The Sensitivity of Springtime Arctic Mixed-Phase Stratocumulus Clouds to Surface-Layer and Cloud-Top Inversion-Layer Moisture Sources

1. Introduction

Since the early 1990s the cooling influence of subtropical stratocumulus has been recognized as a major contributor to Earth's global-average energy budget (Stephens and Greenwald 1991; Hartmann et al. 1992). The importance of stratocumulus-topped boundary layers (STBLs) in polar climate only became clear during the Surface Heat Budget of the Arctic Ocean Experiment (SHEBA) (Uttal et al. 2002), which revealed that STBLs are prevalent and long lived in the Arctic. Arctic STBLs were found to consist of a combination of ice and liquid water even at temperatures significantly below freezing (Curry et al. 2000; Intrieri et al. 2002; Korolev and Isaac 2003; Shupe and Intrieri 2004; Verlinde et al. 2007; de Boer et al. 2011; McFarquhar et al. 2011). Despite the rapid depletion of liquid water due to the lower saturation vapor pressure of ice compared to liquid [the Wegener–Bergeron–Findeisen (WBF) mechanism] (Wegener 1911; Bergeron 1935; Findeisen 1938), Arctic mixed-phase stratocumulus (AMPS) were observed to persist for days (Shupe et al. 2006) owing to compensating feedbacks between the formation and growth of ice and cloud droplets, radiative cooling, turbulence, entrainment, and surface fluxes of heat and moisture (Morrison et al. 2012).

Owing to the presence of liquid water and related processes in these cloud systems, AMPS play an important role in determining the structure of the Arctic atmospheric boundary layer and magnitudes of surface energy budget terms (Herman and Goody 1976; Curry and Ebert 1992; Schweiger and Key 1994; Zhang et al. 1996; Walsh and Chapman 1998; Intrieri et al. 2002; Shupe and Intrieri 2004; Inoue et al. 2006; Shupe et al. 2013). For example, Zuidema et al. (2005) estimated that a springtime AMPS observed during SHEBA had a net surface cloud forcing of 41 W m⁻² due to the presence of cloud water, which increased cloud emissivity and, thus, downwelling longwave radiation (Sun and Shine 1994; Intrieri et al. 2002; Hogan et al. 2003; Shupe and Intrieri 2004; Dong et al. 2010).

The environments in which subtropical and Arctic stratocumuli occur are substantially different. For example, AMPS are observed above both stable surface boundary layers and open water (Intrieri et al. 2002; Shupe et al. 2013), while subtropical stratocumulus typically occur over open ocean. Another difference between subtropical and Arctic stratocumulus is that in the Arctic specific humidity inversions (specific humidity increasing with height, hereafter referred to as humidity inversion) are frequently observed to occur coincident with temperature inversions near cloud top. This feature is due primarily to horizontal advection aloft and moisture depletion near the surface (Curry 1983; Curry et al. 1996; Tjernström et al. 2004; Sedlar et al. 2012). Further key differences owing to the presence of ice in AMPS are the rapid conversion of cloud to precipitation by the WBF mechanism, the impact of latent heat due to freezing, and sublimation of ice precipitation below cloud base due to the lower saturation vapor pressure of ice compared to liquid.

Previous studies based on observations (Curry et al. 1996; Tjernström et al. 2004; Sedlar et al. 2012) and cloud-resolving models (Solomon et al. 2011) suggest that humidity inversions play an important role in maintaining AMPS by providing moisture within the temperature inversion, which is entrained into the cloud system. We extend the findings of these previous studies by quantifying the relative role of cloud-top and subcloud-layer sources of moisture in the persistence of AMPS. We demonstrate that a similar quasi-equilibrium state is reached when either or both of the moisture sources are present. Specifically, we show that a humidity inversion is a sufficient but not a necessary condition for the maintenance of an AMPS. To do this we use a series of idealized large-eddy simulations (LESs) based on a case study from the Department of Energy Atmospheric Radiation Measurement Program’s Indirect and Semi-Direct Aerosol Campaign (ISDAC) (McFarquhar et al. 2011) near Barrow, Alaska.

The goal of this paper is to clarify important details of the moisture and moist static energy (MSE) budgets by examining the potential impact of ice in mixed-phase clouds, humidity inversions coincident with temperature inversions as a source of moisture for the cloud system, and the presence of cloud liquid water () above the mixed-layer top. Microphysical processes such as ice formation mechanisms are of clear importance in AMPS (see Fridlind et al. 2007) but are not the subject of this paper.

2. Theoretical framework from subtropical STBLs studies

To provide a theoretical framework for this study, we first present an overview of microphysical–dynamical–radiative feedbacks in subtropical marine STBLs. Idealized models of STBLs are primarily based on observations of subtropical cloud systems over relatively cold sea surface temperatures where the large-scale atmospheric circulation is characterized by subsidence on the order of 2–4 mm s⁻¹ (Wood and Bretherton 2004). Warm, dry air in a temperature inversion caps the cloud layer and damps upward motion in cloud plumes that overshoot their level of neutral buoyancy.

Stratocumulus layers are ensembles of convective eddies maintained primarily by turbulence owing to longwave cooling near the top of the cloud layer. Turbulent motions within the STBL adiabatically mix moist-conserved fields over an eddy length scale forming a well-mixed layer. The upward movement of the cloud system due to entrainment of inversion air opposes mean subsidence. The entrainment velocity at the top and bottom of the mixed layer is diagnosed as

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where is used to denote fields at the top ) or bottom ) of the mixed layer and D is the large-scale horizontal divergence, assumed constant in the mixed layer.

