1) King Air data

Data obtained during the first King Air flight in support of IOP 6 spanned ∼0400 to 0800 UTC and are displayed in two time intervals in Figs. 3 and 4. Figures 3a–c and 4a–c show (a) T′ with w′, (b) u′ with w′, and (c) u′ with υ′, with (u′, υ′, w′) to the east, north, and vertical, independent of flight direction or mean wind orientation. Flight track times and directions are displayed to the left of each track and approximate altitudes (in decameters AGL) are displayed to the right. The means for each variable on each flight segment have been removed for convenience.

A number of features of the motion fields can immediately be inferred. First, there are wavelike motions present much of the time, primarily below 1 km AGL, having apparent wavelengths ranging from less than 1 km to greater than 10 km, though true wavelengths will be smaller (larger) than measured if the direction of wave propagation is parallel (antiparallel) to the flight track and smaller than measured if there is a component of wave propagation normal to the flight track. Second, vertical motions are typically comparable to or larger than horizontal motions, zonal and meridional motions may be correlated or anticorrelated, and vertical motions are typically in approximate quadrature with both components of horizontal motion. The quadrature relations between horizontal and vertical velocities imply small or zero vertical momentum fluxes, u′w′ or υ′w′, no vertical propagation, and a likelihood that these motions are trapped or ducted within the NBL. Third, vertical velocities and perturbation temperatures T′ are in approximate quadrature, as required for approximately adiabatic motions, with w′ maxima westward of T′ minima, implying a westward component of phase progression for virtually all motions. Together, these data suggest ducted motions of several kilometer wavelengths propagating generally westward, with some directional variations depending on specific sources and the local NBL structure.

Exceptions to these general observations include typically small-scale motions having apparent wavelengths of 1 km or less, seen at the east ends of the flight tracks from 0415 to 0435 UTC, the center of the flight track from 0513 to 0518 UTC, and the east end of the flight tracks from 0625 to 0629 UTC. These motions typically have the opposite correlation between w′ and T′, suggesting propagation against the mean westward flow, but perhaps not propagation eastward. While the geographic localization of most of these motions and their w′ and T′ correlations suggest a possible stationary lee wave response to slight terrain east of the CASES-99 main site, these small-scale motions are not our focus here. It is also possible that these motions are KH shear instability occurring at levels of enhanced shear, but it is difficult to make this assessment without additional quantification of the local environment.

2) Raman lidar and HRDL

Other CASES-99 instrumentation obtained data providing additional insights into the character of the motions discussed above. The Raman lidar and HRDL provided vertical profiles of humidity and velocity, enabling an evaluation of the vertical structure of these motions. The Raman lidar yielded estimates of mixing ratio, thus perturbation humidity by subtraction of the mean humidity at each altitude, which is a tracer of vertical motions in the presence of a well-defined mean vertical gradient of humidity.

Small humidity and velocity perturbations are related through

View Expanded

where overbars denote local means (which may have horizontal and vertical gradients) and primes denote perturbations about the means. For well-defined q_z(z) and small q_x and q_y (where subscripts denote derivatives), Eq. (2) provides a direct relationship between w′ and q′ when the properties of the perturbation fields are known sufficiently well. Where q_z(z) is small, however, as occurs across much of the NBL and above the upper inversion layer, Eq. (2) is ill conditioned and w′ estimates based on q′ are subject to large uncertainties.

