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  • View in gallery

    Geostationary Operational Environmental Satellite-12 (GOES-12) visible channel imagery (black and white shaded) overlaid with S-Pol reflectivity (color shaded) at (a) 1145 UTC 11 Jan and (b) 1606 UTC 19 Jan 2005, with pink curves outlining the clouds organized along cold pool outflow boundaries and a red arrow indicating ship location and ship-reported surface wind vector. Pink square indicates the innermost domain of the nested-WRF simulation.

  • View in gallery

    For 1540–1600 UTC 19 Jan 2005, (a) the shipboard X-band radar signal-to-noise ratio (gray shaded), with lidar-observed positive (red arrow) and negative (blue arrow) vertical velocities superimposed. Filled yellow triangle indicates the downwind-side surface cold pool boundary identified by the onset of surface rain. The ship-observed (b) surface rain rate, (c) surface air temperature, and (d) surface water vapor mixing ratio.

  • View in gallery

    The average profile of (a) potential temperature, (b) water vapor mixing ratio, and (c) zonal and (d) meridional wind speeds for the innermost model domain averaged over the 24-h simulation period (black line; WRF), the average of six radiosondes launched from 0700 UTC 19 Jan to 0300 UTC 20 Jan from the ship (red line; 19RVSJ), all of the radiosondes launched from the ship during 9–24 Jan (green dotted line; allRVSJ), and all radiosondes launched from Spanish Point from 16 Dec 2004 through 8 Jan 2005 (blue dotted line; SPNT).

  • View in gallery

    A snapshot of the innermost domain from the simulation, with the size and location as indicated by the pink square in Fig. 1b. (a) WRF-simulated 3-m-level temperature (gray shaded) overlaid with the vertically integrated cloud water path (0–2 cm; white contours). (b) WRF-simulated 3-m-level water vapor mixing ratio overlaid with 3-m-level wind vectors.

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    (a) Probability density function of RRa with the dashed line indicating the threshold for 10% highest RRa. (b) Cloud cover as a function of RRa with the shading indicating the number density of output minutes. Dashed line indicates the mean cloud cover of the 24-h period. Two dashed–dotted lines extending to the right and left of the top 10% RRa threshold indicate the averaged cloud cover over the 10% output minutes with highest RRa and the other output minutes, respectively.

  • View in gallery

    For output minutes containing RRa > 0, with one standard deviation shaded: (a) domain-mean cloud fraction (solid), with the mean buoyant cloud-core fraction profile indicated separately (triangles); (b) horizontally averaged cloud water mixing ratio over cloudy region; (c) horizontally averaged water vapor mixing ratio over cloudy region; and (d) horizontally averaged rainwater mixing ratio within rain shaft.

  • View in gallery

    Composite of 13-m-level air properties across the domain-maximum surface rain rate (0 on x axis) from all 1441 simulation output minutes (black solid line with filled circle) and the output minutes of highest 10% RRa values (black dotted line), as compared to the observed flux tower measurements at 15 m averaged over the passages of the three cold pools documented on 19 Jan (red line with filled circle) of (a) rain rate, (b) wind speed, (c) temperature, (d) water vapor mixing ratio, (e) virtual temperature, (f) equivalent potential temperature, (g) sensible heat flux, and (h) latent heat flux.

  • View in gallery

    The maximum surface changes within individual cold pools, observed on 19 Jan (red filled circles) and other “undisturbed” RICO days (pink filled circles), and contoured frequency distribution for the maximum anomalies within individual simulated cold pools represented by the composite of Fig. 7, for (a) qυ, (b) θe, and (c) wind speed, all as functions of the change in θ. (d) The change in LHF as a function of change in SHF using the same plotting conventions.

  • View in gallery

    Snapshots focusing on the 80-m-level cold pool downwind boundary (black stippled) from 2105 to 2123 UTC in 6-min intervals, showing the 80-m-level updraft area (red stippled), positive and negative Δqυ (light and dark shading, respectively), Δθe = 2 K contours (light green) that coincide with Δqυ = 0.7 g kg−1 (light shaded contours), and areas with surface rain rates ≥2 mm h−1 (light blue contours). Dashed black lines correspond to the cross sections in Fig. 16.

  • View in gallery

    The accumulated probability density function of length along the cold pool boundary arc at the 3- (solid black) and 80-m (dashed black) levels and the cold pool boundary depth (solid blue).

  • View in gallery

    For the 80-m level, (a) contoured frequency distributions of as a function of Δθup for CPAR updrafts (red; based on the 560 output minutes) and non-CPAR updrafts (black; based on all the 1441 output minutes). (b) Contoured frequency distributions of the difference between the CPAR updrafts and the non-CPAR updrafts within the same output minute, as a function of the θup difference, based on 560 output minutes containing CPAR updrafts. (c) The probability distribution of for the CPAR updrafts (red; based on the 560 output minutes) and non-CPAR updrafts (black; based on all the 1441 output minutes).

  • View in gallery

    For the 80-m level, contoured frequency distributions of Δqυ averaged over all CPAR points as a function of (a) the difference between the CPAR updrafts and non-CPAR updrafts and (b) the cold pool expansion rate. Both plots based on the 560 output minutes containing CPAR updrafts.

  • View in gallery

    For the 80-m level, contoured frequency distributions of the updraft vertical velocity wup as a function of the buoyancy bup for (a) updrafts, (b) buoyant portion of updrafts, and (c) nonbuoyant portion of updrafts, within CPAR (red; based on the 560 output minutes) and outside CPAR (black; based on the 1441 output minutes). Buoyancy of each grid cell is assessed relative to the domain mean: , where g is the gravitational acceleration.

  • View in gallery

    For the 80-m level, contoured frequency distributions of the vertical velocity difference between the CPAR updrafts and non-CPAR updrafts (CPAR − non-CPAR) as a function of (a) corresponding difference in updraft buoyancy and (b) cold pool expansion rate. Both based on the 560 output minutes containing CPAR updrafts.

  • View in gallery

    Schematics of the three scenarios of the relationship between cold pool downwind boundary and ambient wind shear that cause different orientations of the force-lifted updrafts. Black arrows indicate mean/ambient horizontal wind U; blue arrows indicate the cold pool expansion rate C*. The tilted solid blue lines represent the interface between the cold pool downwind boundary and the environment. (a) The cold pool downwind boundary circulation is too weak to counter the ambient wind circulation; lifted updrafts follow the ambient wind shear direction. (b) The two circulations are about the same strength; the lifted updrafts rise upright. (c) The cold pool downwind boundary circulation is stronger than the ambient wind circulation; the lifted updrafts follow the wind shear direction within cold pool boundary.

  • View in gallery

    Snapshots of cross section along the dashed black line indicated in Fig. 9 for 2105–2123 UTC. (a)–(d) Cloud mixing ratio qc > 0 g kg−1 (black contours), rain mixing ratio qr > 0 g kg−1 (light blue contours) with denser contours indicating higher qr, and plane-projected wind vectors relative to the domain-averaged wind for updrafts (red arrows) and downdrafts (deep blue arrows) below cloud-base level (dotted line). Negative buoyancy below cloud-base level (dark shaded). (e)–(h) The speed of domain-averaged horizontal wind projected onto the cross section. Note that the negative wind speed on the x axis suggests northeasterly.

  • View in gallery

    For the 450-m cloud-base level, (a) the probability density of for CPAR updrafts (red; based on the 560 output minutes) and non-CPAR updrafts (black; based on the 1441 output minutes). Contoured frequency distributions of differences between CPAR updrafts and non-CPAR updrafts (CPAR − non-CPAR ) for (b) difference as a function of the θup difference, (c) the wup difference as a function the bup difference, and (d) the wup difference as a function the 80-m-level cold pool expansion rate. The 560 output minutes containing CPAR updrafts are the basis for (b)–(d).

