Observation of particle fall velocity in cirriform cloud by VHF and millimeter-wave Doppler radars

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi: /2007jd009125, 2008 Observation of particle fall velocity in cirriform cloud by VHF and millimeter-wave Doppler radars Masayuki K. Yamamoto, 1 Yuichi Ohno, 2 Hiroaki Horie, 2 Noriyuki Nishi, 3 Hajime Okamoto, 4 Kaori Sato, 4 Hiroshi Kumagai, 2 Mamoru Yamamoto, 1 Hiroyuki Hashiguchi, 1 Shuichi Mori, 5 Noriko O. Hashiguchi, 6 Hajime Nagata, 1 and Shoichiro Fukao 1,7 Received 4 July 2007; revised 9 February 2008; accepted 28 February 2008; published 26 June [1] In this study, it is demonstrated that a combination of VHF and millimeter-wave Doppler radars is a key tool for observing particle fall velocity in cirriform clouds. VHF (47-MHz) and millimeter-wave (95-GHz) Doppler radars observed cirriform clouds at West Sumatra, Indonesia (0.2 S, E) from 2000 LT 14 to 0800 LT 15 November Radar reflectivity factor (Z e ) observed by the 95-GHz radar showed that echoes from cloud particles had tops around km and bottoms around 8 10 km. Doppler velocity observed by the vertically pointed beam of the 95-GHz radar (V air+z ) was compared with vertical air velocity (V air ) observed by the 47-MHz radar to confirm that V air+z, a sum of V air and reflectivity-weighted particle fall velocity (V Z ), showed consistent changes with V air and hence V Z is able to be retrieved by subtracting V air from V air+z. The correlation coefficient between V Z and Z e in the middle part of clouds ( km) was 0.81, which was higher than that ( 0.47) in the bottom part ( km). The change of V Z for Z e in the middle part was larger (Z e = 31.9 V Z 32.2) than that in the bottom part (Z e = 90.2 V Z 71.8). These results suggest that particle size was a dominant factor that determined Z e in the middle part. Using V Z, median volume diameter (D 0 ) was estimated to suggest that D 0 was larger than 70 mm in the bottom part and ranged from 40 mm to larger than 106 mm in the middle part. Citation: Yamamoto, M. K., et al. (2008), Observation of particle fall velocity in cirriform cloud by VHF and millimeter-wave Doppler radars, J. Geophys. Res., 113,, doi: /2007jd Introduction [2] Cirriform clouds (cirrus, cirrostratus, cirrocumulus) existing in the upper part of the troposphere consist almost entirely of ice particles [Houze, 1993], and play a significant role in regulating the radiation balance of the earthatmosphere system [e.g., Liou, 1986]. Particle fall velocity in cirriform clouds is one of crucial factors that determine microphysical processes in cloud models [e.g., Petch et al., 1997; Starr and Cox, 1985]. Unlike water drops, ice 1 Research Institute for Sustainable Humanosphere, Kyoto University, Kyoto, Japan. 2 Applied Electromagnetic Research Center, National Institute of Information and Communications Technology, Tokyo, Japan. 3 Division of Earth and Planetary Sciences, Graduate School of Science, Kyoto University, Kyoto, Japan. 4 Center for Atmospheric and Oceanic Studies, Graduate School of Science, Tohoku University, Sendai, Japan. 5 Institute of Observational Research for Global Change, Japan Agency for Marine-Earth Science and Technology, Kanagawa, Japan. 6 Graduate School of Human Development and Environment, Kobe University, Hyogo, Japan. 7 Research Institute of Science and Technology, Tokai University, Tokyo, Japan. Copyright 2008 by the American Geophysical Union /08/2007JD particles of a given size can have different fall velocities depending on their shape, bulk density, and fall altitude. Therefore previous studies have investigated particle fall velocity of ice particles in relation to particle size and shapes [e.g., Heymsfield and Iaquinta, 2000; Matrosov and Heymsfield, 2000; Mitchell, 1996]. [3] Millimeter-wave Doppler radars typically operated near 35 GHz or 94 GHz (8.6-mm or 3.2-mm wavelength) are useful for observing particle fall velocity due to their high sensitivity for particles in cirriform clouds [e.g., Kropfli and Kelly, 1996]. However, an unknown factor exists in observing particle fall velocity by millimeterwave Doppler radars. Because Doppler velocity observed by vertically pointed radar beam of millimeter-wave Doppler radars (hereafter V air+z ) is a sum of vertical air velocity (hereafter V air ) and reflectivity-weighted particle fall velocity (hereafter V Z ), time average of V air+z to reduce effects of V air hasbeenusedtoretrievev Z from V air+z [e.g., Orr and Kropfli, 1999]. [4] VHF Doppler radars operated near 50 MHz (6-m wavelength; hereafter VHF radars) have the capability to directly observe V air both in clear and cloudy regions, because they observe vertical profiles of V air by receiving echoes from fluctuations of refractive index [e.g., Röttger, 1of12

