear patterns of cloud streets are obvious in S2. Those cloud streets appear over the marginal ice zone in different distances downstream. We found that at the initial stage cloud streets represent a superposition of plumes generated by individual leads, rather than patterns of self organized convection. To confirm this, Figure 1b shows the sea-ice and areas with positive vertical motion (at z = 150 m) superimposed, since the band-like areas of upward motion are a prerequisite for cloud streets. If we regard both as equivalent, it can be concluded from Figure 1b that almost any cloud street has its origin in some plume between y = −4 and −12 km. All band-like structures are stationary and oriented about 5° to the left of the geostrophic wind (i.e., tilt angle α = +5°) which coincides with the boundary-layer wind direction. Over ice, the distance λ between these bands is varying between 400 m and 3000 m. Further downstream over open sea the structure is more regular. For example, the distance between cloud streets varies between 3400 and 4500 m at y = −100 km. This suggests that under absence of inhomogeneities in surface temperature the structure of preexisting convective bands become self organized further downstream over open sea. This is also in agreement with Figure 1c where x-z-cross sections of the secondary flow are shown: Close to the ice (y = −50 km) both irregular circulations and roll convection are present. Further downstream (y = −100 km), roll convection becomes apparently regular with opposite secondary circulations to each other.

3.2. Full Simulation: S3

[16] The field of the liquid water path of S3 (Figure 2) looks very similar to satellite images of typical cloud streets during CAOs. In general there is a stationary band-like structure with same orientation of about α ≈ +5° (i.e., tilted to the left) as in S2, even at y = −400 km where ζ reaches its maximum value of 50. Some bands are very pronounced and exist over distances of several hundred kilometers and grow in width from initially about 1000 m at y ≈ −100 km to 11000 m at y ≈ −400 km. In the following we will call them “leading bands” (LB). In Contrast to S2, where the whole cloud field is characterized by such LBs, the structure is more complex in S3. In some areas more cellular structures (e.g., at x = 50 km, y = −240 km) are present. The differences in flow structures in S2 and S3 can only be caused by differences in ice distribution or the different handling of roughness lengths, since all other initial and boundary conditions (except the model domain size) are identical.

image

Figure 2. As Figure 1a but for S3 after 8 hours. Note that the right panel represents the downstream continuation of the left panel.

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[17] In S3, the ice field is apparently structured on a much wider range of scales than in S2 (Figures 1b and 2). It appears, however, that not all of the sea-ice inhomogeneities are able to initiate leading bands. For example, the flow downstream of the ice region 30 km < x < 50 km does not exhibit pronounced LBs. Instead, short cloud streets with a length of about 10 km and an orientation of α ≈ −25° are found downstream (see the area marked by the yellow ellipse around x = 45 km, y = −160 km in Figure 2).

[18] Nevertheless, from y = −260 km onwards, the whole cloud field has a band-like structure with α ≈ +5°. Apparently, this is due to the impact of the LBs on their environment in terms of the self organization mentioned in Section 3.1. As cloud streets are growing downstream, they merge resulting in wider bands (as known from satellite pictures). In the secondary flow in the x-z-plane this can be seen in terms of broadening circulations (analogous to Figure 1c), not shown here).

[19] In Figure 2, the influence of the shape of the ice edge onto the cloud field is obvious. In particular, the effect of the “peninsula” at x = 20 km and y = −60 km can be noticed by a continuous gap in the cloud field stretching out to the outflow (x = 40 km, y = −400 km). The CBL height in this gap is up to 15% (up to 200 m) lower than on the average. The cloud pattern near y≈ −400 km suggests that the cloud streets between x ≈ 20 km and x ≈ 60 km have merged to only two bands with the mentioned gap in between. The secondary flow, however, shows multiple separate circulations within each of these cloud bands (not shown here). The same was observed by, for example, Renfrew and Moore [1999] and Hein and Brown [1988].

[20] The aspect ratios λ/zi amount to around 2 at y = −100 km and increase up to 10 at y = −400 km. This is within the range of observational studies [Brümmer, 1999].

