Editorial Type:
Article
Article Type:
Research Article

Thermally Forced Convection over a Mountainous Tropical Island

Chun-Chih Wang Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

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Daniel J. Kirshbaum Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

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Print Publication:
01 Jun 2015
DOI:
https://doi.org/10.1175/JAS-D-14-0325.1
Page(s):
2484–2506
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Abstract

Observations from the Dominica Experiment (DOMEX) and cloud-resolving numerical simulations are used to study a thermally forced convection event over the Caribbean island of Dominica on 18 April 2011. A clear diurnal cycle of island thermal forcing and cumulus convection was observed, with cumuli initiating over the southwestern flank of the ridge and deepening as they drifted eastward. Apart from errors in cloud fraction and (notably) precipitation, the simulations verified well against the observations, provided horizontal grid spacings of 500 m or less were used. The simulated flows developed an island-scale solenoidal circulation with an organized and intense updraft over the ridge that focused convective initiation. Sensitivity tests investigated the impacts of topographic forcing, subcloud winds, and cloud–radiative feedbacks on the island-scale horizontal inflow and cloud vertical mass flux. These experiments confirmed that thermal forcing drove the island convection and that the inflow and cloud mass flux were maximized under weak ambient cross-island winds. The simulations also indicated that cloud shading and precipitation each reduced the island inflow by ~20% while cloud latent heat release enhanced it by ~20%. However, precipitation caused a much smaller reduction in cloud mass flux (10%) than did cloud shading (50%) owing to effective secondary convective initiation by subcloud cold pools. Thermodynamic heat-engine theory provided accurate predictions of the simulated solenoidal updraft magnitudes in selected cases. It also provided a simple explanation for the weakening of the simulated thermal circulation in the presence of island orography: a shallower mixed layer reduced the efficiency of the thermal circulation.

Corresponding author address: Daniel J. Kirshbaum, Department of Atmospheric and Oceanic Sciences, McGill University, 805 Sherbrooke St. West, Montreal QC H3A 0B9, Canada. E-mail: daniel.kirshbaum@mcgill.ca

Abstract

Observations from the Dominica Experiment (DOMEX) and cloud-resolving numerical simulations are used to study a thermally forced convection event over the Caribbean island of Dominica on 18 April 2011. A clear diurnal cycle of island thermal forcing and cumulus convection was observed, with cumuli initiating over the southwestern flank of the ridge and deepening as they drifted eastward. Apart from errors in cloud fraction and (notably) precipitation, the simulations verified well against the observations, provided horizontal grid spacings of 500 m or less were used. The simulated flows developed an island-scale solenoidal circulation with an organized and intense updraft over the ridge that focused convective initiation. Sensitivity tests investigated the impacts of topographic forcing, subcloud winds, and cloud–radiative feedbacks on the island-scale horizontal inflow and cloud vertical mass flux. These experiments confirmed that thermal forcing drove the island convection and that the inflow and cloud mass flux were maximized under weak ambient cross-island winds. The simulations also indicated that cloud shading and precipitation each reduced the island inflow by ~20% while cloud latent heat release enhanced it by ~20%. However, precipitation caused a much smaller reduction in cloud mass flux (10%) than did cloud shading (50%) owing to effective secondary convective initiation by subcloud cold pools. Thermodynamic heat-engine theory provided accurate predictions of the simulated solenoidal updraft magnitudes in selected cases. It also provided a simple explanation for the weakening of the simulated thermal circulation in the presence of island orography: a shallower mixed layer reduced the efficiency of the thermal circulation.

Corresponding author address: Daniel J. Kirshbaum, Department of Atmospheric and Oceanic Sciences, McGill University, 805 Sherbrooke St. West, Montreal QC H3A 0B9, Canada. E-mail: daniel.kirshbaum@mcgill.ca
Keywords: Convective clouds; Cumulus clouds; Diurnal effects; Sea breezes; Valley/mountain flows; Cloud resolving models

1. Introduction

Tropical islands are hot spots for cumulus convection because of their strong perturbation of conditionally unstable airflow (e.g., Qian 2008; Smith et al. 2009). Under weak winds, the stronger daytime heating over land than over the surrounding sea destabilizes the island flow and gives rise to thermally direct circulations that promote vertical motion. These thermal circulations often collapse into sea breeze–land breeze fronts, with potent updrafts along and ahead of their frontal surfaces (e.g., Kingsmill 1995; Carbone et al. 2000; Fovell 2005). As the wind strengthens and/or the island narrows, the island heat anomaly is carried into the wake and organizes into quasi-linear convergence zones. The associated updrafts may initiate cloud trails extending far downwind (e.g., Yang et al. 2008; Kirshbaum and Fairman 2015).

Convection may also be initiated mechanically as impinging moist flow is forced to ascend or divert around mountainous island terrain. Over the Hawaiian islands of Kauai and Oahu, trade winds are often strong enough to surmount the 1000–1500-m-terrain crests, leading to persistent heavy precipitation over the windward slopes (e.g., Schroeder 1977; Ramage and Schroeder 1999). As the island height increases (e.g., over the island of Hawaii) or the cross-barrier wind decreases, the impinging airflow eventually becomes blocked, with convergence zones shifting upwind and/or downwind of the island (e.g., Smolarkiewicz et al. 1988; Yang and Chen 2008). Mechanical and thermal forcings often interact, particularly in blocked flows over taller and larger islands like Hawaii and Taiwan, to produce rich diurnal variations in clouds and precipitation (e.g., Yeh and Chen 1998; Yang and Chen 2008).

Although less studied than Hawaii, the Lesser Antilles islands in the Caribbean Sea also regularly initiate cumulus convection. These islands are situated in the subtropical Atlantic trade wind belt with similar heights and sizes as Kauai. The island of Dominica, with a peak height of ~1.5 km (see Fig. 1), has received recent attention because of its dramatic orographic enhancement of trade wind precipitation and its pronounced dynamical wakes (Kirshbaum and Smith 2009; Smith et al. 2009, 2012; Minder et al. 2013). During the Dominica Experiment (DOMEX) in April–May 2011, surface rain gauges, meteorological stations, operational radars, and the Wyoming King Air (WKA) research aircraft observed Dominican airflow and convection (Smith et al. 2012, hereafter S12). As expected, many events featured strong trade winds, large orographic precipitation enhancements, and turbulent island wakes. However, four other events featured unexpectedly weak trade winds and thermally driven convection, with strikingly different dynamical and microphysical signatures from the strong-wind events.

Fig. 1.
Fig. 1.

(top) Map of the western Atlantic Ocean and Caribbean Sea, (bottom left) the DOMEX study region with data sites, and (bottom right) Dominica’s terrain. Filled squares are surface stations, open triangles are operational radar locations, and open circle is the TFFR radiosonde location.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

While thermally forced convection over flat islands and mechanically forced convection over mountainous islands have each received attention separately, few studies have examined thermally forced convection over mountainous islands. This subject is important because a large fraction of tropical islands (e.g., the Lesser Antilles, Hawaii, and the Maritime Continent) are mountainous, and the mountains may play a pivotal role in convection initiation. In particular, elevated heating enhances local baroclinicity, which may enhance flow convergence and convection initiation (e.g., Kirshbaum and Wang 2014). On the other hand, high terrain can block the inland penetration of sea breezes, thus inhibiting island convection (Qian et al. 2012; Barthlott and Kirshbaum 2013). While recent studies have attempted to quantify elevated-heating effects over idealized terrain using linear models and heat-engine theory (e.g., Tian and Parker 2003; Crook and Tucker 2005; Kirshbaum and Wang 2014), the applicability of such simple models to turbulent flows over realistic topography remains uncertain.

Herein we exploit DOMEX observations and cloud-resolving numerical simulations to investigate thermally forced convection over Dominica. We study the “golden” event of 18 April 2011, which was characterized by the most vigorous and quasi-steady cumulus convection of the four weak-wind events. Section 2 provides an observational overview of this event, illustrating the diurnal evolution and finescale structure of the island convection. To complement the observations, sections 3 and 4 provide cloud-resolving numerical simulations of the event. Section 3 observationally verifies a set of “control” simulations at different grid resolutions, and section 4 presents sensitivity experiments that evaluate the impacts of specific environmental and topographic parameters on the island circulations and convection. Section 5 uses heat-engine theory to quantify and interpret the subcloud thermal circulations, and section 6 presents the conclusions.

2. Observations

The 18 April 2011 convection event over Dominica, observed by the seventh research flight (RF07) of DOMEX, was identified by S12 as a prototypical case of thermally forced island convection under weak background winds. In a preliminary analysis of the event, S12 contrasted WKA observations of RF07 against a prototypical strong-wind event (research flight 13, or RF13) on 27 April 2011. Whereas the cross-barrier winds in the lowest kilometer were less than 2 m s−1 in RF07, they exceeded 12 m s−1 in RF13. S12 identified several key differences between the two events, including (i) a transition from divergent (RF07) to convergent (RF13) flight-level (1.8 km) winds over the island terrain; (ii) a sharp increase in the cloud aerosol and droplet-number concentrations, and a corresponding decrease in the droplet diameter, in RF07; and (iii) much heavier precipitation in RF13. These striking differences have motivated more detailed studies of each event: the RF13 case was studied by Minder et al. (2013) and the RF07 case is studied herein. In contrast to S12, we focus primarily on the island thermal circulations, rather than the cloud microphysics, of RF07.

a. Data sources

A full description of the DOMEX observational facilities is provided in S12. Here we briefly review the subset of DOMEX observations used in this study, which are summarized in Fig. 1. Operational surface meteorological data were obtained from Météo France stations on Martinique (Aimé Césaire Airport, station identifier TFFF) and Guadeloupe (Pointe-à-Pitre Airport, station identifier TFFR). An additional “mountain weather” station on Dominica was installed for DOMEX on an east-facing ridge near Freshwater Lake (FWL) at a height of 860 m above mean sea level (MSL), with data at 2-min resolution. Plan-position-indicator scans were provided from an operational Météo France radar on Martinique with a nominal frequency of 5 min (a radar was also present on Guadeloupe but it was not used). The radar elevation angle was 0.5° everywhere except over and past terrain obstacles, where the lowest unblocked elevation above ground was used. In addition, raw visible satellite data from the National Oceanic and Atmospheric Administration (NOAA) Geostationary Operational Environmental Satellite-13 (GOES-13), with a pixel spacing of 1 km and a nominal time resolution of 30 min, were obtained from NOAA’s Comprehensive Large Array-Data Stewardship System (CLASS).