  • View in gallery

    (a) Contoured frequency distributions of the cloud water path of updraft columns as a function of the cloud-base-level vertical velocity for CPAR updrafts (red; based on the 560 output minutes) and non-CPAR updraft (black; based on the 1441 output minutes). (b) Contoured frequency distributions of the difference in cloud water path of CPAR updrafts relative to non-CPAR updrafts as a function of the cloud-base-level vertical velocity difference, based on the 560 output minutes containing CPAR updrafts.

  • View in gallery

    Schematic of an instantaneous view on a propagating cold pool being strengthened by a convective downdraft due to precipitation, while invigorating further convection on the downwind-side cold pool boundary through the modification of updraft properties.

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Simulated Convective Invigoration Processes at Trade Wind Cumulus Cold Pool Boundaries

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  • 1 Rosenstiel School of Marine and Atmospheric Sciences, University of Miami, Miami, Florida
  • | 2 Department of Earth and Environment, Florida International University, Miami, Florida
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Abstract

Observations of precipitating trade wind cumuli show convective invigoration on the downwind side of their cold pools. The authors study convection and cold pools using a nested–Weather Research and Forecasting Model simulation of 19 January 2005—a day from the Rain in Cumulus over the Ocean experiment. The temperature and water vapor mixing ratio drops in simulated cold pools fall within the envelope of observed cases, and the wind enhancement matches observations more closely. Subcloud updrafts downwind and near the cold pool boundary are statistically compared to updrafts further from cold pools. Updrafts near cold pool outflows are moister than the other updrafts and are more likely to originate from overall moister regions. Cold pool–influenced updrafts tend to exceed the other updrafts in vertical velocity and are associated with more cloud liquid water. The strength of circulation within the cold pool boundary is unable to match that because of the low-level environmental wind shear, and the lifted updrafts advect faster than the environmental wind, thereby accessing the ambient environmental moisture converged by cold pool expansion. Cases with higher rain rates correspond to larger cloud cover through the shearing off of the upper-level cloud, consistent with observations. This study suggests that it is the ability of cold pools to lift thermodynamically favorable air that is critical for secondary convection of trade wind cumuli.

Denotes Open Access content.

Corresponding author address: Zhujun Li, RSMAS/MPO, 4600 Rickenbacker Cswy., Miami, FL 33149. E-mail: zli@rsmas.miami.edu

Abstract

Observations of precipitating trade wind cumuli show convective invigoration on the downwind side of their cold pools. The authors study convection and cold pools using a nested–Weather Research and Forecasting Model simulation of 19 January 2005—a day from the Rain in Cumulus over the Ocean experiment. The temperature and water vapor mixing ratio drops in simulated cold pools fall within the envelope of observed cases, and the wind enhancement matches observations more closely. Subcloud updrafts downwind and near the cold pool boundary are statistically compared to updrafts further from cold pools. Updrafts near cold pool outflows are moister than the other updrafts and are more likely to originate from overall moister regions. Cold pool–influenced updrafts tend to exceed the other updrafts in vertical velocity and are associated with more cloud liquid water. The strength of circulation within the cold pool boundary is unable to match that because of the low-level environmental wind shear, and the lifted updrafts advect faster than the environmental wind, thereby accessing the ambient environmental moisture converged by cold pool expansion. Cases with higher rain rates correspond to larger cloud cover through the shearing off of the upper-level cloud, consistent with observations. This study suggests that it is the ability of cold pools to lift thermodynamically favorable air that is critical for secondary convection of trade wind cumuli.

Denotes Open Access content.

Corresponding author address: Zhujun Li, RSMAS/MPO, 4600 Rickenbacker Cswy., Miami, FL 33149. E-mail: zli@rsmas.miami.edu

1. Introduction

Precipitation radar observations, both from space (Short and Nakamura 2000) and collected at the surface during the Rain in Cumulus over the Ocean (RICO) experiment (Rauber et al. 2007; Snodgrass et al. 2009; Nuijens et al. 2009), reveal rain rates exceeding 2 mm h−1 for shallow precipitating cumuli in the Caribbean trade wind region. Ship-based observations have associated such precipitation with a decrease in surface specific humidity and equivalent potential temperature (Zuidema et al. 2012), confirming the presence of large (40–60 km in diameter) cold pools visible from space as mesoscale arcs organized around cloud-free areas (Fig. 1a). Unlike light (≈1 mm day−1) precipitation that generally cools and moistens the well-mixed subcloud layer while keeping the equivalent potential temperature θe constant (Nitta and Esbensen 1974; Albrecht 1993), the heavier shallow precipitation appears capable of generating convective downdrafts that originate above cloud base and descend into the subcloud layer (Zuidema et al. 2012), similar to what has been observed for deeper convection (e.g., Zipser 1969; Barnes and Garstang 1982). If the downdrafts are able to impact the surface air, a pool of evaporatively cooled air that is also drier than the surrounding surface environmental air is formed. Analysis of radar reflectivities collected during RICO find that the leading edges of precipitating shallow cumuli propagate at speeds higher than the mean low-level wind speeds and similar to the estimated propagation speed of the associated cold pool outflow (Zuidema et al. 2012). Cold pools are therefore considered to be responsible for the observed arc-shaped organizations of precipitating shallow cumuli, with the cold pools invigorating convection at their downwind boundary and suppressing thermals inside the stable cold pool area.

Fig. 1.
Fig. 1.

Geostationary Operational Environmental Satellite-12 (GOES-12) visible channel imagery (black and white shaded) overlaid with S-Pol reflectivity (color shaded) at (a) 1145 UTC 11 Jan and (b) 1606 UTC 19 Jan 2005, with pink curves outlining the clouds organized along cold pool outflow boundaries and a red arrow indicating ship location and ship-reported surface wind vector. Pink square indicates the innermost domain of the nested-WRF simulation.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

Cold pools occurring in the trade wind regions are worthy of research interest, not only for their participation within the global hydrological cycle, but also because of their relationship to the global radiative budget through their influence on cloud fraction. Cold pools influence cloud fraction both by representing areas of low surface buoyancy that discourage bottom-up shallow convection and by encouraging secondary convection at the cold pool boundaries. An earlier study on feedbacks of shallow-cloud precipitation upon cloud cover neglecting cold pools suggests light precipitation should reduce cloud cover by removing liquid water (Albrecht 1993). Results from an ensemble of high-resolution simulations of precipitating cumuli, based on RICO soundings, indeed show a slight trend of decreasing shallow cloud cover with increase of the precipitation rate (vanZanten et al. 2011). RICO analyses of scanning surface-based radar data, however, find a slight positive correlation (Nuijens et al. 2009). The discrepancy can be explained by the shearing off of the upper portions of the more heavily precipitating clouds (4–5 km; Zuidema et al. 2012), compared to the modeled cloud top heights of 2–3 km in vanZanten et al. (2011). More variation in the upper levels of shallow cumulus cloud cover rather than lower levels has also been noted in a longer time series at Barbados (Nuijens et al. 2014). The deeper clouds that are associated with cold pools suggest subcloud processes at the cold pool–precipitation interface are critical for understanding how the necessary cloud depth is achieved that can allow overall cloud cover to vary.

Cold pools are also becoming an area of increasing interest to the large-scale modeling community because their parameterization is suggesting new solutions to old modeling problems. For example, cold pools as a tool for organizing convection according to the scale of the convection provides an approach for overcoming inadequacies in entrainment assumptions (Mapes and Neale 2011). The parameterization of cold pools is also one approach for improving the representation of the diurnal cycle in precipitation within large-scale models (Rio et al. 2009). Such parameterizations can build on the increasing ability to pursue model simulations possessing both the necessary resolution and domain size to represent cold pool processes (e.g., Seifert and Heus 2013). By comparing high-resolution simulations to observations at similar process-level scales, as will be done here, greater confidence can be gained in the high-resolution simulations themselves.

Several mechanisms have been proposed to explain cold pool invigoration of further convection, for both shallow and deep clouds. One purely thermodynamic mechanism is highlighted within a cloud-resolving modeling study of deep convection, with early-stage subcloud evaporation providing the surrounding air with moisture that then enhances the convective available potential energy at the boundaries and thereby encourages convection without any other forcing (Tompkins 2001). This mechanism for the mesoscale organization of shallow precipitating cumuli is further supported in the large-eddy simulations of Seifert and Heus (2013), with moist rings generated from the evaporation of rain around the cold pool boundaries.