4. Discussion and Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Setup
  5. 3. Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[21] In case of strong CAOs, our results show clearly that sea-ice inhomogeneities in the marginal ice zone are favorable for the generation of roll convection. Secondary circulations lateral to the mean CBL wind originate at sea-ice leads (as demonstrated for a checkerboard-shaped surface heat flux distribution by Raasch and Harbusch [2000]) and force rolls over open sea. We will call this type of rolls “forced rolls” in the following. This is consistent with Tripoli [2005], who used a cloud resolving model with 400 m horizontal resolution to study roll convection in a CAO over Lake Michigan. Surface heat fluxes over water were of the same order as in the present study. In the simulations by Tripoli [2005], cloud streets appear over the lake in case of an undulating shoreline and are absent in case of a straight shoreline. Tripoli [2005] found cloud streets that are parallel to the CBL wind and stationary, which is in agreement with observations [Tripoli, 2005] and with our findings, as well. Tripoli [2005] showed λ around 5 km and the cloud structure as rather homogeneous. In the present study, rolls with λ of about 1 km are observed as well, due to a smaller grid size (50 m compared to 400 m).

[22] In case of weaker surface heating, the rolls presented by Gryschka and Raasch [2005] developed purely by self organization, without any forcing by surface inhomogeneities upstream. Therefore we will call them “free rolls”. They appeared in the whole model domain simultaneously while their axes were oriented along the mean wind shear vector equation image. In contrast to forced rolls, the free rolls drifted laterally with the cross-axis component of the CBL wind vector. There were also no LBs and the rolls appeared to be broken into fractions of some ten kilometers length.

[23] In accordance to the literature mentioned in Section 1 we propose that CBL rolls in general can be classified into forced or free rolls. Combinations of both types are possible. For example, dynamically driven free rolls [Brown, 1972; Foster, 1997] preexisting in a neutral or weakly stratified boundary-layer over homogeneous ice may force rolls in the CBL over open water (even for large ζ). Such forced rolls generated by free rolls could exhibit a drift and tilt relative to the CBL wind (depending on the preexisting free rolls), which is in contrast to forced rolls bound on single leads. Since in our simulation no dynamical driven preexisting rolls over ice were present, the investigation of such a mechanism needs further research which is out of the scope of this paper. Free rolls and forced rolls may also coexist in areas, where ζ < 20, if for example the right tilted short cloud streets mentioned in Section 3.2 embedded within LBs (associated with forced rolls) exhibit characteristics of free rolls.

[24] It is worth mentioning that some cases of rolls in literature do not perfectly fit our classification. In case of the rolls mentioned in Cooper et al. [2000] for large ζ but strong low level shear, neither preexisting rolls nor surface inhomogeneities were reported. Hence, they can be assigned as some kind of free rolls too, although ζ > 20. The cloud streets presented by Liu et al. [2004] appeared under similar conditions except weak low level wind shear (free slip surface boundary conditions). This is possibly due to strong vertical shear in the inflow wind profile.

[25] To summarize, varying combinations of forced and free rolls could explain the contrasting results in literature concerning the dependency of roll convection on the stability parameter ζ. In case of polar CAOs, we propose that some of the dominant cloud bands can be explained by forced rolls due to sea-ice inhomogeneities, since many high resolution satellite images give the impression, that LBs are confined to sea-ice structures. Since the inhomogeneities in surface forcing are not particular to sea-ice, cloud streets can also be forced by other surface inhomogeneities, including coast lines [Tripoli, 2005] and terrain [Kawase et al., 2005].

[26] Generally speaking, rolls become increasingly unlikely if surface heat fluxes increase and increasingly likely if wind shear strengthens or some forcing upstream in terms of surface inhomogeneities exists.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Setup
  5. 3. Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[27] We would like to thank J. Hartmann for providing data from the ARTIST experiment. All runs were performed on an IBM pSeries 690 supercomputer of the Norddeutscher Verbund für Hoch- und Höchstleistungsrechnen (HLRN). MODIS data were made available by the NASA Goddard Space Flight Center (GSFC). This work was supported by the Deutsche Forschungsgemeinschaft. The helpful comments of two reviewers are very much appreciated.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Setup
  5. 3. Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References