1. Introduction
Studies of atmospheric transport and dispersion (ATD) in complex terrain are becoming increasingly important. Very stable, weak-wind conditions in the stable boundary layer (SBL) limit the ATD of hazardous materials and may produce serious health threats and major challenges for hazard predictions. The problem is even more difficult in mountainous terrain (Steyn et al. 2013).
Studies of local motions are critical to understanding the dispersion of airborne materials in complex terrain (Gohm et al. 2009). Mixing processes in the SBL can be dominated by nonturbulent submesoscale, or “submeso,” atmospheric motions, which are defined for this study as the motions between the largest turbulent scales and the smallest mesogamma (2–20 km) scales, as in Seaman et al. (2012). The definition must be somewhat fluid since the turbulent eddy size is very small for strongly stable conditions and increases substantially with decreasing stability. In addition, observations are generally analyzed in the time domain instead of the space domain.
Common submeso motions in the very stable boundary layer include wavelike motions and solitary waves, quasi-horizontal modes, microfronts, intermittent drainage flows, and more-complex structures, as surveyed in Mahrt (2014). Acevedo et al. (2014) found that submeso motions exhibit a site-dependent dynamic influence on local similarity variables such as the friction velocity. These motions always appear to be present, but their effects are most readily observed when the mean surface wind is weak (<~2 m s−1; Anfossi et al. 2005). In weak-wind conditions, common significant near-surface directional shear (Mahrt et al. 2014) can advect hazardous material in multiple directions and thereby affect a larger fraction of the nearby population. This shear is often caused by submeso transient modes and shallow, terrain-induced motions.
It is well known that synoptic conditions can affect local variations of winds within a mountain–valley terrain environment (e.g., Whiteman and Doran 1993). Many previous studies, as reviewed in Zardi and Whiteman (2013), have focused on the relationship between ambient conditions at or above ridge top and the nature of drainage flows generated by the terrain. In weak-wind, very stable conditions, drainage flows and cold pools can develop even with relatively small terrain features and gentle slopes (Mahrt et al. 2013). Drainage flows, a common occurrence in the “Rock Springs” (RS) network of central Pennsylvania (Mahrt et al. 2010), can also generate gravity waves (Viana et al. 2010; Jackson et al. 2013). Princevac et al. (2008) found that internal waves within drainage flows are partly responsible for the sustained turbulence that is observed in complex-terrain flows, even in very stable conditions. The drainage flow can also interact with the cold pool or become decoupled from the overlying synoptic conditions (Weber and Furger 2001; Mahrt et al. 2010), leading to more-complex motions within the valley. Batchvarova and Gryning (1998) found that local terrain properties can be more important than the effects of differing synoptic flow on the turbulence, highlighting the difficulties associated with complex terrain.
The development of gravity waves is ubiquitous in the SBL, especially in regions of complex terrain (Nappo 2002). Observational evidence suggests that wavelike submeso motions may actively interact with the turbulence (Sun et al. 2015). Empirical and modeling data have shown that propagating waves aloft can affect the surface by generating near-surface submeso motions and intermittent turbulence (Nastrom and Eaton 1993; Young et al. 2009; Seaman et al. 2012). Therefore, an understanding of submeso motions aids in our understanding of the generation of SBL turbulence. Study of such waves is impeded, however, because they are rarely well defined with constant amplitude or period for more than one cycle (i.e., they are “dirty waves”), and nonlinear effects are always present in the flow (Sun et al. 2015).
A case-study approach is used here to examine observed nonturbulent submeso motions in the moderately complex terrain of central Pennsylvania. To improve our understanding in the SBL, we first note the occurrence of small-scale processes and possible submeso events, including wavelike motions, microfronts, and drainage flows, in different flow regimes; we then mathematically analyze how the submeso fluctuations may be related to local indicators and the larger-scale meteorological conditions and terrain. The Pennyslvania State University (PSU) real-time Advanced Research configuration of the Weather Research and Forecasting (WRF-ARW, hereinafter WRF) Model, version 3.1 (Skamarock et al. 2008; Seaman et al. 2012), is used as a supplementary tool to help us to better interpret the analysis of observations. Model cross sections are used with the observational data to discuss spatial temperature and wind structure in the lower atmosphere and to reveal the presence of mesogamma or submeso motions (i.e., gravity waves, drainage flows, etc.).
Whereas Sun et al. (2002, 2004) thoroughly examine the occurrence of three distinct turbulent events over the flat terrain of Kansas using data from the Cooperative Atmospheric Surface Exchange Study October 1999 (CASES-99) field program, our study focuses on complex terrain. The terrain setting of the RS network is similar to that of many cities in the northeastern United States, where populations tend to be more dense and thus more vulnerable to an attack or accidental release involving harmful airborne materials. Thus, the RS network is particularly useful for the study of submeso motions in the SBL and their potential effects on hazard predictions. We will examine the extent to which the synoptic flow and local factors affect the magnitude and characteristics of local submeso motions within our network.
We hypothesize that synoptic flow from the direction of nearby terrain can produce wave motions that generate larger-amplitude submeso motions over the network than does synoptic flow from the direction of more distant terrain. Also, synoptic winds that are parallel to these terrain features or that are weak in general should result in the smallest local submeso fluctuations, following Mahrt et al. (2010), who found that wind direction shifts at RS were small for synoptic along-valley flow. To test the validity of these hypotheses, we employ an exploratory method to compute observed submeso fluctuations of low-level wind and temperature. We split the observed time series into a mean and a time-varying fluctuation over a period within the submeso range. We then investigate whether any relationships exist between these fluctuations and various local indicator variables and the synoptic regime.
2. RS observation network
The RS network in central Pennsylvania is unique in its combination of a long duration of observations, proximity to complex-terrain features, high vertical resolution of observations near the surface and aloft, and accompanying high-resolution, real-time, daily WRF forecasts (e.g., Stauffer et al. 2009; Mahrt et al. 2010, 2013; Seaman et al. 2012). The network is located at the base and on the northwest-facing slope of Tussey Ridge (~300-m valley-to-ridge height) and approximately 15 km southeast of the Allegheny Mountains (~350-m valley-to-ridge height). The network was deployed in the summer of 2007, and, following continuous improvements, it reached the configuration used for this study in the summer of 2011 (Table 1; Fig. 1).
Instrumentation log for fixed towers in the RS network as of summer 2011.