DOMEX featured 21 WKA research flights over April–May 2011. The nominal WKA flight pattern consisted of eight horizontal flight legs plus an upstream aircraft sounding from 150 to 4000 m (S12). Three ocean legs on different sides of the island were flown at two different altitudes (low, or “L,” at ~300 m and high, or “H,” at ~1200 m) to sample upstream and downstream airflow at different levels, and two over-island legs were flown at ~1800 m. On 18 April 2011, however, the flight track was altered to repeatedly sample the island convection in a racetrack pattern over the high terrain. Ten legs were flown, including leg 1 well upstream of Dominica (both low and high), the leg 2 dogleg just off the east coast (both low and high), and three legs 3 and 4 directly over the island (Fig. 1).

In situ aircraft data include positional measurements using an inertial navigation station (INS) corrected with differential GPS (using a base station on Martinique), three-dimensional winds using a gust probe with INS, static temperature using a reverse-flow thermometer, static pressure using a Rosemount 1501 sensor with INS, water-vapor mixing ratio using a LICOR-6262 infrared gas analyzer, cloud-droplet size distributions using a forward-scattering cloud-droplet probe (CDP), and rain size distributions using two-dimensional optical array precipitation probe (2D-P). Although the in situ data were available at a sampling frequency of 25 Hz, we use a lower sampling rate (1 Hz) for ease of analysis. With a WKA airspeed of around 90 m s−1, this gives a sampling distance of around 90 m, which is sufficient for comparison with our numerical simulations. We also incorporate reflectivity and radial velocity profiles from the 95-GHz Wyoming Cloud Radar (WCR; http://www.atmos.uwyo.edu/wcr/) aboard the WKA.

b. Overview of RF07

The WKA sounding, recorded as the WKA looped around the southern half of leg 1 over 1138–1153 local solar time (LST) while descending from ~4000 to ~150 m, is shown in Fig. 2. To deepen the sounding into the stratosphere, we patched the operational 1200 UTC Guadeloupe (TFFR) sounding to the top of the aircraft sounding at 3792 m (642 hPa). Despite the reduced resolution of the TFFR sounding, the two profiles connect smoothly with no obvious jumps in the temperature, dewpoint, or wind profiles.

Fig. 2.
Fig. 2.

Skew T profile showing temperature (black), dewpoint (gray), and wind (vectors to the right) profiles of the merged WKA sounding from RF07 and the TFFR sounding from 1200 UTC 18 Apr 2011. The WKA sounding data were smoothed to a uniform vertical spacing of 50 m. The black horizontal dashed line at 3792 m (~640 hPa) marks the height at which the WKA sounding was connected to the TFFR radiosonde.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

The merged sounding contains a shallow subcloud layer (from 0 to 600 m, or 1007 to 940 hPa) and a dry, conditionally unstable cloud layer (from 800 to 3500 m, or 917 to 660 hPa) separated by a sharp transition layer. Subcloud winds are weak and northerly while cloud-layer winds are also weak and westerly. The cloud layer is overlaid by a very dry and nearly moist-neutral layer extending to ~12 km. The sounding has a mean-layer (0–500 m) convective available potential energy (CAPE) and convective inhibition (CIN) of 119 and 87 J kg−1, respectively, suggesting weak instability and strong inhibition. The lifting condensation level (LCL), level of free convection (LFC), and level of neutral buoyancy (LNB) are 810 m (916 hPa), 1177 m (877 hPa), and 8535 m (347 hPa), respectively.

Time series of surface observations from the FWL mountain weather station reveal that the incoming shortwave radiation () rapidly increased from 0600 to 1000 LST but then decreased sharply and fluctuated for the rest of the day (Fig. 3a). Similarly, the surface temperature () increased from about 17° to 26°C over 0500–1000 LST and then promptly decreased by 3°–4°C, while the relative humidity (RH) decreased from 95% to 70% over 0500–0900 LST and then slowly rebounded during the day (Figs. 3b,c). These variations suggest that full insolation in the early morning hours raised the temperature and the saturation vapor pressure of near-surface air, after which intermittent cloud shadowing limited the heating in the afternoon. The water-vapor mixing ratio (), which increased in the morning owing to evaporation of water off the forested island surface, also reached a peak at around 1000 LST (of 17 g kg−1) then settled into the 14–16 g kg−1 range (Fig. 3d).

Fig. 3.
Fig. 3.

Time series at the FWL mountain weather station for both observations (green) and control simulations (different shades of blue for 125–1000 m): (a) shortwave radiation flux (), (b) temperature (), (c) relative humidity (RH), (d) water vapor mixing ratio (), and (e) ΔSLP (see text for definition). The dashed green vertical lines in all panels denote the timing of the WKA leg-3 and -4 racetrack period.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

The sea level pressure difference between FWL and the base of the ocean sounding (ΔSLP) indicates the diurnal evolution of the thermally induced pressure anomalies that drove the island-scale circulation (Fig. 3e). Care is required in this computation because the FWL time series contains diurnal and semidiurnal tides while the aircraft sounding is instantaneous. To create an ocean SLP time series that is directly comparable to the FWL time series, we follow a similar procedure to Minder et al. (2013): we average the SLP from two coastal surface stations (the Guadeloupe and Martinique airports) and isolate the tidal variations by applying a low-pass Butterworth filter with a cutoff frequency of four cycles per day. We then fit the filtered time series to the instantaneous ocean SLP measurement to create an ocean SLP time series, which is subtracted from the FWL SLP time series to give ΔSLP.

As expected from hydrostatic considerations, the ΔSLP thus produced follows the opposite evolution as : it peaked in the morning (~0.5 hPa), reversed sign and reached a minimum of about −2.4 hPa at 1000 LST, then underwent an abrupt 1-hPa increase and lower-amplitude fluctuations over the remainder of the day. Although FWL is just a point location and not representative of the entire island, these ΔSLP variations hint at the timing of the island thermal circulations. The positive ΔSLP in the early morning, and negative ΔSLP in the late morning and afternoon, suggest nocturnal katabatic flow transitioning to anabatic flow during the strongly insolated morning hours, followed by a weakening of the anabatic flow due to negative cloud feedbacks (shading and precipitation).

The diurnal cloud development is depicted by the satellite-derived effective albedo at four times (0815, 1115, 1415, and 1715 LST) in Figs. 4a–d. The effective albedo is converted from raw satellite counts using online calibration routines for GOES imagers. The island clouds were largely nonexistent in the early morning and formed over the higher terrain at ~1000 LST (Figs. 4a,b). They became more widespread in the afternoon then gradually dissipated (Figs. 4c,d). The cloud fraction (), or the fraction of island pixels with effective albedos exceeding 0.3 (Fig. 4e), increased through the morning to a peak of around 40% at 1315 LST, then decreased to zero again toward sunset. It exceeded 30% during all three over-island racetracks (indicated by the shaded region).

Fig. 4.
Fig. 4.

Satellite data from 18 Apr 2011, including (a)–(d) effective albedo at four different times and (e) time series of island cloud fraction (the fraction of island points with effective albedos > 0.3). The gray shading denotes the WKA leg-3 and -4 racetrack period.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

Figure 5 shows in situ WKA horizontal velocities along legs 1L, 2L, 3, and 4, overlaid upon the averaged cloud albedo over the 1200–1500 LST flight period. Only the third passes of legs 3 and 4 are shown. Over leg 1 the subcloud winds transitioned from north-northeasterly in the north to northerly in the south, suggesting flow deflection around the island. In the absence of thermal forcing, such deflection is favored when the nondimensional mountain height (, where is the crest height and N and U are the Brunt–Väisälä frequency and cross-barrier wind speed in the sub-mountain-crest layer) significantly exceeds unity (e.g., Smolarkiewicz and Rotunno 1989; Jiang 2003). Using km and the layer-averaged N (0.009 s−1) and U (2 m s−1) below 1500 m, we obtain , which indeed favors strong flow deflection. Given that such deflection tends to be maximized at mountain base (e.g., Galewsky 2008), one might expect it to strengthen along leg 2. However, the deflection actually weakened along leg 2, which suggests that it was offset by thermally forced onshore flow (e.g., Reisner and Smolarkiewicz 1994). The over-island legs (legs 3 and 4) indicate elevated flow divergence over the high terrain due to outflow from the island thermal circulation and cumulus convection.

Fig. 5.
Fig. 5.

In situ wind vectors from WKA legs 1 and 2 (both at a height of z = 300 m) and the third pass of legs 3 and 4 (z = 1800 m) over the island. The filled color shadings show averaged effective cloud albedo over 1318–1454 LST when the WKA was flying racetracks over the island. Terrain contours of 500 and 1000 m are also overlaid in gray.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

WCR reflectivity and radial velocity profiles along legs 3 and 4 (again the third pass of each leg) indicate that the leg-4 clouds were shallow with mainly ascending hydrometeors while the leg-3 hydrometeors were deeper and precipitating (Fig. 6). Consistent with S12’s conceptual diagram (their Fig. 15a), the cloud initiation was focused over the western ridge flank because of advection of the island thermal anomaly by the north-northeasterly subcloud winds. The clouds matured as they traversed the ridge (under the westerly cloud-layer winds) and then decayed over eastern Dominica.

Fig. 6.
Fig. 6.

WCR (a),(b) reflectivity and (c),(d) vertical velocity from the third passes of (a),(c) leg 3 and (b),(d) leg 4. The dashed line at z = 1.8 km indicates the aircraft altitude.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

The leg-3 rainshafts produced radar echoes of 10–20 dBZ near flight level ( km), which diminished toward the ground as a result of radar attenuation and evaporation. Despite the 2–3-km cloud depth and the prominence of rainfall along leg 3, the radar-derived cumulative precipitation over 1000–1700 LST was very light (~2 mm or less; section 3c) and the FWL tipping-bucket rain gauge recorded zero precipitation. The island rainfall may have been suppressed by a combination of (i) entrainment of very dry cloud-layer air; (ii) detachment of the cloud tops from the cloud bases, the latter anchored to the ridge by the island thermal circulation; and (iii) unusually high concentrations of cloud-condensation nuclei (CCN) (S12). The high CCN counts were attributable to a combination of long parcel residence times over the island due to the weak ambient winds, scattered island forest fires, and the ascent of primarily surface-based, aerosol-laden air within the island thermal circulations (S12).

