Clear-air VHF/UHF radars worldwide have observed that long-term mean vertical winds are downward in the middle troposphere and usually slightly upward above the jet-stream wind maximum. Kelvin–Helmholtz instability (KHI), which can tilt quasi-specular layers in opposite orientations above and below the jet-stream wind maximum, has been postulated to be one important contributing factor to the radar-measured mean vertical wind (r). This factor is examined here using simultaneous radar interferometric observations of echo centers and layer structures. The altitude of layer structure and the incident angle of echo center were estimated, respectively, with multiple-frequency and multiple-receiver techniques. Radar data were collected with the Japanese MU radar, between 3 km and 22.2 km and over 33 h. The observations of r showed downward tendency in the middle troposphere, with a maximum of ∼10 cm/s at the height of ∼8 km. However the reversal height of r was at ∼15 km, which is higher than the jet-stream wind maximum observed (∼12 km). Positive correlations between the vertical velocities (wr) and the incident angles of echo centers were found in the region of downward r, and moreover, the mean vertical velocities derived from the incident angles of echo centers below ∼10 km were close to r. Statistical distributions of layer slopes, incident angles of echo centers, and echo power imbalance between two symmetrically oblique radar beams provide evidence of asymmetrically tilted layer structures in the region of downward r, suggesting that wind-shear tilted/KHI layers contributed a significant part of r in the middle troposphere.
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 VHF/UHF radars designed for atmospheric observations can measure the tropospheric and lower stratospheric wind fields with high temporal and spatial resolutions (∼1 min and ∼150 m, respectively). One noticeable characteristic of the radar-measured wind field is the change of long-term mean vertical velocity in the troposphere and stratosphere: downward in the middle troposphere and usually slightly upward in the lower stratosphere [e.g., Fukao et al., 1991; Gage et al., 1991; Yoe and Rüster, 1992; Nastrom and VanZandt, 1994; McAfee et al., 1995; Chen, 2006]. Here the radar-measured vertical velocity is usually retrieved from the Doppler shift observed with vertically pointed radar beam, which may be different from the true vertical velocity of the atmosphere or from the vertical velocities defined in other ways [Muschinski et al., 1999]. (In the following, the term “vertical velocity” means the radar-measured one unless other definitions are mentioned.)
 In addition, extra reversals of mean vertical velocities—upward in the lower troposphere (below ∼3 km) and downward in the deeper stratosphere—have also been verified [Worthington, 1999; Worthington et al., 2001]. Even a reversal of mean vertical velocities in the middle troposphere was once observed in the tropical zone [Jagannadha Rao et al., 2002].
 In this study, we examined the possible contribution of KHI under the condition of vertical wind shear in tilting the layer structures asymmetrically, leading to downward and upward vertical velocities below and above the jet-stream wind maximum, respectively [Muschinski, 1996]. There are several stages in the tilted layer structures caused by the KHI development [Browning and Watkins, 1970], and statistically, the tilted layer at a given height tends to slope in a constant direction that is controlled by horizontal wind direction and vertical wind shear [Worthington and Thomas, 1997]. The layer structures can be supposed to be quasi-specular owing to vertical layering of refractive index or anisotropic refractivity irregularities/turbulence embedded in the layer. Anisotropic turbulence however may not be layered all the time. As demonstrated recently by Worthington , the “ramp” structures caused by sheared anisotropic turbulence also exist, which may lead to a variation of echo power with azimuth angle. Such ramp structures are difficult to distinguish from the KHI billows/layers with the methods applied in this study; therefore we consider the model of wind shear-tilted layers depicted by Worthington and Thomas .