The RS instrument network configuration during study period of this paper (23 Aug–13 Sep 2011). Color coding of sites in the key at top left indicates the height of each tower. The horizontal distance scale is given at the bottom left of the map. Refer to Table 1 for instrumentation that is affixed to each tower. Map data are copyright 2013 by Google.
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
During this study period, the network consisted of eight instrumented towers, ranging from 2 to 50 m, and two sound detection and ranging (sodar) systems distributed over a 3-km region along the northwest slope of Tussey Ridge (Fig. 1). Wind measurements were obtained from Vaisala, Inc., model WS425 two-dimensional (2D) sonic anemometers, designed to measure horizontal wind speed and wind direction with an accuracy of ~0.1 m s−1 and ±2°, respectively, and Campbell Scientific, Inc., model CSAT3 three-dimensional (3D) sonic anemometers, designed to sample all three components of the wind vector (u, υ, and w) with measurements of precision of 1, 1, and 0.5 mm s−1, respectively. Air temperature measurements were made using Campbell Scientific model T107 thermistors (accuracy of ±0.4°C), housed in unaspirated, multiplate radiation shields, at every observation site and a high-vertical-resolution array of Omega Engineering, Inc., model TMTSS-020G thermocouples (accuracy of ±0.1°C) at site 9 (Table 1). It is important to note that the sensing junction of the copper–constantan thermocouples is located inside the end of a 6-in. (~15 cm) stainless-steel sheath that is 0.02 in. (~0.5 mm) in diameter. They are unshielded for nighttime measurements, in which case thermal loading on the sensor is small, and it is preferential to maximize air circulation around the sensor.
In addition, two portable Atmospheric Systems Corporation Wind Explorer model 4000we sodar systems are deployed within the RS network (Fig. 1) to provide remotely sensed measurements of the full 3D wind vector and its variance at 5-m vertical intervals (“range gates”) from 30 to ~250 m AGL, depending on atmospheric conditions (Bradley 2008). These measurements are useful for providing wind observations at heights for which we have no in situ measurements but where variability in wind and turbulence is expected to have a significant impact on submeso and turbulence variability in the shallow SBL.
3. Numerical model description
The PSU real-time WRF is used as a supplementary tool to help us to better interpret the analysis of observations. The model domain is composed of four one-way nested grids with 12-, 4-, 1.33-, and 0.444-km grid spacings [as in Seaman et al. (2012)]. The width of the primary terrain features in central Pennsylvania (from kilometers to tens of kilometers) necessitates the use of a subkilometer grid mesh to resolve atmosphere–terrain interactions. The model is configured with 43 vertical layers, the lowest 5 of which have 2-m spacing, thereafter increasing gradually up to the model top at 50 hPa. There are 11 layers in the lowest 68 m AGL. For each of the seven case studies, WRF is initialized at 0000 UTC (1900 LST) and integrated for 12 h. Additional real-time model details for this analysis period in 2011 are summarized in Seaman et al. (2012).
Cross sections of potential temperature and in-plane wind vectors are provided by the daily, real-time WRF run for each of the seven cases. The cross sections, as shown in Fig. 2, extend horizontally about 19 km from northwest to southeast, roughly centered on the RS network. The vertical cross sections extend from 0.2 to 0.8 km above mean sea level (MSL) and include the RS network (~360 m MSL) and Tussey Ridge (~650 m MSL).
PSU real-time WRF domain (Δx = 444 m). The RS instrument network is given by the yellow ellipse. The locations of State College (label S) and Bellefonte (label B) are also given. The red dashed line indicates the location of WRF cross sections to be discussed. Stars at points 1–3 are used for synoptic-analysis discussion and calculations.
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
4. Case-study characterization and analysis
a. Method
Atmospheric stability information at site 9 (see Fig. 1) for the seven case studies including 12-h-averaged (0000–1200 UTC; 1900–0700 LST) thermal stratification between 2 and 9 m, 12-h-averaged wind speed at 9 m AGL (and 2 m AGL), percentage of 1-min values of Rib exceeding 1, and stability classifications.
Nights are classified here as “very stable” when at least 50% of the 1-min Rib values exceed 1.0, and those cases with fewer than 50% exceeding 1.0 are “weakly stable.” Note also that, even excluding cases with nonstationarity and heterogeneity, only the weakly stable regime generally follows similarity theory (Mahrt 2014). Of the seven cases studied here, five are very stable and two are weakly stable (Table 2). Although this simple classification scheme can provide some idea of how stability can affect near-surface submeso motions, individual cases in each class exhibit large variability, and generalizations about the two stability classes may not be immediately evident. Prior to the establishment of RS, Mahrt (2007) found that the strength of submeso motions as based on the velocity variance at networks across the United States can vary by more than an order of magnitude from one night to the next within a given network.
We then categorize the seven cases on the basis of the dominant synoptic wind direction with respect to the local terrain features. Table 3 provides North American Regional Reanalysis (NARR) data at 925 hPa for an overall assessment of the synoptic flow over the valley and near ridge tops. The NARR data are thus provided in space (the three numbered stars, which indicate positions near the Allegheny Mountains, the central valley, and Tussey Ridge; Fig. 2) at three times (0000, 0600, and 1200 UTC) for each case. Day-of-year (DOY) cases 236 and 239, with synoptic winds that cross the nearby Tussey Ridge before reaching the network, are defined as near-terrain-crossing (NTC) cases. As mentioned above, we hypothesize that these cases may exhibit the largest local fluctuations, because of the network’s location on, or just beyond, the slope of the forcing terrain feature. Next, the far-terrain crossing (FTC) cases (DOY 235, 238, and 241) exhibit synoptic winds that cross the Allegheny Mountains before reaching the network. We hypothesize that these cases may have a smaller effect on local flow because the Alleghenies are much farther away from the network (~15 km) than is Tussey Ridge. Cases with winds parallel to the terrain features or with weak flow in general (PW; DOY 256 and 254, respectively) should yield the smallest fluctuations.
Synoptic wind information for seven cases using NARR (Δx = 32 km) values at 925 hPa above labeled points (see Fig. 2). Note that LST = UTC − 5 h.
