a. Airborne dual-Doppler measurements

The capability of airborne dual-Doppler radar to map 3D wind fields over complex terrain is well established (Yu and Smull 2000; Bousquet and Smull 2003a, b). Using the fore/aft scanning technique (Frush et al. 1986; Jorgensen and Smull 1993; Hildebrand 1998), 3D reflectivity and radial velocity data for the 2-h period from 2300 UTC 13 December to 0100 UTC 14 December 2001 were gathered within five overlapping ∼40-km-wide volumes centered along each of five north–south-oriented flight legs (Fig. 1a). Each of these individual legs was flown at a constant altitude and was approximately 130–140 km long, with 40-km interleg spacing in the cross-barrier (east–west) direction. Each leg required approximately 30 min to complete. The first leg was flown over the Willamette Valley at an altitude of 2 km [all heights are mean sea level (MSL)], with the three subsequent legs increasing in altitude to a maximum of 4 km for the leg flown immediately leeward of the Cascade crest. The fifth and final leg was flown at a height of 3.2 km well to the lee of the Cascade crest.

The regular spacing of these five legs provided continuous, high-resolution dual-Doppler coverage over the IMPROVE-2 study area, and is thus extremely well suited for comprehensive evaluation of mesoscale simulations of terrain-modified airflow and precipitation processes. While airborne Doppler measurements are generally regarded as quantitatively useful to a range of ∼40 km, the relatively tight spacing of the P3 legs allowed restriction of analyzed data to a zone within ∼20 km to either side (i.e., east and west) of each track, ensuring a high-fidelity analysis. Prior to interpolation, radial velocity and reflectivity measurements were subjected to automated and manual editing, as described by Bousquet and Smull (2003a), to remove ground clutter contamination, noise, and other artifacts. Radial data were then interpolated to a composite Cartesian grid measuring 240 km × 170 km in the horizontal with 1-km grid spacing in x and y, and 0.25-km resolution in the vertical from immediately above the terrain to a maximum height of 10 km MSL (or echo top, if lower). Multiple radial views from “fore” and “aft” scans were synthesized following Jorgensen and Smull (1993) to yield continuous fields of horizontal airflow (U, V) and reflectivity (dBZ) in regions of detectable echo. Synthesized reflectivity and component airflow fields were subjected to a two-pass Leise filter (Leise 1982) to eliminate poorly resolved small-scale features and to assure smooth, continuous transitions across “seams” separating data from individual flight legs. The absence of notable discontinuities at these locations attests to the success of this approach.

Rudimentary estimates of vertical air motion were performed by downward integration of the anelastic continuity equation. Downward integration serves to minimize error growth (Ray et al. 1980) and these vertical velocity estimates were uniformly bounded and well behaved at the lowest levels. The resulting composite analysis utilized in this study provides a largely uninterrupted view of kinematic and precipitation fields fully spanning the Cascade crest, extending from the Willamette Valley (located >100 km upstream) eastward to the leeside desert plateau of central Oregon. Due to the relatively slow evolution of flow and precipitation structures during this period of prefrontal P3 sampling (Garvert et al. 2005b; Medina et al. 2005), the composite analysis may be viewed as a steady-state depiction of the precipitation and flow pattern during this 2-h period.

b. Mesoscale model setup and description

The MM5 version 3.6 was employed in nonhydrostatic mode to simulate the 13–14 December 2001 system. A 36-km outer domain covering a large area of the eastern Pacific and Pacific Northwest was run for 36 h (Fig. 1b), with a 12-km nest centered over the Pacific Northwest. The model was initialized at 0000 UTC 13 December 2001 by interpolating a modified National Centers for Environmental Prediction (NCEP) Aviation Model (AVN)¹ initialization for 0000 UTC 13 December 2001 to the outermost MM5 grid. The 0000 UTC 13 December AVN gridded analysis was improved by incorporating surface and upper-air observations using a Cressman-type analysis scheme (Benjamin and Seaman 1985). Additional analyses were generated every 6 h using similarly modified AVN initialization and forecast grids, and then linearly interpolated in time to provide continuous lateral boundary conditions for the 36-km domain. To ensure the most accurate simulation, four-dimensional data assimilation (FDDA) was employed during the first 24 h of the forecast on both the 12- and 36-km domains. The FDDA scheme (Stauffer and Seaman 1990; Stauffer et al. 1991) applies a Newtonian relaxation technique to nudge the MM5’s wind, temperature, and moisture fields toward modified AVN surface and upper-air initialization grids at 1200 UTC 13 December 2001 and 0000 UTC 14 December 2001.

Thirty-two unevenly spaced full-sigma levels were used in the vertical, with maximum resolution in the boundary layer. The simulation used the updated (version 3.6) explicit moisture scheme of Reisner 2 (Thompson et al. 2004), Grell cumulus parameterization (Grell 1993), and the Medium-Range Forecast Model (MRF) planetary boundary layer scheme (Hong and Pan 1996). The configuration of the model was identical to the original MM5 simulation presented in Garvert et al. (2005a) except that nudging on the outer domains was extended to 24 h, as opposed to 12 h in the original simulation. As a result, the simulated strength of midlevel wind speeds and the timing of the surface front were both improved. Yet despite the differences between these simulations, the deduced QPF biases were similar, suggesting that the magnitude and influence of errors in the model’s bulk microphysical parameterizations overshadowed those rooted in the kinematic fields.

In addition to the outer 36- and 12-km domains, a separate 4-km simulation with a 1.33-km nest centered over the central Oregon Cascades was run for 24-h starting at 1200 UTC 13 December 2001. The 4-km grid was initialized by linearly interpolating forecasts from the 12-km MM5 simulation. The extent of the 4- and 1.33-km domains are also shown in Fig. 1b. The 1.33-km domain was expanded from the original dimensions employed by Garvert et al. (2005a) in order to encompass a larger area to the east (leeward) of the crest, as well as the coastal mountains to the west. These inner domains did not employ nudging or cumulus parameterization.

c. 13–14 December 2001 case overview

Garvert et al. (2005a) present a detailed account of the evolution of the synoptic fields for the 13–14 December 2001 storm event, including validation against the MM5 control simulation. Although this present paper will predominately focus on a 2-h period from 2300 UTC 13 December to 0100 UTC 14 December, a brief overview of the kinematic and thermodynamic evolution of the storm is included here to provide a context for the mesoscale features described in the subsequent sections.