 Tilted quasi-specular layers have been found to have substantial effect on the radar-measured vertical velocity [e.g., Gage, 1986], and this has also been demonstrated in observations of the echo centers determined by three-receiver spatial interferometry (SI) [Palmer et al., 1991]. Nevertheless, the three-receiver SI obtains only one average center of the echoes for each estimate. To reveal multiple echo centers in the radar volume, we here made use of the interferometric technique with more than three receivers, which is known as coherent radar imaging (CRI) in the MST radar community [Woodman, 1997]. Owing to the merits of obtaining multiple echo centers in the radar volume, CRI has many practical applications already, for example, examination of the distribution of clear air and plasma irregularities, aspect sensitivity, wave activities in the atmosphere, and precipitation [Hysell, 1996; Hysell and Woodman, 1997; Yu et al., 2001; Chilson et al., 2002; Hysell et al., 2002; Chen et al., 2004, 2008; Cheong et al., 2004; Palmer et al., 1998, 2006]. In addition to the echo center, the variation of vertical layer position (layer altitude) is also useful in sensing the motion of the atmosphere. An earlier method to estimate the layer altitude is the two-frequency interferometric method (FDI) [Kudeki and Stitt, 1987]. Nevertheless, the use of two-frequency interferometry is severely restricted owing to its assumption of a layer model, namely, a single Gaussian-distributed layer structure in the radar volume. For multiple-layer conditions, the two-frequency interferometry cannot work well [e.g., Chen and Chu, 2001]. In view of this, the multiple-frequency interferometric technique with more than two frequencies, known as range imaging (RIM) [Palmer et al., 1999] or frequency radar interferometric imaging (FII) [Luce et al., 2001] in the literature, was employed in this study. With the RIM/FII method, we can resolve multiple layers in the radar volume without any assumptions of layer shape and layer number. There have been many potential applications of the RIM/FII method to the atmosphere, for example, KHI instability [Chilson et al., 2003], high-resolution wind profiling [Yu and Brown, 2004], and study of fine-scale layer structures [Chilson et al., 2001; Palmer et al., 2001; Luce et al., 2006, 2007a].
 On the basis of the advantages of CRI and RIM/FII methods, the combined CRI and RIM/FII method is intuitively beneficial for our present study, and may also provide more opportunity to examine the issue deeply. Readers can refer to Yu and Palmer  for more mathematical descriptions and simulation results of the combined CRI and RIM/FII method. Such combination of methods is an improved version of the combined FDI and SI experiments carried out previously [Stitt and Kudeki, 1991; Palmer et al., 1995].
 This paper is organized as follows. In section 2 we describe briefly the MU radar system, the radar parameters used for the present study, and the Capon method which is employed to process the multiple-receiver and multi-frequency radar data. In section 3 we present the radar-measured vertical and horizontal winds, and then examine a wavy layer structure to demonstrate the ability of the combined CRI and RIM/FII method. Following this, we discuss the statistical results of echo centers and layer altitudes, which give supporting evidence for the effect of wind shear-tilted layer structures on the radar-measured mean vertical velocities at different heights. Section 4 contains our conclusions and thoughts for further research.
2. Experiment and Methodology
 The radar data were collected from 0700 LT on 9 February to 1600 LT on 10 February 2006, using the 46.5-MHz MU radar system (34.85°N, 136.10°E). In total there are ∼33 h of data. The MU radar array consists of 475 crossed-Yagi antennas, and each antenna is equipped with an independent but identical type of transmitter-receiver module. The radar array is divided into twenty-five independent groups with 19 crossed-Yagi antennas each. Each antenna group has its own digital receiver for the combined signal. Furthermore, software can combine the outputs of these receivers arbitrarily. Figure 1 shows the radar configuration, in which the 19 antenna groups in the interior part of the array were used in our multiple-receiver observations and the combined output of the full antenna array was employed to estimate vertical wind. Five equally spaced transmitting frequencies—46.00, 46.25, 46.50, 46.75, 47.00 MHz—were employed along with the multiple-receiver mode, with the five frequencies switched pulse-to-pulse. The output of the entire array was used for multiple-frequency analysis. Inter-pulse-period (IPP) and pulse length were 400 μs and 1 μs, respectively. The number of coherent integrations was 128, leading to a sample time resolution of 0.512 s for each transmitting frequency. For transmission, the entire array was used and the radar beam was directed vertically. Sampling range step was 150 m, and the sampling range was between 3 km and 22.2 km. Moreover, five-beam Doppler beam swinging (DBS) mode was performed for approximately 10 mins at about 1-h intervals, with radar beam directions (azimuth, zenith) = (0°, 0°), (0°, 10°), (90°, 10°), (180°, 10°), and (270°, 10°). The DBS data provide referable horizontal wind in addition to the horizontal wind which we derived from the vertical-beam data with the spaced antenna method (SA). There have been many different approaches for SA [e.g., Meek, 1980; Briggs, 1984; Liu et al., 1990; Pan and Liu, 1992]. We used the full-correlation analysis (FCA) developed by Briggs . Such estimated horizontal wind is considered adequate for the purposes of this study although more sophisticated SA algorithms also exist [Doviak et al., 1996; Holloway et al., 1997].
