1. Introduction
Mountains have the potential to initiate, enhance, and modify precipitation, a process known generally as orographic precipitation [see Smith (1989), Roe (2005), Smith (2006), and Houze (2012) for a review]. In recent years, the study of orographic precipitation has evolved at a remarkable pace due to improvements in observation methods and networks, and in numerical weather prediction models. The latter has allowed for significantly higher-resolution mesoscale model simulations and forecasts, facilitating the explicit treatment of cloud processes and precipitation, and capturing important small-scale terrain features.
The present work is a continuation of a study by Watson and Lane (2012, hereinafter WL12) that examined how variations in relatively simple terrain geometries and upstream conditions influenced orographic precipitation in idealized settings. In WL12, a numerical model was used to simulate a moist flow impinging upon three alpine-scale terrain shapes: a straight ridge, a concave ridge, and a convex ridge. The impinging flow was representative of an observed prefrontal northwest flow that generated over 70 mm of precipitation in 24 h in the Australian Alps. The Australian Alps in southeastern Australia are the highest section of Australia’s Great Dividing Range, comprising the only peaks on the continent that exceed 2 km. They impose an arc-shaped barrier in prefrontal flows like the one examined here and feature a climatological precipitation maximum near the vertex (which also coincides with the highest peaks). Many multiscale concave- and convex-shaped ridges make up the Alpine chain, which presumably exert some control on the distribution of precipitation, as seen in the European Alps [see Fig. 2 in Jiang (2006), as well as Rotunno and Ferretti (2001); Rotunno and Houze (2007)]. Understanding how precipitation is influenced by such terrain features is critical for the management of mountain-derived water resources in drought-prone southeastern Australia.
A primary focus of WL12 was to examine how changes to the cross-stream length of straight, concave, and convex ridges influenced the orographic flow response and precipitation for each terrain shape. The present study extends the findings of WL12 by examining the impact of changing the ridge height and the ridge width. Only the straight ridge and the concave ridge are examined here, as the dynamics of the convex ridge are similar to the straight ridge (see WL12).
In the absence of moisture, friction, and rotation, the nonlinearity of an orographically modified flow can be predicted by the nondimensional mountain height, Ĥ = Nhm/U. Here, N is the atmospheric stability given by N2 = (g/θυ)(∂θυ/∂z), hm is the maximum height of the barrier, and U is the wind velocity normal to the barrier (Pierrehumbert and Wyman 1985). Based on linear theory, Smith (1989) developed a flow regime diagram to illustrate how changes to Ĥ can modify the orographic response of an impinging flow. The flow regime diagram identified the critical values of Ĥ for the onset of wave breaking and flow splitting with respect to the spanwise-to-streamwise horizontal aspect ratio of the orography β (Smith 1989, his Fig. 5). When β > 1, the progressive states of orographic flow modification with increasing Ĥ are mountain wave generation, wave breaking, wave breaking and flow splitting, and flow splitting only. When the cross-stream ellipticity of the orography increases (i.e., the ridge length b increases and/or the ridge width a decreases leading to an increase in β), the critical Ĥ for flow regime transition decreases. When β < 1, only mountain wave generation or flow splitting may eventuate.
The impact of varying Ĥ on orographic flow modification and precipitation has been studied extensively (e.g., Smith 1980; Pierrehumbert and Wyman 1985; Smolarkiewicz and Rotunno 1989, 1990; Baines 1995; Miglietta and Buzzi 2001; Jiang 2003; Colle 2004; Jiang 2006; Galewsky 2008). In general, when Ĥ ≪ 1, flow passes over the terrain with relative ease and only mountain waves are generated. As Ĥ increases, more flow is diverted laterally around the mountain and a region of horizontally decelerated flow spreads upstream, effectively creating a barrier for incoming flow (e.g., Marwitz 1980; Smolarkiewicz and Rotunno 1990; Hughes et al. 2009). Wave breaking may also be induced in the lee of the mountain. When Ĥ ≫ 1, flow-stagnation points form on the lower windward slope and approaching low-level flow is diverted around the mountain, becoming effectively constrained within a horizontal plane [Hawaii provides an illustrative example of this; see Rasmussen et al. (1989) for more details]. This reduces flow over the mountain; however, a secondary circulation may develop on the windward slope whereby reverse downslope flow converges with strongly decelerated flow generating local, transient updrafts (e.g., Smolarkiewicz and Rotunno 1990; Jiang 2003). The precipitation patterns associated with each of these flow regimes can differ dramatically (e.g., Rotunno and Houze 2007).
The shape of the orography can also have a significant effect on the distribution of orographic precipitation. Jiang (2006) and WL12 showed that the forward-reaching ridge arms of a concave ridge inhibit flow diffluence upstream of the ridge and intensify the high pressure perturbation on the windward slope. Jiang (2006) performed a systematic study on the influence on orographic precipitation of a concave ridge with flows of varying Ĥ and found that the critical Ĥ for flow regime transition is smaller compared to the corresponding straight ridge, in part because the approaching flow suffers more deceleration as it converges between the ridge arms. Furthermore, Jiang (2006) found a precipitation enhancement near the vertex of the concave ridge whereby incoming flow converged and enhanced vertical motions and precipitation accordingly. The development of these precipitation-enhancing vertical motions diminished when windward flow stagnation was induced.
WL12 obtained a different flow response near the vertex of the concave ridge when flow deceleration was sufficiently strong: the impinging flow separated and flowed around this region of decelerated air, preferentially passing over the ridge arms rather than the vertex. This led to a transition from a single-precipitation maximum at the vertex to dual-precipitation maxima on the ridge arms caused by lateral flow separation upstream of the ridge crest. This flow and precipitation response was not evident in Jiang’s (2006) simulations, probably because the upstream environment used by Jiang (2006) was close to saturation (see WL12 for a discussion). As Ĥ was restricted to unity in all experiments of WL12, this current study expands on those results by exploring the impact of variations in Ĥ on the precipitation-enhancing funneling mechanism, among other flow features.
The impact of variations to a is also explored. This is of particular interest, as variations to the concave ridge width have not previously been examined; variations in a (independent of β) can modify precipitation patterns and the precipitation efficiency (e.g., Jiang 2003; Jiang and Smith 2003; Colle 2004). For example, an increased ridge width increases the time it takes for a parcel of air to be advected across the windward slope. This increased time can improve precipitation efficiency as a more streamwise extensive orographic cloud develops, allowing more time for precipitation to develop and fallout. However, the windward slope angle becomes flatter when a increases, weakening vertical updrafts above the windward slope and reducing the average cloud water mixing ratio (Jiang and Smith 2003). Changes to the ridge width can also alter the upstream tilt of the mountain waves. Durran (1990) showed that when the airflow falls within the hydrostatic regime (Na/U ≫ 1), which is the case for all experiments in this study, vertically propagating waves dominate and the upstream tilt from normal of the wave beams increases with Na/U. Indeed, Colle (2004) found that orographic cloud develops further upstream of a wide mountain compared to a narrow mountain for this reason.
