Retrieval of Microphysical Properties of Water, Ice, and Mixed-Phase Clouds Using a Triple-Wavelength Radar and Microwave Radiometer

Journal of the Meteorological Society of Japan, Vol. 84, No. 6, pp. 1005--1031, 2006 1005

Yukio YOSHIDA, Shoji ASANO

Center for Atmospheric and Oceanic Studies, Tohoku University, Sendai, Japan

and

Koyuru IWANAMI

National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Japan

(Manuscript received 3 October 2005, in ﬁnal form 25 August 2006)

Abstract

An algorithm has been developed to retrieve the vertical profiles of cloud microphysical properties from the surface observation based on three radars operated at three microwave bands (X-band, Ka- band, and W-band) and a microwave-radiometer. This algorithm has the advantage that it can be applied to any mixing condition of liquid and ice particles in clouds (i.e., pure-water clouds, pure-ice clouds, and mixed-phase clouds). To precisely treat the scattering processes of the radar waves in clouds, we pay attention to non-sphericity of ice-particles and radar wave attenuation by scattering, which are fre- quently neglected in the previous studies. The hexagonal ice-particles with various aspect ratios are considered. On the other hand, the observational data used in this algorithm need two assumptions: 1) the observed cloud does not contain precipitating and melting particles, and 2) the water vapor profiles are approximated by successive steady-state representations. The accuracy of the radar calibration required for this algorithm would be within G0.1 dB, which is about the order of uncertainty of radar measurements. In the retrieval procedure, the mixing condition of water-droplets and ice-particles in the target cloud sub-layer can be identified by utilizing the wavelength-dependence of the scattering and attenuation properties. Once the mixing condition of the cloud sub-layer is determined, the microphysical properties of pure-water and pure-ice clouds are estimated by the algorithm, similar to the widely-used dual-wavelength technique, except for the fact that in the present algorithm, an equivalent aspect ratio of ice-particles can be estimated, in addition to ice-water-content and ice-particle size of pure-ice clouds. For mixed-phase clouds, the microphysical profiles, which satisfy the observed radar and microwave- radiometer signals, can be estimated by iteratively changing aspect ratios of ice-particles in each sub- layer. The retrieval algorithm is applied to the observational data obtained in the Vertically Pointing Measurements, Tsukuba, 2001 (VPM_TKB01). The retrieved microphysical profiles for the pure-ice clouds show reasonable performance of the present algorithm, although there are no in-situ measurements to validate the estimated values.