The density-driven outflows can also contribute dynamically to encourage the convergence of moisture at the cold pool boundary, as mentioned in the large-eddy simulation (LES) study on trade wind cumuli mesoscale organization by Xue et al. (2008). Dynamic lifting by the denser cold pool air occurs as the cold pool air subsides and spreads into the environment at the speed of gravity current, with a propagation speed close to the surface exceeding that of the mean wind. The propagation causes convergence at the leading edge that can forcibly lift air parcels. This can strengthen already-buoyant updrafts, or transport humidity to upper levels, preparing for future convection. In addition, dynamic lifting at the cold pool boundary, by producing stronger and wider updrafts, can increase their available kinetic energy and ability to trigger further convection. The influence of such processes on deep convection has been explored as a parameterization within Rio et al. (2009), Grandpeix and Lafore (2010), and Rio et al. (2013). The processes themselves have not yet been investigated in detail for shallow convection.

The influence of the typical wind shear pattern of the trade winds on cold pool–induced updrafts should also be considered. Studies on midlatitude squall lines have noticed that the lifting is strongest when the local circulation associated with the vertical variation of the cold pool boundary propagation is balanced by the circulation of low-level environmental wind shear (Rotunno et al. 1988; Moncrieff and Liu 1999; Weisman and Rotunno 2004). When the environmental wind shear exceeds the vertical gradient in the cold pool propagation speed, the updraft tilts downshear of the environmental wind, and when the circulation within the cold pool boundary dominates, the updraft leans against the cold pool boundary. In the RICO cases, although the shallow cumulus cold pools are much weaker than the midlatitude deep convection, the influence of shear on the lifting process should remain similar.

It is a challenge to disentangle the coexisting thermodynamic and dynamic aspects of cold pool effects, but proper attribution of causes holds the promise of improving those convective parameterizations that can be explicitly formulated to depend on cold pool processes (e.g., Bretherton et al. 2004; Mapes and Neale 2011; Rio et al. 2013). Simulation data provide four-dimensional fields that are more comprehensive for understanding the relevant processes than the two-dimensional (time–height) column data fields acquired observationally from a ship. An example can be made using the shipboard data from a motion-compensated 10-mm-wavelength Doppler lidar, a vertically pointing X-band precipitation radar, and 15-m flux tower meteorological data across the leading edge of a raining cold pool boundary (Fig. 2). The updrafts are located on the downwind side of the major precipitation and are associated with newly developed clouds, while the downdrafts that produce cooling and drying at the surface are associated with the rain shaft of the convection. The onset of surface precipitation, shown as the yellow triangle, coincides with the largest drop in surface temperature and water vapor. The in situ observations are intriguing but, lacking Lagrangian tracking and the full three-dimensional temperature, water vapor, velocity, and precipitation fields, they do not provide enough information for distinguishing between thermodynamic and dynamic mechanisms linking cold pools and convection. Such intriguing but inadequate pieces of information characterize field observations of spatially inhomogeneous time-varying phenomena, reinforcing the need for complementary modeling studies.

Fig. 2.
Fig. 2.

For 1540–1600 UTC 19 Jan 2005, (a) the shipboard X-band radar signal-to-noise ratio (gray shaded), with lidar-observed positive (red arrow) and negative (blue arrow) vertical velocities superimposed. Filled yellow triangle indicates the downwind-side surface cold pool boundary identified by the onset of surface rain. The ship-observed (b) surface rain rate, (c) surface air temperature, and (d) surface water vapor mixing ratio.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

Therefore, this study analyzes realistic, high-resolution model simulation to assess the processes by which shallow cumulus cold pools invigorate further shallow precipitation, motivated by observations of trade wind cumulus cold pools during the RICO experiment (Zuidema et al. 2012). We select 19 January 2005 for the simulation, in part because the day has been previously studied (Abel and Shipway 2007; Snodgrass et al. 2009). Conditions on 19 January reflect the influence of a dissipated cold front (Caesar 2005), with northeasterly winds rather than the easterly trades. A frontal boundary can explain the observed linear cloud lines (Fig. 1b), though no obvious gradient in temperature or moisture is documented in the surface meteorological measurements or the ship soundings. The observed liquid-phase-only precipitation (Fig. 2) is identified as “undisturbed” by Nuijens et al. (2009), meaning that the fractional area covered by precipitation deviates less than three standard deviations from the mean of RICO operating period (from 24 November 2004 to 25 January 2005). The influence of a dissipating cold front arriving from the north is likely a common occurrence for Caribbean trade wind cumuli during the boreal winter, so that 19 January may represent one of several typical conditions for trade wind cumulus.

The simulation uses the Weather Research and Forecasting Model (WRF) (updated version 3.2) with multiple nested domains—a modeling setup that has been previously successfully applied to study continental stratocumulus (Zhu et al. 2010). The nesting technique allows the model to explicitly resolve turbulent-scale processes in the innermost domain of 24 km × 24 km at 100-m resolution, while the open lateral boundary conditions allow a realistic large-scale forcing imposed on the parent domain of size 972 km × 972 km to transmit to the innermost domain. As will be shown, by incorporating a sensitivity to the realistic, spatially inhomogeneous, time-varying large-scale forcing, cold pools can develop within the relatively small inner domain of the nested-WRF simulation.

The ability of this simulation to model cold pools can be compared to the experience with large-eddy-scale simulations that typically apply doubly periodic boundary conditions, idealized initial conditions, and prescribed homogeneous large-scale forcing (e.g., Matheou et al. 2011; Seifert and Heus 2013). Such simulations assume that the turbulent atmosphere at the inflow boundary is identical to that at the outflow boundary—an assumption that is more applicable to the relatively homogeneous conditions of marine stratocumulus or nonprecipitating shallow cumulus than to strongly precipitating shallow-cumulus conditions. When nevertheless large-eddy-scale simulations of strongly precipitating shallow cumulus are undertaken, a sufficiently large domain and sufficiently high resolution of the turbulence processes is required to allow such spatially inhomogeneous features as the asymmetric trade wind cold pools to develop. Indeed, Matheou et al. (2011) are not able to reproduce precipitating mesoscale arcs until a resolution of 20 m is achieved within a comparable domain size of 20 km × 20 km. Seifert and Heus (2013) also find a significant time delay for the development of a cold-pool-dominated regime within their larger domain size of 50 km × 50 km at larger grid spacings (50 and 100 m) compared to a grid spacing of 25 m. Our 1-day hindcast simulation produces convection and cold pools that can be compared to the observations from this particular day, developing an understanding of the modeling strengths and weaknesses for nonhomogeneous conditions.

The specifications of this simulation, and comparisons of simulated convection and cold pools with observations, are presented in section 2. In section 3, we examine thermodynamic and dynamic cold pool convective invigoration mechanisms. The findings of our analyses are summarized and discussed in section 4.

2. Characteristics of simulated convection and cold pools

a. WRF simulation setup

The 19 January case is simulated from 0000 UTC 19 January to 0600 UTC 20 January 2005, with only the last 24 h analyzed. National Centers for Environmental Prediction (NCEP) (Final) Operational Global Analyses data (FNL) at 1° resolution, available at every 6 h, supply the initial and lateral boundary conditions. The sea surface temperature is prescribed from the NCEP FNL and updates every 6 h. One parent domain (972 km × 972 km) and four two-way nested domains centered at 18°N, 61.7°W are configured with nesting ratio of 1:3 (grid spacing of each outer domain is 3 times the grid spacing of its next-level nested domain). The innermost domain covers the track of the Research Vessel Seward Johnson (RVSJ), possessing a size of 24 km × 24 km with a horizontal spacing of 100 m. The vertical domain extends from the surface to 10 hPa with in total 77 levels, of which 48 levels are below 4 km with a vertical spacing varying from 6.5 to 200 m. We refer to the 3-m first model level as the surface level of this simulation. The 3D Smagorinsky scheme (Smagorinsky 1963) treats the subgrid-scale turbulent mixing for domains with 100- and 300-m grid spacing, and the Mellor–Yamada–Janjić boundary layer scheme (Janjić 2001) is used for treating the vertical turbulent mixing for the coarse domains. The simulation uses the single-moment Thompson cloud microphysics scheme (Thompson et al. 2008) (the known bug of WRF, v3.2, Thompson scheme is fixed with the updated code), with a total cloud droplet number concentration Nc = 100 × 106 m−3. Each of the 1441 one-minute simulation outputs from the innermost domain is treated as an individual sample for the statistical analyses.