At 2000 UTC 13 December 2001, a large area of high potential temperature (θ) was located offshore of the West Coast at heights of 1 and 3 km (Figs. 2a,b). East of the high-θ region, there was a weak gradient in θ, with values over western Oregon being 3–4 K lower than those offshore. Coincident with this gradient was a transition in wind direction from westerly offshore to more south-southwesterly near the coast. A second stronger gradient in θ was evident entering the domain from the northwest, and was associated with the approaching forward-tilted cold front as described in Garvert et al. (2005a) and Woods et al. (2005).

An 800-km-long east–west cross section (location shown in Fig. 2) was constructed to illustrate the vertical structure and evolution of the large-scale thermodynamic and kinematic fields (Fig. 3). The cross section showed that at 2000 UTC a cold front (position indicated by dashed gray line) was well offshore (Fig. 3a). West of the front, cold air advection was occurring. To the east of the front, a relatively broad and uniform area of warm air advection was present marked by veering of wind direction with height. There was no indication in this cross section of enhanced southerly flow (i.e., a barrier-parallel jet) over the windward slopes as would be expected in a case of significant blocking. A significant mountain wave was evident, with persistent sharp descent and subsequent downstream rebound of the θ contours to the lee of the Cascade crest. Radar measurements at this time showed a large shield of stratiform precipitation over the study area (cf. Fig. 3a of Garvert et al. 2005a).

Three hours later at 2300 UTC, the low-level θ gradient near the coast had intensified and progressed onshore with southwesterly flow persisting over the study area (Fig. 2c). The leading edge of the cold advection had moved eastward but still was about 150-km west of the study area at 1 km and near the coast at 3 km (Figs. 2c,d). The east–west vertical cross section at this time (Fig. 3b) shows that east of the cold front, the slope of the θ contours had increased significantly. Additionally, over the windward slopes of the Cascades, enhanced vertical gradients in θ (gray shading in Fig. 3b) and equivalent potential temperature (θ_e) were present between 2 and 4 km. Substantial directional shear was present within this zone, with winds veering from southerly at low levels to a more westerly direction above the enhanced thermal (θ and θ_e) gradient.

Measurements of the upstream flow profile, provided by the NCAR Integrated Sounding System (ISS) profiler located at Irish Bend (IB in Figs. 1a and 3b), support the MM5’s depiction of substantial low-level veering in the winds during the prefrontal period. Figure 4 displays profiles of U- and V-wind components at IB at 15-min intervals from 2247 UTC 13 December to 0047 UTC 14 December 2001, as well as an average profile for the entire 2-h period. Although there was some variance in the U and V components, these profiles remained relatively unchanged over the 2-h period. Consistent with the simulated veering at low-level winds, the U component at IB increased from about 5 m s⁻¹ near the surface to an average of 30 m s⁻¹ at 2.5 km, while the V component reached a maximum speed of ∼23 m s⁻¹ at 1.5 km before weakening aloft. Above 2.5 km both the U and V components were relatively uniform with a modest 4–5 m s ⁻¹ increase.

By 0200 UTC the cold front had entered the study area (Figs. 2e,f). The vertical cross section shows that winds throughout the lowest 6 km were from the west behind the front (Fig. 3c). Due to the modification of the θ and θ_e gradients by mountain waves over the Cascades, the position of the cold front at upper levels is difficult to ascertain.

a. Upstream conditions

The basic structure of mountain waves is determined by the size and shape of the underlying terrain and by the vertical profiles of temperature, cross-barrier flow speed, and moisture of the impinging flow. A special sounding (located at UW in Fig. 1a) taken at 0000 UTC 14 December 2001 measured environmental conditions just upstream of the Cascade crest (Fig. 5). Although this sounding was likely somewhat modified by the Cascades and coastal mountains (Medina et al. 2005), it provides the best available source of information on the thermodynamic structure directly upstream of the elevated terrain of the Cascades.

Similar to the IB profiler, the observed U component increased significantly from the surface to a height of 2.9 km, reaching a peak speed of approximately 38 m s⁻¹. Above this strongly sheared layer, U was relatively uniform up to 4.5 km, above which it again began to increase with height. The MM5 1.33-km simulation essentially replicated this structure, but slightly overpredicted the strength of U within the shear layer below 2 km, while underpredicting the magnitude of U above, resulting in an underprediction of the vertical shear magnitude over the windward slopes.

The dry Brunt–Väisälä frequency (N ²_d) calculated from the sounding indicates the profile was stable throughout the lowest 6 km (Fig. 5). An additional calculation of the moist Brunt–Väisälä frequency (N ²_m; Durran and Klemp 1982; Einaudi and Lalas 1973) was also performed, since the atmosphere was saturated below 600 hPa (Garvert et al. 2005a). The inclusion of moisture in the moist Brunt–Väisälä calculation accounts for the latent heat of condensation and thus provides a better indication of the stability of the upstream flow in a saturated environment (Durran and Klemp 1982). Throughout most of the profile, N ²_m remained weakly positive, indicating neutral to stable flow. A layer of increased stability near the top of the U-shear layer was present between 2 and 3 km, where the N ²_d values peaked near 2 × 10⁻¹ s⁻² (Fig. 5). The 1.33-km MM5 simulation also reproduced the observed stratification, including the enhanced stability between 2 and 3 km.