Two moist conserved fields that can be used to define a well-mixed subtropical cloud system (i.e., without ice water) are total water mixing ratio , where is liquid water mixing ratio and is the water vapor mixing ratio, and moist static energy, where is the specific heat capacity of air at constant pressure, is temperature, is latent heat of evaporation, is the acceleration of gravity, and is height (constants not defined in the text are listed in Table 1). In Arctic systems, , where is ice mixing ratio due to all frozen-water species.

Table 1.

Constants and variables not defined in the text.

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Following the formulations of mixed-layer models by Lilly (1968) and Bretherton and Wyant (1997), the mixed layer is composed of two parts: a cloud layer, in which air is saturated with respect to water, and a subsaturated subcloud layer from the base of the mixed layer to the lifting condensation level. In the cloud layer is equal to the saturation water vapor mixing ratio , and , where is the air pressure. In the subcloud layer . The buoyancy flux is defined as , where is vertical velocity and is virtual temperature. Overbars denote horizontal averages and primes denote deviations from the horizontal average. Loading due to frozen water species needs to be included for mixed-phase clouds, .

Using these relationships and the Clausius–Clapeyron equation,

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The buoyancy flux can be expressed in terms of fluxes of the moist conserved variables:

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where and are the heights of mixed layer and cloud base, and is the height of the inversion–mixed-layer interface.

Moist static energy in the mixed layer evolves owing to radiative heating and cooling and divergence of heat and moisture fluxes across the mixed-layer top and base. In the mixed-layer varies because of fluxes of across the mixed-layer top and base. In the subtropics, the flux of at the top of the mixed layer is due to the entrainment (detrainment) of dry (moist) air, and the flux at the bottom of the mixed layer results from an upward flux of from the surface layer into the mixed layer and a downward precipitation flux of out of the mixed layer. Sedimentation can also reduce turbulence at the inversion base owing to longwave cooling by moving cloud water downward away from cloud top (Bretherton et al. 2007). In subtropical STBLs, decoupling of the cloud-driven mixed layer from the surface layer can occur by a number of processes (see Wood 2012, and references therein), which cuts off the supply of moisture from the surface layer to the cloud system.

Even though AMPS clearly form cloud-driven mixed layers, the derivation of an idealized mixed-layer model that includes ice processes remains a challenge. For example, liquid–ice water static energy, is not conserved if sedimentation is allowed. In addition, total water may not be well mixed when formation and sedimentation of ice is allowed. Also, it is unclear how to parameterize the turbulent flux of ice, which needs to be done in order to separate the flux of total water in the cloud layer into fluxes of , , and ice. Resolving these issues will allow for the formulation of a mixed-layer model relevant to AMPS. Even though developing a mixed-phase mixed-layer model remains a challenge, the mixed-layer framework is still a useful diagnostic to identify changes in fluxes into and out of the cloud-driven turbulent layer and to identify how the presence of ice causes the structure of an AMPS turbulent layer to deviate from the structure of a subtropical STBL.

3. Case description

This study focuses on a case derived from observations of a persistent single-layer Arctic mixed-phase stratocumulus cloud deck on 8 April 2008 during the Indirect and Semi-Direct Aerosol Campaign (McFarquhar et al. 2011). The Beaufort Sea was generally ice covered during this time, with significant areas of open water observed east of Barrow, Alaska. An early morning sounding made at 1734 UTC 8 April 2008 at Barrow is shown in Fig. 1. Surface temperature was approximately 265 K. An approximate 4-K temperature inversion with inversion base at 1.05 km was observed at this time, with static stabilities close to neutral within the cloud-driven mixed layer overlaying a stable surface layer with static stabilities greater than 2 K km⁻¹ below 500 m. The water vapor mixing ratio decreases from 1.7 g kg⁻¹ at the surface to 1.2 g kg⁻¹ at cloud top, above which a secondary maximum of 1.6 g kg⁻¹ was observed. Winds were east-southeasterly throughout the lowest 2 km (McFarquhar et al. 2011).

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Sounding measured at 1734 UTC 8 April 2008 at Barrow, Alaska (71.33°N, 156.6°W). Gray shading marks the extent of the cloud layer. The dashed lines show the initial profiles used in the LESs for Control. The dashed line overlaying water vapor mixing ratio is the initial profile for .

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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Measurements from ground-based, vertically pointing, 35-GHz cloud radar, micropulse cloud lidar, and dual-channel microwave radiometer (Shupe 2007) at Barrow indicated a cloud layer extending into the inversion by 100 m, a cloud base at 0.9 km, and cloud top at 1.15 km. Cloud ice water path (IWP), derived from cloud radar reflectivity measurements that have an uncertainty of up to a factor of 2 (Shupe et al. 2006), was 20–120 g m⁻² within 10 min of the sounding. Cloud liquid water path (LWP), derived from dual-channel microwave radiometer measurements that have an uncertainty of 20–30 g m⁻² (Turner et al. 2007), was 39–62 g m⁻² within 10 min of the sounding.

Nested Weather Research and Forecasting (WRF) simulations of this case performed with an inner grid at LES resolution (Solomon et al. 2011) demonstrate that moisture is provided to the cloud system by a total water inversion at cloud top and that the mixed layer is decoupled from surface sources of moisture. In addition, the nested simulations indicate that is maintained within the temperature inversion by downgradient turbulent fluxes of from above and direct condensation driven by radiative cooling. These processes cause at least 20% of to extend into the temperature inversion.

4. Design of LES studies

This study uses the large eddy simulation mode of the Advanced Research WRF model, version 3.3.1 [see Yamaguchi and Feingold (2012) for a detailed description of the LES mode and the statistics package]. Packages and parameterizations used in the model setup are listed in Table 2.

