1. Introduction

There are several mountain ranges worldwide that are well-known for generation of large-amplitude mountain waves. These include the Alps, the Andes, or the New Zealand Alps. In the United States, the most thoroughly documented range is the Colorado Front Range (e.g., Lilly and Zipser 1972; Clark et al. 2000). Another, the Sierra Nevada in California (Fig. 1) has been until recently less well known among scientists, but it is equally well known among amateur and professional pilots for its generation of large-amplitude lee waves, rotors, strong updrafts, and clear-air turbulence (Holmboe and Klieforth 1957; Kuettner 1959; Whelan 2000).

The Sierra Nevada is an approximately 100-km-wide and 600-km-long quasi-two-dimensional mountain range that forms part of the western rim of the Great Basin. Several factors, including the gentle upwind and steep leeside slopes, make the Sierra Nevada an excellent mountain-wave generator. Because of the absence of significant topography upwind, leeside disturbances are almost exclusively generated by the main massif of the Sierra Nevada range. Additionally, the proximity of the Pacific Ocean provides a source of upper-level moisture that commonly gives rise to clouds atop the mountain-wave crests.

Conducting a climatology of mountain-wave events in the Sierra Nevada is difficult because of the lack of routine measurements that can be directly and unambiguously related to mountain-wave activity. While mountain waves do have a profound effect on the state of the atmosphere, only occasionally are they associated with easily detectable strong leeside surface winds. VHF radar wind profilers have been successfully used to observe mountain-wave activity (Ralph et al. 1992; Worthington and Thomas 1996; Vosper and Worthington 2002). The boundary layer wind profilers (UHF) were also successfully used in capturing signatures of mountain-wave activity (Brown et al. 2005) in the recent Sierra Rotors Project (SRP) and the Terrain-induced Rotor Experiment (T-REX) observational campaigns (Grubišić and Doyle 2006; Grubišić et al. 2008, manuscript submitted to Bull. Amer. Meteor. Soc.). However, while the wind profilers are clearly useful in documenting mountain-wave activity, currently there are no routine wind profiler measurements along the lee side of the Sierra Nevada.

As mountain lee waves provide one of the very few obviously and measurably periodic phenomena seen in cloud formations, studying this phenomenon is a good candidate for application of satellite imagery. Since the early days of satellite meteorology, and in particular with increasing sensor resolution of meteorological satellites, it has become evident that satellite imagery provides a wealth of information on small-scale atmospheric processes in addition to the large-scale synoptic features (Scorer 1986). Application of satellite imagery to the study of orographically induced phenomena such as mountain waves and mountain wakes has a long history (Hubert and Krueger 1962; Conover 1964; Fritz 1965; Chopra and Hubert 1965). Satellite imagery continues to be actively used in mountain-wave research today (e.g., Ralph et al. 1997; Smith et al. 1997; Pan and Smith 1999), where, as is true for mesoscale meterological studies in general, it is most effective when used in conjunction with data from other sensors such as surface weather stations, soundings, radars, or in situ measurements by research aircraft in field campaigns (Smith and Grubišić 1993; Johnson et al. 1994). However, with long uninterrupted records, satellite data are also ideal for climatological studies of mesoscale phenomena (Banta and Schaaf 1987; Moore and Renfrew 2005). In this study of mountain waves, in what effectively is a data-sparse region, we rely primarily on the utilization of high-resolution visible satellite imagery for the detection of lee-wave clouds based on their location, shape, and texture.

With many potential benefits to forecasters, climatologists, mesoscale and regional climate modelers, and for selecting optimal sites and timing of observational field campaigns,¹ existence of such climatologies is clearly important. Additionally, availability of climatologies for different mountain ranges that are known for the generation of lee waves (Auer 1992; Mitchell et al. 1990; Smith 1976; Vosper and Mobbs 1996) would allow for easier generalization of physical process study findings obtained in one region to other such regions in the world.

This note is organized as follows: Section 2 describes the source of data and the method of analysis. Climatology results are presented and discussed in section 3. Section 4 concludes the note.

2. Data sources and analysis methods

Mountain lee-wave clouds in the lee of the Sierra Nevada were identified by visual inspection of visible satellite imagery from the National Oceanic and Atmospheric Administration (NOAA) Geostationary Operational Environmental Satellite (GOES-10). GOES-10 visible images were available to us at 1-km horizontal resolution in 15-min intervals during daylight hours for the 2-yr period from 1999 to 2001. High temporal frequency and fixed field of view of this satellite, made the GOES-10 imagery particularly suitable for this study, which takes advantage of regular sequential observations of cloud patterns.

