established during the last few years. Accurate aircraft measurement of the horizontal pressure gradient force requires an independent determination of the height of the airborne platform above some reference level. Here the authors demonstrate a differential GPS technique that uses data from a fixed reference station to refine the vertical position of the aircraft. A series of research flight legs by the University of Wyoming King Air research aircraft (UWKA) were conducted during the winter seasons of 2008 and 2009 over the Medicine Bow Mountains in southern Wyoming. Flight patterns consisted of a series of geographically fixed, parallel legs along a quasi-isobaric surface above the mountainous terrain, allowing the finescale mapping of the horizontal pressure (or geopotential height) field. The removal of the large-scale gradient and tendency isolates the terrain-induced pressure perturbation field. Results obtained using differential GPS measure-ments of aircraft height show that the Medicine Bow Range induces pronounced horizontal pressure per-turbations, with a leeside region of low pressure downwind of the crest, in two cases: on 11 February 2008 and 20 February 2009. A wind maximum is found downwind of the elevated terrain consistent with this pressure gradient. Simulations of these two cases were performed using the Weather Research and Forecasting Model (WRF). The WRF height patterns for the time of the UWKA flight matched the general isobaric height patterns observed. Simulations and observations consistently show that the cross-mountain acceleration is stronger when the perturbation pressure gradient is larger.
1. Introduction
The horizontal pressure gradient force (PGF) is the fundamental driving term in the horizontal equations of motion. Knowledge of the horizontal pressure field is a prerequisite for any study of atmospheric dynamics, allowing winds to be sorted in terms of geostrophic and ageostrophic components. In situ measurement of the PGF using instrumentation on board research aircraft is particularly challenging since an independent measure of aircraft height above some reference level is neces-sary. Until recently, this has implied that both the terrain height of the underlying surface over which the plane passes and the exact geographic position must be known with a high degree of precision. The height above ground can be measured using a radar altimeter. In particular, precise and high-resolution radar altimeters (such as the Stewart–Warner Model APN-159) have
been used to enable height measurements above ground level with an accuracy of 0.5 m (see Brown et al. 1981; Shapiro and Kennedy 1981, 1982; Parish et al.1988; Rodi and Parish 1988; LeMone et al. 1988a,b; Parish 2000). Onboard navigation provides a measurement of hori-zontal position that, using digital terrain datasets, allows the height of the underlying terrain to be determined. By adding the radar altitude of the aircraft to the terrain height, an absolute measure of the height of the isobaric surface is obtained.
As noted in Parish et al. (2007), use of altimetry over irregular terrain requires high-resolution maps of the terrain elevation, and aircraft geolocation. Even when analysis tools include a finescale digital elevation map and GPS data on board research aircraft to refine hori-zontal positioning, the resulting estimate of the height of the aircraft above a reference level is subject to con-siderable error on account mainly of radar beamwidth, vegetation, and aircraft attitude variations. The final signal is the sum of two large terms whose spatial trends are opposed to one another and is inherently noisy, with an uncertainty of about 30 m or 3 hPa. Parish et al. (2007) note that altimetry is insufficient to permit Corresponding author address: Thomas R. Parish, Department
of Atmospheric Science, University of Wyoming, Laramie, WY 82071.
E-mail: parish@uwyo.edu DOI: 10.1175/MWR-D-13-00044.1 Ó 2013 American Meteorological Society
assessment of atmospheric dynamics when applied over complex terrain.
Recently, differential GPS (dGPS) has been used to allow an accurate and independent measurement of aircraft height above sea level and hence the geo-potential height of an isobaric surface (e.g., Parish et al. 2007; Parish and Leon 2013). For airborne measure-ments of the PGF, flight legs are typically conducted using the autopilot and thus the flight path is along a quasi-constant pressure surface. The University of Wyoming King Air research aircraft (UWKA) carries two GPS receivers, an Ashtech Z-Sensor and a Trimble NetRS, both of which track and record the carrier phase on two frequencies (labeled L1 and L2) in addition to the coarse acquisition (C/A) code broadcast on L1. Postprocessing software utilizing the carrier phase on L1 and L2 provides a position solution with higher spatial resolution than can be obtained from the L1 C/A code alone. The dGPS solution offers a means to refine po-sition estimates for the GPS receivers on board the UWKA by using GPS data from one or more fixed reference stations at precisely determined locations. It is estimated that the refined dGPS height estimates of the UWKA are on the order of decimeters (e.g., Parish and Leon 2013).