For the purposes of this study, the credibility of the WRF forecasts is established by comparing the forecast flow near ridge top and over the valley with those values from the NARR analysis. The average magnitude of the differences in the nine-point vector-averaged wind speed from our WRF real-time forecasts and the interpolated NARR analyses over the three locations and three times for all seven cases is ~1.5 m s−1, and the mean absolute difference of wind direction is ~29°. If we exclude the very-light-wind case (DOY 254, with more variable wind directions), the average magnitude of the wind speed difference is ~1.3 m s−1 and the wind direction difference is ~20°. Therefore, the WRF-forecast flows are generally consistent with those in the NARR analyses, and the cross sections and mesogamma-scale features from the WRF high-resolution forecast can assist in the discussion of the observation data.
b. Case-study analysis
The frequency distributions of wind speeds from site 9 (see Fig. 1) were analyzed for all seven cases using 1-min averages of 20-Hz u and υ components (not shown). At 9 m AGL, ~40% of the winds are ≤ 0.5 m s−1, while at 1 m AGL, ~50% of the winds are below this threshold. At all levels, at least 75% of the winds are ≤ 1 m s−1. A vast majority (>85%) of the observed wind speeds during these seven nights at site 9 are below 1.5 m s−1, an approximate maximum wind speed for poor dispersion conditions (Hanna et al. 2012). These cases represent a typical range of nighttime characteristics and submeso variations during the summer and autumn seasons in the RS network.
1) NTC cases
DOY 236 and 239 are both characterized by synoptic winds with a component directed from nearby Tussey Ridge to the south-southeast before reaching the RS network (Table 3). Given that a wind direction of 245° would be parallel to Tussey Ridge, the terrain-crossing angle is smaller for DOY 236 (average direction of 199° at point 3) than for DOY 239 (141°); the larger average wind speeds on DOY 236 (e.g., 8.9 vs 4.9 m s−1 at point 3) lead to DOY 236 actually having the largest cross-mountain wind component from the direction of Tussey Ridge out of any of the seven cases, however.
The WRF cross sections in Fig. 3 allow us to visualize the spatial structure of the wave motions that may be affecting the observed RS network time series. In both cases, the PSU WRF forecasts a lee wave above or within the network. The WRF 0.444-km forecast for DOY 236 produces a wave of larger amplitude and wavelength and stronger near-surface winds in the lee of Tussey Ridge than does that for DOY 239. The wave activity for DOY 236 extends down to the surface whereas that for DOY 239 is dampened near the surface because of the presence of a strongly stratified layer. As a consequence, the model forecast from DOY 236 produces larger temperature and wind fluctuations than that from DOY 239 (not shown), and markedly different near-surface temperature and wind responses for the two cases are observed (Figs. 4 and 5).
PSU real-time WRF (Δx = 444-m domain) cross sections of potential temperature (colored contours; K) and in-plane wind vectors (m s−1) for NTC cases: (a) DOY 236 at 0500 UTC (0000 LST) and (b) DOY 239 at 0600 UTC (0100 LST). The black star represents the approximate location of the RS instrument network at the base of Tussey Ridge. Note the exaggeration of vertical vectors and that maximum speeds are given below the cross section.
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
Low-level observations at site 9 at 9 m AGL from the NTC cases: DOY 236 (blue) and DOY 239 (red), showing (a) temperature (°C), (b) wind speed (m s−1), (c) wind direction (°), and (d) turbulent kinetic energy (m2 s−2). All data are shown as 1-min data with a 5-min running filter applied. The TKE of DOY 239 [red line in (d)] is multiplied by 10 for better visualization.
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
Time series of 1-min RS-network observed temperature (°C) from 0000 to 1200 UTC (from 1900 to 0700 LST) on DOY 236 (NTC) with 5-min running average applied. Data include all available sites in the RS network on DOY 236.
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
Figure 4 shows the 12-h time series of site-9 observational data for these two cases. DOY 236 exhibits larger temperature, wind speed, and TKE fluctuations than does DOY 239. We hypothesize that differences in the wave characteristics and structure may help to explain the differences in the submeso fluctuations over the network. Following ~3 h of nighttime radiational cooling, the temperature on DOY 236 increases abruptly (~6°–7°C in ~3–5 min). At the same time, the 9-m wind speed increases by ~3 m s−1; the wind direction shifts and becomes a more-steady, south-southeasterly flow similar to that of the ridge-top flow; and the TKE increases abruptly. Model forecasts suggest that the observed warming and increased winds in the valley may be associated with the horizontal displacement of the surface cold pool and vertical mixing of relatively warm, southerly air from a lee wave generated by Tussey Ridge under increasing synoptic-flow conditions (Table 3). [Although beyond the scope of this paper, in which the focus is on the observed near-surface fluctuations, the PSU WRF produces similarly correlated temperature and wind speed fluctuations for this challenging day, but with smaller amplitudes and a 3-h temporal phase error (Suarez and Stauffer 2014).]
The stronger wind speeds and steady downslope wind directions after 0300 UTC (2200 LST) are known characteristics of foehn winds, common in the lee of much larger mountain ranges such as the Rockies, where they are known as chinook winds (Beran 1967). This phenomenon is well explored in the western and midwestern United States, but studies of foehn winds near the Appalachian Mountains are relatively few (Gaffin 2002, 2007). The comparatively gentle slopes and lower elevation of the Appalachians do not usually lend to the development of foehn winds (Gaffin 2002). Nonetheless, RS observations suggest that DOY 236 may resemble a downslope-wind event, a somewhat rare and very interesting feature for this region.
Figure 5 shows the large temperature increases at 0300 UTC (2200 LST) occurring down to 2 and 5 m AGL at site 9 and also at 2 m at several nearby sites. This robust signal over the RS network appears weaker for stations farther up the Tussey slope (e.g., sites 6 and 7) and higher above the valley floor (e.g., site 10). The steplike increase in temperatures persists for ~2 h after the initial warming, a characteristic of warm microfronts (Belušic and Mahrt 2012; Mahrt 2010). Except for brief cold periods, the increased temperature, turbulence, and wind speed remain for the rest of the night.
