1. Introduction
One simple but common orographic precipitation mechanism involves the ascent of moist low-level air over a hill, where it saturates and produces precipitation (e.g., Houze 1993). When this “cap” cloud is statically unstable, convective structures may develop that influence the rate, efficiency, and fallout of precipitation. Results from observational studies (e.g., Elliott and Hovind 1964; Dirks 1973) and, more recently, numerical studies (Kirshbaum and Durran 2004; Fuhrer and Schär 2005) all suggest that orographic precipitation is enhanced in convective events compared to stratiform events.
In addition to increasing the area-averaged precipitation, orographic convection may take the form of quasi-stationary banded structures that concentrate most of their rainfall over specific locations. Observations of banded orographic precipitation events over the western Kyushu region of Japan (Yoshizaki et al. 2000), the Cévennes region of France (Miniscloux et al. 2001; Cosma et al. 2002), and the Oregon Coastal Range (Kirshbaum and Durran 2005b) have suggested that the steadiness of the bands may lead to daily cumulative precipitation amounts in excess of 100 mm. These studies identified some common ingredients for band formation, including potential instability, high relative humidity, and moderate wind speeds in the upstream flow, along with the presence of small-scale topographic obstacles on the terrain upstream of the ridge crest.
Despite the broad consistencies between the cases cited above, their different terrain geometries and upstream flows led to differences in the structures of the bands. For example, the rainbands in Yoshizaki et al. (2000) were triggered by two widely spaced peninsulas upstream of the Kyushu range, while those in Cosma et al. (2002) formed past closely spaced peaks on the upslope of the Cévennes, and those in Kirshbaum and Durran (2005b) formed not just past small-scale peaks but also valleys embedded on the Coastal Range upslope. This may help to explain why the bands over western Kyushu were spaced much farther apart (∼100 km) than those over the Cévennes and Coastal Range (5–15 km). Moreover, the low-level instability of the flow impinging on western Kyushu was much stronger than that over the Cévennes and the Coastal Range, which may have caused the bands over western Kyushu to be deeper (5–6 km) than those in the other two cases (2–4 km). These differences indicate that structural details of the rainbands may strongly depend on both the flow passing over the mountain and the terrain of the region.
Insight into the atmospheric factors promoting quasi-stationary rainbands over the Coastal Range is provided by the numerical experiments of Kirshbaum and Durran (2005a), who found that marginal potential instability and moderate wind speeds (≥10 m s−1) in the cloud layer were the most favorable atmospheric conditions for bands to develop. Their simulated bands formed equally well in both sheared and unsheared environments, implying that shear was not necessary to organize the convection into elongated bands. The authors hypothesized that the bands were triggered by lee waves induced by small-scale terrain features just upstream of the orographic cloud, past which the air ascended convectively into an updraft band.
As a logical follow-up to Kirshbaum and Durran (2005a), this paper provides an in-depth study of the dynamics by which small-scale terrain obstacles trigger quasi-stationary rainbands over a mesoscale orographic barrier. This is accomplished through a combination of observational and numerical analysis. We first revisit radar observations of a banded convective event over the Coastal Range in Kirshbaum and Durran (2005b) to illustrate the locations and horizontal structures of the rainbands. We then introduce the cloud-resolving numerical model and perform a quasi-idealized simulation of this event using the real upstream flow and Coastal Range terrain. A series of idealized simulations are then carried out with simpler upstream flows and terrain profiles to identify the physical processes that govern the preferred locations of orographic rainbands.
2. Observations
The three precipitation events over the Oregon Coastal Range studied in Kirshbaum and Durran (2005b) all occurred in postfrontal synoptic environments with upstream flows containing potential instability from the surface to a height of around 3 km. Once lifted to saturation over the Coastal Range, they generated convective structures with various degrees of banded organization and steadiness. The most banded and steady event of the three (case 2 in that paper) occurred over 12–13 November 2002. A representative upstream sounding profile during this event from Quillayute, Washington (about 200 km north of the Coastal Range), at 0000 UTC 13 November 2002 in Fig. 1a is characterized by moderate (≥10 m s−1) southwesterly winds, weak conditional instability (CAPE ≈ 500 J), and high relative humidity (≈90%) at low levels.
A representative radar reflectivity image from this event, taken from the Next-Generation Weather Radar (NEXRAD) Portland, Oregon, site at 2003 UTC 12 November 2002, is contoured at 5-dBZ intervals in Fig. 2a. These data were obtained from a 0.5° elevation radar scan whose upward-pointing beam reaches a physical height of approximately 1.5 km in the center of the figure. A nine-point spatial filter has been applied that smoothes the contours and decreases the effective horizontal resolution of the radar data above its nominal value of 1 km. Remarkably well organized rainbands are apparent over the mountain upslope that persisted in the same locations for the duration of this event. The upstream edges of these bands are located not directly over the ridge peak at approximately 123.5°W but rather far upstream of it. Although some of the bands in Fig. 2a appear to form over and downstream of small-scale peaks on the gradually sloping barrier, others form past valleys or have no clear connection to obvious small-scale features. The steadiness of these rainbands led to highly variable precipitation accumulations, with Mt. Hebo recording 69 mm in just 6 h and Rye Mountain, located just 20 km to the east but not directly under a band, recording only 8 mm over the same interval. For more details on the structures of these rainbands, or those in other events over the Coastal Range, the reader is referred to Kirshbaum and Durran (2005b).
