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    Location and mountainous terrain of Dominica. (top) The position of Dominica in the eastern Caribbean Sea north of South America. (bottom) Progressively smaller insets show (left) Dominica and its surrounding islands and (right) Dominica only with its terrain contours. Overlaid circles in the bottom right panel are the locations of four rain gauge stations: LP is Le Plaine, FWL is Freshwater Lake, SF is Springfield, and CF is Canefield.

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    MODIS Aqua visible satellite image on 1 Jul 2008 showing a typical cloud pattern in trade wind flow over Dominica.

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    Data from the Yale Dominica Precipitation Project. (a) Precipitation rates derived from the Guadeloupe radar over Dominica (gray lines). The three precipitation types correspond to upstream open-ocean precipitation rates of <2 (type I), 2–10 (type II), and >10 mm day−1 (type III). (b) Diurnal cycle of precipitation over Dominica from the four rain gauges shown in Fig. 1, where the abscissa is time (UTC). Data from a 1-yr period are averaged in 2-h blocks. The largest precipitation events associated with tropical cyclones were removed for this calculation.

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    Upstream sounding for the REF simulation. The long wind barbs denote values of 5–10 m s−1; the short wind barbs indicate 0–5 m s−1.

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    Numerical setup and comparison with the east–west transect across Dominica from Fig. 1.

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    Isosurfaces of qc = 0.1 g kg−1 from the REF simulation at t = 4 h. Two cycles are shown in y.

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    Meridionally averaged qc (filled), θL (thin lines), and qr (thick lines) fields at t = 4 h. Contours of θ increase upward from 300 K in intervals of 2 K; the single contour of qr is 0.001 g kg−1.

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    Horizontal profiles of time-averaged statistics from the REF simulation: (a) liquid water path and (b) cloud cover over the vertical column, (c) surface rain rate, (d) convective mass flux, (e) buoyancy flux, and (f) water vapor flux. The flux distributions in (d)–(f) are computed at z = 1.5 km as described in the text and are multiplied by the y-averaged density ρ. To give units of W m−2 in (e) and (f), the heat fluxes are scaled by cp, the specific heat at constant pressure, and Lυ, the latent heat of condensation, respectively. All profiles are smoothed in x using a 10-point averaging operator.

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    Time- (3–6 h) and y-averaged (a) liquid water potential temperature (θL) and (b) qt far upwind of the island at x = 192 km (black solid line), closer to the island at x = 96 km (gray solid), and downwind of the island at x = 32 km (black dashed) from the REF simulation. For reference, corresponding profiles from the BOMEX simulation [specified as in Siebesma et al. (2003)] are overlaid, in which the spatial averaging is computed over the full domain at each output time and then averaged over all output times from 3 to 6 h.

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    Profiles of vertical velocity at three different x locations: (a) mean vertical motion (w); (b) conditional mean over the convective cores (), where the cores are defined as saturated grid points satisfying w′, θρ > 0; and (c) conditional mean over the descending unsaturated grid points (). These profiles are computed at each output time using the local 2D sampling technique described in section 4 and then averaged over all output times from 3 to 6 h.

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    Two types of convective triggering in the REF simulation. (a)–(c) Isosurfaces of qc (0.1 g kg−1; cyan) and qr (0.02 g kg−1; red) of an upstream cumulus cloud that develops into a precipitating cell over the mountain. (d),(e) Isosurfaces of qυ = qυ (1 g kg−1; blue), qc (0.2 g kg−1; cyan), and qr (0.02 g kg−1; red) depicting the transition from a moist subcloud anomaly into a precipitating cell. In both panels, only a small moving box of data is shown to isolate the single feature of interest; qυ in (d)–(f) is masked above 700 m to clearly expose the subcloud moisture perturbation.

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    Profiles of time- and y-averaged cloud fraction from the REF simulation at three different x locations.

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    Horizontal profiles of y-averaged and vertically integrated (over the convective core depth) forcings (a) S, O, and S + O and (b) S + O and Ubx. The mean upstream value of ∫c (S + O) = 8 m2 s−3 is subtracted from the forcing function in (b) to allow a direct comparison between the forcing and response. Note that just as the orographic forcing of buoyancy increases over the upwind slope in (a), the forcing by convection weakens and becomes negative. As predicted by (8), the increased net forcing over the mountain leads to a maximum response at x = 69 km in (b). All profiles are smoothed by averaging over the nearest 10 grid points.

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    Entrainment profiles at four different x locations. These profiles are computed at each output time using the local 2D sampling technique described in section 4 and then averaged over all output times from 3 to 6 h.

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    (a) Horizontal profiles of maximum and y-averaged cloud-top height (smoothed using an averaging box over the nearest 10 grid points) and (b) mean vertical profiles of qc within the convective cores at different x locations. The vertical profiles in (b) are computed at each output time using the local 2D sampling technique described in section 4 and then averaged over all output times from 3 to 6 h. The mean cloud-top heights at the three locations in (b) are shown by hash marks and the 1 g kg−1 autoconversion threshold is overlaid.

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    Microphysical aspects of the REF simulation. (a) Vertically integrated and y-averaged autoconversion and accretion rates within the convective cores, along with (b) the ratio of y-averaged surface precipitation rate to y-averaged cloud-base precipitation rate. All profiles are smoothed by averaging over the nearest 10 grid points.

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    Plots of Δw from the analytical solutions [(14), (15)] in flows over triangular mountains with different widths (am). The abscissa is scaled by the width of the mountain in the Φam = π case, which is (am)0 = 7.1 km.

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    Plots of Δw obtained in flows over a Gaussian mountain with hm = 1000 m, xm = 64 km, and varying parameters (α, Hc, and am). Analytical solutions to (18) are shown for (a) various damping coefficients α (10−3 s−1) with the convecting layer height Hc = 0 and the ridge width am = 5 km; (b) various Hc (km) with α = 0.005 s−1 and am = 5 km (overlaid by results from REF simulation in gray); and (c) various am (km) with Hc = 1000 m and α = 0.005 s−1. (d) Numerical from the A2.5, REF, and A10 simulations, computed from the time-averaged conditional mean and as in Fig. 13.

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    Comparison of various quantities from the A10, REF, and A2.5 simulations: (a) Surface rain rate, (b) buoyancy flux, (c) water vapor flux at z = 1.5 km, and (d) integrated rain evaporation rate (∫ Er dz).

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    As in Figs. 19a–c, but for the REF, DRAG, and HEAT simulations.

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Orographic Precipitation in the Tropics: Large-Eddy Simulations and Theory

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  • 1 University of Reading, Reading, United Kingdom
  • | 2 Yale University, New Haven, Connecticut
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Abstract

Recent radar and rain gauge observations from the Caribbean island of Dominica (15°N) show a strong orographic enhancement of trade wind precipitation. The mechanisms behind this enhancement are investigated using idealized large-eddy simulations with a realistic representation of the shallow trade wind cumuli over the open ocean upstream of the island. The dominant mechanism is found to be the rapid growth of convection by the bulk lifting of the inhomogenous impinging flow. When rapidly lifted by the terrain, existing clouds and other moist parcels gain buoyancy relative to rising dry air because of their different adiabatic lapse rates. The resulting energetic, closely packed convection forms precipitation readily and brings frequent heavy showers to the high terrain. Despite this strong precipitation enhancement, only a small fraction (1%) of the impinging moisture flux is lost over the island. However, an extensive rain shadow forms to the lee of Dominica due to the convective stabilization, forced descent, and wave breaking. A linear model is developed to explain the convective enhancement over the steep terrain.