Table 2.

WRF LES model setup.

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All simulations are run with a horizontal grid spacing of 50 m and vertical grid spacing of 10 m. The domain has 72 (x) × 72 (y) × 180 (z) grid points and is periodic in both the x and y directions. The top of the domain is at 1.8 km, which is 0.7 km above cloud top in this case. The model time step is 0.5 s.

The structure of the cloud layer is insensitive to changes in resolution and domain size. However, increasing the vertical and horizontal resolution by a factor of 2 results in an increase in LWP (IWP) by 5% (1%). Increasing the domain size by a factor of 2 in both the x and y directions results in an increase in LWP and IWP by less than 1%. The simulations are insensitive to a decrease in time step by a factor of 2 and a decrease in the acoustic Courant number by a factor of 2.

Sensible and latent heat fluxes between the ice-covered surface and atmosphere under the considered conditions are typically small (<10 W m⁻²). Thus, for simplicity, both sensible and latent surface heat fluxes are set to zero in these simulations. In addition, because of small shortwave heating rates at cloud top at the time of the sounding [1 K day⁻¹ for shortwave compared to −100 K day⁻¹ for longwave based on nested WRF simulations (Solomon et al. 2011)], solar radiation is set to zero. Solar radiation cannot be neglected when considering the diurnal evolution of the cloud layer. Simulations to test the impact of diurnally varying solar radiation indicate that during the day there is significant near-surface heating, which drives buoyant production of turbulence. The impact of these processes on the results presented in this paper will be investigated in a follow-up study focused on perturbations to the quasi-equilibrium state.

The concentration of ice nuclei acting in deposition and condensation freezing modes is relaxed to a value of 1.0 L⁻¹, the mean from measurements using the continuous flow diffusion chamber (McFarquhar et al. 2011), with ice nucleation rate equations developed in Morrison et al. (2011) and Ovchinnikov et al. (2011). The aerosol accumulation mode is specified with concentrations of 165 cm⁻³, modal diameter of 0.2 μm, and geometric standard deviation of 1.4 μm (based on in situ ISDAC measurements).

Large-scale subsidence is specified by integrating the prescribed horizontal wind divergence from the surface upward. Divergence is assumed to be equal to 3.5 × 10⁻⁶ s⁻¹ below the inversion and zero above. This gives a linear increase in large-scale subsidence from zero at the surface to 3.85 mm s⁻¹ at the base of the initial inversion (z = 1100 m), above which the large-scale vertical wind is constant:

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Temperature and moisture profiles are nudged to the initial profiles in the top 100 m of the domain with a time scale of 1 h. Horizontal winds are nudged to the initial profiles at and above the initial inversion base with a time scale of 2 h. Initial temperature and subgrid turbulent kinetic energy (TKE) are perturbed below the top of the mixed layer with pseudorandom fluctuations with amplitude of 0.1 K and 0.1 m² s⁻².

The dotted lines in Fig. 1 show the initial profiles used for the control simulation. Note that the profile overlaying is for total water. Only initial profiles for total water mixing ratio are varied for the sensitivity studies described below. The liquid layer is allowed to form in the absence of ice during the first hour of the integration to prevent potential glaciation during spinup.

Figure 2 shows the initial total water profiles used for the sensitivity studies. These profiles are designed to identify the impact of moisture sources above and below the mixed layer on the dynamics of the cloud system. Core simulations for this study are

1. Control run: initial total water as shown in Fig. 1;

2. DryAbove run: same as Control, except that total water decreased to 0.5 g kg⁻¹ above inversion base;

3. DryBelow run: same as Control, except that total water below the base of the cloud-driven mixed layer linearly reduced to 1 g kg⁻¹ at the surface;

4. DryAbove&Below run: total water decreased to 0.5 g kg⁻¹ above inversion base and reduced linearly from the base of the cloud-driven mixed layer to the surface.

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Total water mixing ratio () profiles used to initialize LESs (g kg⁻¹). (a) Control and NoIce initial (observational sounding) minus inversion plus linearly increasing from mixed layer to surface. (b) DryAbove minus no inversion plus linearly increasing from mixed layer to surface. (c) DryBelow minus inversion plus linearly decreasing from mixed layer to surface. (d) DryAbove&Below minus no inversion plus linearly decreasing from mixed layer to surface. Base of temperature inversion indicated with thin horizontal black dashed line.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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Horizontally averaged fields output every minute from the statistics package are used in the analysis. Conditional averages are used to calculate averages in updrafts and downdrafts, where an updraft is defined as having a vertical velocity greater than zero at the base of the cloud layer. The mixed layer is defined as the region where the liquid–ice water static energy is approximately constant with height. We define the boundaries of the mixed-layer top and base to occur where the slope of liquid–ice static energy exceeds 5 × 10⁻³ and 1 × 10⁻³ K m⁻¹, respectively. Cloud top and base are defined as the heights where 1 × 10⁻⁴ g kg⁻¹.

Since well-mixed layers are vertically homogenous for moist-conserved variables, evolution of mixed-layer quantities with no internal sources or sinks can be described by fluxes of these quantities through the top and bottom mixed-layer boundaries. Thus, mixed-layer MSE and tendencies can be derived from radiative fluxes, vertical advective fluxes (including resolved-scale transports, subgrid-scale transports, and transport due to mean subsidence), and precipitation fluxes. In the following discussion, we also plot the total MSE flux (radiative plus advective MSE fluxes) and flux (precipitation plus advective water fluxes). Positive fluxes result from an upward transport of a positive anomaly or a downward transport of a negative anomaly (and oppositely for negative fluxes). Fluxes that increase with height produce a flux divergence and a negative tendency (and oppositely for fluxes that decrease with height).