3. A quasi-idealized simulation of the event
The numerical model used for all the simulations is cloud resolving, nonhydrostatic, and fully nonlinear, with governing equations described in Bryan and Fritsch (2002). Solutions to these equations are achieved using a split time step technique to maintain stability of acoustic modes (Klemp and Wilhelmson 1978), with the acoustic terms treated explicitly in the horizontal direction and implicitly in the vertical. Integration of variables on the larger time step is performed using the Runge–Kutta technique formulated for compressible models by Wicker and Skamarock (2002). Advection is performed with a centered sixth-order scheme, and sixth-order artificial diffusion is applied to all variables in the horizontal direction. Microphysical processes are parameterized through a warm rain Kessler scheme (e.g., Klemp and Wilhelmson 1978), and subgrid-scale turbulence is parameterized using Smagorinsky-type first-order closure (e.g., Lilly 1962). The experimental domain has dimensions of Lx × Ly × Lz, with a free-slip lower boundary and the uppermost 5 km in z serving as a Rayleigh damping layer to absorb vertically propagating waves. Lateral boundary conditions are periodic in y and outflow in x using a one-way wave equation (e.g., Durran and Klemp 1983) with a constant phase speed of 25 m s−1. Rotational effects are neglected due to the high characteristic Rossby numbers of the flows under consideration, and ice processes are neglected because the cloud tops in these simulations generally do not extend far above the freezing level.
The study area for this analysis, shown by the box in Fig. 3a, is a quasi-2D section of the northwestern Oregon Coastal Range terrain downloaded from the U.S. Geological Survey’s (USGS) Global 30 Arc-Second Elevation Dataset (Gtopo30) global elevation model with a resolution of 1/120°. To prepare this terrain map for use in the model, it is first linearly interpolated to a Cartesian grid whose centerpoint lies along the main ridge axis at 45.4°N and 123.5°W (Fig. 3b). This grid has a horizontal spacing of Δh = Δx = Δy = 500 m, which is similar to the nominal Gtopo30 resolution, and a size of 160 km × 40 km. Periodicity in the y direction is achieved by adding a mirror image of the terrain over 40 < y ≤ 80 km, which sets Ly = 80 km (Fig. 3c). The topography is then low-pass filtered to remove all variance at horizontal scales less than 6Δh that are poorly resolved by the numerical model (Fig. 3d). Finally, to minimize the potential spurious effects of gravity wave reflection at the outflow x boundaries, we expand the domain to Lx = 320 km while keeping the ridge axis positioned at its center (x = 160 km).
The numerical model’s ability to reproduce observed convective features is evaluated through a quasi-idealized simulation, hereafter called CTL, of the 12–13 November precipitation event over western Oregon. For this simulation we use the periodic Coastal Range terrain in Fig. 3d and an upstream flow that is identical to that in Fig. 1a, except that the winds have been rotated clockwise by 10° to account for mesoscale variations in wind direction between Quillayute and the Coastal Range apparent from reanalysis data of this event (not shown). The numerical grid has a horizontal spacing of Δh = 500 m and a variable vertical spacing that is Δz = 125 m at low levels (z ≤ 5 km), stretches to 500 m over 5 < z ≤ 10 km, and remains constant at 500 m to the top of the domain at Lz = 15 km. Approximately 2 h of integration time are needed for the flow to become quasi-steady, and we display output fields at the final integration time of t = 4 h. Horizontal cross sections of this simulation, and all subsequent simulations, are shown at a height of z = 1.5 km that is similar to the 0.5° beam height that the Portland radar reaches over the western slopes of the Coastal Range.
In Figs. 2b,c the observed radar reflectivities over the study area are directly compared to simulated reflectivities from the CTL simulation over 0 ≤ y ≤ 40 km.1 For consistency the simulated reflectivities in Fig. 2c are first smoothed to the nominal radar resolution of 1 km, then filtered by the same nine-point operator that was applied to the radar data. The three stationary bands in the simulation (S1, S2, and S3 in Fig. 2c) are clearly in the same locations over the upslope as those in the radar data (R1, R2, and R3 in Fig. 2b), though with slight differences in the intensity and width of each band. Discrepancies among these finer details are not surprising, considering that the idealized setup of the simulation neglects or simplifies numerous physical processes that may contribute to the observed reflectivity pattern. Nonetheless, the strong agreement in the band locations between the observations and the simulation suggests that this idealized numerical approach is able to accurately capture the primary subject of this study—the physics that control the triggering, and hence the locations, of the rainbands.
4. Idealized simulations
Having demonstrated that the numerical model provides a reasonable solution for a given test case, we now use the model as a tool to investigate the dynamics behind the orographic rainbands. To this end, we perform a series of simulations that are progressively simplified until the physical processes behind rainband triggering are easily identified.
a. Simplifying the upstream flow
As a first step in the idealization process, we perform a simulation named IDEAL that is identical to the CTL case except for the use of the idealized sounding in Fig. 1b. This sounding is designed to capture the gross low-level features of the observed sounding while greatly simplifying the atmospheric structure so that it is defined by just a few parameters. The winds are simplified by setting their magnitude |U| = U = 10 m s−1 and direction ∠U = Θ = 230° (measured clockwise from due north) to uniform values representative of the low-level conditions in the real sounding. Similarly, thermodynamic conditions at the surface (Ts = 285 K; RHs = 90%) are identical in both soundings, but in the idealized case the square of the dry Brunt–Väisälä frequency is set to a uniform value (N 2d = 1 × 10−4 s−2) and relative humidity is given by a piecewise linear function of height with constant values of RH = 90% at the surface and RH = 1% aloft with a linear transition zone over 5 ≤ z ≤ 10 km. Note that this idealized sounding neglects the vertical shear as well as the stable layers aloft between 600 and 400 mb and above the tropopause at 225 mb in the real sounding (Fig. 1a).
