Motion of echo structures observed with volume imaging atmospheric radar

ARTICLE IN PRESS Journal of Atmospheric and Solar-Terrestrial Physics 70 (2008) 1651–1659

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Motion of echo structures observed with volume imaging atmospheric radar R.M. Worthington RASC, Kyoto University, Uji, Kyoto 611-0011, Japan

a r t i c l e in fo

abstract

Article history: Received 7 December 2007 Received in revised form 6 June 2008 Accepted 18 June 2008 Available online 24 June 2008

Volume imaging radar often shows echo patterns on horizontal scale 10021000 m, moving across the radar. The echoes could be from convection, and moving at near the background wind velocity; other explanations are clouds or regions of turbulence. This paper studies the motion of echoes, with a two-dimensional correlation method widely used for cloud motion winds and tracking weather radar echoes, but not applied before to wind profiling radar. Data are from the MU (middle and upper atmosphere) radar, Japan. Several factors causing an underreading of echo speed are removed; however, remaining data still show echoes moving a few m s1 slower than the background wind, with similar direction. This could be explained by convection, consistent also with some increased vertical-beam spectral width showing turbulence. Motion of convective echoes slower than the background wind could bias other radar wind measurements. & 2008 Elsevier Ltd. All rights reserved.

Keywords: MST radar Volume imaging Convection Wind profiling

1. Introduction Wind-profiling radar measurements often assume scattering from continuous isotropic turbulence, moving with the wind, giving an unbiased average wind vector over the sampling volume and time. However, actual measurements can be a weighted average. For instance, echo power can be greater from parts of a radar beam pointing nearer to zenith, measuring a smaller component of the horizontal wind (Hocking, 1997). Decreasing echo power with height can bias wind measurements to the lower part of range gates (Johnston et al., 2002), thin layers can cause apparent wind shears (Fukao et al., 1988), and variations of echo power and wind velocity can be correlated in turbulence (Tatarskii and Muschinski, 2001) and gravity waves (Nastrom and VanZandt, 1996). Gradients of echo power and wind also occur in cellular structures of convection (‘thermals’), shown by nearhorizontally scanning radar (Hardy and Ottersten, 1969; Konrad, 1970).

E-mail addresses: [email protected], [email protected] (R.M. Worthington). 1364-6826/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2008.06.004

For wind profiling radars pointed near vertical, using the Doppler beam swinging (DBS) method, horizontal wind v ¼ ðr 1  r 2 Þ=2 sin y, where r 1 and r 2 are radial velocities in symmetric beams at zenith angle y, and r 1 ¼ u1 sin y þ w1 cos y;

r 2 ¼ u2 sin y þ w2 cos y,

where u1 , u2 are horizontal wind, and w1 , w2 are vertical wind at the two beam locations. Horizontal gradients in convection could cause u1 au2 and w1 aw2 , corrupting instantaneous wind measurements, although maybe u1 ¼ u2 and w1 ¼ w2 on average if convective effects are statistically similar in both beams. However, variations of humidity, stability, wind and turbulence in thermals are correlated, and typical echo spectra integration times of a few tens of seconds could be enough for small thermals to move through a radar beam; so instead of resolving actual time variations of the wind vector, spectra can give a weighted average of echo power and velocity. If thermals have generally higher humidity and turbulence than their surroundings, giving higher echo power, and move at a horizontal speed

ARTICLE IN PRESS R.M. Worthington / Journal of Atmospheric and Solar-Terrestrial Physics 70 (2008) 1651–1659