3. Control simulations

a. Setup

The Advanced Research Weather Research and Forecasting (WRF) Model version 3.5 is used to perform quasi-idealized simulations. The simulations use a third-order Runge–Kutta time-integration scheme and fifth (third)-order advection in the horizontal (vertical). The simulations are nonhydrostatic and apply the Coriolis force to perturbations from the initial state (which is assumed to be geostrophically balanced) using an f-plane approximation at a latitude of 15°N. A single domain is used with dimensions of == 180 km in the horizontal (with Dominica centered in the domain) and =12 km in the vertical. The lateral boundaries are periodic and the top is rigid with a 4-km-deep Rayleigh damping layer to absorb gravity waves. The simulated convection only extends to ~(4–5) km and is thus largely undistorted by the upper damping. The grid uses a terrain-following vertical coordinate with 81 stretched levels and a Cartesian horizontal grid with a spacing (Δ) that varies from 1000 to 125 m in different simulations. The bottom boundary is no slip with fluxes of sensible heat, latent heat, and momentum determined by a five-layer thermal diffusion scheme. The surface types are prescribed as water over the ocean and broadleaf forest over land (the latter representing Dominica’s tropical rain forest). The initial sea surface temperature is set to 300 K and the land skin temperature is set to 292 K at sea level with a 5 K km−1 lapse rate.

Other parameterizations include shortwave (Dudhia scheme) and longwave [Rapid Radiative Transfer Model (RRTM)] radiation. Sloping-terrain effects and topographic shading are considered in the shortwave scheme. Surface-layer physics are parameterized based on Monin–Obukhov similarity theory, and the atmospheric boundary layer is either represented explicitly (for m) or parameterized using the Mellor–Yamada–Janjić prognostic turbulent kinetic energy (TKE) scheme. Whereas the simulations with explicit boundary layer turbulence use a three-dimensional TKE-based subgrid turbulence closure, those with parameterized boundary layer turbulence use a two-dimensional Smagorinsky-type scheme in the horizontal.

Cumulus convection is represented explicitly and cloud microphysics are parameterized using the Thompson scheme, which is double moment for rain and ice and single moment for cloud liquid water, snow, and graupel. At the largest grid spacing ( m), shallow convection is so poorly resolved that its representation may arguably be improved through a convection parameterization scheme. However, to maximize the consistency between the different cases, such a scheme was not used. The cloud-droplet concentration is fixed at = 200 cm−3, consistent with RF07 observations (S12).

The simulations use a horizontally homogeneous, single-sounding initialization based on the sounding in Fig. 2 and are integrated for 12 h (from 0500 to 1700 LST) to capture half the diurnal cycle. Because the ocean has a weak diurnal cycle, we assume a quasi-steady oceanic trade wind flow throughout the day. To enforce this steady state we add tendencies to the model variables at each time step to offset the two key processes causing model drift: low-level moistening due to ocean evaporation and clear-air radiative cooling. Because few cumuli develop over the ocean, no additional tendencies are required to offset their effects. To quantify these forcings, we performed a separate simulation with m that was configured as above except for using two dimensions (2D) with a pure ocean surface. From this ocean-only simulation we diagnosed a time-and-space-averaged latent-heat flux of 80 W m−2 and a tropospheric clear-air cooling rate of 1 K day−1. To maintain a steady state in the full simulations, we subtract the former tendency bodily over the subcloud layer (0–600 m) and the latter tendency uniformly over the entire troposphere.

In the course of our numerical experimentation a complication arose in simulations with Δ = 125 m: large-amplitude sound waves developed aloft directly over the island. To alleviate this problem we changed the WRF time off-centering parameter (or epssm) from its default value of 0.1 to 0.2, which eliminated the sound waves without noticeably changing the flow dynamics and convection of interest. However, by the time this problem was diagnosed and corrected we had already conducted most of our sensitivity simulations of section 4. Thus, the sensitivity simulations (which use Δ = 250 m and do not exhibit noticeable sound-wave propagation) use a different value of epssm (0.1) than the control simulations herein (0.2).

b. Description

The four “control” simulations use the above configuration with Δ progressively halved from 1000 m (CTL-1000), to 500 m (CTL-500), to 250 m (CTL-250), to 125 m (CTL-125), the last being the finest resolution permitted by our computing resources. These grid spacings span the range from modern limited-area explicit-convection forecasts (e.g., Lean et al. 2008) to large-eddy simulations of shallow convection (e.g., Kirshbaum and Grant 2012). Because the smallest Δ (125 m) is just sufficient to resolve deep convection (Bryan et al. 2003), it is still too coarse to resolve the shallow convection during RF07. Nonetheless, as will be demonstrated shortly, the CTL-250 and CTL-125 cases verify similarly against observations, suggesting diminishing marginal returns of higher resolution.

Before proceeding to the model verification, we illustrate the diurnal cycle for the CTL-250 case, which is revealed by snapshots of liquid water path (LWP) and first-model-level wind vectors at 0800, 1100, 1400, and 1700 LST in Figs. 7a–d. A katabatic land breeze propagates offshore in the morning hours, causing flow convergence over the surrounding ocean at 0800 LST. By 1100 LST strong thermally forced onshore flow develops over the high terrain, with intense convergence over the ridge axis giving rise to a band of densely packed shallow cumuli. Although the convergence and convection continue into the afternoon, both become less sharply focused over the ridge axis by 1400 LST, as cumulus detrainment produces shallow stratiform clouds in the upper cloud layer that drift eastward. As the insolation weakens so does the thermal forcing and horizontal convergence, causing the cumuli to largely dissipate by 1700 LST. Although LWP and albedo are not directly comparable, this simulated diurnal cloud evolution is qualitatively consistent with the RF07 satellite observations in Fig. 4.

Fig. 7.
Fig. 7.

Snapshots of liquid water path (filled color contours) and wind vectors at the first model level of the CTL-250 simulation at four different times. The island terrain is contoured in gray at levels of 1, 250, 500, 750, and 1000 m.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

Figure 8 compares surface wind vectors and LWP at 1400 LST for the four simulations. The mesoscale flow patterns are similar except for enhanced small-scale wind variability over the more rugged terrain at smaller Δ. Compared to the in situ wind observations at 300 m MSL along legs 1 and 2 (Fig. 5), the simulated surface winds are more northerly. This difference is owing to two effects: (i) the surface winds undergo more frictional backing than the flight-level winds at 300 m and (ii) the simulation was initialized by the aircraft sounding, which was flown over the southern half of leg 1 where the island-deflected winds were more northerly (see Fig. 5). As the grid resolution increases the simulated cumuli become more turbulent and irregular, with the area of nonzero LWP increasing but the patches of large LWP (2 kg m−2 and higher) shrinking. The stratiform clouds east of the ridge develop only in simulations with m.

Fig. 8.
Fig. 8.

As in Fig. 7, but for the four control simulations at 1400 LST.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

A vertical cross section of liquid-water mixing ratio () and time-averaged wind perturbation (relative to the initial state) over 1100–1500 LST across the southern ridge peak (see Fig. 8c) reveals upslope flow along both ridge faces that converge over the ridge to initiate precipitating cumuli that drift eastward (Fig. 9). The circulation is weaker and shallower over the eastern slope because (i) the onshore component of the subcloud ambient flow weakens the thermal gradients that drive the thermal circulation (e.g., Crosman and Horel 2010) and (ii) evaporative cold pools prevent the upslope flow from reaching the crest. By contrast, the lack of precipitation and offshore ambient-wind component over the western slope causes much stronger and deeper upslope flow there. Consistent with the WCR images in Fig. 6, the cumuli are based at ~1.2 km and reach a maximum height of ~4 km. Strong outflow occurs in the upper branch of the low-level thermal circulation, with weaker cumulus outflow in the upper cloud layer.

Fig. 9.
Fig. 9.

Vertical cross section of time-averaged perturbation winds (vectors), potential temperature (black lines), and liquid water mixing ratio (, color-filled contours) from the CTL-250 simulation over 1100–1500 UTC, along the transect shown in Fig. 8c.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

c. Verification

Because of various numerical idealizations such as the highly simplified land surface scheme, poorly constrained skin temperatures, and steady-state background flow, the quasi-idealized simulations should not be expected to exactly reproduce the observations. However, some model verification is useful to establish whether the simulated flows are broadly realistic. We begin with a comparison of simulated and observed FWL surface data, in which is well represented by all simulations, at least until cumuli begin to block the incident radiation at around 1000 LST (Fig. 3a). The commencement of cloud shading at FWL is well timed in all simulations except the CTL-1000 case, where it develops an hour later. The surface temperature is initially overestimated in the CTL-1000 case because of its smoother terrain (and hence lower FWL elevation) and underestimated in the three other cases (Fig. 3b), possibly because of erroneous initial land skin temperatures or shortcomings of the land surface scheme. While the diurnal range of in CTL-1000 is smaller than that observed, it is accurate for the three other simulations despite their ~2°C cold bias.

Similarly, the diurnal RH variations are muted in the CTL-1000 case yet highly accurate for the other three cases (Fig. 3c). However, the impressive performance of the latter group is partially owing to a cancellation of errors. Both and are underestimated throughout the day (Figs. 3b,d), leading to offsetting effects on RH. The errors likely arise from similar sources as the errors above, along with the inability of the single-sounding initialization to represent the humidified environment over the forested island. Finally, as expected from hydrostatic considerations, the evolution of simulated ΔSLP closely follows : the CTL-1000 case exhibits an underestimated diurnal range while the three other cases show an accurate diurnal range with a small (0.5 hPa) positive offset.

To verify simulated flight-track data along legs 3 and 4, we interpolate the model data onto the flight legs using an along-leg grid spacing of Δ. As with the observed flight legs, we conduct three model “passes” for each leg, each at the model-output time closest to the start time of the observed leg. For a fair comparison, we average the data from each observed flight leg onto the same grid as the simulated flight legs. Thus, the observations of a given quantity depend on the Δ of the simulation to which they are compared. We compare the following quantities: mean zonal wind (u), conditionally averaged vertical velocity () and buoyancy () within the convective cloud cores, conditionally averaged liquid-water () and rain () mixing ratios within clouds, vertical velocity variance (), vertical cloud mass flux (), cloud fraction (, the fraction of flight-level points with g kg−1), and rain fraction (, the fraction of flight-level points with g kg−1). Convective cores are defined as data points with exceeding 0.1 g kg−1 and positive w and b, where b is defined as
e1
g is the gravitational acceleration, is the density potential temperature, and is the mean over the leg. Only over-island points are considered in these calculations.