UWKA flight legs invariably show minor departures from isobaric surfaces owing to effects such as turbu-lence. Such deviations can be accurately accounted for by use of the hydrostatic equation. Standard instru-mentation on the UWKA include a pair of redundant Rosemount 1501 HADS pressure sensors to allow pre-cise static pressure measurements (e.g., Rodi and Leon 2012). Ambient temperature is measured by a Rose-mount reverse-flow temperature sensor and specific humidity by a Cambridge Model 137 C3 chilled mirror. This permits determination of the virtual temperature. An integrated form of the hydrostatic equation can thus be expressed as dz 5RTgVln p p ,
where R is the gas constant for dry air, TV is the mean
virtual temperature between the instantaneous flight level pressure and mean isobaric pressure level, g is the acceleration due to gravity, p is the instantaneous static pressure measurement, and p is the mean isobaric leg pressure. The resulting isobaric height is simply the sum of the dGPS height and the typically small hydrostatic corrected height: H5 zdGPS1 dz. Calculations of the
PGF can employ either the isobaric height or, equiva-lently, pressure along a constant height surface. For applications to follow, height of an isobaric surface is
used. Details of the dGPS technique, sources of error, and limitations to the measurement accuracy are given in Parish et al. (2007) or Parish and Leon (2013).
The purpose of this paper is to demonstrate the ability of an airborne platform to map the finescale isobaric height field above complex terrain using dGPS tech-nology to refine the vertical position of the aircraft, and to validate the observed mountain-induced wave struc-ture by means of a simple numerical simulation. Flight legs conducted by the UWKA conducted over the Medicine Bow Range in winter of 2008 and 2009 are used since flight level was maintained on an isobaric surface and the sampling pattern was repeated over a section of mountainous terrain. This allows for one of the first attempts to spatially map the finescale terrain-induced geopotential height variations from an airborne platform.
Mesoscale surface pressure patterns induced by wind impinging on relatively isolated terrain, and associated flow patterns, have been documented before (e.g., Reed 1980; Ferber and Mass 1990; Chen and Li 1995). At the same time, aircraft measurements have amply docu-mented the patterns aloft of mesoscale gravity waves generated by stratified flow over mountains (e.g., Lilly et al. 1982; Smith 1976; Smith et al. 2008). These gravity waves are generally described in terms of vertical ve-locity and potential temperature (i.e., the most readily available aircraft measurements). Undular pressure (or height) perturbations, which are commonly illustrated in modeling studies, have hardly been instrumentally documented.
The ambient conditions and airborne measurements are presented in section 2. Results from high-resolution numerical simulations are provided in section 3. Con-clusions are given in section 4.
2. UWKA measurements of the isobaric height field
a. Experimental design
The Wyoming Weather Modification Pilot Program is an orographic cloud seeding program funded by the State of Wyoming through the Wyoming Water De-velopment Commission (Breed et al. 2008). The Medi-cine Bow Range, Sierra Madre Range, and Wind River Range (Fig. 1) were target areas for the cloud seeding. Goals of the program are to establish a randomized cloud seeding experiment and to evaluate the effec-tiveness of seeding in enhancing winter snowpack. UWKA flights were conducted on days in which the mean wind direction was between 2708 and 3308, such that the three AgI generators were situation roughly normal to the mean wind and upwind of the
mountainous terrain. UWKA flight legs were arranged relative to this line in an isobaric [fixed flight level of 14 kft (;4267 m), or ;590 hPa], parallel-track sampling pattern (Fig. 1) to detect evidence of seeding. This flight level is about 600 m above Medicine Bow Peak. Each set of legs consisted of five segments (Fig. 1b) of about 45 km in length that are oriented along an axis trending northeast (NE)/southwest (SW), each segment separated by a distance of 4.3 km. Tracks followed nearly identical patterns for each case and originated slightly downwind of the main crest of the Medicine Bow Mountains, pass-ing over Medicine Bow Peak, the highest point in this range, and extending 13 km upwind. The full ‘‘ladder’’ pattern required about 45 min to complete.