Despite the simplifications made to its upstream flow, the IDEAL simulation develops organized rainbands at similar locations (IS1, IS2, and IS3 in Fig. 2d) as in the CTL case (S1, S2, and S3 in Fig. 2c). These bands form in the absence of any basic-state vertical shear, which supports the argument of Kirshbaum and Durran (2005a) that shear is not necessary for band formation, and in some cases may actually hinder it. In particular, directional shear was found to partially suppress rainbands triggered by small-scale topographic features, which lost their vertical coherence when the wind direction turned with height. This may explain the one extra band (labeled IS4 in Fig. 2d) in the IDEAL simulation that was not present in the CTL case. This relatively weak and short band may have been suppressed by the low-level directional shear in the CTL sounding (Fig. 1a) but is able to emerge in the unsheared IDEAL sounding (Fig. 1b).
A second idealization is to rotate the basic-state wind vector from Θ = 230° to Θ = 270° so that it is oriented purely from the west. This wind rotation not only aligns the flow with the grid axes, but it demonstrates the influence of wind direction on band alignment. Horizontal cross sections of cloud water (qc) from the IDEAL simulation (Fig. 4a) and the TH270 simulation (Fig. 4b), which is identical except for using this rotated wind field, indicate that the cloud bands in this case rotate in phase with the 40° mean wind rotation, suggesting that their alignments are parallel to the flow direction. Two vertical x–z cross sections of vertical velocity (w) and qc taken through a band (y = 15 km) and between bands (y = 12 km) in Fig. 4b are shown in Figs. 4c,d. In both cases a cloud forms in an elevated, upstream-tilted region of positive vertical motion past small-scale terrain obstacles near x = 125 km, yet a strong rainband only forms at y = 15 km, not at y = 12 km. Although a cloud is evident at y = 12 km, its vertical motion does not intensify with distance downstream like the updraft at y = 15 km.
b. Simplifying the terrain
The vertical cross sections in Figs. 4c,d suggest that the small-scale terrain just upstream of the orographic cloud edge causes flow perturbations that intersect the cloud and influence the moist dynamics farther downstream. The extent to which the terrain over this limited area controls the overall convective response is examined by a simulation (TH270-PA) that is identical to the TH270 simulation except that h̃ = 0 everywhere except for 40 < x < 60 km, leaving only a narrow patch of topographic variability well upstream of the ridge crest. The qc field of this simulation in Fig. 6a reveals that the convective pattern in the TH270 case (Fig. 4b) is virtually unchanged when most of h̃ is removed in the TH270-PA simulation. Similarly, vertical cross sections of the TH270-PA simulation, taken through a band at y = 15 km (Fig. 6b) and between two bands at y = 12 km (Fig. 6c), exhibit similar vertical velocity patterns and cloud extent as the TH270 case (Figs. 4c,d). This comparison suggests that, for a given mesoscale terrain profile
The flow response in the complete absence of h̃ is examined by a simulation (NoHs) in which h̃ is zero everywhere. Since the terrain resolution is no longer limited by that of the Gtopo30 dataset, we increase the numerical resolution of this simulation, and all of those to follow, by decreasing Δh to 250 m. To minimize the added computational expense associated with this higher resolution, we decrease Lx and Ly by a factor of 2 (to 160 and 20 km, respectively, with the domain still centered around the terrain centerpoint). Note that, because
The horizontal cross section of qc in the NoHs simulation in Fig. 7a demonstrates that, in contrast to the previous simulations with nonzero h̃, convection does not occur. The flow exhibits no perceptible y variability and is essentially 2D, varying only in x and z. A vertical cross section of the cloud outline and static stability (N 2 in dry regions, N 2m in saturated regions) at y = 10 km indicates that virtually all of the cloud possesses moist instability (N 2m < 0), yet little to no convection develops within it. In the absence of h̃ or any other small-scale forcing mechanism, little to no energy is projected onto rapidly growing small-scale convective modes and, as a result, the residence times of air parcels within the cap cloud is too short to allow noticeable convection to develop from numerical round-off errors alone (Kirshbaum and Durran 2004).
c. A single small-scale feature
The sensitivity of the cloud patterns in the HILL and VALLEY simulations to the topographic obstacles at x = 40 km is demonstrated in the qc plots in Figs. 8a,b. The HILL simulation (Fig. 8a) develops a strong cloud band downstream of the isolated hill, with desaturated regions surrounding it. Although this result suggests that bands tend to form in the lee of small-scale hills, the VALLEY simulation (Fig. 8b) reveals that bands may also form downstream of a valley. Three bands are evident in this case: a weak band just downstream of the valley at y = 10 km and two stronger bands surrounding it.
The differences between the HILL and VALLEY simulations are highlighted in Figs. 8c,d, which, like Figs. 4c,d and 6b,c, show vertical cross sections of w and qc past the terrain obstacles at y = 10 km. In addition, the streamlines of parcels originating at z = 562.5 m are overlaid on the plots to indicate the different paths that near-surface parcels take through the clouds (because the flow is quasi-steady, these streamlines are nearly equivalent to trajectories and we henceforth use the latter term to describe them). Despite the much simpler h̃ fields in these cases, the dynamics of the bands and the nonbanded areas appear qualitatively similar to those in the TH270 and TH270-PA simulations (Figs. 4c,d and 6b,c). In Fig. 8c an oscillating vertical velocity pattern is evident prior to saturation, in which the parcel first rises over the hill, descends past it, and then rises again. Saturation occurs in the ascending air parcel at x ≈ 47 km, beyond which it gains qc as it rises convectively to the top of the cloud layer. The vertical velocity pattern near x ≈ 40 km in the VALLEY simulation differs in sign from that in the HILL case but has approximately the same amplitude. As a consequence saturation occurs farther upstream at x ≈ 42 km; the vertical motion is weak in the saturated region and the parcel does not rise convectively.