where BC(k) indicates the Capon brightness distribution, k = (2π/λ)[sinθsinϕ, sinθcosϕ, cosθ] in Cartesian coordinates is the wavenumber vector in the direction where the brightness is to be estimated, λ is the radar wavelength, and θ and ϕ are the zenith and azimuth angles, respectively. The superscript H in (1a) represents the Hermitian operator. Rij is the zero-lag cross-correlation value of the signals received at antenna groups i and j (without normalization). Di denotes the position vector of the center of the i-th receiving antenna group relative to the center of the full antenna array.
 For multiple-frequency data, the form of equation (1) also applies, except that frequency replaces the position vector of the receiving antenna group and scanning range (relative to the center of a range gate) replaces the scanning wavenumber vector. As a result, BC(k) converts into BC(r) and e = , where r denotes the relative range and kn is the wavenumber of the n-th transmitting frequency. Rij becomes the zero-lag cross-correlation function of the signals calculated for a pair of frequencies (without normalization). After Capon processing, BC(k) and BC(r) may possess several distinct brightness maxima, indicating multiple resolvable objects or layers in the radar volume. The resolvable number of objects/layers depends partly on the number of receivers/frequencies. We have used the optimal capability of the MU radar system for CRI and RIM/FII experiments.
2.3. Determining Location of Brightness Maxima
 To determine the positions of brightness maxima more precisely, phase calibration of the radar system is needed. In the upgraded MU system, where each antenna group has its own dedicated digital receiver, and phase calibration at the operating frequency is regularly carried out during maintenance, we assume that no calibration is required for the multiple-receiver observations. For multiple frequencies, the phase distribution of the zero-lag cross-correlations of two signals with different frequencies (called frequency-domain-interferometry (FDI) phase in the following) [Kilburn et al., 1995; Brown and Fraser, 1996] was used for calibrating the phase bias.
 To find multiple brightness maxima, the contour-based approach introduced by Chen et al.  can be employed. We show some observational examples in Figure 2. In the brightness distribution shown in Figure 2a, the grating pattern can be observed clearly, which reveals that the imitations are separated from the true echo (around the center) by over 20° in zenith. Figure 2b exhibits a double-center brightness map of CRI (upper panel) as well as the locating result (lower panel), where the symbol + indicates the estimated mean position of the brightness center. As for the RIM/FII imaging, only one-dimensional brightness distribution in range is obtained. We have to extend the brightness values horizontally to two dimensions so that the contour method can be applied. Figure 2c shows an example, which reveals that the imitations are at a distance of ∼600 m from the true echoes (around the center). Disregarding the imitations, we can find two maxima—a possible two-layer case. Note that the imitations in the CRI and RIM/FII imaging are far outside the examined spatial region (range: ±75 ∼ ±150 m, zenith: several degrees) so they are not likely to affect the following study.
 It should be mentioned that in theory the weighting effects of transmitting beam pattern and pulse shape-filtering on the brightness distributions, BC(k) and BC(r), respectively, should be removed. In RIM/FII, the brightness can be corrected approximately by using the inverse of the range-weighting function W2(z) = exp(−z2/σz2), where σz = 75 m for 1-μs pulse length and its matched filter [Luce et al., 2001, 2006]. In CRI, however, the correction using the two-dimensional beam pattern weighting function produces spurious peaks in the brightness distribution as the scanned position approaches the beam width (also mentioned by Yu et al. ), making the usefulness of imaging and locating results questionable. In view of this, the transmitting beam pattern was not removed in this study. Readers should be aware that the true zenith angle of the reflection point within the radar beam is slightly larger than the one obtained from the uncorrected CRI brightness distribution.
