Abstract

Marine boundary layer (MBL) cloud morphology associated with two summertime cold fronts over the eastern North Atlantic (ENA) is investigated using high-resolution simulations from the Weather Research and Forecasting (WRF) Model and observations from the Atmospheric Radiation Measurement (ARM) ENA Climate Research Facility. Lagrangian trajectories are used to study the evolution of post-cold-frontal MBL clouds from solid stratocumulus to broken cumulus. Clouds within specified domains in the vicinity of transitions are classified according to their degree of decoupling, and cloud-base and cloud-top breakup processes are evaluated. The Lagrangian derivative of the surface latent heat flux is found to be strongly correlated with that of the cloud fraction at cloud base in the simulations. Cloud-top entrainment instability (CTEI) is shown to operate only in the decoupled MBL. A new indicator of inversion strength at cloud top that employs the vertical gradients of equivalent potential temperature and saturation equivalent potential temperature, which can be computed directly from soundings, is proposed as an alternative to CTEI. Overall, results suggest that the deepening–warming hypothesis suggested by Bretherton and Wyant explains many of the characteristics of the summertime postfrontal MBL evolution of cloud structure over the ENA, thereby widening the phase space over which the hypothesis may be applied. A subset of the deepening–warming hypothesis involving warming initially dominating over moistening is proposed. It is postulated that changes in climate change–induced modifications in cold-frontal structure over the ENA may be accompanied by coincident changes in the location and timing of MBL cloud transitions in the post-cold-frontal environment.

1. Introduction

Marine boundary layer (MBL) clouds exhibit a seemingly endless array of complex configurations and cover a large fraction of Earth’s oceans. They are seminal components of the planetary radiation budget that act to cool the ocean surface and are potentially susceptible to global climate change. An extensive and variable MBL cloud system is present over the eastern North Atlantic (ENA) that undergoes a morphological transition with latitude. Clouds over the northern reaches of the ENA tend to be layered while those to the south tend to be more broken. Conceptual models of this cloud transition depict reductions in inversion strength and increasing sea surface temperatures toward the intertropical convergence zone accompanying the evolution to broken cloud structure. These large-scale changes in the upper and lower boundary conditions of the MBL are related to the semipermanent subtropical high pressure systems that are part of the Hadley circulation. Changes in the location or function of the ENA cloud transition region in response to anthropogenic warming would likely impart significant changes in the regional and planetary radiation budgets (Bretherton et al. 2013).

Stratocumulus, shallow cumulus, and complex combinations of these cloud types, often exhibiting mesoscale organization, are present in the transition MBL cloudiness over the ENA. Several studies have detailed the MBL cloud morphology, thermodynamic environment, and precipitation during the summertime (Albrecht et al. 1995; Miller and Albrecht 1995; Wood 2005; Dong et al. 2014a,b; Wood et al. 2015; and others), while additional studies have examined the basic life cycle of clouds through the transition process (Bretherton and Pincus 1995; de Roode and Duynkerke 1997; Bretherton et al. 1999; and Lloyd et al. 2018). Changes in cloud morphology over the ENA are often related to a process known as decoupling (Nicholls 1984), whereby the MBL comprises two layers separated by an intermittent, weak inversion: a moist subcloud layer immediately above the ocean surface and a cloud layer above capped by the marine inversion (Albrecht et al. 1995). A deepening–warming decoupling process first proposed by Bretherton and Wyant (1997, hereafter BW97) is thought to be a key initiator of the transition from a sheet of stratocumulus to more broken cloud structures. According to this hypothesis, the cloud-base buoyancy flux increases in proportion to latent heating, while the MBL average buoyancy flux does not, leading to decoupling. At the onset of decoupling and the transition in cloud structure, the lifting condensation levels (LCLs) in updrafts and downdrafts gradually diverge and the cloud layer dries.

Past modeling studies have employed 1D mixed-layer models (Schubert et al. 1979; Wakefield and Schubert 1981; Nicholls 1984; Albrecht 1984; BW97), and 2D eddy-resolving models (Moeng and Arakawa 1980; Krueger et al. 1995; Wyant et al. 1997) to investigate marine stratocumulus cloud transitions and the role of decoupling in the transition process. Some of the earliest regional simulations included a two-layer, 1D model of the stratocumulus transition, which produced a regional gradient in the cloud structure (Wang et al. 1993), and a mesoscale model with 5-km horizontal resolution that was used to test cloudiness parameterizations (Mocko and Cotton 1995). Regional simulations designed to test the impacts of drizzle and microphysics on mesoscale organization showed that mesoscale structures were created in simulations using 2-km horizontal resolution when many physical processes were resolved, especially those involving drizzle production, but not when the resolution was increased to 18-km and parameterizations were required (Mechem and Kogan 2003). A regional simulation using a mesoscale model with a resolution compatible with current climate models (60 km), which used MBL turbulence and shallow convection parameterizations, was able to successfully simulate the stratocumulus to cumulus transition (Bretherton et al. 2013; McCaa and Bretherton 2004). A key finding of this study was that shallow convection scheme was required to faithfully reproduce the stratocumulus to cumulus transition. A later study demonstrated that mesoscale models with coarser resolution are sensitive to the parameterization of shallow convection and to the parameterization of penetrative mixing at the top of the cumuli, which acts to deepen the trade inversion (Bretherton et al. 2004). Sensitivities in the representation of cloud-top entrainment were also reported in another regional study (Wang et al. 1993).

Cascading cold-frontal cloud bands are integral components of the ENA transition region and are observed in all seasons (Reed 1960; Giangrande et al. 2019). Cold fronts in this region have higher average maximum and minimum integrated water vapor contents than North Pacific fronts in the summertime, a difference that can be attributed to higher sea surface temperatures and, consequently, higher evaporation and moisture flux in the region (McMurdie and Katsaros 1991). A recent study by Naud et al. (2018) documented the climatology of post-cold-frontal conditions over the ENA associated with 77 cold-frontal passages, 15 of which occurred during the summertime. They reported that “post-cold frontal periods (including all seasons) were more dynamically active, drier, and more unstable” than periods that did not involve frontal passages. Naud et al. (2018) also found that post-cold-frontal MBL clouds are deeper, colder, and have higher cloud tops, and possess higher liquid water paths than non-post-frontal clouds. Cloud depth was suggested in their study to be more dependent upon surface forcing than to inversion strength when winds were northerly. Another finding in their study was that the air–sea temperature gradients in post-cold-frontal situations likely enhance cloud liquid water path and that the weaker inversions and deeper MBLs that are observed in these environments tend to be more decoupled.

These studies motivate us to investigate the applicability of the BW97 deepening–warming hypothesis in the context of MBL cloud transitions often observed in satellite images behind cold fronts in the ENA region. We examine the life cycle of MBL clouds associated with two summertime cold fronts that moved through the ENA region. High-resolution, large-domain simulations using the Weather Research and Forecasting (WRF) Model are used to produce a Lagrangian time series of the MBL cloud evolution in two postfrontal cases over periods of several tens of hours. Remote and in situ data from the ENA site are used to evaluate the results of these simulations.

The goal of this study is to improve understanding of the decoupling process and its impact on MBL cloud morphology in summertime post-cold-frontal air masses traversing the eastern North Atlantic and beyond. Another goal is to determine if the deepening–warming hypothesis can be used to explain MBL cloud transitions in post-cold-frontal air masses. One particular focus is the feedback between decoupling and the surface latent heat flux, which is thought to be a driver of the transition process in the deepening–warming schema. In addition, the simulations presented herein do not employ a shallow convective parameterization and are thus intended to reduce uncertainties associated with lower-resolution models that require such a parameterization. Convection arises in a grid cell in our simulations primarily as a consequence of the interactions between the subgrid-scale turbulence and surface flux parameterizations, which are driven by the external conditions supplied to the cell. The cloud fraction reported at each height in each grid cell ranges from zero to one. If the cloud fraction is one at a given height, we view the convection as being “explicitly resolved” at that height, but if it is less than one the subgrid-scale structure of the convection is determined by the turbulence scheme and is not explicitly resolved. Many convective clouds over the ENA and in the MBL in general have dimensions that are smaller than the 1350-m horizontal resolution and ~100-m vertical resolution used in our simulations and would require large-eddy simulations with scales on the order of 100 m or less to fully resolve. The simulations presented herein straddle the mesoscale–LES model continuum, so MBL turbulence including the mixing process at cloud top must still be parameterized. Finally, the simulations are compatible with measurements of transition structure using cloud remote sensing technology deployed at ENA on scales of many days. This synergism provides a means to evaluate the results of the transition simulations at a single location.

2. Methods and tools

Two principal resources are utilized in this study: data collected using the suite of sensors deployed at the ENA site and the WRF Model. These tools are described in the sections that follow.

a. Observations from ENA

Observations used in this study were collected at the Atmospheric Radiation Measurement (ARM) ENA Climate Research Facility located on Graciosa Island in the Azores archipelago (39°5′29.76″N, 28°1′32.52″W). This location and much of the instrumentation are described in Wood et al. (2015). Data from the surface meteorology station (SMET) are used to characterize the chronology of the surface temperature, relative humidity, pressure, and winds that are compared with output from the WRF Model. The SMET sensors are mounted on a 10-m mast and include a Vaisala Model HMP45-D temperature and relative humidity probe, a digital barometer, Vaisala Model PTB201A, and two R. M. Young Model 05106 wind monitors that consist of a propeller anemometer and a wind vane. The ENA site is also equipped with a Doppler lidar (DL) that detects aerosol backscatter and uses it to measure the Doppler velocity with an accuracy of 10 cm s−1. The DL operates in the near-IR (1.5 μm) and transmits laser pulses with a range resolution of 30 m, a maximum measurement range of 9600 m, and a temporal resolution of about 1 s. When the DL pulse reaches the boundary of a cloud, its pulse is scattered such that it operates as a cloud-base height detector. Extremely thin clouds may allow the laser pulse to transmit through without being decimated thereby enabling additional cloud boundary detection above. Two minute averages of instantaneous vertical velocity measured by the DL that are centered on the half-hour output times of the WRF Model are used in this study.