Since the vertical resolution of NCEP FNL does not resolve the fine vertical structure of cumulus topped marine boundary layer, the thermodynamic profiles from radiosondes launched from the RVSJ every 6 h are assimilated and nudged in the outer domains. Figure 3 shows the average of the ship soundings from 19 January (19RVSJ) and the average of the profiles from the innermost model domain (19WRF). These are compared with the average of all soundings launched from RVSJ between 9 and 24 January (allRVSJ) and the average of the two- to six-times-daily soundings from Spanish Point, Barbuda, from 16 December 2004 through 8 January 2005 (SPNT). Spanish Point is located to the south-southwest of the ship. One of the ship radiosondes launched on 19 January penetrates a cloud that reaches above 4 km, causing the 19RVSJ water vapor mixing ratio above 3 km to be significantly higher than the simulated domain-average 19WRF values. The composite ship sounding of 19 January also reveals a moister atmosphere column above 1 km than the average of all soundings from the ship, indicating the additional moisture available for this day. The most significant difference is between the 19 January wind profiles and those of the 4-week-mean SPNT profile and 2-week January allRVSJ mean, with the allRVSJ wind profile more sheared than the SPNT profile. The winds are weaker on 19 January compared to allRVSJ, with the wind shear at 2.5–3 km. RICO-mean conditions at Spanish Point, Barbuda, show more easterly winds above 2 km and drier and warmer air above 2.5 km compared to the January-mean ship profile. The simulations described in vanZanten et al. (2011) are initiated by the mean soundings from SPNT, producing cloud tops that extend up to 2.5 km, with weak precipitation and no cold pools.

Fig. 3.
Fig. 3.

The average profile of (a) potential temperature, (b) water vapor mixing ratio, and (c) zonal and (d) meridional wind speeds for the innermost model domain averaged over the 24-h simulation period (black line; WRF), the average of six radiosondes launched from 0700 UTC 19 Jan to 0300 UTC 20 Jan from the ship (red line; 19RVSJ), all of the radiosondes launched from the ship during 9–24 Jan (green dotted line; allRVSJ), and all radiosondes launched from Spanish Point from 16 Dec 2004 through 8 Jan 2005 (blue dotted line; SPNT).

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

b. Comparisons to observed convection and cold pool air properties

The simulated surface air temperature reveals cold pools embedded within the larger-scale defined cloud line (Fig. 4a). Three shallow precipitating convection cases along with associated surface cold pools are documented within these cloud lines by the RVSJ flux tower. The flux tower measurements are gathered approximately 15 m above sea level with more detailed information regarding the instruments and data processing available in the appendix of Zuidema et al. (2012). The average and standard deviation of the 24-h flux tower measurements are compared to the 24-h simulation data from all grid points for air temperature, water vapor mixing ratio, and wind speed at 13-m level, as well as surface rain rate, sensible heat flux (SHF), and latent heat flux (LHF) (Table 1). The mean simulated air temperatures and water vapor mixing ratio match the average shipboard values well. The ship mean wind speeds are slightly higher than those of the WRF domain, yet the ship mean turbulent fluxes are less, implying higher transfer coefficients are used within the model. The relatively higher variability of the simulated wind speed is thought to reflect its variability across the domain, whereas the ship mostly remained within the linear cloud line, reporting mostly north-northeasterly winds (e.g., Fig. 1b, with a wind speed of 4.7 m s−1 at 1606 UTC).

Fig. 4.
Fig. 4.

A snapshot of the innermost domain from the simulation, with the size and location as indicated by the pink square in Fig. 1b. (a) WRF-simulated 3-m-level temperature (gray shaded) overlaid with the vertically integrated cloud water path (0–2 cm; white contours). (b) WRF-simulated 3-m-level water vapor mixing ratio overlaid with 3-m-level wind vectors.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

Table 1.

Mean and standard deviation σ of the 13-m-level simulated temperature, water vapor mixing ratio, Tυ, θe, wind speed, and sensible and latent heat fluxes are compared to the corresponding ship measurements during RICO.

Table 1.

The 24-h domain-averaged simulated surface rainfall rate is 2.1 mm day−1, which is relatively close to the daily area-averaged rainfall rate 1.87 mm day−1 derived from scanning precipitation radar reflectivities for this day (Snodgrass et al. 2009). The domain-averaged nonzero surface rain rate (RRa), is calculated for each output minute by averaging the surface rain rate of all grid points with rain rates of 0.1 mm h−1 or more, and RRa is set to zero when no such rain rates are present. RRa ranges up to 10 mm h−1, with 95% of the values exceeding 0 and below 6 mm h−1 (Fig. 5a). Rainier time periods were also cloudier, as shown in Fig. 5b. The cloud cover is defined as the fraction of grid columns that contain cloud at any level, and the mean cloud cover of all 1441 output minutes is about 0.13. This is comparable to the cloud cover reported by Matheou et al. (2011) using a grid spacing of 40 m. The average cloud cover of the top 10th percentile of RRa is 0.05 higher than the average of the remaining output minutes (Fig. 5b). The cloud cover increases with higher RRa for a correlation coefficient of 0.47.

Fig. 5.
Fig. 5.

(a) Probability density function of RRa with the dashed line indicating the threshold for 10% highest RRa. (b) Cloud cover as a function of RRa with the shading indicating the number density of output minutes. Dashed line indicates the mean cloud cover of the 24-h period. Two dashed–dotted lines extending to the right and left of the top 10% RRa threshold indicate the averaged cloud cover over the 10% output minutes with highest RRa and the other output minutes, respectively.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

The simulated surface temperature and cloud water path in Fig. 4a reveal the circular cold pools embedded within the linearly oriented cloud lines. The colder regions mostly correspond to drier air, as seen by the anomalous water vapor mixing ratio (Fig. 4b). The apparent change in surface wind can be spotted at some of these cold and dry boundaries (Fig. 4b). The simulated clouds also extend above 3 km (Fig. 6)—similar to the observations (Fig. 2). For output minutes with RRa > 0, the averaged vertical profile of cloud fraction shows three local peaks: at the cloud base (500 m), 1.6 km, and the level right below 3 km (Fig. 6a). The two upper peaks coincide with layers of slight enhanced wind shear (Figs. 3c,d). The buoyant cloud-core fraction, defined as the portion of cloudy grid cells (qc > 0.1 g kg−1) that are positively buoyant relative to the domain mean increasingly deviate from the averaged cloud fraction up to 1.6 km (Fig. 6a) as environmental air is mixed into the cloud. The clouds that do reach up to 2 km provide the peak at 2 km in the averaged cloud and rainwater mixing ratio (Figs. 6b,d), with drier conditions aloft.

Fig. 6.
Fig. 6.