Linear theory can be used to predict the character of mountain waves provided that the barrier height is small compared with the vertical wavelength of the resulting wave (Durran 2003). The “nonlinearity parameter” or inverse Froude number [viz. Nh/U, where N is the dry or moist Brunt–Väisälä frequency, h is the average height of the mountain (assumed here to be 1.68 km), and U is the cross-barrier wind] was calculated for the sounding in Fig. 5. In the surface layer below 0.75 km, N_mh/U was greater than unity while above this layer the nonlinearity parameter remained close to 0.5 for both moist and dry N ² values. Theory predicts that a nonlinearity parameter value of 0.5 is associated with a linear (i.e., “flow over”) mountain-wave regime (Smith 1989).

b. Windward slopes

At a height of 1.5 km MSL, composite airborne Doppler measurements showed southwesterly flow over the Willamette Valley (Fig. 6a). As this flow encountered the elevated terrain of the Cascade foothills, its speed markedly decreased. Observed reflectivity showed relatively heavy precipitation over the entire study area, with pockets of enhanced reflectivity reaching 40 dBZ over the windward slopes and a sharp reduction of values leeward of the crest. (Fig. 6b). Winds at 3 km (i.e., above crest level) were more westerly (Fig. 6c), with a pronounced maximum in wind speeds to the lee of the Cascade crest. The observed veering of winds between 3.0 and 4.5 km (cf. Figs. 6c,e) was consistent with warm advection ahead of the frontal system, as previously seen in Fig. 3b. Reflectivity patterns seen in Figs. 6b,d,f will be more extensively discussed in section 4.

Averaged east–west cross sections of the radar-observed U- and V-component flow provide a general view of kinematic fields across the Cascades (Figs. 7a,c). These sections were constructed by meridionally averaging the gridded 1-km dual-Doppler data over the 140-km north–south region between 44.0° and 45.0°N (boxed region in Fig. 6e). Analogous mean cross sections of simulated flow (Figs. 7b,d) were created using the U and V fields from the MM5 1.33-km simulation. The MM5 cross sections were averaged for the time period of the P3 flight, from 2300 to 0100 UTC 13–14 December 2001 (forecast hours 11–13) using model output at 15-min intervals.

As previously suggested by the UW sounding and IB profiler, airborne dual-Doppler data indicate that the incoming flow was strongly sheared upwind of the crest, with the U component increasing more than 20 m s⁻¹ from the surface to the top of the shear layer at approximately 2-km MSL (Fig. 7a). The depth of this shear layer remained relatively constant as flow ascended the windward slopes. Above the shear layer, a jet of stronger (>36 m s⁻¹) cross-barrier flow centered at 3–4 km progressively increased strength over a 90-km interval upstream of the mean crest, ultimately reaching speeds greater than 40 m s⁻¹ over and immediately leeward of the crest. The U-wind (cross barrier) flow structure documented over the windward Cascade slopes differs appreciably from cases of profoundly blocked flow observed adjacent to taller mountain ranges such as the Sierras (Marwitz 1987a) and Alps (Bousquet and Smull 2003a, b). In those events, radar and in situ measurements depicted the cross-barrier shear layer as being mainly concentrated below the crest level, with the depth and strength of the shear layer decreasing with proximity to the crest (cf. Fig. 3c of Marwitz 1987a; Fig. 8b of Bousquet and Smull 2003b).

In the present case, strong V-component (along barrier) flow was coincident with the aforementioned U-component shear layer and decreased with height above this layer (Fig. 7c). There was a ∼4 m s⁻¹ enhancement in the V flow over the Willamette Valley (∼100 km upstream of the crest), but the absence of a clearly defined V maximum (or “barrier jet”) below crest level further distinguishes this IMPROVE-2 case from aforementioned examples of profoundly blocked flow.

To better illustrate the alteration of the wind components by terrain, “upstream” U and V profiles were created by averaging the dual-Doppler wind fields over a section of the Willamette Valley between −123.30° and −123.06°W (dashed boxed region at left edge in Fig. 7a). Since the elevation of the Willamette Valley is near sea level, the upstream profile’s wind values in MSL are roughly equal to those above the ground level (or AGL). The upstream U (and V) AGL profiles were subtracted from the corresponding U (and V) values AGL over the rest of the cross section in Fig. 7 to create the U ′ and V ′ plots in Fig. 8. Using this methodology, the frictional deceleration of the U flow following the sloping terrain is largely eliminated, allowing other terrain influences such as blocking to be better illuminated.²

Immediately above the foothills, U ′ values were predominantly between −1 and 1 m s⁻¹, indicating that, excluding height-dependent frictional effects, the cross-barrier flow at the lowest radar-sampled levels was relatively unperturbed (Fig. 8a). In contrast, large positive U ′ values were concentrated over the lower lee slopes and extended westward to a height of 6 km over the crest. This pattern can be attributed to a vertically propagating mountain wave that will be discussed in more detail in the next section. For the along-barrier flow, a small area of positive V ′ values of 5–7 m s⁻¹ was centered 100 km upstream of the crest below 2.0 km (Fig. 8b). Otherwise, V ′ values over the windward slope were close to zero, corroborating observations in Fig. 7c that failed to indicate a pronounced barrier jet or other signs of pronounced upstream blocking. The observed flow patterns and computed flow perturbations thus support the calculations of the nonlinearity parameter in Fig. 5, which predicted a flow-over regime in which blocking effects are minimal. Based upon idealized high-resolution 2D simulations, however, Medina et al. (2005) concluded that that some modification of the cross-barrier during 13–14 December 2001 may be attributed to nonlinear interactions between stably stratified flow and the orographic barrier.

MM5-averaged east–west cross sections of U and V are displayed in Figs. 7b,d. The MM5 successfully simulated the broad characteristics of the flow, including the low-level shear in the U component and core of stronger U above. The model also correctly simulated the core of stronger V component at low levels rising over the windward slopes, as well as the observed decrease of V with height above 2–3 km. Over the windward slopes, the strength of U shear was underpredicted, with low-level U values being too strong while those above 2 km were 5–8 m s⁻¹ too weak. Additionally, the height of the modeled U-wind shear layer over the windward slopes was about 0.5 km less than observed. Low-level V-component flow was 4–6 m s⁻¹ stronger than that observed, with the elevated core of maximum V values extending farther east toward the lee than observed. The implications of these errors on the structure and strength of mountain waves will be explored in the section 3c.