different from the background wind, then radar measurements could be biased to the horizontal speed of the thermal. Cumulus clouds above thermals are found to move with the background wind at a height near cloud base (Hasler et al., 1976, 1979), and their motion on satellite images is used to obtain ‘cloud motion winds’ (Schmetz et al., 1993; Nieman et al., 1997). Decaying cumulus clouds (Glass and Carlson, 1963) and weather radar echoes (Tuttle and Foote, 1990) can move with the wind. Pal et al. (1994) found cloud motion measured with a vertically pointing camera was similar to background wind from radiosondes. However, thermals can move at a different speed from the background wind, retaining their horizontal momentum while rising through wind shear (Chiyu et al., 1973; Kuettner et al., 1987). Shiino and Aoyagi (1981) report active convection moving at 0:35 or less of the background wind speed. Early radar studies (Gunn et al., 1954) found cellular echoes, not explained by birds (Harper, 1958), which moved with the wind velocity at a different height. Moving radar echoes could have atmospheric causes other than thermals, such as, waves (Boucher and Ottersten, 1971; Ru¨ster et al., 1996); turbulence moving with the background wind (Balsley and Peterson, 1981; Ru¨ster and Klostermeyer, 1987) or with the phase lines of gravity waves (Yamamoto et al., 1989); or precipitation areas moving at the horizontal speed of their source region (Uematsu et al., 2005). Lidar wind measurements (Eloranta et al., 1975; Buttler et al., 2001) assume turbulent aerosol structures, as more likely than thermals to move with the wind. Volume imaging radar can also show examples of moving echoes (Mead et al., 1998; Pollard et al., 2000; Worthington, 2004). This paper uses volume imaging radar to study if radar echoes are moving at the wind velocity, and caused by thermals. Results could be compared with cloud motion studies, as if thermals are observed at the same sequence of locations visually and on radar, this indicates the same velocity. If radar shows thermals not moving with the background wind, there could be more potential for radar wind bias, and also in spaced antenna wind measurements (Briggs, 1984; Larsen and Ro¨ttger, 1989; Hocking et al., 1989), which use motion of smaller-scale echo structures.

2. Method Fig. 1 shows the volume imaging method, using the 46.5 MHz MU (middle and upper atmosphere) radar, located 34.851N, 136.101E. The radar beam direction is moved through 64 positions, switching every 400 ms, to measure an entire volume in effect simultaneously in 6.55 or 13.1 s. Data sets are used previously in Worthington (2004, 2005). Range resolution is 150 m, and off-vertical beams are linearly interpolated to vertical-beam height gates. Heights are given above ground level, 385 m above sea level. Horizontal maps of echo power can be measured in all weather, including clear air or rain, with co-located

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Fig. 1. Three-dimensional view of the MU radar in volume-imaging mode (from Worthington, 2005). Dots show beam directions, at zenith angles 01, 21, 41, 61, 81, 101, 141, 201 and 301, with 150 m range gates. The shaded surface is land height.

wind measurements. More complex imaging methods also exist (Palmer et al., 2005). Sequences of echo power maps often show motion with a measurable speed and direction. Fig. 2 shows a possible method to measure motion, using the threedimensional autocorrelation of a sequence of maps; motion could be apparent over several maps even if individual maps are noisy. Echo motion components can be obtained from the major axis of the three-dimensional autocorrelation, Fig. 2b. Data are from Fig. 4b of Worthington (2005). Another method included in Fig. 2a is Hovmoller plots of echo power in north–south and east–west lines of beams against time; the slope of structures on distance–time plots gives the echo motion component along each line of beams. However, the autocorrelation axis is often indistinct, and time resolution is reduced, possibly mixing convective and nonconvective data. Echo motion could also be found from timing when echoes cross the map edges. However, the echo patterns gradually change shape and features appear or disappear (Fig. 3a). Instead, echo motion is found from the zonal and meridional shift giving the best match of one twodimensional map to the next (Fig. 3), as used for cloud motion wind (Leese et al., 1971) and particle image velocimetry (Prasad, 2000). Maps are interpolated from beam positions (Fig. 1) to a square array of 25  25 pixels which gives a similar horizontal resolution. Three methods are compared to find the shift that: (a) Maximises cross-correlation, P ðða  AÞðb  BÞÞ ffi, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P ða  AÞ2 ðb  BÞ2

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Fig. 2. Possible method of obtaining radar echo motion using three-dimensional autocorrelation. In (a), data from horizontal echo power maps are in vertical planes, in sequence from left to right. Dots and parallel lines are radar beam positions as in Fig. 1. The semi-transparent shaded volumes show o25 dB isosurfaces of echo power, with beam position lines not plotted within the volumes to show three-dimensional position. Hovmoller plots for north–south and east–west lines of beams through zenith are shown, shifted to the sides of the diagram. (b) Three-dimensional autocorrelation of echo power data in (a). The shaded volume is correlation 40:5. Contour plots are averages of east–west and north–south shifts, with the major axes giving zonal and meridional components of echo motion. Data are from Fig. 4b of Worthington (2005), for 1.425 km AGL, 1432–1443 JST, 12 December 2002.