5. Results

a. Control simulation with and without ice

Figure 3 shows liquid water path (LWP) and ice plus LWP [total water path (TWP)] for the first 12 h of Control (black line) compared to NoIce (red line). Control equilibrates after 4 h with an approximate LWP of 37 g m⁻² and TWP of 64 g m⁻², giving a liquid fraction (LWP/TWP) of 0.6. Interestingly, NoIce follows a similar TWP trajectory until hour 4. The addition of ice processes in Control causes to equilibrate when the upward turbulent flux balances the downward precipitation flux at cloud base, when LWP/IWP ≈ 2.5, 2 h after ice processes are turned on. However, IWP in Control continues to increase for another 2 h because of the slow growth of snow by vapor deposition. The continuous increase in in NoIce causes the cloud base to descend at a rate of 4 × 10⁻³ m s⁻¹ (the inversion base ascends at a slower rate of 6 × 10⁻⁴ m s⁻¹), whereas in Control the continuous depletion of at cloud base by the growth of ice causes the cloud base to descend at a slower rate of 8 × 10⁻⁴ m s⁻¹.

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Evolution of liquid water path (solid line) and total water path (dashed line) from Control (black) and NoIce (red) runs (g m⁻²).

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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1) Simulation without ice (NoIce)

While NoIce is similar to subtropical stratocumulus in condensate phase and in the presence of a well-mixed layer (Figs. 4a,b), it differs by not having the mixed layer extend to the surface, by having a inversion at cloud top (Fig. 4b), and by having a cloud layer that extends into the inversion above the mixed-layer top (though maximum liquid water content still occurs at the inversion base, Fig. 4c). As a result of the cloud layer extending into the inversion, sedimentation of liquid water is a source of water to the mixed layer, (e.g., Solomon et al. 2011; Fig. 5a). Also, under the conditions of liquid water content and number concentration observed during this case study, the production of drizzle is very limited. Thus, in NoIce there is negligible precipitation at the base of the mixed layer and sedimentation of liquid water is a net source of water to the mixed layer.

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Horizontally averaged profiles from Control (black) and NoIce (red) averaged over hours 4–5 using minute output: (a) MSE (K), (b) (g kg⁻¹), (c) (g kg⁻¹), and (d) (g kg⁻¹). Dashed lines indicate top and bottom of the mixed layer. Shading indicates extent of the cloud liquid water layer. Initial profiles shown with dash–dotted lines in (a),(b), and (d).

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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Horizontally averaged profiles from Control (black) and NoIce (red) averaged over hours 4–5 using minute output. (left) Water fluxes (g m⁻³ m s⁻¹): (a) precipitation flux, (c) advective water flux (resolved + subgrid + subsidence), and (e) total water flux [=(a) + (c)]. (right) Energy fluxes (K m s⁻¹): (b) radiative flux, (d) advective MSE flux (resolved + subgrid + subsidence), and (f) total MSE flux [=(b) + (d)]. Dashed lines indicate top and bottom of the mixed layer. Shading indicates extent of the cloud liquid water layer.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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(i) Water fluxes

The inversion coincident with the temperature inversion produces a positive tendency between the base of the temperature inversion and the cloud top owing to the advective flux (Fig. 5c). The precipitation flux dominates over the advective flux resulting in a downward flux from the cloud top into the mixed layer to approximately 1 km, with an upward flux in the mixed layer below 1 km (Fig. 5e). It is interesting to note this net downward flux into the mixed layer does not remove the inversion after 4 h. At the base of the mixed layer there is an upward advective flux of (Fig. 5c). In summary, sources from both above and below moisten the mixed layer, while no water precipitates out, resulting in a continually increasing LWP (Fig. 3).

Although is larger above cloud top and is relatively constant within the mixed layer, the cloudy portion of the inversion layer exhibits a distinct minimum (Fig. 4b) due to sedimentation (Fig. 5a). As a result, advection moistens this transitional layer by moving overlying moist air downward across cloud top and by exchanging dry air for moist via turbulence at the top of the mixed layer (Fig. 5c).

(ii) Energy fluxes

Figures 5b, 5d, and 5f show that radiative fluxes, entrainment due to subsidence, and turbulent eddies contribute to the positive MSE fluxes at the mixed-layer top, which are a factor of 5–6 larger than at the mixed-layer base, resulting in negative MSE tendencies in the mixed layer (dMSE/dt in the mixed layer = −3 × 10⁻⁵ K s⁻¹). Different from subtropical systems, the largest negative tendencies occur just below cloud top, which in this case is above the mixed-layer top and within the temperature inversion.

Figures 5e and 5f show the approximate linear change in net flux and MSE flux from the base to the top of the mixed layer (resulting in a constant tendency), indicating that the sources and sinks of this well-mixed layer are at the base and top of the mixed layer and that the theoretical framework outlined in section 2 can be applied to this NoIce simulation.

(iii) Buoyancy fluxes

Evaporation at the cloud base in downdrafts exceeds condensation in updrafts (Fig. 6b) because of the continual flux of into the cloud layer at cloud top, increasing the buoyancy fluxes in the subcloud layer and reducing the buoyancy jump at cloud base (Fig. 6a).