A Ka-band, zenith-pointing radar (KAZR) operating at λ = 8.0 mm detects hydrometeors to a height of 18 km with an initial measurement height of 72 m. A profile of cloud location and hydrometeor Doppler vertical velocity is collected every 2 s in all but heavy precipitation when its beam is attenuated by liquid water absorption. When a cloud is drizzling and the droplet spectrum is bimodal, the Doppler velocity becomes ambiguous unless spectral processing techniques are applied. These techniques may, at times, introduce considerable uncertainty in the estimation of the Doppler velocity of cloud droplets, so in-cloud KAZR measurements of the in-cloud vertical velocity are not used in this study. The KAZR data are used to compute the average, height-dependent cloud fraction over 30-min averaging interval.

b. WRF configuration

Simulations were performed using WRF-ARW, version 4.0 (Skamarock et al. 2008), on NCAR’s Cheyenne supercomputer (Computational and Information Systems Laboratory 2017). Two domains centered on Graciosa Island in the Azores have been constructed using NOAA Earth System Research Laboratory’s WRF Domain Wizard, version 2.84 (NOAA 2013) (Fig. 1). Analysis and 3-h forecast data from NCEP GDAS/Final (FNL) 0.25° global tropospheric analyses and forecast grids (GDAS 2015) were used as input to WRF Preprocessing System (WPS). A horizontal resolution of 4050 m was chosen for the parent domain, which produces a downscaling ratio of approximately 1:5. A parent-to-nest grid ratio of 1:3 equates to a horizontal resolution of the second domain of 1350 m. Both simulations were run for 72 h (0000 UTC 17 July to 0000 UTC 20 July 2017, and 0000 UTC 29 July to 0000 UTC 1 August 2018) to capture the passage of the cold fronts, as well as the post-cold-frontal episodes downwind of the Aerosol and Cloud Experiment—Eastern North Atlantic (ACE-ENA) site. The model outputs used in this study are from the second domain, which were written out every 30 min.

Fig. 1.

Two domains centered on ACE-ENA site on Graciosa Island in the Azores, Portugal (39.1°N, 28°W), with horizontal resolutions of 4050 and 1350 m and 750 × 750 and 1050 × 1050 grid points, respectively. The domains were set using NOAA Earth System Research Laboratory’s WRF Domain Wizard, version 2.84.

Fig. 1.

Two domains centered on ACE-ENA site on Graciosa Island in the Azores, Portugal (39.1°N, 28°W), with horizontal resolutions of 4050 and 1350 m and 750 × 750 and 1050 × 1050 grid points, respectively. The domains were set using NOAA Earth System Research Laboratory’s WRF Domain Wizard, version 2.84.

The dimension of the parent domain was chosen such that its center is approximately 1500 m from each edge following Lamraoui et al. (2018) to improve the timing of the passage of fronts and their strength. Hence the domains have sizes of 750 × 750 and 1050 × 1050 horizontal grid points, respectively. In addition, 82 vertical levels were designated such that the vertical grid spacing in the first 1 km is initially 15 m and becomes much larger beyond this point up to 50 hPa. Thus 41 levels are located in the lowest 3 km (~700 hPa). To satisfy the Courant–Friedrichs–Lewy (CFL) criterion, time steps of 15 and 5 s were used for the two domains, respectively, since the recommended time step is about 6 times the respective domain’s resolution (km).

c. Parameterizations used in WRF

The focus of the WRF simulations was the life cycle of marine stratocumulus in the post-cold-frontal environment. To achieve the best possible representation of the observed conditions, various combinations of parameterizations and dynamic options were tested. Given the computational resources available at the time, the combination of the following options rendered the closest results to the satellite images and observation data from the site for the aforementioned periods. The following paragraphs describe the parameterizations used in this study.

The cloud microphysics scheme used in the simulations was the Thompson aerosol-aware cloud parameterization (Thompson and Eidhammer 2014). This scheme provides an aerosol climatology dataset of monthly averaged aerosol variables (organic carbon, black carbon, sea salts, sulfates, and dust) from a 7-yr simulation with Goddard Chemistry Aerosol Radiation and Transport (GOCART). The Rapid Radiative Transfer Model for GCMs (RRTMG), which is a new version of RRTM (Iacono et al. 2008), was used in the longwave and shortwave radiation calculations.

Mellor–Yamada–Nakanishi–Niino, level 3 (MYNN3) (Nakanishi and Niino 2006, 2009), was adopted as the planetary boundary layer (PBL) parameterization. This PBL scheme is based on the Mellor–Yamada model (MY) (Mellor and Yamada 1974, 1982), both of which are prognostic turbulent kinetic energy (TKE) schemes. The other PBL parameterization in WRF that predicts TKE values is the Mellor–Yamada–Janjić (MYJ) (Janjić 1994). Huang et al. (2013) used WRF in single-column mode to conduct three case studies over subtropical oceanic regions to assess the performance of various PBL schemes. Included in their study were the MYNN and MYJ parameterizations and the results were evaluated according to their ability to represent stratocumulus and shallow cumulus clouds when compared to LES data from those regions. Their study concluded that in all three cases, MYNN better simulated vertical profiles of liquid water and potential temperature than MYJ. The following optional settings in MYNN3 were also utilized: TKE advection, stochastic eddy diffusivity mass flux (StEM) (Sušelj et al. 2013), momentum and TKE transport in mass flux scheme, a modified cloud-scale mixing length (Ito et al. 2015), and cloud-top radiational cooling contributing to TKE production.

The land surfaces on the islands were parameterized using the unified Noah land surface model (Tewari et al. 2004), and since MYNN3 was used as the PBL scheme, the MYNN surface layer was required. Since the duration of the simulations were not long enough (on the order of months or years), time-varying data such as monthly albedo values, sea surface temperature (SST), and vegetation fraction were unnecessary and these fields remained constant and equal to their input values throughout the simulation period. Finally, the resolution of the parent domain was fine enough to explicitly resolve deep convection (<10 km), so no cumulus parameterization was necessary.

d. Identifying fronts

We initially identified potential frontal passages in the vicinity of the Azores and at the ENA site using MODIS/Aqua satellite images from NASA Worldview for the summers of 2017 and 2018. The two shown in Fig. 2 were chosen as potential cold-front examples for our study because of their distinct frontal cloud structures advancing south around a low pressure system. The first of these cases, 17 July 2017, occurred during ACE-ENA, which adds to usefulness of these simulations for future studies because the Gulfstream-1 aircraft sampled the postfrontal cloudiness. Next, surface meteorological data from the ENA were analyzed to detect the progression of five surface variables that would indicate a cold-front passage. Figure 3 shows the time series of surface wind speed and wind direction, pressure, relative humidity, and temperature over the ENA site. The same variables from the WRF simulations at the same location are plotted in conjunction with the ENA observations in order to compare the performance of the model.

Fig. 2.

MODIS Aqua true-color images obtained at NASA Worldview centered on Azores showing the cold front advancing from the north-west on (left) midday 17 July 2017, and (right) midday 29 July 2018. (https://worldview.earthdata.nasa.gov)

Fig. 2.

MODIS Aqua true-color images obtained at NASA Worldview centered on Azores showing the cold front advancing from the north-west on (left) midday 17 July 2017, and (right) midday 29 July 2018. (https://worldview.earthdata.nasa.gov)

Fig. 3.

Time series of (top to bottom) surface wind direction and wind speed, surface air pressure, relative humidity, and temperature over the 3-day WRF simulations during (left) July 2017 and (right) July 2018, obtained from surface meteorology data from ACE-ENA (dot–dashed blue line) and WRF (solid red line) located over Graciosa Island, Azores.

Fig. 3.

Time series of (top to bottom) surface wind direction and wind speed, surface air pressure, relative humidity, and temperature over the 3-day WRF simulations during (left) July 2017 and (right) July 2018, obtained from surface meteorology data from ACE-ENA (dot–dashed blue line) and WRF (solid red line) located over Graciosa Island, Azores.

Passage of cold fronts in the 2017 and 2018 cases were accompanied by a small drop in surface air temperature, which are somewhat masked by island thermal effects that are responsible for the diurnal temperature changes in the observations and the simulations. Evidence of the passage of these weak cold fronts is found in the decrease in the daytime and nighttime maximum and minimum temperatures during the first two days in the 2017 case and in the nighttime temperatures in the 2018 case. In addition, decreased relative humidity, a surface pressure minimum, and veering of the surface winds from southerly to northerly/northwesterly are observed as the fronts pass ENA. Post-cold-frontal conditions are assumed to conclude when the surface temperature, pressure and winds return to their prefrontal state. In the summer 2017 case, the leading edge of the front passed Graciosa at approximately 0200 UTC 18 July 2017, and the postfrontal region persisted until approximately 1800 UTC 19 July 2017 when an abrupt change in the wind direction signaled the onset of a new synoptic regime. Around this transition period the wind speed decreased from 6 to 2 m s−1, and winds gradually shifted from northwesterly to southeasterly. Also, surface pressure reached a minimum of about 1017.5 hPa from a prefrontal maximum of 1025.0 hPa. A corresponding decrease in surface air temperature and relative humidity can be seen around this point. However, simulated values of these two variables show a cold daytime bias that can be linked to the island effect phenomenon. The drop in measured surface relative humidity values was from 100% to a little less than 70%, while simulated relative humidity only decreased by about 20%. Surface temperature values from measurements decreased from about 26° to 20°C, whereas the simulated values dropped from 25° to a little less than 20°C.

Larger perturbations in the surface variables were observed and simulated in the 2018 case. The front reached the Azores at approximately 1800 UTC 29 July 2018 and the postfrontal environment existed until early on 31 July 2018. Winds veered as the front passed the ENA site, as expected, and a more northerly flow was observed in the postfrontal environment than was observed in the 2017 case. In association with the frontal passage in the 2018 case, wind speed changed from 9 to about 1 m s−1. Relative humidity from observed values dropped from about 90% to a little above 50%, while those from simulation decreased from 100% to 80%. Also, surface temperature decreased from 25° to 20°C and from 23° to 16°C for those obtained from measurements and WRF Model, respectively.