The aim of this study is to investigate how the height, length, and width of a concave ridge modify orographic precipitation. Results for a straight ridge of comparable, varying geometries are used to inform these results. A primary focus is the role of windward flow deceleration and flow confluence in moderating the precipitation-enhancing funneling mechanism. Section 2 describes the model characteristics and numerical setup of the experiments conducted. Sections 3 and 4 describe the dynamics of a moist flow impinging upon the different terrain shapes, presenting the impact of changes to Ĥ, a, and b on the flow response and the resulting precipitation patterns. Section 5 discusses these parameter changes in the context of the precipitation-enhancing funneling mechanism and changes to relative humidity (RH), and section 6 presents flow regime diagrams for the straight and concave ridges. Section 7 summarizes these results.
2. Model configuration
Version 3.1.1 of the Weather Research and Forecasting Model (WRF) [Advanced Research WRF (ARW); Skamarock et al. 2008] is used to perform all idealized simulations in this study and is configured identically as in WL12 (see their section 2.1). Briefly, the simulations have a single domain with 400 grid points in the x and y directions with 2.5-km horizontal grid spacing. There are 70 grid points in the z direction with vertical grid spacing that is approximately 250 m in the troposphere and 800 m at the model top (z = 25 km). Microphysics is parameterized using the Thompson scheme (Thompson et al. 2004), and for simplicity there is no surface friction, radiation, or Coriolis effects. In most simulations, a steady state is achieved after 6–10 h of model integration, though when the ridge is tall only a quasi-steady flow is achieved. Model snapshots for all simulations are examined at 16 h. The average hourly accumulated precipitation is measured between 14 and 20 h. An additional series of simulations was performed using the Purdue–Lin microphysics scheme (Lin et al. 1983) instead of the Thompson scheme (not shown). Precipitation generally increased everywhere by around 5%–20% in each of these additional simulations; however, the dynamics clearly dominates the overall flow and precipitation response.
The model is initialized everywhere with the same control sounding used in WL12 (Fig. 1). The sounding is based on an observed sounding from Wagga Wagga, New South Wales, Australia (35.2°S, 147.7°E), and is representative of a prefrontal flow that produced heavy precipitation in the Australian Alps on 3 August 2005 [see Landvogt et al. (2008) for details]. Modifications were made to the observed sounding to simplify the interpretation, including an unidirectional wind profile (along the x axis) with a uniform wind velocity of u = 20 m s−1 and an average relative humidity of 75% and average N of 0.011 s−1 in the lowest 3 km of the atmosphere. The atmosphere is stable to parcel ascent, although there is a potentially unstable layer between 1 and 2 km where the equivalent potential temperature θe decreases with height (Fig. 2). The lifting condensation level for a surface parcel is approximately 750 m. To calculate Ĥ, the average N from the surface to the ridge top is used. However, as the sounding is representative of a real atmosphere, N is nonuniform with height and the average N decreases as the ridge height increases. See Table 1 for more details.
The atmospheric sounding (skew T–logp) used in all control simulations, representative of a real sounding recorded in Wagga Wagga during a heavy-precipitation event in the Australian Alps. The solid line is temperature and dashed lines are dewpoint temperature. Modified dewpoint temperatures for RH experiments—RH−5, RH+5, and RH+15—are presented with thin dashed lines and labeled where different from the control sounding (thick lines).
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
The equivalent potential temperature profile from the control sounding.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
Summary of parameters used in idealized experiments: N is the mean Brunt–Väisälä frequency over the depth of the ridge, u is constant at 20 m s−1 and unidirectional in line with the x axis, and other terms are defined in the text. For the RH experiments, RH is modified by the stated amount uniformly below 2 km and linearly smoothed to the control value from 2 to 4 km.
The upstream environment in each simulation is unsaturated, though saturation occurs above the windward slope as the moist flow is lifted by the ridge. Moist processes can have a substantial impact on the orographic flow response through the release of latent heat, and Fig. 3 of WL12 shows the release of latent heat from condensation has a significant influence on the orographic flow response. Three additional soundings are used in this study to test the influence of changes to low-level relative humidity (gray dashed lines in Fig. 1). Only the water vapor (WV) mixing ratio is modified, with changes to the control sounding below 2 km modifying the relative humidity by −5%, +5%, and +15% (referred to as RH−5, RH+5, and RH+15, respectively). From 2 to 4 km, the water vapor mixing ratio is linearly smoothed to its control value.
The two terrain shapes used in this study—the straight ridge (ST) and the concave ridge (CC)—are described by the same formulas as in WL12 (see their section 2.2). The concave ridge has a vertex angle of α = 45°, Ĥ is varied via adjustments to the maximum ridge height (hm = 1.0–3.4 km), and β (≡b/a) is varied via adjustments to the ridge width (a = 12.5, 25, and 50 km, referred to as the narrow, control, and wide ridges, respectively) and the ridge length [b = 50 and 100 km, referred to as the short ridge (SR) and long ridge (LR), respectively]. The resulting Ĥ varies from 0.66 to 2.0 and β from 1.0 to 8.0. It should be emphasized that variations to the atmospheric stability (which also change Ĥ) can be of equal or greater importance to the precipitation and flow response [see, e.g., section 2 in Rotunno and Houze (2007)]; however, here we focus primarily on variations to the terrain geometry. Table 1 provides a summary of the experimental variables used.
3. Sensitivity to Ĥ
WL12 examined the influence of ridge length on the flow response and precipitation distribution for the four ridges examined in this study (ST-SR, ST-LR, CC-SR, and CC-LR). However, in WL12 Ĥ was restricted to 1.0. In this section, Ĥ is increased from 0.66 to 2.0 for these four ridges.
a. Straight ridge
1) Straight short ridge (ST-SR, β = 2.0)
When Ĥ equals 0.66 for ST-SR with β = 2.0 (Figs. 3a–c), flow passes over the 1.0-km-tall ridge relatively unimpeded and mountain waves are generated above the ridge crest, indicative of a linear flow regime. Windward flow deceleration is weak and has an upstream extent of about 70 km (measured from the ridge crest to the −2 m s−1 perturbation u contour; Fig. 3a). The surface streamlines indicate approaching flow moves away from the centerline, consistent with widespread flow diffluence upstream of the ridge (Fig. 3b).1 Here, flow diffluence is defined as ∂υ/∂y and is positive in regions where streamlines separate. Equivalently, flow confluence corresponds to regions where streamlines move toward each other (∂υ/∂y < 0) and is present near the ridge ends (hatched). An orographic cloud develops above the windward slope at 700-m altitude and extends to 1.5 km (Fig. 3c). The strong cross-barrier flow velocity and shallow cloud results in only small precipitation accumulations near the ridge crest (not visible in Fig. 3b, as the maximum average hourly precipitation is less than 0.5 mm).
