1. Introduction
Mountains dramatically influence the airflow, clouds, and precipitation (e.g., Lin 2007; Houze 2012). The distribution of precipitation on opposite sides of a mountain crest is of great practical importance in regions of complex terrain, especially if that mountain crest is a significant watershed divide (e.g., Roe 2005). The detailed cross-mountain distribution and amount of precipitation primarily depends on terrain geometry (height, width, and barrier length), but for a given mountain range, it depends on both dynamical and cloud microphysical factors (Sinclair et al. 1997; Chater and Sturman 1998; Smith and Barstad 2004).
The two most important dynamical factors are the potential of the low-level air mass to cross the mountain barrier (Smolarkiewicz et al. 1988; Jiang and Smith 2003; Colle 2004), and the potential for convection to emerge from the lifted air mass (Kirshbaum and Durran 2004; Kirshbaum et al. 2007). The first factor is evaluated in terms of the bulk Froude number (Fr, i.e., the ratio of the cross-mountain wind speed to the mountain height and the Brunt–Väisälä frequency). Blocked flow (Fr < 1) tends to move the precipitation upwind of the barrier (Smolarkiewicz et al. 1988; Rotunno and Houze 2007). Terrain-induced gravity waves in stratified flow can affect the spatial distribution of precipitation, generally shifting precipitation upwind (Colle 2004; Medina et al. 2005).
Orographic convection is not uncommon in winter storms (e.g., Marwitz 1980; Lee 1984; Steenburgh 2003; Shafer et al. 2006; Kumjian et al. 2014). Shallow, small-scale convection often occurs during cold-air advection in postfrontal flow (e.g., Abbs and Jensen 1993; Kusunoki et al. 2004; Colle et al. 2008; Geerts et al. 2011; Cunningham and Yuter 2014), notwithstanding the limited surface heat flux in winter. This convection is not embedded in stratiform precipitation, and is largely contained within a well-mixed layer above the surface, so we refer to it as boundary layer (BL) convection. This convection may be present well ahead of the mountain barrier and may become deeper and/or more gregarious as it ascends the terrain (e.g., Fig. 9.21 in Lackmann 2011). In other cases potential instability is released as stratified flow ascends a barrier, resulting in purely orographic convection. On the smaller side of the spectrum, such elevated convective cells emerging from a stratiform cloud deck are often referred to as generating cells because they generate ice particles that grow at lower levels (e.g., Rosenow et al. 2014; Kumjian et al. 2014). The distribution of precipitation from such cells across a mountain depends on the location of convection initiation relative to the crest, as well as the ambient wind speed and mountain width.
Cloud microphysical factors in cold clouds relate to droplet concentrations, ice crystal concentrations, and, related to the first two parameters, hydrometeor fall speed, that is, terminal velocity (e.g., Fraser et al. 1973; Saleeby et al. 2011). The dynamical factors controlling snow growth, transport, and sedimentation across a mountain are more first order, less subtle than the microphysical factors; therefore, this study addresses dynamical factors only.
Few direct measurements of the actual hydrometeor streamlines in orographic storms exist. In this study, a unique observational tool is used, the airborne 95-GHz Doppler radar, the Wyoming Cloud Radar (WCR), with fixed beams pointing to zenith, nadir, and slant forward (Damiani and Haimov 2006). The synthesis of the nadir and slant-forward Doppler velocities provides a direct measurement of the two-dimensional motion below the flight track.
The following are the specific goals of this study: 1) to document vertical velocity, radar reflectivity, and hydrometeor streamline patterns over a mountain range, in order to better understand snow growth mechanisms in winter storms, and 2) to examine reflectivity profiles on opposite sides of the mountain crest, in order to learn how an upstream flow and stability conditions affect snow growth, transport, and sedimentation across a mountain range.
The outline of this paper is as follows. The instruments, flight strategy, and analysis technique are described in section 2, and the upstream atmospheric conditions for all storms are summarized in section 3. In section 4, four case studies are presented. Three orographic flow and precipitation distribution patterns are distinguished in section 5. The main findings are summarized in section 6.
2. Experimental design, instruments, and analysis technique
a. Flight pattern
The mountain targeted in this study is the Medicine Bow (MB) range in Wyoming, which sits on a ~2.0-km-high plain, and peaks at an elevation of 3661 m (Fig. 1). Its main axis is meridionally oriented, >100 km long, and its zonal width is ~50 km. The primary dataset used in this study was collected aboard the University of Wyoming King Air (UWKA) research aircraft flying along the prevailing wind over the MB range in Wyoming in winter storms in early 2006, 2008, 2009, and 2013. On each of the 16 flights used herein, at least two geographically nearly identical transects were flown over the MB range, in a direction that by design was aligned with the mean low-level wind. With the exception of the flights in 2006, all flights were intended primarily to evaluate weather modification activities, and most of the flight time was dedicated to other flight patterns (Pokharel and Geerts 2014). This explains why relatively few along-wind flight legs were flown in most cases (Table 1), and why these legs were relatively short.
Terrain map around the Medicine Bow range in south-central WY, and flight tracks on 16 days, labeled YYYYMMDD.
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
Summary of the 16 flights used in this study. The capital letters following the date in the first column refer to cases A–D. The precipitation types in the fourth column elevated convection present (EL-C), boundary layer convection present (BL-C), and stratiform precipitation (STRF), as detailed in the text. In the fifth column, A refers to aircraft soundings upwind of the mountain, and R to radiosondes released at the airport in Saratoga (Fig. 1). The LCL in column 6 is the sounding-based lifting condensation level. The PUD in column 7 is the depth of the potentially unstable layer. It is shown only if a significant layer (at least 200 m deep) is potentially unstable. In column 8, α is the angle between the flight legs and the mean wind direction between the surface and flight level (positive if the wind direction is clockwise relative to the flight direction). The wind speed U, the bulk Brunt–Väisälä frequency Nb, and the bulk Froude number Fr are calculated over a depth from the valley floor to mountaintop level.
b. Data sources
The UWKA carried a series of in situ probes, measuring 3D wind, temperature, humidity, pressure, precision aircraft position, liquid water content, and the concentration and size distribution of droplets and ice particles. These data show that all storms included in this study are mixed phase; that is, they contain both ice and supercooled droplets. The main instrument on the UWKA was the WCR, described below.