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Fig. 3. (a) Horizontal maps of echo power, showing a structure moving through the radar volume, at 7.125 km AGL, 0922-0933 JST, 15 July 2002. Time step is 6.55 s, north is at the top of each 3550  3550 m square and þ marks zenith. (b) Cross-correlation of echo power data from adjacent pairs of maps in (a), with position in (b) corresponding to the second of each pair of maps. Numbers and  are maximum cross-correlations and their locations, and þ marks zero shift.

where A, B are the arrays of echo power data, and a, b are overlapping regions for some zonal and meridional shift. Averaging and summation are over all pixels of arrays or sub-arrays. (b) Maximises cross-correlation using fast Fourier transform, F 1 ðFðAÞF  ðBÞÞ, where F is the two-dimensional Fourier transform, F 1 the inverse transform, and F  the complex conjugate.

Arrays have their means subtracted and are surrounded with zero padding. (c) Minimises the mean magnitude of the difference between arrays, ja  bj, which uses information in background gradients of echo power across maps, partly discarded in subtracting the mean for cross-correlation methods (a) and (b).

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Cross-correlation can decrease as the shift between maps increases, causing an underestimate of echo motion speed (Phillips et al., 1972). Such artefacts are checked using artificial echo power data: a square grid of random echo powers with spacing half the map width, then cubic interpolation to the same resolution as actual data. Artificial patterns are shifted with random speeds and directions, and noise added, to test the shift calculation. Direction of motion is similar for methods (a)–(c), and the methods give similar speed for small scale patterns such as dots, as expected. For increasingly larger scale patterns similar to Fig. 3a, method (a) underreads speed several m s1 , method (b) underreads worse, while method (c) shows increased noise rather than under or overreading. Therefore, method (a) is used for maximum crosscorrelation, as a standard measure of the similarity of shifted images, and method (c) gives a more accurate magnitude of the shift. For wind speeds of a few tens of m s1 , the shift between consecutive maps is often only a few pixels, so using a weighted mean of the maximum correlation region gives sub-pixel resolution. In actual radar data,there are more effects to remove,which mostly cause an underreading of echo motion speed.

(1) Aspect sensitivity causes increased echo power from horizontally layered or anisotropic scatterers,in beams pointed near zenith (Hocking, 1997). Aspect-sensitive echo power is often similar from one map to the next,causing high correlation with an average motion near zero. Extracting small isotropic power components from aspect-sensitive maps may be inexact;instead,aspect-sensitive maps are identified for removal,using the echo power difference of vertical and off-vertical beams. With many radar beams as in Fig. 1,an improved estimate of aspect sensitivity is possible. Since maximum echo power can be tilted a few degrees off zenith (Worthington, 2005),maximum echo power of 0–41 beams is used instead of vertical. Isotropic echo power level is estimated from maximum of beams 141 off zenith;use of the maximum identifies patches of convective high echo power covering only a few 141 beams,whereas aspect sensitivity causes only slight increase of echo power in any azimuth at 141. Echo power maps are categorised as aspect sensitive if 0–41 power is at least 1 dB more than at 141;a 1 dB offset is used,as for isotropic scattering with equal echo power in all zenith angles,0–41 power is randomly slightly more or less than 141 power. (2) Measurement noise: Echo motion vectors can be more scattered than wind vectors—instead of a measurement plus noise,appearing as noise with an increase in probability distribution for some echo speed and direction. Averaging of such data can be biased to the mean value of the noise,causing an underread of echo motion speed,so the most probable velocity is used instead (Gaby and Poteat, 1973). For 6.55 s time resolution there are over 500 wind and echo motion measurements per hour,which are sorted into 1 m s1