2 Table 1. Observation Parameters of the 47-MHz Radar Used in This Study a Item Inter pulse period, ms 400 Vertical resolution, m 150 Beam direction (Az, Ze) (0, 0 ), (0, 0 ), (0, 0 ) N coh 64 N FFT 1024 N icoh 1 Observation time, s Spectral resolution, Hz Spectral resolution, m s a N coh,n FFT, and N icoh denote a number of coherent integrations (timedomain averaging), FFT points, and incoherent integrations (spectral averaging), respectively. Radar beams were steered on a pulse-to-pulse basis. 1980; Gage, 1990]. VHF radars have been used to observe vertical profiles of vertical and horizontal air velocities in and around cirriform clouds. Using a VHF radar and lidar, Kumar et al. [2001] have reported vertical profiles of air velocities and turbulence in tropical cirriform clouds. Using VHF and 35-GHz radars, Wada et al. [2005] have described a case in which frontal cirriform clouds developed in the presence of shear instability and background upward wind. VHF radars are also an excellent tool for retrieving raindrop size distribution in the lower troposphere due to their capability of receiving echoes from raindrops and atmospheric turbulence separately [e.g., Sato et al., 1990]. However, VHF radars are not sufficiently sensitive to detect small-sized ice particles and so cannot be used to observe particle fall velocities in cirriform clouds. [5] In this study, it is demonstrated that a combination of VHF and millimeter-wave Doppler radars is a key tool to observe particle fall velocities in cirriform clouds. Observational results from the evening on 14 November to the morning on 15 November 2005 are shown. In section 2, data used in this study are described. In section 3, observational results obtained by VHF and millimeter-wave Doppler radars are presented. Discussion and conclusions follow in sections 4 and Data 2.1. VHF Doppler Radar [6] Doppler radar operated at VHF frequency (47 MHz or radar wavelength of 6.38 m), referred to as the Equatorial Atmosphere Radar (hereafter 47-MHz radar), has been operated at Kototabang, West Sumatra, Indonesia (hereafter KT; 0.2 S, E, 865 m above the mean sea level). For a description of the 47-MHz radar system, see Fukao et al. [2003]. The observation mode used in this study (hereafter vertical wind mode) pointed radar beams only to the vertical direction to improve estimation accuracy and data acquisition rate of V air. Table 1 lists the observation parameters of the 47-MHz radar. In addition to the vertical wind mode, the 47-MHz radar was operated by an observation mode to observe vertical and horizontal winds by steering radar beams to vertical, northward, eastward, southward, and westward directions. Two observation modes were alternately carried out. [7] The vertical wind mode was used to improve the observation range and accuracy of V air. In the vertical wind mode, all of radar beams were pointed vertically during the observation time of 78.6 s; it contributes a signal-to-noise ratio (SNR) improvement of 7 db for Doppler spectra obtained by the vertical wind mode, when compared to Doppler spectra obtained with the vertically pointed radar beam of the routine 5-beam observation mode [Nishi et al., 2007]. Values of V air were computed using the vertical wind mode. First, Doppler spectra obtained simultaneously by three vertically pointing beams were averaged in prior to the estimation of V air. Second, off-line incoherent integrations were applied using four successive spectra in time domain to reduce fluctuations in the Doppler spectra for deriving 12-min resolution data. Though V air computation using four successive spectra had a time resolution of 12 min, start times for V air computation were selected every 3 min to smooth V air profiles. Finally, the values of V air were estimated by assuming a Gaussian distribution of the atmospheric echo, and applying a least squares fitting method to the Doppler spectra. When equation (13) of Yamamoto et al. [1988] is applied, estimated error in V air is m s 1 even in considerably turbulent conditions for a spectral width of 0.5 m s Millimeter-Wave Doppler Radar [8] During November 2005, a millimeter-wave Doppler radar operated at millimeter wavelength ( GHz or 3.2 mm; hereafter 95-GHz radar) temporarily carried out observations of cirriform clouds at KT. The 95-GHz radar is able to observe Doppler velocity (V air+z ) from cloud particles using pulse-pair method. For a description of the 95-GHz radar system, see Horie et al. [2000]. [9] Radar reflectivity factor (hereafter Z e ) and V air+z observed by the 95-GHz radar were used for data analysis. Transmitted pulse width used by the 95-GHz radar was 1100 ns (165 m vertical resolution), and data were sampled with an interval of 82.5 m. The beam width of the 95-GHz radar was 0.4 in two-way half-power full width (equivalent to the horizontal resolution of 60 m at 10 km altitude), and that of the 47-MHz radar was 2.4 (equivalent to the horizontal resolution of 380 m at 10 km altitude). [10] 72 radiosonde soundings were carried out at KT from 15 to 21 October 2005 and from 15 to 24 November Because