Overall, the WRF simulations for the two cases reasonably reproduce the surface observations of the frontal and postfrontal environments at the ENA site, as demonstrated in Fig. 3. Island effects, which have been reported in past studies from islands in this region (Miller and Albrecht 1995), are evident in the observations and in the simulations. The daytime cold bias in the temperature simulations, which also leads to increases in the surface relative humidity, is likely attributable to sampling biases because a portion of the model’s grid cell lies over the ocean. Given that WRF Model simulations did a reasonable job of reproducing surface changes associated with the passage of these weak cold fronts, we are relatively confident that the simulated frontal and postfrontal environments over the entirety of the ENA domain bear some resemblance to reality.

e. Simulated and observed MBL structure at ENA

Next we examine aspects of the observed and simulated vertical structure of the MBL. Figure 4 shows time series of the vertical structure of hydrometeor location, vertical velocities [W (m s−1)] in the column (WRF) and in the subcloud layer (ENA observations), vertical structure of horizontal velocity, and LCL over the specified 72-h periods in summer 2017 and 2018, from ENA observations and WRF simulations of conditions at Graciosa Island. The observed hydrometeor locations in the observations, shown in the first and third panels in Fig. 4, are from the KAZR and represent the fractional coverage of all hydrometeors, cloud droplets and falling precipitation. In contrast, the WRF cloud fraction includes only cloud droplets, so the black dots at cloud base flag the presence of precipitation that exceeds a rainwater mixing ratio of 0.01 g kg−1 anywhere beneath the cloud base.

Fig. 4.

Time series of vertical structure of cloud fraction, vertical and horizontal velocities, and lifting condensation level (LCL) from observation and WRF data at Graciosa Island for (left) 2017 and (right) 2018 simulations. Note that DL can measure vertical velocity W only below the cloud base.

Fig. 4.

Time series of vertical structure of cloud fraction, vertical and horizontal velocities, and lifting condensation level (LCL) from observation and WRF data at Graciosa Island for (left) 2017 and (right) 2018 simulations. Note that DL can measure vertical velocity W only below the cloud base.

Even though the simulated cloud structures are not exactly the same as those from observation data for each year, they follow a similar trend in most places along the time series. Average marine boundary layer heights (judging by the cloud-top height values) during the designated 3-day periods are deeper in WRF simulations than those observed by approximately 120 and 190 m in summer 2017 and 2018, respectively. Subcloud vertical wind velocities are considerably weaker in model simulations; however, simulated horizontal wind velocities are consistent with the observed values in both cases. Last, LCLs simulated by WRF are lower than ENA observations by 200 and 300 m on average for 2017 and 2018 cases, respectively, although their general trends are the same. This difference is due to island effects; simulated variables at grid scale over the island used to calculate LCL are biased toward conditions over the ocean, and thus are smaller than those obtained from measurements over the island because the land warms faster than the ocean surface.

In general, the simulated MBL and cloud structures produce marine boundary layer clouds and MBL structures that appear relatively similar to those observed at ENA, though some important differences are evident. Updrafts in the simulations represent gridscale vertical velocities in the subcloud layer, while the observations are 2-min averages of 1-s profiles from the DL of the vertical velocity with 30-m vertical resolution. Averaging of the DL data are necessary because the observations are not comparable on a one-to-one basis. Applying a time–space conversion, average wind speeds in the MBL for the two simulations have an upper bound of ~8–9 m s−1, so the velocity mean at each level corresponds to nearly 1000–1100-m horizontal distance, which is roughly compatible with the gridscale velocity in the simulations. This analysis suggests that vertical velocities at grid scale are considerably weaker in model simulations than those suggested by time–space conversion of the DL data, and do not demonstrate the repeating patterns of strong updrafts/downdrafts evident in the latter; however, simulated horizontal wind velocities are consistent with the observed values in both cases.

The MBL cloudiness on 18 July 2017 at ENA is thicker and less broken than the WRF-simulated structure. Similarly, MBL clouds are observed to be less broken in the 30 July 2018 case and, in addition, possess considerably more vigorous subcloud vertical velocities than those in the simulations. These observations echo a trend found in comparison with satellite images in these cases: the WRF simulations produce less MBL cloud than observed in post-cold-frontal conditions. In both cold-frontal cases, simulated low-cloudiness appears more broken than the observed structures by the time the column has reached ENA. This may be due to the deeper MBL in the simulations than observed. Nonetheless, there is enough similarity to justify a further investigation of the upstream cloud transitions in the simulations.

3. Cloud life cycle overview

In both 2017 and 2018 simulations, the cold fronts were accompanied by a solid deck of stratocumulus in their wake. As the fronts journeyed south, this stratocumulus disintegrated into fragments and gradually became transition cloudiness, which was characterized by the presence of both cumulus and stratocumulus in various combinations. To study the transition process of the boundary layer and cloud structures in the simulations, we used Flexible Particle dispersion model (FLEXPART)-WRF, version 3.3.2 (Brioude et al. 2013), to calculate forward Lagrangian trajectories initialized in the solid stratocumulus decks in 3D. FLEXPART-WRF is a free Lagrangian particle dispersion model (LPDM) that uses mesoscale meteorological output from WRF to simulate trajectories of infinitesimally small air parcels (particles) in three-dimensional space (latitude, longitude, and altitude). Hegarty et al. (2013) studied three LPDMs, including FLEXPART, Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) and Stochastic Time-Inverted Lagrangian Transport (STILT), using North American Regional Reanalysis (NARR) and a number of different WRF configurations as meteorological inputs and found all three to be competent models to compute plume trajectories. The model’s reliability has been further demonstrated in Brioude et al. (2011, 2012b), where FLEXPART-WRF is used to conduct successful simulations of pollutant transport for two case studies. Further details on FLEXPART-WRF configuration used in this study are provided in  appendix A.

The trajectories following passive air tracer particles released from a 0.02° × 0.02° domain located in the stratocumulus deck are shown in Fig. 5 for the 2017 and 2018 simulations. A prominent band of simulated cloud demarcated the leading edge of the cold front and in both cases the solid cloud layer located north of the frontal zone evolved into broken mesoscale cloud elements over a period of a few hours. The red star indicates the location of the parcel at each of the three times indicated above the respective plots and the black line depicts the trajectory that the parcel followed to reach this point. Figure 6 depicts conditions along the entirety of the Lagrangian trajectory, from start to finish, and serves as an overarching view of the conditions experienced by the parcel. Detailed mesoscale views illustrating conditions over vertical cross sections of less than 100 km in length centered at the location of the red stars and aligned with the direction of the parcel trajectory at those points are shown in Fig. 7.

Fig. 5.

Forward Lagrangian trajectories performed with FLEXPART-WRF on the (top) 2017 and (bottom) 2018 simulations. The starting point is the northernmost point, and the red star shows the location of the tracked parcel at time shown above each plot.

Fig. 5.

Forward Lagrangian trajectories performed with FLEXPART-WRF on the (top) 2017 and (bottom) 2018 simulations. The starting point is the northernmost point, and the red star shows the location of the tracked parcel at time shown above each plot.

Fig. 6.

Time series of cloud fraction, vertical and horizontal velocities, cloud-base and cloud-top heights (zb and zt, respectively), lifting condensation level (LCL), temperature at 2 m (T2), and latent heat flux from surface (LH) along trajectories shown in Fig. 5 for (left) 2017 and (right) 2018 simulations.

Fig. 6.

Time series of cloud fraction, vertical and horizontal velocities, cloud-base and cloud-top heights (zb and zt, respectively), lifting condensation level (LCL), temperature at 2 m (T2), and latent heat flux from surface (LH) along trajectories shown in Fig. 5 for (left) 2017 and (right) 2018 simulations.

Fig. 7.

Vertical cross sections of vertical velocity W, horizontal wind speed, vertical structures of cloud fraction, cloud-base and cloud-top heights (zb and zt, respectively), lifting condensation level (LCL), 2-m temperature (T2), and latent heat flux from surface (LH), centered on the red star at each time shown in Fig. 5 and aligned with the Lagrangian trajectory of the parcels at that point for (a) 2017 and (b) 2018 simulations. Cloud fraction is overlaid the first two variables [ top two panels of (a) an (b)]. Vertical axes of the first three panels in each column show the height from the surface (m), and the left and right axes of the bottom panels [in (a) and (b)] correspond to T2 (K) and LH (W m−2), respectively.

Fig. 7.

Vertical cross sections of vertical velocity W, horizontal wind speed, vertical structures of cloud fraction, cloud-base and cloud-top heights (zb and zt, respectively), lifting condensation level (LCL), 2-m temperature (T2), and latent heat flux from surface (LH), centered on the red star at each time shown in Fig. 5 and aligned with the Lagrangian trajectory of the parcels at that point for (a) 2017 and (b) 2018 simulations. Cloud fraction is overlaid the first two variables [ top two panels of (a) an (b)]. Vertical axes of the first three panels in each column show the height from the surface (m), and the left and right axes of the bottom panels [in (a) and (b)] correspond to T2 (K) and LH (W m−2), respectively.

The process of marine stratocumulus breakup is depicted in full 32-h time series of the Lagrangian cloud fraction, vertical velocity (W), vertical structure of the horizontal wind, cloud-base and cloud-top heights (zb and zt, respectively), LCL, 2-m air temperature (T2), and the upward latent flux at the surface (LH) along the trajectories in Fig. 6 for 2017 and 2018 simulations. In both cases, the solid stratocumulus decks were accompanied by weak updrafts and nearly constant LCL. Initially, the stratocumulus deck undergoes erosion at its base with time as LH and T2 rise along the trajectory. Along with these changes, the LCL increases and downdrafts appear when the deck begins to disintegrate. As the conditions become more unstable further along the trajectory as indicated by frequent fluctuations in LCL, LH, and T2, the breakup process accelerates both from below and above the cloud until the stratocumulus deck breaks into individual cloud elements. The broken cloud structure after 0730 UTC 18 July 2017 and after approximately 1400 UTC 29 July 2018 are similar, although the clouds linger for a slightly longer period in the 2018 simulation. One notable difference between the two cases is the larger LH values in 2017, which may be related to the simulated differences in postbreakup cloud structure.