Table 1 compares observed and simulated values of the above quantities, averaged over all points sampled in the three legs. While the simulations reproduce conditionally averaged quantities such as (leg 3), (legs 3 and 4), and (legs 3 and 4) reasonably well (particularly for m), and are grossly overpredicted on both legs. The simulations also underestimate bulk measures of convective activity such as , , , and the interleg differences in u. We hypothesize that the latter errors, which are common to all the simulations, relate to the aforementioned underprediction of land–sea thermal contrast, as implied by the underestimated and at FWL (Figs. 3b and 3d). Another contributing factor may be the northerly bias in the low-level winds from the aircraft sounding, which slightly alters the geometry of the island thermal circulation and, hence, the spatial distribution of island clouds.

Table 1.

Comparison of in situ WKA aircraft observations with corresponding quantities from the control simulations. All quantities are defined in the text. The entries contain the corresponding observed/simulated values at the grid resolutions (Δ) shown in the top row for legs 3 and 4. A value of “NA,” or not applicable, denotes zero samples of the quantity along the flight leg.

Table 1.

Despite the underestimated and in the simulations (Fig. 3), the simulated on leg 4 is actually larger than that observed. Part of this enhancement may be explained by the “slice” method of Bjerknes (1938) and Kirshbaum and Smith (2009), which relates cloud buoyancy to cloud fraction. Larger causes stronger compensating descent between the clouds, which heats the environment and thus decreases . According to (7) of Kirshbaum and Smith (2009), the underpredicted in the CTL-250 simulation accounts for a 14% increase in . The remaining model overprediction of along leg 4 may arise from insufficient entrainment of dry air into the simulated convective cores, a process that remains poorly resolved even at Δ = 125 m.

The simulations with m produce average cloud bases and cloud tops of ~1.2 and ~4.2 km (see Fig. 9), which are broadly similar to the leg-3 WCR observations in Fig. 6. Despite this reasonable representation of cloud morphology, the simulated and at flight level (Table 1) and cumulative surface rainfall over 1000–1700 LST are grossly overpredicted. Figure 10 shows that the simulated cumulative rainfall is widespread over the ridge with maxima exceeding 40 mm, which dwarfs the small area of 1–2-mm rainfall over the island center observed by the TFFF radar [using a reflectivity (Z) to rain-rate (R) relation of (Smith et al. 2009)]. Although the model errors decrease at higher resolution, the overprediction remains pronounced even at m. These errors are not unique to the Thompson microphysics scheme: similar rainfall is obtained when this scheme is replaced by the Morrison two-moment microphysics scheme (MOR-250; Fig. 10f).

Fig. 10.
Fig. 10.

Cumulative precipitation (filled color contours) over 1000–1700 LST from (a) the TFFF radar and (b)–(f) various control simulations. The island terrain is contoured in gray at levels of 1, 250, 500, 750, and 1000 m.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

Part of the above discrepancy between observed and simulated rainfall likely stems from radar precipitation underestimation. The TFFF radar was insensitive to echoes weaker than 12 dBZ, implying that the lighter rain over the ridge was undetectable. Moreover, the radar grid resolution (nominally 1 km) was coarser than most of the island showers, which reduced their effective reflectivity and caused some of them to go undetected. For a characteristic rain shower width of 500 m, averaging over a grid cell implies a 6-dBZ reduction in reflectivity and a 69% reduction in radar-derived rain rate. Finally, beam blocking past the southern island peaks (see Fig. 1) may also have shielded the TFFF radar from some of the heavier rainfall cores over the central island.

The remaining rainfall discrepancies likely stem from deficiencies in the numerical simulations. Given that the cloud macrophysics (e.g., b, w, , and cloud depth) were reasonably well represented for m, a logical suspect is cloud microphysics—in particular, autoconversion from cloud water to rain (which represents the collision and coalescence process). In liquid-rich tropical cumuli, small autoconversion errors may grow into large rainfall errors owing to the rapid collection of cloud water by rain. Figure 11a compares the simulated and observed cloud-droplet spectra [, where D is the droplet diameter] averaged along leg 4, where the errors in Table 1 were the most pronounced. The simulated gamma distribution misses the bimodality of the observed distribution and exhibits a much longer tail extending to mm. At such large droplet sizes precipitation-sized particles may begin to form via collision and coalescence (e.g., Rogers and Yau 1989). Figure 11b compares observed and simulated distributions along leg 4, with reference lines showing the values required to produce a moderate autoconversion rate of 10−9 kg m−3 s−1. Nearly half of the sampled clouds exceed this threshold, implying substantial autoconversion even at flight level where little rain was observed. While the underestimated simulated (200 versus 255 cm−3 for the CDP) contributes to the error, it is not decisive: increasing the simulated to 300 cm−3 reduces the mean island accumulation by only 6% (not shown).

Fig. 11.
Fig. 11.

Cloud microphysical comparison between WKA in situ observations and CTL-250 simulation, conditionally averaged over all clouds along the three leg-4 passes. (a) Cloud-droplet size distribution and (b) probability density of along with corresponding threshold autoconversion rates of 10−9 kg m−3 s−1 (based on the Thompson cloud microphysics parameterization).

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

Overall, the control simulations are far from perfect, with underestimated cloud-layer mass fluxes and substantially overestimated precipitation. Nonetheless, the simulated thermal circulations and cloud macrophysics are sufficiently realistic (for m, at least) to justify their use as a tool for studying the mechanisms and sensitivities of thermally forced convection. Although more verification would help to pinpoint and remedy the model errors, we defer such analysis to future work and retain a focus on the dynamics of thermally forced island convection.

4. Sensitivity tests

To better understand the processes regulating thermally forced island convection, we perform a series of “sensitivity” simulations that isolate the impacts of various environmental, topographic, and cloud-related parameters. The reference case for these experiments is the CTL-250 simulation with epssm = 0.1, which for convenience (and to distinguish it from the original CTL-250 simulation with epssm = 0.2) will be henceforth denoted as the reference (REF) simulation. We choose m for these experiments because the CTL-250 case performed similarly to the CTL-125 case in section 3c at a small fraction of the computational cost.

a. Topographic forcing

To quantify the impacts of island topography on the simulated convection, we perform two simulations that are identical to REF except that in one the terrain height is capped at 2 m (THERM) and in the other the surface heat fluxes are shut off over the domain (MECH). The former corresponds to pure thermal forcing while the latter corresponds to pure mechanical forcing. As shown in the LWP and surface wind comparison at 1400 LST in Figs. 12a–c, both REF and THERM produce strong low-level inflow and cumulus convection while MECH exhibits upstream blocking, a turbulent wake, and cloud-free conditions. This comparison supports the hypothesis that thermal (rather than mechanical) forcing drove the cumulus convection in RF07. The field of island cumuli in THERM is similar to REF except that the patches of large LWP are more focused over the western side of the island, coinciding with a narrow zone of sea-breeze convergence.

Fig. 12.
Fig. 12.

As in Fig. 8, but for the 10 sensitivity simulations of section 4.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

The island-averaged mean-layer (0–500 m above ground level, or AGL) equivalent potential temperature () and CAPE remain quasi steady throughout the day in MECH but undergo large variations in REF and THERM (Figs. 13a,b). In the REF case, both quantities are small at initialization because the elevated mountain surface reaches very dry air aloft. They subsequently decrease in the early morning because of longwave cooling and then increase in the late morning because of shortwave insolation. After 1100 LST they flatten as negative cloud feedbacks and convective mixing with the dry layer above inhibit additional warming and moistening. The THERM case follows a similar evolution except for its much larger initial and CAPE, which follows from its flat surface lying entirely within warm and humid air at sea level.

Fig. 13.
Fig. 13.

Time series of various quantities from the topographic sensitivity tests: (a) mean-layer (0–500 m AGL) and (b) CAPE, (c) surface-based horizontal inflow crossing the island perimeter , (d) cloud-layer vertical mass flux , (e) island convergence fraction , and (f) island cloud fraction .

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

To characterize the bulk island-scale circulation we compare the island horizontal influx (), defined as the net surface-based horizontal mass flux across the island perimeter, and the vertical cloud mass flux at flight level () (see appendix for details). Assuming that the island convection arises from convergence of low-level onshore flow, these two quantities should reach similar magnitudes in a given simulation. Both are nearly zero in the cloud-free MECH case but undergo clear diurnal cycles in the REF and THERM cases: they are small until ~0800 LST, rapidly increase to their maxima by midday (1100–1300 LST), then gradually decrease in the afternoon (Figs. 13c,d). In each case the peak magnitudes of and are similar but the latter lags the former by about 30 min. This lag roughly matches the time required for onshore flow to converge over the ridge axis and ascend through the cloud layer.

Interestingly, the maximum is slightly larger for the THERM case while the maximum is larger for the REF case. While an explanation for the former is deferred until section 5, the latter is explained by Figs. 13e,f, which compare (the convergence fraction, or fraction of island points with convergence exceeding 4 × 10−3 s−1 at the lowest model level) and (the cloud fraction, or the fraction of island points with g kg−1 at flight level) for the two simulations. The REF case exhibits the largest owing to the many small-scale convergence/divergence couplets distributed over its irregular surface. By contrast, the THERM case exhibits a lower because its convergence is narrowly focused along the sea-breeze collision axis. The larger areal coverage of surface-based convergence in the REF case initiates more cumuli, which gives rise to enhanced and .

b. Boundary layer winds

In conditionally unstable flow over mountainous islands, the convection-initiation regime transitions from thermal to mechanical as the ambient cross-barrier winds increase. For typical trade wind flows over Dominica, this transition occurs at a cross-barrier wind speed of ~5 m s−1 (Nugent et al. 2014). Of the four thermally forced cases observed in DOMEX, the range of low-level wind speeds was small (1.6–3.6 m s−1) but the range of WKA-observed was large (0.09–1.47 m2 s−2) (Wang 2014). While the large variations may be partially attributable to other factors (e.g., cloud-layer stability and large-scale cloud shading), they nevertheless motivate us to explore the impact of low-level winds on the thermally forced convection in RF07.