Selected fields for ST-SR with a = 25 km and (a)–(c) Ĥ = 0.66, (d)–(f) Ĥ = 1.33, and (g)–(i) Ĥ = 2.0. (left) A plan view of surface streamlines (solid contours) and perturbation u (dotted contours; every 2 m s−1); (middle) a plan view of average hourly accumulated precipitation (shaded; every 1 mm from 0.5 mm) and confluent flow (hatched), where Pmax is the maximum average hourly precipitation (mm) and Ptot is the average hourly total precipitation mass (109 kg); and (right) a vertical cross section along the centerline of potential temperature (solid contours; every 2 K), positive vertical velocity (shaded; every 0.1 m s−1; black represents >1 m s−1), perturbation u (dotted contours; every 2 m s−1), and cloud water mixing ratio (dashed contours; every 0.2 g kg−1). Terrain contours in the left and middle columns are at an interval of 410 m. Model snapshots for all simulations are examined at 16 h, and average precipitation is measured between 14 and 20 h.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
A flow regime transition occurs when Ĥ is doubled to 1.33 for ST-SR (Figs. 3d–f), with wave breaking induced in the lee of the 2.25-km-tall ridge. Wave breaking is identified by the steepening and overturning of θ and θe contours, as in WL12. Windward flow deceleration strengthens and expands more than 150 km upstream, and although surface flow continues to flow over the ridge crest, it is subject to much stronger upstream flow diffluence. Despite the reduced cross-barrier flow velocity compared to the smaller ridge, the maximum vertical velocity above the windward slope almost doubles because of the steeper windward slope (note that a remains constant here) and a reduced atmospheric stability above 1.5 km (see WL12, their Fig. 2). Approaching flow also experiences a larger vertical displacement to pass over the ridge crest, and a deeper orographic cloud develops that generates substantially more precipitation along the upper windward slope. A local vertical velocity maximum also develops above the lower windward slope, generated by the lowest updraft of a secondary vertically propagating gravity wave. This secondary gravity wave is launched when approaching flow impinges upon the region of decelerated flow (e.g., Smolarkiewicz and Rotunno 1990; Galewsky 2008; WL12) and is evident in Fig. 3f, where the θ contours display an upward kink coincident with the −6 to −8 m s−1 perturbation u contour (also visible in θe contours; not shown).
When Ĥ is increased to 2.0 (Figs. 3g–i), the ridge extends beyond 3 km and becomes insurmountable to surface flow. The windward flow stagnates and regions of reverse downslope flow develop on the windward slope. Incoming low-level flow impinges upon the stagnant air and either splits and flows around the ridge ends or ascends and flows over the region of stagnant air. A secondary gravity wave is also initiated around 70 km upstream of the ridge crest that generates widespread upward motion and cloud aloft. Between the secondary gravity wave and the ridge crest, several other local vertical velocity maxima develop above the windward slope. These local updrafts are reminiscent of the secondary circulation discussed by Jiang (2003, Fig. 11), whereby reverse downslope flow converges with strongly decelerated flow to generate updrafts detached from the surface (see also Smolarkiewicz and Rotunno 1990). Although these updrafts are deep enough to form cloud and rainwater, negligible precipitation accumulates at the surface (probably because of the drying influence of the downdrafts within the secondary circulation). Flow near crest level continues to pass over the ridge, generating a small amount of precipitation near the ridge crest. Despite the ridge extending well above the freezing level (thick dashed line at 2.1 km in Fig. 3i), cloud near the ridge crest is composed of only supercooled liquid water. Ice forms above the lee slope (not shown); however, it does not appear to influence the windward flow dynamics.
Table 2 provides a summary of the values of Ĥ at which the flow regime transitions are induced for ST-SR. The transition to wave breaking and then flow splitting occurs with higher values of Ĥ than what would be expected from Smith’s (1989) flow regime diagram for a barrier with β = 2.0. This can be primarily attributed to the influence of moisture and the reduced effective stability in saturated regions.
The value of Ĥ at which flow regime transitions are induced for all ridges examined.
2) Straight long ridge (ST-LR, β = 4.0)
The flow response for ST-LR with Ĥ = 0.66 (Figs. 4a–c) is similar to ST-SR with Ĥ = 0.66. However, ST-LR has a slightly stronger cross-barrier flow compared to ST-SR, as flow near the centerline experiences less deflection away from the centerline due to the longer ridge length, leading to an overall smaller change in u. This enhances the strength of vertical motions and depth of orographic cloud over the windward slope. Accordingly, precipitation is stronger for ST-LR compared to ST-SR when Ĥ = 0.66, although the maximum average hourly precipitation remains below 0.5 mm.
As in Fig. 3, but for ST-LR with a = 25 km.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
When Ĥ is increased to 1.33 (Figs. 4d–f), windward flow deceleration strengthens and expands more than 300 km upstream of the ridge crest, around 200 km farther upstream than the corresponding ST-SR. Precipitation is more widespread and of greater intensity along the upper windward slopes due to the taller ridge height, and a secondary gravity wave develops 60 km upstream of the ridge crest that appears to contribute additional precipitation. Compared to ST-SR (cf. Fig. 3e), the distribution of precipitation is similar; however, the longer barrier forces more flow over the ridge rather than around, resulting in approximately 75% more precipitation for ST-LR (normalized by b). The increased ridge height also induces wave breaking in the lee.
When Ĥ = 2.0 (Figs. 4g–i), ST-LR becomes insurmountable to surface flow and approaching flow splits 50 km farther upstream than in ST-SR. Regions of flow reversal develop on the windward slope, establishing a secondary circulation. The distribution of precipitation is similar to the corresponding ST-SR; however, unlike ST-SR, a small amount of snow and graupel is generated near the ridge crest (Fig. 5a) where flow from below the crest level (although above the stagnant region) continues to traverse the ridge. The generation of graupel and the cellular structure of the updrafts above the windward slope (not shown) suggest convection is triggered in this area [although the graupel is in relatively low concentrations (<0.1 g kg−1) and some ice species would be expected above the freezing level]. The triggering of convection is discussed in the following section.