bins of zonal and meridional velocity. A ‘noise floor’ estimated from median of the distribution is subtracted,then a weighted mean of remaining histogram points gives unbiased zonal and meridional velocities,for both echo motion and wind. (3) Finite measurement area: Echo motion should be more measurable with a larger shift of echo structures. However,finite width of the radar measuring area could again reduce measured echo speed;if a patch of high echo power is moving partly off the map area,cross-correlation is to the portion still within the area,with a smaller shift than if the off-edge region could be included. Time resolution of mostly 6.55 s is low enough that echo shift is much less than map width. (4) Stationary echo power structures: Echo power maps can have features other than aspect sensitivity, which remain nearly stationary. Wind speed near zero causes spectra with near zero Doppler shift, and removal of the zero point of narrow spectra removes atmospheric signal, causing reduced echo power in beams perpendicular to the wind direction. For fairly constant wind, this effect persists from one map to the next, causing high cross-correlation with near zero motion. This can be avoided using a minimum limit on echo speed, which should also remove any remaining aspect sensitivity effect. Echo power patterns such as lines or edges (Lohou et al., 1998) can appear stationery if their motion is parallel to the lines or edges. There is a similar problem for cloud motion wind, parallel to cloud streets. However, there is usually some structure along lines or edges, similar to cloud streets containing separate thermals; so echo motion is measurable. Echo motion could underread if there is a concentric decrease of echo power with increasing zenith angle, similar to aspect sensitivity, caused by reduced effective area of the radar for off-vertical beams. Echo powers are corrected for this effect. Also, there are comparable problems to remove, of ground clutter for motion of weather radar echoes (Tuttle and Foote, 1990). Cloud motion winds can underread if including slower-moving lower cloud (Schmetz et al., 1993), orographic cloud or land surface, and overread if clouds are semi-transparent and their estimated height is too low (Shenk and Kreins, 1970). 3. Results Fig. 4 shows a summary of six data sets, reduced to conventional height–time plots. Height coverage increases in later data. Total data amount is 83 h excluding gaps. There are regions of high vertical-beam echo power in Fig. 4a, which are aspect sensitive in Fig. 4b, with high correlation in Fig. 4c from similarity of the aspect sensitivity pattern in consecutive echo power maps. Vertical lines above 5 km on 16 July and 12 December 2002 are from radio interference. Some other regions have high echo power, low aspect sensitivity and high

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Fig. 4. Height–time plots of (a) vertical-beam echo power, (b) anisotropy, difference of 0–41 and 141 echo power (see text), (c) maximum cross-correlation of adjacent echo power maps, (d) horizontal wind vectors and (e) echo motion vectors for structures similar to Fig. 3a. For August 2001, panels (d) and (e), the vector magnitudes are multiplied 4. The time interval of Fig. 7 is marked  below the 16 July 2002 data.

correlation, such as 27–28 February 2002, 27–32 h; 15 July 2002, 9 and 12 h; and 16 July 2002, 14–18 h, below 7 km. Echo power maps in these regions show moving structures as in Fig. 3a. Fig. 4d shows horizontal wind vectors, and Fig. 4e echo motion vectors, for height–time intervals of 0:5 km  1 h. Wind vectors are from symmetric beam pairs at zenith angles 61, 81, 101 and 141, and vectors are plotted darker for standard deviation of wind speed less than 10 m s1 . Echo motion vectors use maps with maximum correlation 40.5, not aspect sensitive, echo speed 425% of wind speed, and standard deviation o20 m s1 for points above the noise level. Echo motion vectors are more patchy than Fig. 4d; however, their continuity and similarity to the wind vectors suggests that they are meaningful. Figs. 5 and 6 show data from Figs. 4d and e as speed and direction profiles, for times when there are most echo motion vectors. Echo motion can refer to different echoes at different heights, and are not continuous profiles. Also, echoes could occur in only a fraction of the data, similar to radiosonde winds referring to a small time and volume of atmosphere. Wind data are categorised as whether aspect sensitive or not, with correlation greater or less than 0.5. To check radar winds, there are also independent wind data from GDAS (Global Data Assimilation System), for 850, 700, 500 and 400 mB height above the radar site at

0300, 0900, 1500 and 2100 JST (Japan Standard Time, UTC þ 9 h). The various wind measurements and model mostly agree, whereas echo motion speed is several m s1 less. Echo motion slower than background wind at the same height could suggest convection, rather than regions of turbulence or cloud moving with the wind. Lumpy echo structures from convection could give high correlation between consecutive maps. Cloud motion winds are typically faster than surface wind (Halpern, 1978; Wylie et al., 1981), and the slowest echo motions in Figs. 5 and 6 are also mostly faster than the surface wind from an anemometer at the MU radar site, or from the GDAS model. Data from a 1357 MHz radar colocated with the MU radar show a brightband at 1–2 km height, implying stratiform rain on 27–28 February 2002 (Worthington, 2004),1 and Figs. 5f and g show echoes near 2 km moving with the wind velocity. Above 2 km, echo motion slower than the wind could be from upper level convection (Williams et al., 1995; Hogan et al., 2002), which could also explain echo motion separated from the ground by an

1 In Fig. 4 of Worthington (2004), radiosonde heights are above sea level and should be shifted 0.4 km down, and surface rainfall data should be shifted 2 h later.