We thus perform three simulations that are all identical to the REF case except for minor modifications to the 0–2-km wind profile: the HALFWIND and DBLWIND cases respectively halve and double the wind speeds over 0–1 km with no change in direction, and the CBWIND case rotates the 0–1-km winds to a more cross-barrier orientation (60° clockwise from due north) with no change in wind speed. The modified winds are linearly relaxed back to the REF profile over 1–2 km. Because the modified winds in HALFWIND and DBLWIND change the oceanic latent heat fluxes, we perform separate 2D ocean-only simulations (as described in section 3) to recompute for each case. By contrast, remains fixed in all the simulations.

Although the above changes to the ambient winds are small (less than 2 m s−1 in magnitude), they significantly impact the island thermal circulation and cumulus convection. While the island flow pattern is broadly similar among the REF, HALFWIND, and DBLWIND cases, the CBWIND case forms a distinct island wake with lee vortices and reversed (westerly) flow in the center (Figs. 12d–f). Qualitative changes in the cloud fields include a more prominent stratiform outflow layer in HALFWIND, a southward cloud-field displacement in DBLWIND, and a narrower cloud field centered over the ridge axis in CBWIND.

Relative to the REF case, the island mean-layer and CAPE increase in HALFWIND but decrease in DBLWIND and CBWIND (Figs. 14a,b). These differences are linked to the air parcel residence times over the heated island, which are the longest in HALFWIND and shortest in DBLWIND. While the winds in CBWIND are identical in speed to those in REF, their cross-island orientation significantly reduces the time required for parcels to traverse the island. The longer residence times in HALFWIND increase the time-integrated diabatic heating of island air parcels, which enhances both the land–sea contrast and the island moist instability, with the opposite effect in the DBLWIND and CBWIND cases. As a result, both and increase (decrease) substantially in the HALFWIND (DBLWIND and CBWIND) cases (Figs. 14c,d).

Fig. 14.
Fig. 14.

As in Fig. 13, but for the wind sensitivity tests and (e) conditionally averaged within the convective cores at z = 1.8 km.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

The differences in low-level between these four cases can be tracked into the cloud layer, where the conditionally averaged core () is again the largest in HALFWIND and the smallest in DBLWIND and CBWIND (Fig. 14e). While changes in ambient-wind speed in HALFWIND and DBLWIND only modestly influence , the wind rotation in CBWIND causes it to decrease significantly (Fig. 14f). The latter sensitivity arises from a more symmetric orientation of the solenoidal circulation over the ridge axis in the CBWIND case. The position of the descending branch of the thermal circulation shifts from the downwind (southeastern) side of the ridge to directly over its central flanks (not shown), which effectively suppresses the stratiform outflow layer and thus lowers .

c. Cloud feedbacks

The island clouds feed back both positively (through latent heat release) and negatively (through shading and evaporative cold pools) on the thermal circulations giving rise to them. As an obvious example, Fig. 3 suggests a strong negative feedback on the thermal forcing at FWL once cumuli develop and locally block solar insolation. To quantify such effects we perform four additional simulations that are identical to REF except for changes to the microphysics and radiation schemes: NORN shuts off the autoconversion from clouds to rain in the microphysics scheme (eliminating precipitation), NOCOD shuts off the cloud effects on optical depth in the shortwave radiation scheme (eliminating cloud shading), NORNCOD eliminates both above effects, and NOMP shuts off the microphysics scheme (eliminating clouds entirely).

Relative to the REF case, the convection appears to be suppressed to the east of the ridge in the NORN and NORNCOD cases and intensified in the NOCOD case (Figs. 12g–i). The latter arises from a stronger island thermal anomaly, and a correspondingly stronger thermal circulation, in the absence of cloud shading. The former likely stems from the elimination of subcloud cold pools, which tend to initiate secondary cumuli away from the ridge crest. Because the thermal circulation and convection in the rain-free NORN and NORNCOD cases are stronger and more focused directly over the ridge, they create more organized and stronger compensating subsidence over the ridge flanks, which effectively suppresses convection there. As for the NOMP case, its flow appears broadly similar to the REF case despite the absence of clouds (Fig. 12j).

The partial to complete elimination of negative cloud feedbacks in the NORN, NOCOD, and NORNCOD cases causes and to increase substantially relative to the REF case (Figs. 15c,d). However, the island-averaged mean-layer and CAPE are largely unchanged (Figs. 15a,b), which seems inconsistent with the notion of a stronger island thermal anomaly. This apparent contradiction is reconciled by Fig. 16, which shows the mean-layer and wind differences between the NORNCOD and REF simulations over the WKA racetrack period. The absence of cloud shading and rainfall in the NORNCOD simulation causes to locally increase over the ridge where cloud cover is maximized. This locally enhanced thermal forcing strengthens the island thermal circulation, including its onshore flow and compensating descent, which both supply low- air to the ridge flanks. Thus, the increased over the ridge crest is balanced by reduced in the surrounding flow, leaving the island-averaged largely unchanged. A similar argument holds for CAPE (not shown).

Fig. 15.
Fig. 15.

As in Fig. 14, but for the cloud-feedback sensitivity tests.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

Fig. 16.
Fig. 16.

Comparison of mean-layer (0–500 m AGL) (color shading) and wind vectors between the NORNCOD and REF simulations, averaged over the time period encompassing the three over-island racetracks (1330–1450 LST). To avoid chaotic wind fluctuations near the ridge crest, wind vectors from points above 500 m, or with wind speed differences exceeding 3 m s−1, are omitted.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

Cloud shading, precipitation, and latent-heat release all have similar-magnitude impacts on (Fig. 15c). Comparison of the NOCOD and REF simulations (or the NORNCOD and NORN simulations) indicates that cloud shading reduces by ~20%. Similarly, comparison of the NORN and REF (or the NORNCOD and NOCOD) simulations indicates that precipitation reduces by ~20%. Finally, comparison of the NOMP and NORNCOD simulations (which differ only in the presence of clouds) reveal that cloud latent heating increases by ~20%. Despite their similar impacts on , cloud shading and precipitation have very different impacts on , in that cloud shading reduces by a much larger amount (~50%) than does precipitation (~10%) (the impact of cloud latent heating on cannot be quantified because the NOMP simulation has no clouds). The muted effect of precipitation on is due to enhanced subcloud lifting by evaporative cold pools, which offsets the reduced by effectively initiating secondary convection. This effect is reminiscent of section 4a, where more widespread convergence in the mountainous REF case caused its to exceed that of the flat THERM case despite its smaller .

5. Heat-engine theory

Recent studies have used thermodynamic heat-engine theory to quantify the strength of mountain thermal circulations in highly idealized simulations (Tian and Parker 2003; Kirshbaum 2013; Kirshbaum and Wang 2014). To evaluate whether such theory holds for the more realistic simulations considered in this study, we apply it to a subset of our experiments: the REF and THERM cases from section 4a, the latter of which exhibits slightly larger than the former (Fig. 13c). Herein we investigate whether heat-engine theory can reproduce this sensitivity and provide a physical explanation for it. To isolate the dry subcloud circulations in the absence of complicated cloud feedbacks, we consider two simulations that are identical to REF and THERM except for the absence of clouds (NOMP and THERM-NOMP).

For brevity, we provide only a short description of the heat-engine theory and refer the reader to the above studies for the detailed derivations. The theory assumes a steady, closed, thermally direct circulation joining two regions of different temperature. Under these assumptions, the combination of the first law of thermodynamics and Bernoulli’s equation yields an equivalence between net heat input and frictional dissipation around the circulation trajectory. The former is , where η is the circulation efficiency, is the specific heat of air at constant pressure, is the nonadiabatic temperature difference and the water vapor mixing ratio difference between the warm and cold regions, and is the latent heat of vaporization. The frictional dissipation is given by , where μ is a dissipation coefficient and the circulation strength. Solving for gives
e2
where , g is the acceleration of gravity, H is the mixed-layer depth, and is the average temperature of the warm and cold regions. The dissipation is estimated as (Tian and Parker 2003), where L is the distance between the warm and cold regions.

To diagnose the variables in (2) from the simulations, we create 40 parallel transects crossing the central portion of the ridge axis, spaced at 1-km intervals with an along-transect grid spacing of Δ (Fig. 17). For reference, we define the along- and cross-transect coordinates as and . Along each transect (), we interpolate the model and onto each point and extrapolate dry adiabatically to sea level to get . We then subtract the averaged of the ocean points from the maximum over the land points (the latter averaged over a 2-km segment surrounding the peak value to avoid local extremes) to obtain . Similarly, we subtract the averaged ocean from the island , the latter averaged over the same 2-km segment defined above, to get . The distance between the maximum island and the nearest coastline along the same transect is taken as , and the average of the land and ocean surface air temperatures is used for . Next, we create vertical cross sections along each transect, which we use to obtain the mixed-layer top (defined as the lowest height where s−2) and the vertical velocity (defined as the maximum w below h). We take the maximum of to get and average the mixed-layer depth , where is the terrain height, to get (both over land points only). Finally, we average , , , , and to yield scalar values of , , , H, and at each time.

Fig. 17.
Fig. 17.

Locations of 40 cross-island cross sections used for the heat-engine calculations.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

Figure 18 shows time series of , H, and [where is both calculated from (2) and diagnosed from the simulations] for the NOMP and THERM-NOMP simulations. The daytime is slightly larger in the NOMP case owing to the static stability of the subcrest atmospheric layer (Fig. 18a). By contrast, H is smaller for the NOMP case because, on average, the island mixed layer rises by a smaller amount (~200 m) than does the terrain (~400 m) (Fig. 18b). Consistent with the comparison in the REF and THERM simulations (Fig. 13c), is slightly larger in the THERM-NOMP case than in the NOMP case. The heat-engine prediction from (2) closely matches the simulated evolution of in both cases, suggesting that it succeeds in quantitatively predicting and capturing its terrain sensitivities (Fig. 18c). The theory thus offers an attractively simple explanation for the differences in and between the two simulations: despite its stronger land–sea contrast, the mountainous REF case exhibits a generally shallower mixed layer, which reduces the efficiency of its thermal circulation and thus weakens its and .

Fig. 18.
Fig. 18.