Vertical cross section of the rainwater (filled contours), snow (solid contours), and graupel (dashed contours) mixing ratios, all plotted at 0.01, 0.1, and 0.5 g kg−1 for (a) ST-LR and (b) CC-LR with Ĥ = 2.0 and a = 25 km.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
b. Concave ridge
1) Concave short ridge (CC-SR, β = 2.0)
When Ĥ = 0.66 for CC-SR (Figs. 6a–c), many aspects of the flow response are similar to that of ST-SR with Ĥ = 0.66 (cf. Figs. 4a–c). The main difference is the region of flow confluence between the ridge arms (hatched region in Fig. 6b), where approaching flow is funneled toward the vertex. A vertical velocity maximum is located on the surface near the ridge crest associated with the upslope ascent of flow. This is accompanied by an additional (local) vertical velocity maximum that develops above the lower windward slope, detached from the surface (Fig. 6c). This secondary maximum is generated by the confluence of low-level flow between the ridge arms. Orographic cloud therefore develops farther upstream and extends higher in CC-SR compared to ST-SR, and precipitation is enhanced near the vertex accordingly (Fig. 6b). The stronger and deeper updrafts above the windward slope of CC-SR also increases the amplitude of the mountain wave, resulting in a steeper and stronger descent of flow in the lee (inferred from θ contours in Fig. 6c).
As in Fig. 3, but for CC-SR with a = 25 km.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
When Ĥ is increased to 1.33 (Figs. 6d–f), a deeper orographic cloud develops above the windward slope of the taller ridge and precipitation increases substantially near the vertex. Windward flow deceleration strengthens and expands far upstream, initiating a precipitation-enhancing secondary gravity wave, reducing the size of the flow confluence zone significantly and facilitating the transition to dual-precipitation maxima on the ridge arms. There is little difference between the strength and upstream extent of the flow deceleration zone for CC-SR and ST-SR with Ĥ = 1.33.
When Ĥ is increased to 2.0 (Figs. 6g–i), the approaching flow is blocked by CC-SR and flows around the ridge ends. Like ST-SR with Ĥ = 2.0, regions of flow reversal develop along the windward slope and wave breaking is present in the lee. Despite the flow being blocked, the flow confluence zone unexpectedly reexpands. However, its morphology is unlike that when the flow is unblocked; it is now generated by the funneling of reverse downslope flow toward the centerline. A vertical cross section through this renewed flow confluence zone shows strong updrafts aloft and a precipitation maximum near the vertex (Fig. 6i). This suggests the concave ridge amplifies the strength of the secondary circulation described by Jiang (2003) and, despite the onset of windward flow stagnation, it continues to enhance precipitation near the vertex. This is an important result because it is different from the results of Jiang (2006), who found the enhancement of precipitation by a concave ridge is negligible when the approaching flow is blocked.
Figure 7b shows the cross-stream distribution of precipitation for CC-SR and illustrates the transition from a single-precipitation maximum to dual-precipitation maxima when 1.0 < Ĥ < 1.33. This is followed by a strong decrease in overall precipitation when the upstream flow becomes blocked (1.33 < Ĥ < 2.0), although precipitation near the vertex increases dramatically when Ĥ = 2.0. Compared to ST-SR, wave breaking is induced by CC-SR when Ĥ is smaller (see Table 2) due to stronger windward flow deceleration and an amplified mountain wave above the ridge crest.
Average cross-stream precipitation (mm) as Ĥ increases from 0.66 to 2.0 and a = 25 km: (a) ST-SR, (b) CC-SR, (c) ST-LR, and (d) CC-LR. Note different precipitation scale in (d). Thick black line represents the maximum cross-stream terrain height.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
2) Concave long ridge (CC-LR, β = 4.0)
Compared to CC-SR, the longer ridge arms of CC-LR strengthen and increase the upstream extent of windward flow deceleration when Ĥ = 0.66 (Figs. 8a–c). Wave breaking is also induced in the lee. The flow confluence zone is significantly larger (relative to b) and stronger near the vertex, and a stronger and deeper region of ascending air develops above the windward slope composed of two distinct vertical velocity maxima (generated by the upslope ascent of flow and the secondary gravity wave). The longer ridge arms of CC-LR therefore seem to effectuate a stronger funneling mechanism compared to CC-SR, supported by the much larger enhancement of precipitation relative to the corresponding straight ridges. An additional simulation was performed for CC-LR with Ĥ = 0.33 to locate the regime boundary for mountain wave generation only. No precipitation was initiated by this low (506 m) concave ridge.
As in Fig. 3, but for CC-LR with a = 25 km.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
When Ĥ is increased to 1.33 (Figs. 8d–f), windward flow stagnation is induced, which diminishes the flow confluence zone and reduces precipitation near the vertex. However, the upstream flow stagnation point is located between the ridge arms and approaching flow is deflected over the ridge arms rather than entirely around the ridge; that is, despite the transition to flow splitting, dual-precipitation maxima persist on the ridge arms.
When Ĥ = 2.0 for CC-LR (Figs. 8g–i), flow stagnation occurs around 150 km upstream of the vertex peak and approaching low-level flow is forced to pass entirely around the ridge. A precipitation maximum develops near the vertex, where the secondary circulation above the windward slope is strengthened, along with a weak but relatively uniform distribution of precipitation along the ridge arms. This spatial pattern of precipitation is similar to CC-SR when Ĥ = 2.0 and represents a significant enhancement of precipitation near the vertex compared to the corresponding ST-LR.
The flow confluence zone also grows when Ĥ is increased to 2.0; however, unlike the flow confluence zone for CC-SR with Ĥ = 2.0, it is interspersed with regions of flow diffluence. Numerous local, transient updrafts develop between the ridge arms (Fig. 8i) and, like ST-LR with Ĥ = 2.0, θe contours along the centerline exhibit a weakly negative vertical gradient (Fig. 9). This suggests a region of weak instability exists upstream of the vertex peak, and the formation of snow and graupel within this same region implies cellular convection is initiated (Fig. 5b).
Vertical cross section for CC-LR with Ĥ = 2.0 and a = 25 km of equivalent potential temperature (solid contours; every 0.5 K), and snow and graupel mixing ratios (filled contours plotted at 0.01, 0.1, and 0.5 g kg−1).
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
Given that the triggering of convection occurs exclusively for ST-LR and CC-LR when Ĥ = 2.0, the enhanced flow blocking by the larger ridge arms presumably plays a pivotal role. It may be that the deeper ascent of the upstream layer activates potential instability in the atmosphere, possibly aided by the additional latent heating associated with the ice phase. A small amount of precipitation (<1.5 mm h−1) also accumulates along the centerline, coincident with these regions of snow and graupel (Fig. 8h). However, precipitation does not accumulate along the centerline from x = 640 to 660 km because of a persistent, surface-based region of potentially warm air in which falling hydrometeors evaporate (indicated by the cross in Fig. 9). This warm air mass is maintained by the reverse downslope flow and is coincident with a local surface high pressure perturbation and surface flow diffluence. It is relatively small, extending only 10 km from the centerline in the y direction, and its time-averaged relative humidity is roughly equivalent to that of the surrounding environment. The rainwater mixing ratio concentration aloft is small (<0.2 g kg−1); hence, evaporation of rainfall probably has a negligible effect on the thermodynamic characteristics.