d. A sinusoidal column
Although simulations with a single obstacle provide useful insight into the formation of one or more orographic rainbands, real orographic flows tend to have multiple small-scale terrain features capable of generating rainbands (e.g., Fig. 2a). Here we take a first step in exploring the influence of multiple topographic features on orographic rainbands by representing h̃ as a column of hills and valleys that extend across the width of the domain. This is implemented by defining h̃ by the 2D cosine wave in (3) except that, rather than being zero for |y − yb| > λb/4, it spans Ly with two full wavelengths. As in the HILL simulation, hb = 100 m and yb = 10 km so that a small-scale hill lies at the y centerpoint of the domain. The value of λb = 10 km, which is representative of the y distance between the strongest convective bands apparent in the radar observations of the 12–13 November precipitation event (Fig. 2a), is also unchanged.
The qc fields of three simulations with sinusoidal columns of h̃ at xb = 20 km (Xb20), xb = 40 km (Xb40), and xb = 60 km (Xb60) in Figs. 9a–c reinforce the idea that the convective response depends on the location of the terrain perturbations. Two bands form over the mountain upslope in each case, with the longest bands forming past the two small-scale valleys in the Xb20 case (Fig. 9a), strong but shorter bands forming past the two hills in the Xb40 case (Fig. 9b), and very weak, short bands again forming past the two hills in the Xb60 case (Fig. 9c). This comparison demonstrates that bands may form past either hills or valleys depending on the position of h̃. The relative impacts of the different h̃ fields in the Xb20, Xb40, and Xb60 simulations are assessed in a fourth simulation (3Xb) that superposes the h̃ fields of all three of these cases so that sinusoidal columns are present at x = 20, 40, and 60 km. The two bands apparent in the qc field in Fig. 9d bear the closest resemblance to those in the Xb40 case (Fig. 9b), suggesting that the column of h̃ at xb = 40 km dominates the convective triggering. This result is consistent with the TH270 and TH270-PA simulations, in which the noise field over a limited area just upstream of the cloud leading edge dictated the overall convective response.
To isolate the flow response to the dominant hills at xb = 40 km, a vertical cross section of w, qc, and the trajectory of a parcel originating at z = 562.5 m in the Xb40 simulation is shown at y = 10 km in Fig. 10a. A pattern of fluctuating velocity perturbations reminiscent of the HILL simulation (Fig. 8c) is apparent near the band leading edge. Moreover, a vertical cross section plotting the same fields past the valleys at y = 15 km in Fig. 10b resembles the y = 10 km cross section in the VALLEY simulation (Fig. 8d). In the upcoming section we examine the dynamical processes that explain these velocity fluctuations and the reasons why bands form past certain obstacles and not others.
5. Dynamics of the rainbands
The region of h̃ that appears to dominate the convective response in the simulations discussed thus far lies just upstream of the nominal leading edge of the orographic cloud. Over this area, the combination of large-scale ascent induced by
The importance of lee waves in triggering convection is demonstrated in Figs. 10c,d, which show w, qc, and parcel trajectories of a simulation (Xb40-DRY) that is identical to the Xb40 case except that RH = 0, which precludes the formation of clouds and convection. The oscillating patterns of upward motion upstream of the clouds in the Xb40 simulation still exist in Figs. 10c,d, suggesting that they are a stable response of the flow to h̃. Thus, the cloud at y = 10 km in the Xb40 simulation is triggered in an elevated lee-wave updraft at x ≈ 47 km (Figs. 10a,c) and the cloud at y = 15 km is triggered in a lee-wave updraft at x ≈ 42 km (Figs. 10b,d).
a. HILL simulation
The dynamics of air parcels in the HILL simulation are illustrated in Fig. 11a, which plots the values of ζ (thin lines, bottom section) and b (heavy lines, top section) along two different parcel trajectories in the x–z plane. One parcel at y = 10 km (solid lines) travels over the small-scale hill and the other at y = 0 (dashed lines) is far enough from the hill to be virtually unaffected by its presence, representing the laminar “reference” flow response in the absence of h̃. The b lines are black where the parcels are unsaturated (N 2 = N 2d > 0) and gray where they are saturated (N 2 = N 2m < 0). Considering first the unperturbed parcel at y = 0, monotonically increasing displacement occurs throughout its trajectory over 30 ≤ x ≤ 60 km. Because the parcel displacement and stability are positive prior to saturation, it accumulates negative buoyancy through (4) until it reaches saturation at x = 47 km. An abrupt shift in ∂b/∂x from negative to positive in Fig. 11a occurs at saturation because the sign of N 2 changes from positive to negative, which reverses the phase relationship between b and ζ in (4) so that the saturated parcel starts to gain buoyancy as it continues to ascend.