When q_z(z) is well defined, a wave motion of the form

ϕx,y,z,tϕ₀e^{i(kx+ly+mz−ωt)}(3)

with wavenumber k = (k, l, m), intrinsic frequency ω_i = k_hc_i, k_h = k² + l², and c_i the intrinsic phase speed in the direction of propagation given by k_h/|k_h|, with k_h = (k, l), yields an expression for w′ given by

View Expanded

To explore the implications of these data for wave character, we display q′ fields from 0300 to 0900 UTC during IOP 6 in Fig. 5a. A crude estimate of w′ from q′ at heights near the maximum humidity gradient (see Fig. 5b) is shown in Figs. 6a–c. For this estimate, we assume that k_x = k_y = 0, or alternatively that u = υ = 0, ω = ω_i, and w′ = −(∂q′/∂t)/q_z = iωq′/q_z in Eq. (4). This amounts to an overestimate of w′ by the ratio ω/ω_i. Given that the mean horizontal wind u_h at ∼500 m is ∼1/2 the maximum at lower altitudes and that c_h > u_h, this ratio is likely ∼2 to 3 at most. Direct measurements of vertical motions were obtained with HRDL during the interval from 0617 to 0647 UTC. These data at altitudes from ∼270 to 500 m AGL are displayed in Fig. 6d. Comparison of the w′ magnitudes in Figs. 6c and 6d seems to support the above arguments.

Examination of both lidar datasets suggests that large vertical motions 1) were confined to altitudes below ∼1.5 km AGL, 2) were highly coherent vertically with little or no evidence of phase variations of q′ or w′ with altitude, and 3) had peak amplitudes of ∼0.3 m s⁻¹ or larger, consistent with King Air measurements. We also note that the HRDL data suggest significant vertical velocities extending over a larger altitude range than inferred from the q′ data. This is because q′ is maximum where q_z(z) is large, and this appears to be a more restricted altitude range than the occurrence of large w′. The lidar data suggest several intervals of particularly strong and coherent wave motions, and these will be examined further below. Examination of Figs. 6c and 6d reveals that the vertical velocities at the two sites are in approximate antiphase up to ∼0630 UTC.

3) TLS, 60-m tower, and microbarograph data

Several other datasets corroborate the apparent ducted wave structure described above. TLS horizontal wind and temperature data obtained during the constant-altitude segment from ∼0415 to 0520 UTC (see Fig. 7) exhibit ∼4- to 5-min oscillations with in-phase temperature and (westward positive) horizontal wind perturbations, consistent with King Air inferences (both T′ and u′ were in quadrature with w′). These perturbations cannot be the result of vertical advection u′ ≈ iw′u_z/ω_i because the mean wind is essentially unsheared at this altitude and time. TLS T′ (at ∼460 m) are also seen to be in approximate quadrature with Raman lidar vertical velocities (at 500 m) from ∼0500 to 0520 UTC (compare Figs. 6a and 7), with w′ maxima leading T′ minima, confirming the lack of phase variation with altitude seen in the lidar data above.

Anemometers and hot-wire probes on the 60-m tower also exhibit ∼4- to 5-min oscillations, together with higher-frequency oscillations that are not as apparent at higher altitudes. The 55-m perturbation winds and temperature are displayed in the same manner as the King Air data, with w′ and T′, u′ and w′, and u′ and υ′ shown together in Figs. 8 to 10, respectively. Much of the higher-frequency activity appears primarily in the u′, w′, and T′ fields and is likely Doppler shifted to higher frequencies (relative to the atmospheric reference frame), ducted, propagating westward, and more confined in altitude and thus not as evident in TLS and lidar data at higher altitudes. These multiple motions complicate identification of the relative phases between the velocity and temperature perturbations more in the tower data than at greater altitudes. Other motions may be signatures of flow instabilities and turbulence at smaller scales due to the strong shears below ∼100 m (see section 5 below).

Velocities measured on the tower, while somewhat correlated with data collected at higher altitudes, are ambiguous in their implications for wave structure and propagation direction. One reason for this is the much higher wind shears at tower altitudes than at higher altitudes, and the greater potential for horizontal velocity perturbations to be imposed by vertical advection of vertical wind shears. With a zonal mean wind shear of u_z ∼ 0.1 s⁻¹, a mean temperature gradient of T_z ∼ 0.03 K m⁻¹, and T′ ∼ 0.05 K (implying vertical displacements of ∼1 to 2 m), w′ ∼ 0.05 m s⁻¹ implies u′ ∼ 0.1 to 0.2 m s⁻¹. These velocity fluctuations are comparable to observed u′ and υ′ fluctuations, though vertical advection is only able to account for large u′ and υ′ fluctuations proportional to the mean shears in these directions. Such perturbations likely contribute to less well defined phase relations between horizontal and vertical velocities in the tower winds than are observed at greater altitudes.