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aspect-sensitive layer at 2.5 km height on 12 December 2002, Figs. 4b and 6g. Fig. 7 shows 40 photographs of the view north from the MU radar, at 1 min intervals, 1403–1442 JST 16 July 2002. Images are histogram equalised and noise reduced. Shallow cumulus clouds move left to right in westerly wind (Fig. 6e), and could be a visual equivalent of the moving radar echoes.

Echo motion at 14–18 JST, 16 July 2002 in Fig. 4e is to over 6 km height. Radar spectral width could show if there is deep and not only shallow convection (Sato et al., 1995; Hashiguchi et al., 1995). However, spectral width and vertical wind measurements typically use a vertical beam, whereas turbulence and updrafts of convection may not be at the centre of the map area. Horizontal area of the vertical beam is only 5% of the total map area. Whereas

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Fig. 7. Sequence of photographs at 1 min intervals, looking north from the MU radar, 1403–1442 JST, 16 July 2002, showing motion of shallow convective clouds.

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features of spectral width above 2 km; however, these are merged clear-air and rain echoes with downward motion of a few m s1 and not definitely convective. Fig. 9 shows a summary of echo and wind velocity for data sets in Fig. 4. August 26–27 2001 data are clustered near zero and are omitted. Each point is for 1 h and one 150-m height gate, with correlation 40:5 and echo speed 425% of wind speed. Wind and echo motion measurements are at the same heights and times. Echo speed is a few m s1 less than wind speed, while directions are similar. For comparison, Fig. 9 includes results from Table 1 of Chiyu et al. (1973), on motion of shallow cumulus clouds above land near Sapporo (43.11N, 141.41E)—27 measurements from stereo photographs, on 12 summer and autumn mornings, compared to the wind vector from radiosondes a few km away. Maximum cloud and wind speeds from Chiyu et al. are lower as measurements are up to 1.5 km above ground. Cloud motion has a similar slow bias as radar echo motion, expected if the radar is also measuring motion of thermals.

4. Discussion vertical wind variations of gravity waves could cover the entire map area, convective updrafts could be narrower (Fig. 7b of Worthington, 2004). However, for extensive convection there could be increased vertical-beam spectral width. Fig. 8 shows height–time plots of spectral width on 15 and 16 July 2002; in the vicinity of high correlation and low aspect sensitivity in Fig. 4, there are vertical features of high spectral width, consistent with deep convection. There is also surface rain at the MU radar site on 15 July 2002. On 27–28 February 2002 there are similar vertical

Measurement of echo motion depends on adequate removal of artefacts listed in Section 2, and there is no independent measurement to check the results, for this data set. Instead, radar processing can be varied to find if measured echo velocity is robust. Varying the number of map array pixels to 15  15 or 45  45, removing more maps adjacent to aspect sensitivity, or varying the correlation limit from 0.5 gives results similar to Fig. 9. Effect of echo shift similar to map width can be checked using non-consecutive pairs of maps, with increased time

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separations. Results are similar using a separation of two maps instead of one, then as separation is increased to three maps or more, measured echo speed gradually decreases. However, modified processing seems unable to remove the underreading of echo speed compared to wind speed. Data with high and low correlation of echo power maps, in low aspect sensitivity, could correspond to thermals and surrounding areas, with high-correlation wind speeds expected to be less than low-correlation wind speeds. However, Figs. 5 and 6 show less differences among wind measurements than compared to echo motion, with median differences near zero. This could be explained if: slow echo motion is an artefact of data processing or a radar problem, although this should all be corrected; thermal echoes often occupy only part of the map area, so surrounding wind data are still being measured; there is flow speed-up around and over slowmoving thermal obstacles, which increases the average measured wind velocity; or, the wind and echo velocities refer to different measurement scales (Fujita et al., 1975), 3 m and 10021000 m, which can move at different speeds—as with a chimney or fire viewed from above, where the overall position of the plume remains stationary, but much of the smaller-scale cloud and turbulence move with the wind. Spaced antenna radars use correlation of moving echo patterns in horizontally separated receivers. Echoes not moving with the wind velocity could corrupt spaced antenna wind measurements; for instance, varying specular reflections as waves move across a radar, although these could be of spatial and time scales separable from turbulent echoes (Hocking et al., 1989; Tsuda et al., 1997). However, thermals can also contain structure on scale of tens of metres used for spaced antenna radars, giving correlated signals in spaced receivers, and could be an atmospheric component of a slow bias reported for spaced antenna winds (Vincent et al., 2004). A slow bias is also found for jet-stream cloud motion winds (Nieman et al., 1997). Motion of structures as in Fig. 3a might not be used