3. Results and Discussion
3.1. Wind Observations
 The height-time intensity plot of signal-to-noise ratio (SNR) of our observations is shown in Figure 3a, where many echo layers can be observed in the troposphere. Figures 3b and 3c display the vertical velocity and horizontal wind derived from the vertical radar beam using the autocorrelation function method [Woodman and Guillén, 1974] and the spaced antenna FCA method [Briggs, 1984], respectively. We also estimated vertical velocity and horizontal wind with spectral and DBS methods, respectively, and the results were similar to those shown in Figures 3b and 3c (see Figure 3d for later discussion). Each vertical velocity was first estimated from ∼33-s data, and each horizontal velocity was first estimated from ∼5-min data, and then averages in time and in range were performed to show clearer diagrams. In Figure 3b, we can observe that downward motion prevailed over the whole time period. According to Figure 3c, on the other hand, the jet-stream wind maximum varied in range interval between 11 km and 15 km.
Figure 3d shows the mean profiles of vertical velocity and horizontal wind averaged from the data within a one-kilometer range interval. As seen in the left panel, the two profiles of vertical velocities, obtained from the spectral method and from the autocorrelation function, respectively, are in good agreement, demonstrating that the systematic variation of the radar-measured mean vertical velocities is not owing to the retrieval methods used here. To verify the horizontal wind, we show the results of SA, DBS and balloon-observed winds in the right panel of Figure 3d. Basically, the three profiles of horizontal winds vary consistently with altitude although their values are not very close. No matter which profile of horizontal wind is considered, it is clear that the mean jet-stream wind maximum was located at ∼12 km, and dominated by the zonal wind. On the other hand, mean vertical velocities in the left panel show negative values below ∼15 km and slightly positive values above ∼15 km. The most negative value of mean vertical velocity is at ∼8 km, where strong wind shear can be observed. The reversal height of vertical velocity was about 3 km higher than the jet-stream wind maximum, which is not in agreement with the long-term mean results reported in the literature [e.g., Fukao et al., 1991]. We will discuss this discrepancy in more detail based on the statistical features of echo centers and layer altitudes. Before discussing the statistical results, a layer structure is shown in order to demonstrate the ability of the combined CRI and RIM/FII method to reveal the relationships between echo center, layer structure, and radar-measured vertical velocity.
3.2. A Case Study
Figure 4a shows a wavy layer structure observed with the RIM/FII mode, which is asymmetrically tilted to the downstream side (right direction in the map) a little bit. The asymmetrical tilt of the layer could be caused by wind shear (see the wind field in Figure 3c around 30 h), but the layer structure was not shaped into fully developed KHI billows. The period of the wavy layer was about 4 min. Corresponding vertical velocities are displayed in Figure 4b, and Figure 4c shows the echo centers in zonal and meridional directions, respectively. Notice that the time axis is reversed, starting from the right side of the abscissa, which makes it more convenient to compare with the layer shape depicted later.
 Assuming that the wavy layer structure moves with the background horizontal wind, namely, drifts from left to right in Figure 4a, then the variation in vertical velocity caused by the tilt of the layer should have a 90° phase difference from the variation in layer altitude. This can be roughly observed by comparing Figure 4b with Figure 4a. The correlation coefficients of layer altitudes and vertical velocities at different phase shifts can be estimated by shifting the layer structure toward the right in the map; the result is shown in Figure 4d. As seen, maximum correlation coefficients appear at 1-min, 5-min, and 9-min shifts, corresponding to a 90° phase shift of the wavy structure. Notice that the short-period wavy layer structure was superimposed on a long-period wave (period: ∼18 min; amplitude: ∼65 m) and so modulation of the long wave was removed before estimating the correlation coefficient.