Observations from sodar 2027 indicate an increase in downward vertical velocities w from 30 to ~120 m AGL at ~0300 UTC (Fig. 6a), the approximate time of the large temperature increase (Fig. 5). Given the location of Sodar 2027 near the base of Tussey Ridge (Fig. 1), the strong, persistent downward motions are likely generated by the descending branch of the quasi-stationary lee wave (cf. how well Fig. 6a sodar vertical motion data agree with those in Fig. 6b from WRF). Throughout the night, the wave strength fluctuates such that downward motions are strongest from ~0500 to ~0600, ~0700 to ~0900, and ~1000 to ~1100 UTC. These periods coincide with observations of relatively warm, fast-moving air within the network (Fig. 4). Several times throughout the night, the lee wave in the model recedes away from the network (not shown), allowing cool, weak wind air to briefly return to the network (as suggested in Figs. 4 and 5), possibly in the form of a microfront or gravity-driven density current. As expected, there is a general lack of directional preference in the cold air during the cool periods. These intermittent periods of relatively cool, calm air are opposite to a more typical nighttime period, in which bursts of turbulent air are interspersed through otherwise calm SBL conditions (Sun et al. 2002).
Time–height series of vertical velocity (m s−1) from (a) sodar 2027 and (b) PSU WRF from 0000 to 1200 UTC (from 1900 to 0700 LST) on DOY 236 (NTC). Note that upstream Tussey Ridge is ~300 m above the valley floor.
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
DOY 239, exhibiting weaker wave forcing than DOY 236, is characterized by small temperature fluctuations of ~1°–2°C, wind speeds less than 1 m s−1, highly variable wind directions, and little TKE through most of the night (Fig. 4). Sodar observations suggest wavelike fluctuations in the echo intensity extending from 80 to 240 m AGL (Fig. 7). These regions of enhanced turbulence may be mostly decoupled from the surface.
Time–height cross section of sodar 2027 echo intensity (dB) from 0000 to 1200 UTC (from 1900 to 0700 LST) on DOY 239 (NTC).
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
The degree of coupling between the waves/elevated turbulent regions and the surface may help to explain some of the differences in the near-surface temperature and wind measurements for DOY 236 and DOY 239. Whereas DOY 239 shows turbulence aloft with quasi-periodic amplitude that is possibly associated with waves (Fig. 7), DOY 236 is dominated by a nearly unchanging pattern of strong echo intensity extending from 30 to ~200 m AGL after 0300 UTC (2200 LST), possibly related to wind shear and turbulence associated with a large-amplitude lee wave. Thus, despite both cases showing synoptic-flow wind components from Tussey Ridge and lee-wave behavior, the wave-motion details and their effect on turbulence and the SBL over the network are very different.
2) FTC cases
DOY 235, 238, and 241 all exhibit synoptic wind with a northerly component that forces air over the Allegheny Mountains before reaching the RS network (Fig. 8, Table 3). According to WRF, some wave activity over the network is present but is generally reduced in amplitude relative to that for the two NTC cases in Fig. 3. For each of the FTC cases, cross sections spanning the entire valley (not shown) indicate that the model forecasts partially trapped waves generated by the Allegheny Mountains and rapidly decreasing in amplitude before reaching the RS network (Fig. 8). Model forecasts for DOY 235 also appear to exhibit some wave breaking over the network (see isentropic shading in Fig. 8a). These results are similar to those of Young et al. (2009) that show waves from the Allegheny Mountains breaking and affecting the cold pool over the RS network.
As in Fig. 3, but at 0600 UTC (0100 LST) for FTC cases: DOYs (a) 235, (b) 238, and (c) 241. Arrows correspond to maximum speeds in the cross section.
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
Figure 9 shows site-9 temperature, wind speed, wind direction, and TKE for all three cases. Temperatures generally decrease through the night for all three cases at roughly the same rate, although cooling is delayed on DOY 235 and mean temperatures for DOY 238 are several degrees warmer than for the other cases. All of the cases are characterized by weak near-surface wind speeds (<2 m s−1), highly variable wind directions, and highly fluctuating TKE that may indicate the effect of various turbulence-generating submeso motions (e.g., solitary waves, microfronts, and density currents) that can be very difficult to identify. Although an exact identification of features may not be possible or would be beyond the scope of this work, some submeso phenomena appear to be present. For example, drainage flow may be possible during the first ~1 h (or more) of the time series for DOY 238 as indicated by the southerly winds at site 9 (Fig. 9) and persistent southerly winds at site 6 (not shown). Drainage flows in the RS network have been shown to begin up to 2 h before sunset at site 6 and can be seen in the valley until the cold pool is established (Mahrt et al. 2010).
As in Fig. 4, but for the FTC cases: DOY 235 (blue), DOY 238 (red), and DOY 241 (black). Here, MF and arrow in (a) denote passage of a warm microfront on DOY 238.
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
In addition, a notable increase in the temperature for DOY 238 from 0300 to ~0600 UTC (from 2200 to ~0100 LST) suggests the passage of a warm microfront (Fig. 10). Figure 9 shows an increase in wind speed and TKE and the shift in wind direction at this time as well, supporting the possibility of a warm microfront (Mahrt 2010). The warming associated with this feature is observed to occur at sites 10, 3, 9, and 12 successively, as well as from higher levels to lower levels (Fig. 10), suggesting a downward propagation from the northwest.
As in Fig. 5, but for DOY 238 (FTC). Data include all available sites in the RS network on DOY 238.
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
Sodar measurements from DOY 238 indicate that the height of enhanced turbulence intensity thickened to ~200 m AGL before increasing abruptly at ~0315 UTC (Fig. 11). Also at this time, horizontal wind vectors up to 150 m above the sodar and at 33 and 47 m AGL at site 10 indicate northwesterly flow (not shown), confirming the propagation direction in the network. The spike in turbulence could signify the passage of the microfront over the sodar, which takes place approximately 15 min after its passage by site 10 (Fig. 10). After the surge, the turbulence steadily decreases with time through the layer (Figs. 9 and 11). Downward motions during the passage of the microfront (below ~50 m AGL), and their strengthening shortly after (~0350 UTC; up to ~120 m AGL), are observed by the sodar and at 33 and 47 m AGL at site 10 (not shown).
Time–height series of vertical velocity (m s−1) from sodar 2027 from 0000 to 1200 UTC (from 1900 to 0700 LST) on DOY 238 (FTC).
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
For the FTC cases, weaker wave activity allows other submeso motions such as drainage flows and microfronts to be seen. The fact that the three FTC cases appear to show signatures of different submeso phenomena suggests that local submeso motions are not solely dependent on the synoptic conditions but depend on local conditions as well. Overall, many factors appear to play a role in the nature of the submeso motions that affect SBL turbulence; submeso motions are generally thought to be nondeterministic (Mahrt et al. 2012). This further motivates an investigation into statistical relationships between the magnitude of the submeso temperature and wind fluctuations with various local indicators and synoptic regimes (section 5).