For output minutes containing RRa > 0, with one standard deviation shaded: (a) domain-mean cloud fraction (solid), with the mean buoyant cloud-core fraction profile indicated separately (triangles); (b) horizontally averaged cloud water mixing ratio over cloudy region; (c) horizontally averaged water vapor mixing ratio over cloudy region; and (d) horizontally averaged rainwater mixing ratio within rain shaft.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

One assessment of the simulated cold pools is shown in Fig. 7 as a composite of all 1441 output minutes centered upon each output’s most intense instant rain center and the same composite for only those output minutes associated with the upper 10th percentile of RRa. For each of these output minutes, we first locate the grid point containing the domain-maximum surface rain rate, then consecutively sample the nearby grid points that align with the domain-averaged surface wind vector within the same moment in time, and average these surface air properties from the selected output minutes. The negative distance on the x axis corresponds to the downwind (southwestern) side and positive distance to the upwind (northeastern) side of the domain-maximum surface rain rate. Figure 7 also shows the average of the three observed cold pool passages from this day. These correspond to maximum surface rain rates of 7.4, 7.5, and 45 mm h−1. The ship moves in the same direction as the surface wind during the three cold pool passages, meaning that the ship samples its cold pool for longer than if it were stationary.

Fig. 7.
Fig. 7.

Composite of 13-m-level air properties across the domain-maximum surface rain rate (0 on x axis) from all 1441 simulation output minutes (black solid line with filled circle) and the output minutes of highest 10% RRa values (black dotted line), as compared to the observed flux tower measurements at 15 m averaged over the passages of the three cold pools documented on 19 Jan (red line with filled circle) of (a) rain rate, (b) wind speed, (c) temperature, (d) water vapor mixing ratio, (e) virtual temperature, (f) equivalent potential temperature, (g) sensible heat flux, and (h) latent heat flux.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

Figure 7 clearly shows that the simulated cold pools are, like the observations, asymmetric along the mean wind direction. The temperature change is steeper on the downwind side of cold pool, which is where the rain occurs. The wind increases ahead of the rain, enhancing the surface fluxes, and indicating the cold pool outflow. The mean rain rates in the simulation match observed values, while the average cold pool is obviously weaker than observed. The temperature depression is at best 0.5 K and the change in surface water vapor mixing ratio is negligible. The cold pools corresponding to the upper 10% of the RRa are significantly stronger than the average but still weaker than the observations. To some extent, the composite may reflect the process of averaging, but, nevertheless, the weak simulated cold pools also reflect on the ability of the simulation to produce cold pools. The 19 January observation captures only the change in wind direction at the cold pool boundary rather than wind speed [see Fig. 12g in Zuidema et al. (2012)], which we attribute to ship location.

The decreasing of the water vapor mixing ratio qυ and θe with θ in simulated cold pool cases are consistent with the observed cases (Figs. 8a,b). The wind changes in the simulation are stronger for the same change in θ than in the available observations, resulting in slightly larger surface fluxes (Figs. 8c,d). The simulated cold pools may be weaker than those observed in their thermodynamic properties, but the gustiness changes at the cold pool boundaries and the resulting convergence appear adequately captured.

Fig. 8.
Fig. 8.

The maximum surface changes within individual cold pools, observed on 19 Jan (red filled circles) and other “undisturbed” RICO days (pink filled circles), and contoured frequency distribution for the maximum anomalies within individual simulated cold pools represented by the composite of Fig. 7, for (a) qυ, (b) θe, and (c) wind speed, all as functions of the change in θ. (d) The change in LHF as a function of change in SHF using the same plotting conventions.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

c. Terminology and statistics of simulated cold pools

Since the objective of this study is to examine the ability of precipitation-induced cold pools to invigorate further convection at the downwind boundary, a necessary first step is to articulate how arc-shaped cold pool downwind boundaries and their influences are identified within the simulation. Strict criteria are imposed to appropriately identify precipitation-driven cold pool downwind boundaries. First, the cold pools’ characters as density currents are preserved through a criterion based on virtual potential temperature θυ. Second, a negative anomaly of θυ must be associated with the cold pool and not represent a preexisting condition. The horizontal θυ anomaly is calculated at each individual level below cloud base , and the horizontal anomalies of other scalars Δχ are calculated in the same manner. For output minute t, the cold pool downwind boundary grid points must be less buoyant than the domain mean [Δθυ(x, y, z)|t < 0] and must have been equally or more buoyant than the domain mean within the previous minute [Δθυ(x, y, z)|t−1 ≥ 0]. Third, the grid point wind speed must be higher than the speed of domain-averaged wind .

In addition, a connection of the cold pool downwind boundary to the precipitation and its catchment area are maintained by only selecting grid cells that already satisfy the conditions above and are in the proximity of significant rain. A grid point is considered near significant rain if the rectangle horizontal area of 6 km × 6 km centered on the grid point contains precipitating points and the average surface rain rate of these points are greater than 2 mm h−1. The rain-rate threshold and the size of the precipitation catchment area are reasonable if subjective choices. The 6-km-spatial-scale estimate is shown adequate to encompass most of the related rain catchment area (including the top 10% of strongest rain events) (Fig. 7) but still restrictive enough to exclude other irrelevant rainy points. The 2 mm h−1 catchment-area-average threshold has been identified previously as a way to distinguish cold pools that are dried by convective downdrafts from those that are moistened (Barnes and Garstang 1982). A catchment-area criterion also excludes those boundaries of cold pools that are dissipating with the decaying of convection. Based on these conditions, the cold pool downwind boundary can be automatically identified as shown in the example of Fig. 9. Overall, the combined criteria provide us with confidence that we are examining the subset of cold pool boundaries that are actively involved with promoting secondary convection. Of the 1441 output minutes, 620 contain at least one cold pool boundary satisfying this criterion—or, 43% of the total. The depth of the cold pool boundaries hcpb is estimated by the buoyancy of grid cells within the columns above the 3-m-level cold pool boundary points. For each output minute, the hcpb is the level where the number of negative Δθυ points within the columns becomes less than 10% of the 3-m-level cold pool boundary points.

Fig. 9.
Fig. 9.

Snapshots focusing on the 80-m-level cold pool downwind boundary (black stippled) from 2105 to 2123 UTC in 6-min intervals, showing the 80-m-level updraft area (red stippled), positive and negative Δqυ (light and dark shading, respectively), Δθe = 2 K contours (light green) that coincide with Δqυ = 0.7 g kg−1 (light shaded contours), and areas with surface rain rates ≥2 mm h−1 (light blue contours). Dashed black lines correspond to the cross sections in Fig. 16.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

Based on these definitions, about 91% of the cold pool boundaries have hcpb of 80 m or greater (Fig. 10), corresponding to 565 output minutes. The negative Δθυ extends through the whole subcloud layer for 31% of the boundaries, indicating deeper cold pools than Seifert and Heus (2013). The length along the 3-m-level cold pool downwind boundary arc Lcpb are below 20 km for all applicable output minutes, with 144 output minutes greater than 6.8 km (equivalent to cold pool diameters of about 12.7 and 4.3 km, respectively), the latter corresponding roughly to the scale of the highest 10% of rain catchment area in Fig. 7. The smaller Lcpb at the 80-m level relative to the surface level reflects the vertical reduction in cold pool size. Satellite images reveal arc-shaped organization of clouds spanning up to 40–60 km in equivalent diameter during RICO, and the ship-launched soundings identify some cold pools of 200 m in depth (Zuidema et al. 2012).

Fig. 10.
Fig. 10.

The accumulated probability density function of length along the cold pool boundary arc at the 3- (solid black) and 80-m (dashed black) levels and the cold pool boundary depth (solid blue).

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

The difference between the wind averaged within the cold pool downwind boundary and the domain-averaged wind is defined as the expansion rate of cold pool downwind boundary C*. Its magnitude is similar to the propagation speed of a density current that the expansion rate depends on the magnitude of negative buoyancy within the cold pools and the cold pool depth (Grandpeix and Lafore 2010). For output minutes that have multiple cold pools present in the domain, C* of each output minute is the average rate for all the cold pool downwind boundaries. In the following section, a subscripted number indicates the altitude level at which the C* is estimated.