A radiosonde was released from the Saratoga airport located some 30 km upstream of the MB range (Fig. 1), for each flight in 2008, 2009, and 2013. No radiosondes were available in 2006; instead, the UWKA conducted a missed approach into Saratoga airport, yielding two soundings between the near surface and ~4.2 km above mean sea level (MSL). A drawback of aircraft soundings is that more low-level horizontal variability (e.g., due to gravity waves) may be included into the profiles as the aircraft descends–ascends over a larger horizontal distance than typical radiosonde balloon tracks.
c. Vertical-plane dual-Doppler synthesis
The UWKA was equipped with the WCR, a 3-mm (95 GHz) multiantenna Doppler radar (Wang et al. 2012). In this study the fixed beams pointing to zenith, nadir, and slant forward are used. The latter two beams have a 30° along-track separation (see Fig. A1 in Geerts et al. 2006). The main advantage of airborne vertical-plane dual-Doppler VPDD) data collected along the prevailing wind is that the VPDD vector field represents the true horizontal and vertical motion of hydrometeors. Thus, in contrast with dual-Doppler data from volume-scanning ground-based radars, the vertical hydrometeor motion is measured directly. Two other advantages of airborne vertical-incidence radar data over scanning ground-based radar data are that data can be collected very close to the surface, even in complex terrain, and that the aircraft can cover a long distance over a short period. Along-wind flight tracks have the specific advantage that the nadir and slant-forward beams are aligned and sample the same air parcels, since the along-track wind component dominates. Thus, the accuracy of VPDD is higher than in a crosswind direction.
Details concerning the technique and accuracy of VPDD synthesis aboard the UWKA can be found in Damiani and Haimov (2006). The conceptual basis of the airborne VPDD synthesis is that a specific volume is illuminated by two nonparallel beams within short separation in time (linear function of range). The radial velocities from the beams are then synthesized to provide orthogonal components of the velocity of echoes in the specific volume. Even for millimeter-wave “cloud” radars, the reflectivity is dominated by the largest particles (i.e., the snow or graupel particles), in the winter storms examined here, not cloud droplets. Doppler velocity measurements are weighted by the reflectivity of individual particles within an illumination volume. Thus, the radial Doppler velocities are biased toward the motion of the larger hydrometeors.
A common grid is designed in which the data from two beams are merged, before synthesis. Since the flight legs are sufficiently straight for all flights (Fig. 1), the grid layout is construed as a two-dimensional (2D) vertical plane, by projecting the 3D data from the two beams onto this vertical plane along the average flight track. Any aliased Doppler data from either beam are unfolded before further processing. To account for the hydrometeors’ spatial shift during the time separation between the beams illuminating them, a grid advection scheme using the mean winds at flight level is selected (Damiani and Haimov 2006). The advected distance is very small (<30 m) since the time separation between the two beams is just 6 s per 1 km of range. The data from the two beams then are assigned to grid cells according to their proximity, using an inverse distance weighting interpolation (Damiani and Haimov 2006).
The radial velocities measured by the two beams are only two components of the 3D velocity vector. Aircraft attitude changes, especially roll angle, such that the two beams are forced out of vertical plane, can produce an erroneous reading of the in-plane velocity due to the contamination of the radial velocities by the across-plane wind. To reduce the error due to possible contamination from the cross-track wind component, the dual-Doppler solver utilizes an a priori guess of the crosswind (Damiani and Haimov 2006). This crosswind profile is derived from the upwind soundings (section 2b). In general, only straight and level flight legs are used in this analysis, and several along-wind legs were excluded because of locally large roll angles.
The use of sounding data for this purpose, rather than flight-level winds, is justified by the considerable directional wind shear typically present between the surface and the flight level [e.g., Fig. 3 in Geerts et al. (2011); Fig. 4 in Chu et al. (2014)]. The use of sounding winds generally results in small area-average corrections in dual-Doppler motion. An evaluation of the impact of sounding data, using several theoretical along-track and cross-track wind profiles and real aircraft attitude variations, can be found in Yang (2014); in all cases, the spatially averaged change in along-track motion (vertical motion) was less than 1 m s−1 (0.1 m s−1).
For along-wind tracks, the streamlines of hydrometeor motion across the mountain range can be visualized as lines tangential to the VPDD velocity vectors. It should be noted that these streamlines are based on a quasi-instantaneous vector field; thus, they do not represent the time-integrated paths (or “trajectories”) of hydrometeors. Streamlines become trajectories only if the flow is steady. The Doppler velocity is biased toward the larger particles in a radar resolution volume. Differences in fall speed may exist between particles of different sizes, although the fall speed of unrimed snow is rather size insensitive (e.g., Locatelli and Hobbs 1974). The VPDD streamlines do not represent the motion of air nor of cloud droplets, whose fall speed is negligible.
3. Ambient conditions of the orographic snow storms
This study uses WCR data from 61 transects collected on 16 flights across the MB range between 2006 and 2013. The mean tracks for multiple transects on each flight are shown in Fig. 1. These tracks were oriented within 20° of the direction of the mean wind between the surface and flight level, as determined by an upwind sounding (Table 1). A diversity of snow distributions and flow patterns was observed on these 15 days over the MB range. The clouds were often confined to the mountain range. The storms were rather shallow, with mean WCR echo-top heights over the mountain ranging between 4.1 and 6.6 km above mean sea level (Table 1 in Geerts et al. 2011). The WCR vertical velocity transects revealed a 0.5–1.0-km-deep turbulent planetary BL (PBL). The cloud base was below mountaintop level in all cases, ranging from 2.3 to 2.8 km MSL, and the cloud base temperature was below −5°C in all storms; thus, hydrometeor growth was controlled by cold cloud processes.