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Horizontally averaged profiles from Control (black) and NoIce (red) averaged over hours 4–5 using minute output. (a) Buoyancy flux (K m s⁻¹). (b) Latent heating (K s⁻¹). Green line shows latent heating due to condensation minus evaporation in Control (i.e., liquid processes). Dashed lines indicate top and bottom of the mixed layer. Shading indicates extent of the cloud liquid water layer.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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(iv) Sensitivity to sedimentation and latent heating

Removing sedimentation removes the minima just above the mixed-layer top (Fig. 7a), increases the LWP, and moves the cloud top higher into the inversion (Fig. 7c). This increase in liquid water content increases the longwave radiative cooling rates (Fig. 7e). However, the increase in radiative cooling occurs within the transition layer between cloud top and mixed-layer top, with radiative cooling rates actually decreasing at the top of the mixed layer relative to NoIce (Fig. 7e). This causes TKE and MSE tendencies to decrease in the mixed layer relative to NoIce (results not shown). In addition, reduced turbulence in the mixed layer in NoSedimentation reduces entrainment of into the mixed layer at the mixed-layer base.

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Horizontally averaged profiles averaged over hours 4–5 from NoIce (red) compared to (left) NoSedimentation (gray) and (right) NoSedimentation–NoLH (teal): (a),(b) (g kg⁻¹); (c),(d) (g kg⁻¹); (e) radiative flux divergence (K s⁻¹); and (f) MSE (K). Dashed lines indicate top and bottom of the mixed layer. Shading indicates extent of the cloud liquid water layer. Initial profiles shown with dash–dotted lines in (a),(b), and (f).

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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When both sedimentation and latent heating are removed, the cloud system shows no indication of collapsing. LWP increases and the cloud system extends farther into the inversion relative to NoSedimentation (Figs. 7b,d). The essential difference between NoSedimentation and NoSedimentation–NoLH is that potential temperature is the conserved and well-mixed field in the mixed layer in the absence of latent heating (as opposed to equivalent potential temperature when latent heating is allowed). This causes temperatures to be colder in the cloud layer, which reduces the saturation vapor pressure, reducing and increasing . In both NoSedimentation and NoSedimentation-NoLH, the increase in radiative cooling rates that results from the increase in LWP occurs primarily in the transition layer and does not increase TKE in the mixed layer relative to NoIce. Removing latent heating has almost no impact on water fluxes in the mixed layer.

2) Effect of ice (Control)

(i) Water fluxes

The initial conditions in Control specify increased moisture below the mixed layer. Therefore, the advective flux at the mixed-layer base is positive (i.e., upward into the mixed layer). Fluxes of moisture into the mixed layer due to sedimentation at mixed-layer top and entrainment at mixed-layer base and top are compensated by the sink due to ice-phase precipitation at the mixed-layer base. As a result, TWP stabilizes in Control but continues to grow in NoIce (Fig. 3). Including the ice phase increases precipitation because ice hydrometeors grow to precipitation size quickly through vapor deposition via the WBF mechanism and ice can persist below liquid cloud base (since saturation vapor pressure over ice is lower than over liquid). Sublimation of ice precipitation moistens the surface layer and lower portion of the mixed layer. Thus, precipitation has the effect of transporting from the top portion of the cloud layer to the surface layer and lower portion of the mixed layer (Figs. 4b, 5a).

It is important to note that is clearly not well mixed throughout the mixed layer when ice is allowed to form (Fig. 4b). This fact can also be deduced by noticing that the total flux for Control is clearly not linear in the mixed layer, as required for flux convergence to maintain a height-independent profile. When ice processes are allowed, liquid water plus vapor is well mixed in the cloud layer but not in the subcloud layer owing to deposition in the upper half of the subcloud layer, sublimation in the lower half, and the fallout of ice.

In the NoIce cloud layer away from the cloud top and base, condensation almost balances evaporation, and net horizontally averaged latent heating is a weak cooling. Latent heating is also small within the cloud layer in Control owing to a balance between net cooling from liquid processes and depositional warming associated with the WBF process (e.g., Korolev and Mazin 2003; Fig. 6b), that is, the depletion of due to the growth of ice and snow is balanced by increased evaporation. At the cloud-layer base, allowing ice to form causes condensation in updrafts to exceed evaporation in downdrafts (Fig. 6b).

Similar to nested WRF simulations of the same case (Solomon et al. 2011), turbulence advects upward from the liquid water content maximum into the inversion. This is balanced in part by the downward turbulent advection of from cloud top to the liquid water content maximum and the upward turbulent advection of to the liquid water maximum from below. Therefore, turbulent downgradient transport of and results in detrainment of liquid water into the temperature inversion and convergence of at the liquid water content maximum, promoting further condensation. The transport of cloud water above the mixed-layer top does not cause a buoyancy reversal because of the small jump at the temperature inversion base (de Roode and Wang 2007). The increase (decrease) in () due to subsidence below cloud top (in the inversion) opposes tendencies due to turbulent downgradient transports. In Control, turbulent fluxes oppose but do not exceed the precipitation flux, resulting in a net −1 × 10⁻³ g m⁻² s⁻¹ flux at the mixed-layer top; that is, there is a net downward flux of into the mixed layer from above (Fig. 5e).

(ii) MSE fluxes

Radiative fluxes at cloud top and base are similar for Control and NoIce because, although NoIce has more condensate (resulting in a larger flux jump at cloud top), Control is warmer (seen as a larger flux within cloud) and has smaller droplets (not shown). As a result, radiation cools the mixed layer of both simulations roughly equally (Fig. 5b). Total MSE fluxes are roughly linear across the mixed layer (as required for MSE in this region to remain independent of height), though Control exhibits slight deviations because MSE is not conserved during freezing (Fig. 5f).