Here results from the UWKA flights over the Medi-cine Bow Range conducted on 11 February 2008 and 20 February 2009 are presented. The ladder pattern was repeated 4 times during the 11 February 2008 flight and 3 times during the 20 February 2009 case. The repeating nature of the flight lines provides a practical means to infer an isobaric height field from which the horizontal pressure field can be determined. Nearly identical pressure maps thus obtained during a period of insig-nificant wind changes add confidence in the reliability of the method and in the attribution of the observed structure to the underlying terrain. A base GPS station was maintained at the airport in Laramie, Wyoming (located just east of the Medicine Bow Range). Its 1-Hz data were used for the differential GPS corrections.
The instruments on board the UWKA used in this study, in addition to the GPS receiver, include standard probes to measure state variables, a gust probe, and a profiling millimeter-wave Doppler radar, the Wyoming
Cloud Radar (WCR; Wang et al. 2012). Along straight and level flights sections, such as those shown in Fig. 1b, the WCR provides a continuous vertical profile of re-flectivity and (hydrometeor) vertical velocity. A third WCR antenna points 308 forward of nadir. The synthesis of radial velocities from this and the nadir antennas can be used to obtain the horizontal (along track) and ver-tical velocities (Damiani and Haimov 2006). In this paper the along-track component is shown. While the dual-Doppler vertical component includes the hydro-meteor fall speed, the horizontal component represents the air motion.
b. Stability and wind profiles
Radiosondes were released near the middle of both flights (about 2 h after take-off) from Saratoga, Wyoming, located on the upwind side of the Medicine Bow Range. The profiles of u, ue, and wind are shown in Fig. 2. The
low- to midtropospheric flow was northwesterly on both days. The lower troposphere was stably stratified for dry processes, and weakly stratified for moist ascent. We computed the average Brunt–V€ais€al€a frequency N be-tween ground level and the elevation of Medicine Bow Peak for both soundings. The Brunt–V€ais€al€a frequency N is the dry (moist) value below (above) the cloud base, defined as the lifting condensation level (LCL). For 11 February 2008 and 20 February 2009, this value of N was 0.79 and 0.973 1022s21, respectively. In other words the flow impinging on the mountain was moderately stably stratified. A bulk Froude number Fr can be calculated as the wind speed U divided by N and the height of Medicine Bow Peak above Saratoga. Here U and N are computed as average values between the surface (at Saratoga, FIG. 1. (a) Location of the WWDC study, including Medicine Bow Mountains. Saratoga, WY, indicated by SAA.
(b) Close-up view of Medicine Bow Peak area with terrain contours in 200-m increments with light shading indicating highest elevations. Typical flight track of the UWKA indicated by the bold, dashed line with identifying leg numbers.
upwind of the mountain) and the mountain-top height. On both days Fr was slightly larger than one (1.3 and 1.1, respectively). This implies that the lower-tropospheric layers are likely to be advected over the mountain ob-stacle, although not without resistance. The width of the
Medicine Bow Range implies that under the wind and stability conditions observed on either day, gravity waves should be vertically propagating to the 600-hPa level and above (Uk N, with k the mountain wavenumber). The ratio of the crosswind to the along-wind mountain width was about 1.5 on these two days (Fig. 1b). This ratio and the Froude number estimates suggest that flow stagnation could occur aloft, leading to wave breaking (Smith 1989), although there is no evidence of this on the two cases examined here. Mountain-scale gravity waves were evi-dent in WCR along-wind [from northwest (NW) to southeast (SE)] transects during both flights. An example of such transect, for the second case (20 February 2009), can be found in Geerts and Miao (2010); the vertical velocity field in their Fig. 2 suggests a horizontal wave-length of;35 km. If Fr had been well below one (Fr 1.0), then the low-level flow would have been detoured around the mountain, possibly producing lee vortices, and the flight-level flow would likely be less disturbed by the mountain. Some channeling of the flow is evident in the slightly more stable second case, with nearly northerly low-level flow through the valley west of the Medicine Bow Range (Fig. 2b).