radiosonde observations were not carried out during the period focused on (2000 LT 14 to 0800 LT 15 November 2005), signal attenuation by gases was corrected using vertical profiles of pressure, temperature, and humidity computed by averaging the 72 vertical profiles obtained by radiosondes. Gaseous absorption was 5 db above 7 km, where the 95-GHz radar observed echoes from cloud particles. The averaged vertical profiles of pressure and temperature were also used for correcting V Z variability due to vertical changes of pressure and temperature. Minimum detectable level of the 95-GHz radar was about 25 dbz e at 10.0 km altitude. Original observation data of the 95-GHz was recorded every 1 s. Vertical profiles of Z e and V air+z were produced every 3 min, and further smoothed every 12 min to compare V air observed by the 47-MHz radar Weather Satellite [11] To investigate horizontal distribution of cumulus activity, equivalent blackbody brightness temperature (hereafter T BB ) observed by IR-1 ( mm) channel of the 2of12

3 weather satellite (MTSAT-1R) was used. Using T BB and the vertical profile of temperature computed by averaging the 72 radiosonde profiles, cloud top altitudes were inferred. It is noted that T BB is generally higher than real temperature at cloud top because clouds are not regarded as perfect black bodies [Sherwood et al., 2004]; it means that cloud top altitudes inferred from T BB are generally lower than real cloud tops, and indicate lowest altitudes where cloud top can exist. 3. Results 3.1. Horizontal Distribution of Cumulus Convection [12] Using T BB observed from the evening on 14 November to the morning on 15 November 2005, cloudiness around KT is described. Figure 1 shows horizontal distributions of T BB. Note that time is expressed by local standard time (hereafter LT). LT is 7 h earlier than universal time coordinated. After 2050 LT, T BB of less than 205 K, which indicates presence of deep cumulus convection with a cloud top of higher than 14.1 km, was observed in the east and north of KT (Figure 1a). At 0050 LT, a center of cumulus convection, as indicated by T BB of less than 195 K (cloud top inferred was higher than 15.4 km), existed in the northeast of KT (Figure 1b). Cloud tops higher than 14.1 km, as indicated by T BB of less than 205 K, extended southwestward and covered KT. Figure 2 shows time series of T BB at KT. At KT, a sharp decrease of T BB (increase of cloud top) was observed after 2050 LT 14 November. At 0150 LT 15 November, T BB at KT reached to the minimum (198 K), which indicates that the cloud top was higher than 14.9 km. [13] After 0150 LT 15 November, T BB at KT showed a gradual increase. However, low T BB of less than 215 K, which indicates that cloud tops was higher than 13.0 km, existed at KT until around 0550 LT (Figures 1c and 2). T BB at KT reached to 232 K at 0750 LT, which suggests that cloud tops around KT became 11.1 km or optically very thin even if cloud tops were still higher than 11.1 km (Figure 2) Time-Altitude Variations of Radar Reflectivity Factor and Reflectivity-Weighted Doppler Velocity Observed by the 95-GHz Radar and Vertical Air Velocity Observed by the 47-MHz Radar [14] The 95-GHz radar observed echoes from particles in cirriform clouds from 2030 LT 14 to 0730 LT 15 November Figure 3a shows a time-altitude plot of Z e observed by the 95-GHz radar. Echo tops observed by the 95-GHz radar were almost always located above 12 km, and reached to higher or around 14 km from 2320 LT 14 to 0420 LT 15 Figure 1. Longitude-latitude plots of equivalent blackbody brightness temperature (T BB ) observed by the IR-1 channel of the weather satellite (MTSAT-1R) from 2050 LT 14 to 0450 LT 15 November T BB are plotted with an interval of 4 h. Line contours are drawn from 235 K to 195 K with an interval of 5 K. In each panel, circle at 0.2 S, E and solid curves without shading indicate the location of Kototabang (KT) and coastline, respectively. 3of12

4 Figure 2. Time series of T BB at KT from 1200 LT 14 to 1200 LT 15 November T BB are averaged over the region centered on KT. Altitudes where T BB are located are shown on the right side. November. Most of the time, echo bottoms were located around 8 10 km. Surface rainfall was not observed at KT during the observation period (not shown). These observational results indicate that the clouds around KT were cirriform and existed only in the upper part of the troposphere. [15] V air+z generally showed consistent changes with Z e ; relatively larger downward V air+z was observed for larger Z e (see Figures 3a and 3b). Cirriform clouds do not contain significant numbers of spherical particles larger than 60 mm in maximum dimension [Korolev and Isaac, 2003], and nonsphericity of particles can cause variability of Z e. Using Figure 3. Time-altitude plots of (a) radar reflectivity factor (Z e ), (b) Doppler velocity observed by the 95-GHz radar (V air+z ), and (c) vertical air velocity observed by the 47-MHz radar (V air ) from 2000 LT 14 to 0800 LT 15 November A unit of Z e is mm 6 m 3. Solid curves in Figure 3c indicate the region where the 95-GHz radar received echoes from cloud particles. In this figure, Z e and V air+z are produced every 3 min and not smoothed every 12 min. 4of12