Simulated θ and θ_e contours are also plotted in Figs. 7b,d. Since the environment during the 13–14 December case was near saturation up to 4 km (Garvert et al. 2005a), θ_e can be treated as a tracer of the steady-state flow, except in areas where diabatic processes such as melting are active. Enhanced vertical gradients of θ (dashed white lines) and θ_e (solid black lines) were found surmounting the zone of weaker low-level U winds and within the zone of enhanced U aloft (Fig. 7b). This corresponds well with the UW sounding shown in Fig. 5 (position of UW labeled in Figs. 7a,b), which shows the strongest N ² values (and increased stability) between 2 and 3 km coinciding with the top of the shear layer. Stronger V-component flow was centered below the θ_e gradient and rapidly decreased with height above (Fig. 7d). Decreasing values of θ toward the crest are consistent with reflectivity observations from the P3 radar that showed a tendency for the bright band (and the associated 0°C level) to descend with approach to the Cascade crest, as will be shown in section 4. A MM5 simulation in which diabatic effects of melting were excluded (not shown) indicated, however, that melting had a minimal influence on θ values on the windward slopes.

Trajectories were calculated using the 4-km domain MM5 simulation to determine the origin of the θ_e and θ gradient present in Figs. 7b,d. Figure 9a shows the paths of four trajectories ending at 2300 UTC 13 December (forecast hour 12). All terminate at the same horizontal location (44.3°N, −122.3°W) but at heights ranging from 1 to 4 km (cf. Fig. 7b). These trajectories were calculated using 600-s time steps from MM5 4-km hourly output. Lagrangian values of pressure, θ, θ_e, and relative humidity values for the four trajectories are displayed in Fig. 9b.

The parcel ending at 1 km moved northward nearly parallel to the Cascades, at a relatively constant pressure level of 910 hPa from 1200 to 2300 UTC 13 December. This parcel was subsaturated from 1200–1800 UTC 13 December, although relative humidities increased from 75%–90% along its northward track. After 1800 UTC, the parcel’s relative humidity remained close to 100% as it neared the zone of enhanced orographic precipitation over the IMPROVE-2 study area. The values of θ_e and θ for this parcel showed a 5–6 K increase during its northward trajectory, apparently as a result of terrain-induced mixing. The parcel ending at 2 km followed a similar course, originating to the south-southwest off the coast of California. This parcel remained around 950 hPa between 1200 and 2000 UTC, but then rose to level of 784 hPa as it encountered the higher terrain of the Cascade foothills. The θ and θ_e values along this trajectory also experienced a 5 K increase during the 4-h interval plotted, again indicative of warming induced by mixing.

The two parcels that ended at 3 and 4 km both originated within a distinctly different air mass and region than the lower trajectories. Both originated to the west-southwest of the study area over the open waters of the Pacific, in a nearly saturated air mass characterized by higher θ_e. The 3- and 4-km parcels experienced significantly more ascent than the lower parcels, rising over 225 hPa in less than 5 h. The θ_e of these elevated parcels remained relatively steady, while θ dramatically warmed due to release of latent heat of condensation. These results imply that the θ and θ_e gradients over the windward slopes in the prefrontal regime were the product of dissimilar airmass origins in combination with sharply veering flow upstream of the Cascade terrain.

c. Leeside region

The extension of radar-detectable precipitation into the lee of the Cascades presents a unique opportunity to examine the strength and amplitude of a standing wave anchored to a mountain barrier. In association with strong cross-barrier flow surmounting the Cascades, dual-Doppler observations showed this high-momentum air plunging downward immediately to the lee of the crest (Fig. 7a). The observed 32 m s⁻¹ contour, which approximately delineates the top of the U-shear layer, dropped from a maximum height of 3.0 km just upstream of the crest to 2.1 km MSL (1.0 km AGL) approximately 10 km downstream (Fig. 7a). The 32 m s⁻¹ contour then rebounded slightly, before leveling out at about 2.2 km. Independent ground-based observations around this time indicated strong winds reaching the surface, with reports of downed trees in the immediate lee of the crest (Medina et al. 2005). The aforementioned positive U ′ perturbations in the lee of the mountain crest (Fig. 8a) are consistent with the presence of a vertically propagating mountain wave (Durran 2003).

The MM5 also depicted a core of strong U momentum ascending the windward slopes and plunging downward in the lee of the Cascades (Fig. 7b). The modeled 32 m s⁻¹ contour line dropped by approximately 1.2 km over a horizontal distance of 10 km, which is comparable in amplitude to the radar-observed displacement. However, the simulated core of strong U momentum penetrated much closer to the ground and spanned a larger horizontal downstream distance than was observed. Such errors in the model depiction of the mountain wave can increase the amount of precipitation spillover reaching the ground, and may contribute to an overprediction of precipitation in the leeside region as discussed in Garvert et al. (2005a).

Previous research has shown that the structure and amplitude of mountain waves are sensitive to the depth of the boundary layer and upstream shear (Smith 1979; Peng and Thompson 2003). As discussed above, the model underpredicted the strength and depth of the shear layer over the windward slopes of the Cascades. Since the depth of the modeled shear layer was less than that observed, this upstream effect might account for subsequent errors in the model depiction of the mountain-wave structure over and leeward of the crest.