Finally, some of the motions discussed above are apparent in the microbarograph data at various locations around the CASES-99 main site. Data obtained at 5 m on the 60-m tower and six surrounding towers (see Fig. 1) for the interval from 0400 to 0800 UTC are displayed in Fig. 11a. A Morlet wavelet analysis of the data from station 1 subjected to a 1- to 30-min bandpass is shown in Fig. 11b. These data reveal a dominance of fluctuations with ∼4- to 5-min periods, as noted above, with both smaller-amplitude fluctuations at shorter periods and more sporadic responses at longer periods. These results are confirmed by a cross S-transform (Stockwell and Lowe 2001) analysis designed to identify responses that are coherent across two spatially displaced sensors (see Fig. 12). These results suggest a typical coherent wave packet duration of ∼3 to 6 cycles, consistent with the various time series and spatial data discussed above.

Both these analyses identify about six discrete events, three of which will be examined more closely below. We note, however, that there is not a complete correlation between events that are significant in the microbarograph data and those that are more apparent at higher altitudes. One example is the motions detected in the King Air and Raman lidar data prior to 0500 UTC (particularly w′ and q′), but which contribute little in terms of surface pressure or tower velocity and temperature fluctuations. Other examples are the motions observed from ∼0520 to 0550, 0610 to 0640, and 0710 to 0730 UTC with significant surface pressure signatures for which there are corresponding fluctuations in the King Air, TLS, and lidar data. Below, we discuss three case studies for which (a) King Air, TLS, lidar, and/or tower data exhibit significant wavelike motions, and (b) microbarograph data permit estimates of wave propagation direction and phase speed.

1) Case 1: 0400 to 0500 UTC

As noted above, the dominant motions during this interval at upper levels have periods of ∼4 to 5 min, w′ ∼ 0.5 m s⁻¹, w′ maxima westward of T′ minima (i.e., westward propagation), u′ and w′ in apparent quadrature with u′ leading w′, and generally small u′ and smaller υ′. The stratification during this interval exhibits an extended maximum from ∼450 to 700 m, and the q′ measurements and w′ inferences with the Raman lidar indicate that vertical motions are highly coherent across this altitude range (see Figs. 5a and 6a). We also note from Fig. 3 that u′ is much smaller than w′ at these altitudes, but that u′ is larger and in approximate quadrature with w′ at lower and higher altitudes.

Velocity perturbations obtained with the King Air indicate u′ and υ′ most often in antiphase, but with u′ typically larger, indicating a largely westward wave propagation (given the w′ and T′ correlations discussed above). Likewise, u′ most often leads w′, except within the layer of higher stratification, where this correlation is less apparent or inverted. These correlations have been confirmed by S-transform cospectra and quadrature spectra of u′ and υ′, but these plots provide little additional insight beyond that obtained from the data shown in Figs. 3 and 4 and are not shown.

Data from the TLS (see Fig. 7) exhibit a clear correlation between T′ and wind speed (or westward velocity) within the layer of higher stratification (∼470 m), which appears to contradict the more general correlations implied by the King Air data, but which agrees with King Air data for the flight segments from 0423 to 0435 UTC within this same layer. TLS temperatures are in approximate quadrature with Raman lidar vertical velocities at greater altitudes, confirming the vertical coherence of the wave motions described above.