 The incident angle of echo center is also related to the tilted layer structure if the layer structure is quasi-specular. Since the wavy layer structure moves with the background horizontal wind, the incident angle of echo center should vary from one side to the opposite side of the zenith periodically. Letting the incident angle from the upstream direction of the horizontal wind be negative, the variation in incident angle will exhibit a 90° phase difference from the variation in layer altitude, but has coherent phase with the variation in radar-observed vertical velocity. Since the zonal wind dominated the horizontal wind in our observations, we expect that the variation in zonal incident angle would be more coincident with the expected phase relationships mentioned above. An estimate of the correlation coefficient of zonal incident angle and vertical velocity was found to be ∼0.60, but it was ∼−0.25 for meridional incident angle and vertical velocity, indicating that the wavy layer structure indeed drifted mainly with the zonal wind. It should be mentioned that the incident angles represented by the asterisks in Figure 4c were used for estimating the correlation coefficient. The circle symbol indicates the second center in the brightness distribution. We display the original brightness distributions of these double-center structures in Figure 3e, as indicated by the letters “a”, “b” and “c”. The brightness distributions before and after one time step of the double-center structures are also shown. Apparently, the echo centers moved from one side to the other side of the zenith before and after the occurrence of double centers. Moreover, these double-center cases were observed at instants near the humps of the wavy layer. This is similar to the feature of waves in the mesosphere presented by Yu et al. .
 In the situation of multiple echo centers, each echoing region contributes a quantity to the radar-measured vertical velocity. In the case “a” shown in Figure 4e, the left echoing region is more important than the right one, resulting in a net downward vertical velocity under the domination of zonal wind. In contrast, the case “b” produces upward vertical velocity. For the case “c”, the two echoing regions are comparable and located on either side of the zenith, causing the vertical velocity to be near zero. All these features/relationships can be found in Figures 4b and 4c (zonal component).
 In addition to the above findings, it is worth investigating whether the incident angle of echo center is related to the layer slope or not. We estimated the layer slope from the change of layer altitudes by performing a linear fitting with three consecutive layer altitudes. However, multiple layers could cause problems because in RIM/FII the echo center with largest brightness is selected as the layer altitude. In case a second layer or an irregularity patch appears in the radar volume and has more intense brightness than the traced one, it may cause an abrupt change of layer altitude and then result in a steep layer slope. We avoided this problem by inspecting the brightness map in this case study. For example, in Figure 4a the strong brightness observed at the upper edge around 5.25 h is not considered as a portion of the wavy layer (such discrimination is difficult to implement from the two-frequency FDI result). The layer slope was first estimated in units of meters per unit time. To obtain the layer slope in space, the horizontal wind is needed. Since the zonal component was dominant, we ignored the meridional wind. After converting the layer slope into the slope angle of the layer, we are able to compare the slope angle with the CRI-observed incident angle, as shown in Figure 5a. As seen, the slope angles of the layers are mostly larger than the incident angles of echo centers. This feature could be explained by Figure 2 given in Muschinski , where the axis of the effective beam is closer to the vertical than the axis perpendicular to the isentropic surface (namely, the sloping surface of the layer) for a vertically directed radar beam. The CRI-derived incident angle homologizes the zenith angle of the effective beam and the slope angle of the layer represents the zenith angle of the axis perpendicular to the isentropic surface. A comparison between the observed and the derived vertical velocities is shown in Figure 5b. For a better comparison, the vertical velocities estimated from the slope angles of the layer (solid curve) have been divided by three. As seen, the three kinds of vertical velocities are generally coherent. The observed (circle) and the CRI-derived (star) vertical velocities are very close in spite of a large difference at some instants (e.g., between 5.20 h and 5.25 h, and between 5.40 h and 5.45 h). In view of this, the echoes indeed returned mostly from the region around the direction of the effective beam. By comparison, the vertical velocities derived from the slope angles (solid curve) have much larger values than the observed ones, which is a consequence of the difference in vertical velocities shown in Figure 5a. We noticed that Luce et al. [2007b] demonstrated a case with high similarity between the vertical velocities observed by the radar and those derived from layer altitudes; however the vertical velocities examined by Luce et al. [2007b] are associated with strong cumulus convection and vary sinusoidally with an amplitude of several meters per second, so the atmospheric condition is quite different from that of our case.