c. Synoptic conditions
Analyses from the National Centers for Environ-mental Prediction (NCEP) 12-km horizontal resolution North American Mesoscale Model (NAM) for 11 Feb-ruary 2008 and 20 FebFeb-ruary 2009 showed that northwest flow at 600 hPa was present at the time of the flight on both days (Fig. 3) with speeds between 15 and 20 m s21 over the mountains of southern Wyoming. The 12-km NAM 600-hPa height field only shows limited influence of the elevated terrain, in part because of the relatively course horizontal resolution. Both cases are postfrontal, near the maximum cold anomaly in a wave cyclone, well behind the region of 600-hPa warm-air advection. In FIG. 2. Stability and wind profiles near Saratoga, upstream of the
Medicine Bow Range (Fig. 1b) during the two flights analyzed herein. In each case, the profiles of (equivalent) potential temper-ature (u and ue, solid and dashed lines) are shown on the left and the wind profile on the right (full barb equals 10 m s21). The radiosonde release time and an isothermal lapse rate are shown for reference.
FIG. 3. Map of 600-hPa heights (solid line, m), temperatures (dashed,8C), and wind barbs (full barb is 10 m s21) at (left) 2100 UTC 11 Feb 2008 and (right) 0000 UTC 21 Feb 2009 taken from NCEP 12-km NAM analysis fields.
such a synoptic situation orographic clouds typically become rather shallow because of deep-tropospheric subsidence. During these two flights, WCR echo-top heights were still rather high [5.4 and 6.6 km MSL on 11 February 2008 and 20 February 2009, respectively, on average for all flight legs; see Table 1 in Geerts et al. (2011)], but they were lowering during the 4-h flights (Fig. 4 in Geerts et al. 2010).
d. Mapping isobaric height: Case 1
A longstanding issue when interpreting isobaric heights as measured from an airborne platform is the time–space transformation. Parish et al. (1988) recog-nized that it is imperative to correct for local height change during the time of flight to capture an accurate representation of the height or pressure field. For ex-ample, suppose the wind to be near geostrophic from 3158 and heights were falling by 10 m h21(roughly cor-responding to a 1 hPa h21 pressure fall). In the cases examined here, primary flight legs are oriented nearly orthogonal to the mean wind and thus an isobaric leg conducted from SW to NE would experience lower heights to the northeast. Given the height falls, an iso-baric slope would be exaggerated for a SW-to-NE leg. At typical UWKA speeds, a leg of 45 km requires about 8 min and thus mean heights over the entire domain would drop by about 1.4 m over the course of the leg. For a 10 m s21geostrophic wind, airborne measurements not corrected for the height falls would overestimate the geostrophic wind by 3.2 m s21. Similarly, an isobaric leg directed from NE to SW would experience higher heights to the SW. The local height falls would thus compensate for the isobaric slope and the net effect would be a geostrophic wind underestimate by 30%.
Reciprocal (back and forth) legs would thus yield a re-peating pattern of errors in the geostrophic wind esti-mates in presence of persistent mean height changes in which one heading leads to an overestimate and the return heading an underestimate of actual magnitudes. Corrections need to be applied for such mean height/ pressure changes to estimate an accurate horizontal pressure gradient force.
For the cases here, an estimate of the mean height at flight level was obtained for each pattern and since the pattern was repeated 4 times on the 11 February 2008 case and 3 times for the 20 February 2009 case, an esti-mate of the local height change could be estiesti-mated. The mean trend was 6 m h21 on 11 February 2008 and 7 m h21on 20 February 2009. All subsequent analyses of isobaric heights have been corrected using these estimates.
Figure 4 illustrates the 595-hPa height data based on dGPS processing of data collected by the UWKA plat-form for the first three isobaric ladder patterns con-ducted from 2004 to 2214 UTC 11 February 2008. All deviations of the UWKA platform from the 595-hPa surface have been hydrostatically corrected as discussed previously and the slope of the isobaric surface shown in proportional to the PGF. UWKA observations during the time period showed mean wind speeds of about 20 m s21from 3108. Although the height field from the NAM analyses in Fig. 3 suggests primarily northwest flow with height contours directed along a 1358/3158 axis, finescale analyses shows that the elevated terrain sig-nificantly impacts the height field. Lowest heights are observed northeast of the Medicine Bow Peak. For reference, a contour interval of 2 m shown in Fig. 4 corresponds to a pressure interval of 0.15 hPa on FIG. 4. Height contours (2-m increments) of 595-hPa surface based on dGPS processing of UWKA position for (a) 2004–2046, (b) 2049– 2130, and (c) 2134–2214 UTC 11 Feb 2008. UWKA wind barbs (m s21), flight track (dashed lines), and underlying terrain heights (shaded contours) also shown.
