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

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 q_c (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 (θ_L), q_c, and rainwater mixing ratio (q_r) 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, θ_ρ is the density temperature

View Expanded

where R_d and R_υ are the gas constants for dry and moist air and q_t = q_υ + q_c + q_r 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 (θ_L) and q_t 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 L_x = L_y = 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 q_υ by about 0.2 g kg⁻¹, also yields a net heating of about 0.5 K (using c_pΔT = L_υΔq_υ, where c_p is the specific heat at constant pressure and L_υ 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 q_t 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 q_t is far more dramatic. The large q_t at x = 96 km results from upstream flow deceleration, which converges moisture into the air column, and the much smaller q_t 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 l_y = L_y. The along-flow length (l_x) is also equal to L_y far upwind of the mountain (x = 89 km) where the clouds are isolated and more sampling is needed, but it is contracted to l_x = L_y/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 (q_c, w′, θ′_ρ > 0 for the cores and q_c = 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.

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 (N_m² < 0), a horizontally averaged updraft velocity of w_c > 0, and a horizontally averaged density potential temperature θ_ρc, whereas the unsaturated environment is represented by a dry Brunt–Väisälä frequency of N_d² > 0, w_d < 0, and θ_ρd. Using standard formulas in Emanuel (1994), these stabilities may be estimated from the cloud layer of the upstream sounding as N_d² ≈ 10⁻⁴ s⁻² and N_m² ≈ −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

View Expanded

where θ_ρ0 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

View Expanded

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

View Expanded

where is the horizontally averaged vertical motion and A_c and A_d are the areas of clouds and dry air within the patch. In the special case of , (3) and (4) combine to give

View Expanded

where N_s² 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, A_c/A_d must satisfy

View Expanded

In the current case N_d²/N_m² = −2, so b can only increase for cloud fractions below A_c/(A_c + A_d) = 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)

View Expanded

where Δw = w_c − w_d is the relative motion between the updrafts and downdrafts. The effect of moist convection on the mean buoyancy is given by S. When N_s² < 0, convection directly enhances b, but when N_s² > 0, which is possible even when N_m² < 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 (N_s² < 0) and “forces” convection in a neutral or marginally stable atmosphere (N_s² ≥ 0).

An interesting limit occurs when both the updraft and downdraft are saturated, which is treated by setting N_d² and N_s² to N_m² in (7). This eliminates O so that the convection proceeds as in a saturated layer over flat ground with N_m² < 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 U∂_x, 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

View Expanded

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 θ_ρc, θ_ρd, and ), simple time averages (for w, A_c, and A_d), and constant parameters (for U = −8 m s⁻¹ and N_m² and N_d² 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

View Expanded

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.

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

View Expanded

where μ² = N_s²/(1 + A_c/A_d); 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

View Expanded

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

View Expanded

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 U∂_x. In this formulation we consider A_c/A_d 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 N_s² and μ² are positive, which from (6) requires A_c/A_d > 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:

View Expanded

With α = 0, N_m² = −5.0 × 10⁻⁵ s⁻², N_d² = 10⁻⁴ s⁻², and A_c/A_d = 1 (which represents the average cloud fraction at x = 66.5 km in Fig. 11), (13) gives Δw_eq = 6w. For a mean ascent of 1 m s⁻¹, the equilibrium updraft speed is w_c = 4 m s⁻¹ and the downdraft speed is w_d = −2 m s⁻¹. These equilibrium solutions demonstrate the importance of moist instability in controlling the vertical motions. If N_m² is set to zero in (13) with all the other parameters unchanged, then at equilibrium the magnitudes of Δw = 2w = 2 m s⁻¹, w_c = 2 m s⁻¹, and w_d = 0 are greatly reduced. Moreover, positive values of N_m² are associated with rising downdrafts (w_d > 0), which violates our original assumption of w_d < 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 2a_m and height h_m. If the ascent rate is given by the free-slip surface condition (U∂_xh), the solution becomes

View Expanded

over the windward slope and

View Expanded

over the lee slope, where

View Expanded

View Expanded

Solutions for three different mountain widths (a_m = 3.5, 7.1, and 14.2 km) that are chosen to yield Φa_m = π/2, π, and 2π are presented in Fig. 17 and Table 1. Other parameters are h_m = 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 Δw_max 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 (H_c) above the surface. These factors can be included if we write the solution in Fourier space as [from (12)]

View Expanded

where γ = Uk − iα 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 H_c increases (Fig. 18b). The combination of α = 0.005 s⁻¹ and H_c = 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 (A_c/A_d = 1) that inhibits convection in these areas. Solutions for different Gaussian half-widths (along with α = 0.005 s⁻¹ and H_c = 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

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 c_d over the island surface to represent its higher frictional drag. As in the REF simulation, the value of c_d over the sea is still computed interactively from Siebesma et al. (2003) as

View Expanded

where c_d = −(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 c_d ≈ 0.001. As a modification to better represent the roughened island surface, we increase c_d to 0.01 over x_c − 2a_m ≤ x ≤ x_c + 2a_m, 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 c_d 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 N_s², 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.