Examination of the three-dimensional general flow structure above the windward slope (not shown) reveals flow-stagnation points exist along the centerline from the surface to 2-km altitude (the ridge top is at hm = 3.4 km). Although flow diffluence weakens above this height, it persists up to 6-km altitude, indicating that even flow above the pool of stagnant air is prevented from converging toward the centerline when Ĥ is large. This implies that the local, transient updrafts are responsible for generating precipitation along the centerline, as the funneling mechanism is largely diminished at all levels. We hesitate to provide further detail of this very complicated flow regime as the convection, which dominates the flow near the vertex, is probably not well resolved in the model simulations (dx = 2.5 km, dz ≈ 250 m in the troposphere).
Wave breaking is present for all values of Ĥ ≥ 0.66 for CC-LR. The average cross-stream precipitation (Fig. 7d) shows the transition from a single-precipitation maximum to dual-precipitation maxima when 0.8 < Ĥ < 1.0. Flow splitting and wave breaking is induced when Ĥ = 1.33, although unlike for previous ridge geometries, this transition does not prevent flow from passing over the ridge arms. Precipitation is only slightly enhanced with respect to ST-LR when Ĥ = 1.33; however, when Ĥ = 2.0, the precipitation enhancement strengthens despite the approaching flow being blocked a sufficient distance upstream to ensure it is deflected around the ridge ends.
c. Precipitation response to flow regime transition
1) Mountain wave regime
The mountain wave regime is characterized by the generation of mountain waves above the ridge crest and in the lee. For ST-SR and ST-LR, the development of precipitation in the mountain wave regime is relatively straightforward. Impinging flow passes over the ridge crest with relative ease, generating positive vertical motions above the windward slope via upslope ascent. Clouds develop aloft and precipitation accumulates relatively uniformly near the ridge crest. When Ĥ increases from 0.66 to 1.0 (wave breaking is induced when Ĥ > 1.0), precipitation increases rapidly as the taller ridge height forces a greater vertical displacement of flow and creates deeper cloud with higher cloud water content (Fig. 10). The strength and upstream extent of windward flow deceleration increases relatively slowly as Ĥ increases (Fig. 11).
(a) Total and (b) maximum precipitation (109 kg) for ST-LR (solid) and CC-LR (dotted) where Ĥ increases from 0.66 to 2.0 and a = 12.5 (diamonds), 25 (asterisks), and 50 km (squares).
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
Maximum strength and upstream extent of windward flow deceleration as Ĥ increases from 0.66 to 2.0 and a = 25 km for the straight ridge (asterisks) and CC (diamonds) with b = 50 (solid) and 100 km (dashed). (a) Minimum perturbation u (vertical dotted line represents flow stagnation). (b) Upstream extent of flow deceleration (measured along the centerline from the ridge crest to the −2 m s−1 perturbation u contour).
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
A smaller critical Ĥ for flow regime transition exists for the concave ridges compared to the straight ridges (Table 2). Only mountain waves are generated when Ĥ = 0.33 for CC-LR and CC-SR, though no precipitation accumulates upon the 506-m-tall ridge.
2) Wave-breaking regime
The wave-breaking regime occurs when lee waves steepen, become unstable, and break. The transition to wave breaking is accompanied by a notable increase in the upstream extent of the flow deceleration zone for the two long ridges, especially ST-LR (Fig. 11b). There is also a simultaneous strengthening of windward flow deceleration for three of the four ridge geometries (Fig. 11a). This may be related to the generation of upstream-propagating modes near the ridge crest.
According to Baines (1987, 1995), when flow transitions from a subcritical to a supercritical state, a change in the depth of the leeside stagnant region generates a disturbance mode at the ridge crest that propagates upstream. These modes are typically of small amplitude and the motion is mostly horizontal (Pierrehumbert and Wyman 1985; Baines 1987). Smolarkiewicz and Rotunno (1990) noted the upwind flow reversal in their simulations of blocked flow displayed weak pulsations in amplitude and area, possibly related to the building, breaking, and subsequent rebuilding of the wave above the barrier. In the present study, it is difficult to determine the impact they have on the windward flow deceleration zone and precipitation; indeed, Bauer et al. (2000) found that for barriers with β ≤ 4.0 (all ridges examined thus far have 2.0 ≤ β ≤ 4.0), upstream-propagating modes do not exert a discernible influence on the low-level windward flow dynamics. However, the simultaneous strengthening of windward flow deceleration in the cases examined here suggests there is a connection. For example, Fig. 11b shows the upstream extent of the flow deceleration zone for the longer ridges is around twice that of the shorter ridges when wave breaking is induced, consistent with the upstream-propagating modes extending upstream a distance relative to the ridges’ half-length b. Further examination of the possible impact of these upstream-propagating modes is beyond the scope of this study.
For the straight ridges, wave breaking is not associated with a substantial change to total precipitation, as the reduction in precipitation from diminished upslope ascent is offset by an enhancement from the secondary gravity wave (Fig. 10a). For CC-SR, the transition from a single precipitation maximum to dual precipitation maxima is coincident with the flow regime transition to wave breaking. In contrast, CC-LR maintains a single precipitation maximum when wave breaking is present in the lee (Ĥ = 0.66).
3) Flow stagnation
The onset of windward flow stagnation marks the transition to the flow splitting and wave-breaking flow regime. Smith (1989) estimates that flow stagnation occurs when Ĥ ≈ 1.0 and β > 2.0; however, the value of Ĥ at which it occurs cannot be precisely determined from linear theory (estimating stagnation requires a full nonlinear solution). Past studies using nonlinear models and (nearly) saturated flows have found values from Ĥ = 1.5 (Jiang 2006) to Ĥ = 3.0 (Colle 2004) are sufficient to induce flow splitting, though this depends on a variety of factors (e.g., upstream thermodynamic profile and mountain geometry).
Windward flow stagnation has an important role in determining the distribution and amount of precipitation. For the straight ridges, the transition to flow splitting and wave breaking results in a dramatic reduction in precipitation, as flow passes almost entirely around the ridge ends (e.g., Figs. 4g–i). For the concave ridges, the precipitation response to the onset of windward flow stagnation is more complex.
Jiang (2006) found that the strength of the precipitation enhancement by a concave ridge (compared to a corresponding straight ridge) is directly related to the strength of windward flow deceleration, which in turn is related to the size of the flow confluence zone and Ĥ. In the present simulations, when the approaching flow is unblocked (Ĥ < 1.33), the flow confluence zone for CC-SR and CC-LR shrinks as Ĥ increases (Fig. 12a). Consistent with Jiang (2006), the enhancement of precipitation by the concave ridge relative to the straight ridge is almost negligible as the flow confluence zone shrinks and flow stagnation is approached (1.0 < Ĥ < 1.33). However, the establishment of a secondary circulation reexpands the flow confluence zone and strengthens the precipitation enhancement (Fig. 12), different from the findings of Jiang (2006).