5 Figure 4. Scatterplots between (a) V air and V air+z, and (b) V air and V Z at km from 2000 LT 14 to 0800 LT 15 November the discrete dipole approximation model, lognormal particle size distribution (hereafter PSD), and 95-GHz frequency, Okamoto [2002] have shown that maximum Z e differences between particle shapes with the same effective radius (r eff ) reach to 2 db for r eff less than 100 mm, and 8 db for r eff larger than 100 mm. Further, V air+z can change for the same Z e because ice particles of a given size (e.g., maximum dimension) have different fall velocities due to their shapes, bulk density, and fall altitude. Though such factors can cause variability of Z e and V air+z, the observed feature in V air+z indicates that cloud particles with larger Z e have larger fall velocity, as shown in previous studies [e.g., Heymsfield and Iaquinta, 2000]. [16] In addition to consistent changes with Z e, V air+z had consistent changes with V air. With a timescale of longer than several tens of min, downward V air+z of less than 0.4 m s 1 tended to be found when upward (positive) V air was observed. For example, this tendency was observed especially around 2140 LT and during LT 14 November, and during LT and LT on 15 November (see Figures 3b and 3c). Further, throughout the observation period, V air+z showed vertically standing changes in altitude with a timescale of shorter than 20 min. The vertically standing changes were not observed in Z e, but observed in V air (see Figures 3a and 3c) Retrieval of Reflectivity-Weighted Particle Fall Velocity [17] It is shown that V air observed by the 47-MHz radar is useful for retrieving particle fall velocity. The 47-MHz radar tended to fail in observing V air above 12.2 km due to lack of sensitivity; the data acquisition rate of V air from 2000 LT 14 to 0800 LT 15 November 2005 began to decrease (less than 96%) above 12.2 km, and had the minimum of 58% at 14.2 km (see Figure 3c). Therefore V air and V air+z below 12.2 km were used. Note that slight changes (several hundred meters) of the upper limit (12.2 km) do not significantly affect findings presented in the subsection. Because horizontal winds observed by the 47-MHz radar were almost always 5 m s 1 or less below 12.2 km, horizontal movements of cirriform clouds were 3.6 km or less during the average time of 12 min (not shown). [18] Figure 4a shows a scatterplot between V air and V air+z at km from 2000 LT 14 to 0800 LT 15 November It is clear that V air+z, a sum of V air and V Z, showed consistent changes with V air. The correlation coefficient between V air and V air+z was Figure 4b shows a scatterplot between V air and V Z (=V air+z V air ). Variations in V Z did not have significant relationship with V air ;the correlation coefficient between V air and V Z was Therefore consistent changes between V air+z and V air were caused by V air component in V air+z. Figures 5b, 5c, and 5d show time-altitude plots of V air+z, V Z, and V air, respectively. By subtracting V air from V air+z, the vertically standing changes observed in V air+z and V air disappeared in V Z. [19] Figure 6a shows a scatterplot between V air+z and Z e. The negative correlation between V air+z and Z e suggests that cloud particles with relatively large size have larger fall velocity (see also Figures 5a and 5b). However, V air+z contained large fluctuations for Z e ; the correlation coefficient between V air+z and Z e was Figure 6b shows a scatterplot between V Z and Z e. Note that variability of V Z due to vertical changes of pressure and temperature was not corrected in Figure 6b. The correlation coefficient between V Z and Z e was 0.59, which was better than that between V air+z and Z e ( 0.45). This improvement in the correlation coefficient indicates that the lower correlation between V air+z and Z e occurred due to changes of V air component included in V air+z (see also Figures 5b, 5c, and 5d). The improvement in the correlation coefficient indicates that V air observation by the 47-MHz radar is useful for retrieving V Z in cirriform clouds with better accuracy. [20] In previous studies, time average of V air+z has been used to retrieve V Z from V air+z [e.g., Orr and Kropfli, 1999]. Because V air causes a discrepancy between V Z and V air+z, standard deviation of V air below 12.2 km was used to 5of12