Results from heat-engine analysis of the NOMP and THERM-NOMP simulations. (a) Nonadiabatic temperature difference between the island and the ocean , (b) island mixed-layer depth H, and (c) thermal updraft strength ; solid lines indicate values diagnosed from the simulations and dashed lines indicate theoretical predictions.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0325.1

6. Conclusions

We have performed an observational and numerical investigation of a thermally forced cumulus convection event over the mountainous Caribbean island of Dominica during the Dominica Experiment (DOMEX) field campaign. Surface meteorological data from a mountain weather station at Freshwater Lake (FWL) and visible satellite observations revealed a clear diurnal cycle in island thermal forcing and cumulus convection, with strong insolation and a rapid temperature increase (and pressure decrease) in the morning hours. Shallow, lightly precipitating cumuli formed by midday, which gradually weakened in the afternoon. Wyoming King Air (WKA) in situ observations from flight legs on both sides of the ridge indicated flow divergence at flight level (1.8 km), reflecting outflow from the island thermal circulation and cumulus convection. The clouds tended to initiate just downwind of the ridge axis (on its southwestern side) and deepen as they drifted eastward across the ridge.

To better understand the mechanisms and sensitivities of the island convection, we performed cloud-resolving numerical simulations with the WRF Model. Although these quasi-idealized simulations could not represent the full complexity of the observed flows, the higher-resolution runs (with horizontal grid spacings m) exhibited reasonable agreement with observations in the island diurnal cycle and cloud macrophysics (depth, liquid-water content, etc.). However, the simulations underestimated the island cloud fraction and cloud vertical mass flux, which likely stemmed from their weaker land–sea contrasts and island moist instabilities. Nonetheless, the simulations produced much larger rainfall amounts ( mm) than those observed by radar (~2 mm), which likely stemmed from a combination of radar underestimation and model overestimation. In particular, the simulated clouds formed rain too readily, which may be owing to the long-tailed gamma function representing the cloud droplet size distribution.

Sensitivity tests varying the island heating and terrain revealed that, as expected, the cumulus convection was driven by island thermal forcing. Perhaps counterintuitively, however, flattening the terrain led to stronger island-scale mass convergence (or the bulk surface-based inflow crossing the island perimeter) but weaker cloud vertical mass flux . The latter difference was due to the rugged Dominican terrain, which produced more small-scale convergence–divergence couplets than the flat island. The increased areal coverage of convergence over the mountainous island initiated more cumuli, which increased the cloud fraction and relative to the flat case. Experiments varying the ambient winds indicated that the island thermal anomaly was controlled by the residence time of air parcels over the heated island. Weaker cross-island winds led to longer residence times and thus stronger land–sea contrasts and island moist instability, which strengthened both and .

Simulations were also conducted to isolate and quantify the feedbacks of cloud shading, rainfall, and latent-heat release on the island-scale horizontal inflow and cumulus convection. While cloud shading and rainfall each reduced by ~20%, cloud latent-heat release enhanced it by ~20%, leading to a cumulative negative cloud feedback of ~20%. However, cloud shading had a much more suppressive effect on the cloud-layer convection than did rainfall, reducing by nearly 50% (compared to 10% for rainfall). This difference may be attributed to the more vigorous low-level ascent produced by evaporative cold pools, which compensated for the reduced by effectively initiating secondary convection.

To evaluate the skill of thermodynamic heat-engine theory at predicting the island thermal circulations, we applied the theory to the above comparison between mountainous and flat islands, except that the simulations were run in “dry” mode without cloud microphysics. Consistent with the moist simulations, the island thermal circulation strengthened slightly when the terrain was flattened. The heat-engine theory captured this sensitivity and offered a simple explanation for it: the elevated terrain in the mountain case reduced the mixed-layer depth and thus lowered the circulation’s thermodynamic efficiency. This finding contrasts with recent studies of continental mountains, where taller terrain tended to enhance the circulation strength (Tian and Parker 2003; Kirshbaum and Wang 2014). We hypothesize that this disagreement stems from differences in effective thermal forcing between islands and continental mountains. Whereas islands experience strong thermal forcing regardless of terrain height, continental mountains are the main source of regional baroclinicity and, as a result, more responsible for driving thermal circulations. Further investigation is required to quantify the impacts of orography on island thermal circulations under a broad range of environmental conditions.

Acknowledgments

We thank Ron Smith for sharing the DOMEX dataset, Justin Minder for the tidal pressure correction and Météo France radar analysis, Jeff French and Samuel Haimov for help deciphering the WKA data, and Greg Thompson for insight into the cloud microphysics. Comments from two anonymous reviewers and Christian Barthlott helped to improve the manuscript. Funding was provided by the Natural Science and Engineering Research Council Discovery Grant NSERC/RGPIN 418372-12, Fonds de Recherche Nature et Techonologies (FRQNT) Grant FQRNT NC-171838. Numerical simulations were performed on the Guillimin supercomputer at McGill University, under the auspices of Calcul Québec and Compute Canada.

APPENDIX

Calculating and

The island-scale horizontal mass flux is defined as the vertically integrated surface-based horizontal mass flux across the island perimeter. To obtain it mathematically, we first find the fluid velocity normal to the contour defining the island perimeter () at all vertical levels, where is the horizontal fluid velocity and n is the local normal vector (directed toward the island interior). We then interpolate these data to a regular vertical grid (56 evenly spaced levels from = 100 to 5600 m) and integrate (where ρ is the fluid density) around the perimeter at each vertical level, which gives a vertical profile of horizontal mass flux. To isolate the near-surface inflow, we define the lowest zero crossing of this mass flux profile as the level of nondivergence () and vertically integrate the profile below to give :
ea1
where C is the curve defining the island perimeter. Note that (A1) is similar to the “mountain-scale convergence” defined by (8) of Geerts et al. (2008) except for its consideration of mass flux (rather than just ) and its vertical integration.
The quantity is defined as the horizontally integrated vertical cloud mass flux at flight level ( km), which is found by first interpolating model variables to and then identifying all points above land that meet the following conditions: g kg−1 and . We conditionally horizontally integrate at all of these points to give :
ea2
where S is the island surface and is an incremental area upon it.

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  • Fovell, R. G., 2005: Convective initiation ahead of the sea-breeze front. Mon. Wea. Rev., 133, 264–278, doi:10.1175/MWR-2852.1.

  • Galewsky, J., 2008: Orographic clouds in terrain-blocked flows: An idealized modeling study. J. Atmos. Sci., 65, 3460–3478, doi:10.1175/2008JAS2435.1.

    • Search Google Scholar
    • Export Citation

  • Geerts, B., Q. Miao, and J. C. Demko, 2008: Pressure perturbations and upslope flow over a heated, isolated mountain. Mon. Wea. Rev., 136, 4272–4288, doi:10.1175/2008MWR2546.1.

    • Search Google Scholar
    • Export Citation

  • Jiang, Q., 2003: Moist dynamics and orographic precipitation. Tellus, 55A, 301–316, doi:10.1034/j.1600-0870.2003.00025.x.

  • Kingsmill, D. E., 1995: Convection initiation associated with a sea-breeze front, a gust front, and their collision. Mon. Wea. Rev., 123, 2913–2933, doi:10.1175/1520-0493(1995)123<2913:CIAWAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Kirshbaum, D. J., 2013: On thermally forced circulations over heated terrain. J. Atmos. Sci., 70, 1690–1709, doi:10.1175/JAS-D-12-0199.1.

    • Search Google Scholar
    • Export Citation

  • Kirshbaum, D. J., and R. B. Smith, 2009: Orographic precipitation in the tropics: Large-eddy simulations and theory. J. Atmos. Sci., 66, 2559–2578, doi:10.1175/2009JAS2990.1.

    • Search Google Scholar
    • Export Citation

  • Kirshbaum, D. J., and A. L. M. Grant, 2012: Invigoration of cumulus cloud fields by mesoscale ascent. Quart. J. Roy. Meteor. Soc., 138, 2136–2150, doi:10.1002/qj.1954.

    • Search Google Scholar
    • Export Citation

  • Kirshbaum, D. J., and C.-C. Wang, 2014: Boundary layer updrafts driven by airflow over heated terrain. J. Atmos. Sci., 71, 1425–1442, doi:10.1175/JAS-D-13-0287.1.

    • Search Google Scholar
    • Export Citation

  • Kirshbaum, D. J., and J. G. Fairman Jr., 2015: Cloud trails past the Lesser Antilles. Mon. Wea. Rev., 143, 995–1017, doi:10.1175/MWR-D-14-00254.1.

    • Search Google Scholar
    • Export Citation

  • Lean, H. W., P. A. Clark, M. Dixon, N. M. Roberts, A. Fitch, R. Forbes, and C. Halliwell, 2008: Characteristics of high-resolution versions of the Met Office Unified Model for forecasting convection over the United Kingdom. Mon. Wea. Rev., 136, 3408–3424, doi:10.1175/2008MWR2332.1.

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    • Export Citation

  • Minder, J., R. B. Smith, and A. D. Nugent, 2013: The dynamics of ascent-forced orographic convection in the tropics: Results from Dominica. J. Atmos. Sci., 70, 4067–4088, doi:10.1175/JAS-D-13-016.1.

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    • Export Citation

  • Nugent, A. D., R. B. Smith, and J. R. Minder, 2014: Wind speed control of tropical orographic convection. J. Atmos. Sci., 71, 2695–2712, doi:10.1175/JAS-D-13-0399.1.

    • Search Google Scholar
    • Export Citation

  • Qian, J.-H., 2008: Why precipitation is mostly concentrated over islands in the Maritime Continent. J. Atmos. Sci., 65, 1428–1441, doi:10.1175/2007JAS2422.1.

    • Search Google Scholar
    • Export Citation

  • Qian, T., C. C. Epifanio, and F. Zhang, 2012: Topographic effects on the tropical land and sea breeze. J. Atmos. Sci., 69, 130–149, doi:10.1175/JAS-D-11-011.1.

    • Search Google Scholar
    • Export Citation

  • Ramage, C. S., and T. A. Schroeder, 1999: Trade wind rainfall atop Mount Waialeale, Kauai. Mon. Wea. Rev., 127, 2217–2226, doi:10.1175/1520-0493(1999)127<2217:TWRAMW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Reisner, J. M., and P. K. Smolarkiewicz, 1994: Thermally forced low Froude number flow past three-dimensional obstacles. J. Atmos. Sci., 51, 117–133, doi:10.1175/1520-0469(1994)051<0117:TFLFNF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Rogers, R. R., and M. K. Yau, 1989: A Short Course in Cloud Physics. Butterworth-Heineman, 290 pp.