1. Introduction Corresponding author and present affiliation: Yu- kio Yoshida, Center for Global Environmental It is well recognized that clouds have signifi- Research, National Institute for Environmental cant influence on Earth’s radiation budget as Studies, Tsukuba, Ibaraki, 305-8506, Japan. E-mail: [email protected] well as the hydrologic cycle in the atmosphere ( 2006, Meteorological Society of Japan (Stephens et al. 1990; Baker 1997). In order to 1006 Journal of the Meteorological Society of Japan Vol. 84, No. 6 estimate their effect on the radiation budget, lidar is limited to optically thin clouds with the their microphysical properties, such as liquid- visible optical thickness of less than 2@3, due water-content ðLWCÞ, ice-water-content ðIWCÞ, to large attenuation of the laser beam by cloud and characteristic size and shape of cloud par- particles. ticles have to be known. The vertical profiles of On the other hand, cloud radars can pene- these cloud microphysical properties, and the trate optically thicker clouds, and thus are sen- cloud-boundary altitudes are also important sitive to larger cloud particles such as rain- parameters for estimating the radiative heat- droplets and ice-particles than optical lidars ing rate profile and cloud radiative forcing, are. There are many studies on radar measure- which greatly affect the Earth’s climate sys- ments of precipitating clouds and pure-ice tem. For example, in our previous studies, we clouds. For pure-ice clouds, the simple power- performed simultaneous measurements of cloud law relationship between IWC and the radar radiative and microphysical properties of fron- reflectivity factor, Z, has been proposed by tal ice clouds, and showed that the shortwave- various studies (e.g., Sassen 1987; Atlas et al. and longwave-radiative heating make the 1995; Brown et al. 1995): daytime ice cloud layers thermodynamically IWC ¼ aZb: ð1Þ unstable (Yoshida et al. 2004). Also, it was shown that the radiative properties of mixed- This relationship has been widely used to de- phase clouds are significantly affected by the rive vertical profiles of IWC. If the so-called vertical profiles of water-droplets and ice- Doppler radar is used, the vertical profile of particles, especially in the near-infrared wave- ice-particle size can also be obtained from the length region (Yoshida and Asano 2005). experimental relationship between Doppler ve- However, the radiative and microphysical prop- locity and particle size (Matrosov et al. 1994). erties of these clouds containing ice-particles But, the coefficients a and b of Eq. (1) may are not well understood due to insufficient ob- vary from cloud to cloud, and the estimated servations, although these clouds occur fre- IWC can differ by as much as an order of mag- quently; cirrus clouds cover about 20% to 30% nitude, depending on the relationship used of the globe (Wylie et al. 1994), and the mixed- (Matrosov 1999). phase condition accounts for 20% to 90% of By using multiple radars, vertical profiles of clouds with temperatures less than 0C (Riley IWC and ice-particle size can be estimated 1998). To improve our knowledge on the global even without Doppler capability (Sekelsky et al. radiation budget, microphysical profiles of these 1999; Hogan et al. 2000; Wang et al. 2005). clouds should be investigated. However, most of multi-wavelength radar algo- Unfortunately, passive instruments such rithms assume that ice-particles are Rayleigh- as microwave-radiometers and spectro- scatterer of spherical shape for the radar wave- radiometers can only measure vertically- lengths, although ice-particles have various integrated microphysical parameters, and shapes. In these algorithms, the non-spherical cannot provide the vertical profiles of cloud mi- effects of ice-particles are approximated by the crophysical properties nor the cloud bounda- change of particle bulk density as a function of ries. On the other hand, active instruments the particle size. However, the scattering prop- such as lidar and radar can provide detailed in- erties of such approximated spherical particles formation of the vertical distributions of cloud greatly differ from those of non-spherical par- microphysical properties. Platt (1973, 1979) de- ticles, especially for large ice-particles (Sekel- veloped the method for the ground-based obser- sky et al. 1999; Wang et al. 2005). Moreover, vation of high-level ice clouds by combining an there are a few algorithms which include the optical lidar and an infrared radiometer, and attenuation of radar wave by ice-particles. estimated the cloud optical thickness and infra- Wang et al. (2005) estimate the 94 GHz attenu- red emissivity of cirrus clouds. Recently, Oka- ation due to ice-particles by utilizing the moto et al. (2003) proposed a new technique to 9.6 GHz radar reflectivity factor. The assump- retrieve the vertical profiles of IWC and ice- tion of no radar wave attenuation by ice- particle size of cirrus clouds by using a lidar particles leads to substantial error in the esti- and a 95 GHz cloud radar. However, the use of mated microphysical properties when they are December 2006 Y. YOSHIDA et al. 1007 measured by radars of short-wavelength, such onal shape with various aspect ratios, and try as a 95 GHz cloud radar. to estimate equivalent aspect ratio of ice- Some cloud radars with high-sensitivity particles. The radar wave attenuation due to can detect not only ice clouds but also non- scattering by ice-particles is considered in our precipitating water clouds. As in the case of algorithm. On the other hand, the observatio- pure-ice clouds, similar power-law relationship nal data used in this algorithm need to follow between LWC and Z for water clouds has two criteria: 1) the observed cloud does not con- been proposed by several studies (Sauvageot tain precipitating and melting particles, and 2) and Omar 1987; Fox and Illingworth 1997). the water vapor profiles are approximated by Using a high-sensitivity Ka-band (wave- successive steady-state representations. Fur- length ¼ 8:66 mm) radar and a microwave- thermore, the accuracy of the radar calibration radiometer, Frisch et al. (2002) retrieved the required for this algorithm would be within vertical profile of effective radius of stratus G0.1 dB, which is about the order of uncer- clouds. For mixed-phase condition, Vivekanan- tainty of radar measurements. In section 2, the dan et al. (1999) discriminated between LWC mathematical expressions for the attenuated and IWC of mixed-phase clouds by using dual- radar reflectivity factor and the treatment of wavelength radars. Gaussiat et al. (2003) scattering properties of cloud particles are pre- retrieved LWC, IWC, and characteristic ice- sented. In section 3, the retrieval algorithm is particle size of precipitating clouds from triple- explained in detail. In section 4, performance wavelength radars with the assumption of no of the algorithm is examined through sensitiv- attenuation of radar waves by ice-particles. Be- ity tests simulated for assumed cloud models. cause such precipitating clouds show the strong In section 5, the developed algorithm is applied attenuation by liquid-water, the attenuation by to the observational data taken by the ground- ice may be negligible. However, the assump- based triple-band multiparameter radar sys- tions of spherical ice-particle and/or the negligi- tem and a microwave-radiometer in Tsukuba, ble radar wave attenuation by ice-particles in Japan. Finally, a summary is given in section 6. these studies may affect the estimated cloud microphysical values, especially for non- 2. Theoretical background precipitating mixed-phase clouds. This study exclusively focuses on non- In this study, we develop a new algorithm precipitating clouds. Instead of neglecting melt- to retrieve the microphysical parameters of ing and precipitation processes, we consider pure-water, pure-ice, and mixed-phase clouds pure-water and pure-ice clouds and clouds in from the ground-based observation by using a mixed-phase condition, in which water-droplets ‘‘triple-band radar system’’, which consists of and ice-particles coexist within the same cloud highly sensitive and accurate three radars of volume. Before describing details of the algo- X-band (wavelength 31.98 mm; frequency rithm, the basic physical theory of radar and 9.4 GHz), Ka-band (8.48 mm; 35 GHz), and microwave-radiometer measurements is pre- W-band (3.15 mm; 95 GHz), together with a sented in the following section. microwave-radiometer. To reduce a number of unknown cloud microphysical parameters, we 2.1 Radar equation first distinguish a mixing condition of each In this study, we consider three radars: X- cloud sub-layer from the triple-band radar sys- band (9.4 GHz; 31.98 mm), Ka-band (35 GHz; tem data. The retrieval algorithm can estimate 8.48 mm), and W-band (95 GHz; 3.15 mm). LWC and effective water-droplet radius reff ; wat The radars at these wavelengths, especially for pure-water cloud sub-layer, and LWC, IWC, Ka-band and W-band radars, have good sensi- effective ice-particle radius reff ; ice, as well as an tivity to detect cloud particles. Hereafter, we equivalent aspect ratio of ice-particles for pure- call the combined three radars a triple-band ice and/or mixed-phase cloud sub-layers. In our radar system. retrieval procedure, no assumption concerning We start with the radar equation, and derive the vertical profiles of mixing ratio between the attenuated radar reflectivity factor. The water-droplets and ice-particles is included. radar equation for a cloud sub-layer with a fi- Also, we assume that ice-particles are of hexag- nite thickness can be expressed as follows, 1008 Journal of the Meteorological Society of Japan Vol. 84, No. 6 ð Rt; i Cl where t is the optical thickness from the sur- PlðRiÞ¼ 2 Ze; lðRÞ face to the altitude R, and can be defined as, Rb; i R ð ð R R 0 0 0 0 exp 2 slðR Þ dR dR; ð2Þ tlðRÞ¼ slðR Þ dR : ð8Þ 0 0 To simplify Eq. (7), we expand the second expo- where P is the received radar power, C is the nential term into a polynomial series of s, and calibration constant, R is the range, and R de- i neglect terms of the order of s2 and higher. notes the altitude of the center of the i-th sub- This approximation may be reasonable for layer. The subscript l indicates wavelength de- clouds measured at the considered radar wave- pendence. Further, R and R are the top and t; i b; i lengths, for which the value of s is relatively bottom boundaries of the i-th sub-layer, respec- small. Then, Eq. (7) becomes, tively, and they can be written as, ClDR Rt; i ¼ Ri þ DR/2 P ðR Þ¼ Z ðR Þ exp½2t ðR Þ 3 l i 2 e; l i l b; i ð Þ Ri Rb; i ¼ Ri DR/2; 2 Ri where DR is the sub-layer thickness which is þ 2slðRiÞ Rt; iRb; i assumed to be 100 m in this study. The equiva- 2 2 lent radar reflectivity factor Ze, in unit of Ri Rb; i Ri 6 3 ln þ : ð9Þ mm m , and the extinction coefficient s,in DR Rt; i Rt; i unit of m1, are defined as follows, ð In this paper, we use the attenuated radar re- 4 l flectivity factor Zobs, defined as Eq. (10), instead Ze; lðRÞ¼ NðR; rÞCbk; lðR; rÞ dr; 5 2 p jKref ; lj of the received radar power P, as observational ð4Þ data by the radar. ð s R N R; r C R; r dr b R ; Zobs; lðRiÞ lð Þ¼ ð Þ ext; lð Þ þ gas; lð Þ 2 Ri ð5Þ ¼ Ze; lðRiÞ þ 2slðRiÞ Rt; iRb; i where Cbk and Cext are the back-scattering and R2 R R2 the extinction cross section as a function of the i ln b; i þ i cloud particle radius r, respectively. In the DR Rt; i Rt; i equations, bgas denotes the gaseous absorption exp½2tlðR Þ: ð10Þ coefficient and NðrÞ denotes the size distribu- b; i tion of cloud particles. The parameter Kref is expressed in terms of the complex refractive 2.2 Scattering properties of cloud particles index m of water at 0C as a reference medium, The single scattering properties, such as extinction cross section and back-scattering cross m2 1 ref section, of water-droplets and ice-particles are Kref ¼ 2 ; ð6Þ mref þ 2 calculated by Mie theory and the discrete dipole approximation (DDA; Draine and Flatau 2 and jKref j ¼ 0:93; 0:88, and 0.68 for X-band, 2003), respectively. Validity of using the DDA Ka-band, and W-band radar wavelength, re- for scattering calculations at the radar wave- spectively. lengths has been studied by several authors, Here, we assume that the cloud micro- and it is concluded that DDA has sufficient physical properties are uniform in each sub- accuracy on back-scattering calculations (e.g., layer, then Eq. (2) becomes, Liu and Illingworth 1997; Lemke et al. 1998; ð R Okamoto 2002). Based on in-situ observations, t; i 1 P ðR Þ¼C Z ðR Þ exp½2t ðR Þ the width D of an ice-particle may be related to l i l e; l i l b; i R2 Rb; i the length L, and several dimensional relation- exp½2ðR Rb; iÞslðRiÞ dR; ð7Þ ships have been proposed in previous studies December 2006 Y. YOSHIDA et al. 1009