Mesoscale height–distance cross sections covering distances of ~100 km for the 2017 (Fig. 7a) and 2018 (Fig. 7b) cases provide a more detailed perspective of the spatial distribution of the cloud structure immediately upstream and downstream of the tracked parcel (red star) along its path. These cross sections center on the parcel location and align with the direction of the trajectory thereby representing instantaneous moments in time at three stages of the evolution. Initially the cloud layer existed under rather quiescent conditions characterized by relatively weak vertical velocities and relatively weak wind shear for both simulations in the northernmost latitudes (leftmost column). These quiescent periods were sporadically interrupted by temporary fractures in the solid cloud deck, although, overall, stratified structures prevailed. Moving from a location upstream of the parcel to a location downstream (Figs. 7a,b), the LCL, LH, and T2 slowly rose. While it is more subtle in the 2018 simulation, the breakup of the cloud deck appeared to begin mainly from the cloud base (left panels) because it rises and cloud-base cloud fraction decreases without similar changes at cloud top.

As the column moved farther southeast, the solid cloud deck decomposed into cloudy fragments accompanied by notable disturbances in all variables (Figs. 7a,b, center column). Steadily increasing SSTs, erratic fluctuations in cloud fraction, vertical structures of wind, LCL, LH, and T2 corresponded to the destruction of the clouds both at the base and top. Columns upstream and downstream of the parcel’s location were intermittently cloudy and clear in both simulations, and mesoscale circulations were indicated by oscillations in the variables. As the column became more diluted from above and below, downdrafts became dominant, and the column became periodically decoupled from the ocean surface moisture source. Multilevel cloud layers coexisted with convective clusters in this phase of the transition process.

Almost half a day after the onset of the breakup of the stratocumulus deck, the column transitioned into widely scattered, large mesoscale cloud clusters (Figs. 7a,b, right column). These clusters contained relatively strong deep cumulus updrafts rising to nearly 1.5 km, and laterally detrained stratocumulus. These elements extend at least 300 m deeper than the broken clouds earlier along the trajectory (center column).

4. Choice of decoupling measure

Simulated postfrontal clouds experienced breakup prior to their arrival at ENA in both cases, which lead to the supposition that the simulated transition occurred too far upstream. It is of interest, therefore, to analyze the physical processes operating before and after the transition in the simulations in hopes of gaining insight into model behavior and, perhaps, the transition process itself. Past studies have documented that decoupling is an important contributor to the breakup of a solid deck of stratocumulus. BW97 attributed decoupling in subtropical cloud-topped boundary layers to negative buoyancy fluxes below cloud base that acted to suppress convection in the subcloud region. They suggested that, as the cloud moved over warmer SSTs, increased surface latent heat fluxes (or equivalently, surface moisture fluxes) accompanied by lower surface relative humidity due to cloud-top mixing were the instigators of decoupling. As the Bowen ratio decreased, the increase in the surface latent heat/moisture flux caused increased buoyancy and liquid water fluxes within the cloud proportional to the surface fluxes, and subsequently led to a cloud-base minimum in the buoyancy flux. The difference between cloud-base and in-cloud buoyancy fluxes created a stable region below the cloud, marking the onset of decoupling. As the surface latent heat flux became greater than the net in-cloud radiative cooling, the stratocumulus layer became less well mixed and drier, and the gap between the lifting condensation level and cloud base widened, a phenomenon that was referred to as “deepening warming.” To study subcloud and cloud-top processes that contributed to the breakup of the marine stratocumulus deck in the simulations and the effect of decoupling on these processes, rectangular regions that straddled the transition from solid cloud to broken cloudy patches for the 2017 and 2018 simulations shown in Fig. 8 were selected for further analysis.

Fig. 8.

Average cloud fraction over the lowest 2 km at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018. The red rectangles show the domains over which all analyses were conducted.

Fig. 8.

Average cloud fraction over the lowest 2 km at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018. The red rectangles show the domains over which all analyses were conducted.

Classifying the clouds in these regions as residing in a coupled or decoupled environment required an objective criteria. Jones et al. (2011) proposed three separate decoupling diagnostics that were tested for this purpose. The first diagnostic considers the vertical structure of the boundary layer in the context of changes in two moist-conserved variables θ and qT between the surface and inversion, where θ is the liquid potential temperature and qT, the total water mixing ratio. These definitions are

 
θθLcpq,
(1)
 
qT=q+qυ,
(2)

where θ is the potential temperature, L the latent heat of vaporization, cp the dry-air specific heat at constant pressure, and q and qυ are liquid water and water vapor mixing ratios, respectively. When the MBL is well mixed, θ and qT are approximately constant beneath the capping inversion. Conversely, vertical gradients in θ and qT are observed when the MBL is decoupled. The first decoupling diagnostic proposed by Jones et al. (2011) quantifies the vertical gradients of moisture and temperature, and is given by

 
Δq=qbotqtop,
(3)
 
Δθ=θ,topθ,bot,
(4)

where variables with subscripts “bot” and “top” are calculated as the mean over the lower and upper 25% of the boundary layer below the inversion. Note that the subscript T has been omitted in Eq. (3) and hereafter in this section. Jones et al. (2011) found profiles where Δq > 0.5 g kg−1 and Δθ>0.5K to be decoupled, based on data collected during the VAMOS Ocean–Cloud–Atmosphere–Land Study Regional Experiment (VOCALS-REx) in October–November 2008 in the MBL over the southeast Pacific.

The second decoupling diagnostic suggested by Jones et al. (2011) is a subcloud decoupling measure prescribed by the difference between LCL and cloud-base height zb, which is expressed as

 
Δzb=zbzLCL.
(5)

A smaller Δzb indicates a well-mixed boundary layer where cloud base is in close proximity to the LCL. As the boundary layer becomes more decoupled, the gap between the cloud base and LCL widens, and Δzb increases. The decoupling threshold recommended by Jones et al. (2011) is Δzb > 150 m.

The final decoupling diagnostic proposed by Jones et al. (2011) is referred to as the “mixed layer cloud thickness” and is the difference between the inversion height zi and LCL, or

 
ΔzM=zizLCL.
(6)

When the MBL is well mixed, ΔzM is equivalent to the cloud thickness. Latent heat released due to condensation within moist updrafts generates a buoyancy flux within the cloud layer. Thus, a thicker cloud layer can have larger values of vertically integrated buoyancy flux along its depth, and consequently, more in-cloud turbulence. A more turbulent cloud layer generates more entrainment, which in turn facilitates mixing of dry and warm air above the inversion with the in-cloud air mass and helps the cloud layer become decoupled from the subcloud layer. Therefore, larger values of ΔzM should correspond to more decoupled cloud layers.

The procedure used in Jones et al. (2011) was adopted to determine which of the diagnostics was best suited for use with the WRF simulations, so we tested the second and third decoupling criteria against Δq, which represented the first diagnostic. To calculate Δq, the capping inversion height zi is required. Because the capping inversion in the simulations is not sharp in most cases, two methods have been adopted to identify and cross-check zi. The first method is from Jones et al. (2011), where zi is determined as the vertical level with the minimum temperature and relative humidity of at least 45%. The second approach identifies the inversion height as the level where (d/dz)θ and (d/dz)qT are maximum, while the relative humidity is greater than or equal to 45%. The results were almost the same in both cases for both 2017 and 2018 simulations, and wherever they did not coincide, the zi from the first approach was chosen.

Figures 9 and 10 show scatterplots of Δzb and ΔzM with respect to Δq, respectively, from the rectangular domains for the 2017 and 2018 simulations shown in Fig. 8. Note that the color schemes in all scatterplots in this study reflect the density of points, with dark red and dark blue signifying the areas with the maximum and minimum point densities for each given plot, respectively. The correlation between Δzb and Δq in both 2017 and 2018 simulations is almost negligible, as seen in Fig. 9, while ΔzM exhibits a positive correlation with Δq in both cases (Fig. 10). However, no clear decoupling threshold in terms of Δzm could be determined in the data from the designated domains that would also coincide with a corresponding decoupling threshold value in Δq, which would be suitable for both simulations. The fact that the model is prescribed with discrete vertical levels for the entire atmosphere could partly explain the inefficiency of Δzb and Δzm as successful decoupling diagnostics for the model data. Cloud-base and inversion heights in the model can only be estimated in terms of fixed vertical levels and this rather crude estimation could negatively impact the ability of second and third decoupling diagnostics to successfully characterize the decoupling range. Hence, the first decoupling diagnostic suggested by Jones et al. (2011) is employed in this study.

Fig. 9.

Scatterplots of Δzb vs Δq at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Fig. 9.

Scatterplots of Δzb vs Δq at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Fig. 10.

Scatterplots of ΔzM vs Δq at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Fig. 10.

Scatterplots of ΔzM vs Δq at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Figure 11 shows the composite profiles of qT (dark blue line), θ (black line), and cloud fraction (green line) with different ranges of Δq as the decoupling measure. The dashed black and red lines are zi and LCL, respectively. To improve the visualization, 10 times the cloud fraction is plotted. To create the composites, first the profiles were interpolated over the same number of vertical levels below the LCL, between LCL and zi, and between zi and 1500 m, to ensure that LCL and zi were aligned across all profiles. The variables were then averaged across all profiles, and the vertical axis was scaled so that zi and LCL reflected mean zi and LCL values. Clouds with Δq > 2.0 and Δq > 2.1 for 2017 and 2018 simulations, respectively, exhibit a higher degree of decoupling, since qT and θ values change with height from surface to the inversion height. Those with Δq < 1.6 and Δq < 1.7, on the other hand, indicate well-mixed boundary layer conditions, judging by how qT and θ remain relatively constant in the region below the capping inversion.