6 Figure 5. Same as Figure 3, except for (a) Z e,(b)v air+z,(c)v Z, and (d) V air at km. In this figure, Z e and V air+z are produced every 3 min and further smoothed every 12 min. examine an accuracy of V Z estimated by time average of V air+z. Smaller standard deviations of V air were found for longer average times (0.12, 0.09, 0.08 m s 1 for 12, 24, and 36 min, respectively). Further, higher correlation coefficients between V Z and V air+z were found for longer average times (0.77, 0.84, and 0.86 for 12, 24, and 36 min, respectively). The mean value of V air was m s 1. These results indicate that a longer time average of V air+z contributes to a better estimation of V Z Comparison of Reflectivity-Weighted Particle Fall Velocity Between the Bottom and Middle Part of Cirriform Clouds [21] Relations between V Z and Z e are investigated by separating the bottom part and the middle part of the cirriform clouds. The threshold altitude between the bottom and middle part is set to 10.5 km. Note that slight changes (several hundred meters) of the threshold do not significantly affect findings presented in the subsection, though the threshold (10.5 km) is not completely objective one. Variability of V Z caused by the vertical changes of pressure and temperature was corrected to match the pressure and temperature averaged over the altitude ranges considered. Equation (A31) of Heymsfield and Iaquinta [2000] was used for correcting V Z. In the bottom part, the averaged pressure and temperature were hpa and K, respectively. Correction factors ranged from 0.94 at the highest altitude (10.5 km) to 1.05 at the lowest altitude (7.3 km). In the middle part, the averaged pressure and temperature were hpa and K, respectively. Correction factors ranged 0.97 at the highest altitude (12.2 km) to 1.03 at the lowest altitude (10.5 km). Figures 7a and 7b show scatterplots between V Z and Z e in the bottom part ( km) and middle part ( km) of clouds, respectively. The changes of V Z for Z e in the bottom part were scattered as compared to those in the middle part; the correlation coefficient between V Z and Z e at the bottom part was 0.47, and that at the middle part was [22] Though changes of V Z for Z e were relatively scattered in the bottom part, a negative correlation between V Z and Z e was still observed; a regression line was Z e = 90.2 V Z In the middle part, changes of V Z for Z e were relatively large; a regression line was Z e = 31.9 V Z The larger negative slope in the bottom part than in the middle part indicates that relatively large-sized particles with larger fall velocities dominantly existed in the bottom part. Previous studies have reported dominance of largesized particles in the bottom part. Previous balloon measurements have shown dominance of large-sized particles in the bottom part of clouds [Heymsfield and Iaquinta, 2000; Miloshevich and Heymsfield, 1997]. Using a 95-GHz radar 6of12

7 Figure 6. Scatterplots between (a) V air+z and Z e and (b) V Z and Z e at km from 2000 LT 14 to 0800 LT 15 November and 532-nm lidar, Okamoto et al. [2003] have retrieved r eff to show dominance of larger r eff and V air+z in the bottom part of cirriform clouds. Previous observations by millimeter-wave radars also have reported dominance of larger downward V air+z in the bottom part of cirriform clouds [e.g., Heymsfield and Iaquinta, 2000; Orr and Kropfli, 1999]. [23] V Z component in V air+z is weighted by backscattering cross section of ice particles (hereafter s), while V air is not weighted by s. Therefore an estimation error of V Z becomes large if large fluctuations of PSD occur within the time and vertical resolutions. Mamma which indicate large variations of PSD at cloud bottoms are candidates that can produce small time- and vertical-scale fluctuations of V Z and V air through processes associated with them. Spectral width observed by the 47-MHz radar shows variance of V air within the time and vertical resolutions (12 min and 150 m). The spectral width was intermittently larger than 0.5 m s 1 within 500 m above the echo bottoms observed by the 95-GHz radar (not shown), which suggests the existence of mamma at the cloud bottoms. However, such regions were limited not only in altitude ( km) but also in time. Figure 7. Same as Figure 6b except at (a) km and (b) km. Discrepancy of V Z caused by the vertical difference of pressure and temperature is corrected to match the pressure and temperature averaged over the altitude ranges plotted. Broken line in Figure 7a and dash-dotted line in Figure 7b show regression lines computed in the ranges of km (Z e = 90.2 V Z 71.8), and km (Z e = 31.9 V Z 32.2), respectively. 7of12