(e.g., Auer and Veal 1970; Davis 1974). Al- 2.3 Sensitivity of cloud microphysical though there exist some differences between parameters to radar reﬂectivity factors these dimensional relationships, all of these re- Before the construction of the algorithm, we lationships show that the aspect ratio of ice- examine how the triple-band radar signals particle, D/L tends to deviate from unity as the change with cloud microphysical parameters maximum dimension of the ice-particle in- (i.e., LWC, reff ; wat, IWC, reff ; ice, and D/L). creases. Since the size sensitivity of triple- Figure 1 shows the dependence of Ze and s band radars decreases with the size, especially on reff ; wat for pure-water clouds with LWC ¼ 3 for the particles with maximum dimensions 1:0g m and mwat ¼ 2. Because we neglect less than about 200 mm (e.g., Hogan et al. precipitation such as rain and drizzle, cloud 2000), an ice-particle is treated as being a droplets are small enough to be assumed as hexagon with the aspect ratio of D/L ¼ Rayleigh-scatterer at the radar wavelengths. 1/3; 1/4; 1/5; 3/1; 4/1, or 5/1. These ratios cor- As a result, Ze depends on reff ; wat and LWC, but respond to those of ice-particles with maximum not on the radar wavelengths. On the other dimensions larger than 200 mm. We calculate hand, s is independent of reff ; wat, and it strongly the single scattering properties of ice-particles depends on the radar wavelengths due to under the assumption of 3D-random orienta- tion. We also assume the density of ice to be 0.92 g cm3. We use a radius of volume- equivalent sphere as a characteristic particle size of an ice-particle. We assume that the particle size distributions of mixed-phase clouds can be expressed by the following gamma distribution functions as,

NmixðrÞ¼NwatðrÞþNiceðrÞ m mwat þ 3 ¼ N0; watr wat exp r reff ; wat m mice þ 3 þ N0; icer ice exp r ; ð11Þ reff ; ice where Nwat, Nice, and Nmix denotes the size distribution functions for water-droplets, ice- particles, and mixed-phase clouds, respectively; m is the dispersion parameter of the size distribution; r is the cloud particle radius; and reff is the effective radius. According to the in-situ measurements of cloud microphysical properties, the values of m are reported to be approxi- mately 2 for water clouds (Pruppacher and Klett 1997), and between 0 to 2 for ice clouds (Kosarev and Mazin 1991). This study assumes a ﬁxed value of mwat ¼ 2 for water clouds, and mice ¼ 1 for ice clouds. As a result, the attenuated radar reﬂectivity factor, Zobs, is a function of LWC and reff ; wat for pure-water clouds, and of IWC, reff ; ice, and D/L for pure-ice clouds. For mixed-phase clouds, the unknown parameters controlling Zobs are LWC, reff ; wat, IWC, reff ; ice, Fig. 1. (a) Ze and (b) s of pure-water and D/L. clouds as functions of reff ; wat. 1010 Journal of the Meteorological Society of Japan Vol. 84, No. 6

the difference of water absorptivity at the dif- DWRwat; l1 /l2 ferent wavelengths. Figure 2 shows the dual- 0 1 R2 R2 R R2 BZ i þ 2s ðR Þ i ln b; i þ i C wavelength ratio ðDWRÞ as a function of LWC B e; wat; l1 R R wat; l1 i DR R R C 10 logB t; i b; i t; i t; i C ¼ @ 2 2 2 A and reff ; wat. The ratio DWRl1/l2 is deﬁned as fol- Ri Ri Rb; i Ri Ze; wat; l2 þ 2swat; l2 ðRiÞ ln þ lows, Rt; iRb; i DR Rt; i Rt; i 0 1 R2 R2 R R2 Z i i b; i i obs; l1 B þ 2swat; l1 ðRiÞ ln þ C DWR / ¼ 10 log ; ð12Þ B Rt; iRb; i DR Rt; i Rt; i C l1 l2 ¼ 10 logB C: (13) Zobs; l2 @ 2 2 2 A Ri Ri Rb; i Ri þ 2swat; l2 ðRiÞ ln þ Rt; iRb; i DR Rt; i Rt; i where the sufﬁx l1/l2 represents a pair of the dual-wavelengths l1 and l2, for which l1 > l2. Since the attenuation of radar wave by water