Fig. 11.

Composite profiles for (a) Δq < 1.6 g kg−1 and Δq > 2.0 g kg−1 at 1800 UTC 17 Jul 2017 and (b) Δq < 1.7 g kg−1 and Δq > 2.1 g kg−1 at 1130 UTC 29 Jul 2018; qT is indicated by the navy blue line and θ by the black line. The green line shows 10 times the cloud fraction for better visualization. The inversion height zi and LCL are also shown as dashed black and red lines, respectively.

Fig. 11.

Composite profiles for (a) Δq < 1.6 g kg−1 and Δq > 2.0 g kg−1 at 1800 UTC 17 Jul 2017 and (b) Δq < 1.7 g kg−1 and Δq > 2.1 g kg−1 at 1130 UTC 29 Jul 2018; qT is indicated by the navy blue line and θ by the black line. The green line shows 10 times the cloud fraction for better visualization. The inversion height zi and LCL are also shown as dashed black and red lines, respectively.

We note that decoupling is a gradual process whereby the conditions in the boundary layer become less well mixed (i.e., the cloud element becomes less coupled, until the cloud-base and in-cloud regions form separate stable entities). Therefore, we suspect that there is no exact threshold value for distinguishing between the decoupled and coupled clouds, and we adhere to this assumption in our attempts to classify clouds in the simulations according to their coupling state. Hence, the plots designated as “coupled” and “decoupled” clouds in the following sections are not necessarily those that reside in absolutely well-mixed conditions, or are completely decoupled from the subcloud region, respectively, but rather encompass examples that fall somewhere in the decoupling range, leaning toward being more coupled or decoupled than otherwise, respectively.

With this explanation, for both simulations, we designated cloud layers with Δq < 1.6 as coupled and those with Δq > 2.1 as decoupled, and neglect those that fall somewhere between these values. While these threshold values have an element of subjectivity, they are consistent with the decoupling continuum that exists during the decoupling process in both simulations.

5. Cloud-base processes

In the left panels of Figs. 7a and 7b, locations where the stratocumulus deck is starting to transition into broken cloud structures coincide with increases in LH. Following BW97, we first compute the correlation between LH and cloud fraction in the lowest 100 m of cloud layers (this cloud fraction is hereafter designated as CLDB). The cloudy elements within the study regions shown in Fig. 8 are divided into coupled and decoupled categories based on the decoupling criteria described in the previous section. The top row of Fig. 12 shows the corresponding plots for the 2017 and 2018 simulations, respectively. In both cases, CLDB for decoupled clouds does not show a strong correlation with LH; 0.305 and −0.216 for 2017 and 2018, respectively. The coupled CLDB exhibits a negative and relatively better correlation with LH as compared to the decoupled cloud elements for each simulation. The correlation coefficient between coupled CLDB and LH in 2017 is −0.391 versus −0.54 in 2018. There also does not appear to be a threshold in LH value for the onset of decoupling (as suggested by BW97), at least in these WRF simulations, since in both cases, coupled and decoupled elements correspond to the same range of LH, with the majority of points roughly from 90 to 140 W m−2 and from 120 to 170 W m−2 for 2017 and 2018 cases, respectively. It is also observed that values of LH and the correlation coefficient with coupled clouds are larger in 2018 than in 2017. It can be inferred that as long as the stratocumulus deck is coupled, changes in LH have a tendency to inversely affect cloud fraction in the lower levels of the cloud deck. Conversely, when the clouds become decoupled from the subcloud region and CLDB significantly decreases, changes in LH have little impact on CLDB. This latter observation may be due to the buffering effect of decoupling, which enables moisture accumulation near the surface (Albrecht et al. 1995; Miller and Albrecht 1995; and others).

Fig. 12.

Correlations (top) between average cloud fraction across the lower 100 m of MSC (CLDB) and latent heat flux from the surface (LH) and (bottom) between (D/Dt)CLDB and (D/Dt)LH for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Fig. 12.

Correlations (top) between average cloud fraction across the lower 100 m of MSC (CLDB) and latent heat flux from the surface (LH) and (bottom) between (D/Dt)CLDB and (D/Dt)LH for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Figure 6 and plots in the left column of Fig. 7 suggest that local fluctuations in LH, rather than a threshold value, coincide with areas where cloud-base thinning and decoupling commence and the solid cloud deck becomes broken. To investigate the effect of variations in LH directly below the cloud layer on changes in CLDB following the cloudy air parcels in the vicinity of the cloud base, we computed correlations between the average of Lagrangian derivatives (material or total derivatives) of cloud fraction across 100 m above cloud base and the Lagrangian derivative of LH directly below the cloud base. The Lagrangian derivatives of CLDB and LH following the cloud base are laid out in Eqs. (7) and (8), respectively:

 
DDtCLDB=tCLDB+uxCLDB+υyCLDB+wzCLDB¯,
(7)
 
DDtLH=tLH+u¯xLH+υ¯yLH.
(8)

The first term on the right-hand side of each equation above represents the local time derivative, and the rest of the terms characterize advection of each variable by the wind. The overbars in the right-hand side of Eq. (7) indicate that first cloud-base cloud fraction at each model vertical level that fell within the lowest 100 m of the cloud layer was used to estimate the local time derivative, as well as the advection terms for each of the zonal, meridional, and vertical components with the corresponding velocities at those levels (u, υ, and w, respectively). The value of (D/Dt)CLDB for each cloud element was then calculated as the average of the Lagrangian derivatives of cloud fraction at each level (equivalent to the sum of the time derivative and advection terms at the corresponding vertical level). Since we were interested in estimating the Lagrangian derivative of LH directly below the cloud, average horizontal velocities across the vertical levels within the lowest 100 m from the cloud base (u¯ and υ¯) were used in the advection terms in Eq. (8). Finally, there is no advection of LH by the wind in the vertical direction, since LH is a 3D variable with no vertical component.

The Lagrangian derivatives in Eqs. (7) and (8) using WRF data were then estimated by adopting the finite difference method. Equations (9) and (10) show the finite-difference representation of the Lagrangian derivative terms on the right-hand side of Eqs. (7) and (8), respectively:

 
CLDB{i,j,k}n+1CLDB{i,j,k}nΔt+u{i,j,k}nCLDB{i+1,j,k}nCLDB{i1,j,k}n2Δx+υ{i,j,k}nCLDB{i,j+1,k}nCLDB{i,j1,k}n2Δy+w{i,j,k}nCLDB{i,j,k+1}nCLDB{i,j,k1}n2Δz,
(9)
 
LH{i,j}n+1LH{i,j}nΔt+u{i,j}n¯LH{i+1,j}nLH{i1,j}n2Δx+υ{i,j}n¯LH{i,j+1}nLH{i,j1}n2Δy,
(10)

where n refers to the current time step; i, j, and k are the zonal, meridional, and vertical spatial directions; and u, υ, and w are the zonal, meridional, and vertical velocities, respectively. In the denominators, Δx and Δy are equal to the longitudinal and latitudinal lengths of each grid point and Δz is the vertical distance between the layer k and the one above it, while Δt is the simulation time step. Also, u{i,j}n¯ and υ{i,j}n¯ in Eq. (10) are the average zonal and meridional velocities across the lowest 100 m from the cloud base at grid point (i, j), respectively.

Results of this analysis are shown in the second row of Fig. 12. The correlation coefficients for coupled cases are now much improved, −0.515 and −0.651 for 2017 and 2018, respectively, compared to the correlations between CLDB and LH for coupled clouds in each simulation. On the other hand, in the case of decoupled clouds, there is negligible correlation between total derivatives of CLDB and LH in 2017 (0.008) and it is weaker than the corresponding correlation for coupled clouds in 2018 (−0.376), although it is slightly better than the correlation between decoupled CLDB and LH in 2018. Therefore, erosion and breakup in the lower levels of the cloud deck (CLDB) in these simulations is loosely linked to instantaneous fluctuations in the surface LH following the cloud base in coupled regions rather than the absolute values of latent heat flux from the ocean surface below the cloud. The coefficients of determination for the Lagrangian derivatives of LH and CLDB (square of the correlation coefficient) are 0.265 and 0.424 for the 2017 and 2018 cases, respectively, which means that approximately one-quarter and slightly less than half of the variance in the Lagrangian derivative of CLDB is explained by the Lagrangian derivative of LH. Hence, there are other processes that contribute to the changes in CLDB.

Latent heat flux modulates the LCL and past studies have also reported strong connections between the height of the LCL and the occurrence of coupled regions within a transition cloud field (Miller and Albrecht 1995). Figure 13 shows correlations between the LCL and CLDB (top panels) in the 2017 and 2018 cases. Moderate and strong correlations between the LCL and the CLDB in coupled clouds are found in both cases (−0.339 and −0.724 for 2017 and 2018, respectively). While the correlation for decoupled clouds in 2018 is poor (−0.194), a positive and moderate correlation is exhibited for decoupled clouds in 2017 (0.345). The Lagrangian derivative of the LCL below the cloud base and CLDB is calculated similar to (D/Dt)LH [Eqs. (8)(10)] and shown in the bottom panels of Fig. 13. The correlation coefficients for the Lagrangian derivatives compared to their counterpart in the top panel for coupled clouds is slightly improved in 2017 (−0.4 vs −0.339), whereas it is smaller in 2018 (−0.629 vs −0.724). The correlation coefficients for the decoupled clouds follow the same pattern as those for latent heat flux shown in Fig. 12; negligible and relatively weak correlations for the Lagrangian derivatives in 2017 and 2018 (0.107 and −0.268, respectively). In fact, the plots are virtually identical to those in Fig. 12, which reflects the strong relationship between LH and LCL. Similar to the case for latent heat flux, Lagrangian derivatives of the LCL demonstrate a moderate and strong correlation with the Lagrangian derivative of CLDB for coupled clouds, for 2017 and 2018 simulations, respectively. However, in terms of absolute values, the local LCL is more important in determining CLDB than steady changes in the LCL observed following the parcel trajectory for coupled clouds only in 2018. While this relationship in 2018 is strong, this signal lacks the year-to-year consistency exhibited in the Lagrangian correlations between LH and CLDB.