Corresponding author address: Daniel J. Kirshbaum, Dept. of Meteorology, University of Reading, Earley Gate, Reading, Berkshire RG6 6BB, United Kingdom. Email: d.kirshbaum@reading.ac.uk

Abstract

Recent radar and rain gauge observations from the Caribbean island of Dominica (15°N) show a strong orographic enhancement of trade wind precipitation. The mechanisms behind this enhancement are investigated using idealized large-eddy simulations with a realistic representation of the shallow trade wind cumuli over the open ocean upstream of the island. The dominant mechanism is found to be the rapid growth of convection by the bulk lifting of the inhomogenous impinging flow. When rapidly lifted by the terrain, existing clouds and other moist parcels gain buoyancy relative to rising dry air because of their different adiabatic lapse rates. The resulting energetic, closely packed convection forms precipitation readily and brings frequent heavy showers to the high terrain. Despite this strong precipitation enhancement, only a small fraction (1%) of the impinging moisture flux is lost over the island. However, an extensive rain shadow forms to the lee of Dominica due to the convective stabilization, forced descent, and wave breaking. A linear model is developed to explain the convective enhancement over the steep terrain.

Corresponding author address: Daniel J. Kirshbaum, Dept. of Meteorology, University of Reading, Earley Gate, Reading, Berkshire RG6 6BB, United Kingdom. Email: d.kirshbaum@reading.ac.uk

1. Introduction

Orographic precipitation occurs around the globe in various climates and synoptic settings. Some of its most common manifestations are the enhancement or modulation of precipitation from midlatitude cyclones (e.g., Douglas and Glasspoole 1947; Browning et al. 1974) and tropical cyclones (e.g., Yu and Cheng 2008; Smith et al. 2009a) and the triggering of moist convection by thermal heating over high terrain (e.g., Tripoli and Cotton 1989; Tucker and Crook 2005). Orography also triggers moist convection by forcing conditionally unstable air to rise over a mountain massif, which is commonly observed in midlatitutes along the west coast of North America (e.g., Kirshbaum and Durran 2005), the southern Andes (Smith and Evans 2007), and the Cévennes Vivarais region of France (e.g., Anquetin et al. 2003), among other locations. This mechanism also operates in the tropics when trade wind flow encounters mountainous terrain, which can occur along a continental coastline or an island at sea.

Trade wind flow is often characterized by scattered shallow cumuli beneath a sharp inversion. These cumuli may generate little to no precipitation over the ocean, but they can rapidly transition into moderate to intense showers after landfall and subsequent orographic ascent. Although the trade wind inversion usually prevents these cells from rising deep into the troposphere and organizing into mesoscale systems, the high frequency of these showers can generate remarkably large precipitation amounts. Previous studies of trade wind precipitation over orography have focused on the persistent showers over the island of Hawaii (e.g., Woodcock 1960; Smolarkiewicz et al. 1988; Yang and Chen 2008). As shown by these studies, this precipitation is controlled by a complex mixture of processes, among them flow splitting around the island, vertically propagating mountain waves, and thermally driven circulations over the large land body. As a result, the pure effects of forced ascent are difficult to isolate.

Our search for a purer example of forced orographic lifting led us to Dominica, a lower and narrower island in the Lesser Antilles islands of the Caribbean Sea at 15°N. Scientists have long been fascinated by Dominica’s intense orographic precipitation enhancement. Reed (1926) found that Dominica’s steep volcanic mountains, which rise to nearly 1.5 km over a horizontal distance of around 5 km (Fig. 1), receive 2–3 times more precipitation than the coastlines. This precipitation develops within synoptic disturbances such as tropical cyclones as well as during the more common undisturbed trade wind conditions. A plan view of the typical trade wind convection over Dominica is presented in Fig. 2 by the Moderate Resolution Imaging Spectroradiometer (MODIS) Aqua satellite image from 1 July 2008, which shows scattered clouds over the open ocean to the east of Dominica, closely packed cumuli over the island, and cloud-free air in the lee.

To better understand the precipitation mechanisms over Dominica, the Yale Dominica Precipitation Project (Smith et al. 2009a,b) installed four HOBO tipping buckets across the island in March 2007 (Fig. 1) for accurate measurements of rainfall rate and accumulation. Complementary radar observations are supplied by two operational Météo-France 2.8-GHz S-band radars on the surrounding islands of Guadeloupe and Martinique (Fig. 1). The mean precipitation profiles in Fig. 3a, derived from a full year of 5-min scans from the Guadeloupe radar along the transect from Fig. 1, confirm the intense precipitation enhancement over Dominica. The sensitivity of the island precipitation to the upstream conditions is seen by partitioning the observations into three types based on their upstream precipitation rates (type I: <2 mm day−1; type II: 2–10 mm day−1; type III: >10 mm day−1). Although the absolute increase in precipitation is the largest for type III, which corresponds to synoptically disturbed conditions, the enhancement ratio is the largest in undisturbed trade wind flow (type I). Moreover, the averaged precipitation over Dominica exhibits little to no diurnal variability (Fig. 3b), which suggests that it is mainly driven by mechanical lifting of the impinging flow rather than by diurnal heating patterns.

As a follow-up to Smith et al. (2009b), this paper investigates the mechanisms by which a narrow tropical island like Dominica can enhance the precipitation from shallow cumulus clouds. This is carried out through large-eddy simulations (LES) in which a realistic field of trade wind cumuli impinges on an idealized ridge based on Dominica. Unlike previous studies of shallow orographic convection (e.g., Kirshbaum and Durran 2004; Fuhrer and Schär 2005), these simulations explicitly resolve both the upstream shallow cumuli and the orographic convection rather than just the latter. This technique is more computationally expensive, but it offers a superior representation of the transition in cumulus development over the island.

2. Numerical model and reference setup

a. Forcings, fluxes, and the upstream flow

The cloud-resolving model used for the simulations (Bryan and Fritsch 2002) is fully nonlinear, fully compressible, and nonhydrostatic. A vertically implicit time-splitting scheme with 10 small time steps per large step is used to filter sound waves (Klemp and Wilhelmson 1978). Forward time integration is performed with a third-order Runge–Kutta scheme. Sixth-order horizontal advection and fifth-order vertical advection are used with positive-definite advection for all moisture variables to conserve water substance. Sixth-order monotonic horizontal diffusion is applied to all variables for stability and to minimize spurious behavior at poorly resolved scales. Cloud microphysics are parameterized using the Kessler (1969) warm-rain scheme, and subgrid-scale turbulence is parameterized with a first-order eddy diffusivity scheme (e.g., Smagorinsky 1963). The initial state (defined shortly) is assumed to be in geostrophic balance, so the Coriolis force is applied only to perturbations from that state using an f-plane approximation with f = 0.376 × 10−4 s−1.

To simulate a realistic field of trade wind cumuli over the open ocean upstream of Dominica, we use observations from the 1969 Barbados Oceanographic and Meteorological Experiment (BOMEX; Holland and Rasmusson 1973), which was conducted in the Atlantic Ocean just to the east of Dominica. Siebesma et al. (2003) used these data to initialize and constrain an intercomparison of numerical simulations of shallow cumulus convection. The conditions specified in their appendix B, which have since been used in several numerical studies (e.g., Zhao and Austin 2005; Kuang and Bretherton 2006), are also adopted here. They allow for a balance between shallow convection driven by surface fluxes off the ocean and the imposed large-scale forcings (subsidence, radiative cooling, and moisture advection) to yield a quasi-steady cumulus field. To isolate the effect of forced lifting on the trade wind convection, the forcings and surface fluxes are imposed as horizontally uniform even in regions of complex terrain. This idealization is relaxed in section 6 where differential surface fluxes over land are considered. One notable difference between our simulations and those of Siebesma et al. (2003) is that because the orography induces mesoscale variability, the large-scale subsidence is applied to local thermodynamic and velocity variables rather than to the area mean.