The flights were conducted under southwesterly-to-westerly flow in 2006 while the flow was from west to northwest during the other flights (Fig. 1). Under southwesterly flow, the stability and wind profiles may be affected by a neighboring mountain, the Sierra Madre (Fig. 1). Relatively steady surface weather conditions were observed during most flights. The average wind speed below mountaintop level (U) was quite strong, ranging between 11 and 22 m s−1.
The bulk Brunt–Väisälä (BV) frequency (
Nondimensional mountain height plotted against aspect ratio of an isolated mountain, for the 16 flights listed in Table 1. The inset image shows the mountain scale in the (a) along- and (b) across-wind directions. [Diagram adapted from Smith (1989).]
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
Stability and wind shear vary with height, and thus wave energy can be trapped at some level. Trapped waves in the lee of a 2D mountain have been examined using a two-layer fluid (e.g., Scorer 1949; Durran 2003a). The necessary condition for trapped lee wave development is a decrease of 
4. Cases studies of hydrometeor flow patterns across the mountain
We now illustrate the horizontal and vertical wind, the reflectivity distribution, and hydrometeor transport pattern across the MB range in relation to upwind conditions in four distinct storms, before generalizing findings for all storms in section 5.
a. Case A: 18 January 2006
Data from the 18 January 2006 flight (referred to as case A) have also been studied by Geerts et al. (2011) and Vali et al. (2012), both for different purposes. A short sounding collected aboard the UWKA near Saratoga, upwind of the MB range, around 2000 UTC, is shown in Fig. 3a. A southwesterly low-level jet (LLJ) with a peak wind speed of 22 m s−1 is evident in the wind profile, between 2.5 and 3.2 km MSL [0.4–1.1 km above ground level (AGL)], possibly in part due to flow acceleration in the lee of the Sierra Madre (Fig. 1). Synoptically, warm air was advected by a strong SW flow at 700 hPa in response to a deep low to the north.
Skew T diagrams near Saratoga (Fig. 1), upwind of the mountain for cases (a) A on 18 Jan 2006, (b) e B on 11 Feb 2008, (c) C on 26 Jan 2006, and (d) D on 29 Jan 2013.
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
While the average upstream low-level wind speed was quite strong (18 m s−1), the bulk Froude number below mountaintop level was around unity only (Table 1) on account of high low-level static stability (Figs. 4a and 5a). The layer below 2.8 km MSL was rather stable. This layer may have been channeled around the MB range (Fig. 1). Between 2.8 and 3.5 km MSL, θe was rather constant and the flow more westerly; this layer clearly was unblocked. Between 3.5 and 4.3 km MSL, θe decreased with height, implying that potential instability could be released in the strong current ascending the MB range.
Potential temperature and wind profiles for the four soundings shown in Fig. 3. The solid (dashed) lines represent (equivalent) potential temperature. The wind profiles are shown on the right for each case. A long barb equals 10 kt (1 kt = 0.51 m s−1). The “mountaintop” is the height of Medicine Bow Peak.
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
Vertical profiles of the squared Scorer parameter, l2 (solid line) and the squared BV frequency ( N2, dashed line), for the four soundings in Fig. 3. The dry BV frequency is shown; but in saturated layers, the moist BV frequency is plotted.
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
Two of the five along-wind WCR transects flown in case A over the MB range are shown in Fig. 6. The top panels show radar reflectivity, obtained from the WCR profiling antennas above and below flight level. This level was at 4.2 km MSL in the first transect, and almost 1 km higher in the second, flown nearly 1 h later (Figs. 6a,d). The horizontal black belt across the storm is the radar’s blind zone, centered at flight level. In this and all other transects, the flow is from left to right. In this case deep orographic clouds produced snowfall across the mountain range, while it remained dry in Saratoga during the flight.
WCR data for two transects flown on 18 Jan 2006 (case A). (a),(d) Reflectivity above and below flight level, respectively. The black belt is the radar blind zone centered at flight level. (b),(e) Hydrometeor vertical motion above and below flight level, respectively. Positive is upward. Note that the WCR vertical velocity color key is centered at −1 m s−1 rather than at 0 m s−1, such that the color field can be interpreted as air vertical motion, assuming a snowfall speed of 1 m s−1. The air vertical velocity, measured by a gust probe, is also shown at flight level, with a color scale centered at 0 m s−1. (c),(f) Dual-Doppler synthesized along-track horizontal wind below flight level. The horizontal axes are labeled in terms of flight time (UTC, top and middle panels)) and distance relative to the mountain crest (bottom panels. In all panels, the solid black lines are hydrometeor streamlines derived from dual-Doppler synthesis. In this and other transects, the flow is from left (west) to right (east).
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
Figures 6b and 6e show hydrometeor vertical velocity transects. The WCR vertical velocity color key is centered at −1 m s−1 rather than at 0 m s−1, such that the color field can be interpreted as air vertical motion, assuming a fall speed of (unrimed) snow of 1 m s−1. The air vertical velocity, measured by a gust probe, is shown at flight level, within the WCR blind zone. Its color scale is centered at 0 m s−1. Other than the 1 m s−1 offset for the WCR, both vertical velocity fields have the same color scale, and the cold (warm) colors can be interpreted as updrafts (downdrafts). The air mostly rises (sinks) on the upwind (lee) side of the mountain. The updraft–downdraft boundary is located near the crest and does not noticeably tilt windward with height. Finescale turbulent eddies are present near the ground, marking the PBL.
The WCR dual-Doppler horizontal (along track) wind speed is shown in Figs. 6c and 6f. Note the difference in vertical scale between Figs. 6c and 6f, on account of the higher flight level for the second transect. In this case the along-track wind in the lowest 1 km is substantially weaker, in part due to turbulent momentum exchange, in part because the wind has a ~35° angle into the transect (yielding a 18% reduction of the full wind speed) (Fig. 4a). The LLJ evident over Saratoga (Fig. 3a) continues over the MB range, at about the same height [~(0.5–1.0) km AGL]. The LLJ clearly follows the terrain contour (Figs. 6c,f), suggesting momentum conservation in stratified flow. A careful comparison between the location of the updrafts in the PBL (Figs. 6b,e) and the horizontal wind minima near the base of the LLJ in both transects shows that eddy updrafts at the base of the LLJ are associated with weaker cross-mountain along-track winds; in other words, the LLJ is eroded from below near the PBL top. The depth of the turbulent PBL can be estimated from the change in power spectrum of WCR vertical velocities as a function of height above ground level (Geerts et al. 2011). It is about 1.0 km in this case.