3) PW cases
DOY 254 and 256 do not exhibit strong terrain-crossing synoptic flow over central Pennsylvania (Table 3), and the wave motions in the model cross sections are generally absent or weak (not shown). DOY 254 is characterized by very weak winds at 925 hPa (~1–4 m s−1) and wind directions varying from 250° to 320° (Table 3). Table 2 shows that, despite the weak ambient near-surface 12-h average wind speed (0.6 m s−1), the weak average thermal stratification (0.2°C between 2 and 9 m) present in the RS network leads to reduced local stability (~0.03°C m−1) and a “weakly stable” characterization that results from cloud cover (not shown). In fact, DOY 254 is very different from all other cases in this study because of the presence of ambient cloud cover or fog in the valley and somewhat weaker radiative forcing for drainage flows. The temperature and TKE fluctuations in Fig. 12 are generally small relative to those in the NTC and FTC cases. These types of perturbations, without a clear source or coherent signal in all fields, highlight the difficulty often encountered when attempting to identify submeso motions. Although DOY 236 [NTC cases; section 4b(1)] is also classified as weakly stable, the dynamics of these two cases are very different because of the influence of synoptic wind speed and direction.
As in Fig. 4, but for the PW cases: DOY 254 (blue) and DOY 256 (red).
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
DOY 256 has even stronger average 925-hPa synoptic winds (9.5 m s−1) than DOY 236 (8.9 m s−1), but its flow is from ~260°, within 15° of the orientation of Tussey Ridge and 25° of the Allegheny Mountains. Unlike the FTC and NTC cases, characteristics of any specific submeso phenomenon on DOY 256 are difficult to analyze because of its much weaker signature in network observations (Fig. 12). This is reflected in the temperature time series and the weaker wind speed, which leads to larger variations in wind direction and generally weak TKE throughout the night. There is also much reduced spatial coherence across the network (not shown).
Both PW cases exhibit drainage-flow signatures during the earlier hours of the night. Weaker synoptic forcing allows the development of some drainage flows within the network and strongly stratified cold pools that may contribute to the lack of spatial coherence among the network stations for PW cases. At 2 m AGL, DOY 254 has < 3 m s−1, southeasterly (downslope) flow at sites 7 and 6 (higher up the slope) and weak (<2 m s−1), omnidirectional flow at sites 3 and 12 (lower in the valley) during the first 3 h of the night (not shown). The observed site 9 time series shows some periods of southerly flow from 0000 to 0200 UTC (from 1900 to 2100 LST; Fig. 12), but the southerly flow at 9 m AGL yields to more variable wind directions in the deepening cold pool in the later period. Similar temperature and wind structures are also observed and forecast for DOY 256, and drainage flows are also apparent at sites 6 and 7 in the first ~4 h (not shown).
c. Summary of NTC, FTC, and PW case analyses
As a result of nearby Tussey Ridge lee-wave activity, temperature and velocity fluctuations in network observations can be very large in the NTC cases (DOY 236 and 239). Conversely, the FTC cases (DOY 235, 238, and 241) generally show lower-amplitude wave motions or waves not reaching the surface and more modest fluctuations in the time series. Because the terrain responsible for the forcing of these waves (Allegheny Mountains) is much farther away and the synoptic environment may not support wave trapping, its influence on network observations is weaker in these cases. The PW cases (DOY 254 and 256) exhibit the weakest fluctuations in the network, and the near-surface motions are more incoherent. Section 5 will quantitatively discuss these submeso fluctuations and their relation to synoptic and local forcing.
5. Computation of characteristic submeso fluctuations
a. Method
In the previous section we performed a subjective analysis of the observed time series of temporal fluctuations on the basis of the three regimes of large-scale flow with respect to upstream terrain. In this section, we quantify the average fluctuations for each of the seven cases and examine the relationships of local indicators and synoptic forcing to the observed submeso motions over all cases. We first isolate time scales relevant to submeso motions. Beginning with 12 h (0000–1200 UTC; 1900–0700 LST) of 1-min temperature and wind speed data at 9 m AGL from site 9 for each case, we filter the data by removing a 2-h running mean. This has been deemed to be a conservative time scale for deterministic predictions (Gaudet et al. 2008; Seaman et al. 2012). To avoid the near-edge effects of this filtering method, we proceed with analysis of the 10-h period between 0100 and 1100 UTC (between 2000 and 0600 LST). We characterize the submeso fluctuations in terms of the standard-deviation values of wind speed and temperature computed over varying interval lengths on the basis of the number of 1-min-averaged data records. The averaging is intended to eliminate turbulence under the assumption that turbulent motions are confined to time scales of less than 1 min. In reality, the largest turbulent fluctuations may correspond to time scales that range from as small as a few seconds for extremely stable conditions to greater than 1 min for windy near-neutral conditions. Using a variable averaging width to accommodate this variability is an uncertain process and complicates interpretation. Therefore, we choose a constant averaging window of 1 min with the recognition that it inadvertently captures some of the submeso motions for the most stable conditions. The upper limit for the submeso range of time scales will be varied to examine the sensitivity to such a choice. For the upper limit, we choose N = 5, 10, 20, and 40 min. These values for N allow the total number of intervals to vary from 120 to 15 for each case.
Next, two separate goals are accomplished using two different methods. The first goal is to determine the local factors, or “indicators,” that may contribute to the magnitude of the submeso wind and temperature fluctuations at site 9. The 1-min data are first block averaged over each interval length N. These averaged data are then used to calculate five indicator variables: Rib, low-level (9 m) wind speed, thermal stratification (between 2 and 9 m AGL), and wind speed and directional shears (between 2 and 9 m AGL). We then compare the standard-deviation values of wind speed and temperature for a given N with each indicator variable for that N. Note that, because of instrument accuracy, any value of the thermal stratification that is less than 0.1 K is not included in the calculations. To calculate the mean characteristic submeso fluctuation strength for each case and N, the standard deviations of site-9 9-m temperature and wind speed are averaged over the period from 0100 to 1100 UTC (from 2000 to 0600 LST). Our second goal is to perform case-to-case and synoptic-regime (NTC, FTC, or PW) comparisons to identify any dependence on the larger-scale synoptic flow and the proximity of network observations to upstream terrain features.
b. Results
Table 4 shows the magnitude of the characteristic submeso fluctuations for both wind speed and temperature for each case and for N = 5, 10, 20, and 40 min. We first note that the magnitude of the fluctuations monotonically increases with the length of the averaging interval N for each case and variable. This result is reflective of the fact that submeso variance is present at all scales from 1 min up to at least 40 min.