Until encountering the hill at x = 40 km, the parcel at y = 10 km in Fig. 11a behaves similarly to the reference parcel at y = 0. As it ascends over the hill (36 < x < 39 km), it accumulates positive ζ and negative b relative to the reference parcel. For convenience we henceforth denote all departures from properties of the reference state at y = 0 as the perturbation fields ζ′, b′, etc., which allows the 3D perturbations associated with h̃ to be separated from the larger-scale 2D signature associated with
If the parcel at y = 10 km remained unsaturated, its lee-wave oscillations would continue as it progressed downstream and its trajectory would resemble that of the Xb40-DRY simulation in Fig. 10c. However, the parcel’s lee-wave circulation abruptly ends at x ≈ 47 km where saturation occurs, N 2 becomes negative, and the phase relationship between ζ and b in (4) reverses. At this point, ζ′ and b′ at y = 10 km are nearly zero, implying that the y-buoyancy gradients that tend to oppose the existing lee-wave circulation are minimal. This is evident in the y–z cross section at x = 47 km in Fig. 11d in which the buoyancy anomalies are weak and diffuse compared to those farther upstream (Fig. 11c) and nearly zero above z = 1 km. As a consequence, the lee-wave circulation present at saturation continues into the cloud. Now that the parcel is saturated and unstable, farther upward motion causes the buoyancy to increase from (4) rather than continue decreasing. Thus b′ becomes positive within the updraft at y = 10 km, which is apparent in Fig. 11a past x = 47 km and in the y–z cross section at x = 52 km in Fig. 11e. Now the counterrotating vortices initiated by the lee wave and their tendencies are phase-locked together, which characterizes a convectively amplifying circulation. The continued growth of this circulation, evident in the cross section at x = 56 km in Fig. 11f, generates a convective rainband past the hill.
b. VALLEY simulation
The flow dynamics of the VALLEY simulation in Fig. 12 contrast strongly with that in the HILL simulation in Fig. 11. While the unperturbed parcel at y = 0 (dashed lines in Fig. 12a) follows a nearly identical relationship between ζ and b as in the HILL case, the perturbation dynamics of the parcel over the valley at y = 10 km (solid lines) are much different. This parcel initially descends over the valley, which creates strongly negative ζ′ and strongly positive b′ over 36 < x < 39 km in Fig. 12a. This generates ξ tendencies in Fig. 12b that strongly oppose the existing circulation, leading to a phase reversal of the lee wave at x ≈ 39 km. The parcel ascends and loses buoyancy over 39 < x < 42 km until saturation occurs at x ≈ 42 km (Figs. 12a,c), approximately 5 km upstream of that in the HILL simulation. More importantly, saturation occurs at a different phase in the lee wave. Whereas the parcel passing over the hill reached saturation with slightly positive ζ′ and slightly negative b′, the parcel over the valley saturates with strongly positive ζ′ and strongly negative b′ (Figs. 12a,c). Thus ∂b/∂y at cloud entry is much stronger and more concentrated near the y centerpoint of the domain than in the HILL simulation, and its stronger associated vorticity tendencies suppress further upward motion past the valley. By x = 47 km (Fig. 12d) the parcel at y = 10 km is no longer ascending, but two updrafts are generated in the rising branches of the buoyancy-induced circulation on either side of the valley (y ≈ 7 km and y ≈ 13 km). Saturated ascent in these areas leads to positive b′ and convective growth, which progressively strengthens as the parcel travels downstream at x = 52 km (Fig. 12e) and x = 56 km (Fig. 12f). From Figs. 8a,b it is apparent that these cloud bands on the flanks of the valley form slightly farther downstream than the single updraft in the HILL simulation.
c. Xb40 simulation
A similar analysis to that outlined above explains why bands form past the hills and not the valleys in the Xb40 simulation (Fig. 9b). The ζ and b values of air parcels passing over a hill at y = 10 km and a valley at y = 15 km are shown in Fig. 13a (along with a reference parcel halfway between them at y = 12.5 km), indicating the opposite phases of these two parcels prior to saturation. Whereas the parcel at y = 10 km rises and loses buoyancy over the hill (36 < x < 39 km), the parcel at y = 15 km sinks and gains buoyancy over the valley. The b′ field at x = 38 km in Fig. 13b creates ξ tendencies that reverse the lee-wave circulation, which is apparent in Fig. 13a over 39 < x < 43 km and in the y–z cross section at x = 42 km in Fig. 13c. As in the VALLEY simulation, the parcel traveling past the valleys in Fig. 13a saturates farther upstream with strongly positive ζ′ and strongly negative b′. Likewise, this parcel is forced downward and does not rise convectively. As in the HILL simulation, the parcel at y = 10 km saturates at x ≈ 47 km with ζ′ ≈ 0 and b′ ≈ 0 (Figs. 13a,d), which allows the existing lee-wave circulation to continue into the cloud. Saturated, unstable ascent causes b′ > 0 past the hills at x = 52 km (Fig. 13e) and the circulation strengthens farther downstream at x = 56 km (Fig. 13f).
The series of hills and valleys in the Xb40 simulation (Fig. 13) produces a stronger convective circulation than either the HILL (Fig. 11) or VALLEY (Fig. 12) simulation alone. This is because the regions of b′ > 0 past the hills are surrounded by b′ < 0 past the valleys, which increases the strength and scale of the circulation beyond that produced by an isolated feature. As a consequence, the Xb40 simulation exhibits stronger upward motion and more rapid increase of b′ past the hills than in the HILL simulation, as well as stronger downward motion and desaturation past the valleys than in the VALLEY simulation. Moreover, the faster initial growth of the convective elements leads to stronger suppression of any convective cells developing between the bands. For example, the two strong bands on the flanks of the valley in the VALLEY simulation, which emerged slightly farther downstream than the single band in the HILL simulation, are unable to develop in the face of strong compensating subsidence from the updrafts on either side. In addition, the enhanced descent past the valleys apparent in Fig. 13d causes low-level desaturation and positive buoyancy anomalies at x = 52 km (Fig. 13e) that tend to reverse the sinking motion in these areas. This shallow lee wave causes uplift and resaturation by x = 56 km (Fig. 13f), but again the growth of this cloud is suppressed by the subsiding environment in which it develops.