a constant height surface. While basic features of the height pattern are similar for each ladder pattern shown, some differences exist from pattern to pattern that imply some transience to the height field for this time period. Interpretation of such an isobaric height field is that the elevated terrain results in development of a leeside trough near and downstream from Medicine Bow peak that perturbs the ambient height field as shown in Fig. 3. To a first approximation the height field can be thought of as the sum of the large-scale mean gradient (called the geostrophic component) and a residual (‘‘ageostrophic’’) component that is primarily the result of topographic modulation. Removal of the mean height and the height gradient associated with an estimate of the larger-scale geostrophic wind may provide a depiction of the terrain-induced forcing of the height field. For this analysis, determination of the geostrophic wind is necessary but not without challenges. It is thought that the sampling area of the ladder pattern is marginal to define the larger-scale forcing since the actual height field itself is significantly modified by topography as illustrated in Fig. 4. Analyses from the 12-km NAM suggest modest variations in the geostrophic wind magnitude within the regional area. Shown here are analyses conducted as-suming that the mean wind is 20 m s21from 3158, which is representative of the observed winds and model analyses. It is assumed that to a first-order approxima-tion the pressure field consists of some mean geostrophic state and an ageostrophic component, p5 pg1 pa,
where p refers to pressure, pgrefers to pressure induced
by the geostrophic component, and parefers to pressure
from the ageostrophic component that is assumed to be primarily due to the terrain. Further, if it is assumed that the mean wind from above is representative of the geostrophic state, then k3 $pg[ rf Vmean, where the
term Vmeanis the mean wind vector as defined above and
other symbols have their standard meteorological meaning. It follows then that the acceleration is in re-sponse to the ageostrophic pressure field:
dV dt 5 2 1 r$pa2 1 r$pg2 f k 3 Vmean ffi 2 1 r$pa. Figure 5 illustrates the height field after the mean and slope associated with the geostrophic wind have been re-moved. This height field is an estimate of the topograph-ically induced perturbation. Although this ageostrophic height field no doubt shows transient features, a similar pattern is apparent in each case with heights that gen-erally decrease from NW to SE across the crest of the mountain range. Although some uncertainty exists re-garding the mean geostrophic wind, the inferred ageo-strophic height pattern has a significant amplitude and thus is not very sensitive to the choice of geostrophic wind. A wake low is located (or suggested) over or just downwind of Medicine Bow Peak along legs 4 and/or 5, and a weak closed high is present just upwind of the mountain. The persistence of this basic pattern serves as evidence for the mountain’s influence on the flow aloft. This basic pattern is consistent with analytical represen-tations and numerical simulations of stratified flow over an isolated mountain (e.g., Smith 1980; Smolarkiewicz and Rotunno 1989). The magnitude of the height per-turbation is largest for the second pattern and is equiv-alent to about a 60.3-hPa pressure perturbation on a horizontal surface near the 595-hPa level.