The 10-h mean characteristic submeso fluctuations for seven cases and synoptic regimes at site 9 at 9 m AGL. Fluctuations of temperature (TEMP) and wind speed (WSP) for all averaging periods N are given in degrees Celsius and meters per second, respectively.
Figure 13 shows scatterplots of the characteristic submeso wind speed fluctuations versus the corresponding site-9 average 9-m wind speed for each value of N, with different-colored symbols representing each case. The degree of correlation between the submeso wind speed fluctuations and the average speed serves as a measure of the effectiveness of 9-m wind speed as an indicator. A solid black line represents the bin-averaged fluctuation size for 10 bins, each containing M/10 data points, where M is the total number of data points (one for each N-minute interval) summed over all seven cases. The vertical error bars represent the plus/minus standard deviation about the mean value for that bin. The dashed black line (nearly collocated with the solid back line) represents the bin average for the six cases, excluding DOY 236 because many of the largest values come from DOY 236 (green asterisks). Large fluctuations on DOY 236 are likely due to its strong lee-wave dynamics, and we wish to explore the relationships between the mean fluctuations and the indicator values both with and without this case. Figure 13 shows that the wind speed fluctuations exhibit a fairly strong positive relationship with 9-m wind speed with or without DOY 236. It also shows that, while as expected, the variances tend to increase as the averaging interval N is increased, the positive relationship between fluctuations and this indicator is not greatly affected by choice of N. The general insensitivity to N is found for other indicators as well (not shown). Thus, we will proceed with results for N = 10 min as a typical time scale for submeso motions, giving M = 60 × 7 = 420 data points over all seven cases.
Observed submeso fluctuation scatterplots at site 9 showing 9-m wind speed fluctuations vs 9-m wind speed for different averaging periods N, where N = (a) 5, (b) 10, (c) 20, and (d) 40 min. Cases are color coded, and the total number of data points M is divided by 10 to provide bin averages plotted at the center of each bin on the x axis. Within-bin standard deviations are shown by vertical solid black lines. The dashed black line represents bin averages of all data excluding DOY 236 because of its much larger fluctuations.
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
The temperature fluctuations exhibit less dependence on 9-m wind speed, at least in the horizontal plane; only a weakly positive relationship with wind speed is present (not shown). On the other hand, temperature fluctuations exhibit a positive trend with increasing ΔΘ (9 − 2 m) stratification (Fig. 14); the wind speed fluctuation dependence on stratification is quasi-parabolic as a result of DOY 236 producing larger values for near-neutral conditions (not shown). We also find that the wind and temperature fluctuations generally have weak relationships with the indicators of Rib, speed ratio (ratio of 9- to 2-m speed), and direction shear (magnitude of difference in 9- and 2-m wind direction) (not shown), suggesting that these provide no new information. The wind fluctuations appear larger for small Rib and small direction shear when including DOY 236, a result of their inverse relationship with the wind speed.
Similar to Fig. 13, but as based on an N = 10 min averaging period for 9-m temperature fluctuations (K) vs thermal stratification between 2 and 9 m (K).
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
Given that the strongest relationship is found between the 9-m wind fluctuations and wind speed, we conducted another analysis to determine if a secondary dependence with some other indicator could be identified. In other words, might one of the other indicators be largely responsible for the large scatter from the bin-average lines in Fig. 13b? Therefore, we compared the difference between each fluctuation and its bin average with the other indicator variables. We found that variance from the relationship between characteristic submeso wind fluctuations and wind speed showed very little correlation to the four other indicators (not shown).
We then hypothesized that there may be a dependence of the submeso wind fluctuations on the wind direction that is related to the local terrain features, because the magnitude of the wind and temperature fluctuations in the RS time series analyses (section 4) showed some such dependence on the large-scale flow direction. Figure 15 shows the observed frequency of 10-min wind fluctuations versus wind direction at 2 and 9 m AGL at site 9. Figure 15a shows that the larger-than-average fluctuations have a preference for flow from 160° to 180°, which is from the direction of Tussey Ridge. Conversely, smaller-than-average fluctuations in Fig. 15b show a preference for flow from 70° to 80° and 210° to 230°, or roughly along Nittany Valley. Note, however, there is a secondary maximum from 170° to 180° for the smaller fluctuations, possibly related to drainage/blocked flows. These results suggest that when the flow is parallel to the Nittany Valley the wind speed fluctuations are predominantly weak. Thus, local flow directed from Tussey Ridge appears to be important for the generation of larger-amplitude submeso motions over the RS network, providing as hypothesized a strong terrain dependence for these local fluctuations.
Observed frequency distributions of 9- and 2-m wind speed fluctuations vs wind direction in 10° intervals at site 9: (a) fluctuations larger than their bin average (from Fig. 13b) and (b) fluctuations smaller than their bin average (from Fig. 13b).
Citation: Journal of Applied Meteorology and Climatology 54, 2; 10.1175/JAMC-D-14-0128.1
Further support for this hypothesis is provided by the synoptic-regime dependence within Table 4. We see that the average fluctuations are largest for the NTC cases. Note that, as indicated in the previous section, both NTC cases are characterized by lee-wave activity on the nearby slope of Tussey Ridge by WRF. In the network time series, fluctuations on these nights (especially DOY 236) can be very large. The next-largest average fluctuations of temperature and wind speed are found for FTC cases: DOY 235, 238, and 241. Recall that wave forcing from the Alleghenies is generally weaker over the RS network on these nights, and observations indicate the presence of a microfront or drainage flows. The two PW cases exhibit the smallest average fluctuations. These results suggest that, in complex terrain, synoptic forcing can serve a role as an indicator for the presence and size of submeso motions, but the importance of this role depends on distance from terrain and the impact of wave motions near the surface. All of these factors may have implications for parameterization of turbulence that is due to submeso motions in numerical models to better represent the effects of wave–turbulence interactions on ATD in complex terrain.