  • Schroeder, T. A., 1977: Meteorological analysis of an Oahu flood. Mon. Wea. Rev., 105, 458–468, doi:10.1175/1520-0493(1977)105<0458:MAOAOF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Smith, R. B., P. Schafer, D. J. Kirshbaum, and E. Regina, 2009: Orographic precipitation in the tropics: Experiments in Dominica. J. Atmos. Sci., 66, 1698–1716, doi:10.1175/2008JAS2920.1.

    • Search Google Scholar
    • Export Citation

  • Smith, R. B., and Coauthors, 2012: Orographic precipitation in the tropics: The Dominica Experiment. Bull. Amer. Meteor. Soc., 93, 1567–1579, doi:10.1175/BAMS-D-11-00194.1.

    • Search Google Scholar
    • Export Citation

  • Smolarkiewicz, P. K., and R. Rotunno, 1989: Low Froude number flow past three-dimensional obstacles. Part I: Baroclinically generated lee vortices. J. Atmos. Sci., 46, 1154–1164, doi:10.1175/1520-0469(1989)046<1154:LFNFPT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Smolarkiewicz, P. K., R. M. Rasmussen, and T. L. Clark, 1988: On the dynamics of Hawaiian cloud bands: Island forcing. J. Atmos. Sci.,45, 1872–1905, doi:10.1175/1520-0469(1988)045<1872:OTDOHC>2.0.CO;2.

  • Tian, W. S., and D. J. Parker, 2003: A modeling study and scaling analysis of orographic effects on boundary layer shallow convection. J. Atmos. Sci., 60, 1981–1991, doi:10.1175/1520-0469(2003)060<1981:AMSASA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Wang, C.-C., 2014: Thermally-driven circulation and convection over a mountainous tropical island. M.S. thesis, Dept. of Atmospheric and Oceanic Sciences, McGill University, 90 pp.

  • Yang, Y., and Y.-L. Chen, 2008: Effects of terrain heights and sizes on island-scale circulations and rainfall for the island of Hawaii during HaRP. Mon. Wea. Rev., 136, 120–146, doi:10.1175/2007MWR1984.1.

    • Search Google Scholar
    • Export Citation

  • Yang, Y., S.-P. Xie, and J. Hafner, 2008: The thermal wake of Kauai Island: Satellite observations and numerical simulations. J. Climate, 21, 4568–4586, doi:10.1175/2008JCLI1895.1.

    • Search Google Scholar
    • Export Citation

  • Yeh, H.-C., and Y.-L. Chen, 1998: Characteristics of rainfall distributions over Taiwan during the Taiwan Area Mesoscale Experiment (TAMEX). J. Appl. Meteor., 37, 1457–1469, doi:10.1175/1520-0450(1998)037<1457:CORDOT>2.0.CO;2.

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  • Barthlott, C., and D. J. Kirshbaum, 2013: Sensitivity of deep convection to terrain forcing over Mediterranean islands. Quart. J. Roy. Meteor. Soc., 139, 1762–1779, doi:10.1002/qj.2089.

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  • Bjerknes, J., 1938: Satured-adiabatic ascent of air through dry-adiabatically descending environment. Quart. J. Roy. Meteor. Soc., 64, 325–330.

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  • Bryan, G. H., J. C. Wyngaard, and J. M. Fritsch, 2003: Resolution requirements for the simulation of deep moist convection. Mon. Wea. Rev., 131, 2394–2416, doi:10.1175/1520-0493(2003)131<2394:RRFTSO>2.0.CO;2.

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  • Carbone, R. E., J. W. Wilson, T. D. Keenan, and J. M. Hacker, 2000: Tropical island convection in the absence of significant topography. Part I: Life cycle of diurnally forced convection. Mon. Wea. Rev., 128, 3459–3480, doi:10.1175/1520-0493(2000)128<3459:TICITA>2.0.CO;2.

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  • Crook, N. A., and D. F. Tucker, 2005: Flow over heated terrain. Part I: Linear theory and idealized numerical simulations. Mon. Wea. Rev., 133, 2552–2564, doi:10.1175/MWR2964.1.

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  • Crosman, E. T., and J. D. Horel, 2010: Sea and lake breezes: A review of numerical studies. Bound.-Layer Meteor., 137, 1–29, doi:10.1007/s10546-010-9517-9.

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    • Export Citation

  • Fovell, R. G., 2005: Convective initiation ahead of the sea-breeze front. Mon. Wea. Rev., 133, 264–278, doi:10.1175/MWR-2852.1.

  • Galewsky, J., 2008: Orographic clouds in terrain-blocked flows: An idealized modeling study. J. Atmos. Sci., 65, 3460–3478, doi:10.1175/2008JAS2435.1.

    • Search Google Scholar
    • Export Citation

  • Geerts, B., Q. Miao, and J. C. Demko, 2008: Pressure perturbations and upslope flow over a heated, isolated mountain. Mon. Wea. Rev., 136, 4272–4288, doi:10.1175/2008MWR2546.1.

    • Search Google Scholar
    • Export Citation

  • Jiang, Q., 2003: Moist dynamics and orographic precipitation. Tellus, 55A, 301–316, doi:10.1034/j.1600-0870.2003.00025.x.

  • Kingsmill, D. E., 1995: Convection initiation associated with a sea-breeze front, a gust front, and their collision. Mon. Wea. Rev., 123, 2913–2933, doi:10.1175/1520-0493(1995)123<2913:CIAWAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Kirshbaum, D. J., 2013: On thermally forced circulations over heated terrain. J. Atmos. Sci., 70, 1690–1709, doi:10.1175/JAS-D-12-0199.1.

    • Search Google Scholar
    • Export Citation

  • Kirshbaum, D. J., and R. B. Smith, 2009: Orographic precipitation in the tropics: Large-eddy simulations and theory. J. Atmos. Sci., 66, 2559–2578, doi:10.1175/2009JAS2990.1.

    • Search Google Scholar
    • Export Citation

  • Kirshbaum, D. J., and A. L. M. Grant, 2012: Invigoration of cumulus cloud fields by mesoscale ascent. Quart. J. Roy. Meteor. Soc., 138, 2136–2150, doi:10.1002/qj.1954.

    • Search Google Scholar
    • Export Citation

  • Kirshbaum, D. J., and C.-C. Wang, 2014: Boundary layer updrafts driven by airflow over heated terrain. J. Atmos. Sci., 71, 1425–1442, doi:10.1175/JAS-D-13-0287.1.

    • Search Google Scholar
    • Export Citation

  • Kirshbaum, D. J., and J. G. Fairman Jr., 2015: Cloud trails past the Lesser Antilles. Mon. Wea. Rev., 143, 995–1017, doi:10.1175/MWR-D-14-00254.1.

    • Search Google Scholar
    • Export Citation

  • Lean, H. W., P. A. Clark, M. Dixon, N. M. Roberts, A. Fitch, R. Forbes, and C. Halliwell, 2008: Characteristics of high-resolution versions of the Met Office Unified Model for forecasting convection over the United Kingdom. Mon. Wea. Rev., 136, 3408–3424, doi:10.1175/2008MWR2332.1.

    • Search Google Scholar
    • Export Citation

  • Minder, J., R. B. Smith, and A. D. Nugent, 2013: The dynamics of ascent-forced orographic convection in the tropics: Results from Dominica. J. Atmos. Sci., 70, 4067–4088, doi:10.1175/JAS-D-13-016.1.

    • Search Google Scholar
    • Export Citation

  • Nugent, A. D., R. B. Smith, and J. R. Minder, 2014: Wind speed control of tropical orographic convection. J. Atmos. Sci., 71, 2695–2712, doi:10.1175/JAS-D-13-0399.1.

    • Search Google Scholar
    • Export Citation

  • Qian, J.-H., 2008: Why precipitation is mostly concentrated over islands in the Maritime Continent. J. Atmos. Sci., 65, 1428–1441, doi:10.1175/2007JAS2422.1.

    • Search Google Scholar
    • Export Citation

  • Qian, T., C. C. Epifanio, and F. Zhang, 2012: Topographic effects on the tropical land and sea breeze. J. Atmos. Sci., 69, 130–149, doi:10.1175/JAS-D-11-011.1.

    • Search Google Scholar
    • Export Citation

  • Ramage, C. S., and T. A. Schroeder, 1999: Trade wind rainfall atop Mount Waialeale, Kauai. Mon. Wea. Rev., 127, 2217–2226, doi:10.1175/1520-0493(1999)127<2217:TWRAMW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Reisner, J. M., and P. K. Smolarkiewicz, 1994: Thermally forced low Froude number flow past three-dimensional obstacles. J. Atmos. Sci., 51, 117–133, doi:10.1175/1520-0469(1994)051<0117:TFLFNF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Rogers, R. R., and M. K. Yau, 1989: A Short Course in Cloud Physics. Butterworth-Heineman, 290 pp.

  • Schroeder, T. A., 1977: Meteorological analysis of an Oahu flood. Mon. Wea. Rev., 105, 458–468, doi:10.1175/1520-0493(1977)105<0458:MAOAOF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Smith, R. B., P. Schafer, D. J. Kirshbaum, and E. Regina, 2009: Orographic precipitation in the tropics: Experiments in Dominica. J. Atmos. Sci., 66, 1698–1716, doi:10.1175/2008JAS2920.1.

    • Search Google Scholar
    • Export Citation

  • Smith, R. B., and Coauthors, 2012: Orographic precipitation in the tropics: The Dominica Experiment. Bull. Amer. Meteor. Soc., 93, 1567–1579, doi:10.1175/BAMS-D-11-00194.1.

    • Search Google Scholar
    • Export Citation

  • Smolarkiewicz, P. K., and R. Rotunno, 1989: Low Froude number flow past three-dimensional obstacles. Part I: Baroclinically generated lee vortices. J. Atmos. Sci., 46, 1154–1164, doi:10.1175/1520-0469(1989)046<1154:LFNFPT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Smolarkiewicz, P. K., R. M. Rasmussen, and T. L. Clark, 1988: On the dynamics of Hawaiian cloud bands: Island forcing. J. Atmos. Sci.,45, 1872–1905, doi:10.1175/1520-0469(1988)045<1872:OTDOHC>2.0.CO;2.

  • Tian, W. S., and D. J. Parker, 2003: A modeling study and scaling analysis of orographic effects on boundary layer shallow convection. J. Atmos. Sci., 60, 1981–1991, doi:10.1175/1520-0469(2003)060<1981:AMSASA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Wang, C.-C., 2014: Thermally-driven circulation and convection over a mountainous tropical island. M.S. thesis, Dept. of Atmospheric and Oceanic Sciences, McGill University, 90 pp.