The ageostrophic pressure gradient shown in Fig. 5 implies a downgradient flow acceleration from NW to SE over the crest of the Medicine Bow Mountains. In-deed, significant cross-contour flow exists with wind di-rections throughout the domain (not shown) remaining FIG. 5. As in Fig. 4, but that mean height and mean geostrophic pressure gradient have been removed, to isolate terrain influence. Height
within 108 of the mean 3108 direction, suggesting accel-erations in the vicinity of the elevated terrain. Wind speeds as measured by the UWKA (Fig. 6) display sig-nificant unsteadiness although strongest winds were found on the lee side of the barrier in each case. Given the unsteady nature of the wind, it is not possible to assess a simple relationship between the wind field and the height field. Previous work such as Smith et al. (2008) and Parish and Oolman (2012) adjacent to the Sierra Nevada documented speed increases associated with mountain-induced pressure perturbations. This case is more complex in that the height perturbations are smaller and relatively nonsteady. From the analysis in Parish and Oolman (2012) based on the steady, inviscid isobaric equation of motion, height perturbations of 6 m seen on the second ladder pattern conducted on 11 February 2008
are consistent with the observed speed increase from roughly 21 to 24 m s21across the Medicine Bow Peak. e. Mapping isobaric height: Case 2
A second example of finescale mapping of the isobaric height field is taken from the case of 20 February 2009. UWKA data were collected again following the identi-cal sampling pattern flown in the 11 February 2008 case under slightly more stable conditions and similar northwesterly flow below flight level (Fig. 2). The height fields of the 592-hPa isobaric surface, obtained through dGPS processing of the UWKA vertical position for the three ladder passes, are shown in Fig. 7. The pattern of isobaric heights is similar to that of 11 February 2008 with lowest heights to the northeast of Medicine Bow Peak. Height gradients are considerably larger for this FIG. 6. As in Fig. 4, but for UWKA measurements of wind speed (m s21).
FIG. 7. Height contours (2-m increments) of 592-hPa surface based on dGPS processing of UWKA position for (a) 2154–2234, (b) 2237– 2320, and (c) 2332–2410 UTC 20 Feb 2009. UWKA wind barbs (m s21), flight track (dashed lines), and underlying terrain heights (shaded contours) also shown.
case. Not surprisingly, winds as measured by the UWKA platform were roughly 5 m s21stronger than seen on 11 February 2008 with a mean direction from about 2958. Wind speed decreases throughout the flight and the heights depicted in Fig. 7c suggest a relaxing of the gra-dient. As in the previous case, wind vectors are directed with a significant cross-contour component, consistent with acceleration associated with the height anomalies.
An estimate of the terrain-induced ageostrophic height field (Fig. 8) was obtained as before. Results are similar to that observed in the 11 February 2008 case with lower heights revealed above and downwind from Medicine Bow Peak. In both cases a low is present above the peak (on leg 4) in at least one of the ladder passes, and the strongest height gradient is on the upwind side, between legs 3 and 4. This is consistent with an upwind tilting hydrostatic gravity wave (e.g., Durran 1990). The terrain-induced height anomalies for the first two
patterns (Figs. 8a,b) are in excess of 14 m, corresponding to about 1.1 hPa, nearly twice as large as the first case.
Wind speeds for the three sampling periods (Fig. 9) indicate correspondingly larger leeside acceleration, about twice as large as the first case for the first two passes. Upwind of the Medicine Bow Peak wind speeds for the first pattern (Fig. 7a) are about 20 m s21, in-creasing to 28 m s21directly downwind of the peak. Flight patterns in Figs. 7a–c show some variability in wind speed, yet display strong gradients in wind speed and persistent accelerations downwind of the Medicine Bow Range. Enhanced gradients of wind speed are consistent with the larger height gradients shown in Fig. 7.
f. Cross-mountain wind below flight level
On both flights two along-wind legs were flown across the Medicine Bow Range, in addition to the ladder pat-terns. The WCR vertical-plane dual-Doppler technique FIG. 8. As in Fig. 7, but that mean height and mean geostrophic pressure gradient have been removed, to isolate terrain influence. Height
increment of 1 m.
(section 2a) is used to estimate the cross-mountain wind field along these legs. This field is gridded in a geo-located grid, for the two transects; then the scalar wind is averaged (Fig. 10). The geolocation of the two transects was not exactly the same, hence, the differences in the terrain profiles (Fig. 10). Clearly only the wind compo-nent in the plane of the transect can be captured. The angle between the flight-level mean wind direction and the flight orientation was small in both cases (Fig. 10), but a more significant cross-track component may have been present below flight level (Fig. 2). The transects are 40–45 km long and thus capture most of the mountain range, whereas the ladder pattern is only 17 km wide (Fig. 2).
The cross-mountain wind pattern confirms the stron-ger wind, and the more significant cross-mountain ac-celeration, in the second case (20 February 2009; Fig. 10b). The acceleration below flight level is as large as 8 m s21over a distance of 40 km in that case. No ac-celeration is evident at all below flight level in the first case. Also, neither case shows a developing downslope windstorm near the surface, as has been documented on some other flights over this mountain (French et al. 2008).