for radar wind measurement; however, spaced antenna methods could be studied (Holdsworth and Reid, 1995) using subsets of volume imaging data, or e.g. five-beam DBS data as echo structures can be tracked across typical DBS beam separations. All-weather measurement of convection motion could have other applications, such as identifying ‘oscillator’ or ‘obstacle’ causes of convection waves, from convection moving at or slower than the background wind (Fritts and Alexander, 2003). 5. Conclusions Volume imaging radar can measure the motion of echoes, on horizontal scale 10021000 m, with twodimensional cross-correlation methods previously used to track weather radar echoes or clouds on satellite images. After causes of nearly stationary echoes are removed, remaining data still show a slow bias of echo speed compared to background wind speed. This could be explained by convection, causing echo structures often moving with the wind speed at a lower height.

Acknowledgements The author was funded by Japan Society for the Promotion of Science, April 2001—March 2003 at Radio Science Center for Space and Atmosphere (now Research Institute for Sustainable Humanosphere), Kyoto University, Kyoto, Japan. GDAS model data are from the NOAA Air Resources Laboratory. References Balsley, B., Peterson, V.L., 1981. Doppler-radar measurements of clear air atmospheric turbulence at 1290 MHz. Journal of Applied Meteorology 20, 266–274. Boucher, R.J., Ottersten, H., 1971. Doppler radar observation of wind structure in snow. Journal of Applied Meteorology 10, 228–233.

ARTICLE IN PRESS R.M. Worthington / Journal of Atmospheric and Solar-Terrestrial Physics 70 (2008) 1651–1659