The dynamics of the Xb40 simulation, and of the triggering process in general, may be more easily visualized by the 3D plot of the qc = 0.05 g kg−1 contour (light blue surface) and parcel trajectories at y = 10 km and y = 15 km that are colorized to indicate the sign of b′ in Fig. 14. The 3D structure of the orographic cloud demonstrates that saturation first occurs past the valley at y = 15 km, but the cloud does not immediately experience convective growth. This is because the large lee-wave displacements in that region create strongly negative b′, which leads to sinking motion and desaturation past the cloud leading edge. At y = 10 km, the flow saturates with b′ ≈ 0 and consequently continues its saturated, unstable ascent into a convective updraft.
d. A condition for lee-wave triggering
This theory is evaluated in Figs. 15a–c, in which shaded contours of qc in the HILL, VALLEY, and Xb40 simulations are overlaid by the farthest-upstream points where (10) is satisfied. In all three cases, satisfaction of (10) (shown by the black asterisks) accurately predicts the leading edges of bands that, farther downstream, generate high values of qc and darker contours. Note that for this calculation U and N 2m are again given by representative values of 10 m s−1 and −1.5 × 10−5 s−2 (the latter estimated from Fig. 7b). In addition, only the upstream-most triggering points are shown because the complexity of the flow after bands are initiated cannot be described by this simplified parcel theory.
From (10) it readily follows that in weakly moist unstable environments like those in this study, rainbands form more easily over the upslope of a mesoscale ridge than over a nonsloping surface. This is illustrated by the schematic diagram in Fig. 16. Over a nonsloping surface (Fig. 16a), unsaturated parcels require a finite amount of lee-wave displacement ζc to reach saturation, and as a result bc tends to be negative at cloud entry. When |Nm| is small, this negative bc strongly resists convective growth and may force the air to subside and desaturate. Such nonconvective clouds may also develop over a sloping surface (Fig. 16b) when a lee-wave updraft like that at x ≈ 38 km is positioned well upstream of the nominal cloud edge. However, as the air advances up the hill, it becomes progressively more humid and the amount of lee-wave-induced displacement necessary for it to saturate decreases. This allows the oscillating lee wave to resaturate with strongly positive wc yet nearly zero ζc and bc, which from (10) is a more conducive combination for band triggering. Note that in more unstable environments with larger |Nm|, the suppressive effects of negative bc are diminished in (10) and rising air parcels are more likely to continue their ascent after saturating.
6. Sensitivity of rainband locations
The phases of small-scale lee waves at saturation, and thus the locations of orographic rainbands, strongly depend on both atmospheric and terrain-related parameters over a range of horizontal scales. For example, the vertical structures of the lee waves upstream of the orographic cloud are determined not only by h̃, but by the wind speed U and static stability N 2d of the large-scale impinging flow. The location at which the flow saturates also depends on parameters in the upstream sounding profile (e.g., U, N 2d, and RH), as well as the shape of the ridge
As in the Xb40 case (Fig. 9b), the qc field of the Xb45 simulation (Fig. 17a) exhibits two dominant orographic rainbands. However, instead of lying downstream of the two hills in h̃, the bands are now located downstream of the two valleys, reinforcing the idea that both hills and valleys are capable of triggering bands. Plots of ζ and b at y = 10 km (between bands) and at y = 15 km (along a band) in Fig. 18a reveal that, with xb now farther downstream, the strip of nonzero h̃ lies much closer to the leading edge of the cloud. As a result, the ascending flow over the hill at y = 10 km saturates earlier (x ≈ 43 km) than that over the valley at y = 15 km (x ≈ 47 km). However, the parcel over the hill saturates with wc ≈ 0 and bc ≪ 0, a nonconducive combination for the triggering of convection. This is illustrated in Fig. 15d, where the initial triggering points found from (10) are past the valleys rather than the hills. The parcel traveling over the valley saturates with strongly positive wc and bc ≈ 0 (ϕ ≈ 0°), a more favorable cloud-entry phase that satisfies (10) and leads to convective growth downstream.
The influence of larger-scale flow parameters on rainband location is demonstrated by the qc field of the Xb45-RH85 simulation (Fig. 17b), in which the bands return to the same locations relative to the hills as in the Xb40 case. This small reduction in moisture increases the amount of upward displacement necessary for saturation, which consequently alters the nominal cloud location and in turn the phase of the small-scale lee waves at cloud entry. This is shown in Fig. 18b, where the parcel over the hill experiences oscillations until saturating at x ≈ 52 km, while the parcel over the valley saturates at x ≈ 47 km. In this case, the parcels traveling past the valleys have strongly negative bc and weakly positive wc, which from (10) is not conducive for band triggering. The parcels past the hills have just slightly negative bc and nearly maximum wc, which satisfies (10) and leads to band formation past the small-scale hills (Fig. 15e).
7. Conclusions
An observational and numerical investigation into the triggering of convective orographic rainbands by small-scale topographic obstacles has been presented. Radar observations of quasi-stationary rainbands in one event over the Coastal Range in western Oregon are accurately reproduced by a quasi-idealized simulation of the event that uses realistic representations of the upstream flow conditions and the Coastal Range terrain. The simulated bands have similar locations and structures as those in the radar data, indicating that the simulation accurately captures the key dynamical processes leading to band formation.