Selected fields to illustrate the influence of the funneling mechanism as Ĥ increases from 0.66 to 2.0 and a = 25 km. (a) Total area of windward flow confluence (normalized by b; km2). Enhancement of (b) the total accumulated precipitation and (c) the maximum precipitation intensity by CC-SR and CC-LR compared to the corresponding ST-SR and ST-LR, respectively (%).
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
4. Effect of the ridge width
This section investigates the influence of variations to a for straight and concave ridges. Three values of a are adopted: 12.5, 25, and 50 km (narrow, control, and wide, respectively) corresponding to β = 8.0, 4.0, and 2.0 for the long ridge and β = 4.0, 2.0, and 1.0 for the short ridge, respectively. CC-LR is the primary focus of this section, as the flow and precipitation response for the straight ridges are qualitatively similar to previous studies (e.g., Jiang 2003; Colle 2004) and generally consistent with Smith’s (1989) flow regime diagram.
When Ĥ = 1.0 for CC-LR, both the narrow and control ridges induce dual-precipitation maxima (Figs. 13b,e), whereas the wide ridge induces a single-precipitation maximum (Fig. 13h). Windward flow deceleration near the ridge vertex is much weaker for the wide ridge, allowing the confluence zone to extend farther up the windward slope. However, the narrow ridge creates the most expansive flow confluence zone and has the strongest funneling influence on the approaching flow (inferred from |dυ/dy|; not shown). The angle of the windward slope appears to be an important factor in determining the effectiveness of the funneling mechanism, although its influence is complicated by the sensitivity of flow deceleration to ridge width.
As in Fig. 3, but for CC-LR.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
The cross-stream distribution of precipitation for CC-LR shows that precipitation is restricted to near the centerline of the narrow ridge when Ĥ is small; as Ĥ increases, it is redistributed toward the ridge ends (Fig. 14a). In contrast, precipitation for the wide ridge retains a more uniform cross-stream distribution as Ĥ increases (Fig. 14c). The spatial distribution of precipitation generated by the narrow ridge is therefore more sensitive to changes in Ĥ than the wide ridge; although when the flow becomes blocked, the precipitation distribution changes dramatically for all ridge widths.
As in Fig. 7, but for CC-LR with (a) a = 12.5 km, (b) a = 25 km, and (c) a = 50 km.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
When Ĥ ≤ 1.0 for CC-LR, Fig. 10 shows that the precipitation maximum is sensitive to ridge width, while the total precipitation is relatively insensitive; when Ĥ ≥ 1.33 the reverse is true. This contrast is due to the transition from an unblocked to a blocked flow regime around Ĥ = 1.33: if the approaching flow is unblocked, then the steeper slopes of the narrow ridge generate stronger, deeper updrafts and more intense precipitation compared to the wider ridges, though with a smaller accumulation area; if the approaching flow is blocked and flow splitting is induced, then the precipitation maximum for the narrow and control ridge widths reduces to be comparable to that of the wide ridge. Total precipitation, on the other hand, is more sensitive to ridge width when the flow is blocked: the wide ridge generates almost 3 times the amount of precipitation as the narrow ridge when Ĥ = 2.0.
Precipitation efficiency has been shown to be sensitive to ridge width and is usually defined as the ratio of the total precipitation rate over a certain area to the total condensation rate. As the local condensation rate is unavailable from simulations in this study, a new parameter called the P/C ratio is hereby defined to express the ratio of the average hourly total mass of accumulated precipitation (Ptot; kg h−1) to the average total instantaneous mass of condensate C (where C includes cloud, rain, ice, graupel, and snow; kg) within an area sufficiently large to include all the precipitation and condensate generated by the ridge. The inverse of the P/C ratio quantifies the time it would take for all condensate to be removed as precipitation.
The highest P/C ratio for ST-LR (and ST-SR) is when Ĥ = 1.0 with the control ridge width (Fig. 15). This is because of 1) stronger updrafts above the windward slope compared to the wide ridge, which appears to promotes deeper clouds, a higher concentration of condensate, and therefore more efficient microphysical processes; and 2) an orographic cloud of greater streamwise extent compared to the narrow ridge, which allows greater in-cloud residence time for traversing air parcels. When Ĥ increases beyond 1.0 for the straight ridges, the ridge width has less effect on the P/C ratio as the flow becomes blocked, nullifying the influence of the slope angle on the updraft strength.
Ratio of P/C (h−1) for ST-LR (solid) and CC-LR (dotted), where Ĥ increases from 0.66 to 2.0 and a = 12.5 (diamonds), 25 (asterisks), and 50 km (squares).
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
For CC-LR, the highest P/C ratio also occurs when Ĥ = 1.0, although it is associated with the narrow ridge. This difference is likely due to the increased upstream extent of windward flow deceleration induced by the concave ridge, which extends the effective influence of the terrain upstream and increases the streamwise extent of orographic cloud. While it is relatively straightforward to quantify the updraft strength and cloud depth and streamwise extent, these variables provide little insight into why the P/C ratio is largest for the straight and concave ridges when Ĥ = 1.0 with the control and narrow ridge widths, respectively. It is also worth noting that the microphysical processes to generate precipitation that subsequently falls out is nonlinear and presumably not well represented by this simple quantitative parameter. The limitation of using a time scale to understand orographic precipitation efficiency was also noted by Jiang and Smith (2003), citing the absence of a characteristic time scale for hydrometeor formation as the critical issue. This is a good topic for future investigation.
Finally, although the upstream extent of windward flow deceleration for each ridge is generally largest for the wide ridge (not shown), the ridge width has little bearing on the distance upstream at which flow splitting occurs. For example, flow splitting occurs around 100 km upstream of the crest of ST-LR irrespective of a, and around 50 km for ST-SR. This is equivalent to the ridge length 2b and consistent with the discussion of Baines (1995). The distance upstream that flow splitting occurs for the concave ridges is also intimately tied to the ridge length.
5. Precipitation enhancement and relative humidity experiments
a. Flow confluence and precipitation enhancement
The relationship between flow confluence and the precipitation enhancement by a concave ridge is hereby examined as a function of the ridge geometry. Figure 16a illustrates the progressive changes in the size of the flow confluence zone (normalized by b) to variations in Ĥ. The additional influence of β is illustrated in Fig. 17a, where the size of the flow confluence zone is represented by the size of each circle; β seems to have little influence on the size of the flow confluence zone compared to Ĥ. However, this is not to say the ridge length or width has a negligible effect; on the contrary, a longer concave ridge typically has a larger flow confluence zone, while a wider concave ridge has a smaller flow confluence zone. These competing effects ensure that β has notably less influence on the flow confluence zone compared to Ĥ.