  • Yang, Y., and Y.-L. Chen, 2008: Effects of terrain heights and sizes on island-scale circulations and rainfall for the island of Hawaii during HaRP. Mon. Wea. Rev., 136, 120–146, doi:10.1175/2007MWR1984.1.

    • Search Google Scholar
    • Export Citation

  • Yang, Y., S.-P. Xie, and J. Hafner, 2008: The thermal wake of Kauai Island: Satellite observations and numerical simulations. J. Climate, 21, 4568–4586, doi:10.1175/2008JCLI1895.1.

    • Search Google Scholar
    • Export Citation

  • Yeh, H.-C., and Y.-L. Chen, 1998: Characteristics of rainfall distributions over Taiwan during the Taiwan Area Mesoscale Experiment (TAMEX). J. Appl. Meteor., 37, 1457–1469, doi:10.1175/1520-0450(1998)037<1457:CORDOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    (top) Map of the western Atlantic Ocean and Caribbean Sea, (bottom left) the DOMEX study region with data sites, and (bottom right) Dominica’s terrain. Filled squares are surface stations, open triangles are operational radar locations, and open circle is the TFFR radiosonde location.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Skew T profile showing temperature (black), dewpoint (gray), and wind (vectors to the right) profiles of the merged WKA sounding from RF07 and the TFFR sounding from 1200 UTC 18 Apr 2011. The WKA sounding data were smoothed to a uniform vertical spacing of 50 m. The black horizontal dashed line at 3792 m (~640 hPa) marks the height at which the WKA sounding was connected to the TFFR radiosonde.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Time series at the FWL mountain weather station for both observations (green) and control simulations (different shades of blue for 125–1000 m): (a) shortwave radiation flux (), (b) temperature (), (c) relative humidity (RH), (d) water vapor mixing ratio (), and (e) ΔSLP (see text for definition). The dashed green vertical lines in all panels denote the timing of the WKA leg-3 and -4 racetrack period.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Satellite data from 18 Apr 2011, including (a)–(d) effective albedo at four different times and (e) time series of island cloud fraction (the fraction of island points with effective albedos > 0.3). The gray shading denotes the WKA leg-3 and -4 racetrack period.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    In situ wind vectors from WKA legs 1 and 2 (both at a height of z = 300 m) and the third pass of legs 3 and 4 (z = 1800 m) over the island. The filled color shadings show averaged effective cloud albedo over 1318–1454 LST when the WKA was flying racetracks over the island. Terrain contours of 500 and 1000 m are also overlaid in gray.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    WCR (a),(b) reflectivity and (c),(d) vertical velocity from the third passes of (a),(c) leg 3 and (b),(d) leg 4. The dashed line at z = 1.8 km indicates the aircraft altitude.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    Snapshots of liquid water path (filled color contours) and wind vectors at the first model level of the CTL-250 simulation at four different times. The island terrain is contoured in gray at levels of 1, 250, 500, 750, and 1000 m.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    As in Fig. 7, but for the four control simulations at 1400 LST.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    Vertical cross section of time-averaged perturbation winds (vectors), potential temperature (black lines), and liquid water mixing ratio (, color-filled contours) from the CTL-250 simulation over 1100–1500 UTC, along the transect shown in Fig. 8c.

  • <sc>Fig</sc>. 10.
    View in gallery
    Fig. 10.

    Cumulative precipitation (filled color contours) over 1000–1700 LST from (a) the TFFF radar and (b)–(f) various control simulations. The island terrain is contoured in gray at levels of 1, 250, 500, 750, and 1000 m.

  • <sc>Fig</sc>. 11.
    View in gallery
    Fig. 11.

    Cloud microphysical comparison between WKA in situ observations and CTL-250 simulation, conditionally averaged over all clouds along the three leg-4 passes. (a) Cloud-droplet size distribution and (b) probability density of along with corresponding threshold autoconversion rates of 10−9 kg m−3 s−1 (based on the Thompson cloud microphysics parameterization).

  • <sc>Fig</sc>. 12.
    View in gallery
    Fig. 12.

    As in Fig. 8, but for the 10 sensitivity simulations of section 4.

  • <sc>Fig</sc>. 13.
    View in gallery
    Fig. 13.

    Time series of various quantities from the topographic sensitivity tests: (a) mean-layer (0–500 m AGL) and (b) CAPE, (c) surface-based horizontal inflow crossing the island perimeter , (d) cloud-layer vertical mass flux , (e) island convergence fraction , and (f) island cloud fraction .

  • <sc>Fig</sc>. 14.
    View in gallery
    Fig. 14.

    As in Fig. 13, but for the wind sensitivity tests and (e) conditionally averaged within the convective cores at z = 1.8 km.

  • <sc>Fig</sc>. 15.
    View in gallery
    Fig. 15.

    As in Fig. 14, but for the cloud-feedback sensitivity tests.

  • <sc>Fig</sc>. 16.
    View in gallery
    Fig. 16.

    Comparison of mean-layer (0–500 m AGL) (color shading) and wind vectors between the NORNCOD and REF simulations, averaged over the time period encompassing the three over-island racetracks (1330–1450 LST). To avoid chaotic wind fluctuations near the ridge crest, wind vectors from points above 500 m, or with wind speed differences exceeding 3 m s−1, are omitted.

  • <sc>Fig</sc>. 17.
    View in gallery
    Fig. 17.

    Locations of 40 cross-island cross sections used for the heat-engine calculations.

  • <sc>Fig</sc>. 18.
    View in gallery
    Fig. 18.

    Results from heat-engine analysis of the NOMP and THERM-NOMP simulations. (a) Nonadiabatic temperature difference between the island and the ocean , (b) island mixed-layer depth H, and (c) thermal updraft strength ; solid lines indicate values diagnosed from the simulations and dashed lines indicate theoretical predictions.

Fig. 1.

(top) Map of the western Atlantic Ocean and Caribbean Sea, (bottom left) the DOMEX study region with data sites, and (bottom right) Dominica’s terrain. Filled squares are surface stations, open triangles are operational radar locations, and open circle is the TFFR radiosonde location.
Fig. 2.

Skew T profile showing temperature (black), dewpoint (gray), and wind (vectors to the right) profiles of the merged WKA sounding from RF07 and the TFFR sounding from 1200 UTC 18 Apr 2011. The WKA sounding data were smoothed to a uniform vertical spacing of 50 m. The black horizontal dashed line at 3792 m (~640 hPa) marks the height at which the WKA sounding was connected to the TFFR radiosonde.
Fig. 3.

Time series at the FWL mountain weather station for both observations (green) and control simulations (different shades of blue for 125–1000 m): (a) shortwave radiation flux (), (b) temperature (), (c) relative humidity (RH), (d) water vapor mixing ratio (), and (e) ΔSLP (see text for definition). The dashed green vertical lines in all panels denote the timing of the WKA leg-3 and -4 racetrack period.
Fig. 4.

Satellite data from 18 Apr 2011, including (a)–(d) effective albedo at four different times and (e) time series of island cloud fraction (the fraction of island points with effective albedos > 0.3). The gray shading denotes the WKA leg-3 and -4 racetrack period.
Fig. 5.

In situ wind vectors from WKA legs 1 and 2 (both at a height of z = 300 m) and the third pass of legs 3 and 4 (z = 1800 m) over the island. The filled color shadings show averaged effective cloud albedo over 1318–1454 LST when the WKA was flying racetracks over the island. Terrain contours of 500 and 1000 m are also overlaid in gray.
Fig. 6.

WCR (a),(b) reflectivity and (c),(d) vertical velocity from the third passes of (a),(c) leg 3 and (b),(d) leg 4. The dashed line at z = 1.8 km indicates the aircraft altitude.
Fig. 7.

Snapshots of liquid water path (filled color contours) and wind vectors at the first model level of the CTL-250 simulation at four different times. The island terrain is contoured in gray at levels of 1, 250, 500, 750, and 1000 m.
Fig. 8.

As in Fig. 7, but for the four control simulations at 1400 LST.
Fig. 9.

Vertical cross section of time-averaged perturbation winds (vectors), potential temperature (black lines), and liquid water mixing ratio (, color-filled contours) from the CTL-250 simulation over 1100–1500 UTC, along the transect shown in Fig. 8c.
Fig. 10.

Cumulative precipitation (filled color contours) over 1000–1700 LST from (a) the TFFF radar and (b)–(f) various control simulations. The island terrain is contoured in gray at levels of 1, 250, 500, 750, and 1000 m.
Fig. 11.

Cloud microphysical comparison between WKA in situ observations and CTL-250 simulation, conditionally averaged over all clouds along the three leg-4 passes. (a) Cloud-droplet size distribution and (b) probability density of along with corresponding threshold autoconversion rates of 10−9 kg m−3 s−1 (based on the Thompson cloud microphysics parameterization).
Fig. 12.

As in Fig. 8, but for the 10 sensitivity simulations of section 4.
Fig. 13.

Time series of various quantities from the topographic sensitivity tests: (a) mean-layer (0–500 m AGL) and (b) CAPE, (c) surface-based horizontal inflow crossing the island perimeter , (d) cloud-layer vertical mass flux , (e) island convergence fraction , and (f) island cloud fraction .
Fig. 14.

As in Fig. 13, but for the wind sensitivity tests and (e) conditionally averaged within the convective cores at z = 1.8 km.
Fig. 15.

As in Fig. 14, but for the cloud-feedback sensitivity tests.
Fig. 16.

Comparison of mean-layer (0–500 m AGL) (color shading) and wind vectors between the NORNCOD and REF simulations, averaged over the time period encompassing the three over-island racetracks (1330–1450 LST). To avoid chaotic wind fluctuations near the ridge crest, wind vectors from points above 500 m, or with wind speed differences exceeding 3 m s−1, are omitted.
Fig. 17.

Locations of 40 cross-island cross sections used for the heat-engine calculations.
Fig. 18.

Results from heat-engine analysis of the NOMP and THERM-NOMP simulations. (a) Nonadiabatic temperature difference between the island and the ocean , (b) island mixed-layer depth H, and (c) thermal updraft strength ; solid lines indicate values diagnosed from the simulations and dashed lines indicate theoretical predictions.
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