The numerical simulations are progressively simplified to address the influence of both environmental and terrain-related parameters on band formation. Idealized simulations with uniform wind profiles indicate that the rainbands do not require background vertical shear to develop, and that they tend to align parallel to the low-level flow direction. Simulations with simplified terrain profiles reveal several important aspects of orographic convection, including 1) the small-scale terrain over a limited area just upstream of the leading edge of the orographic cap cloud dictates the convective signature, 2) both small-scale hills and valleys are able to trigger bands, and 3) the locations where rainbands form are very sensitive to large-scale flow conditions and the position of small-scale topographic features relative to the cloud leading edge.
The dynamics by which orographic rainbands are triggered by small-scale topographic obstacles are summarized as follows. As the moist impinging flow is lifted en masse toward saturation by the smooth mesoscale ridge
This threshold relationship between wc and bc may be understood by considering the dynamics of airflow at the leading cloud edge. Oscillating air parcels tend to saturate with positive wc and ζc, the latter of which implies negative buoyancy accumulation (bc < 0) in the statically stable flow upstream of the cloud. Upon entering the unstable cloud, the phase relationship between wc and bc reverses, causing parcels to warm as they continue to ascend. This unstable upward motion does not always lead to convective growth because an initially cold parcel will ultimately sink and desaturate if it stays cold relative to its surroundings (i.e., if its buoyancy anomaly remains negative). Convection thus develops only when wc is sufficiently large for the parcel to overcome its negative bc and become positively buoyant, after which it ascends into an updraft core as it moves downstream.
A full picture of the dynamics of orographic rainbands requires a physical understanding of not just the band formation process but also the preferred spatial scales of the bands. The latter is a complex issue that is addressed in a follow-on study currently underway that, like this study, uses a combination of numerical simulations and analytical theory. Because the theories developed here are based on just a single event over the Coastal Range, future efforts will also focus on applying these concepts to other cases of banded orographic convection over the Coastal Range, as well as to banded convection over other mountain ranges around the world.
Acknowledgments
The work performed by Daniel Kirshbaum is supported by NCAR’s Advanced Study Program (ASP) and that performed by D. R. Durran is supported by the National Science Foundation under Grants ATM-0225441 and ATM-0506589. The authors thank Chris Snyder, Chih-Chieh (Jack) Chen, and Kristen Corbosiero of NCAR for their contributions. We also thank the two anonymous reviewers for their insightful comments and suggestions.
REFERENCES
Bryan, G. H., and J. M. Fritsch, 2002: A benchmark simulation for moist nonhydrostatic models. Mon. Wea. Rev., 130 , 2917–2928.
Cosma, S., E. Richard, and F. Miniscloux, 2002: The role of small-scale orographic features in the spatial distribution of precipitation. Quart. J. Roy. Meteor. Soc., 128 , 75–92.
Dirks, R. A., 1973: The precipitation efficiency of orographic clouds. J. Rech. Atmos., 7 , 177–184.
Douglas, R. H., 1964: Hail size distributions. Proc. Conf. on Radio Meteorology and 11th Weather Radar Conf., Boulder, CO, Amer. Meteor. Soc., 146–149.
Durran, D. R., and J. B. Klemp, 1982: On the effects of moisture on the Brunt–Väisälä frequency. J. Atmos. Sci., 39 , 2152–2158.
Durran, D. R., and J. B. Klemp, 1983: A compressible model for the simulation of moist mountain waves. Mon. Wea. Rev., 111 , 2341–2361.
Elliott, R. D., and E. L. Hovind, 1964: The water balance of orographic clouds. J. Appl. Meteor., 3 , 235–239.
Fuhrer, O., and C. Schär, 2005: Embedded cellular convection in moist flow past topography. J. Atmos. Sci., 62 , 2810–2828.
Houze, R. A., 1993: Cloud Dynamics. Academic Press, 573 pp.
Kirshbaum, D. J., and D. R. Durran, 2004: Factors governing cellular convection in orographic precipitation. J. Atmos. Sci., 61 , 682–698.
Kirshbaum, D. J., and D. R. Durran, 2005a: Atmospheric factors governing banded orographic convection. J. Atmos. Sci., 62 , 3758–3774.
Kirshbaum, D. J., and D. R. Durran, 2005b: Observations and modeling of banded orographic convection. J. Atmos. Sci., 62 , 1463–1479.
Klemp, J. B., and R. Wilhelmson, 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35 , 1070–1096.
Lilly, D. K., 1962: On the numerical simulation of buoyant convection. Tellus, 14 , 148–172.
Miniscloux, F., J. D. Creutin, and S. Anquetin, 2001: Geostatistical analysis of orographic rainbands. J. Appl. Meteor., 40 , 1835–1854.
Wicker, L. J., and W. C. Skamarock, 2002: Time splitting methods for elastic models using forward time schemes. Mon. Wea. Rev., 130 , 2088–2097.
Yoshizaki, M., T. Kato, Y. Tanaka, H. Takayama, Y. Shoji, and H. Seko, 2000: Analytical and numerical study of the 26 June 1998 orographic rainband observed in western Kyushu, Japan. J. Meteor. Soc. Japan, 78 , 835–856.