The upstream sounding in Fig. 4, which is taken from Siebesma et al. (2003) up to 3 km, consists of a subcloud layer from the surface up to 500 m, a nearly saturated and conditionally unstable “cloud” layer up to 1500 m, and an inversion up to 2100 m topped by very dry air. The magnitude of the purely easterly wind is the highest at the surface (8.75 m s−1) and decreases linearly to 4.61 m s−1 from 700 to 3000 m. We extend this sounding to the upper boundary at Lz = 12 km by fixing the relative humidity (RH) and winds to their 3-km values and integrating upward using a uniform dry Brunt–Väisälä frequency (Nd = 0.01 s−1). The convective available potential energy (CAPE) for a surface parcel brought to the top of the trade wind inversion is 75 J kg−1. A much deeper reservoir of CAPE exists in the free troposphere (over 2000 J kg−1), but the simulated convection never accesses this instability after losing most of its buoyancy across the inversion and then mixing with dry air aloft.

b. Domain and terrain

Because fine resolution is needed to resolve the shallow cumuli but a large domain is needed to capture the mountain wave pattern, some compromises must be made to avoid prohibitive computational cost. Chief among these is the use of periodic boundaries and a 1D mountain in the y direction that forces all of the impinging flow to rise over it rather than detouring around it (Fig. 5). The terrain used in the reference (REF) simulation (Fig. 5) is a 1D Gaussian ridge centered at xm = 64 km with a height hm = 1 km and half-width am = 5 km to mimic the real Dominica terrain along the transect in Fig. 1. This 1D terrain representation causes several undesirable effects, including stronger upslope lifting than over a finite-length ridge of the same height (e.g., Kirshbaum and Smith 2008) and increased wave breaking over the crest. At the onset of wave breaking, an upstream-propagating bore develops that lifts the upstream flow by approximately 100 m. Although the Coriolis force would eventually cause this wave to retreat back to the mountain, this adjustment at 15°N would require about 2 days to complete, which is too computationally expensive to carry out. Thus, we are forced to accept this upstream lifting and its effects on the impinging flow.

Because computational constraints limit the realism of our numerical configuration, we stress that these simulations are only intended to give a qualitative picture of the orographic impacts on shallow cumulus convection. For this reason we do not directly compare the numerical results to observations. Such a comparison is only meaningful if a realistic 2D terrain and larger open domain is used capture the full 3D orographic response, along with sufficient numerical resolution to produce resolution-independent results. The horizontal resolution of Δx = Δy = 100 m, while sufficient to capture the quasi-steady behavior of cumuli in Siebesma et al. (2003), is barely adequate to resolve the characteristic cloud scales of 200–1000 m. Exploratory tests at higher resolution (Δx = Δy = 50 m) showed similar overall behavior but slightly weaker orographic convection, which suggests that higher resolution is needed for statistical convergence. Nonetheless, because the simulated quantities analyzed (e.g., precipitation and turbulent heat fluxes) decreased by less than 30%, we deemed Δx = Δy = 100 m to be sufficient to capture the basic physics of interest.

The domain has a cross-flow length of Ly = 6.4 km, which is wide enough to resolve several cumuli with characteristic diameters of 1 km. The along-flow dimension is much greater (Lx = 204.8 km), with outflow boundaries to transmit gravity waves out of the domain. The long fetch between the inflow boundary and the mountain crest at x = 64 km provides upstream perturbations at least 3 h to develop before climbing the windward slope, which is just long enough to produce a mature, quasi-steady cumulus field (Siebesma et al. 2003). The upper boundary (Lz = 12 km) is placed well above the inversion to minimize distortion of low-level gravity waves and to allow moist convection to rise freely into the troposphere. The terrain-following vertical grid has a spacing of Δz = 50 m from the surface up to 4 km; it then stretches to 200 m over a 4-km layer and then remains fixed at 200 m above 8 km, which gives Nz = 132.

To seed convective motions, we add uniformly distributed, three-dimensional fields of random noise to the initial potential temperature (θ) and water vapor mixing ratio (qυ) fields over x ≤ 192 km and z ≤ 2 km. These fields are filtered in wavenumber space to remove all variance at wavelengths below 6Δx and scaled to have maximum amplitudes of (θ′)max = 0.1 K and (qυ)max = 0.025 g kg−1. These perturbations are replenished at x = 192 km over the course of the simulation to continually seed the fresh inflow air. The region defined as 192 < xLx is kept free of perturbations and relaxed back to the initial state through a Rayleigh damping layer to prevent spurious reflections of perturbation energy from the inflow boundary. The mountain is added impulsively to the domain at t = 0 and the simulation is integrated to t = 6 h with an output resolution of 10 min. In the following analysis, all time averages are taken over 3–6 h and all y averages are taken over Ly (unless specified otherwise).

3. Results

By t = 3 h in the REF simulation the mountain wave is established and the upstream-propagating bore produced by flow blocking has propagated away from the mountain, which leaves the flow near the mountain in a quasi-steady state. The solution over 3–6 h is illustrated by 3D isosurfaces of cloud water mixing ratio qc (0.1 g kg−1) at t = 4 h in Fig. 6. Scattered cumuli of variable height form over the sea, which multiply and widen over the upwind slope to form closely packed cells. The cumuli are slightly deeper and more vigorous over the upwind slope and crest and vanish completely in the lee.

The characteristic vertical flow structure is shown by the y-averaged liquid water potential temperature (θL), qc, and rainwater mixing ratio (qr) at t = 4 h in Fig. 7. Upstream of the mountain, only a few clouds penetrate into the trade wind inversion and generate precipitation. The mean cloud water and precipitation both increase as the flow ascends the mountain, with some rainfall spilling over the crest and into the lee. The inversion base rises only slightly over the ridge and then plunges below a layer of lee wave breaking. This wave response can be explained by 1D hydraulic theory of a fluid layer beneath a density continuity (e.g., Long 1954; Schär and Smith 1993). When applied to typical trade wind soundings, this theory predicts wave breaking over ridges higher than 400–500 m, which is exceeded here by a wide margin (Smith et al. 1997, 2009b). The “subcritical” flow over the upwind slope speeds up and thins and then transitions to “supercritical” over the lee, where it accelerates and thins further until breaking. This theory also predicts that an upstream-propagating bore should develop as the mountain rises above the critical height needed to force wave breaking.

The strong impact of orography on the trade wind flow is demonstrated by the various horizontal profiles in Fig. 8, which are computed from the y statistics of the REF simulation and averaged in time. Over the open ocean, the vertically integrated liquid water path (LWP) and the total cloud cover (CT)—the latter defined as the fraction of vertical columns that contain cloud—are approximately 10 g m−2 and 0.05, which fall within the range of values reported in Siebesma et al. (2003). As the air rises over the high terrain, the dense population of cells increases LWP and CT to 640 g m−2 and 0.95, while the y-averaged rain rate (R) increases 200-fold from around 0.01 mm hr−1 to over 2 mm hr−1 (Figs. 8a–c). The island convection, which releases all of the low-level CAPE from the impinging flow between x = 68 km and x = 64 km, also dramatically increases the convective mass flux (), buoyancy flux (), and water-vapor flux () at the 1.5-km level. In the preceding, all y-averaged quantities like R are denoted with an overbar, and perturbation quantities [e.g., w′(x, y, z)] are found by subtracting the y-averaged value [w(x, z)] from the full value [w(x, y, z)]. Also, θρ is the density temperature
i1520-0469-66-9-2559-e1
where Rd and Rυ are the gas constants for dry and moist air and qt = qυ + qc + qr is the total water mixing ratio.