3. WRF simulations of the 11 February 2008 and 20 February 2009 cases
Differential GPS measurements based on observa-tions collected by the UWKA show that the Medicine Bow Mountains perturb the ambient pressure field in response to moderate winds pushing stably stratified flow against the elevated terrain. The spatial patterns suggest that low-amplitude waves result with a pressure minimum in the lee of the mountains. Such airborne measurements permit the two-dimensional height field to be computed, yet little independent evidence of the existence of such height fields is available. Operational models, even at a resolution of 12 km, are too coarse to resolve such height perturbations. As a means of ex-amining the effect of the local topography on the hori-zontal pressure fields, numerical simulations have been conducted using the Advanced Research Weather Re-search and Forecasting Model (WRF) version 3.3 for the 11 February 2008 and 20 February 2009 cases. A com-plete description of WRF is given in Skamarock et al. (2008). For this case a model domain was used that consisted of three nested grids with 18-, 6-, and 2-km grid spacing centered over the Medicine Bow Peak. Vertical FIG. 10. The mean wind speed below the UWKA on a transect closely aligned with the
flight-level mean wind, from (left) NW to (right) SE, based on two flight passes each on (a) 11 Feb 2008 and (b) 20 Feb 2009. This wind estimate is derived from vertical-plane dual-Doppler synthesis using two airborne radar antennas (see text for details), and is available only in re-gions of snowfall. The variable a is the wind direction offset, positive if the flight-level mean wind direction is clockwise relative to the flight orientation.
resolution consists of 30 sigma levels with increasing resolution toward the surface. The parameters used for the run are the following: WRF single-moment 3-class (WSM3) ice microphysics scheme, Rapid Radiative Transfer Model (RRTM) longwave radiation scheme, Dudia shortwave radiation scheme, fifth-generation Pennsylvania State University–National Center for At-mospheric Research Mesoscale Model (MM5) surface layer similarity with the Pleim–Xiu land surface model, and the Yonsei University boundary layer physics scheme and the Kain–Fritsch cumulus parameterization scheme in the outer domain and none for the inner two domains. Although no detailed sensitivity testing was conducted, it is thought that selection of individual pa-rameterizations is not critical for this simulation of the height field. The model was initialized at 0000 UTC 11 February 2008 and 20 February 2009 using the op-erational NCEP 212 NAM grids (40-km horizontal resolution). Each simulation was run for 24 h with the purpose of examining height field adjacent to the Med-icine Bow Range that can be compared with the UWKA measurements and dGPS isobaric height fields. Com-parisons with UWKA observations presented here will focus on the 2-km WRF inner domain near the time periods closest to the UWKA flight times.
Heights at 600 hPa from the innermost domain of the WRF simulation for times coincident with the UWKA flight on 11 February 2008 are shown in Fig. 11. Large-scale gradients of the 600-hPa heights support northwest flow throughout the period similar to that shown in Fig. 4, yet significant modulation of the 600-hPa height field is obvious in each panel with height minima found in the lee of the Medicine Bow Peak, and ridging on the windward side. Amplitudes of the height perturbations in the lee as simulated by WRF for the 11 February 2008 case are approximately 10 m. Note that the orientation of the height contours over the windward side of Med-icine Bow Peak becomes nearly orthogonal to that of the large-scale height pattern and similar to what was ob-served by the UWKA (Fig. 4). The influence of the el-evated terrain on the height field in the WRF simulation is persistent. Heights over the entire domain rise by about 6 m from 2000 to 2300 UTC for the 11 February 2008 case, yet the pattern of the height contours in the lee of Medicine Bow Peak remains similar.
Wind speeds as simulated by WRF for the 11 Febru-ary 2008 case display sensitivity to the topographic modulation of the height field. Figure 12 illustrates the 595-hPa wind speeds and wind directions associated with the horizontal pressure field. Although the winds FIG. 11. Height contours for 595-hPa surface (solid lines, contour increment 2 m) for innermost grid from WRF simulation for (a) 2000,
(b) 2100, and (c) 2200 UTC 11 Feb 2008. UWKA flight track in thin, solid line.
in the lee of the mountain range with a minimum gen-erally upstream. These results compare favorably with observations such as shown in Fig. 6 in that stronger winds are found in the lee of the Medicine Bow Peak.