Because water-droplets can be treated as clouds is proportional to LWC, DWRwat; l1/l2 is

Rayleigh-scatterer, DWRwat; l1/l2 are related to also proportional to LWC. the different degree of attenuation between the Figure 3 shows the dependence of Ze and s on 3 two wavelengths and can be expressed as fol- reff ; ice for pure-ice clouds with IWC ¼ 1:0gm , lows, mice ¼ 1, and D/L ¼ 1/3. Unlike water-droplets,

Fig. 2. The relationships of DWR for different radar-band pairs with (a) LWC Fig. 3. (a) Ze and (b) s of pure-ice clouds and (b) reff ; wat for pure-water clouds. as functions of reff ; ice. December 2006 Y. YOSHIDA et al. 1011 for large values of reff ; ice, Ze differ depending on line) and those for spherical particles (thin the radar wavelength; s also shows the size de- black line) are also shown in Fig. 4(b). The at- pendency caused by ice-particles scattering ef- tenuation effect becomes large as reff ; ice in- fects. Small difference in Ze at reff ; ice < 150 mm creases, while, the non-spherical effect is ap- 2 is caused from the difference of jKj values of parent independent of reff ; ice and larger than ice and water. These characteristic features the attenuation effect. Unlike the water cloud are the same for ice-particles with other cases shown in Fig. 2, Figs. 4(a) and (b) imply

D/L (ﬁgures not shown). Figure 4 shows that DWRice; l1/l2 of ice-particles depends on the the corresponding DWRice; l1/l2 . The results different magnitudes of scattering rather than without having the radar wave attenuation absorption at l1 and l2, because ice-particles A ðDWRice; l1/l2 10 logðZe; ice; l1 /Ze; ice; l2 ÞÞ (gray hardly absorb the radar waves. The magni-

tude of DWRice; l1/l2 depends on reff ; ice and D/L through the scattering properties. Similar relationship between DWR and rice is often used for the estimation of ice cloud characteristic particle size from dual-band radar observations (Ho- gan et al. 2000). Figure 4(b) suggests that estimated microphysical properties from some retrieval procedure, which uses the dual-band radar under the assumptions of spherical ice- particle and/or negligible radar-wave attenuation by ice-particles, tend to have large errors. Figure 5 shows the correlations between DWRice; X/Ka and DWRice; X/W for different aspect ratios. Concerning the relationship, these for hexagonal ice-particles with several aspect ra-

Fig. 4. The relationships of DWR for different radar-band pairs with (a) IWC and (b) reff ; ice for pure-ice clouds with D/L ¼ 1/3. In Fig. 4(b), the results without radar wave attenuation are shown Fig. 5. The relationships between as gray lines and those for spherical DWRX/Ka and DWRX/W for various D/L ice-particles are shown as thin black of ice-particles with IWC ¼ 1g m3 line. and reff ; ice between 10 mm to 500 mm. 1012 Journal of the Meteorological Society of Japan Vol. 84, No. 6

Fig. 6. Radar reflectivity factors ðZeÞ and extinction coefficients ðsÞ for mixed-phase clouds. (a) Ze and (b) s as functions of LWC; and (c) Ze and (d) s as functions of reff ; wat. Microphysical parameters 3 for ice-particles are fixed to reff ; ice ¼ 300 mm, IWC ¼ 0:1gm , and D/L ¼ 1/3. tios and it for spherical ice-particles calculated in the mixed-phase clouds, and this makes rela- by Mie theory can be distinguished. The figure tively large ice-particles compared with water- suggests that the aspect ratio D/L of ice- droplets. These characteristics further result in particles can be identified from the correlations relatively large IWC values. In this case, the between DWRice; X/Ka and DWRice; X/W . This is effects of the attenuation by scattering of ice- possible only by using radars of more than particles need to be considered explicitly. Fig- three wavelengths. But, D/L cannot be distin- ure 6 shows examples of Ze and s of mixed- guished when DWRice; X/Ka and DWRice; X/W are phase clouds (black line) and these of pure-ice very small: reff ; ice is smaller than 200 mm. clouds (gray line) as a function of LWC (Figs. If we consider a mixed-phase condition, Ze 6(a) and (b)) and reff ; wat (Figs. 6(c) and (d)). and s can be expressed, respectively, as the Also, Figure 7 shows another examples of Ze sums of the corresponding Ze and s of water- and s of mixed-phase clouds (black line) and droplets and ice-particles. Below the freezing these of pure-water clouds (gray line) as a func- point, the conversion from water-droplets to tion of IWC (Figs. 7(a) and (b)) and reff ; ice (Figs. ice-particles, due to the difference of saturation 7(c) and (d)). If reff ; ice > reff ; wat, Ze of mixed- vapor pressures with respect to water and ice phase clouds is mainly controlled by that of (Bergeron-Findeisen mechanism), is dominant ice-particles, because Ze is largely dependent December 2006 Y. YOSHIDA et al. 1013

Fig. 7. Radar reflectivity factors ðZeÞ and extinction coefficients ðsÞ for mixed-phase clouds. (a) Ze and (b) s as functions of IWC; and (c) Ze and (d) s as functions of reff ; ice. Microphysical parameters 3 are fixed to reff ; wat ¼ 10 mm and LWC ¼ 0:1g m for water-droplets, and D/L ¼ 1/3 for ice- particles.