To assess the impact of the planetary boundary layer (PBL) representation and associated shear on the mountain wave, a variety of sensitivity tests were conducted using different PBL parameterization schemes available in MM5. As noted in section 2, the control simulation was run with the MRF-PBL, which utilizes the Troen–Mahrt representation of the countergradient term (Hong and Pan 1996). A second run was performed that was identical to the control except that the Eta-PBL was used on the inner 4- and 1.33-km domains. The Eta-PBL, which is used in the operational Eta Model (Janjic 1990, 1994), is a 1.5-order closure scheme in which turbulent kinetic energy (TKE) is predicted through a prognostic energy equation, as adapted from the Mellor–Yamada scheme.

The vertical extent of the low θ_e and associated depth of the shear layer over the windward slopes was further reduced in the Eta-PBL simulation compared to the control run (Figs. 10a,b), contrasting even more with the observations Fig. 7a. Yet, the cross-barrier shear was stronger than that in the control simulation, better matching observations. In contrast to the dual-Doppler observations, the Eta-PBL simulation brought unrealistically stronger U-momentum values even closer to the surface and over a wider area to the lee of the Cascade crest. Additionally, the wave structures as depicted by vertical velocity in the Eta simulation were significantly different than those in the control, with higher amplitude and downward displaced vertical motions in the lee (Figs. 10b,d).

A third simulation was performed using a modified version of the MRF-PBL (referred to an Yonsei PBL), as outlined in Noh et al. (2003). Inclusion of the Yonsei-PBL produced results similar to the Eta-PBL simulation, reducing the depth of the upstream shear layer and increasing the amplitude of the lee-wave response (Figs. 10e,f). Inclusion of the Yonsei-PBL, however, did not correct the underprediction in the strength of the upstream shear layer as significantly as the Eta simulation.

a. Larger-scale (>20 km) precipitation features

A meridionally averaged east–west cross section of radar reflectivity was constructed from the composite airborne Doppler analysis (Figs. 6b,d,f) and is shown in Fig. 11a. The observed slope of the distinct bright band indicates that the melting layer decreased in height from 2 km over the Willamette Valley to just 1.5 km over the elevated terrain, consistent with the presence of cooler air on the windward side of the Cascades (as previously suggested by MM5-based depictions; cf. Fig. 7b). Radar reflectivities decreased rapidly downstream of the crest, indicative of large evaporation and/or fallout rates. Locally increased reflectivity values were observed over the Willamette Valley (∼100 km upstream of the crest), the windward foothills (centered ∼70 km upstream of the crest), and within a broad area commencing ∼44 km upstream of the crest and extending into the lee. These structures are also clearly evident in the composite airborne Doppler radar analyses at 3 km (Fig. 6d).

To explore the origins of these prominent reflectivity features, model-predicted CLW and snow (q_s) fields were averaged using 15-min interval MM5 output from 2300 to 0100 UTC 13–14 December 2001 and overlaid on the observed Doppler reflectivity fields (Figs. 1la,b). By comparing these model-based mixing ratios with the Doppler radar observations, the origins of these precipitation structures can be better ascertained. The time-averaged model fields indicated increases in the amount of CLW at 100 and 70 km upstream of the crest, over virtually the same regions where the reflectivity perturbations were observed (Fig. 11a). The fact that these perturbations in CLW remain clearly evident even after averaging over a 2-h period indicates the stationary and persistent nature of these perturbations, an aspect also evident in ground-based radar data collected during this interval (cf. Figs. 8a,b of Medina et al. 2005).

Maximum values in the simulated snowfield (>0.9 g kg⁻¹) extended from 40 km upstream of the crest to the immediate lee, and were collocated with the observed higher reflectivity values aloft (Fig. 11b). The vertically pointing National Oceanic and Atmospheric Administration (NOAA) Environmental Technology Laboratory (ETL) S-band radar (MB in Fig. 1a), positioned about 20 km upstream of the Cascade crest, also showed a layer of enhanced reflectivity between 4 and 5 km that remained relatively stationary over the radar site for the duration of the prefrontal precipitation event (cf. Fig. 2 of Garvert et al. 2005b). These high snow mixing ratios were then advected over the crest by the strong cross-barrier flow before being shunted earthward in the immediate lee of the Cascades (Fig. 11b) by the strong downward motion (P3 in situ measurements reaching −4 m s⁻¹; Fig. 12 of Garvert et al. 2005a) within the deep, vertically propagating gravity wave. Additionally, as snow reached the 0°C level, enhanced reflectivity associated with melting likely contributed to the observed reflectivity maximum in the immediate lee. In an analysis of the modeled and observed microphysical processes associated with the 13–14 December 2001 case, Colle et al. (2005) noted that in the immediate lee of the Cascades melting snow and graupel were the predominant contributions to rain generation and precipitation at the surface. The simulated large gradient of snow mixing ratios in the lee of the Cascades corresponds quite well to the rapid reduction of observed reflectivity values.

To further trace the origins of these observed reflectivity structures, the depictions of the east–west cross section of simulated CLW were expanded westward by 80 km to include the coastal mountains, as shown in Fig. 12a. Two additional MM5 1.33-km simulations were performed, one with the coastal mountains removed (designated as “Noco” in Figs. 12c,d), and another employing a lower 36-km resolution version of the topography (“smooth” in Figs. 12e,f). These runs were identical to the control simulation except for the differences in the underlying topography.

Figures 12a,b show an enhanced area of CLW and strong upward motion between 180 and 140 km upstream of the crest in association with the incoming flow encountering the coastal mountains. The lack of observations over this area prevents an independent evaluation of the veracity of this particular simulated feature. An area of descent and reduced model CLW was collocated with the zone of lower-reflectivity values observed in the lee of the coastal mountains (i.e., 120–140 km upstream of the Cascade crest). A significant rebound both in the simulated CLW and observed dBZ fields was evident over the relatively flat Willamette Valley, centered ∼100 km upstream of the Cascade crest. As seen in Figs. 12c,d, the strong vertical velocity oscillations apparent between 180 and 120 km (i.e., over the coastal mountain zone) in the control run were absent in the Noco simulation, being replaced by a broad but weaker (0–0.2 m s⁻¹) updraft. Nonetheless, there is a significant response in the model CLW field at low levels below 2 km between 160 and 180 km upstream of the crest, which is attributed to frictional convergence as the flow over the Pacific slowed over the land. Without the coastal mountains, the upward vertical velocity and CLW maximum over the Willamette Valley (100 km upstream of crest) failed to develop. It is also noteworthy that within the smooth run, which contains a rudimentary representation of the coastal mountains, the enhancement of CLW over the Willamette Valley remained evident. These differences suggest a lee-wave response downwind of the coastal mountains effectively enhancing precipitation over the Willamette Valley.