(iii) Buoyancy fluxes

As demonstrated in NoSedimentation–NoLH, latent heating is playing a limited role in driving buoyancy fluxes in these simulations. However, including ice processes causes a reduction in buoyancy fluxes in the subcloud layer and a larger jump at the cloud-layer base (Fig. 6a) owing to the increase in condensation in updrafts relative to evaporation in downdrafts at cloud base (Fig. 6b).

b. Impact of removing the humidity inversion

Figure 8 shows the evolution of LWP and IWP for Control and the three sensitivity simulations defined in section 4 with reduced above and/or below the cloud-driven mixed layer. It is seen that the simulation where air above the mixed layer has specific humidity reduced to 0.5 g kg⁻¹ (DryAbove) diverges from Control after approximately 5 min; that is, it diverges after subgrid-scale turbulence (and numerical mixing associated with large-scale subsidence) has mixed dry air downward but before resolved turbulence has developed. This divergence so soon after initialization is due to the evaporation of cloud water at cloud top and reduction of condensational warming throughout the cloud layer, seen clearly in Fig. 9. This process causes the cloud top to be capped by the temperature inversion. However, evaporation of cloud water in the cloud-top region tends to moisten the dry inversion such that eventually it becomes moist enough to support cloud formation.

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Evolution of liquid water path (solid line) and ice water path (dashed line) from Control (black), DryAbove (blue), DryBelow (green), and DryAbove&Below (magenta) runs (g m⁻²). Note Control and DryAbove diverge after ~5 min, Control and DryBelow diverge after ~50–60 min, and DryAbove and DryAbove&Below diverge after ~40–50 min.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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Cloud-layer structure in (a)–(c) Control and (d)–(e) DryAbove at 5 min (i.e., before resolved turbulence develops): (a),(d) (g m⁻³); (b),(e) theta tendency due to microphysics (K day⁻¹); (c),(f) total diabatic heating tendency (K day⁻¹). Contours show isotherms in degrees Celsius.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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1) Quasi-equilibrium state

DryAbove reaches quasi-equilibrium after 9 h. In this quasi-equilibrium-state LWP in DryAbove is within 6% of Control while IWP is significantly less than Control (~30%). IWP in DryAbove continually increases until ~19 h while IWP in Control continually decreases after peaking at 5 h, resulting in similar TWP by 20 h. Also, while the cloud base height is essentially stationary in Control, the cloud base in DryAbove descends at a rate of 0.08 m s⁻¹ as increased TKE (Fig. 10b) allows the mixed layer to tap more effectively into the moisture source below mixed-layer base.

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Horizontally averaged profiles from Control (black) and DryAbove (blue) averaged over hours 9–10 using minute output: (a) buoyancy flux (K m s⁻¹), (b) TKE (m² s⁻²). Latent heating (K s⁻¹) averaged (c) in updrafts and (d) in downdrafts. Dashed lines indicate top and bottom of the mixed layer. Dash–dotted lines indicate extent of the cloud liquid water layer.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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By 9 h the inversion layer in DryAbove has moistened relative to the overlying air, with a weak humidity inversion forming just below cloud top (Fig. 11d). As a result, the cloud layer extends into the inversion with maximum liquid water content at the mixed-layer top, similar to Control (Fig. 11c). This moistening of the inversion in DryAbove during the adjustment to the quasi-equilibrium state causes a larger decrease in MSE and by 9 h in DryAbove compared to Control (Figs. 11a,b) because of larger upward fluxes into the inversion. We hypothesize that the weak inversion strength in the current simulations allows moisture to escape the mixed-layer top. Tjernström and Graversen (2009) found that weak elevated inversions (2–8 K) dominate in springtime over Arctic sea ice.

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(a)–(d) As in Fig. 4, but for Control (black) and DryAbove (blue) averaged over hours 9–10. (e) DryAbove resolved eddy advective water tendencies at cloud top (g m⁻³ s⁻¹, is dash–dotted line and is solid line). (f) (g kg⁻¹).

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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2) Water fluxes

The impact at mixed-layer top of reducing overlying is a small reduction in precipitation flux due to decreased (Fig. 12a) and a large increase in the upward advective flux owing to entrainment bringing down dry air from above (Fig. 12c). Similarly, the precipitation flux decreases and upward advective flux increases at the mixed-layer base. Therefore, even though the total mixed-layer flux is downward in Control and upward in DryAbove, the mixed-layer tendencies (flux divergence of Fig. 12e) are both negative, with the magnitude of DryAbove tendencies 54% larger than Control. It is interesting to note that the mixed-layer total flux deviates from a constant slope in the upper 50–100 m of the mixed layer, resulting in larger drying tendencies because of precipitation flux divergence near the mixed-layer top.

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As in Fig. 5, but for Control (black) and DryAbove (blue) averaged over hours 9–10.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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The weak humidity inversion is maintained in DryAbove by a downgradient transport of from mixed-layer top to cloud top, which evaporates, that is almost compensated by a downgradient transport of from cloud top to mixed-layer top, which condenses (Fig. 11e). However, transport of dry air aloft downward at and above cloud top by mean subsidence causes a reduction in above the liquid water content maximum. In addition, less ice is produced in DryAbove owing to a reduction in (Fig. 11f). By hours 18–19, both LWP and IWP are similar for the two runs, although they reached this state via different pathways.

3) MSE fluxes

Both radiation and turbulence contribute to an increased upward moist static energy flux through the top of the mixed layer in DryAbove compared to Control (Figs. 12b,d,f). Radiative flux increases over Control because of overlying air having a higher (colder) effective longwave emission level under drier conditions (Caldwell and Bretherton 2009). Advective MSE flux at mixed-layer top increases primarily owing to an increase in the turbulent transport of MSE (Fig. 12d) resulting from increased TKE (Fig. 10b). At mixed-layer base DryAbove and Control have similar weakly positive radiative and MSE fluxes. The net result of reducing in the inversion in DryAbove is to produce larger negative MSE tendencies in the mixed layer and larger positive MSE tendencies in the inversion.