The simulated updrafts are identified as points with vertical velocity w ≥ 0.5 m s−1. The updrafts that can potentially be influenced by the cold pool outflow by virtue of proximity need to be distinguished from the updrafts that occur thermodynamically regardless of the presence of a cold pool. This is done by delineating the area that encounters the propagating cold pool downwind boundary. A “cold pool ambient region” (CPAR) is defined as the area within 1 km downwind of the cold pool boundary at the 80-m level (with the cold pool boundary not included). Almost all (560 of the 565) output minutes with 80-m-level cold pool boundaries contain updrafts within 1 km of the boundary. Another distance choice of 1.5 km does not increase the sample size of updrafts within CPAR significantly, indicating the 1-km distance is capturing most of the updrafts. In contrast, a distance threshold of 0.5 km reduces the sample size significantly. Ultimately, while the choice of a 1-km distance is subjective, the choice is also reasonable. The potential reach of spatially inhomogeneous cold pool outflow to the updrafts in their vicinity is a statistical correspondence. More distant updrafts may still be influenced by cold pool density currents, and some updrafts downwind of the cold pool will already be thermodynamically buoyant, but as our results will show, a clear statistical signal of the influence of the upwind cold pool can be inferred based on a 1-km choice for the CPAR.

3. Cold pool effects

The cold pool effects on organizing subsequent precipitating shallow convection are examined in this section. The thermodynamic and dynamic properties of the updrafts within and outside the CPAR are compared to demonstrate the existence of cold pool effects, and the cold pool–affected updrafts are diagnosed thereafter for the mechanisms by which the convection is invigorated.

a. Cold pool effects on low-level updrafts

The 80-m-level anomalies of qυ, θ, and θe from the domain-mean values are averaged over the updraft points within and outside (including the output minutes lacking any cold pools) the CPAR for each applicable output minute (Fig. 11). Not surprisingly, updrafts tend to be moister and warmer than the domain-mean regardless of proximity to the cold pool boundary. The moisture content differs markedly between the two populations. The updrafts influenced by cold pool outflows are generally moister than for the other updrafts (Fig. 11a). When only compared to the updrafts within the same output minutes, the CPAR updrafts are moister than the other updrafts by a mean of 0.07 g kg−1 and are also slightly warmer (Fig. 11b). The impact of both the enhanced moisture and warmth can be seen in the distribution of the updraft θe anomaly values from their domain mean in Fig. 11c.

Fig. 11.
Fig. 11.

For the 80-m level, (a) contoured frequency distributions of as a function of Δθup for CPAR updrafts (red; based on the 560 output minutes) and non-CPAR updrafts (black; based on all the 1441 output minutes). (b) Contoured frequency distributions of the difference between the CPAR updrafts and the non-CPAR updrafts within the same output minute, as a function of the θup difference, based on 560 output minutes containing CPAR updrafts. (c) The probability distribution of for the CPAR updrafts (red; based on the 560 output minutes) and non-CPAR updrafts (black; based on all the 1441 output minutes).

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

In Fig. 12, the relationships of the overall moisture content of the CPAR relative to the domain mean with the difference between two populations of updrafts and the cold pool expansion rate are examined. On average, the CPAR updrafts only cover 16% of the CPAR area; CPARs that are uniformly moister are more capable of supporting individual moister updrafts (Fig. 12a). More interesting is the finding that moister CPARs are also associated with faster-expanding cold pools (Fig. 12b), possibly because of the more efficient converging of moisture by the cold pool expansion.

Fig. 12.
Fig. 12.

For the 80-m level, contoured frequency distributions of Δqυ averaged over all CPAR points as a function of (a) the difference between the CPAR updrafts and non-CPAR updrafts and (b) the cold pool expansion rate. Both plots based on the 560 output minutes containing CPAR updrafts.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

Although many of the cold pool–influenced updrafts are more buoyant than the other updrafts within the same moment (Fig. 11b), enhanced buoyancy is not the main factor affecting the speed of the CPAR updrafts. This is made clear when the vertical velocities of CPAR and non-CPAR updrafts are compared to their buoyancy, and then each group of updrafts is divided into their buoyant and nonbuoyant (relative to the domain mean) portion (Fig. 13). Overall, the CPAR updrafts are capable of attaining higher vertical velocities than the non-CPAR updrafts (Fig. 13a). The buoyant portion non-CPAR updraft vertical velocities increase with positive buoyancy (Fig. 13b) and likewise as the stability of the nonbuoyant portion increases (Fig. 13c)—indicating compensation between the buoyant and nonbuoyant portions (Fig. 13a). In contrast, the vertical velocities of buoyant CPAR updrafts do not show an increasing trend with the positive buoyancy (Fig. 13b), and the nonbuoyant portion of CPAR updrafts are closer to neutrally buoyant than the non-CPAR updrafts (Fig. 13c); the latter contribute to the higher buoyancy of CPAR updrafts relative to the non-CPAR updrafts.

Fig. 13.
Fig. 13.

For the 80-m level, contoured frequency distributions of the updraft vertical velocity wup as a function of the buoyancy bup for (a) updrafts, (b) buoyant portion of updrafts, and (c) nonbuoyant portion of updrafts, within CPAR (red; based on the 560 output minutes) and outside CPAR (black; based on the 1441 output minutes). Buoyancy of each grid cell is assessed relative to the domain mean: , where g is the gravitational acceleration.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

As a result of the CPAR updrafts not driven by buoyancy and the non-CPAR updrafts showing little effect of buoyancy on controlling the average updraft vertical velocities, the difference between the vertical velocity of the CPAR and non-CPAR updrafts taken from the same output minutes does not increase with higher buoyancy difference (Fig. 14a). However, we can infer from Fig. 14b that the dynamic lifting by the cold pool outflow contributes to strengthen the CPAR updrafts. The difference in vertical velocity between the CPAR and non-CPAR updrafts is enhanced with the cold pool expansion rate, as compared to the weak negative correlation of the relationship shown in Fig. 14a.

Fig. 14.
Fig. 14.

For the 80-m level, contoured frequency distributions of the vertical velocity difference between the CPAR updrafts and non-CPAR updrafts (CPAR − non-CPAR) as a function of (a) corresponding difference in updraft buoyancy and (b) cold pool expansion rate. Both based on the 560 output minutes containing CPAR updrafts.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

The cold pool expansion strengthens the updrafts by lifting air parcels preferably with high θe. The example of a cold pool occurring between 2105 and 2123 UTC provided in Fig. 9 helps to visualize these processes. In Fig. 9, the majority of the CPAR updrafts coincide with a high θe anomaly (Δθe > 2 K) as well as a high qυ anomaly (Δqυ > 0.7 g kg−1). A moisture patch located about 1–2 km to the downwind (southwestern) side of the cold pool boundary at 2105 UTC eventually converges with the cold pool boundary, becoming the locus for further updrafts.

b. Impact of ambient wind shear on the lifted updrafts

The relationship between the cold pool boundary and the ambient vertical wind shear can influence the orientation of the lifted updrafts and thereby the ability to further propagate convection (e.g., Liu and Moncrieff 1996; Weisman and Rotunno 2004). Figure 15 shows three possible scenarios of the relationship. The mean cold pool ambient horizontal wind U, which resembles the mean horizontal wind in this simulation, increases with height up to the cloud-base level, with a difference dU between vertical level z and z + dz of dU = U(z + dz) − U(z). By the definition of C*, the mean horizontal wind within the cold pool downwind boundary equals C* + U, and dC* = C*(z + dz) − C*(z). Since the environmental wind below cloud-base level enhances with height (e.g., Fig. 3), assume dU > 0, and cold pool expansion rate decreases with height; dC* and dU are of opposite sign. The sign and magnitude of dU and (dC* + dU) determine the direction and strength of the circulation associated with the ambient vertical wind shear and the wind shear within the cold pool downwind boundary, respectively. When the two circulations compensate for each other dU ~ −(dC* + dU) and dC* ~ −2dU (Fig. 15b). When the ambient wind circulation is stronger, dU > −(dC* + dU), and |dC*| < |2dU| (Fig. 15a). In addition, dU < −(dC* + dU) and |dC*| > |2dU| are true when the cold pool boundary circulation dominates over that of the ambient wind (Fig. 15c). The force-lifted updrafts follow the direction of the dominant circulation or rise upright when the two circulations counter each other. This, in turn, has an impact on the air feeding farther into the cloud.