Elevated convection materialized over the mountain, as evident from the WCR transects: the spatial scale and strength of the vertical motions above flight level are indicative of convection, especially in the second transect, within ~10 km from the mountain crest (Fig. 6e). The texture of the reflectivity field in the same region corroborates this interpretation, with towers of higher reflectivity separated by nearly snow-free regions (Fig. 6d). Ice is often generated in such elevated convection, or the typically smaller “generating cells” aloft, due to the strong updrafts and resulting high LWC (e.g., Plummer et al. 2014; Kumjian et al. 2014). This convection was not rooted in the PBL. Rather, it appears to be the result of elevated potential instability release due to ascent over the mountain (Fig. 4a). This convection was not suppressed because there was no windward-tilting band of deep subsidence (Figs. 6b,e). The WCR reflectivity pattern (Figs. 6a,d) shows that much snow growth occurs in the deep, broad updraft upwind of the mountain crest, as well as in the smaller convective updrafts. The bulk of the snowfall reaches the ground only in the lee.
The streamlines below flight level in all panels of Fig. 6 are lines tangential to the VPDD wind vectors. These lines represent the 2D directional motion of hydrometeors. In the absence of the mountain, the streamlines would have a rather constant slope, becoming steeper near the ground on account of the lower wind speed there (Fig. 6c). The kink in the streamlines above the crest, mainly in the first transect, highlights the transition from mostly lofted snow on the windward side to rapidly settling snow on the lee side. Reflectivity values decrease to very low values near the downwind echo edge, and streamlines terminate along this edge, ~(20–25) km downwind of the crest. This indicates sublimating snow. At low levels the snow is carried farther in the lee, producing a snow “foot,” mainly because of the LLJ. The hydrometeor streamlines terminating on the mountain crest, and those reaching the ground 10 km downwind of the crest, are isolated for the two transects in case A (Fig. 7a). We refer to the former streamlines as “critical lines,” from a watershed perspective. A more vertical critical line implies less transfer of snow grown on the upwind side toward the lee. A more horizontal critical line may imply, other things being equal, more low-level snow growth on the windward side and more snow deposition in the lee.
Hydrometeor streamlines terminating at the mountaintop (red lines) and 10 km downwind of the crest (blue lines) for two transects for cases (a) A, (b) B, (c) C, and (d) D. The x-axis origin is at the mountain crest; positive is in the lee (east). The scale and aspect ratio are the same for all panels.
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
The wind pattern across the mountain does not change substantially between the two transects (Figs. 6c,f). The transition from mostly updrafts (blue in Fig. 6e) to mostly downdrafts (red) is more gradual in the second transect, and thus the streamlines gradually steepen across the crest, without a clear kink. This is probably due to the terrain: the early transect crosses a high ridge called the Snowy Range (Fig. 1), while the later transect remains just south of this ridge. Farther in the lee, the downdrafts (Figs. 6b,e) and the streamline slopes (Fig. 7a) are about the same. The increase in streamline slope near the mountain crest is both persistent (present on all five transects flown on this flight) and significant, as it distinguishes prevailing updrafts from downdrafts.
The generating cells aloft contributed to significant snow growth near the crest and in the lee during this storm, as is evident in Fig. 6. The presence of cells in the lee can be explained simply by the convective growth cycle time scale, being not insignificant compared to the advection time scale across the mountain. But it is likely that little of this snow reached the ground in the downwind valley, given the sublimation signature mentioned above. In other words, the precipitation efficiency (defined as the fraction of liquid or frozen water produced over the mountain to the surface precipitation across the mountain) of this orographic storm likely was low, as is typical for summertime orographic convection in the western United States (e.g., Demko and Geerts 2010). To quantify the distribution of hydrometeors across the crest, the distribution of reflectivity is composited with height for all five transects collected for case A, on the windward side and, separately, on the lee side. These frequencies are then normalized by all counts (all levels, all reflectivity bins), such that the sum of all bin values in two dimensions equals 1. The difference of normalized frequencies (lee minus windward values) is shown on a frequency-by-altitude display (FAD) in Fig. 8a. Height is expressed above local ground level, not only to maintain an equal maximum sample size at all levels, but also to examine growth processes relative to the ground and to estimate near-surface precipitation.
Difference in reflectivity (Z) frequency between lee and upwind sides (lee − upwind), plotted by altitude AGL for cases (a) A, (b) B, (c) C, and (d) D. The solid (dashed) line is the mean reflectivity profile for the lee (upwind) side. The snow rate (S) is shown in the top abscissa and is inferred from S = 0.11Z1.25 (Matrosov 2007). The number of flight transects in the composite is listed. (e),(f) The mean WCR vertical velocity profiles for the four cases, both upwind (dashed) and in the lee (solid).
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
The WCR near-surface reflectivity gives a first-order estimate of surface snowfall rate (e.g., Pokharel et al. 2014a). Also, the reflectivity at any level is proportional to the snow mass mixing ratio, according to an experimental relationship developed for winter storms over the MB range using in situ probes and close-gate WCR reflectivity data (Pokharel and Vali 2011). Both the hydrometeor sedimentation rate and mixing ratio estimates are quite uncertain, mostly because of uncertainty in snow density (Rasmussen et al. 2003), but in general, an increasing W-band reflectivity generally implies a higher snowfall rate and a higher snow mass (Matrosov 2007; Geerts et al. 2010; Pokharel and Vali 2011). The black lines in Fig. 8a show mean reflectivity profiles on both sides of the mountain crest. These lines can be used to evaluate mean snowfall rate, shown in the upper abscissa in Fig. 8a. Note that the mean near-surface reflectivity should not be interpreted as a measure of total snowfall on either side of the mountain. Total instantaneous snowfall could be estimated by integrating along the flight path, but we refrain from taking such an extra step, given that many transects do not cover the entire mountain range (Fig. 1).