4) Buoyancy fluxes

Because entrainment drying in DryAbove is stronger than in Control, evaporative cooling is enhanced in downdrafts (Figs. 12c,d). As mentioned before, drier overlying air also makes radiative cooling at the mixed-layer top stronger (Fig. 12b). These factors result in larger buoyancy fluxes in DryAbove than Control, producing significantly larger TKE (Fig. 10b). Evaporative cooling of entrained air is visible in Figs. 10c and 10d as negative spikes near cloud top. Despite this enhancement and larger TKE, inversion-base entrainment is weaker (evident by a lower mixed-layer top) because the mixed layer is colder and, hence, the inversion is more stable to erosion by entrainment compared to Control.

c. Impact of reducing surface-layer moisture sources

Reducing specific humidity below the cloud-driven mixed layer (DryBelow) causes LWP to divergence from Control after ~50 min (Fig. 8), that is, after resolved turbulence develops and air from below the mixed layer is entrained into the cloud system. This reduces condensational warming in updrafts, which damps buoyancy fluxes and decreases cloud-top TKE. Weaker radiative cooling in DryBelow may also contribute to the weaker TKE and buoyancy fluxes within the cloud layer. Note that this divergence occurs before ice processes are allowed to begin.

1) Quasi-equilibrium state

In DryBelow, a quasi-equilibrium state is reached when the rate of ice production slows, after which both IWP and LWP continually increase at a rate less than 0.4 g m⁻² h⁻¹. In the quasi-equilibrium state at 9 h, DryBelow and Control have similar (within 15%) , cloud-top height, and cloud-base height, but IWP is smaller in DryBelow by 50% (Figs. 8, 13c). The magnitude of the quasi-equilibrium MSE fluxes is slightly larger for Control, but the DryBelow and Control tendencies are similar (within 20%).

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As in Fig. 4, but for Control (black) and DryBelow (green) averaged over hours 9–10.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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2) Water fluxes

In DryBelow and Control, downward precipitation flux exceeds upward advective flux at mixed-layer top, resulting in negative fluxes with similar values (Fig. 14c). However, in the subcloud layer is reduced in DryBelow due to the entrainment of dry air at the base of the mixed layer (Figs. 13d, 14b). This causes less ice to be produced in DryBelow. The reduction in ice production in DryBelow causes less precipitation flux through the mixed-layer base (Fig. 14a), resulting in a negative total flux across the mixed-layer base in DryBelow that is 50% smaller than Control. As a result, Control has a larger mixed-layer drying tendency than DryBelow (Fig. 15b), even though DryBelow is entraining drier air from the surface layer.

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Horizontally averaged profiles from Control (black) and DryBelow (green) averaged over hours 9–10 using minute output. Water fluxes: (a) precipitation flux, (b) advective water flux (resolved + subgrid + subsidence), and (c) total water flux [=(a) + (b), (g m⁻³ m s⁻¹)]. Dashed lines indicate top and bottom of the mixed layer, and shading indicates extent of the cloud liquid water layer.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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Horizontally averaged profiles from Control (black) and DryBelow (green) averaged over hours 9–10 using minute output: (a) buoyancy flux (K m s⁻¹) and (b) MSE tendency (dashed lines, K day⁻¹) and tendency (solid lines, g kg⁻¹ day⁻¹), calculated using difference over 3 h. In (a), dashed lines indicate top and bottom of the mixed layer and shading indicates extent of the cloud liquid water layer.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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3) Buoyancy fluxes

Drying the bottom of the mixed layer reduces buoyant enhancement of updrafts and downdrafts by latent heating, reducing the buoyancy flux (Fig. 15a). As a result, mixed-layer-top entrainment decreases relative to cloud-top radiative cooling (evident as a reduction in inversion height in Fig. 15). This causes subcloud buoyancy flux to increase.

d. Decreasing moisture sources above and below the mixed layer

Figure 8 clearly shows that reducing moisture aloft or in the surface layer impacts the evolution of the cloud system, yet these two cases reach a similar quasi-equilibrium state to Control, with LWPs within 9%. However, Fig. 8 also shows that, when dry air is entrained from both above and below (DryAbove&Below), the cloud system never reaches a quasi-equilibrium state and slowly decays at a rate of dLWP/dt = −0.3 g m⁻² h⁻¹. In addition, there is no loss of moisture because of precipitation to the surface. Thus, in DryAbove&Below the steady decline of the cloud system (decreasing LWP and IWP) is due to the steady detrainment of moisture above and below the cloud and a very small precipitation flux across the mixed-layer base that evaporates before reaching the surface. It is interesting to note that the cloud system does not reach a threshold during the 20-h simulation, where turbulence cannot maintain the production of , causing the cloud system to collapse.

Comparing DryAbove&Below to DryAbove at 9 h (Fig. 16), it is clear that the cloud layer thins when surface-layer moisture is reduced (Figs. 16a,b). The thinning in DryAbove&Below is due to the dominance of subsidence drying over weak turbulent transports at cloud top, which lowers the cloud top, and enhanced evaporation in downdrafts and reduced condensation in updrafts at cloud base (owing to the relatively dry air below cloud base), which prevents the cloud base from moving downward. The dry air below cloud base in DryAbove&Below causes net latent heating at cloud base to be a cooling, while in DryAbove it is a warming. In DryAbove, the upward turbulent transport of to cloud top, which evaporates, moistens the inversion and limits the downward movement of the cloud top. Enhanced evaporative cooling in downdrafts in DryAbove&Below produces eddy circulations with velocities similar to DryAbove (Fig. 16c), despite having significantly reduced , production of ice/snow, and buoyancy fluxes in the cloud layer (Figs. 16a,d).