6. Summary and conclusions
Seven case studies of the nocturnal SBL within the moderately complex terrain of central Pennsylvania are chosen and analyzed using observations from a network of fast- and slow-response instruments as well as supplemental information from the NARR analysis product and the PSU real-time WRF Model. These cases, representing both weak and strong atmospheric stability, as based on Rib, are then grouped by synoptic-flow regime and the proximity of the network to the upstream terrain. The analysis suggests that, in addition to local stability, synoptic regime and nearby terrain are important for submeso motions and SBL turbulence.
The analyses have revealed that submeso mean wind speed and temperature fluctuations (5-, 10-, 20-, and 40-min intervals) are larger when low-level wind speed and stratification are greater, respectively. Other indicator variables, including Rib, and wind speed and directional shears, show weak relationships with submeso fluctuations. A dependence on local wind direction was also found for velocity fluctuations, such that larger-than-average perturbations are associated with flow from nearby Tussey Ridge. This finding suggests that the magnitude of submeso motions is enhanced by topographical influences.
A similar relationship was found for synoptic regime as well. Cases with southerly large-scale flow exhibit the largest submeso fluctuations as a result of enhanced wave activity from the nearby Tussey Ridge. Of the two NTC cases, DOY 236 is characterized by stronger wave activity related to a downslope-wind event, but on a smaller spatial scale with smaller elevation differences when compared with those locations that are more commonly analyzed in the literature (e.g., Rocky Mountains). DOY 239, on the other hand, shows characteristics similar to a trapped lee wave, with moderately sized undulations in the observed time series. Cases with northerly synoptic flow exhibit smaller submeso fluctuations because of a weaker influence from the more distant (~15 km) Allegheny Mountains. These FTC cases are characterized by various nonturbulent motions including drainage flows and microfronts. The PW cases are characterized by the smallest submeso fluctuations in the network, and local observations indicate weak and spatially incoherent motions. Again, the influence of the topography on local motions is apparent.
We believe that this study is the first in the literature to investigate general relationships between various local and synoptic indicators and submeso motions, which are important for understanding and predicting turbulence in the SBL. This work highlights the complexity of the nocturnal SBL in the presence of varying synoptic forcing and moderate-terrain features but also suggests the possibility for some degree of stochastic predictability of submeso motions and SBL turbulence that result from wave–turbulence interactions. This type of research may also have important repercussions in the field of atmospheric transport and dispersion, especially for the densely populated northeastern United States, where these moderate-terrain features are very common. Future work should include a larger number of cases such that statistical methods can be expanded to better determine the relationships between these and other local indicators and synoptic regimes on submeso motions.
Acknowledgments
This project received support from the Defense Threat Reduction Agency (DTRA; Grant HDTRA1-10-1-0033) under the supervision of Dr. John Hannan. Funding for sodars and additional site-9 instrumentation was provided by the U.S. Army Research Office under DURIP Grant W911NF-10-1-0238, and we are grateful to Dr. Walter Bach for his interest and support. Glenn Hunter of PSU assisted with WRF data processing; Dr. Kenneth Underwood and Mr. Josh Underwood at Atmospheric Systems Corporation provided sodar installation services, maintenance assistance, and knowledge of sodar operating principles; and Dr. Dennis Thomson lent helpful insight on acoustic measurements of the atmosphere.
REFERENCES
Acevedo, O. C., F. D. Costa, P. E. S. Oliveira, F. S. Puhales, G. A. Degrazia, and D. R. Roberti, 2014: The influence of submeso processes on stable boundary layer similarity relationships. J. Atmos. Sci., 71, 207–225, doi:10.1175/JAS-D-13-0131.1.
Anfossi, D., D. Oetti, G. Degrazia, and A. Goulart, 2005: An analysis of sonic anemometer observations in low wind speed conditions. Bound.-Layer Meteor., 114, 179–203, doi:10.1007/s10546-004-1984-4.
Batchvarova, E., and S. Gryning, 1998: Wind climatology, atmospheric turbulence and internal boundary-layer development in Athens during the MEDCAPHOT-TRACE experiment. Atmos. Environ., 32, 2055–2069, doi:10.1016/S1352-2310(97)00422-6.
Belušic, D., and L. Mahrt, 2012: Is geometry more universal than physics in atmospheric boundary layer flow? J. Geophys. Res., 117, D09115, doi:10.1029/2011JD016987.
Beran, D., 1967: Large amplitude lee waves and Chinook winds. J. Appl. Meteor., 6, 865–877, doi:10.1175/1520-0450(1967)006<0865:LALWAC>2.0.CO;2.
Bradley, S., 2008: Atmospheric Acoustic Remote Sensing. CRC Press, 271 pp.
Gaffin, D., 2002: Unexpected warming induced by foehn winds in the lee of the Smoky Mountains. Wea. Forecasting, 17, 907–915, doi:10.1175/1520-0434(2002)017<0907:UWIBFW>2.0.CO;2.
Gaffin, D., 2007: Foehn winds that produced large temperature differences near the southern Appalachian Mountains. Wea. Forecasting, 22, 145–159, doi:10.1175/WAF970.1.
Gaudet, B. J., N. L. Seaman, D. R. Stauffer, S. Richardson, L. Mahrt, and J. C. Wyngaard, 2008: Verification of WRF-predicted mesogamma-scale spectra in the SBL using a high-frequency filter decomposition. Ninth WRF Users’ Workshop, Boulder, CO, University Corporation for Atmospheric Research, P8.1. [Available online at http://www2.mmm.ucar.edu/wrf/users/workshops/WS2008/abstracts/8-01.pdf.]
Gohm, A., and Coauthors, 2009: Air pollution transport in an alpine valley: Results from airborne and ground-based observations. Bound.-Layer Meteor., 131, 441–463, doi:10.1007/s10546-009-9371-9.
Hanna, S. R., 1983: Lateral turbulence intensity and plume meandering during stable conditions. J. Appl. Meteor., 22, 1424–1430, doi:10.1175/1520-0450(1983)022<1424:LTIAPM>2.0.CO;2.
Hanna, S. R., R. Britter, E. Argenta, and J. Chang, 2012: The Jack Rabbit chlorine release experiments: Implications of dense gas removal from a depression and downwind concentrations. J. Hazard. Mater., 213-214, 406–412, doi:10.1016/j.jhazmat.2012.02.013.