In case A the surface snowfall rate is higher in the lee, on account of the strong winds advecting snow downslope (the snow foot) (Fig. 8a). Yet the flow is mostly subsident in the lowest 2 km (Fig. 8e), on average −1 m s−1 (in addition to a 1 m s−1 estimated fall speed), leading to sublimation. Updrafts persist in the lee above 2 km AGL due to the generating cells. Between 1 and 3 km AGL, both low- and high-reflectivity values tend to be more common in the lee. This broader spread in reflectivity (and velocity; not shown) is due to generating cells and their fall streaks. The very low reflectivity values are the interstitial areas between generating cells. This is consistent with the observed short-lived convective cells over the MB range.
b. Case B: 11 February 2008
The 11 February 2008 flight (referred to as case B) took place in postfrontal conditions with cold-air advection (Fig. 3b). The cold-air advection, the strong winds, and the time of day (2100 UTC) are all consistent with a deep mixed layer, up to ~3.0 km MSL at Saratoga (Fig. 4b). The surface air was rather dry, yielding a high LCL, near the top of this deep PBL (Table 1). The air was drier above the deep PBL, resulting in potential instability above the PBL. The atmosphere was more stable above flight level (4.2 km), but θe remained almost constant with height up to an inversion starting at 6.3 km MSL (just above the maximum level shown in Fig. 4b). This inversion and dry air aloft clearly capped the cloud tops. The BV frequency and Scorer parameter were rather small below this inversion (Fig. 5b). The low-level wind was strong, 16 m s−1, pushing the PBL air mass over the mountain (Fr > 1).
Again, two along-wind WCR transects are analyzed (Fig. 9). In this case the transects were flown early and late in the flight, hence the large time separation between them, just over 3 h. The transects were oriented northwest (NW)–southeast (SE) and aligned rather well with the mean wind (Table 1). The echo and vertical velocity structure in both transects reveal small-scale, mostly shallow convection. Convective towers (Fig. 9, top) appear to grow over the higher terrain and then drift in the lee, but decreasing amounts of precipitation reach the ground in the lee, as is evident from the low-level reflectivity decrease toward the ground, especially farther downwind in the second transect. Unfortunately, the flight legs did not extend to the downwind echo edges. The vertical motion field (Fig. 9, middle) reveals low-level turbulence and terrain-driven updraft–downdraft dipoles across smaller-scale ridges surrounding the MB range. These velocity dipoles are shallow, possibly because l2 is quite small at low levels (Fig. 5b). As in case A, there is no clear evidence of deep windward-tilting gravity waves. Rather, regularly spaced convective updrafts are evident mainly upwind of the crest. Unlike case A, these updrafts are found mainly at low levels. (Some updrafts and echoes reached higher, to ~6 km MSL, in the first transect.) Although many convective cells are deeper than the PBL in this case (~1 km deep, but ill-defined), we refer to this as BL convection (BL-C), because the convection is rooted and largely contained in the PBL (Table 1).
As in Fig. 6, but for two transects flown on 11 Feb 2008 (case B).
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
The horizontal flow is rather continuous across the mountain (Fig. 9, bottom). In both transects the along-track wind tends to be much weaker within the ~1-km-deep PBL than aloft, as in case A. There is little flow acceleration across the crest. The cross-mountain wind is much weaker in the second transect. This weakening of the flow and of the storm in general is consistent with synoptic changes over the 3-h period.
The hydrometeor streamlines again reveal a kink across the crest (Figs. 9c,f and 7b). The increase in reflectivity toward the crest on the upwind side in both transects likely is due to particle growth along a nearly horizontal trajectory. The low-level reflectivity peaks at the crest due to the strong downdraft just to the lee of the crest, resulting in sublimation. The critical lines have a rather shallow slope (Fig. 7b), on account of the prevailing updrafts on the windward side. One may wonder why the streamlines do not seem to respond more obviously to local variations in vertical velocity (e.g., in the convective cells just upwind of the crest). The reason is the relative dominance of the horizontal wind. The decrease in horizontal wind speed causes more vertically inclined streamlines in the second transect.
The reflectivity difference FAD for both transects (Fig. 8b) reveals a more intense echo profile on the lee side, as in case A. Low-level lee subsidence is stronger than upwind ascent, also as in case A (Fig. 8e). In this case the average near-surface reflectivity (and snowfall rate) was not significantly higher in the lee, as much of the snow mass aloft sublimated before reaching the ground. This sublimation is evident from the decrease in mean reflectivity (dashed line in Fig. 8b) in the lee from ~2 km AGL down to ground level. Thus, while the orographically generated convective cells produced large snowflakes aloft as they drifted across the crest, they produced little snowfall at the surface. With just two transects in case B, these findings are not very robust. Fortunately, 26 other transects with BL-C were flown, on different days (Table 1).
c. Case C: 26 January 2006
The flight on 26 January 2006 (referred to as case C) was conducted in the warm sector well south of the polar jet. The aircraft-measured sounding (Fig. 3c) shows gradual veering of the winds with height, and an LLJ, as on 18 January 2006, but the low-level wind was weaker (15 m s−1) and more westerly. Both potential temperature θ and θe change little with height from the lowest flight level to ~1.0 km AGL, indicating a deep mixed layer (Fig. 4c). The 4-K θe drop near 4 km MSL reflects horizontal variations along the flight track, possible due to the upwind mountain range, the Sierra Madre (Fig. 1). (The aircraft remained level for some distance at 4 km MSL during its ascent out of Saratoga.) The warm anomaly just below 4.0 km MSL corresponds with a cloud (Fig. 3c) penetrated in an ascent path toward the Sierra Madre. Ignoring this anomaly, apparently due to horizontal variability, θe increases slightly from near the surface to 5.0 km MSL. A very stable layer is present above 5.0 km (Fig. 4c), with cirrostratus around 7–8 km MSL, according to WCR data. The Scorer parameter l2 is large and generally decreases with height up to mountaintop level (Fig. 5c), suggesting the possibility of trapped lee waves.