3.3. Statistical Studies
 The layer structure shown in Figure 4a is similar to the wind shear-tilted layer although its shape does not correspond to well-developed KHI billows. In fact, well-developed KHI billows are not identified clearly by clear-air VHF pulsed radars very often. Among the reasons could be the finite spatial and time resolutions of pulsed radars. RIM/FII provides a chance to resolve small-amplitude KHI billows; nevertheless, finite time resolution may smear these structures. Consequently, we observe only asymmetrically tilted wavy layers that have longer periods and can be resolved by the radar. Referring to the wind shear-tilted layer model given by Worthington and Thomas , Figure 6 depicts a simplified model of the layers below and above the jet-stream wind maximum. At least four statistical characteristics related to this layer model can be examined:
 (1) The radar echoes coming from the upstream and downstream sides of the crest contribute, respectively, downward and upward vertical velocities, irrespective of the layer being located below or above the jet-stream wind maximum. Letting the incident angle in the upstream (or downstream) direction be negative (or positive), the correlation between the radar-measured vertical velocity and the incident angle of echo center should be positive.
 (2) Below the jet-stream wind maximum, the reflecting echoes coming from the downstream side of the crest have larger incident angles than those coming from the upstream side of the crest. Consequently, the downstream-side echoes are more difficult to receive by a narrow radar beam like that of the MU radar. Moreover, the extent of the layer on the upstream side is longer than that on the downstream side. Therefore, the part of the layer on the upstream side spends more time traveling through the radar beam, and then contributes more reflection echoes than that on the downstream side. As a result, the reflection echoes coming from the upstream side dominate the distribution of incident angles of the echo centers. The situation above the jet-stream wind maximum is the opposite of this.
 (3) Upstream and downstream sides of the crest are tilted downward to, respectively, the upstream and the downstream directions. The tilted refractivity surfaces lead to a difference between the two echo powers obtained from the two radar beams directed in opposite zenith angles along the tilting surface. Since the layers below the jet-stream wind maximum are tilted downward to the upstream direction for most of the time, on average there will be stronger echo power from the upstream-oblique radar beam than the downstream-oblique radar beam. The situation above the jet-stream wind maximum is the opposite of this.
 (4) Categorizing the layers on the upstream and downstream sides of the crest as positively- and negatively-sloped for convenience, there will be a larger number of positive slopes if we use the same points of layer altitudes to estimate each layer slope. The situation above the jet-stream wind maximum is the opposite of this.
 The four statistical characteristics are more visible to the radar in the region having large vertical wind shear. An estimate of mean vertical wind shear with 600-m range resolution is shown in Figure 7. Also demonstrated in Figure 7 is the mean Richardson number (Ri) obtained from the sounding data of the balloons launched routinely at Yonago (35.4°N, 133.3°E) and Hamamatsu (34.8°N, 137.7°E) during the radar experiment. As shown, the mean Ri was smaller above the height of 12 km and between the heights of 5 km and 9 km, and two extremely low values were observed at around 8.5 km and 7 km. We should consider the mean Ri in Figure 7 as only a rough indicator of KHI occurrence because of the long distance between the radar site and the balloon stations (two to three hundred kilometers), as well as the coarse time resolution of balloon data (12 h). Although the KHI threshold of Ri, 0.25, is not satisfied, Figure 7 suggests that the heights below and above the jet-stream wind maximum have more possibility of developing asymmetrically tilted layers. Investigations of various statistical characteristics are presented in the following paragraphs.
3.3.1. Characteristic (1)
Figure 8a shows the scatter plots of vertical velocities versus incident angles of echo centers between 3 km and 13 km, in which each panel collects the data within a height interval of one kilometer. Each incident angle (and vertical velocity) was derived from sixty-four data points, resulting in a time resolution of ∼33 s. Only the data with SNR ≥ 0.5 are included in the plot, in which the noise level was estimated from the averaged power of the uppermost four range gates during the observations. Positive incident angle is defined as coming from the east and the north, respectively, for zonal and meridional directions. Moreover, we selected only the cases with single echo center to clarify the relationship between the radar-measured vertical velocity and the location of echo center. Such selection of only single-center cases can only be achieved with the multiple-receiver method applied here (one advantage over three-receiver interferometry). One can see in Figure 8a that the linear relationship between vertical velocity and zonal incident angle is more positive between 5 km and 8 km, as indicated by the values of linear-regression slopes—4.15, 4.06 and 3.58—that are larger than those at other places. Complete estimates and distributions of correlation coefficients are shown in Figure 8b, in which each correlation coefficient was estimated with the vertical velocities and incident angles within 30 min. We can see clearly that, in the middle troposphere (∼4–8 km), the zonal distributions of correlation coefficients are different from other locations and most of the correlation coefficients in the zonal direction are positive. The mean profiling curve demonstrates the tendency clearly.