Briggs, B.H., 1984. The analysis of spaced sensor records by correlation techniques. In: Vincent, R.A. (Ed.), Middle Atmosphere Program, Handbook for MAP, vol. 13. SCOSTEP Secretariat, University of Illinois, Urbana, pp. 166–186. Buttler, W.T., Soriano, C., Baldasano, J.M., Nickel, G.H., 2001. Remote sensing of three-dimensional winds with elastic lidar: explanation of maximum cross-correlation method. Boundary Layer Meteorology 101, 305–328. Chiyu, T., Kon, H., Magono, C., 1973. The moving velocity of cumulus humilis clouds. Journal of the Meteorological Society of Japan 51, 43–53. Eloranta, E.W., King, J.M., Weinman, J.A., 1975. The determination of wind speeds in the boundary layer by monostatic lidar. Journal of Applied Meteorology 14, 1485–1489. Fritts, D.C., Alexander, M.J., 2003. Gravity wave dynamics and effects in the middle atmosphere. Reviews of Geophysics 41, 1003. Fujita, T.T., Pearl, E.W., Shenk, W.E., 1975. Satellite-tracked cumulus velocities. Journal of Applied Meteorology 14, 407–413. Fukao, S., Sato, T., May, P.T., Tsuda, T., Kato, S., Inaba, M., Kimura, I., 1988. A systematic error in MST/ST radar wind measurement induced by a finite range volume effect. 1. Observational results. Radio Science 23, 59–73. Gaby, D.C., Poteat, K.O., 1973. ATS-3 satellite-derived low-level winds: a provisional climatology. Journal of Applied Meteorology 12, 1054–1061. Glass, M., Carlson, T.N., 1963. The growth characteristics of small cumulus clouds. Journal of the Atmospheric Sciences 20, 397–406. Gunn, K.L.S., Langleben, M.P., Dennis, A.S., Power, B.A., 1954. Radar evidence of a generating level for snow. Journal of Meteorology 11, 20–26. Halpern, D., 1978. Comparison of low-level cloud motion vectors and moored buoy winds. Journal of Applied Meteorology 17, 1866–1871. Hardy, K.R., Ottersten, H., 1969. Radar investigations of convective patterns in the clear atmosphere. Journal of the Atmospheric Sciences 26, 666–672. Harper, W.G., 1958. Detection of bird migration by centimetric radar—a cause of radar ‘angels’. Proceedings of the Royal Society B 149, 484–502. Hashiguchi, H., Yamanaka, M.D., Tsuda, T., Yamamoto, M., Nakamura, T., Adachi, T., Fukao, S., Sato, T., Tobing, D.L., 1995. Diurnal variations of the planetary boundary layer observed with an L-band clear-air Doppler radar. Boundary-Layer Meteorology 74, 419–424. Hasler, A.F., Shenk, W., Skillman, W., 1976. Wind estimates from cloud motions: phase 1 of an in situ aircraft verification experiment. Journal of Applied Meteorology 15, 10–15. Hasler, A.F., Skillman, W.C., Shenk, W.E., Steranka, J., 1979. In situ aircraft verification of the quality of satellite cloud winds over oceanic regions. Journal of Applied Meteorology 18, 1481–1489. Hocking, W.K., 1997. Strengths and limitations of MST radar measurements of middle-atmosphere winds. Annales Geophysicae 15, 1111–1122. Hocking, W.K., May, P., Ro¨ttger, J., 1989. Interpretation, reliability and accuracies of parameters deduced by the spaced antenna method in middle atmosphere applications. Pure and Applied Geophysics 130, 571–604. Hogan, R.J., Field, P.R., Illingworth, A.J., Cotton, R.J., Choularton, T.W., 2002. Properties of embedded convection in warm-frontal mixedphase cloud from aircraft and polarimetric radar. Quarterly Journal of the Royal Meteorological Society 128, 451–476. Holdsworth, D.A., Reid, I.M., 1995. A simple model of atmospheric radar backscatter: description and application to the full correlation analysis of spaced antenna data. Radio Science 30, 1263–1280. Johnston, P.E., Hartten, L.M., Love, C.H., Carter, D.A., Gage, K.S., 2002. Range errors in wind profiling caused by strong reflectivity gradients. Journal of Atmospheric and Oceanic Technology 19, 934–953. Konrad, T.G., 1970. The dynamics of the convective process in clear air as seen by radar. Journal of the Atmospheric Sciences 27, 1138–1147. Kuettner, J.P., Hildebrand, P.A., Clark, T.L., 1987. Convection waves: observations of gravity wave systems over convectively active boundary layers. Quarterly Journal of the Royal Meteorological Society 113, 445–467. Larsen, M.F., Ro¨ttger, J., 1989. The spaced antenna technique for radar wind profiling. Journal of Atmospheric and Oceanic Technology 6, 920–938. Leese, J.A., Novak, C.S., Clark, B.B., 1971. An automated technique for obtaining cloud motion from geosynchronous satellite data using cross correlation. Journal of Applied Meteorology 10, 118–132. Lohou, F., Druilhet, A., Campistron, B., 1998. Spatial and temporal characteristics of horizontal rolls and cells in the atmospheric