Real and idealized sounding data. (a) Radiosonde at 0000 UTC 13 Nov 2002 from Quillayute during the Coastal Range orographic precipitation event, and (b) a simplified version of (a) used in the idealized experiments. In these skew T–logp plots, temperature is the thick black line, dewpoint is the thick gray line, dry adiabats are thin solid lines, moist adiabats are thin dashed lines, and wind barbs with flags at intervals of 10 m s−1 are shown to the right.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Comparison between radar observations and simulated reflectivity fields. (a) Radar reflectivity field at 2003 UTC 12 Nov 2002 over Coastal Range, (b) cropped image of (a) over study area, (c) simulated reflectivity from CTL simulation, and (d) simulated reflectivity from IDEAL simulation. Grayscale topographic contours are in intervals of 250 m and overlaid reflectivity lines are contoured in intervals of 5 dBZ.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Topography of northwestern Oregon. (a) Raw data imported from Gtopo30 at 1/120° resolution; (b) 160 km × 40 km section of topography [corresponding to the boxed area in (a)] interpolated to Cartesian grid with Δh = 500 m; (c) same as in (b), but with topography from 0 ≤ y ≤ 40 mirrored over 40 < y ≤ 80 km; and (d) same as in (c), but with 6Δx filter applied.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Comparison between CTL and TH270 simulation, as well as vertical slices through the TH270 simulation. Cloud liquid water field at t = 4 h and z = 1.5 km overlying shaded topography in 250-m intervals of (a) CTL simulation and (b) TH270 simulation. Contours of qc are in intervals of 0.4 g kg−1. (c) Vertical cross sections of ω (thin lines, solid for ω > 0, and dashed for ω < 0) and qc (0.001 and 0.4 g kg−1) along line A–A′ at y = 15 km and (d) along line B–B′ at y = 12 km. Contours of ω are −1, −0.5, −0.2, −0.1, 0.1, 0.2, 0.5, 1, and 2 m s−1.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Decomposition of Coastal Range topography into (a)
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Same as in Figs. 4b–d but for TH270-PA simulation.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Cross sections of NoHs simulation. (a) Cloud water qc at 0.1 g kg−1 overlying shaded topography at 250-m intervals at t = 4 h and z = 1.5 km. (b) Squared Brunt–Väisälä frequency in solid lines for positive values and dashed for negative values, with labeled contour values multiplied by 10−4 s−2. Cloud outline, as estimated by 0.001 g kg−1 contour, is shaded.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Horizontal cross sections of qc at z = 1.5 km of (a) HILL and (b) VALLEY simulations. Vertical cross sections at y = 10 km of ω, cloud outline, and the forward trajectory of parcel originating at z = 562.5 m of (c) HILL and (d) VALLEY simulations. Grayscale topography in (a), (b) is contoured at 250-m intervals, with h̃ also contoured by lines at 25-m intervals (solid for positive values, dashed for negative values). The qc contours in (a), (b) are the same as in Fig. 4a, and the ω and qc contours in (c), (d) are the same as in Figs. 4c,d.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Cloud water qc of (a) Xb20, (b) Xb40, (c) Xb60, and (d) 3Xb simulations at t = 4 h and z = 1.5 km. Contours of qc are the same as in Fig. 4a. Shaded contours of h are in intervals of 250 m. The small-scale topography h̃ is shown in 25-m contour intervals, with positive values in solid lines and negative values in dashed lines.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Vertical cross sections of ω and qc of the Xb40 simulation at (a) y = 10 km and (b) y = 15 km. Contours of w and qc are the same as in Fig. 4c,d. Arrowed lines overlaid on the two panels are forward trajectories of air parcels that originate at z = 562.5 m. (c), (d) Same as in (a), (b) but for moisture-free Xb40-DRY simulation.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Dynamical analysis of HILL simulation, showing (a) ζ (thin, lower section) and b (thick, upper section) curves at y = 10 km (solid lines) and y = 0 (dashed lines). Portions of the b curves in black (gray) correspond to unsaturated (saturated) flow. Underlying topography is shown for illustrative purposes and is not to scale. Cross sections in the y–z plane of cloud outline (shaded), b′ (thin lines, solid for b′ > 0, and dashed for b′ < 0), plane-parallel velocity vectors (arrows), and heights of parcels originating at z = 562.5 m (solid quasi-horizontal line) at (b) x = 38 km, (c) x = 42 km, (d) x = 47 km, (e) x = 52 km, and (f) x = 56 km. Vorticity tendency directions in (b)–(f) are shown by thick semicircles with arrows.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Same as in Fig. 11, but for VALLEY simulation.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Same as in Fig. 11, but for Xb40 simulation. (a) The parcel at y = 10 km is the solid line, the parcel at y = 12.5 km is the dashed line, and the parcel at y = 15 km is the dashed–dotted line.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Three-dimensional diagram of band formation in the Xb40 simulation. The underlying terrain is green, and the qc = 0.05 g kg−1 contour is light blue. Parcel trajectories at y = 10 km and y = 15 km overlaid on these fields are red (blue) when the parcel’s buoyancy is positive (negative) relative to the nodal line at y = 12.5 km.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Prediction of rainband locations using the criteria (10) for (a) HILL, (b) VALLEY, (c) Xb40, (d) Xb45, and (e) Xb45-rh85 simulations. Cloud water in grayscale is contoured at 0.001 and 0.04 g kg−1, small-scale terrain h̃ is contoured at 25-m intervals, and the farthest-upstream triggering locations are shown by black asterisks.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Schematic diagram of the differences in cloud formation between (a) nonsloping and (b) upward-sloping terrain in marginally conditionally unstable flow over a small-scale hill.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Same as in Fig. 9 but for (a) Xb45 and (b) Xb45-RH85 simulations.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
Same as in Fig. 11a, but for (a) Xb45 and (b) Xb45-RH85 simulations.
Citation: Journal of the Atmospheric Sciences 64, 5; 10.1175/JAS3924.1
The conversion algorithm is provided by Douglas (1964): Z = 2.4 × 104 (ρdryqr)1.82, where ρdry = (p − e*)/(RdT), T is the air temperature, Rd the specific gas constant for dry air, p the air pressure, e* is the saturation vapor pressure of water at T, and qr is the rainwater mixing ratio.