 One may notice that the correlation coefficients in Figure 8b are generally not very high. As well known, the radar-measured vertical velocity contains at least two components: a quantity from horizontal wind via tilted irregularity structures/layers, and the true vertical motion of the atmosphere. The latter component is not necessarily related to the incident angle of echo center and so may degrade the correlation between radar-measured vertical velocity and incident angle of echo center. Another possible cause could be the occasional irregularity patches possibly appearing at different places in the radar volume, contributing various quantities to the radar-measured vertical velocity; this cause is difficult to verify.
3.3.2. Characteristic (2)
Figure 9 shows the zonal and meridional distributions of incident angles of the echo centers. Here we have considered all cases of single and multiple echo centers, differing from the selection of only single-center cases made in Figure 8.
 The profiling curve of number difference in the zonal direction (left panel) indicates that there were more echoes coming back from the west (upstream direction) in the middle troposphere, with the maximum at the height of ∼8 km where the greatest downward mean vertical velocity was observed (see Figure 3d). On the other hand, there were more echoes returning from the south direction below the jet-stream wind maximum; this could be due to an intrinsic tilt of the echoing surfaces in meridional direction, or other causes, which were not verified in this study.
 Mean zonal and meridional incident angles are shown in Figure 10a. With the SA horizontal wind shown in Figure 3d, we calculated the vertical velocity associated with the mean incident angles, and the result is presented in Figure 10b. Interestingly, below ∼9 km the order and variation of the estimated vertical velocities (thick-solid curve) are very close to the observed ones (thin-solid curve). Large differences appear in the height interval of ∼10–14 km, where the jet-stream wind maximum was observed. In addition, the reversal of the estimated vertical velocities is unremarkable around/above the jet-stream wind maximum. These results suggest that only the vertical velocities below ∼9 km were closely related to the incident angles of echo centers for the present observation; in other words, the wind shear-tilted layer structures were important for downward vertical velocities in this region.
3.3.3. Characteristic (3)
 The echo power difference between symmetric radar beams is the so-called echo power imbalance (EPI). Evident EPI related to the KHI effect has been examined [e.g., Worthington and Thomas, 1997; Yamamoto et al., 2003a, 2003b]. With the DBS data in the observations, we present the zonal and meridional distributions of EPI in Figure 11. Here the zonal (or meridional) EPI is defined as the ratio of the echo power in the westward (or southward) beam to that in the eastward (or northward) beam. Although the EPI was estimated from DBS data acquired only for ∼10 min at about 1-h intervals, the feature of EPI still makes it possible to indicate the occurrence of tilted layers if such layers exist frequently. As one can see in the left panel of Figure 11, the zonal EPI between 4 km and 9 km is apparently larger than those at other places, revealing evidence of the layers tilting mainly downward to the upstream direction in the middle troposphere.
3.3.4. Characteristic (4)
 This characteristic can be examined with RIM/FII observations. The procedure for estimating layer altitude has been detailed in section 3.2, and as mentioned there, multiple layers could cause problems in estimating the layer slope precisely. In view of this, the cases of multiple layers were excluded in the calculation of layer slope (such selection cannot be achieved using two-frequency interferometry). The percentage of multiple-layer cases varying with altitude is shown in Figure 12c. As seen, the percentage of multiple-layer cases is mostly smaller than 10%, and so the rejection of multiple-layer cases should not degrade the statistical estimates of the layer slopes. Also notice that the layer slope was estimated in units of meters per minute, which is not the real slope of the layer in space. However this is not an issue in the present study because negative and positive slopes of the layers are the desired information here.
Figure 12a shows the distributions of layer slopes, and Figure 12b displays the difference between the positive-slope number and the negative-slope number. Apparently, below the height of the jet-stream wind maximum, the number of positive slopes is larger than that of negative slopes, irrespective of time resolution. A larger number of positively sloped layers may bias the mean vertical velocity downward, consistent with the observations below the jet-stream wind maximum.