The two MB transects flown on 26 January 2006 were aligned well with the prevailing westerly wind (Fig. 10). The first was flown at 4.2 km MSL, the second at 5.2 km MSL. In both cases the WCR echoes reveal a snow layer tilted from high levels on the windward side down to the surface near the mountain crest and into the lee, suggesting a deep windward-tilting, vertically propagating gravity wave. The absence of echoes above this tilted snow layer and the downward air motion measured at flight level across this region (Figs. 10b,e) indicate deep wave motion. The upper-level cloud farther east (top-right corners of Figs. 10a,d) probably is the leading trapped lee wave. Since l2 is quite large at low levels, even small terrain features (wavelength ~ 10 km) produce vertically propagating gravity waves, with a vertical velocity amplitude of ~1 m s−1 (Figs. 10b,e). Hydrometeors are generated mostly on the windward side, but they only reach the ground over the highest terrain. The lack of low-level echoes farther upwind (west of x = −16 km) may be due to persistent updrafts (Fig. 10b): snow may grow above the cloud base (~2.67 km MSL), but the streamlines suggest that the snowflakes do not lose altitude. Since precipitation growth in this case occurs in orographic waves, whose updrafts are broader but weaker than convective updrafts, we refer to case C as a stratiform (STRF) case (Table 1). Some snow falls in the lee, but reflectivity decreases from the crest down, due to sublimation.
As in Fig. 6, but for two transects flown on 26 Jan 2006 (case C).
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
The low-level flow upwind of the mountain again is decelerated by PBL turbulence (Figs. 10c,f). The winds accelerate dramatically across the crest, almost doubling in speed along the steeper leeward slopes. This current subsides rapidly (Figs. 10b,e), and in the second transect the plunging flow encounters a hydraulic jump near x = 15 km, with updrafts exceeding 5 m s−1 up to flight level. The reason this hydraulic jump can be seen by the WCR is, at least in part, due to blowing snow being separated from the BL. A weaker, possibly dissipating hydraulic jump is intersected by the WCR nadir beam in the first transect at 15 < x < 20 km. It may have reached 6 km in height (MSL), given the high reflectivity values there (Fig. 10a), and the intense turbulence (Fig. 10b). The plunging flow and BL separation in case C are explored in more detail in French et al. (2014, manuscript submitted to J. Atmos. Sci.).
The hydrometeor streamlines terminating at the mountain crest, and those terminating 10 km downwind of the crest, agree quite well between the two transects separated by 1.5 h, suggesting that the basic flow pattern across the mountain was quite steady (Fig. 7c), compared to case A, which had convective generating cells aloft. The streamlines terminating in the lee are quite steep, consistent with the prevailing subsidence, but those terminating on the crest are more level just upwind of the crest.
A steady flow pattern implies a steady precipitation distribution pattern in equilibrium with the vertical velocity field. Most precipitation fell over the higher terrain, with a fairly even distribution across the crest, according to the composite reflectivity FADs for five transects available for case C (Fig. 8c). The main difference between upwind and lee sections is the near absence of echoes between 0.5 and 2.5 km AGL, on account of the strong subsidence (Fig. 8f). The shallow lee precipitation clearly is “spillover” from hydrometeors grown on the windward side.
d. Case D: 29 January 2013
The storm sampled on 29 January 2013 (referred to as case D) was another postfrontal case, in a very cold air mass with a low tropopause (Fig. 3d). The upwind lower troposphere was close to moist neutral, with just a ~1-K increase in θe between the surface and 5.5 km MSL (Fig. 4d), similar to case C. The wind during this flight was relatively light at all levels and mostly northwesterly (Table 1). The terrain toward the northwest of the MB range is rather flat (Fig. 1) for at least 200 km. The Fr number was high enough to enable flow over the mountain, producing clouds starting at a rather low LCL (Table 1). Some channeling of the near-surface flow in the plains, around the MB range, may have occurred due to the weak surface winds. Both the N2 and the l2 in the upwind environment were small, but positive, from the surface to ~5.5 km MSL (Fig. 5d). Trapped lee waves are likely as l2 decreases from the layer below mountaintop to higher levels.
Two transects were flown along a relatively long, NW–SE-oriented track over isolated hills both upwind and downwind of the Snowy Range (Fig. 1). Light precipitation fell across the MB range, starting far upwind (Figs. 11a,d) and terminating just downwind of the crest; in other words, almost all precipitation fell on the windward side, with little spillover. The echo and flow patterns are quite similar during two flight transects flown in immediate succession (Fig. 11). This suggests that the reflectivity pattern is close to equilibrium with the flow field. Steady, weak ascent prevails on the windward side, with shallow up–down dipoles over the isolated hills, but without significant vertically propagating gravity waves (Figs. 11b,e). PBL turbulence is suppressed because of the weak winds upwind of the main crest. Both reflectivity and vertical velocity fields are very smooth upwind of the crest, indicating STRF.
As in Fig. 6, but for two transects flown on 29 Jan 2013 (case D).
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
A narrow column of strong descent can be seen in the lee of this crest. This downdraft and its echo boundaries tilt less in the windward direction compared to case C. This downdraft feeds a lee jet 2–3 times stronger than the wind speed upwind of the crest at the same level (Figs. 11c,f). This lee plunging acceleration is not sustained: the flow decelerates again just before all snow sublimates and the WCR echoes vanish. A hydraulic jump with a 2–3 m s−1 updraft at flight level may be present over Sheep Mountain (Fig. 1), the easternmost hill in both transects, near x = 30 km, but it is not captured as well as in case C.