Despite the strong orographic precipitation enhancement seen in Fig. 8c, the total moisture removed by the island (P) is still small compared to the vertically integrated horizontal moisture flux in the upstream sounding (I). From the surface to the inversion base I = 182 kg m−1 s−1, whereas P, which is found by integrating R across the mountain (54 ≤ x ≤ 74 km), is only 2.6 kg m−1 s−1. This gives a subinversion drying ratio (DR = P/I), or fraction of impinging moisture removed as orographic precipitation, of 1.4%. The precipitation is also small compared to the upward turbulent moisture flux of 8.9 kg m−1 s−1 (measured at z = 1.5 km and integrated over the same range of x). This suggests that only a modest fraction of the moisture transported upward by convection actually reaches the ground.

Figure 9 shows time- and y-averaged vertical profiles of liquid water potential temperature (θL) and qt far upstream at x = 192 and on either side of the mountain at x = 96 km and x = 32 km. For reference, the corresponding profiles from a fully periodic simulation with no terrain and Lx = Ly = 6.4 km (BOMEX), which is designed identically to the large-eddy simulations of Siebesma et al. (2003), are also provided. Orographic blocking lifts the inversion base far upwind of the ridge, which disrupts the quasi-equilibrium reached in the BOMEX simulation. Once the inversion is displaced upward from its initial position, the large-scale subsidence, which remains the strongest at the original inversion position, is unable to offset the cooling from convective detrainment. This positive feedback process causes the inversion to continue rising as it approaches the mountain, reaching a height of 1.8 km by x = 96 km. Enhanced convection just upstream of and over the mountain then erodes the inversion base by an additional 200–300 m.

The upstream lifting of the inversion evident in Fig. 9 may be partly unphysical. As mentioned in section 2, the periodic 1D ridge used in the REF simulation produces a higher-amplitude upstream bore than a finite-length ridge of the same height. In addition, the large-scale subsidence profile taken from Siebesma et al. (2003) was originally designed for a much shallower domain and may need modification for this application. It decays linearly from a peak of −0.65 cm s−1 at z = 1.5 km to zero at z = 2.1 km. To evaluate the impact of this rapid decay in subsidence on the inversion height, we conducted a simulation that is identical to the REF case except that the subsidence decayed over a much greater depth (7.5 km rather than 0.6 km in the REF case). Although this strengthened subsidence aloft managed to keep the inversion lower, the difference between the inversion heights in these two realizations was still less than 100 m. Thus the significant lifting of the inversion upstream of the orography appears to be an unavoidable consequence of the overly strong upstream bore.

Figure 9 clearly shows that the lee air at x = 32 km is warmer and drier at low levels, and cooler and moister above, than the impinging flow. Again, because the 1D ridge overestimates the mountain wave amplitude, this flow transformation is likely overestimated. Nonetheless, it explains why the simulated clouds disappear in the lee of the ridge. One major contributor to these changes is the orographic convection, which heats and dries the cloud layer through subsidence warming and cools the inversion through evaporative detrainment. Precipitation loss, which reduces the mean boundary layer qυ by about 0.2 g kg−1, also yields a net heating of about 0.5 K (using cpΔT = LυΔqυ, where cp is the specific heat at constant pressure and Lυ the latent heat of condensation). Another important factor is wave breaking above the inversion, which mixes boundary layer and free-tropospheric air over the lee slope.

Some of the changes between the vertical profiles in Fig. 9 are related not to any irreversible changes in the flow properties but rather to orographically induced patterns of horizontal flow convergence. Consider, for example, the strong changes in qt between x = 96 km and x = 32 km. Although the horizontal moisture flux (which is conserved in nonprecipitating airflow) decreases by only 1.4% because of precipitation removal between these locations, the apparent change in qt is far more dramatic. The large qt at x = 96 km results from upstream flow deceleration, which converges moisture into the air column, and the much smaller qt at x = 32 km results from the opposite effect.

4. Underlying mechanisms

What physical mechanisms are responsible for the intense orographic enhancement of turbulence and precipitation in the REF simulation? The 200-fold increase in R over the high terrain (Fig. 8c) is much higher than the 10-fold increase in cloud cover (Fig. 8b), which suggests that the increased precipitation is not merely a result of increased cloud density. Moreover, the orographic convection is still confined below the inversion layer, which rises only slightly over the mountain (Fig. 7). Nonetheless, the convective circulations are invigorated over the mountain, which is shown by the vertical profiles of the mean vertical motion (w) and the conditional means of w′ within the saturated and buoyant convective “cores” () and within the unsaturated downdrafts () in Fig. 10. As the mean uplift increases over the mountain, both the updrafts and downdrafts accelerate in opposite directions. In this section we explain the mechanisms behind the orographic enhancement of clouds, convective motions, and precipitation in the REF simulation.

We first pause to describe the technique for computing the conditional means like above. To increase the sample size beyond that available from 1D sampling in y, we use a “local 2D sampling” technique that considers a horizontal 2D rectangle centered at a given value of x with a cross-flow width of ly = Ly. The along-flow length (lx) is also equal to Ly far upwind of the mountain (x = 89 km) where the clouds are isolated and more sampling is needed, but it is contracted to lx = Ly/4 over the mountain (x = 69 km and x = 66.5 km) where clouds are more numerous and the flow changes rapidly in x. At each output time, the grid points satisfying the condition of interest (qc, w′, θρ > 0 for the cores and qc = 0, w′ < 0 for the downdrafts) are horizontally averaged over the 2D rectangle at each vertical level. The resulting vertical profiles are then averaged over 3–6 h.

Note that the analysis of conditional means within the cloud cores as the flow traverses the mountain (as in Fig. 10b) may introduce a small sampling bias. Whereas the upstream clouds are equally likely to be found in all stages of their life cycle, the newly triggered orographic clouds tend to be younger on average. However, this potential bias is mitigated somewhat by our definition of cloud cores as positively buoyant air parcels, which naturally selects the younger, developing clouds and avoids the dissipating older clouds with negative buoyancy. For this reason we neglect this source of bias in our subsequent interpretations.

a. Triggering

Because the land surface in the REF simulation is smooth, the convective cells are triggered mainly by preexisting clouds and moisture perturbations in the impinging flow. The upstream clouds form naturally as turbulent eddies in the subcloud layer ascend into the cloud layer to form cumuli. As the cumuli approach the hill, some are invigorated by the orographic ascent and develop precipitation. This process is demonstrated by Figs. 11a–c, which show the transition from a small cumulus cloud over the sea to a larger precipitating cell over the island in 14 min, by which time its surface precipitation rate is over 20 mm hr−1. The dynamical mechanism behind the orographic invigoration of such clouds is described in section 5.

Not all precipitating cells can be easily traced to upstream clouds. Some appear to develop when passive moist anomalies in the subcloud layer, which arise from evaporation off the ocean or from precipitation below cloud base, are orographically lifted to saturation and become buoyant. This mechanism, which has also been linked to trade wind showers over Hawaii (Woodcock 1960), is demonstrated by isosurfaces of qc and qυ = qυqυ in Figs. 11d–f that follow a moist subcloud anomaly as it saturates and grows into a deeper cell over 15 min. Although the precipitation from this cell at t = 262 s is only 4 mm hr−1, this example was chosen because it clearly demonstrates this triggering mechanism.

The triggering of convection from propagating moist anomalies stems from the different lapse rates of saturated and unsaturated air. When lifted by the mountain, the moist parcels saturate first and begin to condense water as the unsaturated parcels continue to cool dry adiabatically. The latent heat release in the moist parcels generates positive buoyancy relative to the dry air and initiates convective motions. This is demonstrated by considering the qυ variations of subcloud air (z = 250 m) at the base of the mountain (x = 74 km) in the REF simulation. From the statistics in y over 3–6 h, the standard deviation of qυ at this level is σ(qυ) = 0.2 g kg−1. If we define a moist (qυ = +σ) and a dry (qυ = −σ) air parcel at this level and lift them both adiabatically until the drier parcel saturates, the latent heat release within the moist parcel allows it to become 0.5 K warmer than the dry parcel, which accelerates it upward by about 0.02 m s−2. After 100 s this gives a vertical velocity of 2 m s−1.

b. Growth

From general considerations it might be expected that the high cloud fraction over the orography would inhibit the continued growth of convection. This is because the increased convective mass flux must be compensated for by stronger descent between the clouds. In the absence of mean uplift, this process rapidly warms the environment and decreases cloud buoyancy, which weakens the convective accelerations. However, in a flow subject to bulk lifting, this negative feedback is weakened or reversed because the lifting offsets the subsidence warming while increasing the latent heating in the clouds. Thus, the updrafts can be maintained or even strengthened over the orography despite their large areal coverage.