As in Fig. 12, but for CC-SR (dotted) and CC-LR (solid), where a = 12.5 (asterisks), 25 (diamonds), and 50 km (triangles). Note that as in Fig. 12a, the total area of windward flow confluence in (a) is normalized by b.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
Influence of Ĥ and β on the flow confluence zone and the total and maximum precipitation enhancement. The size of the circle is proportional to the quantity of the presented variable, and gray circles relate to short ridges (b = 50 km) and black circles relate to long ridges (b = 100 km). (a) Total area of windward flow confluence (normalized by b). (b) Enhancement of total precipitation. (c) Enhancement of the maximum precipitation intensity by the concave ridge relative to the corresponding straight ridge. A cross represents negligible confluence or enhancement. Note that the size of the circles in (b) are not of the same scale as in (c), and the short and long ridges have measurements when β = 2.0 and 4.0 and are therefore presented separated but within the dashed lines (gray and black).
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
The relationship between the precipitation enhancement and Ĥ is reflected in Figs. 16b, 16c, 17b, and 17c. They clearly show diminishing precipitation enhancement as Ĥ increases [consistent with Jiang’s (2006) results], along with the reinvigorated precipitation enhancement when the secondary circulation is established on the windward slope.
It was hypothesized that the size of the flow confluence zone was intimately connected to the precipitation enhancement. However, although the ridge length has a positive influence on the size of the flow confluence zone, its influence on the strength of the precipitation enhancement is more limited (cf. Figs. 16b,c). In contrast, β has a more prominent influence on precipitation enhancement, particularly when Ĥ is small (cf. Fig. 17b). An exception is when Ĥ = 2.0 and the long ridge tends to enhance precipitation more than the short ridge, probably because the secondary circulation above the windward slope is better developed when the ridge is longer. The sensitivity of this complicated secondary circulation to terrain shape is certainly worthy of further exploration.
For some ridge geometries, the strength of the precipitation enhancement by the concave ridge is surprisingly large (e.g., almost 4000% for CC-LR with Ĥ = 0.66, a = 12.5); however, the total precipitation accumulation in such cases are small (<0.2 mm for the same concave ridge). Moreover, the largest drying ratio (DR) simulated in this study is only 5.2% (where the DR is the ratio of the mass of accumulated precipitation over a given area and the water vapor influx far upstream of the ridge; see WL12 for more details). This is substantially smaller than observed drying ratios in other midlatitude locations around the world [e.g., 40% in the Oregon Cascades (Smith et al. 2005) and 50% in the southern Andes (Smith and Evans 2007)], and closer to the tropical island of Dominica (approximately 0.5%; Smith et al. 2012). It is pertinent to ask what relevance these results have to scenarios of heavy orographic precipitation in the Australian Alps and other midlatitude locations.
Heavy orographic precipitation in midlatitude climate zones typically comes about from either the enhancement of existing precipitation in strong cross-barrier flow by a seeder–feeder-type mechanism (e.g., Browning et al. 1975) or the initiation of precipitating convection (e.g., Sénési et al. 1996). The presence of a seeder cloud at an elevated level may not significantly alter the low-level flow dynamics of the seeder cloud, though it may have a significant influence on precipitation. For example, seeding from aloft can drastically speed up the microphysical conversion process which, for an unblocked flow over a narrow ridge, could substantially increase precipitation. As for convective orographic precipitation, the dynamics and microphysics can be vastly different from the (generally) stratiform dynamics examined here (e.g., Kirshbaum and Grant 2012).
b. Sensitivity to relative humidity
Three additional soundings have been developed to test the influence of changes to low-level relative humidity (see section 2). The low-level water vapor mixing ratio has been modified to change the relative humidity by −5%, +5%, and +15% from the control sounding. RH−5 and RH+5 are designed to test how a relatively small change in moisture can alter the orographic flow and precipitation response; RH+15, which is closer to saturation with an average relative humidity of 90% in the lowest 2 km, is designed to be closer to the sounding used in Jiang (2006), which was almost saturated. These variations to relative humidity have a negligible impact on the upstream static stability; hence, Ĥ is comparable to its control value. As the simulations are designed to highlight how changes to the relative humidity can influence upstream flow confluence and precipitation, only a small subset of simulations are performed.
Figure 18 presents selected flow fields for CC-LR with Ĥ = 1.0 and a = 25 and the control sounding, RH−5, and RH+5. The impacts of variations to the lower-tropospheric relative humidity are pronounced. The 5% reduction in RH−5 strengthens windward flow deceleration significantly and induces a regime transition to flow splitting and wave breaking. The flow confluence zone contracts with respect to the control sounding, and precipitation reduces substantially (especially near the vertex; see Fig. 19). The 5% increase in RH+5 nearly merges the dual precipitation maxima into a single precipitation maximum at the vertex as windward flow deceleration weakens and the flow confluence zone expands significantly. Although these adjustments to relative humidity are small, they have a substantial impact on the flow and precipitation response, significantly more than would be expected from a 5% adjustment to the terrain geometry or wind speed.
As in Fig. 3, but for CC-LR with Ĥ = 1.0, a = 25 km, and the modified RH soundings (a)–(c) RH−5, (d)–(f) control, and (g)–(i) RH+5. See section 2 for details.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
As in Fig. 7, but for CC-LR with Ĥ = 1.0, a = 25 km, and the modified RH soundings.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
The drying ratio is computed for these simulations, as the water vapor influx varies with adjustments to the relative humidity (see Table 3). The concave ridge becomes more effective at removing moisture from the atmosphere as precipitation when the water vapor influx is higher (i.e., the drying ratio increases with increasing relative humidity). The extent to which this increase in drying ratio is driven by dynamics versus microphysics poses an interesting problem for future work.
Summary of computations for four experiments with different low-level RH: RH−5, control, RH+5, and RH+15 (see section 3). (from left to right) Low-level RH (average from the surface to 2 km), the total hourly precipitation mass, the accumulated hourly water vapor influx, and the drying ratio.
Finally, it was hypothesized in WL12 that CC-LR generates a dual precipitation maximum when Ĥ = 1.0 rather than a single precipitation maximum as in Jiang (2006) because of a difference in relative humidity. Consistent with the hypothesis, the precipitation distribution for CC-LR with Ĥ = 1.0 and RH+15 (triangle symbols in Fig. 19) very closely resembles the pronounced single precipitation maximum near the vertex found by Jiang (2006, see his Fig. 8).
6. Flow regime diagrams
Based on linear theory, Smith (1989) constructed a flow regime diagram for a dry, inviscid flow impinging upon a Gaussian-shaped hill of varying Ĥ and β to determine the onset of wave breaking and flow splitting. The predictions of Smith (1989) have since been qualitatively supported by numerous studies using nonlinear numerical simulations and, more recently, moist flows (e.g., Smolarkiewicz and Rotunno 1990; Ólafsson and Bougeault 1996; Bauer et al. 2000; Galewsky 2008). Following Smith (1989), a flow regime diagram is constructed from the results of this study for the straight and concave ridges. To construct this diagram, three additional simulations (specifically CC-LR with Ĥ = 0.33 and β = 2, 4, 8) were conducted to isolate the transition from mountain waves to wave breaking.