The hydrometeor streamlines are quite steep, especially on the windward side (Figs. 11c,f), on account of the weak wind. They are especially weak below mountaintop level because of northerly winds (Fig. 4d), pointing out of the page in these transects. The streamlines ending in the lee are deflected horizontally on account of the lee jet (Figs. 7d and 11). The reflectivity difference FAD highlights how precipitation growth and fallout mainly occurs on the windward side due to the light winds, with only some very shallow spillover in the lee (Fig. 8d).
5. Patterns of orographic flow and precipitation
The four cases illustrated above yield insight into the basic flow and stability patterns controlling the distribution of snow growth and precipitation in cold-season orographic storms. The flow is unblocked flow (Fr > 1) in these four and most other cases observed over the MB range (Table 1). In other words, we do not distinguish between orographic growth and precipitation patterns in blocked versus unblocked flow (Rotunno and Houze 2007; Houze 2012). Rather, we contrast three patterns under unblocked flow conditions.
a. Orographic flow with convection
In cases A and B potential instability is present in a low-level layer of significant depth (Table 1), and the ascent resulting from cross-mountain flow is deep enough to release that instability. This instability can be quite weak, and requires no surface-based or elevated convective available potential energy (CAPE) to be present in the upstream sounding. Typically, the temperature profile is close to moist neutral. In case B and many other cases with BL-C (Table 1), snow growth occurs not on the scale of the mountain, but rather in convective updrafts much smaller than the terrain half-width. Other BL-C cases listed in Table 1 are all shallower than case B. They consist of daytime BL convective clouds that are triggered when a postfrontal well-mixed PBL, heated from below, is advected over the MB range. Geerts et al. (2011) describe a case with BL convection, on 2 February 2006 over the MB range. (This case is included in Table 1.)
Snow growth in case A occurs both at low levels as stratified air rises over the mountain (mountain-scale ascent disturbed by PBL turbulence), and at higher levels in the small convective towers (generating cells). These cells of elevated convection (EL-C; Table 1) can substantially alter the distribution of (mostly stratiform) precipitation across a mountain, as shown in a modeling study by Fuhrer and Schär (2005), simply because the convective time scale is not insignificant compared to the advective time scale across the mountain. Convection tends to grow over the higher terrain, and weaken in the lee on account of broad subsidence. Some convective cells may persist far downwind, although generally little snow reaches the ground in the downwind valley due to low-level sublimation. The farther the convective cells are advected leeward, the less efficient they become in surface precipitation production. The cross-mountain wind shows little acceleration in the lee, and lee subsidence is rather weak and broad. Pokharel et al. (2014b) describe another EL-C case with generating cells aloft, over the Sierra Madre (Fig. 1). Most winter orographic storms in Colorado described in Kumjian et al. (2014) using a polarization X-band scanning Doppler radar appear to be of the EL-C type. All convective cases fall in the mountain wave regime in Fig. 2. [Note that the analytical theory in Smith (1989) did not consider convection.]
Composite reflectivity and hydrometeor streamlines are shown for all transects available for cases A–D in Fig. 12. These gridded composites are produced from all geographically overlapping transects during a single flight to minimize transient features: the composite reflectivity field should be in closer balance with the flow field over the mountain and streamlines closer to hydrometeor trajectories. The spatial redistribution on a grid and the averaging, smear out small-scale transient features such as convective cells, while preserving terrain-locked features such as vertical velocity dipoles around a ridge. Grid points with data values from >50% of the transects (e.g., 3 out of 5 or 2 out of 2) are included in the composite; others are left blank. The compositing exercise assumes that the upstream flow and stability conditions do not change during the period of flight. Also, the composites are not available over the full depth of the storm because the dual-Doppler velocity data are available only below flight level. The emphasis thus is on the low-level flow.
Composite WCR reflectivity (color field) and dual-Doppler hydrometeor streamlines for: (a)–(d) the four cases A–D listed in Fig. 7. Note the constrained vertical range of these plots, up to flight level rather than to cloud top, because dual-Doppler synthesis is possible only below flight level.
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
The five-transect composite for case A (Fig. 12a) captures a nice dipole of windward updraft and lee downdraft, and snow growth across the crest, resulting in surface precipitation mainly on the lee slopes. The composite transect for case B (Fig. 12b) shows more finescale reflectivity and vertical velocity structure on the upwind side, due to convective cells. With just two members, the reflectivity distribution across the crest may not be representative of average conditions in this storm.
b. Stratified orographic flow
No small-scale orographic convection is present in cases C and D. The WCR vertical velocity transects in these cases suggest an upwind-tilting vertically propagating gravity wave maintained by the main mountain crest. Lee subsidence starts aloft on the windward side, and extends to lower levels in the lee, leading to the sublimation of snow. In both cases C and D, the Scorer parameter 
Since the vertical velocity is more terrain-controlled in the STRF cases, fewer transects probably are needed to obtain a precipitation field in equilibrium with the flow field. The composite flow and reflectivity patterns for cases C and D are quite similar to the respective member transects (Figs. 10 and 11), not just in terms of reflectivity (Figs. 12c,d), but also in terms of vertical and along-track horizontal velocity. The strong subsidence results in cloud and snow clearing in the lee (Figs. 8c,d). Only a shallow snow foot is advected into the lee, where the snow sublimates over a distance that is larger under heavier snowfall (Figs. 12c,d).
c. Composite vertical structure based on all flights
We classified the prevailing flow and precipitation pattern for the 16 flights discussed in section 3 into either convective (BL-C or EL-C) or stratified flow without convection (STRF) (Table 1). This (subjective) classification is based on the visual presence (or absence) of finescale, strong updrafts not tied to the terrain, and highly variable radar reflectivity with matching spatial scales in along-wind transects such as the one shown for cases A–D. The convective (BL-C and EL-C) and STRF types are neither mutually exclusive nor exhaustive for unblocked orographic flow and precipitation. For instance, potential instability may be released in a wave updraft in stratified flow, but the upwind tilt of the leading wave constrains ascent and potential instability release to a smaller region upwind of the crest. Case A has rather stratified flow in the layer between the PBL and the convective generating cells aloft. In some cases convection intensified or weakened, but in none of the cases did the flow regime change from one type to the other. Seven cases (28 transects) are classified as STRF, eight cases (28 transects) as BL-C, and only one (case A, 5 transects) as EL-C (Table 1).