 In section 3.2, we have calculated the slope angle of the layer from the layer slope and the observed horizontal wind. We carried out the same calculation here with the layer slope at 1-min resolution, as displayed in Figure 13. We focus our attention on the heights below 10 km since the characteristics (1)–(4) were observed more evidently below 10 km. As shown, the mean layer slopes (solid curve) below 12 km are slightly positive, conforming to the wind shear-tilted layer model. By adopting the SA zonal wind displayed in Figure 3d, we obtained the mean slope angle of the layer in space, as indicated by the circle symbol. Comparing with the CRI zonal incident angles (*), the slope angles of the layers were generally smaller, which is not consistent with the case study. In view of this, mean slope angles of the layers do not seem appropriate to represent quantitatively the mean tilt angle of isentropic surfaces in the wavy layer structures. Qualitative investigation, nevertheless, is accessible by statistical study.
 The above investigations of characteristics (1)–(4) have shown one coherent feature in our observations: the existence of wind shear-tilted layer structures was more evident in the middle troposphere and in the zonal direction. It is conceivable that the wind shear-tilted layer structures exist in zonal direction because of the large vertical wind shear in that direction. However, above the jet stream wind maximum, the characteristics predicted by the wind shear-tilted layer model were not found clearly even when the vertical wind shear and Ri are similar to those below the jet stream. This suggests that other structures/mechanisms may be more important than wind shear-tilted layers in the region above the jet-stream wind maximum, for example, turbulent structures caused by the saturation and breaking of gravity waves, or intrinsic tilt of the echoing surfaces. The depressed influence of wind shear-tilted layer structures on vertical wind in the region above the jet-stream wind maximum could be one of the reasons as to why the reversal height of mean vertical velocity observed in Figure 3d was not located near the jet-stream wind maximum (∼12 km).
 We have applied multiple-receiver and multiple-frequency techniques to survey the vertical velocities in the troposphere and lower stratosphere. A study of a wavy layer has revealed a remarkable correlation between radar-measured vertical velocity, layer altitude, and incident angle of echo center, thereby demonstrating the potential ability of the combined multiple-frequency and multiple-receiver method to reveal important information about atmospheric structures and dynamics. Thirty-three hours of radar data were used to acquire estimates of mean vertical velocities at different altitudes. Analysis shows that the mean vertical velocities were downward below ∼15 km with a maximum of ∼-10 cm/s at ∼8 km. In addition, the reversal height of mean vertical velocity was at ∼15 km, which is higher than the observed mean altitude of the jet-stream wind maximum (∼12 km).
 Statistical distributions of layer slopes, incident angles of echo centers, and echo power imbalance between two oppositely oblique radar beams have suggested that asymmetrically tilted layer structures, which might be caused by vertical wind shear, existed in the middle troposphere. Moreover, the mean vertical velocities derived from the incident angles of echo centers were close to the radar-measured mean vertical velocities below ∼10 km, suggesting that wind shear-tilted/KHI layer structures could be a major contributor to the downward mean vertical velocities observed in the middle troposphere during our radar observations. However there are obvious differences between the derived and the radar-measured vertical velocities in the regions around and above the jet-stream wind maximum, indicating that other structures or mechanisms are more important there than the tilted layers. This may explain partly the inconsistency between the reversal heights of vertical velocities observed in our experiment and those reported previously in the literature. To obtain a more complete survey of the effects of wind shear-tilted/KHI layers on the radar-measured mean vertical velocity above the height of the jet stream, more radar data are needed. We suggest that multiple-receiver-frequency observations be operated routinely in the future, and that the investigative methods/processes used in this study be applied and developed further.
 This work was supported by the National Science Council of ROC (Taiwan) through grants NSC94-2111-M-270-001 and NSC95-2111-M-270-001-MY3, and the MUR International Collaborative Research Program (Ref. No. 2005-O25) of Japan. The MU radar is operated by the Research Institute for Sustainable Humanosphere, Kyoto University, Japan. The authors also thank H. Luce for the preliminary suggestions, and some anonymous referees for their valuable comments/suggestions on this study.