For mountain waves to form, vertical profiles of thermal stability and wind of the approaching airstream need to be able to support sustained oscillatory motions. Favorable conditions for wave activity include strong cross-mountain winds, and elevated inversions at or near the ridge-top height. In addition to a sufficiently large wave amplitude, for a wave pattern to become visible in satellite imagery, moisture is needed through a sufficiently thick atmospheric depth. Conditions necessary for mountain-wave and wave-cloud formation in the lee of the Sierra Nevada are typically found near frontal zones associated with midlatitude cold fronts (Holmboe and Klieforth 1957). During summer, dry conditions and weaker westerly flows make mountain-wave clouds relatively rare along the Sierra Nevada lee. Consequently, we have focused on the months of October–May as the Sierra Nevada mountain-wave season, during which midlatitude synoptic systems travel past this mountain range, producing conditions favorable for mountain-wave formation.

We have selected the visual inspection method for detection of cloud types associated with mountain waves. While automated systems for interpretation of satellite imagery have been developed for specific applications (Peak and Tag 1992), the pattern-recognition abilities of the human eye/brain apparatus remain superior to automated procedures. The same set of satellite images was independently visually inspected by two analysts and their findings were subsequently compared and merged. As the imagery interpretation expertise requires a combination of skills, including both pattern recognition and the expertise of inferring the meteorological meaning of those patterns, both analysts underwent training on an independent dataset first.

The observed wave clouds were classified in two categories based on the appearance in satellite images. The two categories are the following: 1) lee-wave trains and 2) single wave (“arch”) clouds. These two types are illustrated in Fig. 2, and correspond to the following two types in the classification of orographic cloud patterns by Conover (1964): 1) the wavelike pattern due to lee waves and 2) the isolated lenticular category. For the first type, vertical propagation of wave energy is limited, by a sharp increase of the cross-mountain wind with height or a pronounced mountain-top inversion or a combination of the two factors, resulting in a low-level wave pattern that can extend significant horizontal distances from the generating terrain (Smith 1979). The resulting wavelike pattern consists of approximately parallel cloud bands corresponding to the crests of waves induced by the flow of air over a ridgelike obstacle (Figs. 2b,d). In contrast, mountain waves giving rise to the second type of wave clouds typically occur when wind direction, speed, and stability tend to be more uniform through a deep layer of atmosphere, allowing vertical wave energy propagation and generation of mid- and high-level clouds. For large obstacles, such as the Sierra Nevada, these waves are expected to be mostly hydrostatic, implying nearly vertical wave energy propagation, and, as viewed from the top, a single wave crest located in the immediate lee of the generating mountain range (Figs. 2a,c).

There are several prominent characteristics of mountain waves and wave clouds that can be used to visually identify them in satellite images. Most important is a narrow formation region on the lee side of a mountain range. Given the orographic origin, the cloud is likely to follow the orientation of the mountain range (Fig. 2d). Also, wave clouds tend to be somewhat elliptical and smoother than most clouds, in particular those in the single-wave-cloud category (Figs. 2a,c). The unique shape and texture allow wave clouds to be distinguished from other cloud formations such as orographic cumulus convection, frontal bands, cumulonimbus, and, in particular, cloud streets. Another distinctive feature of wave clouds is the presence of the foehn gap, a slim area of clear skies directly to the lee of the mountain range (Fig. 2d). This clear slot is caused by the subsidence of air in the lee of the mountain. Since the mountain range of interest is snow covered for the major part of the selected October–May period, it is important to distinguish between wave clouds and snow-covered surfaces. Often, mountain valleys remain snow free, which gives snow cover over the mountains a characteristic dendritic appearance. Also, snow shows at a slightly darker tone than clouds in our two categories. Deeper into the winter, questionable cases can be resolved by examining infrared imagery, since cloud-top temperatures are generally colder than surface snow.

In addition to the wave cloud type, the month and general geographic region in which the clouds formed were recorded. For the latter, we have defined four regions of formation (Fig. 1). The northern region extends from the north end of the Sierra Nevada to the latitude of Topaz Lake, Nevada (38.46°N, 118.50°W); the extent of the southern region is from the north end of the White-Inyo Mountains (37.63°N, 118.26°W) to the south end of the Sierra Nevada, whereas the central region bridges these two. A fourth category was created for wave clouds that form along the entire length of the Sierra Nevada range (Fig. 2d). Occasionally, a single wave cloud is combined with a cirrus “cloud plume” (Conover 1964; Jiang and Doyle 2006), which can extend considerable distances downwind (Fig. 2d). In case of a long wave cloud such as that shown in Fig. 2d, the cirrus plume has an appearance of a cloud deck that can partially or completely mask lower-level clouds. Finally, we have also recorded the event duration and, for the lee-wave trains, the wavelength. The latter was taken to be the measured distance downwind of the obstacle with the wave pattern, divided by the number of waves in the interval.