We composite reflectivity and vertical velocity values in normalized FADs for the 28 BL-C transects and the 28 STRF transects. Two regions, windward and leeward, are distinguished for each transect, and the two regions are composited separately. These composite FADs then are subtracted, and the (lee – upwind) difference FADs are shown in Fig. 13. The mean reflectivity profile indicates that STRF storms are deeper and more intense (higher near-surface reflectivity) than are BL-C storms (dashed lines in Figs. 13a,b).
Difference in WCR reflectivity frequency between lee and upwind sides (lee − upwind), plotted by altitude AGL for (a) all BL-C transects and (b) all STRF transects listed in Table 1. (c),(d) As in (a),(b), but for WCR vertical velocity. The solid (dashed) lines are the mean profiles for the lee (upwind) side.
Citation: Monthly Weather Review 143, 2; 10.1175/MWR-D-14-00199.1
Boundary layer convection is confined more to the upwind side of the crest, where reflectivity tends to increase toward the ground, indicating low-level snow growth: there is a higher probability of high reflectivity values in the lee, at low levels (Fig. 13a). Most BL-C cases are shallower than case B. In some BL-C cases convective cells are present well upstream of the crest, but they tend to intensify toward the crest. Across the crest cells tend to weaken rapidly, as the ambient air mass subsides. The vertical velocity [lee-upwind] difference field shows a simple dipole at all levels, with a large difference in mean vertical motion (Fig. 13c). Convective cells may be carried into the lee, but the vertical reflectivity profile becomes more upright, with a slight sublimation signature in the lowest few hundred meters (Fig. 13a). This signature would be more prominent if the flight legs extended further downwind (Fig. 1): the mean reflectivity for the composite reflectivity FAD for the same transects in the “far lee” (defined as more than 10 km downwind of the crest) shows a clearer sublimation signature (reflectivity decrease from 1.5 km AGL to the surface) (not shown).
The composite BL-C structure is quite different from the EL-C structure, which for case A shows higher reflectivity values and persistent updrafts aloft in the lee, at least in the immediate lee of the crest (Figs. 8a,e). The impact of the pronounced low-level lee subsidence in the STRF cases (Fig. 13d) is obvious in the depressed reflectivity in the lee (Fig. 13b), in the composite of 28 cases (Fig. 8). The average lee vertical velocity profile in the lee in Fig. 13d is deceiving. The vertical velocity FAD for the STRF cases combines strong downdrafts and, in four of the seven cases, strong updrafts due to a hydraulic jump. This wide distribution results in a tripole in Fig. 13d: in the immediate lee strong downdrafts (~−2 m s−1) prevail, and it is these downdraft that depress lee reflectivity in the lowest ~3 km (Fig. 13b). Farther leeward, strong updrafts may occur, but without associated snow growth, as the cloud base is too high in the lee. Snow spillover does occur in the STRF cases in a very shallow snow foot (low-level blue shading in Fig. 13b), due to the downslope accelerated flow. Some of this may be due to the lofting of blowing snow, although such fractured snow particles probably are quite small and thus yield only low-reflectivity values, as in case C (Fig. 10).
In short, the composite structure shown in Fig. 13 clearly reveals the impact of the mountain on the flow and snow distribution. Both the BL-C and STRF cases are characterized by higher low-level reflectivity (snowfall) on the upwind side. The plunging flow in the STRF cases tends to clear the snow rather quickly over the depth of the storm, while some shallow convection may continue some distance in the lee, where an increasing fraction of snow sublimates. Only the EL-C case is characterized by heavier snowfall in the lee.
6. Conclusions
This study uses a unique dataset obtained from a profiling airborne cloud radar, with VPDD capability below flight level, to gain new insights into orographic snow growth, transport, and sedimentation. The data were collected on 61 wind-parallel flight legs over the MB range in Wyoming on 16 flights. An upwind radiosonde sounding was available for each flight. In most cases the wind was strong enough for the flow to be unblocked. The sampled clouds were all mixed phase, of limited depth (typically 1–3 km), and generally produce snowfall over the mountain only. The two main findings are as follow.
Three distinct patterns of vertical velocity and airflow over the mountain are evident: in some cases small-scale, shallow convection is present, either aloft or near the surface. The former, referred to as elevated convection (EL-C), may span a range of dimensions including “generating cells” and is due to the release of potential instability in a layer lifted over the terrain. The latter, referred to as BL convection (BL-C), was encountered more commonly because many flights took place under postfrontal cold-air advection conditions. The cross-mountain flow is relatively undisturbed in the presence of convection. The third pattern, referred to as stratiform (STRF), lacks convective cells: stratified flow ascends the mountain, often with vertically propagating gravity waves, and a strong, shallow, plunging air current in the lee, and in some cases even a hydraulic jump. In all patterns, especially the convective patterns, low-level hydrometeor streamlines tend to show a kink across the mountain crest on account of windward rising air motion suspending the hydrometeors along roughly level paths, followed by subsidence starting at the crest.
These basic patterns affect snow growth and precipitation across the mountain. A comparison of FADs of radar reflectivity on opposite sides of the mountain crest shows that both the BL-C and STRF cases are characterized by higher reflectivity at low levels, and thus higher surface snowfall, on the upwind side. The plunging flow in the STRF cases clears snow rather quickly over the depth of the storm, and produces a very shallow “snow foot.” Cells of BL-C may continue some distance in the lee, where an increasing fraction of snow sublimates. Only the EL-C case is characterized by heavier snowfall in the lee.
Acknowledgments
This work was funded by National Science Foundation Grant AGS-1058426 and by the University of Wyoming Water Research Program. The radiosonde launches were supported by the Wyoming Weather Modification Pilot Program, which is funded by the state of Wyoming. Two anonymous reviews improved this paper significantly.
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