Over the Cascade foothills, the CLW and vertical velocity fields in the Noco simulation are almost identical to those in the control simulation, indicating that the perturbations in the observed reflectivity fields over these areas cannot be attributed to the coastal mountains (Figs. 12c,d). The areas of enhanced model CLW, vertical velocity, and observed reflectivity were all collocated with a significant rise in the underlying topography located approximately 70 km upstream of the Cascade crest. The vertical velocity and CLW fields from the smooth run (Figs. 12e,f) show fewer short-wavelength features than seen in the control simulation (Figs. 12a,b). The smoothed-terrain run thus illustrates the sensitivity of windward mountain waves and microphysical responses to the local steepness and details of the underlying terrain.

b. Smaller-scale (<20 km) precipitation features

Thus, far this paper has focused on the larger-scale (horizontal length scales >20 km) precipitation and vertical velocity perturbations within a meridionally averaged east–west cross section spanning the Cascade crest. Yet as established by Garvert et al. (2005a, b), the strong southerly flow at low levels interacted with the complex terrain of the windward slopes and significantly impacted CLW amounts at smaller scales (<20 km). The top three panels in Fig. 13 show in situ, dual-Doppler-derived, and model-predicted U, V, and W components, respectively, at a height of 2.5-km along leg 2 of the P3’s flight track (as shown in Fig. 1a and by black dot 60 km upstream of the mean crest in Figs. 7a,c). The in situ and Doppler-derived U and V components along leg 2 indicate that the winds varied by 5–7 m s⁻¹ over horizontal distances of 10–15 km in this region. These variations can be directly linked to details of the underlying terrain, with positive V-component perturbations collocated with local peaks and localized stronger U maxima located above valley locations (Garvert et al. 2005a). The MM5 correctly simulated these variations, except for slightly overpredicting their amplitude relative to that observed.

In situ vertical velocities along leg 2 also show evidence of significant terrain-induced variations. As discussed in Garvert et al. (2005a), upward vertical velocities coincided with areas in which the strong V-component flow impinged on higher terrain while negative downward perturbations were preferentially located on the lee (north) side of the ridges and coincident with the stronger V-component flow. Such perturbations have significant impacts on the CLW field, as discussed in Garvert et al. (2005b) and illustrated in Fig. 13. The model has also been shown to accurately represent the magnitude and positions of these vertical velocity oscillations but overpredict the resulting enhancement of CLW (Garvert et al. 2005b).

As described in section 2b, crude dual-Doppler estimates of vertical air motion (w) were derived by downward integration of the anelastic continuity equation subject to a boundary condition of w = 0 immediately at echo top. In the presence of large-amplitude vertically propagating waves, this assumption may be violated and represent a source of error. Nonetheless, comparison of these w estimates by independent observational measures (and simulation results as well) lends increased confidence in their accuracy. In keeping with the inherently coarser spatial resolution of airborne Doppler radar data after required filtering (viz. resolved horizontal scales >8–10 km), the derived vertical velocities were significantly smoother than those directly obtained via flight level measurements, but still showed generally good agreement in terms of the phase and sign of longer-wavelength features of the simulated flow (Fig. 13). In the following discussions comparisons of Doppler-derived vertical motions with simulation results are purely qualitative, relating the approximate location and phase (sign) of vertical motions relative to terrain corrugations.

Doppler-derived vertical velocities are overlaid on the Doppler-observed U- and V-component fields along the north–south cross section of leg 2 in Figs. 14a,c. The strongly sheared U-component flow is clearly depicted below 3 km, with near-surface values of 8 m s⁻¹ increasing to 36–40 m s⁻¹ at a height of 3.5 km. Within this strongly sheared layer, the observed V component reached nearly 30 m s⁻¹. As this strong V flow impinges on the foothill terrain, the strong vertical velocity perturbations seen in the in situ data are also clearly evident in the Doppler-derived w field. Despite the imposed rudimentary boundary condition of w = 0 at echo top, positive w > 0.2 m s⁻¹ are registered at heights of 5 km, indicating the significant upward penetration of these small-scale mountain waves generated over the Cascade foothills.

Due to the presence of strong vertical shear and variable thermodynamic conditions in this case, an accurate calculation of the Scorer parameter (relevant to vertical wave propagation) is difficult to accomplish. Using available sounding and Doppler radar data, values of N_m and V-component flow within the lowest 3 km are estimated to have been near 0.0077 and 22 m s⁻¹, respectively, yielding a Scorer parameter (l = N/V) of 3.5 × 10⁻⁴ m⁻¹, and a corresponding critical horizontal wavelength of ∼18 km. Flow undulations generated by the underlying Cascade foothill topography having wavelengths of <18 km are thus predicted to be evanescent and decay rapidly with height. As seen in Fig. 14, the terrain within the north–south cross section along leg 2 exhibits significant small-scale variability, implying that most waves triggered over the Cascade foothills were likely evanescent. Yet there is some evidence, especially near 30–40 and 70–80 km in Fig. 14, that waves induced by the widest ridge–valley pairs may have exceeded this cutoff wavelength. Moreover, the presence of marked meridional flow accelerations and collocated subsidence in the lee of these localized foothill barriers is consistent with theoretical depictions of vertically propagating mountain-wave behavior (e.g., Smith 1979).