Fig. 15.
Fig. 15.

Schematics of the three scenarios of the relationship between cold pool downwind boundary and ambient wind shear that cause different orientations of the force-lifted updrafts. Black arrows indicate mean/ambient horizontal wind U; blue arrows indicate the cold pool expansion rate C*. The tilted solid blue lines represent the interface between the cold pool downwind boundary and the environment. (a) The cold pool downwind boundary circulation is too weak to counter the ambient wind circulation; lifted updrafts follow the ambient wind shear direction. (b) The two circulations are about the same strength; the lifted updrafts rise upright. (c) The cold pool downwind boundary circulation is stronger than the ambient wind circulation; the lifted updrafts follow the wind shear direction within cold pool boundary.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

The cold pool ambient low-level vertical wind shear is estimated as the difference of mean horizontal wind relative to the 3-m level Usurf, at the 80-m level U80, 170-m level U170, and 300-m level U300, respectively. The ambient vertical wind shear in this simulation closely resembles the domain-mean vertical wind shear. The circulation that may balance the ambient vertical wind shear is associated with the difference in cold pool expansion rate at the 80-m level C*80, 170-m level C*170, and 300-m level C*300 relative to the 3-m level C*surf. The magnitude of C*80,170,300C*surf is smaller than the magnitude of U80,170,300Usurf for nearly all output minutes, with averaged |C*80,170,300C*surf| ≈ 0.6, 0.9, and 1 m s−1 compared to an average ambient wind shear of |U80,170,300Usurf| ≈ 1.8, 2.2, and 2.3 m s−1. Thus, the simulation most closely matches the condition shown in Fig. 15a, so that the lifted updrafts should rise along the downshear of the ambient or mean wind. The scenario may differ in nature, since the simulation underestimates the cold pool strength.

Cross sections 2105–2123 UTC aligned with the domain-averaged surface wind vector illuminate how the vertical structure of the subcloud updraft relates to the cloud and rain field (Figs. 16a–d). At 2105 UTC, the cold pool boundary is still away from some updrafts extending southwestward to about 2 km in Fig. 16a (see also Fig. 9a) that support the convection without the cold pool influence. At 2111 UTC, the surface-based stable cold pool layer diminishes the updrafts, and the updrafts below 300 m along the section are too weak to detect (Figs. 16b and 9b). At 2117 and 2123 UTC, the cross sections are able to capture the rain and strong downdrafts reaching the surface and are expanding the cold pool downwind boundary (Figs. 16c,d). The horizontal wind anomalies of updrafts below 300 m change signs from against the mean wind direction at 2105 UTC to along the mean wind and mean wind shear direction (Figs. 16c,d,g,h). The updrafts that advance faster than the mean wind have better access to the ambient environmental moisture that converged by expanding cold pools. In addition, as evident in Fig. 16, the wind shear above the cloud base tilts the cloud into the wind, allowing the precipitation to fall inside the cold pool and thereby strengthen the already-existing cold pool with its evaporative cooling.

Fig. 16.
Fig. 16.

Snapshots of cross section along the dashed black line indicated in Fig. 9 for 2105–2123 UTC. (a)–(d) Cloud mixing ratio qc > 0 g kg−1 (black contours), rain mixing ratio qr > 0 g kg−1 (light blue contours) with denser contours indicating higher qr, and plane-projected wind vectors relative to the domain-averaged wind for updrafts (red arrows) and downdrafts (deep blue arrows) below cloud-base level (dotted line). Negative buoyancy below cloud-base level (dark shaded). (e)–(h) The speed of domain-averaged horizontal wind projected onto the cross section. Note that the negative wind speed on the x axis suggests northeasterly.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

c. Cold pool effects at the cloud-base level

The updrafts at the cloud-base level are more directly related to the cloud and rain development than the low-level updrafts considered so far. The 450-m level in the simulation is below and most near the average model cloud base (Fig. 6a), and is referred to as the cloud-base level. The thermodynamic and dynamic properties of the cloud-base-level updrafts are analyzed for evidence of cold pool effects. Similar to the updrafts at the 80-m level, the cloud-base-level updrafts are also divided into two groups depending on whether or not they are directly above the 80-m-level CPAR.

The CPAR updrafts retain their high θe anomalies relative to the domain-mean θe from 80 to 450 m, shifting the number density peak from (Figs. 11c and 17a). The higher of the CPAR updrafts is mainly due to their higher humidity, but the moister CPAR updrafts are also cooler than the non-CPAR updrafts (Fig. 17b). The high--but-cold-CPAR updrafts are thereby neutrally even slightly less buoyant relative to non-CPAR updrafts (Fig. 17c), in contrast to a slightly positive relative buoyancy at the 80-m level (Fig. 14a).

Fig. 17.
Fig. 17.

For the 450-m cloud-base level, (a) the probability density of for CPAR updrafts (red; based on the 560 output minutes) and non-CPAR updrafts (black; based on the 1441 output minutes). Contoured frequency distributions of differences between CPAR updrafts and non-CPAR updrafts (CPAR − non-CPAR ) for (b) difference as a function of the θup difference, (c) the wup difference as a function the bup difference, and (d) the wup difference as a function the 80-m-level cold pool expansion rate. The 560 output minutes containing CPAR updrafts are the basis for (b)–(d).

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

The scale of vertical velocity differences (CPAR − non-CPAR) at cloud-base level is 3 times that at the 80-m level (Fig. 17d versus Fig. 14b), attesting to the impact of the cold pool dynamic lifting. Although the correlation of cloud-base-level vertical velocities difference with the 80-m-level cold pool expansion rate is even weaker than the 80-m-level vertical velocity difference, attributed to the weaker correlation between the CPAR updraft vertical velocities at the cloud-base and 80-m levels (r = 0.3) as compared to the non-CPAR updrafts (r = 0.7). Possible interpretations include that the lifting force that depends on the cold pool strength varies over time with the precipitation fall upon the cold pool, and more mixing with environmental air takes place when air is dynamically lifted from 80 m to the cloud-base level under the influence of wind shear interaction between the cold pool boundary and the ambient winds.

The cloud-base-level updraft coverage may also be affected by the presence of cold pool boundary in the domain. A Δθe distribution for the CPAR cloud-base-level updrafts that resembles that for the non-CPAR updrafts (Fig. 17a) can be achieved by removing some current CPAR updrafts that contribute to the excessive number density relative to the non-CPAR updrafts for higher Δθe values, which include around 50% of the current CPAR updrafts. This estimation suggests that cold pool lifting approximately doubles the updraft coverage within CPAR at cloud-base level. However, this contribution to total updraft coverage is very small, since the CPAR updrafts only make up around 3.3% of the total cloud-base-level updrafts.

Nevertheless, the CPAR updrafts are capable of generating more cloud than the non-CPAR updrafts. The average cloud water path (CWP) associated with CPAR updrafts is 254 g m−2, compared to 130 g m−2 for the non-CPAR updrafts. The CWP associated with non-CPAR updrafts depends strongly on the cloud-base-level vertical velocity (Fig. 18a), whereas the CPAR CWPup values are higher in the mean for the same vertical velocity, if also more variable. The CWPup differences (CPAR − non-CPAR) increase from about −200 to 400 g m−2 as the relative vertical velocity increases from about −0.5 to 0.6 m s−1 (Fig. 18b). A similar relationship with CWP does not occur for θ or humidity difference (not shown). Cold pools affect cloud growth by altering the thermodynamic properties of the updrafts to include more humid, cooler air (Fig. 17b) and by enhancing the updraft speed; Fig. 18b suggests the latter is particularly important for encouraging deeper, high–liquid water path clouds.

Fig. 18.
Fig. 18.