Jackson, P. L., G. Mayr, and S. Vosper, 2013: Dynamically-driven winds. Mountain Weather Research and Forecasting: Recent Progress and Current Challenges, F. K. Chow, S. F. J. De Wekker, and B. J. Snyder Eds., Springer, 121–218.
Mahrt, L., 2007: Weak-wind mesoscale meandering in the nocturnal boundary layer. Environ. Fluid Mech., 7, 331–347, doi:10.1007/s10652-007-9024-9.
Mahrt, L., 2010: Common microfronts and other solitary events in the nocturnal boundary layer. Quart. J. Roy. Meteor. Soc., 136, 1712–1722, doi:10.1002/qj.694.
Mahrt, L., 2014: Stably stratified atmospheric boundary layers. Annu. Rev. Fluid Mech., 46, 23–45, doi:10.1146/annurev-fluid-010313-141354.
Mahrt, L., S. Richardson, N. Seaman, and D. Stauffer, 2010: Interaction between drainage flows, the valley cold pool and submeso motions. Tellus, 62A, 698–705.
Mahrt, L., S. Richardson, N. Seaman, and D. Stauffer, 2012: Turbulence in the nocturnal boundary layer with light and variable winds. Quart. J. Roy. Meteor. Soc., 138, 1430–1439, doi:10.1002/qj.1884.
Mahrt, L., C. Thomas, S. Richardson, N. Seaman, D. Stauffer, and M. Zeeman, 2013: Non-stationary generation of weak turbulence for very stable and weak-wind conditions. Bound.-Layer Meteor., 147, 179–199, doi:10.1007/s10546-012-9782-x.
Mahrt, L., S. Richardson, D. Stauffer, and N. Seaman, 2014: Nocturnal wind directional shear in complex terrain. Quart. J. Roy. Meteor. Soc., 140B, 2393–2400, doi:10.1002/qj.2369.
Nappo, C. J., 2002: An Introduction to Atmospheric Gravity Waves. Academic Press, 279 pp.
Nastrom, G. D., and F. D. Eaton, 1993: The coupling of gravity waves and turbulence at White Sands, New Mexico, from VHF radar observations. J. Appl. Meteor., 32, 81–87, doi:10.1175/1520-0450(1993)032<0081:TCOGWA>2.0.CO;2.
Princevac, M., J. C. R. Hunt, and H. J. S. Fernando, 2008: Quasi-steady katabatic winds on slopes in wide valleys: Hydraulic theory and observations. J. Atmos. Sci., 65, 627–643, doi:10.1175/2007JAS2110.1.
Seaman, N. L., B. J. Gaudet, D. R. Stauffer, L. Mahrt, S. J. Richardson, J. R. Zielonka, and J. C. Wyngaard, 2012: Numerical prediction of submesoscale flow in the nocturnal stable boundary layer over complex terrain. Mon. Wea. Rev., 140, 956–977, doi:10.1175/MWR-D-11-00061.1.
Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note. NCAR/TN–475+STR, 113 pp. [Available online at http://www2.mmm.ucar.edu/wrf/users/docs/arw_v3.pdf.]
Stauffer, D. R., B. J. Gaudet, N. L. Seaman, J. C. Wyngaard, L. Mahrt, and S. Richardson, 2009: Sub-kilometer numerical predictions in the nocturnal stable boundary layer. Preprints, 23rd Conf. on Weather Analysis and Forecasting/19th Conf. on Numerical Weather Prediction, Omaha, NE, Amer. Meteor. Soc.,18B.4. [Available online at https://ams.confex.com/ams/pdfpapers/154288.pdf.]
Steyn, D. G., S. F. J. De Wekker, M. Kossmann, and A. Martilli, 2013: Boundary layers and air quality in mountainous terrain. Mountain Weather Research and Forecasting: Recent Progress and Current Challenges, F. K. Chow, S. F. J. De Wekker, and B. J. Snyder Eds., Springer, 261–289.
Suarez, A., and D. R. Stauffer, 2014: Effects of nonstationary wave structures on rotor development and evolution. Preprints, 16th Conf. on Mountain Meteorology, San Diego, CA, Amer. Meteor. Soc., 11.2. [Available online at https://ams.confex.com/ams/16MountMet/webprogram/Paper251598.html.]
Sun, J., S. P. Burns, D. H. Lenschow, R. Banta, and R. Newsom, 2002: Intermittent turbulence associated with a density current passage in the stable boundary layer. Bound.-Layer Meteor., 105, 199–219, doi:10.1023/A:1019969131774.
Sun, J., and Coauthors, 2004: Atmospheric disturbances that generate intermittent turbulence in nocturnal boundary layers. Bound.-Layer Meteor., 110, 255–279, doi:10.1023/A:1026097926169.
Sun, J., L. Mahrt, C. Nappo, and D. H. Lenschow, 2015: Wind and temperature oscillations generated by wave–turbulence interactions in the stably stratified boundary layer. J. Atmos. Sci., doi:10.1175/JAS-D-14-0129.1, in press.
Viana, S., S. Terradellas, and C. Yague, 2010: Analysis of gravity waves generated at the top of a drainage flow. J. Atmos. Sci., 67, 3949–3966, doi:10.1175/2010JAS3508.1.
Weber, R. O., and M. Furger, 2001: Climatology of near-surface wind patterns over Switzerland. Int. J. Climatol., 21, 809–827, doi:10.1002/joc.667.
Whiteman, C. D., and J. C. Doran, 1993: The relationship between overlying synoptic-scale flows and winds within a valley. J. Appl. Meteor., 32, 1669–1682, doi:10.1175/1520-0450(1993)032<1669:TRBOSS>2.0.CO;2.
Young, G. S., B. Gaudet, N. Seaman, and D. Stauffer, 2009: Interaction of a mountain lee wave with a basin cold pool. Preprints, 13th Conf. on Mesoscale Processes, Salt Lake City, UT, Amer. Meteor. Soc., P1.22. [Available online at https://ams.confex.com/ams/pdfpapers/155040.pdf.]
Zardi, D., and C. D. Whiteman, 2013: Diurnal mountain wind systems. Mountain Weather Research and Forecasting: Recent Progress and Current Challenges, F. K. Chow, S. F. J. De Wekker, and B. J. Snyder Eds., Springer, 35–119.