The vertical penetration of such waves may also be influenced by shear. Assuming hydrostaticity, Smith (1980) demonstrated that wave components having phase lines perpendicular to the flow penetrate farther aloft (and consequently generate more upslope condensation) than those that are more oblique. The 13–14 December 2001 storm embodied a strongly sheared southerly wind component at low levels, which would tend to favor limited upward penetration of topographically generated waves having east–west axes (such as those sampled along leg 2). At somewhat higher levels, where prevailing winds veered to become more westerly, damping of these waves would be expected to be consistent with patterns seen in Fig. 14. At the same time, this elevated layer would be expected to favor upward penetration of waves triggered at higher elevations and having north–south axes, such as the profound mountain wave anchored to the Cascade crest shown in Fig. 10. Possible impacts of these contrasting behaviors on surface precipitation rates are discussed in the following section.

The MM5 U- and V-component flows along leg 2 (Figs. 14b,d) are in good agreement with observations, showing significant shear both in U and V below 3 km. As mentioned previously, however, the simulation exhibited notable errors in this layer, with the shear layer in U being shallower and weaker than observed and low-level V winds being 4–8 m s⁻¹ too strong below 3 km. Despite these errors, the model’s vertical velocity field compares well with observations, simulating the dramatic oscillations associated with the strong V values interacting with the complex terrain. These simulated w oscillations also show greater vertical penetration than observed by the Doppler-derived values, which is probably closer to reality given the artificial boundary conditions w = 0 at echo top imposed on the dual-Doppler analysis.

To illustrate the impact of the wave-induced motions on precipitation processes, Fig. 15a displays Doppler-derived vertical velocities overlaid on reflectivity along leg 2. Consistently high dBZ values are located near a height of 1.8 km in conjunction with the radar bright band. Enhancement of radar reflectivities repeatedly occurred at distances 5–8 km north (downstream) of strong positive vertical velocities. For example, at 15 km from the southernmost edge of the cross section and near a height of 2.0 km, a strong vertical velocity maximum is evident where the strong V-component flow impinged upon a 1-km-high ridge. At a distance 5–8 km north of this positive vertical velocity perturbation, an enhancement in the dBZ values is observed, implying increased precipitation rates triggered by this ascent.

Model depictions of the precipitation and CLW fields along leg 2 showed the complex microphysical interactions produced by the strong vertical velocity perturbations (Fig. 15b). Pockets of high CLW (mixing ratios >0.4 g kg⁻¹) are present over the individual ridges coincident with simulated regions of ascent of the areas of strong upward vertical velocity. A large snowfield above these CLW perturbations is simulated, with some enhancement in the snow mixing ratios appearing above the individual ridges. Where the snowfield intersected with the high CLW pockets, riming of the snow and graupel formation above the freezing level was diagnosed. The higher fall speeds of the rimed snow and graupel evidently resulted in the enhancement of the observed bright band over and immediately leeward of the crest as these particles fell through the melting layer. Additionally, as precipitation particles were advected northward in the low-level flow, they encountered strong downdrafts in the lee of the ridges and rapidly fell below the melting layer (Fig. 15a). A corresponding increase in surface precipitation rates is illustrated by higher mixing ratios of rain (>0.4 g kg⁻¹) over the crest and in the immediate lee of several of the ridges along leg 2. The precipitation distribution at the surface was evidently very sensitive to the amount of riming, the fall speed of the particles, and the phase and amplitude of these small-scale terrain-induced waves.

c. Surface precipitation patterns

Using an MM5 simulation virtually identical to the one considered here, Colle et al. (2005) calculated a windward precipitation efficiency (PE; total hydrometeor fallout over the windward slopes divided by the total amount water vapor loss in this region) of 50% for the 13–14 December case. This percentage was less than the PE of 80% calculated over the Sierra Mountains (Colle and Zeng 2004a, b), with the difference attributed to the narrower width of the Cascades and strong cross-barrier flow during the 13–14 December event. To assess the influence of orography on cumulative precipitation at smaller spatial scales, as required for forecasts within individual drainage basins, the results in section 4b indicate that one must consider the impact that mountain waves and associated microphysical processes exert on surface precipitation rates. For this purpose, the 3-h cumulative QPF from the 1.33-km MM5 control simulation during the interval 2200–1000 UTC 13–14 December 2001 is presented in Fig. 16a, while a 1.33-km smoothed-terrain simulation’s QPF for the same 3-h period is shown in Fig. 16b. The terrain used for the smoothed 1.33-km model simulation is identical to that used in the 12-km outer domain. Previous studies have shown that in order for the model to simulate correctly the small-scale waves over the windward Cascade slopes, use of a model grid spacing of 1.33 km with high-resolution terrain is required (Garvert et al. 2005a). By smoothing the terrain and holding the grid spacing of both simulations constant at 1.33 km, variations in precipitation amounts can be more directly attributed to the differences in terrain.

The control simulation shows regions of higher precipitation along the coastal mountains at the western edge of the domain, while over the relatively flat Willamette Valley amounts are reduced and more uniform (Fig. 16a). Over the windward slopes of the Cascades, significant precipitation variations are indicated, with MM5-derived totals ranging from >3.0 cm over the local crests to 1–1.5 cm in some of the valleys (Fig. 16a). The precipitation distribution over the windward slopes is consistent with the findings from a linear model presented in Smith et al. (2005) that used a 1-km grid spacing and prescribed environmental values of wind direction, moist stability, wind speed, and moisture. Smith et al. (2005) noted that the small-scale structure of the precipitation fields (see their Fig. 6) with significant variability on scales of 20 km over the windward slopes is similar to that shown in Fig. 16a. Smith et al. concluded that for waves of horizontal scales on the range of 10–30 km, the effect of condensate advection slightly dominates any upstream wave tilt that may occur, with the resulting maximum precipitation being located over the highest terrain, albeit with some spillover similar to that seen in Fig. 16a. The east–west alignment of the MM5 precipitation maxima over the windward slopes is consistent with the linear model’s precipitation distribution when using a prescribed upstream wind sounding from a southerly direction (see Fig. 6c of Smith et al. 2005). The V component of the wind favors the upward penetration of wave components with phase lines perpendicular to the airflow (east–west direction) generating more upslope condensation and precipitation (Smith et al. 2005).