To analyze the impact of bulk lifting on shallow cumulus clouds, we extend the “slice method” of Bjerknes (1938) and Emanuel (1994). Consider the two dominant airstreams within the cloud layer: ascent in the buoyant cloud cores and compensating descent in the unsaturated air. At a given vertical level, the cloudy updrafts may be represented by a constant moist Brunt–Väisälä frequency (Nm2 < 0), a horizontally averaged updraft velocity of wc > 0, and a horizontally averaged density potential temperature θρc, whereas the unsaturated environment is represented by a dry Brunt–Väisälä frequency of Nd2 > 0, wd < 0, and θρd. Using standard formulas in Emanuel (1994), these stabilities may be estimated from the cloud layer of the upstream sounding as Nd2 ≈ 10−4 s−2 and Nm2 ≈ −0.5 × 10−5 s−2. These stabilities control the horizontal buoyancy gradients at a given vertical level as vertical motion brings parcels to that level. Consider a small horizontal region or “patch” that contains one or more cloudy updrafts. Over this patch, the horizontally averaged buoyancy of the cloudy updrafts relative to the unsaturated environment may be expressed as
i1520-0469-66-9-2559-e2
where θρ0 is the density potential temperature of the hydrostatically balanced basic state. We apply the nondiffusive thermodynamic equation separately to the cloudy and clear regions and subtract the latter from the former to give
i1520-0469-66-9-2559-e3
where the total derivative operator d/dt represents the motion of the entire patch rather than that of the individual cloud cells. The averaged vertical velocities in (3) are constrained by
i1520-0469-66-9-2559-e4
where is the horizontally averaged vertical motion and Ac and Ad are the areas of clouds and dry air within the patch. In the special case of , (3) and (4) combine to give
i1520-0469-66-9-2559-e5
where Ns2 is the “two-stream” stability. The first term in (5) represents the warming of the updrafts by moist ascent and the second represents the warming of the downdrafts by compensating descent. Thus, for the average cloud buoyancy within the patch to increase with time, Ac/Ad must satisfy
i1520-0469-66-9-2559-e6
In the current case Nd2/Nm2 = −2, so b can only increase for cloud fractions below Ac/(Ac + Ad) = ⅓. The simulated cloud fraction falls below this value upwind of the island (Fig. 8b), which suggests that the mean cloud buoyancy should grow indefinitely over the open sea. This, of course, is not the case; the shallow convection reaches a steady state as growth in developing clouds is offset by decay in dissipating clouds. Because the above analysis neglects dissipative effects like entrainment, inversion stability, etc., it cannot describe the quasi-steady convection over the sea. However, as seen below, it is valuable for explaining the increased convective vigor over the mountain, where the cloud fraction exceeds ⅓.
To consider the dynamical effects of bulk lifting, (3) and (4) may be combined to give (after some manipulation)
i1520-0469-66-9-2559-e7
where Δw = wcwd is the relative motion between the updrafts and downdrafts. The effect of moist convection on the mean buoyancy is given by S. When Ns2 < 0, convection directly enhances b, but when Ns2 > 0, which is possible even when Nm2 < 0, it diminishes the updraft buoyancy. The bulk vertical motion of partly cloudy air with contrasting moist and dry stabilities is given by O. To interpret this term, consider a neutrally buoyant and static (Δb = Δw = 0) cloud embedded in an otherwise unsaturated flow. If the air mass is bodily lifted, the cloud cools at a slower rate than the surrounding clear air because of their different adiabatic lapse rates. This causes the cloud to gain buoyancy and accelerate upward while the colder environment begins to sink (relative to the ascending slab). Because this term is always positive when air is ascending, it acts to enhance the convective vigor. Hence, bulk lifting “triggers” convection in a convectively unstable atmosphere (Ns2 < 0) and “forces” convection in a neutral or marginally stable atmosphere (Ns2 ≥ 0).

An interesting limit occurs when both the updraft and downdraft are saturated, which is treated by setting Nd2 and Ns2 to Nm2 in (7). This eliminates O so that the convection proceeds as in a saturated layer over flat ground with Nm2 < 0. Such a simple treatment may explain the growth of small-amplitude perturbations in a fully saturated orographic cloud (Kirshbaum and Durran 2004; Fuhrer and Schär 2005), but it is not applicable to the REF simulation because compensating subsidence keeps broad regions of the flow desaturated. This is shown by the vertical profiles of cloud fraction in the REF simulation in Fig. 12. Although the cloud cover increases substantially over the island, much of the cloud layer remains unsaturated even near the crest at x = 66.5 km, where the cloud fraction is around 0.9 at the surface but decays to around 0.3 by z = 2 km.

The ability of (7) to describe the REF simulation is assessed by manipulating its terms into 1D quantities that can be easily visualized. For the quasi-steady flow under consideration, we may approximate the total derivative operator d/dt with the advective derivative Ux, where U is a constant cloud layer wind speed. Similarly, we replace the x averages in (7) with time averages over 3–6 h. Finally, we integrate vertically over the cloud layer depth to obtain
i1520-0469-66-9-2559-e8
which allows these terms to be viewed as 1D horizontal profiles (we return to the overbar convention to denote y-averaged quantities). They are calculated from the REF simulation using a combination of time-averaged conditional means (for θρc, θρd, and ), simple time averages (for w, Ac, and Ad), and constant parameters (for U = −8 m s−1 and Nm2 and Nd2 as quoted above). Horizontal profiles of the “forcing” terms on the right-hand side of (8) in Fig. 13a show that upstream of the mountain the convective term (∫c S dz) fluctuates about a steady value while the orographic term (∫c O dz) is nearly zero. As the flow ascends the mountain, the orographic term increases rapidly while the convective term plunges from the increased cloud fraction and flow stabilization. The sum of these two contributions reaches a maximum at x = 69 km and then collapses to negative values over the crest and into the lee.

As shown in Fig. 13b, the “response” term on the left-hand side of (8) exhibits a similar pattern over the orography as the summed forcing terms (minus the fixed upstream offset of 8 m2 s−3), which suggests that (8) captures the basic mechanism underlying the orographic enhancement of convection. The main discrepancies in Fig. 13b can be explained by our neglect of dissipative processes. For example, despite the uniformly positive forcing upstream of the mountain (Fig. 13a), the buoyancy term stays roughly constant in Fig. 13b because of the balance between convective growth and decay over the sea. Also, the peak magnitude of the response is less than half that of the forcing because of the dissipation owing to entrainment and inversion layer stability.