1659

boundary layer based on radar and in situ observations. BoundaryLayer Meteorology 89, 407–444. Mead, J.B., Hopcraft, G., Frasier, S.J., Pollard, B.D., Cherry, C.D., Schaubert, D.H., McIntosh, R.E., 1998. A volume-imaging radar wind profiler for atmospheric boundary layer turbulence studies. Journal of Atmospheric and Oceanic Technology 15, 849–859. Nastrom, G.D., VanZandt, T.E., 1996. Biases due to gravity waves in wind profiler measurements of winds. Journal of Applied Meteorology 35, 243–257. Nieman, S.J., Menzel, W.P., Hayden, C.M., Gray, D., Wanzong, S.T., Velden, C.S., Daniels, J., 1997. Fully automated cloud-drift winds in NESDIS operations. Bulletin of the American Meteorological Society 78, 1121–1133. Pal, S.R., Pribluda, I., Carswell, A.I., 1994. Lidar measurements of cloudtracked winds. Journal of Applied Meteorology 33, 35–44. Palmer, R.D., Cheong, B.L., Hoffman, M.W., Frasier, S.J., Lo´pez-Dekker, F.J., 2005. Observations of the small-scale variability of precipitation using an imaging radar. Journal of Atmospheric and Oceanic Technology 22, 1122–1137. Phillips, D.R., Smith, E.A., Suomi, V.E., 1972. Comments on ‘‘An automated technique for obtaining cloud motion from geosynchronous satellite data using cross correlation’’. Journal of Applied Meteorology 11, 752–754. Pollard, B.D., Khanna, S., Frasier, S.J., Wyngaard, J.C., Thomson, D.W., McIntosh, R.E., 2000. Local structure of the convective boundary layer from a volume-imaging radar. Journal of the Atmospheric Sciences 57, 2281–2296. Prasad, A.K., 2000. Particle image velocimetry. Current Science 79, 51–60. Ru¨ster, R., Klostermeyer, J., 1987. Propagation of turbulence structures detected by VHF radar. Journal of Atmospheric and Terrestrial Physics 49, 743–750. Ru¨ster, R., Czechowsky, P., Hoffmann, P., Singer, W., 1996. Gravity wave signatures at mesopause heights. Annales Geophysicae 14, 1186–1191. Sato, K., Hashiguchi, H., Fukao, S., 1995. Gravity waves and turbulence associated with cumulus convection observed with the UHF/VHF clear-air Doppler radars. Journal of Geophysical Research 100, 7111–7119. Schmetz, J., Holmlund, K., Hoffman, J., Strauss, B., Mason, B., Gaertner, V., Koch, A., Van De Berg, L., 1993. Operational cloud-motion winds from Meteosat infrared images. Journal of Applied Meteorology 32, 1206–1225. Shenk, W.E., Kreins, E.R., 1970. A comparison between observed winds and cloud motions derived from satellite infrared measurements. Journal of Applied Meteorology 9, 702–710. Shiino, J., Aoyagi, J., 1981. Three-dimensional distribution of precipitation water in a maritime cumulus cloud as revealed by X-band digitized radar. Journal of the Meteorological Society of Japan 59, 844–863. Tatarskii, V.I., Muschinski, A., 2001. The difference between Doppler velocity and real wind velocity in single scattering from refractive index fluctuations. Radio Science 36, 1405–1423. Tsuda, T., Gordon, W.E., Saito, H., 1997. Azimuth angle variations of specular reflection echoes in the lower atmosphere observed with the MU radar. Journal of Atmospheric and Solar-Terrestrial Physics 59, 777–784. Tuttle, J.D., Foote, G.B., 1990. Determination of the boundary layer airflow from a single Doppler radar. Journal of Atmospheric and Oceanic Technology 7, 218–232. Uematsu, A., Hashiguchi, H., Teshiba, M., Tanaka, H., Hirashima, K., Fukao, S., 2005. Moving cellular structure of fog echoes obtained with a millimeter-wave scanning Doppler radar at Kushiro, Japan. Journal of Applied Meteorology 44, 1260–1273. Vincent, R.A., MacKinnon, A., Reid, I.M., Alexander, M.J., 2004. VHF profiler observations of winds and waves in the troposphere during the Darwin Area Wave Experiment (DAWEX). Journal of Geophysical Research 109, D20S02. Williams, C.R., Ecklund, W.L., Gage, K.S., 1995. Classification of precipitating clouds in the Tropics using 915-MHz wind profilers. Journal of Atmospheric and Oceanic Technology 12, 996–1012. Worthington, R.M., 2004. All-weather volume imaging of the boundary layer and troposphere using the MU radar. Annales Geophysicae 22, 1407–1419. Worthington, R.M., 2005. VHF volume-imaging radar observation of aspect-sensitive scatterers tilted in mountain waves above a convective boundary layer. Annales Geophysicae 23, 1139–1145. Wylie, D.P., Hinton, B.B., Millett, K.M., 1981. A comparison of three satellite-based methods for estimating surface winds over oceans. Journal of Applied Meteorology 20, 439–449. Yamamoto, M., Sato, T., Tsuda, T., Fukao, S., Kato, S., 1989. Full-correlation analysis of turbulent scattering layers in the mesosphere observed by the MU radar. Pure and Applied Geophysics 130, 605–616.