At this point, it is appropriate to discuss some of the limitations of this particular method. The most important limitation is that, while all mountain-wave clouds are caused by mountain waves, not all mountain waves will induce cloud formation. This is especially true in the case of small-amplitude waves and insufficient moisture. Since this method utilizes the identification of wave clouds, “dry mountain waves” will be absent from this climatology. The exclusion of the dry summer months is beneficial in this respect, but this problem can still occur throughout the year.

The number of wave clouds can also be underestimated because of three additional factors. First, since only visible imagery is used, wave clouds that form during nighttime hours but dissipate before daytime will not be identified. The daytime limitation also affects our estimates of the wave event duration, in case of wave events that formed during daylight and extended into nighttime hours or wave events that formed during the night and extended into the daylight hours. Figure 3 shows this error as a function of the month, revealing the largest errors for the months of January–April. While the infrared imagery would help to mitigate this problem by allowing detection of wave clouds during nighttime, the resolution of infrared imagery at 8 km that was available to us proved insufficient to discern finescale features characterizing the majority of detected wave clouds. The second limitation arising from the use of visible satellite imagery is that wave clouds can form underneath higher cloud layers of solid overcast. While highest-amplitude waves may be able to perturb these cloud layers, most wave clouds will be hidden from the satellite’s view. Finally, since the satellite imagery is only 1-km resolution, wave clouds must be relatively large to be identifiable. Small mountain-wave clouds as well as rotor clouds, low-level cumuliform clouds underneath mountain-wave crests that frequently develop in the lee of the Sierra Nevada, are not large enough to be identified in the 1-km imagery. It should be noted that all of these limitations lead to underrepresentation of wave event numbers. Therefore, the climatology presented here represents the lower limits of the frequency of mountain-wave events.

3. Climatology results

This satellite climatology was obtained for two recent seasons, 1999/2000 and 2000/01. While two seasons is far too little to draw final conclusions, it is possible to make some preliminary conclusions on the distribution of mountain waves by type, month, and location.

e. Discussion

Figures 4 and 6 summarize the results on the monthly and spatial distribution of wave events discussed above. While these results are based on a limited dataset and may not accurately represent long-term-average conditions, some patterns are sufficiently pronounced so that it is reasonable to speculate as to the physical processes that might lead to their existence.

Generally there appears to be a predominance of wave events in the northern Sierra Nevada over the southern sierra (Fig. 6). As indicated earlier, the conditions necessary for mountain-wave and wave-cloud formation in the lee of the Sierra Nevada are typically found near frontal zones of midlatitude cold fronts associated with an upper-level trough along the Pacific coast (Holmboe and Klieforth 1957). Strong westerly or southwesterly flow across the sierra range favorable for wave generation is found at the base of this trough; however, the trough must extend sufficiently far southward for this to occur. It is clear that the typical low off the Pacific Northwest will extend its associated trough into the northern sierra more often than into the southern sierra, leading to a larger proportion of wave events in the lee of the northern sierra as reflected in our statistics.

Large interannual variability in the number of events, such as observed for January and May (Fig. 4), can also be related to the synoptic-scale forcing. As Fig. 7 shows, differences in the number of wave events observed in January and May 2000 and 2001 is reflected well in the persistence of strong westerly winds at the 700-hPa level in the 35°–40°N latitude band in these two months in 2000 and their general absence in 2001. This is not surprising given that moderate-to-strong ridge-perpendicular wind (≥8–10 m s⁻¹) at ridge-level height is one of the necessary conditions for wave generation. Some of these long periods of strong cross-mountain winds are due to unusually persistent cutoff lows or blocking highs located off the southern California coast (Fig. 8). Thus, to a large degree the interannual variability of the number of wave events observed in January and May in these two successive wave seasons can be explained by the variability of the synoptic-scale forcing.

In terms of duration, single-wave events appear in general to have shorter duration than lee-wave events. There is some indication also of much longer wave event duration in April and May. Given that April is among the months with the largest underestimate of event duration (cf. Fig. 3), it is quite plausible that April is the month with the longest-lasting wave events in the Sierra Nevada.