The smoothed-terrain simulation shows far more uniform spatial distribution of precipitation over the windward slopes, with precipitation totals consistently near 1.5–2 cm (Fig. 16b). A slight reduction is evident 10–20 km upwind of the crest in both the control and smoothed simulations, while immediate leeward of the Cascade crest precipitation totals are in excess of 3 cm for the control simulation and 2.5–3 cm for the smoothed simulation. Both model runs show a significant dropoff in precipitation amounts farther to the lee, with a sharper gradient appearing in the control simulation.

To highlight differences in the precipitation distributions for these two runs, a meridionally averaged east–west cross section of QPF was calculated for the smoothed-terrain and control simulations (Fig. 17a). Despite significant local differences in the detailed horizontal distributions of precipitation for these two simulations, integrated domainwide precipitation amounts resulted in total precipitation amounts that were very similar: 294 cm for the control simulation and 289 cm for the smoothed simulation. This indicates that the differences in topography did not significantly alter the total amount of precipitation over the domain as a whole, but instead horizontally redistributed this precipitation.

A significant difference in precipitation totals for the two simulations was evident over the windward slopes between 100 and 20 km upstream of the crest, where the control simulation’s meridionally averaged precipitation totals were 4%–17% higher than those in the smoothed simulation. Integrating over the windward slope region (area delimited in Fig. 17a), a 7% increase was observed in the control’s precipitation amount when compared with the smoothed-terrain simulation.

A south–north cross section of the 3-h QPF along leg 2 (black dashed line in Figs. 16a,b) as derived from both the control and smoothed simulations is displayed in Fig. 17b. The control simulation shows significant local variations in QPF, with higher totals over the ridges and lower QPF within the valleys. These precipitation extremes correspond closely to the variations in mixing ratios and Doppler reflectivities seen in Fig. 15. By contrast the smoothed simulation’s QPF pattern along leg 2 failed to resolve the smaller-scale precipitation perturbations caused by the complex terrain. When integrating the QPF along leg 2, the accumulated precipitation total for the control simulation was 171 cm, as compared to the smoothed-terrain run’s total of 161 cm. This represents a 6% increase in precipitation amounts that, ignoring any large-scale differences in the kinematic fields between the two simulations, may be attributed to the small-scale terrain-induced waves and ensuing microphysical processes.

Another interesting feature of the precipitation distribution is the reduction in totals near the crest and concomitant increase in the immediate lee within the control simulation (Fig. 17a). This modulation is apparently caused by the strong mountain wave and associated acceleration of the cross-barrier flow over the Cascade crest, which acted to rapidly advect precipitation toward the lee slopes. The increased QPF in the lee occurs within the area where the MM5 simulated the strong U flow reaching closer to the surface than observed. However, the QPF minimum near the crest and maximum to the lee is consistent with the Doppler reflectivity patterns described in Fig. 11b. The smoothed run showed a similar pattern in the surface precipitation, with a lessened contrast in precipitation between the crest and the lee (Figs. 16b and 17a). This may be due to the reduced wave amplitude near the crest for the smoothed run (Figs. 12b,f), resulting in reduced spillover of precipitation into the lee. Due to a lack of detailed surface observations with sufficient temporal resolution immediately surrounding the Cascade crest, detailed verification of this precipitation distribution is not possible. Yet an examination of observed precipitation amounts from 1400 to 0800 UTC 13–14 December 2001 (Fig. 16 of Garvert et al. 2005a) does indicate a tendency for reduced precipitation totals near the crest as compared to those over the immediate windward and leeward slopes.

To illustrate the importance of the local terrain details during the entire event, Fig. 18a shows a east–west cross section of meridionally averaged QPF from 1400 to 0800 UTC 13–14 December 2001. This extended time period includes prefrontal, frontal, and postfrontal precipitation regimes, and has previously been compared against observations in Garvert et al. (2005a) and Colle et al. (2005). The integrated precipitation amount over the entire cross section showed a net increase of 8% in the control (987 cm) versus the smoothed simulations (911 cm). This increase in the integrated precipitation amounts differs from that computed for the 3-h prefrontal period, during which integrated precipitation amounts were roughly equal for both the smoothed-terrain and control simulations. Therefore, the impact of the increased terrain resolution on precipitation distributions and amounts is apparently sensitive to the thermodynamic and flow properties of the upstream flow. Specifically relatively shallow precipitating features characteristic of postfrontal regimes would be expected to be more sensitive to details of the underlying flow and terrain.

Over the windward slopes, the model predicted a 12% increase in the control’s simulation-integrated precipitation (585 cm) versus the smoothed terrain (518 cm), while over the crest and lee minimal differences in the integrated precipitation amounts were seen (322 versus 320 cm). Increased precipitation amounts over the windward slopes appear to be tied to the presence of the smaller-scale wave perturbations. For example, along a north–south section (leg 2) the QPF within the control simulation is 17% greater than that in the smoothed-terrain simulation (551 versus 471 cm) over the entire 18-h period, indicating the robustness and persistence of the small-scale perturbations identified during leg 2 (Fig. 18b). Meridionally averaged model precipitation for the period from 1400 to 0800 UTC 13–14 December 2001 also exhibited a precipitation minimum along the crest and maximum to the lee, but with much less amplitude than found during the 3-h period from 2200 to 0100 UTC when cross-barrier flow speeds and moisture transport were near their maximum. (Fig. 18a). The reduced difference between the crest and lee QPF values is consistent with model and observational evidence indicating that the mountain wave was strongest from 2300 to 0100 UTC, resulting in a period of increased spillover of precipitation into the lee found during the 3-h time period of P3 aircraft observations.