on scattering particle size (Figs. 6(a) and (c), up-tables (LUTs) of Ze and s for different and Figs. 7(a) and (c)). On the other hand, both values of particle radii are prepared for both s of water-droplets and ice-particles contribute water-droplets and ice-particles, by assuming significantly to s of mixed-phase clouds (Figs. LWC ¼ IWC ¼ 1:0g m3. Several LUTs are 6(b) and (d), and Figs. 7(b) and (d)). Thus, prepared for ice-particles to account for differ- the attenuated radar reflectivity factor Zobs of ent values of D/L. By using these LUTs, for mixed-phase clouds has no sensitivity to reff ; wat, example, Ze of pure-ice clouds can be expressed which affects Ze; wat but not swat. Also, DWRs for as Zeðreff ; ice; D/L; IWCÞ¼Zeðreff ; ice; D/L; IWC ¼ mixed-phase clouds depend on both the attenu- 1:0gm3ÞIWC. The LUTs are used in the fol- ation by water-droplets and the scattering by lowing retrieval procedure. ice-particles, i.e., on LWC, reff ; ice and D/L. It is clear from Eqs. (4), (5), and (11), that Ze 2.4 Sensitivity of cloud microphysical and s of water-droplets and ice-particles are parameters to microwave-radiometer proportional to LWC and IWC, respectively, signals when other microphysical parameters are fixed We also examined the sensitivity of cloud mi- (i.e. reff ; wat and mwat for water-droplets and crophysical properties on brightness tempera- reff ; ice, mice, and D/L for ice-particles). The look- tures at 23.8 GHz ðTb23Þ and 31.4 GHz ðTb31Þ 1014 Journal of the Meteorological Society of Japan Vol. 84, No. 6

cloud-base sub-layer to the cloud-top sub-layer: corrections for the attenuation by gaseous absorption and extinction by cloud droplets are made for each sub-layer. For the mixed-phase condition, the number of unknown parameters (LWC, reff ; wat, IWC, reff ; ice, and D/L for each cloud sub-layer) exceeds that of observational data (triple-band radar data for each cloud sub-layer and brightness temperatures at 23.8 GHz and 31.4 GHz), and we have to make some assumptions to estimate these cloud microphysical parameters. On the other hand, the number of unknown parameters for pure- water or pure-ice condition is less than that of observational data, and no assumption for retrieval needs to be made. In the retrieval procedure, the mixing condition of cloud particles in Fig. 8. The relationships between the mi- the cloud sub-layer is determined first. Then, the unknown microphysical parameters are es- crowave brightness temperatures (Tb23 and Tb31) calculated for various LWP timated for each mixing condition by referring and PW. The units of LWP and PW are to LUTs of Ze and s. The schematic of the re- in g m2 and mm, respectively. trieval algorithm is shown in Fig. 9. The microwave-radiometer can detect the column-integrated LWC or LWP only when the measured by the microwave-radiometer. Figure cloud contains water-droplets. In this algo- 8 shows the dependencies of liquid-water-path rithm, observed values of Tb23 and Tb31 are ðLWPÞ, precipitable water ðPWÞ, and ice-water- compared with the corresponding calculated path ðIWPÞ on Tb23 and Tb31. The brightness values, and their differences are used to deter- temperatures are calculated by the microwave mine whether the target cloud layer contains radiative transfer scheme under the mid- liquid water or not. In this radiative transfer latitude summer model atmosphere. In the calculation, the atmospehric profiles, such as calculations, water vapor concentrations are temperature, pressure, and water vapor pro- adjusted, while keeping the shape of vertical files, are set to these of radiosonde data, or re- profiles of water vapor concentration, to give analysis data, and assumed to be cloudless, be- prescribed PW values. Also, a uniform cloud cause Tb23 and Tb31 depend not only on LWP layer at 4 to 5 km with reff ; wat ¼ 10 mm and but also on temperature and water vapor pro- reff ; ice ¼ 300 mm is considered. It is shown that files. Also these atmospheric profiles are used Tb23 and Tb31 depend on LWP and PW, but for the correction of the radar signals due to at- they are very rarely affected by IWP. This sug- tenuation by gaseous absorption. gests that we can confirm the estimated LWP It is clear that when no LWP is detected in by retrieval algorithm described below with a target cloud layer, all of its cloud sub-layers high accuracy, even when clouds exist in are in pure-ice condition (Case 1 in Fig. 9). In mixed-phase condition. this case, reff ; ice and D/L are determined from the correlations between DWR and 3. Retrieval algorithm X/Ka DWRX/W (see Fig. 5). Thus, we call the esti- This section describes our method for retriev- mated D/L as an equivalent aspect ratio. The ing the cloud microphysical parameters from equivalent aspect ratio does not directly corre- observational data obtained by the triple-band spond to the real aspect ratio of ice-particles radar system and the microwave-radiometer in natural clouds. Rather, it reflects non- at 23.8 GHz and 31.4 GHz. Since we deal with sphericity of ice-particles in the cloud sub- the ground-based observation, the retrieval layers. As shown in Fig. 5, several combina- procedure proceeds sequentially from the tions of reff ; ice and D/L can satisfy the observed December 2006 Y. YOSHIDA et al. 1015

Fig. 9. Schematic of the algorithm for retrieval of cloud microphysical parameters. The shaded area indicates that at least one sub-layer contains water-droplets.

radar signals, when the DWRl1/l2 values are Next, we consider more complicated cases, small. In such situations, we select a combi- for which the microwave-radiometer detects nation of reff ; ice and D/L values closer to LWP, and water-droplets are contained in at spherical shape among the possible pairs least one cloud sub-layer (Case 2). In this case, from each columnar-shape (priority is a cloud sub-layer can be in any mixing condi- D/L ¼ 1/3 > 1/4 > 1/5) and planar-shape tions, except for the case of all cloud sub-layers ð3/1 > 4/1 > 5/1Þ categories, because several in the pure-ice condition. However, we cannot in-situ observations showed that smaller ice- know beforehand which cloud sub-layer con- particles tend to be more spherical (e.g., Ono tains water-droplets. The mixing condition of 1969; Auer and Veal 1970; Davis 1974). Fur- each cloud sub-layer is determined based on ther, when DWRX/W < 1, we set the value of the triple-band radar signals. D/L ¼ 1/3 for practical purposes. After reff ; ice The radar signals are sensitive to reff ; wat and D/L are determined, IWC can be estimated only when the target sub-layer consists of from Zobs by utilizing LUTs. water-droplets only. Therefore, to reduce the 1016 Journal of the Meteorological Society of Japan Vol. 84, No. 6

unknown parameters, whether the cloud sub- due to scattering by ice-particles inside the tar- layer is in pure-water condition needs to be get sub-layer. Specifically, the extinction coeffi- determined. As mentioned in section 2.3, cient of ice is first determined according to the