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Horizontally averaged profiles from DryAbove (blue) and DryAbove&Below (magenta) averaged over hours 9–10 using minute output: (a) (g kg⁻¹), (b) (g kg⁻¹, initial profiles shown with dashed lines), (c) downdraft velocity (cm s⁻¹), (d) buoyancy flux (K m s⁻¹), (e) total water flux (g kg⁻¹), and (f) total MSE flux (K m s⁻¹). Dashed lines indicate top and bottom of the mixed layer. Shading indicates extent of the cloud liquid water layer.

Citation: Journal of the Atmospheric Sciences 71, 2; 10.1175/JAS-D-13-0179.1

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LWP in DryAbove&Below is 80% smaller than DryAbove at 9 h (Fig. 8). The more rapid decrease in LWP in DryAbove&Below (after an initial adjustment) is due to an integrated positive tendency in the portion of the cloud layer that extends into the mixed layer being smaller than the integrated negative tendency in the portion of the cloud layer that extends into the inversion, whereas in DryAbove the opposite relationship is found (results not shown). In spite of these differences in the cloud layer, the two runs have similar negative mixed-layer and MSE tendencies at the time analyzed (Figs. 16e,f). The negative mixed-layer tendency in DryAbove is due to a moistening of the inversion and a weaker moistening of the base of the mixed layer, while in DryAbove&Below it is due to a drying of the cloud layer and a moistening of the surface layer. Therefore, even though the tendencies are similar, the impact of this tendency in DryAbove is to maintain the cloud layer, while the impact in DryAbove&Below is a continuous weakening of the cloud layer.

6. Summary and discussion

In this study, we used a series of idealized large-eddy simulations to quantify the relative impact of cloud top and subcloud-layer sources of moisture on the microphysical–radiative–dynamical feedbacks in an Arctic mixed-phase stratocumulus cloud system, focusing on a case derived from observations of a persistent single-layer AMPS cloud deck during ISDAC. Moisture and moist static energy budgets were used to examine the potential impact of ice in mixed-phase clouds, humidity inversions coincident with temperature inversions as a source of moisture for the cloud system, and the presence of above the mixed-layer top.

In this study, AMPS were found to have remarkable insensitivity to changes in moisture source. When the overlying air is initially dried, radiative cooling and turbulent entrainment increase moisture import from the surface layer. When the surface layer is initially dried, reduction in mixed-layer and a moistening of the surface layer evolve to reduce the loss of water through precipitation and entrainment. As a result, the total condensed water is found to be similar for all three cases. Only when moisture is cut off both above and below the mixed layer does the AMPS consistently decay without reaching a quasi-equilibrium state. These results demonstrate that AMPS can persist in the absence of surface sources of moisture, even in the absence of a total water inversion coincident with a temperature inversion. These results are due in part to the relatively weak temperature inversion, which allows for detrainment of into the inversion.

A number of specific cloud processes were examined here to determine their roles in the moisture and MSE budgets. The inclusion of ice processes was found to

1. lead to a quasi-equilibrium state with constant TWP;

2. diminish by the WBF mechanism [since MSE in the mixed layer decreases at the same rate in NoIce and Control, the cloud layer in Control has similar (same saturation vapor pressure) but less liquid water];

3. decrease cooling rates in the subcloud layer owing to similar MSE tendencies and increased depletion of by the growth of ice;

4. create a moisture sink at the mixed-layer base due to precipitation;

5. redistribute in the subcloud layer, moving vapor from the base of the cloud layer to the lower subcloud and surface layers;

6. maintain cloud-base height by causing the cloud system to descend slower owing to the WBF mechanism;

7. lead to diminished buoyancy flux, primarily in the subcloud layer, and TKE because of less evaporation in downdrafts, primarily due to depositional warming associated with ice processes.

1. moisten the inversion by detraining cloud water and evolve into a quasi-equilibrated state with similar LWP (and less IWP) to Control;

2. increase MSE and radiative fluxes at mixed-layer top, causing the mixed layer to cool faster;

3. increase turbulence (in spite of slightly decreasing LWP) owing to increased radiative fluxes and enhanced evaporation (condensation) in downdrafts (updrafts);

4. reduce in the mixed layer;

5. slow the growth of ice mass and precipitation;

6. cause the mixed layer and cloud-layer base to descend and deepen faster;

7. lead to cloud maintenance via transport of from below the mixed layer.

Removing the moisture source below the cloud was found to

1. reduce the buoyancy jump at the cloud-layer base by reducing condensation in updrafts;

2. reduce the negative tendency in the mixed layer;

3. produce less ice due to lower humidity in the subcloud layer;

4. produce a quasi-equilibrated state with similar LWP (and less IWP) to Control.

The simulations of Arctic stratocumulus presented in this paper differ from liquid-only subtropical stratocumulus in that cloud-top radiative cooling is not collocated with the mixed-layer top in these Arctic simulations. Because the inversion layer is strongly stable, buoyancy flux between cloud top and mixed-layer top remains negative, preventing radiative-cooling-induced turbulence from incorporating inversion-zone cloud into the mixed layer. Also, a positive subcloud buoyancy flux in the current simulations suggests that separation between the inversion and cloud top reduces the efficiency with which turbulence generation is translated to entrainment of warm overlying air. Existent entrainment parameterizations assume mixed-layer and cloud top are collocated [see discussion in Stevens (2002)], so they may not be appropriate for AMPS. Modifying existent parameterizations to account for balances in AMPS detailed in this paper is interesting future work.