Fig. 13.

Correlations (top) between average cloud fraction across the lower 100 m of MSC (CLDB) and LCL and (bottom) between (D/Dt)CLDB and (D/Dt)LCL for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Fig. 13.

Correlations (top) between average cloud fraction across the lower 100 m of MSC (CLDB) and LCL and (bottom) between (D/Dt)CLDB and (D/Dt)LCL for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

The results shown in Fig. 12 suggest that the changes in the surface LH following the cloud base may be partly responsible for the initiation of the decoupling process. There are at least two mechanisms that could lead to this link. One potential mechanism echoes the deepening–warming hypothesis; the LH release at cloud base becomes large enough that it fuels much larger updrafts within the cloud, which in turn increase mixing at cloud top and initiate downdrafts that penetrate the cloud base and dry the air below, locally decoupling the cloud from the surface. Another possibility is that warming dominates moistening, deepening the boundary layer and consequently raising the LCL. A higher LCL leads to local moisture accumulation, which eventually lowers the LCL and enables cumulus to from at the top of the decoupled layer and rise to the base of the inversion. This process requires no inherent contribution from cloud-top instabilities. In decoupled regions, the cloud is no longer substantially supplied with buoyant TKE and moisture from below and, as such, exhibits limited response to changes in the surface LH and moisture flux. While it is possible that both of the LH-related breakup scenarios suggested above operate depending upon conditions, cloud-top processes are explored forthwith to better understand stratocumulus breakup and changes in the decoupled cloud structures beyond the breakup point.

An increase in LH should correspond with reduction in surface relative humidity as described by the deepening–warming hypothesis proposed by BW97, due to cloud-top mixing. Also, fluctuations in horizontal wind speed may induce changes in LH. These correlations are further discussed in  appendix B.

6. Cloud-top processes

The cloud-top processes described herein are thought to help destabilize and potentially break up stratocumulus. They are compared in terms of their strength in diluting clouds in the upper 200 m of the simulated cloud deck. Each process is again examined in the context of coupled and decoupled clouds.

a. Cloud-top buoyancy instability

Among the most established cloud-top processes in the literature responsible for stratocumulus breakup are Randall’s “conditional instability of the first kind upside-down (CIFKU)” (Randall 1980) and Deardorff’s “cloud top entrainment instability (CTEI)” (Deardorff 1980). The instability criteria for stratocumulus-topped boundary layer inversions in both of these studies state that the differences in values of virtual dry static energy or equivalent potential temperature, respectively, between the layer immediately atop the cloud above the inversion and the in-cloud layer below the inversion must be smaller than a threshold value:

 
{CIFKU:Δsυ<(Δsυ)critCTEI:Δθe<(Δθe)crit,
(11)

where

 
{(Δsυ)crit(qsB+qB)(Δθe)crit(qwB+qwB).
(12)

In this expression qs is the saturation mixing ratio, q is the mixing ratio, qw is the total water specific humidity, and B+ and B refer to above-cloud and cloud-top layers, respectively.

The physics behind both criteria are that the mixture of dry and warm air atop the inversion with moist in-cloud air generates parcels that are negatively buoyant and sink through the cloud. Consequently, the unhindered entrainment of dry air into the cloud top can further dilute the cloud mass. An equivalent buoyancy reversal criteria to both of the above expressions is the following (Xiao et al. 2011):

 
κ=cpΔθeLΔqt,
(13)

where Δ is the difference of the respective variables across the cloud-topped inversion, and qt, cp, and L are the total water mixing ratio, specific heat of air at constant pressure, and latent heat of water evaporation, respectively. There are different threshold values for κ proposed in different studies; the instability criteria found by Randall (1980) and Deardorff (1980) is κ > 0.23, MacVean and Mason (1990) suggest that cloud-top buoyancy reversal is only observed for κ > 0.7, while a number of studies, for example, Kuo and Schubert (1988) and Moeng (1986), have found no relationship between κ and stratocumulus breakup at cloud top.

Each of these cloud-top buoyancy instability criteria requires a reference for calculating values corresponding to level B+, which is immediately above the cloud top beyond the inversion. The inversion height is determined using the two methods explained in section 4. Thus, B is the last cloudy level below the inversion and B+ is the interpolated value of the desired variable 10 m above B.

Figure 14 shows correlations between κ from Eq. (13), hereafter referred to as “buoyancy reversal criteria,” and the average cloud fraction across 200 m in the cloud layer below the cloud top, CLDU, for 2017 and 2018, respectively. CLDU for the decoupled clouds have moderate correlation coefficients with respect to the buoyancy reversal criteria compared to their coupled counterparts, in both the 2017 and 2018 simulations. The correlation coefficients for the decoupled clouds are higher in 2017 (−0.516) than in 2018 (−0.332), while coupled clouds show weak correlations coefficients in both years, 0.007 and 0.146 in 2017 and 2018, respectively. It is worth noting that, in both simulations, coupled clouds correspond to higher values of buoyancy reversal criteria, spanning from 0.4 to 0.8, than the decoupled clouds that range from 0.2 to 0.7 in 2017 and from 0.3 to 0.6 in 2018. In these simulations, we conclude that CLDU is moderately correlated with the buoyancy reversal criteria only for decoupled clouds, whereas coupled clouds exhibit little or no correlation. An interesting observation from the results in Fig. 14 is that, even though coupled clouds have higher values of buoyancy reversal criteria than decoupled clouds, which is expected to enhance cloud-top entrainment instability and thinning, their CLDU values either varies independent of the buoyancy reversal criteria values (2017) or even show a slight positive albeit weak correlation with this variable. It can be inferred that, as long as the cloud layer is still coupled to the subcloud layer, cloud-top entrainment due to buoyancy instabilities have little effect in diluting the cloud from above. As the decoupling process progresses, however, these instabilities become more effective at eroding the cloud layer from above, and as the instabilities strengthen, the clouds become even further diluted at cloud top.

Fig. 14.

Correlations between buoyancy reversal criteria κ and average cloud fraction across the upper 200 m of MSC (CLDU) for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Fig. 14.

Correlations between buoyancy reversal criteria κ and average cloud fraction across the upper 200 m of MSC (CLDU) for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

A shortcoming of the CTEI criterion is that in climate models and non-LES regional models, accurately calculating the cloud-top jumps in θe and qt requires assumptions and is not straightforward. The mixing processes that affect CTEI generally occur at scales on the order of a few meters, which are unresolved in our simulations and even in some LES models (Mellado 2017). Hence, the cloud-top mixing processes associated with CTEI in our simulations arise from the MYNN turbulence parameterization, which is responsible for mixing free-tropospheric air into stratocumulus. Our analysis of CTEI therefore represents the relationship between the parameterized cloud-top mixing and the simulated stratocumulus transition. Simulations from WRF in our study have an average vertical resolution of 80 m at marine stratocumulus cloud top. Therefore, Δθe and Δqt need to be interpolated at cloud top, which results in a rather rough estimation of κ that may affect the correlation coefficients with respect to CLDU. It is unclear whether this shortcoming significantly impacts our result, but other studies have found discouraging correlations (Stevens 2010; Mellado 2010; Mellado et al. 2009).

b. Estimated inversion strength

Wood and Bretherton (2006) proposed estimated inversion strength (EIS) as a new measure of the inversion strength for use in parameterizations of the low cloud-cover fraction (CF), especially in the subtropics and midlatitudes. The EIS improves upon the lower-troposphere stability (LTS) (Klein and Hartmann 1993), which has been widely used for this purpose, and Naud et al. (2016) reinforced the conclusion of Wood and Bretherton (2006) by demonstrating improved correlations between post-cold-frontal CF and EIS relative to correlations with LTS over midlatitude oceans in both hemispheres. The EIS is an approximation of potential temperature θ at 850 hPa, which roughly corresponds to the typical inversion height for midlatitude stratocumulus-topped boundary layers. Following Eqs. (4) and (5) from Wood and Bretherton (2006), EIS is calculated as

 
EIS=LTSΓm850(z700LCL),
(14)

where LTS = θ700θ0 (the difference between potential temperature at 700 hPa and the surface), z700 is the height of the 700-hPa isobar, Γm850 is the moist adiabatic potential temperature gradient at T = (T0 + T700)/2, and pressure P = 850 hPa, as a measure of the moist adiabatic lapse rate at 850 hPa, which is given by

 
Γm(T,P)=gcp[11+Lυqs(T,P)/(RaT)1+Lυ2qs(T,P)/(CpRυT2)].
(15)

In this expression, qs is the saturation mixing ratio, Ra and Rυ are the gas constants for dry and water vapor, respectively, and Lυ is the latent heat of vaporization.

Correlations between EIS and cloud-top fraction (CLDU) as a measure of effectiveness of the contribution of EIS changes to MSC breakup are shown in Fig. 15. Correlation coefficients for both coupled and decoupled clouds are very poor for both simulations (−0.005 and 0.129 in 2017 and −0.03 and 0.039 in 2018, respectively). Despite decoupled clouds being slightly better correlated with EIS than the coupled ones, the poor correlation coefficients indicate that when it is considered as the sole criterion, it fails to account for stratocumulus breakup at cloud top in the majority of cases. This may be due to the loss of their moisture and TKE supply from below, which enabled them to become more susceptible to cloud-top instabilities. One problem with the use of EIS as an indicator of breakup is that increases in LCL, decoupling, and the stratocumulus breakup happen nearly simultaneously. Based on Eq. (14), as the LCL increases, EIS coincidentally increases and this link seems contrary to the supposed role of inversion strength on cloud-top breakup, since as the cloud-top jump in moisture and equivalent potential temperature is reduced, the inversion becomes weaker. A weakened inversion should result in increased entrainment of dry and warm air above the inversion into the cloud, and its ultimate destruction.

Fig. 15.

Correlations between EIS and average cloud fraction across the upper 200 m of MSC (CLDU) for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Fig. 15.