Data from the anemometers and hot-wire probe at 55 m on the 60-m tower are displayed in Figs. 8 to 10. The upper panels in these figures exhibit the same ∼4- to 5-min periods observed by the King Air, TLS, and Raman lidar during the interval 0400 to 0500 UTC, with apparent quadrature phase relationships between w′ and both T′ and u′. Additional motions are seen at higher frequencies (periods of ∼1 to 2 min) for which there is also some evidence at higher altitudes. The dominant signatures of these higher-frequency motions appear in the u′, υ′, and T′ fields, suggesting that they propagate preferentially toward the west and are Doppler shifted to observed frequencies significantly higher than intrinsic frequencies. Phase relationships and wave structures appear somewhat more complex in the tower data, however. There are likely several reasons for this. One noted above is the presence of a strong vertical shear of the mean zonal wind, which, in the presence of vertical advection, contributes to perturbation zonal velocities and an imposed quadrature phase relationship expressed by Eq. (2). A second possible explanation for some of the enhanced activity and complexity of the motion field at higher frequencies is the potential for shear instabilities at smaller scales of motion within the strong mean wind shear beneath the low-level jet (see section 5).

Because of the caveats expressed above about the tower wind and temperature data, we consider the King Air, TLS, and Raman lidar data to be more representative of the larger-scale motions within the NBL during this interval. In this case, the horizontal wavelengths apparent in the King Air data provide reasonably accurate estimates of the true wavelengths after accounting for the horizontal phase speed of the wave relative to the horizontal motion of the King Air. Given that the waves are propagating largely westward, they must have a speed greater than the maximum westward mean wind, or c_x > 10 m s⁻¹ to the west. This westward phase progression will decrease (increase) the apparent wavelengths by a fraction of ∼|c_x/U_KA| for eastward (westward) flights, where U_KA ∼ 80 m s⁻¹ is the speed of the King Air. In either case, apparent wavelengths are ∼1 to 3 km, and we will focus on these horizontal scales in our evaluation of possible wave structures below. Estimated phase speeds, assuming the dominant periods apply to all observed horizontal wavelengths, vary from ∼4 to 12 m s⁻¹. These are clearly appropriate only for the larger wavelengths, since there is no evidence of critical-level behavior in the strong shears at the lower altitudes. Interestingly, the surface pressure perturbations during this interval are significantly smaller than those for later periods, even though w′ and its temporal variations at greater altitudes are as large or larger during this interval.

The wave structures and correlations among variables described here are suggestive of the character of ducted motions discussed above. A more detailed analysis of this behavior for the specific cases considered here is provided in section 4c below.

2) Case 2: 0500 to 0600 UTC

Motions observed with the King Air and other instrumentation during this interval differ in important respects from those discussed immediately above. While pressure fluctuations at longer periods are comparable to case 1, there is now much more power at ∼5-min periods. The characteristic horizontal scales are likewise significantly larger, now ∼3 to 8 km, and King Air horizontal velocity perturbations are smaller and vary from being correlated to apparently uncorrelated. Correlations between u′ and w′ continue to suggest a more nearly quadrature than in-phase or antiphase relationship (see the flight tracks from 0505 to 0509 and 0530 to 0534 UTC in Fig. 3b), again suggesting no momentum flux and no vertical propagation. These conclusions are reinforced by S-transform cospectra and quadrature spectra of the perturbation velocities (not shown).

The T′ and w′ correlations continue to imply westward propagation (see the flight track from 0513 to 0518 UTC in Fig. 3a), but because most flight altitudes are above the upper maximum in stratification during this interval, T′ tends to be small. TLS data continue to show an in-phase relation between T′ and westward velocity (consistent with quadrature between u′ and w′), while vertical motions implied by q′ likewise suggest high vertical coherence and no apparent vertical phase progression (also consistent with TLS and King Air inferences). Phase speeds for these motions (inferred from observed wavelengths, propagation directions, and periods) are ∼10 to 25 m s⁻¹, typically faster than mean winds in the direction of propagation, and consistent with a ducted wave interpretation of these motions. Tower velocity and temperature perturbations also exhibit a dominance of ∼4- to 5-min periods, especially in the meridional component, which cannot be attributed to vertical advection. Tower velocities likewise differ in their phase relationships relative to those observed in the King Air and TLS data. Hence tower measurements continue to suggest additional motions at lower altitudes than those imposed by ducted motions at greater altitudes. The higher-frequency motions in the tower data, in particular, are suggestive of small horizontal wavelength (and small phase speed) motions that are more confined at the lowest altitudes.