Because entrainment strongly regulates convective vigor, an important consideration is how the entrainment rate varies as the flow climbs the mountain. In particular, a substantial decrease in entrainment near the mountain (which may arise from the increased cloud size) might contribute to, or provide an alternate explanation for, the increased cloud buoyancy in Fig. 13b. This is examined by the vertical profiles of entrainment rate () at three locations (x = 89 km, x = 69 km, and x = 66.5 km) in Fig. 14, which are computed using
i1520-0469-66-9-2559-e9
where h is the moist static energy (Petch et al. 2008). This figure shows that does not vary significantly among the three locations except over the mountain, where it is relatively large near the surface. This suggests that changes in entrainment alone cannot account for the jump in cloud buoyancy over the mountain, which reinforces the importance of the mechanism proposed above.

c. Cloud microphysics

The enhanced convective vigor over the orography allows for slightly deeper clouds, which increases the precipitation production and growth. Figure 15a shows that both the maximum and the y-averaged cloud-top heights over 3–6 h rise noticeably over the mountain. Because the in-cloud qc increases rapidly with height (Fig. 15b), the heightened cloud tops over the mountain possess higher liquid water content, which increases their precipitation production. As a crude simplification of the nonlinear accretion processes in the atmosphere that lead to raindrop formation, the Kessler (1969) scheme begins converting cloud water to rainfall when qc exceeds an arbitrary threshold value (here 1.0 g kg−1). This “autoconversion” threshold, which is overlaid in Fig. 15b, is exceeded more frequently over the mountain where the mean cloud tops are higher. The increased rain production over the mountain is shown by the horizontal profiles of vertically integrated autoconversion rates (again conditionally averaged within the cores) in Fig. 16a.

Figure 15b shows that the mean qc supply within the entire cloud column is increased over the mountain (Fig. 15b). This is likely owing to a decrease in the entrainment-induced evaporation within the developing clouds. Although the entrainment rate stays roughly constant over the mountain (Fig. 14), the orographic environment surrounding the clouds is closer to saturation, which reduces the cloud evaporation that is caused by a given amount of mixing. Because the accretion rate in Kessler (1969) is a nonlinear function proportional to , the increased concentration of both qc and qr in the orographic cores strongly enhances their accretional growth. This is seen by the horizontal profile of vertically integrated accretion rates (again conditionally averaged within the cores) in Fig. 16a.

The final contribution to the orographic precipitation enhancement is a strong reduction in subcloud evaporation. As the terrain rises toward the LCL, precipitation particles pass through less subcloud air on their way to the ground, which reduces their evaporation. This is shown in Fig. 16b as the ratio of the surface precipitation rate (R) to the cloud-base precipitation rate () increases from 0.2–0.5 far upstream of the hill to near unity over the mountain upslope where the cloud base lies closer to the surface. This ratio rises well above unity in the lee because precipitation spillover past the crest adds a large nonlocal contribution to R.

Compared to observations, the precipitation evaporation upstream of the hill in Fig. 16c appears to be too high. From radar observations of convective clouds over central South Africa, Rosenfeld and Mintz (1988) found that for Rcb values characteristic of those upstream of Dominica (1–40 mm hr−1), R/Rcb ranged between 0.5 and 0.9, which is much higher than in Fig. 16c. Moreover, the trade wind flow impinging on Dominica is characterized by lower cloud bases and higher subcloud humidities than the continental air masses sampled by Rosenfeld and Mintz (1988), which suggests that the true evaporation rates upstream of Dominica are probably even lower than their measurements suggest. Also, the lack of visual virga from time-lapse imagery of the impinging flow argues against the importance of subcloud evaporation.

5. A linear model for forced orographic convection

The simplified analysis in section 4b appears to at least qualitatively capture the basic mechanism by which bulk lifting enhances cumulus convection, which makes it useful for conceptual understanding. In this section, we extend the analysis to obtain analytical solutions for the convection amplitude (Δw) at a given height within the cloud layer and explore some basic parameter sensitivities. We rewrite the equation for the mean cloud buoyancy over a patch containing one or more clouds (7) as
i1520-0469-66-9-2559-e10
where μ2 = Ns2/(1 + Ac/Ad); as before, d/dt is following the translation of the patch, not individual cloud features. We relate the plume buoyancy to its acceleration through the vertical momentum equation
i1520-0469-66-9-2559-e11
where β is an ad hoc factor that represents the effect of pressure gradient accelerations. For deep narrow cells β ≈ 1 whereas for shallow cells β is smaller because more environmental air must be accelerated to accommodate the rising plume. In both equations, the damping term with coefficient α (s−1) is added to represent mixing between the updrafts and downdrafts. Combining (10) and (11) and solving for Δw gives
i1520-0469-66-9-2559-e12
This is a linear, second-order differential equation from which the convection amplitude (Δw) can be predicted from the pattern of mean ascent . For steady-state orographic flow, these quantities may be expressed as functions of x only (e.g., ) and d/dt may be approximated as Ux. In this formulation we consider Ac/Ad as a fixed parameter, so we can use (12) to examine how a cloud system with a given cloud fraction behaves as it encounters the mountain. A similar “modal” approach is used in linear stability theories in which the growth rates of perturbations with different wavenumbers are computed without regard to how they might interact with each other. We only consider bounded solutions where Ns2 and μ2 are positive, which from (6) requires Ac/Ad > ⅓. For such high cloud fractions, convection is inhibited upstream of the mountain (Δw = 0) but “forced” over the upwind slope by the term on the right-hand side of (12). Because we have assumed that updrafts ascend and downdrafts descend, only positive values of Δw are regarded as physical.
One useful property of (12) is that when the mean ascent is relatively uniform, Δw may reach an equilibrium value:
i1520-0469-66-9-2559-e13
With α = 0, Nm2 = −5.0 × 10−5 s−2, Nd2 = 10−4 s−2, and Ac/Ad = 1 (which represents the average cloud fraction at x = 66.5 km in Fig. 11), (13) gives Δweq = 6w. For a mean ascent of 1 m s−1, the equilibrium updraft speed is wc = 4 m s−1 and the downdraft speed is wd = −2 m s−1. These equilibrium solutions demonstrate the importance of moist instability in controlling the vertical motions. If Nm2 is set to zero in (13) with all the other parameters unchanged, then at equilibrium the magnitudes of Δw = 2w = 2 m s−1, wc = 2 m s−1, and wd = 0 are greatly reduced. Moreover, positive values of Nm2 are associated with rising downdrafts (wd > 0), which violates our original assumption of wd < 0 and allows the downdrafts to saturate.
To illustrate the dynamic (i.e., nonequilibrium) properties of (12), we can write analytical solutions for undamped convection (α = 0) driven by airflow over a symmetric triangular ridge of total width 2am and height hm. If the ascent rate is given by the free-slip surface condition (Uxh), the solution becomes
i1520-0469-66-9-2559-e14
over the windward slope and
i1520-0469-66-9-2559-e15
over the lee slope, where
i1520-0469-66-9-2559-e16
i1520-0469-66-9-2559-e17

Solutions for three different mountain widths (am = 3.5, 7.1, and 14.2 km) that are chosen to yield Φam = π/2, π, and 2π are presented in Fig. 17 and Table 1. Other parameters are hm = 1 km, U = −8 m s−1, and β = 0.5. Over the narrowest mountain, the upslope region is not wide enough for the convection to finish its growth cycle, but Δwmax is the greatest because of the stronger forcing by the rapid bulk ascent. In the second or “tuned” case, which most closely matches the terrain of Dominica, the convection just finishes its growth cycle at the crest, giving twice the equilibrium amplitude. The convection is weakest over the wide mountain, where the growth phase finishes halfway up the slope and Δw = 0 at the crest. In all cases, the convection vanishes quickly on the lee side because of the negative forcing.

As will be seen, the convective velocities in the above solution are much stronger than those in corresponding numerical simulations. Although this analysis cannot capture the complex and nonlinear processes at work in the numerical simulations, we may increase the realism of this simple model by adding damping and more realistic terrain and taking into account that the center of the convecting layer exists some height (Hc) above the surface. These factors can be included if we write the solution in Fourier space as [from (12)]
i1520-0469-66-9-2559-e18
where γ = Uk and m(k) is the vertical wavenumber from simple linear mountain wave theory (following Smith and Barstad 2004). When the elevated convecting layer is taken into account, the orographic forcing becomes smoother and weaker and is shifted upstream compared to the surface forcing.