Correlations between EIS and average cloud fraction across the upper 200 m of MSC (CLDU) for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

c. A new measure of inversion strength designed for use in large-scale models

Because the existing measures of inversion strength studied earlier either fall short of explaining the breakup in the WRF simulations (EIS) or require interpolations to compute (the buoyancy reversal criteria κ), we investigated an alternative measure that can be more easily calculated using data from climate and regional models with coarser vertical resolution than LES models.

Equivalent potential temperature θe is another moist-conserved variable that incorporates the heating effect of latent heat release on potential temperature. As an entrained parcel ascends adiabatically across the inversion, a decrease in θe indicates a reduction in the latent heating due to reduced moisture content. Therefore, vertical gradients in θe indicate moisture changes during adiabatic ascent and descent across the inversion. On the other hand, vertical gradients in the saturated equivalent potential temperature θes indicate temperature changes during adiabatic ascents and descents across the inversion. Typically, θes above inversion is higher than below it because the air is warmer, while the opposite is true for θe, since conditions above inversion are drier. The difference between θes and θe at the layers atop and below the inversion indicates how much drier and warmer the air above the inversion is relative to that just below the inversion. Warmer and drier conditions indicated by a greater difference between θes and θe atop the inversion lead to reduced instability of the inversion layer to downward motions from above. Therefore, the inversion is strengthened; that is, there is a greater resistance to entrainment of air above inversion into the layer below. The reverse is true for smaller values of this difference; the inversion becomes more susceptible to downward entrainment of air above that acts to dilute the cloud layer below. Therefore, the profile of these two variables provides a sense of the strength of the inversion in terms of the contrast between both the moisture and temperature of the two air masses.

Figure 16 shows the vertical profiles of equivalent potential temperature θe, saturated equivalent potential temperature θes, 100 times the cloud fraction for ease of viewing, LCL, and the capping inversion height zi for a point in the stratocumulus deck (I) and a semibroken cloud element (II), chosen from the domain shown in Fig. 8 in the 2018 simulation. In the case of point I, θe and θes sharply diverge beyond the inversion height, while having the same value in the in-cloud region. The cloud element at point II is in the broken cloud field downstream of the stratocumulus deck, and is being diluted from above as well as from below, judging by the cloud-fraction values. Unlike point I, θe and θes start diverging slowly in the cloud region for point II. This suggests that the inversion has become weak enough, allowing the dry air to penetrate through the cloud, thereby destroying it from above.

Fig. 16.

Vertical profiles of equivalent potential temperature θe (solid black line), saturated equivalent potential temperature θes (solid navy blue line), 100 times the cloud fraction (solid green line), LCL (dashed red line), and capping inversion height zi (dashed black line) for (left) point I and (right) point II chosen from the domain in the 2018 simulation shown in Fig. 8, where point I is in the solid stratocumulus deck, and II is in the broken cloud field downstream of the stratocumulus deck.

Fig. 16.

Vertical profiles of equivalent potential temperature θe (solid black line), saturated equivalent potential temperature θes (solid navy blue line), 100 times the cloud fraction (solid green line), LCL (dashed red line), and capping inversion height zi (dashed black line) for (left) point I and (right) point II chosen from the domain in the 2018 simulation shown in Fig. 8, where point I is in the solid stratocumulus deck, and II is in the broken cloud field downstream of the stratocumulus deck.

Since the model is prescribed with discrete vertical levels, the layer above inversion may be at a different altitude depending on the inversion height. Therefore, in order to offset the bias of the different distances between inversion and the layer above it, the vertical gradient of θesθe at the inversion is used as a measure of the inversion strength. This variable is hereafter labeled “INV”:

 
INV=ddz(θesθe).
(16)

INV is calculated for each example represented in Fig. 16, and as expected, it is greater in the case of a stronger inversion; 0.125 and 0.025 for the points I and II, corresponding to strong and weak inversions, respectively. Figure 17 shows correlations between coupled and decoupled CLDU and INV for 2017 and 2018 simulations. As expected, weakening of inversion strength is linked to reduction in cloud-top fraction, and that this variable correlates better with decoupled CLDU. The correlation coefficient for decoupled clouds in 2017 is slightly improved compared to that for buoyancy reversal criteria (0.542 vs −0.516), while in 2018, it is slightly smaller than the latter (0.305 vs −0.332). However, there is a poor correlation between this variable and the coupled clouds (−0.175 and −0.049 in 2017 and 2018, respectively). One interpretation of this finding is that as long as the clouds are coupled, they are supplied with latent heat from the subcloud layer and can maintain their cloud-top stability, therefore not allowing for any or much entrainment from above the inversion. This notion is consistent with the greater number of clouds with CLDU exceeding 0.5 as compared to the decoupled ones. However, a positive trend can be seen between those with CLDU smaller than 0.5 and INV, which can be related to how strongly coupled they are to the surface. In other words, those clouds are likely in the beginning of the decoupling process, and are more susceptible to changes in inversion strength at cloud top.

Fig. 17.

Correlations between the vertical gradient of the difference between θes and θe at cloud top [INV = d/dz(θesθe)] and average cloud fraction across the upper 200 m of MSC (CLDU) for coupled and decoupled cases at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Fig. 17.

Correlations between the vertical gradient of the difference between θes and θe at cloud top [INV = d/dz(θesθe)] and average cloud fraction across the upper 200 m of MSC (CLDU) for coupled and decoupled cases at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

In conclusion, INV performs similar to the buoyancy reversal criteria κ in terms of quantifying the impact of inversion instabilities on the breakup of decoupled clouds, while being easier to calculate than the latter in non-LES models. And because it has proved more successful than EIS, it can be viewed as an alternative metric for explaining the relationship between cloud-top instabilities and cloud-top erosion. Also, it can be interpreted that cloud-top instability and inversion strength measures may perhaps be byproducts of the breakup processes at cloud base. The main evidence is that they only seem to be correlated with breakup at cloud top when the cloud has been further decoupled after cloud-base processes such as local fluctuations in LH beneath the cloud have eroded it from below.

7. Discussion and conclusions

Summertime cold-frontal passages and associated postfrontal cloudiness are an important component of the climate in the ENA. The post-cold-frontal environment often exhibits a transition from a continuous MBL cloudiness in the northern ENA to broken cloudiness in the southern ENA. To investigate these post-cold-frontal MBL cloud transitions, we used two high-resolution simulations of regional summertime post-cold-front marine boundary layer clouds in July 2017 and 2018 to investigate the processes that lead to these cloudiness transitions. The resolution of our simulations negated the need for a shallow convection parameterization, so MBL clouds were generated by a combination of the surface flux and MYNN3 turbulence parameterizations. To track the evolution of cloud elements, we used a Lagrangian particle dispersion model (FLEXPART-WRF) to follow the evolution of individual MBL columns in each simulation through the transition process. The WRF simulations produced a range of cloud configurations associated with the transition region that resemble cloud structures in satellite images from the simulation periods. To evaluate the quality of the simulations, we compared them with coincident surface and remote sensor data collected at the ENA site. Surface variables agreed reasonably well with the simulations, though island effects on the surface temperature from WRF simulations led to daytime cold bias at the wake of the cold fronts at the location of the ENA site and influenced surface temperature comparisons. MBL depths simulated by WRF in the two postfrontal cases were comparable to those that are measured at ENA, though 100–200 m deeper than the observed depths. Comparisons between the subcloud and cloud structure measured using the ENA Doppler lidar and KAZR cloud radar showed similar overall structures, but the postfrontal cloudiness was more broken and deeper in both the 2017 and 2018 simulations than the observed structure. The ENA-measured subcloud vertical velocities were noticeably larger than those in the simulations in the post-cold-frontal environment.

Decoupling of the cloud layer from the surface supply of moisture is known to be an important process in this region, especially as it relates to cloud transitions. We tested three diagnostic decoupling parameters suggested by Jones et al. (2011) to classify the simulated cloud cover across the decoupling continuum and found that the diagnostic based upon the vertical moisture gradient yielded the best results. The Lagrangian cloud profiles as the MBL cloud layer evolved suggested changes at cloud base and cloud top as the clouds became more broken, so we examined processes at cloud base and cloud top separately in the context of more coupled and more decoupled cloud populations over a domain at the onset of the transition from a solid deck of marine stratocumulus to broken cloud structures, for each of the 2017 and 2018 simulations.

A finding of particular importance was that cloud-base erosion in the simulations was mainly the result of local fluctuations in LH, which preceded any changes at cloud top as the clouds became more broken. Correlations between the absolute value of LH and changes in the cloud fraction at cloud base were substantially lower than those between the Lagrangian derivatives of LH and cloud fraction at cloud base for more coupled clouds. Similar correlations to those involving LH were found when analyzing the LCL in the context of cloud-base changes, which is expected given that the surface LH and surface LCL are related. The relationship between the Lagrangian derivatives of 10-m wind velocity and the surface RH and LH following the cloud base were strong and positive for both coupled and decoupled clouds, uniformly exceeding 0.7, the implication being that changes in the surface wind and humidity conditions were likely influencing the cloud-base erosion process through their effect on LH as long as the cloud element was still coupled to the subcloud region. Changes in the surface relative humidity and LH were virtually simultaneous making it difficult to determine if the LH affected the humidity as a consequence of cloud-top mixing following deepening–warming or if surface warming led to a lower RH, which subsequently leads to an increase in the LH. In the latter case, a potential feedback loop would exist.

We examined the relationship between CTEI and EIS in the context of decoupling on cloud-top cloud fraction and found that CTEI was moderately correlated with changes in cloud-top cloud fraction only for more decoupled clouds, while EIS exhibited weak correlations for both coupled and decoupled clouds. In addition, we tested a new cloud-top dilution diagnostic based upon estimating the inversion strength using the vertical gradients of the difference between the equivalent and saturation equivalent potential temperature in the vicinity of the capping inversion height and found that it preformed similar to CTEI as an indicator of cloud breakup at cloud top, while being readily computed from soundings. In summary, the degree of decoupling was found to significantly influence the extent to which both cloud-base and cloud-top processes affect the erosion of cloud elements at cloud base and cloud top, respectively. Our findings suggest that cloud-top processes are able to substantially alter the cloud structure only after significant decoupling has occurred.