DWRwat; l1/l2 is proportional to LWC, and initial values of reff ; ice and IWC. Then reff ; ice the ratio of DWRwat; X/Ka :DWRwat; X/W : and LWC are calculated using the first line of DWRwat; Ka/W A1:4.5:3.5 can be used to detect Eq. (14), and IWC is estimated from Zobs; X . cloud sub-layers in pure-water condition (see This procedure is repeated until reff ; ice, LWC, Fig. 2(b)). Additionally, all the radar reflectiv- and IWC converge. ity factors need to be sufficiently small Then, we estimate the cloud microphysical (Zobss < 10 dBZ) in order for a sub-layer to be parameters of the next cloud sub-layer in the in a pure-water condition. Once the cloud sub- same manner, after making the correction for layer is determined to be in pure-water condi- attenuation of the radar signals in sub-layers tion (Case 2-1), LWC can be estimated from below the target sub-layer. Because the re- DWRX/Ka, and then reff ; wat can be estimated trieved reff ; ice, LWC, and IWC profiles are de- from Zobs and retrieved LWC value. pendent on the assumptions of D/L values of It is difficult to discriminate cloud sub-layers each layer, we check the validity of the re- in pure-ice condition from those in mixed-phase trieval result by comparing the microwave condition based on the triple-band radar sig- brightness temperature calculated from the nals (Case 2-2). In this case, we try to estimate retrieved microphysical parameters with the the vertical profiles of LWC, IWC, and reff ; ice, observed one after retrieving the cloud micro- which satisfy the observed radar reflectivity physical parameters for the entire cloud layer. factors and the microwave brightness tempera- The retrieving procedure is repeated by chang- tures, by iteratively changing a value of D/L ing the assumed value of D/L (in order of 1/4, 1/ in each sub-layer. For mixed-phase condition, 5, 3/1, 4/1, 5/1) until differences between reff ; wat is set to be 10 mm for practical purposes. calculated and measured brightness tempera- Without the radar wave attenuation due to tures are less than the observed error of the scattering by ice-particles, DWR for mixed- microwave-radiometer. phase clouds can be expressed as a sum of 4. Sensitivity of the algorithm to the DWRs of pure-water and ice-particles, as fol- microphysical profiles lows (see Section 2.3), As explained in section 3, the proper perfor- DWR ðLWC; r ; D/LÞ l1 /l2 eff ; ice mance of the present algorithm requires the 0 1 R2 R2 R R2 use of the triple-band radars with high- BZ ðR Þ i þ 2s ðR Þ i ln b; i þ i C B e; l1 i R R l1 i DR R R C ¼ 10 logB t; i b; i t; i t; i C sensitivity and high-accuracy. Each of the @ R2 R2 R R2 A Z ðR Þ i þ 2s ðR Þ i ln b; i þ i triple-band radars should have the minimum e; l2 i R R l2 i DR R R t; i b; i t; i t; i sensitivity of radar reflectivity factor of about 0 1 2 2 2 Ri Ri Rb; i Ri 40 dB to detect non-precipitating water BZ ðR Þ þ 2s ðR Þ ln þ C B e; ice; l1 i R R wat; l1 i DR R R C A 10 logB t; i b; i t; i t; i C clouds. Also, to classify a sub-layer consisting @ 2 2 2 A Ri Ri Rb; i Ri Ze; ice; l2 ðRiÞ þ 2swat; l2 ðRiÞ ln þ of pure-water droplets, DWRs should be mea- Rt; iRb; i DR Rt; i Rt; i sured as accurately as possible. The acceptable A DWR r ; D/L DWR LWC ice; l1 /l2 ð eff ; ice Þþ wat; l1 /l2 ð Þ inter-calibration error for the full use of the present algorithm is less than G0.1 dB. These A DWR ðr ; D/LÞþA LWC; (14) ice; l1 /l2 eff ; ice l1 /l2 requirements might be hardly attainable with

where Al1 /l2 indicates the proportional constant the present triple-band radar system. However,

of DWRwat; l1 /l2 to LWC (Fig. 2(a)). At first, if the our algorithm can be modified with some as- target cloud sub-layer is not in pure-water con- sumptions according to the performance of the dition, we fix a value of D/L (D/L ¼ 1/3 as an used triple-band radars as shown in section 5. initial value) for the sub-layer, and calculate Here, the performance of the newly- reff ; ice and LWC from DWRX/Ka and DWRX/W , developed algorithm is examined through then IWC from Zobs; X as initial values. Next, sensitivity simulations for assumed clouds, as- reff ; ice, LWC, and IWC are determined itera- suming that the radar satisfies the above re- tively by explicitly accounting for attenuation quirements. The assumed microphysical pro- December 2006 Y. YOSHIDA et al. 1017

ﬁles are vertically variable from a sub-layer to the next sub-layer, but homogeneous in each sub-layer. The expected radar reﬂectivity factors Zobs are calculated from numerical integra- tion of Eq. (7). Also, to simplify the problem, gaseous absorption is neglected in the sensitivity studies.