The larger pressure fluctuations at ∼5-min periods during this interval suggest that the wave motions observed at upper levels may extend with larger amplitude to lower altitudes than those motions discussed in case 1 above. An understanding of these differences will be sought in terms of the differing modal structures in section 4c.

3) Case 3: 0600 to 0700 UTC

Motions during this interval are more similar to those of case 1 than case 2, above. As in case 1, the dominant motions at upper levels of the NBL have periods of ∼5 min, w′ ∼ 0.5 m s⁻¹, westward propagation (w′ maxima westward of T′ minima), and u′ and w′ in apparent quadrature with u′ (generally) leading w′. In this case, both positive and negative correlations between u′ and υ′ are observed, with largely positive correlations prior to ∼0630 UTC and largely negative correlations thereafter, suggesting propagation preferentially toward the northwest (southwest) at the earlier (later) times. As in cases 1 and 2 above, S-transform cospectra and quadrature spectra of u′ with υ′ and u′ with w′ support these conclusions, but offer little additional insight and are not shown.

Apparent wavelengths are ∼1 to 7 km, implying, with the preferred directions of propagation, real wavelengths smaller by ∼30%. As in case 1, u′ is comparable to or smaller than w′ along the King Air flight tracks. The stratification profile is much like the earlier cases, and the q′ measurements of the Raman lidar again indicate that w′ is highly coherent and there is little or no phase variation across the altitude range of high stratification (and large dq/dz). As noted above, HRDL data available during the interval 0617 to 0647 UTC (see Fig. 6d) reveal both coherent vertical motions supporting inferences from the Raman lidar and a tendency for vertical velocities to decrease away from the upper stratification maximum. Examination of Figs. 6c and 6d reveals that the vertical velocities at the two sites are in approximate antiphase up to ∼0630 UTC. Given a separation of the two lidars by ∼1.5 km, this suggests a wavelength (assuming propagation toward the northwest) of ∼3 km or less, in agreement with the estimates based on King Air data above.

A more quantitative view of the along-track scales of the wave motions measured by King Air instrumentation is provided by the S-transform of the various perturbation fields. Those obtained for w′ and T′ are shown for the flight segment from 0614 to 0619 UTC in Fig. 13. In both datasets, motions are observed west of the CASES-99 main site (and east to a lesser extent) having wavelengths of ∼1.7, 3.5, and 7 km. The approximately integral relationship between these motions suggests a possible nonlinear coupling of wave energy, as examined by Liu et al. (1980, 1982) and Liu and Benney (1981), but further exploration of such a linkage is beyond the scope of this paper. Such an analysis is useful in quantifying the scales of motion present in the King Air data, but it does not facilitate an intercomparison of spatial and temporal data because it is not obvious how to relate events having discrete multiple signatures in frequency or wavenumber.

Tower velocity and temperature perturbations again exhibited primarily ∼4- to 5-min periods, but also ∼1- to 2-min periods more similar to case 1 than case 2. Surface pressure perturbations during this interval are larger than those in case 1, despite smaller wave perturbations in general, and may imply lower ducted motions than were typical during case 1. However, u′ and υ′ fluctuations measured on the tower do not exhibit correlations that agree well with those observed at greater altitudes. As above, this may be due to the more complex factors influencing horizontal velocity perturbations in the presence of strong mean wind shears and vertical advection.