8 Figure 8. Relations between (a) the maximum particle dimension (D max ) and terminal velocities (V t ), (b) D max and the volume equivalent diameter for ice sphere (D eq ), and (c) D eq and V t. Pressure of hpa and temperature of K are used. The curves labeled S, P, B, 2, 3, 4 denote the relations for ice sphere, hexagonal plate, single bullet, bullet rosette with two elements, three elements, and four elements, respectively. Positive values of V t indicate that ice particles move toward the ground. Therefore the existence of mamma did not significantly change the relation between V Z for Z e found in the bottom part. 4. Discussion 4.1. Relations Between Particle Fall Velocity and Volume Equivalent Diameter for Different Kinds of Particle Shape [24] To quantitatively investigate the observed features in the middle and bottom part of cirriform clouds, median volume diameter (D 0 ) was estimated using the observed V Z. To relate V Z to D 0, particle shape and shape parameter (m) were assumed. As ice particle shapes, sphere, single bullet, hexagonal plate, and bullet rosettes with number of branches (hereafter n b ) = 2, 3, and 4 were used. In section 4.1, a method to compute the relation between particle volume equivalent diameter (hereafter D eq ) and fall velocity (hereafter V t ) is described. In section 4.2, first, the relation between D 0 and V Z is computed using the D eq V t relation described in section 4.1. Next, D 0 ranges in the middle and bottom part are estimated using the observed V Z and the D 0 V Z relation. 8of12

9 [25] For ice sphere, the relation between D eq and V t was computed using equation (A24) of Heymsfield and Iaquinta [2000] and the relation between D eq and particle mass (hereafter m) given by 3m 1=3 D eq ¼ 2 ; ð1þ 4pr ice where r ice is the density of solid ice (=0.91 g cm 3 ). The air density used in equation (A24) of Heymsfield and Iaquinta [2000] was computed using the pressure of hpa and temperature of K for the bottom part, and hpa and K for the middle part. For nonspherical shapes, the following processes were carried out to compute the relation between D eq and V t. First, the relation between maximum particle dimension (hereafter D max ) and D eq was computed. Secondly, the relation between D max and V t was computed. Finally, the relation between D eq and V t was obtained using the D max D eq and D max V t relations. [26] The relation between D max and D eq was computed using equation (1) and the relation between m and D max given by m ¼ ad max b ; where a and b are coefficients. For single bullet and bullet rosettes, a and b given by Heymsfield and Iaquinta [2000] were used. For hexagonal plate, a and b given by Mitchell [1996] were used. Figure 8b shows the relation between D max and D eq in the bottom part. [27] For single bullet and bullet rosettes, the relation between V t and D max was given by ð2þ V t ðd max Þ ¼ xd y max ; ð3þ where x and y are coefficients. x and y given by Heymsfield and Iaquinta [2000] were used. As Heymsfield and Iaquinta [2000] gave x and y using the pressure of 300 hpa and temperature of 233 K, equation (A31) of Heymsfield and Iaquinta [2000] was used to correct pressure and temperature dependency of V t. For hexagonal plate, first, m and cross-sectional area (hereafter A) were computed using the m D max and A D max relations given by Mitchell [1996]. Using m, A, and equation (A24) of Heymsfield and Iaquinta [2000], the relation between V t and D max for hexagonal plate was computed. Figure 8a shows the relation between D max and V t in the bottom part. [28] The relation between D eq and V t was computed using the D max D eq and D max V t relations. Figure 8c shows the relation between D eq and V t in the bottom part Particle Size Estimation in the Middle and Bottom Part of Clouds [29] The relation between D 0 and V Z is described. V Z is given by V Z ¼ R N Deq s Deq Vt D eq ddeq R ; ð4þ N Deq s Deq ddeq where N(D eq ) is PSD. Using the modified gamma distribution, PSD was given as N D eq ¼ N0 D m eq 3:67 þ m exp ð D 0 ÞD eq ; ð5þ where N 0 is intercept parameter. The value of m was assumed to compute the relation between D 0 and V Z. s (D eq ) of ice sphere was used to compute V Z for all kinds of the particle shapes. s (D eq ) of ice sphere was compared with ones for nonspherical particle shapes described by Kim [2006] to confirm that differences of s (D eq ) is almost always within 10% for D eq less than 800 mm and so did not significantly change results described in this subsection. s (D eq ) of ice sphere was computed using Mie formulas described by Sauvageot [1992]. The D eq V t relations shown in Figure 8c were used. [30] Figure 9a shows the D 0 V Z relations for ice sphere, single bullet, hexagonal plate, and bullet rosettes in the bottom part. m is 1.0. V Z of hexagonal plate is notably small compared with ones of the different particle shapes. V Z of hexagonal plate reaches to only 0.50 m s 1 at D 0 of 160 mm, though V Z of other particle shapes are larger than 0.9 m s 1. While V Z of hexagonal plate is smaller than 0.5 m s 1, the observed V Z was dominantly larger than 0.5 m s 1 in the bottom part and ranged from m s 1 in the middle part (see Figures 7a and 7b). Therefore the D 0 V Z relation of hexagonal plate is not used in the following discussion. [31] The D 0 range which reproduces the observed ranges of V Z in the bottom part are estimated. V Z observed in the bottom part ranged from 0.35 to 0.90 m s 1 (see Figure 7a). V Z of bullet rosette with n b = 4 