The lee-wave train is clearly a more common wave form in the northern sierra, whereas the single wave cloud is found to be a more common feature in the southern Sierra Nevada. To examine to what degree this difference in the wave form is conditioned by the upstream environment, we have examined the upstream profiles of wind and stability for trapped lee-wave and single-wave events in both the northern and southern Sierra Nevada. The Scorer parameter profiles,

View Expanded

where N is the Brunt–Väisälä frequency and U is the component of the wind normal to the sierra ridge, were computed from available Oakland soundings for the northern wave events and from available Vandenberg soundings for the southern events (cf. Fig. 1). The total number of northern events for which Oakland soundings were available at nearby times are 66 and 11 for trapped and single-wave events, respectively. The corresponding numbers for the south are 19 trapped and 32 single-wave events with available Vandenberg soundings. Virtual potential temperature and mountain normal wind speed (assuming a mean orientation of 6° west of north) were calculated at each sounding level and interpolated to a 50-m grid for finite differencing. Sliding-average filters were applied to the vertical profile of each variable to eliminate small-scale noise from the Scorer parameter curvature term, arising from the computation of the second derivative.

Based on theoretical arguments, the decrease with height of the Scorer parameter is expected for lee-wave trapping, whereas vertical propagation of wave energy is favored by a relatively constant Scorer parameter profile. As expected, in more than one-half of all the lee-wave cases, a sharp decrease of Scorer parameter with height was associated with stable layers due to temperature inversions within strongly vertically sheared flow. However, such stable layers were also present in about one-third of single-wave events. Thus, as a quantitative measure of the Scorer parameter layering, we have computed a decrease of the Scorer parameter over a 2-km-deep layer above the ridge height, expressed as a percentage of the Scorer parameter value at the bottom of this layer. For the average ridge height we specified 2.5 km for the northern Sierra and 3.5 km for the southern Sierra. The average values for the trapped and single-wave events are shown in Table 3. Given the spread in altitude of significant Scorer parameter layering, the numbers in Table 3 represent likely an underestimate for the lee-wave cases. Nevertheless, it is clear that the Scorer parameter drop in the lee-wave cases is on average larger than that for the single-wave cases. The difference becomes even more pronounced if from all single-wave events one isolates only cases with no temperature inversions. Because of the smallness of the northern sample size, in Table 3 we show this last category for the southern Sierra only. These results are consistent with the expectation that the difference in wave propagation characteristics, described by Scorer parameter, has to exceed a certain threshold value before the wave trapping can occur (Durran 1990).

It is necessary to point out that operational soundings are not always available at the same time as the wave clouds in satellite imagery, and so it is possible that the soundings used are not capturing the representative conditions. However, given about one-third of the single-wave cases with strong inversions, it is also possible that some of the single wave clouds are not indicative of vertically propagating waves, but are actually associated with trapped lee waves whose amplitude decreases rapidly downstream, leaving only a single wave cloud in the lee (Grubišić and Billings 2007). The decrease of wave amplitude downwind can be due to an interference of a second mountain range located in the lee, such as the White-Inyo range, that can change the phase and/or amplitude of lee waves generated by the Sierra Nevada. In case of the positive interference or resonance, rotors that form underneath the first wave crest in the Sierra Nevada lee can cause significant dissipation of wave energy and lead to decrease of lee-wave amplitude downwind. Rather than differing upstream conditions for different types of wave clouds, the presence of the White-Inyo range and the formation of rotors may be contributing to some of the single mountain-wave clouds in the southern portion of the Sierra Nevada. The investigation of reasons for such a wave behavior is beyond the scope of this study.

4. Conclusions

This note delivers a satellite-based climatology of the Sierra Nevada mountain-wave events. GOES-10 visible satellite imagery was visually examined for the presence of wave clouds during two wave seasons in the period 1999–2001, including months from October to May. Two types of wave clouds were defined, the lee–wave trains and single wave clouds, and these were detected based on their location, shape, and texture. As mountain waves can be present without wave clouds, the results presented here represent the lower limits of the frequency of mountain-wave events in the lee of the Sierra Nevada.

The frequency of occurrence of two wave types is shown as a function of the month of occurrence (October–May) and region of formation (north, middle, south, or the entire Sierra Nevada range). Results indicate that the maximum number of mountain-wave events in the lee of the Sierra Nevada occurs in the month of April. For several months, including January and May, frequency of wave events displays substantial interannual variability that is shown to be closely related to the interannual variability of synoptic-scale flows. Overall, trapped lee waves appear to be more common, in particular in the lee of the northern Sierra Nevada. The average wavelength of the Sierra Nevada lee waves was found to lie between 10 and 15 km, with a minimum at 4 km and a maximum at 32 km. A single wave cloud on the lee side of the mountain range was found to be a more common feature in the southern Sierra Nevada. While single wave clouds are expected to be signatures of the vertically propagating waves, it is hypothesized that a certain fraction of these events are trapped lee waves whose amplitude decreases rapidly downwind because of the presence of a parallel downwind range in the southern sierra, the White-Inyo Mountains.