(a) Contoured frequency distributions of the cloud water path of updraft columns as a function of the cloud-base-level vertical velocity for CPAR updrafts (red; based on the 560 output minutes) and non-CPAR updraft (black; based on the 1441 output minutes). (b) Contoured frequency distributions of the difference in cloud water path of CPAR updrafts relative to non-CPAR updrafts as a function of the cloud-base-level vertical velocity difference, based on the 560 output minutes containing CPAR updrafts.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

4. Conclusions and discussion

This study attempts to identify the dominant mechanisms supporting the updrafts generating precipitation by shallow trade wind cumuli organized in mesoscale arcs. The mechanisms that are considered include 1) thermodynamically enhanced updrafts due to either environmental moisture from outside the cold pool or moisture generated by the evaporation of rain inside the cold pool (Tompkins 2001) and 2) forced lifting by the expanding cold pool. These mechanisms are not completely independent of each other, since, for example, both mechanisms may be implicated when a cold pool boundary moving faster than the mean wind converges and further lifts high-θe air, as sketched in Fig. 19. The individual mechanisms are examined through statistical comparisons of the updrafts within and outside of the regions near the cold pool boundaries, as is the time evolution of a selected case study.

Fig. 19.
Fig. 19.

Schematic of an instantaneous view on a propagating cold pool being strengthened by a convective downdraft due to precipitation, while invigorating further convection on the downwind-side cold pool boundary through the modification of updraft properties.

Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0184.1

The analyses reveal that the updrafts in the proximity of the downwind cold pool boundary are typically moister than the other updrafts. The higher humidities generate higher θe for the cold pool–influenced updrafts. The temperatures of the CPAR updrafts are slightly warmer than those of the non-CPAR updrafts at the lower subcloud layer but are cooler at the cloud-base level. In contrast to non-CPAR updrafts that rise by their thermodynamic privilege or dynamic lifting along the larger-scale defined convergence lines (Fig. 1b), the CPAR updrafts are more subject to local dynamic processes. The updrafts near the cold pool boundaries generate more cloud water on average than the updrafts away from cold pools. The cold pool boundary collects environmental moisture as it propagates into new environments, causing moisture convergence close to the boundary. The moisture excess of the updrafts within CPARs correlates well with an overall positive moisture anomaly for the CPARs. The cold pool–lifted air parcels originate from the moist air within CPAR and contribute to the broader θe range for the CPAR updrafts. These results speak to a preferential sampling of preexisting environmental moisture pools that may well reflect the remnants of other convective events, but little evidence is found to support the hypothesis that updrafts at the cold pool boundary arise from air premoistened by earlier subcloud evaporation from the same convection (Tompkins 2001). Instead, these results speak more to the ability of secondary convection to thrive and continue when propagating into relatively moist environments.

The strengthening of CPAR updrafts by cold pool dynamic lifting is evident through their enhanced vertical velocities at the 80-m level, as compared to the non-CPAR updrafts. The dynamic lifting by the cold pool outflow slightly increases the area covered by the cloud-base-level updrafts by introducing more air parcels that may not rise otherwise. Since these parcels tend to be moist, they contribute to the higher cloud liquid water paths associated with the CPAR updrafts compared to non-CPAR updrafts.

A parameterization for cold pool dynamic lifting introduced by Grandpeix and Lafore (2010) and Rio et al. (2009, 2013) is based on the idea that greater expansion rates and deeper and larger cold pools favorably induce higher updraft mass flux at the cold pool downwind boundary. Compared to midlatitudes, the tropics provide abundant moisture that is available for the cold pool–enhanced updrafts. The cold pool effects on enhancing the updraft coverage and vertical velocity require consideration in GCM parameterizations of trade wind cumulus. However, such parameterizations would need to be modified to account for the moderate depth and strength of shallow cumulus cold pools, as well as focusing on parameterizing the updraft properties and associated cloud water path rather than those of the cloud-base mass flux.

This study relies on a nested-WRF simulation with an innermost domain size of 24 km × 24 km and a horizontal grid spacing of 100 m and vertical resolution of 48 levels below 4 km. The nesting technique provides open lateral boundary conditions that allow the reanalysis-derived large-scale forcing imposed on the parent domain of 972 km × 972 km to be transmitted to the innermost domain capable of resolving large-eddy-scale circulations. This simulation is able to produce cold pools, as observed for this day, although with weaker changes in surface air properties for rain rates that often exceed those observed. This ability to model cold pools can be compared with the behavior of large-eddy-scale simulations that typically apply doubly periodic boundary conditions and idealized, homogeneous initial conditions and forcings. Such simulations require larger domains at a higher resolution to be able to capture the spatially inhomogeneous, asymmetric trade wind cumulus cold pools (e.g., Matheou et al. 2011; Seifert and Heus 2013). Instead, this study’s modeling approach demonstrates that the ability to explicitly simulate a spectrum of scales—from the large-scale flow, to the mesoscale, and further down to the largest of the turbulent eddies—is also effective for the simulation of cold pools. This connection between the synoptic scale and the mesoscale has typically been ignored for trade wind cumulus but likely represents a common interaction for the trade wind region with the midlatitudes, of which 19 January 2005 is an example.

Wind shear is arguably overly efficient at shearing off upper-level cloud in the simulations compared with the observations (Fig. 16) and this may suggest that the updraft strength is also weaker than in nature. Nevertheless, the increase in cloud fraction with domain-averaged rain rates is in agreement with observations. The weak simulated cold pools on average could reflect issues with the spatial resolution, microphysical parameterization, and turbulent mixing. A reduced grid spacing would allow more resolution of the turbulent-scale processes and amplify the downdrafts and updrafts for forming the cold pools and invigorating convection. This in turn may also affect the relationship of the cold pool circulation with the low-level environmental wind shear. In this simulation, the low-level environmental circulation is consistently stronger than the circulation of the cold pools, and in the case study examination of updrafts lifted by a strong cold pool, the lifted updrafts point downshear, as would be expected.

The trade wind cumulus cold pools are associated with stronger winds in the lower boundary layer, which in turn will generate stronger surface fluxes [Fig. 8; see Zuidema et al. (2012) for a more complete analysis of the observed surface fluxes]. The cold pools provide a mechanism for generating the stronger updraft velocities that can also deepen the boundary layer. As such the cold pools may help stabilize the relative humidity in the trade wind regions by encouraging the drying and warming of the boundary layer through entrainment of drier, warmer air from aloft. This contrasts with the cooler, moister cold pools that have been observed for stratocumulus (Terai and Wood 2013), wherein increased stability traps the moisture introduced by the latent heat fluxes off the ocean near the surface.

Possible reasons for the weak cold pools in this and other simulations despite variations in the imposed boundary conditions include numerical diffusion and grid resolution (Matheou et al. 2011), as well as the microphysical parameterization (Seifert and Heus 2013). This simulation uses the bulk microphysics scheme of Thompson et al. (2008), which employs a single-moment parameterization for rain. Although less explicit than double-moment schemes, the diagnosis of the intercept parameter from the rain mixing ratio enables the Thompson scheme to generate a large number concentration of small raindrops when the rain mixing ratio is low. Because small drops evaporate more readily, this should favor more evaporation, leading to stronger convective downdrafts, than if the intercept parameter were a fixed value. This, in fact, is evident in a one-dimensional model intercomparison where the Thompson scheme produces the largest rain evaporation rates of the microphysics schemes assessed for similar environmental moisture (Shipway and Hill 2012). The modeled surface rain rates are larger than observed, and the use of assimilated soundings help ensure that the subcloud environmental moisture is realistic, so that it seems unlikely that the simulated rain evaporation rates are less than occurred in nature. This does not rule out the importance of turbulent mixing in changing the properties of the downdrafts and updrafts. Further work will assess the influence of choice of microphysical parameterization more completely.

This study focuses on one day only (19 January 2005). The convection generated for this day is associated with a dissipating cold front, but the associated cold pool strength falls within the envelope of values from more truly undisturbed days (Fig. 8). Further comparative modeling studies can help assess the representativeness of these results for days possessing cold pools within other typical trade wind conditions.

Acknowledgments

We thank the NSF Physical and Dynamic Meteorology Division and Program Manager Brad Smull for support through Grant AGS-1114521 and NOAA Climate Project Office Grant NA130AR4310157.

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