4.1 Error analysis for pure-ice cloud case Retrieval errors resulting from biases in the radar signals for pure-ice clouds are investigated. Here, the error in absolute calibration is treated separately from the error in inter- calibration. At ﬁrst, we assume that each of the triple-band radars is properly calibrated with respect to each other, and the absolute calibration error is supposed to be, at most, G1dB in radar signals. The same amount of error is assigned to each of the radar signals. This re-

sults in no error in DWRl1 /l2 . The retrieved microphysical parameters are plotted in Fig. 10. And then, we assume that the X-band radar is properly calibrated, but the Ka-band and W- band radars have some biases which are less than G0.1 dB. The retrieved microphysical parameters of this case are shown in Fig. 11. Here we set mice ¼ 1 and D/L ¼ 1/3 for the assumed (true) clouds. In the retrieval procedure, the biases are added, as well as no biases (mentioned as þ0 dB in Fig. 10), to the radar signals calculated from the assumed profiles. In Fig. 10, the retrieved profiles of IWC, reff ; ice, and D/L for the no biased radar signals show good agreement with the true profiles. For the cases of G1 dB biases in radar signals, the retrieved profiles of reff ; ice and D/L are almost the same as these for the no-bias case, because reff ; ice and D/L are estimated from DWRs with no error. On the other hand, the retrieved profiles of IWC, which are estimated from Zobs, are shifted due to the biases. The effect of this error in IWC on the retrieval of the next sub- layer, through the attenuation correction of ra- Fig. 10. Examples of the vertical profiles dar signals, is relatively small. The relative er- of retrieved microphysical parameters: (a) IWC,(b)r , and (c) D/L for the rors in the retrievals of IWC and reff ; ice,dueto eff ; ice the absolute calibration errors, are G24% and assumed pure-ice cloud models. The G0.2%, respectively. shaded bars indicate the true (assumed) profile, and the markers indicate the If there exists the inter-calibration error in profiles retrieved from the radar signals radar signals (Fig. 11), the retrieved profile of of Zobs with the indicated biases. reff ; ice is slightly shifted according to the DWR biases. These retrieval errors further affect the retrieval of IWC; the overestimation (underesti- 1018 Journal of the Meteorological Society of Japan Vol. 84, No. 6

Next, we investigate the effect of the assumed size distribution parameter mice; mice, represents the degree of dispersion of the size distribution functions, and is fixed to 1 in the retrieval procedure. In the sensitivity test of the m parameter to the retrieval, biases are im- G posed of 1onmice ¼ 1 for the assumed pure- ice cloud models. Figure 12 shows the retrieved microphysical profiles for assumed pure-ice cloud models. The retrieved profiles of reff ; ice with the assumption of mice ¼ 1 are shifted as it deviates from the true mice values. Because the small (large) mice value corresponds to wide (narrow) size distribution, contributions on Zobs and DWR of larger (smaller) particles to the radar signals become important for clouds with the fixed reff ; ice, IWC, and D/L. Figure 13 shows DWRX/W as a function of reff ; ice for several mice values. The value of DWRX/W for mice; true ¼ 0 and reff ; ice; true ¼ 250 mm (point A in Fig. 13) is regarded as that for mice; rtrv ¼ 1 and 0 reff ; ice; rtrv ¼ 288 mm (point A ) in the retrieval algorithm. The retrieval errors in IWC and reff ; ice, G due to the mice biases, are about 13% and G14%, respectively. As mentioned in section 3, when DWRs are small, a D/L value which is close to unity is selected, although it might not be a perfect estimation. In the sensitivity test of D/L value to the retrieval, two true pure-ice cloud models are assumed; one with D/L ¼ 1/5, another with D/L ¼ 5/1, and both having mice ¼ 1, and the retrieval errors due to mislabeled of D/L value are evaluated. Figure 14 shows the retrieved microphysical profiles for the assumed pure-ice cloud models. It is clear that there exist sys- tematical differences between the assumed and the retrieved profiles of IWC and reff ; ice, caused by the miss-estimation of D/L value. For example, in the sensitivity test for the assumed cloud model with D/L ¼ 1/5 (downward Fig. 11. Same as Fig. 10, except that the triangular marker), the correlation between markers indicate the profiles retrieved DWRX/Ka and DWRX/W , for sub-layers with from the radar signals containing the reff ; ice larger than 130 mm, can be clearly distin- inter-calibration errors. guished from those with D/L ¼ 1/3, but not from those of D/L ¼ 1/4 and 1/5 (see Fig. 5). This indicates both combinations of D/L ¼ 1/4 mation) of reff ; ice causes the underestimation and reff ; ice value, and of D/L ¼ 1/5 and another (overestimation) of IWC. The retrieval errors reff ; ice value, can satisfy the observed radar sig- in IWC and reff ; ice, due to the inter-calibration nals, and the combination with D/L ¼ 1/4 errors, are estimated to be G30% and G12%, re- should be selected. For sub-layers with reff ; ice spectively. smaller than 100 mm, DWRs are too small to December 2006 Y. YOSHIDA et al. 1019

Fig. 13. The relationships between DWRX/W and reff ; ice for several mice values. Dotted (broken) gray arrow illustrates the error in reff ; ice when assuming mice; rtrv ¼ 1, whereas the actual values of reff ; ice; true and mice; true are 250 mm and 0 (2), respectively.

Fig. 15 for reff ; ice overestimation). These tendencies of reff ; ice overestimation and IWC underestimation are the same as planar-particles except for the cases with DWRX/W < 1. If DWRX/W < 1, these error tendencies are re- versed: underestimation of reff ; ice and overestimation of IWC. These tendencies occur due to the different relationship between reff ; ice and DWRs (see Fig. 15). The retrieval errors in IWC and reff ; ice, due to the D/L failure, are G61% and G27%, respectively. When considering the possible combinations of the above mentioned errors, the total errors in the retrievals of IWC and reff ; ice for pure-ice clouds are estimated to be about G53% and G24%, respectively. These results are summar- ized in Table 1. Fig. 12. Same as Fig. 10, except that 4.2 Error analysis for pure-water cloud case the markers indicate the proﬁles based Figures 16 and 17 show the retrieved micro- on the cloud model with the indicated physical proﬁles for assumed pure-water cloud amount of biases in m . ice models with the absolute calibration errors and the inter-calibration errors in radar signals, respectively. Here, we set mwat ¼ 2 for the distinguish D/L value, and the value of assumed pure-water clouds. Also, the magni- D/L ¼ 1/3 is selected. The mislabeled D/L tudes of these biases are the same as the pure- values further affect the retrieval of reff ; ice (over- ice cloud case. estimation) and IWC (underestimation) (see Even when there are no biases in the radar 1020 Journal of the Meteorological Society of Japan Vol. 84, No. 6

Fig. 15. The relationships between DWRX/Ka and reff ; ice with several D/L values. Gray arrows show the estimated values of reff ; ice and D/L corresponding to the assumed values. (From left to right: D/Lrtrv ¼ 1/3 when reff ; ice; true ¼ 60 mm and D/Ltrue ¼ 1/5; D/Lrtrv ¼ 1/3 when reff ; ice; true ¼ 120 mm and D/Ltrue ¼ 5/1; and D/Lrtrv ¼ 1/4 when reff ; ice; true ¼ 120 mm and D/Ltrue ¼ 1/5.)