is smallest for the same D 0, and is 0.35 m s 1 at D 0 of 72 mm (see Figure 9a). V Z of bullet rosette with n b = 2 is largest for the same D 0, and is 0.90 m s 1 for D 0 of 122 mm. The D 0 ranges were also estimated using m of 0.0 and 2.0. For m = 0.0 and 2.0, the D 0 ranges were estimated to be mm and mm, respectively (Figures not shown). Therefore varying m causes D 0 variability of 7 +6 mm inthe lower boundary and mm in the upper boundary. However, discrepancy of D 0 by varying m is comparatively small when the D 0 ranges are compared between in the bottom and in the middle part (described later). Therefore D 0 of mm would be reasonable to explain variability of V Z observed in the bottom part. [32] The computed V Z variability for the same D 0 suggests that V Z variability due to differences of particle shapes is able to explain a considerable part of observed variability of V Z for the same Z e. The observed V Z in the bottom part dominantly has variability of m s 1 for the same Z e (see Figure 7a), and the maximum difference of V Z for the same D 0 is m s 1 for D 0 of mm (see Figure 9b). These values obtained by the observation and numerical computation suggest that the considerable part of the observed variability of V Z is explained by variability of V Z caused by differences in particle shapes, even when all the parameters which determine Z e (N 0, m, and D 0 ) are assumed to be constant for the same Z e. [33] The D 0 range which reproduces the observed ranges of V Z in the middle part is estimated. Variability of V Z for the same Z e is smaller in the middle part than in the bottom 9of12

10 Figure 9. (a) Relations between the median volume diameter (D 0 ) and V Z. (b) Differences of V Z from V Z of ice sphere for the given D 0. Shape parameter (m) of 1.0, pressure of hpa and temperature of K are used. The curves labeled as n b =2, n b =3, n b = 4 are the relations for bullet rosette with two elements, three elements, and four elements, respectively. Positive values of V Z indicate that ice particles move toward the ground. part (see Figure 7). This smaller variability of V Z suggests that variability of particle shapes was small in the middle part. Therefore the D 0 range is estimated using the D 0 V Z relation for single particle shape and m of 1. For V Z observed in the middle part ranged from 0.20 to 0.85 m s 1 (see Figure 7b), the D 0 range is estimated to be mm for ice sphere, mm for bullet, mm for bullet rosettes with n b = 2, and mm for bullet rosettes with n b = 4. Though the maximum D 0 has considerable variability ( mm), it would be safe to conclude that small D 0 of 40 mm is necessary to explain V Z of 0.20 m s 1 observed in the middle part. The estimated D 0 ranges suggest that D 0 was larger than 70 mm in the bottom part and ranged from 40 mm to larger than 106 mm in the middle part. [34] The observed change of V Z for Z e was larger (Z e = 31.9 V Z 32.2) than those in the bottom part (Z e = 90.2 V Z 71.8; see Figure 7). Further, the correlation coefficient between V Z and Z e was higher in the middle part ( 0.81) than in the bottom part ( 0.47). Because particle size is a dominant factor that determines V Z (see Figure 9a), the larger change of V Z for Z e and higher correlation coefficient in the middle part suggest that the particle size was a dominant factor that determined Z e in the middle part. The smaller change of V Z for Z e and lower correlation coefficient in the bottom part suggest that not only particle size but also other factors determined Z e in the bottom part. 5. Conclusions [35] Doppler velocity observed by vertically pointed radar beam of millimeter-wave Doppler radars (V air+z )isa sum of vertical air velocity (V air ) and reflectivity-weighted particle fall velocity (V Z ). Because of lack of information on V air, time average of V air+z to reduce effects of V air has been used to retrieve V Z from V air+z [e.g., Orr and Kropfli, 1999]. [36] In this study, it has been demonstrated that V Z in cirriform clouds is able to be retrieved using V air observed by VHF Doppler radar and V air+z observed by millimeterwave Doppler radar. First, equivalent blackbody brightness temperature (T BB ) observed by the weather satellite has been used to describe horizontal distribution of cloudiness around Kototabang, West Sumatra, Indonesia (KT; 0.2 S, E) from the evening on 14 November to the morning 15 November 2005 (Figures 1 and 2). Next, radar reflectivity factor (Z e ) observed by the 95-GHz radar was used to show that cirriform clouds with echo tops around km and echo bottoms around 8 10 km existed at KT (Figure 3a). Further data analyses have confirmed that V air+z observed by the 95-GHz radar showed a good correlation with V air observed the 47-MHz radar (Figure 4), and that V Z is able to be retrieved by subtracting V air from V air+z (Figures 5 and 6). [37] The accuracy of V Z estimated by time average of V air+z has been examined. Smaller standard deviations of V air were found for longer average times (0.12, 0.09, 0.08 m s 1 for 12, 24, and 36 min, respectively). Further, higher correlation coefficients between V Z and V air+z were found for longer average times (0.77, 0.84, and 0.86 for 12, 24, and 36 min, respectively). These results indicate that a longer time average of V air+z contributes to a better estimation of V Z. [38] Different V Z Z e relationships between in the bottom ( km) and middle ( km) part of cirriform clouds have been presented (Figure 7). The correlation 10 of 12