Solutions to (18) over a Gaussian ridge for varying parameter values are shown in Figs. 18a,b. As the damping increases, the maximum Δw decreases from 12 m s−1 (α = 0) to less than 1 m s−1 (α = 0.01 s−1) (Fig. 18a). The convection amplitude also decreases and shifts upstream as Hc increases (Fig. 18b). The combination of α = 0.005 s−1 and Hc = 500–1000 m brings the analytical solution into reasonable agreement with from the REF simulation over the upwind slope.1 Away from the upwind slope, however, the two solutions show less agreement, which is expected because the analytical solution assumes a high cloud fraction (Ac/Ad = 1) that inhibits convection in these areas. Solutions for different Gaussian half-widths (along with α = 0.005 s−1 and Hc = 1000 m) in Fig. 18c show that the maximum Δw increases as the ridge narrows. This highlights the importance of the external forcing term in (12), which increases in magnitude as the underlying terrain steepens.

6. Sensitivity experiments

a. Mountain width

To verify the analytical result from Fig. 18c that forced orographic convection is strongly sensitive to the island width, we conduct three simulations in which am is varied from 2.5 (A2.5) to 5 (REF) to 10 km (A10). The profiles of obtained from these three simulations are similar in character to the analytical solutions (Figs. 18c,d), further demonstrating that the convective motions strengthen over steeper slopes. As with the comparison in Fig. 18b, the best agreement between the analytical and numerical solutions is found over the windward sides of the ridges. The strengthened convection over the narrower mountains is reflected by the and profiles in Figs. 19b,c. Although the area-integrated turbulence is similar in the three simulations, the turbulence grows the fastest and reaches the highest magnitudes in the A2.5 simulation (Figs. 19b,c).

Although convection grows the fastest over the narrowest massif, the surface precipitation is still limited by the ability of hydrometeors to reach precipitation size and fall to the ground before evaporating in the lee, which favors wider mountains that provide longer advection times over the upwind slope. As a result, the lee evaporation increases over the narrower mountains, which is seen by the profiles of vertically integrated rain evaporation (∫ Er dz) along the mountain transect in Fig. 19d. This causes the A2.5 simulation to receive the lowest area-averaged precipitation, whereas the REF simulation receives the heaviest precipitation thanks to its combination of strong convection and weak leeside evaporation (Fig. 19a). Because this simulation most closely matches the real terrain of Dominica, it suggests that Dominica may possess a nearly optimal cross-flow width for extracting precipitation from the trade wind flow via forced convection.

b. Island surface fluxes

The specification of identical surface fluxes over sea and land in the previous simulations was a useful, though highly unrealistic, simplification that allowed the impacts of forced lifting over the island to be isolated. Two potentially important processes that were neglected are frictional convergence along the eastern coastline and thermal heating over high terrain, which both induce vertical ascent and may thus influence the convective precipitation. We briefly investigate the effects of these processes through two additional simulations, the first of which (DRAG) increases the bulk thermodynamic drag coefficient cd over the island surface to represent its higher frictional drag. As in the REF simulation, the value of cd over the sea is still computed interactively from Siebesma et al. (2003) as
i1520-0469-66-9-2559-e19
where cd = −(u*/‖v1‖)2, u* = 0.28 m s−1, and the subscript 1 denotes the lowest grid level above the surface, which results in a typical value of cd ≈ 0.001. As a modification to better represent the roughened island surface, we increase cd to 0.01 over xc − 2amxxc + 2am, which approximates a typical aerodynamic roughness length of z0 = 0.1 m for land surfaces. In the second experiment (HEAT), we represent the stronger sensible heating over land by increasing the sensible heat flux over this same area 10-fold (from 10 to 100 W m−2) while reducing the latent heat flux from 157 to 67 W m−2 to keep the total surface heat flux unchanged.

Although the above changes in surface fluxes are chosen arbitrarily and do not adequately characterize the complexities of the island surface, they give some basic hints as to the sensitivity of the orographic response to changes in land surface forcing. Figure 20 shows that despite their radical changes in surface fluxes, the resulting precipitation amounts and turbulent intensities in the DRAG and HEAT simulations are very similar to the REF simulation. The area-averaged precipitation increases in both cases, but only by 15% in the DRAG simulation and 5% in the HEAT simulation (Fig. 20a), and the turbulence profiles are virtually indistinguishable among the three cases. Note that if cd is increased by an order of magnitude to simulate a more rugged land surface, the strengthened coastal convergence increases the orographic precipitation by 30% and shifts its peak slightly upstream relative to the REF simulation.

7. Conclusions

Emerging observations from the Yale Dominica Precipitation Project indicate a strong (2–10-fold) enhancement of trade wind precipitation over the mountainous Caribbean island of Dominica (Smith et al. 2009b) driven by mechanical lifting of the easterly flow. This study uses large-eddy simulations to understand the basic physical processes underlying this behavior. These simulations are highly idealized and not intended to reproduce the quantitative precipitation amounts upstream of the island or over it. However, they allow for a close inspection of the dynamical and microphysical processes that can give rise to such a strong orographic enhancement of shallow cumulus convection.

The initialization, surface fluxes, and large-scale forcings for the reference simulation (REF) are adopted from the BOMEX shallow cumulus intercomparison study of Siebesma et al. (2003), and the terrain is an idealized 1D ridge based on Dominica. The trade wind cumuli develop and reach a quasi-steady state before encountering the upwind slope, where the cells increase in number and intensity. This convection generates brief, moderate showers that increase the average precipitation 200-fold from that upstream to a peak of 2 mm hr−1 over the crest. Although this precipitation removes only a small fraction (1%) of the impinging moisture flux, a long cloud shadow develops in the lee. This arises from convection-related effects over the upwind slope (mixing, stabilization, and moisture loss) as well as wave breaking over the lee slope, which mixes warm and dry free-tropospheric air into the boundary layer.

The three dominant mechanisms underlying the simulated orographic precipitation enhancement are the following:

  1. Triggering: Both cumuli drifting in from the ocean and passive subcloud moisture anomalies seed convection over the island. The cumuli already possess positive buoyancy when they encounter the terrain and become invigorated by the orographic uplift. The subcloud moisture anomalies gain buoyancy after saturation as they begin to cool moist adiabatically while the surrounding unsaturated air continues to cools dry adiabatically.
  2. Growth: Despite the increasing cloud fraction over the higher terrain, which increases the two-stream flow stability Ns2, the convection strengthens over the orography. This is because the bulk lifting weakens the subsidence warming in the unsaturated downdrafts and increases the latent heat release within the updrafts, which keeps the clouds positively buoyant and fuels convective growth.
  3. Microphysics: The more vigorous orographic cells rise slightly higher, which increases the liquid water contents and precipitation formation. As they fall through the orographic clouds, the precipitation particles accrete more water because of the higher liquid water content in the stronger orographic updrafts. Subcloud evaporation is also minimized as the cloud base lies close to the surface.

A simple linear model is developed to explain the forced cumulus convection over the island. This model, which considers the direct dynamical impact of lifting on a partly cloudy layer with fixed cloud fraction and moist/dry stabilities, is a forced oscillator equation with an external forcing term related to the bulk lifting rate and cloud-layer stabilities. Analytical solutions from the linear model suggest that narrower mountains experience stronger convection because of their faster mean ascent, which qualitatively agrees with a set of numerical sensitivity tests over the same parameter space.

Although the numerical sensitivity tests confirm that the convection grows more rapidly over narrower mountains, the simulated precipitation is maximized for an intermediate mountain half-width of 5 km. This terrain, which best matches the terrain of Dominica, yields a combination of strong upwind convection and sufficient advection time for precipitation to form and reach the ground. Two additional sensitivity experiments that vary the surface momentum and heat fluxes over the island indicate that the convective response is only weakly sensitive to these changes. This suggests that the impact of forced lifting by the steep island terrain dominates that of coastal convergence and surface heating.