Our results suggest that the deepening–warming process proposed by BW97 may be operating in the post-cold-frontal environment in ENA, which may broaden its applicability in the marine atmosphere. A variation of the deepening–warming hypothesis in which the warming initially dominates the moistening leading to a deeper MBL and higher LCL could also explain some of our findings. In that scenario, a higher LCL resulting from warming leads to moisture accumulation in the subcloud layer, which subsequently drives the LCL lower and initiates convection. We view this possibility as a potential subset of the original hypothesis rather than a separate process.

The latent-heat driven, deepening–warming decoupling process is a key instigator of the stratocumulus transition. The 2017 and 2018 cases represent two slightly different manifestations of the transition. In the 2018 case, the latent heat flux gradient over the ENA behind the cold front is smaller than in the 2017 case, and the transition occurs farther downstream at a lower latitude (see Fig. 7). The deepening–warming post-cold-frontal transition that is evident in these simulations is one process in the continuum of transition processes that likely exist in the post-cold-frontal environment. Images of the two simulated cases (Fig. 5) suggest a rich array of transitions occurring at different scales that do not follow a latitudinal pattern. While some of these transitions may be related to aerosol–cloud interactions, others may involve mesoscale instabilities inherent within the post-cold-frontal air mass, or other yet undiscovered instabilities. The transition continuum also likely includes processes that reverse the breakup and lead from partly cloudy conditions to solid or complex overcast. Future studies will hopefully address these other transition modes.

To the extent that these two cases represent different cold-frontal climatology and produce transitions at different latitudes, they suggest a sensitivity to changing post-cold-frontal airmass characteristics in a warming climate. Warming in northern Canada and an increasingly ice-free Arctic are likely to produce less impressive cold-air outbreaks during summer and, at least initially, potentially smaller gradients of latent heat flux across the ENA. A reduction in the gradient of the latent heat flux in this region suggests that the stratocumulus transition might occur at lower latitudes than at present until the warming of the ocean, which takes longer, potentially offsets the process. In any event, a near-term reduction in the gradient, which seems quite feasible given the current amplitude and speed of the Arctic warming, could produce (or is already producing) a decoupling-induced, negative cloud feedback during the summertime.

Holistically, WRF simulations combined with observations from the ENA surface site is a potent research combination. The model provides hints at the specific data and process combinations that might reveal a much more statistically defensible modus operandi for the transition region when applied to a longer-term record from the ENA site. Future combined observational and modeling studies are recommended to further clarify the connection between the surface fluxes, decoupling, and cloud transitions.

Acknowledgments

This work was funded by the U.S. Department of Energy’s Atmospheric System Research program under Grant DE-SC0013489. The WRF runs were completed on the NCAR Cheyenne Supercomputer through an 800 hour time allocation as part of an educational program. The NCAR Command Language (NCL), version 6.6.2, was used for processing the data and creating all the plots in the manuscript. The authors benefitted from useful discussions with Dr. Thijs Heus, Dr. Robert Wood, and Dr. Michael Jensen, and thank Dave Gill and WRFHelp services for their help with running WRF simulations. Finally, the authors deeply appreciate the time and effort of three anonymous reviewers whose input greatly improved our manuscript.

APPENDIX A

FLEXPART-WRF Settings

FLEXPART-WRF comes with different options available for choosing the input wind field (WIND_OPTION), PBL parameters such as friction velocity u*, surface sensible heat flux, and PBL height (SFC_OPTION), PBL turbulence parameterization (TURB_OPTION), and land-use schemes (LU_OPTION). All trajectory simulations have been conducted with the following configuration.

WIND_OPTION: There are four options available in FLEXPART-WRF for input vertical wind velocity. Option 0 uses instantaneous vertical velocity W on Cartesian coordinates that is the default output from WRF; option 1, the time-averaged wind; option 2, the instantaneous mass-weighted time derivative of sigma levels as vertical velocity σ˙; and option −1, a divergence-based vertical wind velocity that determines vertical velocity with mass-conservation and hydrostatic assumptions. WRF needs additional settings to output the instantaneous and time-averaged vertical wind velocity on sigma levels. According to Brioude et al. (2012a), W from option 0 produces the largest uncertainties when the orography of the domain is complicated, whereas instantaneous and time-averaged σ˙ give better results. Also, even though the conditions required for computing vertical velocity from the last option do not necessarily hold at the mesoscale, it leads to much smaller uncertainties than option 0. Given that the only output available from our WRF simulations was instantaneous W on geometric vertical coordinate, the last option (−1) was opted to optimize the trajectories despite its higher computational cost, even though most of the domain is located on the eastern North Atlantic Ocean where almost no complex orography exists, which would have justified using option 0.

TURB_OPTION: Four options are available for parameterizing the turbulent wind field in the PBL. Option 0 completely ignores turbulence; option 1 uses the Hanna scheme (Hanna 1982) for the PBL turbulent mixing; and option 2, the prognostic TKE from WRF. Option 3 is similar to option 2, but partitions TKE obtained from WRF such that turbulent energy production and dissipation are equal. Brioude et al. (2013) found that options 2 and 3 cannot keep the tracer well mixed in the planetary boundary layer. They found out that when the Hanna scheme for turbulence parameterization is used in conjunction with skewed turbulence (rather than Gaussian) in the convective boundary layer (activated by the switch CBL = 1), the tracer particles are almost homogenously well mixed throughout the depth of the convective boundary layer. They recommend this setting and it is what we used in all trajectories in this article.

SFC_OPTION: Two options exist in FLEXPART_WRF for computing PBL height. It is either derived directly from the WRF output PBLH (option 1) or estimated by FLEXPART-WRF using a Richardson number threshold (Brioude et al. 2013) (option 0). Here, option 0 has been chosen to characterize the boundary layer in order to be more in line with the choice of TURB_OPTION described above.

LU_OPTION: The same land-use scheme used in WRF is adopted by FLEXPART-WRF with option 1.

APPENDIX B

Correlations between Horizontal Wind Speed and Relative Humidity and Surface Latent Heat Flux

Figure B1 below shows the correlations between latent heat flux (LH) and relative humidity (RH) (top rows) and the Lagrangian derivatives of LH and RH (bottom rows) for 2017 and 2018 simulations. RH exhibits an inverse correlation with LH, and increases in LH are strongly correlated with decreases in RH in almost all cases. Correlation coefficients between coupled and decoupled clouds in 2017 are noticeably different compared to those in 2018 (−0.812 and −0.505 for coupled and decoupled clouds, and −0.727 and −0.845 for those for 2017 and 2018, respectively). However, that is not the case for the Lagrangian derivatives of LH and RH following the cloud base; that is, for each simulation, coupled and decoupled clouds have similar correlation coefficients and almost the same distribution (−0.712 and −0.710 for coupled and decoupled clouds in 2017, and −0.838 and −0.880 for those in 2018, respectively). Therefore, Lagrangian changes in RH and LH are more consistent in each simulation regardless of the coupling state of the cloud above.

Fig. B1.

Correlations (top) between latent heat flux from surface (LH) and surface relative humidity (RH) and (bottom) between (D/Dt)LH and (D/Dt)RH for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Fig. B1.

Correlations (top) between latent heat flux from surface (LH) and surface relative humidity (RH) and (bottom) between (D/Dt)LH and (D/Dt)RH for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

This contrast in correlation coefficients between coupled and decoupled clouds is also found in correlations between the surface latent heat flux and horizontal wind velocity at 10 m (UV10), shown in Fig. B2. There is even a more stark disparity between coupled and decoupled clouds in the case of UV10 than RH, as well as between the two simulations, with weak negative correlation coefficients between UV10 and LH in 2017 in contrast to positive and moderately strong ones in 2018 (−0.259 and −0.092, and 0.660 and 0.207 for coupled and decoupled clouds in 2017 and 2018, respectively). However, similar to the Lagrangian derivatives of RH and LH, Lagrangian derivative of UV10 below the cloud is strongly correlated with that of LH for both simulations, with positive correlation coefficients 0.735 and 0.831, and 0.815 and 0.883 for coupled and decoupled clouds in 2017 and 2018, respectively.

Fig. B2.

Correlations (top) between latent heat flux from surface (LH) and horizontal wind speed at 10 m (UV10) and (bottom) between (D/Dt)LH and (D/Dt)UV10 for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Fig. B2.

Correlations (top) between latent heat flux from surface (LH) and horizontal wind speed at 10 m (UV10) and (bottom) between (D/Dt)LH and (D/Dt)UV10 for coupled and decoupled clouds at (left) 1800 UTC 17 Jul 2017 and (right) 1130 UTC 29 Jul 2018.

Concentrating on the Lagrangian correlations between RH and LH and UV10 and LH because of their consistency and integrative nature, we conclude that both variables are contributors to the observed behavior in the Lagrangian changes in LH. Further, we note that their respective relationships with LH are consistent with the expected behavior of these surface variables in the context of BW97. We should also add that even though cloud-top mixing may perhaps play a role in reducing RH near the ocean surface under less well-mixed MBL conditions, we cannot definitely link these changes exclusively with cloud-top processes. The difference between correlation coefficients for coupled and decoupled clouds in the case of Lagrangian derivatives is only minor for both 2017 and 2018 simulations, and there is an inconsistency in terms of comparing the magnitude of correlation coefficients between coupled and decoupled clouds in 2017 versus 2018. However, coupled clouds encompass slightly larger values of RH, the trends and ranges of values of RH and LH are almost similar in all cases. Therefore, the impact of stronger cloud-top mixing on changes in surface RH due to updrafts from the cloud base in decoupled cases cannot be separated from other factors. The other dominant factor may be changes in SST; as the SST increases, for example, the RH will decrease in response, regardless of cloud-top processes, which in turn affects LH. Increased LH may also help further reduce RH, creating a feedback loop between the two variables.

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