Conditions on 20 February 2009 again consisted of northwest winds above the Medicine Bow Peak. Winds were directed with a slightly more northerly component as compared to the 11 February 2008 case that is in ev-idence in Fig. 3. Figure 13 illustrates the 592-hPa height field from the innermost domain of the WRF simulation for times bracketing the UWKA mission on 20 February 2009. Isobaric height gradients as simulated by WRF are larger than seen in the previous case, yet the 600-hPa surface is again altered in response to the elevated ter-rain of the Medicine Bow Mountains. The larger mag-nitude of the trough–ridge anomaly across the mountain on this day, compared to the 11 February 2008 case, is consistent with the slightly higher low-level stability on this day (section 2). As before, orientation of the height contours is modified such that higher heights are simu-lated on the windward side of Medicine Bow Peak and a leeside trough to the east. Height contours adjacent to the elevated terrain as simulated by the WRF run roughly along a north–south axis just north of the Med-icine Bow Peak. For this case the height perturbations
2000 to 2100 UTC and relax slightly by 2300 UTC. The orientation of the height contours and modification of the intensity of the height gradient in time as modeled by WRF agree well with observations from the UWKA (Fig. 7) for that period.
WRF simulations of wind speed for the 20 February case (Fig. 14) again indicate unsteady conditions. Max-imum winds are simulated in the lee of the Medicine Bow Mountains. Wind speeds are greater than those simulated in case 1 by about 5 m s21, which is consistent with the stronger height gradients. UWKA observations during the period (Fig. 9) show more pronounced wind speed changes across the mountainous terrain than are present in the WRF simulations. This may be the result of the 2-km resolution of the model terrain that may not be as steep as the actual terrain, yet appears to be an adequate model resolution to capture the essential structure of orographic gravity waves induced by a mountain;30 km in diameter.
4. Summary
Flight patterns conducted by the UWKA over a rela-tively isolated mountain range enable detailed mapping of the orographically forced horizontal pressure variations.
Differential processing of raw data collected by an air-borne GPS platform with GPS data from a fixed base station provides a means by which the vertical position of the aircraft can be detected to within O(1021) m. Combined with accurate measurement of static pressure and temperature, isobaric heights can be evaluated and thus the horizontal pressure gradient can be detected. Height tendencies can impact the spatial height patterns thus obtained, because of noninstantaneous measure-ments, but the height trend can be measured, and thus its impact on spatial patterns removed. Large-scale pres-sure variations associated with the mean wind can be removed to isolate the local topographic forcing. Such measurements can be used to understand atmospheric dynamics acting to influence wind patterns associated with elevated terrain, and to validate high-resolution numerical simulations. Case studies were conducted on two days with a similar wind profile, rather low static stability and a bulk Froude number slightly larger than unity. Data collected on these days, 11 February 2008 and 20 February 2009, show significant modification of the isobaric height field adjacent to the Medicine Bow Mountains with leeside troughing, and less pro-nounced windward ridging. The perturbation height field reveals patterns consistent with the theory of stratified flow over an isolated mountain. Comparison of airborne measurements with the WRF results show striking similarities in terrain-induced modulation of the height field. The spatial pattern and magnitude of the height perturbations are repeatable and compara-ble with numerical simulations, leaving no doubt as to the ability of accurately located aircraft to map the finescale horizontal pressure field. The observations and simulations consistently demonstrated a slight difference between the two cases: the case with slightly higher stability yielded a stronger impact of the mountain on the 600-hPa flow, including a stronger height gradient and flow acceleration across the mountain.
Acknowledgments. This research was supported in part by the National Science Foundation through Grant ATM- 0715077. The UWKA flights were funded by the University of Wyoming Water Research Program. The authors wish to thank pilots Tom Drew and Brett Wadsworth, and scientists Jeff French and Larry Oolman, for help with the UWKA field measurements. The NAM 212 grids were obtained from the Research Data Archive, managed by the Data Support Section of the Computational and Information Systems Laboratory at the National Center for Atmospheric Research. The manuscript benefitted from the input of two anonymous reviewers.
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