Acknowledgments

This research was supported by a grant to Yale University from the National Science Foundation (ATM-112354). The numerical simulations were performed using supercomputing allocations granted through the Computer and Information Systems Laboratory (CISL) of the National Center for Atmospheric Research (NCAR). The authors wish to thank the two anonymous reviewers, as well as Maarten Ambaum, Richard Rotunno, Robert Wood, Peter Blossey, and Dale R. Durran for their constructive comments.

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Fig. 1.
Fig. 1.

Location and mountainous terrain of Dominica. (top) The position of Dominica in the eastern Caribbean Sea north of South America. (bottom) Progressively smaller insets show (left) Dominica and its surrounding islands and (right) Dominica only with its terrain contours. Overlaid circles in the bottom right panel are the locations of four rain gauge stations: LP is Le Plaine, FWL is Freshwater Lake, SF is Springfield, and CF is Canefield.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 2.
Fig. 2.

MODIS Aqua visible satellite image on 1 Jul 2008 showing a typical cloud pattern in trade wind flow over Dominica.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 3.
Fig. 3.

Data from the Yale Dominica Precipitation Project. (a) Precipitation rates derived from the Guadeloupe radar over Dominica (gray lines). The three precipitation types correspond to upstream open-ocean precipitation rates of <2 (type I), 2–10 (type II), and >10 mm day−1 (type III). (b) Diurnal cycle of precipitation over Dominica from the four rain gauges shown in Fig. 1, where the abscissa is time (UTC). Data from a 1-yr period are averaged in 2-h blocks. The largest precipitation events associated with tropical cyclones were removed for this calculation.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 4.
Fig. 4.

Upstream sounding for the REF simulation. The long wind barbs denote values of 5–10 m s−1; the short wind barbs indicate 0–5 m s−1.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 5.
Fig. 5.

Numerical setup and comparison with the east–west transect across Dominica from Fig. 1.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 6.
Fig. 6.

Isosurfaces of qc = 0.1 g kg−1 from the REF simulation at t = 4 h. Two cycles are shown in y.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 7.
Fig. 7.

Meridionally averaged qc (filled), θL (thin lines), and qr (thick lines) fields at t = 4 h. Contours of θ increase upward from 300 K in intervals of 2 K; the single contour of qr is 0.001 g kg−1.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 8.
Fig. 8.

Horizontal profiles of time-averaged statistics from the REF simulation: (a) liquid water path and (b) cloud cover over the vertical column, (c) surface rain rate, (d) convective mass flux, (e) buoyancy flux, and (f) water vapor flux. The flux distributions in (d)–(f) are computed at z = 1.5 km as described in the text and are multiplied by the y-averaged density ρ. To give units of W m−2 in (e) and (f), the heat fluxes are scaled by cp, the specific heat at constant pressure, and Lυ, the latent heat of condensation, respectively. All profiles are smoothed in x using a 10-point averaging operator.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 9.
Fig. 9.

Time- (3–6 h) and y-averaged (a) liquid water potential temperature (θL) and (b) qt far upwind of the island at x = 192 km (black solid line), closer to the island at x = 96 km (gray solid), and downwind of the island at x = 32 km (black dashed) from the REF simulation. For reference, corresponding profiles from the BOMEX simulation [specified as in Siebesma et al. (2003)] are overlaid, in which the spatial averaging is computed over the full domain at each output time and then averaged over all output times from 3 to 6 h.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 10.
Fig. 10.

Profiles of vertical velocity at three different x locations: (a) mean vertical motion (w); (b) conditional mean over the convective cores (), where the cores are defined as saturated grid points satisfying w′, θρ > 0; and (c) conditional mean over the descending unsaturated grid points (). These profiles are computed at each output time using the local 2D sampling technique described in section 4 and then averaged over all output times from 3 to 6 h.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 11.
Fig. 11.

Two types of convective triggering in the REF simulation. (a)–(c) Isosurfaces of qc (0.1 g kg−1; cyan) and qr (0.02 g kg−1; red) of an upstream cumulus cloud that develops into a precipitating cell over the mountain. (d),(e) Isosurfaces of qυ = qυ (1 g kg−1; blue), qc (0.2 g kg−1; cyan), and qr (0.02 g kg−1; red) depicting the transition from a moist subcloud anomaly into a precipitating cell. In both panels, only a small moving box of data is shown to isolate the single feature of interest; qυ in (d)–(f) is masked above 700 m to clearly expose the subcloud moisture perturbation.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 12.
Fig. 12.

Profiles of time- and y-averaged cloud fraction from the REF simulation at three different x locations.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 13.
Fig. 13.

Horizontal profiles of y-averaged and vertically integrated (over the convective core depth) forcings (a) S, O, and S + O and (b) S + O and Ubx. The mean upstream value of ∫c (S + O) = 8 m2 s−3 is subtracted from the forcing function in (b) to allow a direct comparison between the forcing and response. Note that just as the orographic forcing of buoyancy increases over the upwind slope in (a), the forcing by convection weakens and becomes negative. As predicted by (8), the increased net forcing over the mountain leads to a maximum response at x = 69 km in (b). All profiles are smoothed by averaging over the nearest 10 grid points.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 14.
Fig. 14.

Entrainment profiles at four different x locations. These profiles are computed at each output time using the local 2D sampling technique described in section 4 and then averaged over all output times from 3 to 6 h.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 15.
Fig. 15.

(a) Horizontal profiles of maximum and y-averaged cloud-top height (smoothed using an averaging box over the nearest 10 grid points) and (b) mean vertical profiles of qc within the convective cores at different x locations. The vertical profiles in (b) are computed at each output time using the local 2D sampling technique described in section 4 and then averaged over all output times from 3 to 6 h. The mean cloud-top heights at the three locations in (b) are shown by hash marks and the 1 g kg−1 autoconversion threshold is overlaid.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 16.
Fig. 16.

Microphysical aspects of the REF simulation. (a) Vertically integrated and y-averaged autoconversion and accretion rates within the convective cores, along with (b) the ratio of y-averaged surface precipitation rate to y-averaged cloud-base precipitation rate. All profiles are smoothed by averaging over the nearest 10 grid points.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 17.
Fig. 17.

Plots of Δw from the analytical solutions [(14), (15)] in flows over triangular mountains with different widths (am). The abscissa is scaled by the width of the mountain in the Φam = π case, which is (am)0 = 7.1 km.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 18.
Fig. 18.

Plots of Δw obtained in flows over a Gaussian mountain with hm = 1000 m, xm = 64 km, and varying parameters (α, Hc, and am). Analytical solutions to (18) are shown for (a) various damping coefficients α (10−3 s−1) with the convecting layer height Hc = 0 and the ridge width am = 5 km; (b) various Hc (km) with α = 0.005 s−1 and am = 5 km (overlaid by results from REF simulation in gray); and (c) various am (km) with Hc = 1000 m and α = 0.005 s−1. (d) Numerical from the A2.5, REF, and A10 simulations, computed from the time-averaged conditional mean and as in Fig. 13.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 19.
Fig. 19.

Comparison of various quantities from the A10, REF, and A2.5 simulations: (a) Surface rain rate, (b) buoyancy flux, (c) water vapor flux at z = 1.5 km, and (d) integrated rain evaporation rate (∫ Er dz).

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Fig. 20.
Fig. 20.

As in Figs. 19a–c, but for the REF, DRAG, and HEAT simulations.

Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2990.1

Table 1.

Comparison of analytical solutions [(14), (15)] for flows over triangular hills of different widths.

Table 1.

1

Here, = from the numerical simulations is computed following the same procedure used to compute the quantities in Fig. 13 except for averaging, rather than integrating, vertically over the cloud depth.

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