The regime diagram for the straight ridge (Fig. 20a) shows good qualitative agreement with Smith’s (1989) flow regime diagram. There is a downward trend in the critical Ĥ threshold for wave breaking (curve A) as β increases from 1.0, consistent with Smith (1989). A downward trend in the critical Ĥ for flow splitting and wave breaking (curve B) may also exist; however, the limited values of Ĥ examined here prevent confirmation. An encouraging aspect of the regime diagram and consistent with Smith’s (1989) calculations is the intersection of the curves A and B when β = 1.0.
Regime diagram delineating the value of Ĥ at which flow regime transitions are induced by (a) the straight ridge and (b) the concave ridge based on the simulations conducted in this study. The dashed line shows the approximate threshold for wave breaking, and the solid line shows the approximate threshold for flow splitting and wave breaking. Error bars (dotted lines) are included to indicate the range of Ĥ in which the flow regime transition may be induced. The regime boundaries derived by Smith (1989) are shown in (a) in gray.
Citation: Journal of the Atmospheric Sciences 71, 8; 10.1175/JAS-D-13-0318.1
The concave ridge typically reduced the critical Ĥ for flow regime transition compared to the straight ridge (Fig. 20b). Both curves C and D exhibit a downward trend as β increases, with wave breaking persisting until Ĥ approaches 0.33. The point at which curves C and D intersect (if ever) is unknown, as no experiments were conducted for a concave ridge with β < 1.0 (it begins to resemble a blob with a shallow valley rather than a concave ridge at this extreme). A 5% reduction in the low-level relative humidity was shown to induce flow regime transition for CC-LR with Ĥ = 1.0, highlighting the sensitivity of the orographic flow response and precipitation to changes in the effective stability.
It is evident in Fig. 20a that curves A and B are up to 50% higher than what was predicted by Smith (1989). This is primarily because of the influence of moisture. Simulations in WL12 in which moist processes were neglected demonstrated that the addition of moisture, and the associated reduction in stability in saturated regions, can induce a flow regime transition from blocked to unblocked flow holding all else equal (e.g., see Fig. 3 in WL12). The influence of moisture and saturation may be accounted for in Ĥ by replacing N with its moist (viz. saturated) counterpart Nm [see Durran and Klemp (1982) for derivation] to estimate the moist nondimensional mountain height Ĥm. This formulation has been commonly used in studies of moist flow over a hill; however, such studies typically adopt an upstream flow that is saturated (or nearly saturated) in the lower levels (e.g., Colle 2004; Miglietta and Rotunno 2005; Jiang 2006; Galewsky 2008). This makes the calculation of Nm and thereby Ĥm relatively straightforward. However, in the present study the upstream environment is unsaturated, perhaps emphasizing the challenge of bridging the gap between complicated case studies and idealized studies. The reader is directed to Rotunno and Houze (2007; specifically their section 5) for further discussion.
7. Summary and conclusions
This study has examined how variations to the nondimensional mountain height Ĥ and the horizontal aspect ratio β of two relatively simple terrain geometries influence the orographic flow response and associated precipitation. An idealized configuration of the Weather Research and Forecasting Model was used to simulate a moist but initially unsaturated flow impinging upon two different ridge geometries: a straight ridge and a concave ridge.
A primary aim of this study was to explore how the geometry of a concave ridge impacts the precipitation-enhancing funneling mechanism. This mechanism was explored by Jiang (2006) and found to be sensitive to Ĥ due to the strength of windward flow deceleration. The present study found that when Ĥ was small and flow deceleration was weak, a single precipitation maximum developed at the vertex of the concave ridge; when Ĥ increased and flow deceleration strengthened, impinging flow separated around this region of decelerated air and preferentially passed over the ridge arms rather than the vertex. This created dual precipitation maxima on the ridge arms. The onset of flow stagnation typically induced a transition from flow over to flow around the concave ridge, though not in all cases; if the most upstream point of flow stagnation were located between the ridge arms, dual precipitation maxima may persist.
Consistent with Jiang (2006), the enhancement of precipitation by the concave ridge relative to the corresponding straight ridge was closely related to the development of flow confluence between the ridge arms. The largest precipitation enhancement occurred when Ĥ was small and flow deceleration was weak. When flow stagnation was induced and the impinging flow became blocked, flow confluence and the strength of the precipitation enhancement diminished. When Ĥ was sufficiently large, reverse downslope flow established a secondary circulation on the windward slope of each ridge. The updrafts associated with this circulation were strengthened by the funneling of reverse downslope flow toward the centerline of the concave ridge and, despite the flow being blocked, it reexpanded the flow confluence zone and enhanced precipitation near the vertex.
The influence of the ridge length and width was also examined. The competing effects of the concave ridge length and width on the size of the flow confluence zone rendered it mostly insensitive to changes in β. The strength of the precipitation enhancement by the concave ridge relative to the corresponding straight ridge was largely controlled by Ĥ. A relatively strong correlation between the size of the flow confluence zone and the strength of the precipitation enhancement was found.
A set of simulations with modified low-level relative humidity was also performed. These highlighted the substantial influence variations in the effective stability in saturated regions can have on the orographic flow response and precipitation. There remain many outstanding questions; for example, how do details of the upstream environment influence flow regime transition thresholds and associated precipitation patterns as Ĥ and β vary? This is an especially important topic because modern numerical weather prediction models are now capable of resolving realistic terrain features with complicated geometries. However, there remains a lack of real world observations of the funneling mechanism that makes us mindful of the relevance of these experimental results. It is the authors’ ambitions to develop a detailed observational dataset of conditions associated with heavy precipitation events in the Australian Alps. This will provide a more comprehensive understanding of the parameter space associated with such events, allowing further idealized studies that aim to untangle the common ingredients of heavy precipitation in the region.
Acknowledgments
Campbell Watson was supported by a Melbourne Research Scholarship, and Todd Lane was supported by the Australian Research Council’s Future Fellowships Scheme (Grant FT0990892). Computing was performed at the Victorian Partnership for Advanced Computing (VPAC) facility and at the National Computational Infrastructure (NCI) facility. The work benefitted from computational support provided by the ARC Centre of Excellence for Climate System Science (Grant CE110001028). We would also like to thank Dan Kirshbaum and Alison Nugent for their comments on an earlier version of the paper, Rich Rotunno for the useful discussion in the early parts of the study and feedback, and two anonymous reviewers.
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Surface trajectories are used to represent streamlines—a valid assumption, as the flow is approximately steady.