11 coefficient between V Z and Z e in the middle part ( 0.81) was higher than that ( 0.47) in the bottom part ( km). The observed change of V Z for Z e in the middle part was larger (Z e = 31.9 V Z 32.2) than that in the bottom part (Z e = 90.2 V Z 71.8). As particle size is a dominant factor that determines V Z (Figure 9a), the larger change of V Z for Z e and higher correlation coefficient observed in the middle part suggest that particle size was a dominant factor that determined Z e in the middle part. [39] The range of median volume diameter (D 0 ) has been estimated using the V Z ranges observed in the bottom part ( m s 1 ) and the middle part ( m s 1 ). Particle shapes (ice sphere, single bullet, hexagonal plate, and bullet rosettes with number of branches of 2, 3, and 4) and shape parameter (m) were assumed to relate V Z to D 0 (Figures 8 and 9). The D 0 estimation has suggested that D 0 was larger than 70 mm in the bottom part and ranged from 40 mm to larger than 106 mm in the middle part. [40] Using millimeter-wave radars, methods to retrieve microphysical properties in cirriform clouds (e.g., effective diameter and ice water content) has been studied [e.g., Intrieri et al., 1993; Matrosov et al., 2002; Okamoto et al., 2003]. Using a millimeter-wave radar and an infrared radiometer, Matrosov and Heymsfield [2000] have generalized the relation between particle fall velocities and particle size. Use of millimeter-wave radars is not limited to cirriform clouds. Using Doppler spectra observed by millimeterwave radars, methods to retrieve of PSD in lower-tropospheric clouds have been studied [e.g., Babb et al., 2000; Gossard et al., 1997]. By improving estimation accuracy of particle fall velocities, V air observations by VHF radars would be able to play a role in improvements of such methods. [41] Both of particle fall velocity and vertical air velocity in cirriform clouds are crucial factors that determine microphysical processes in cloud models [e.g., Starr and Cox, 1985]. Recently, Mitchell et al. [2006] have developed a snow growth model that is able to predict the vertical evolution of ice particle size spectra using operational radar reflectivities. V air observations by VHF radars would contribute to validate and improve such cloud models. [42] Acknowledgments. 47-MHz radar (the Equatorial Atmosphere Radar) data are provided from the joint project between Japan and Indonesia, called Coupling Processes in the Equatorial Atmosphere (CPEA). The former (Japan) side is supported by a grant-in-aid for Scientific Research on Priority Area-764 funded by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan. MTSAT-1R is operated by the Japan Meteorological Agency, and T BB used in this study are distributed by Kochi University, Japan. 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12 Wada, E., H. Hashiguchi, M. K. Yamamoto, M. Teshiba, and S. Fukao (2005), Simultaneous observations of cirrus clouds with a millimeterwave radar and the MU radar, J. Appl. Meteorol., 44, Yamamoto, M., T. Sato, P. T. May, T. Tsuda, S. Fukao, and S. Kato (1988), Estimation error of spectral parameters of mesosphere-stratosphere-troposphere radars obtained by least squares fitting method and its lower bound, Radio Sci., 23(6), S. Fukao, H. Hashiguchi, H. Nagata, M. Yamamoto, and M. K. Yamamoto, Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto , Japan. (fukao@rish.kyoto-u.ac.jp; hasiguti@rish.kyoto-u.ac.jp; h-nagata@rish.kyoto-u.ac.jp; yamamoto@ rish.kyoto-u.ac.jp; m-yamamo@rish.kyoto-u.ac.jp) N. O. Hashiguchi, Graduate School of Human Development and Environment, Kobe University, Hyogo, Japan. (nhashi@radix.h.kobeu.ac.jp) H. Horie, H. Kumagai, and Y. Ohno, Applied Electromagnetic Research Center, National Institute of Information and Communications Technology, Tokyo, Japan. (horie@nict.go.jp; kumagai@nict.go.jp; ohno@nict.go.jp) S. Mori, Institute of Observational Research for Global Change, Japan Agency for Marine-Earth Science and Technology, Kanagawa, Japan. (morishu@jamstec.go.jp) N. Nishi, Division of Earth and Planetary Sciences, Graduate School of Science, Kyoto University, Kyoto, Japan. (nishi@kugi.kyoto-u.ac.jp) H. Okamoto and K. Sato, Center for Atmospheric and Oceanic Studies, Graduate School of Science, Tohoku University, Sendai, Japan. (okamoto@ caos-a.geophys.tohoku.ac.jp; ksato@caos-a.geophys.tohoku.ac.jp) 12 of 12