Table 1. Summary of the error analyses of the algorithm for pure-ice cloud case.

pure-ice cloud IWC reff ; ice IWP absolute calibration G24% G0.2% G24% inter-calibration G30% G12% G25% G G G assumption ðmiceÞ 13% 14% 12% D/L failure G61% G27% G37% TOTAL G53% G24% G35%

signals, there exist some differences between Fig. 14. Examples of the vertical profiles retrieved and assumed LWC profiles (Fig. 16). of retrieved microphysical parameters: This difference is about G7%, and caused by (a) IWC,(b)reff ; ice, and (c) D/L for the small signals of the triple-band radars for non- assumed pure-ice cloud model. The precipitating water clouds. However, there is shaded bars indicate the assumed pro- almost no difference between retrieved and as- file, and the markers indicate the re- sumed LWPs. The retrieved reff ; wat profile for trieved profiles of the assumed cloud no biased radar signals shows almost no differ- model. ence compared with the assumed one. The biases of G1 dB in radar signals do not disturb the retrieval of LWC, because LWC is estimated from DWRs with no error. On the other December 2006 Y. YOSHIDA et al. 1021

ing the upper layers as being in pure-water condition. The retrieval errors in LWC and reff ; wat, due to the inter-calibration error, are about G49% and G34%, respectively. However, the retrieved LWP error is about G20%. Our algorithm assumes the dispersion parameter mwat ¼ 2 of the gamma size distribution. To study effects of this assumption on the results of retrieval, we impose biases of G1on mwat for the assumed pure-water cloud models. Figure 18 shows the retrieved results of reff ; wat and LWC for pure-water cloud models with the different values of mwat. As in the pure-ice sub-layer case, the contribution of larger (smaller) particles on Zobs becomes important with smaller (larger) mwat value for clouds with equal reff ; wat and LWC. However, unlike ice particles, water-droplets are comparatively small and the effects of mwat on Zobs at different radar bands are almost the same. Therefore, DWRs, and thus the retrieved LWC profiles, are not significantly affected by mwat. On the other hand, there remains the effect of mwat change in Zobs. The retrieved profiles of reff ; wat with the assumption of mwat ¼ 2 are slightly shifted according to the true mwat values (see Fig. 19). The retrieval errors in LWC and reff ; wat, due to G mwat biases, are estimated to be 0.4% and G6%, respectively. From the above sensitivity studies, the over- Fig. 16. Examples of the vertical profiles all estimated errors in LWC, LWP, and reff ; wat of retrieved microphysical parameters: G G (a) LWC and (b) r for the assumed for pure-water sub-layers are 49%, 20%, eff ; wat G pure-water cloud models. The shaded and 34%, respectively (see Table 2). bars indicate the assumed profile, and the markers indicate the profiles re- 4.3 Error analysis for mixed-phase cloud case trieved from the radar signals of Zobs Figures 20 and 21 show the retrieved micro- with the indicated biases. physical profiles for assumed mixed-phase cloud models with the absolute calibration errors and the inter-calibration errors in radar hand, the retrieved profiles of reff ; wat are signals, respectively. Here, mwat ¼ 2, mice ¼ 1, shifted from the assumed profiles due to the and D/L ¼ 1/3 are set. Also, the magnitudes of biases. The retrieval errors in LWC and reff ; wat, these biases are the same as the pure-ice cloud due to the absolute calibration errors, are ap- case. proximately G0.4% and G8%, respectively. If there are no biases in the radar signals If there exists inter-calibration error in radar (the case of þ0 dB in Fig. 20), the retrieved pro- signals, pure-water sub-layers are sometimes files of LWC, IWC and reff ; ice show good agree- considered as mixed-phase sub-layers with lit- ment with the assumed ones. However, for the tle IWC, and it results in the large error in re- cases of G1 dB biases, the retrieved profile of trieved reff ; wat and LWC profiles (Fig. 17). How- LWC shows large fluctuations, whereas the ever, mislabeling of the mixing condition of one characteristic features of the retrieved profiles sub-layer tends to cancel the inter-calibration of IWC and reff ; ice are similar to those of pure- error of sub-layers above it, correctly identify- ice clouds. Since the back-scattering effect by 1022 Journal of the Meteorological Society of Japan Vol. 84, No. 6

Fig. 17. Examples of the vertical profiles of retrieved microphysical parameters: (a) LWC,(b)reff ; wat, (c) IWC, (d) reff ; ice, and (e) D/L for the assumed pure-water cloud model. The shaded bars indicate the assumed profile, and the markers indicate the profiles retrieved from the radar signals containing the inter-calibration errors. ice-particles on the radar signals is larger than effect. The retrieval errors for LWC, IWC, and the attenuation effect due to water-droplets, reff ; ice due to the absolute calibration error are small errors in IWC and reff ; ice can bring large estimated to be G109%, G33%, and G12%, re- errors in LWC. These LWC errors further affect spectively, but for LWP, the error is about the retrieval of upper sub-layers through the G18%. attenuation correction processes. In this case, If radar signals have inter-calibration errors, the upper four mixed-phase sub-layers are the retrieved microphysical profiles sometimes identified to be pure-ice sub-layers due to this show large differences compared with the as- December 2006 Y. YOSHIDA et al. 1023

Fig. 19. The relationships between Zobs; X and reff ; wat for several mwat values. Dot- ted (broken) gray arrow illustrates the error in reff ; wat when assuming mwat; rtrv ¼ 2, whereas the actual values of reff ; wat; true and mwat; true are 10 mm and 1 (3), respectively.

Table 2. Summary of the error analyses of the algorithm for pure-water cloud case.

pure-water cloud LWC reff ; wat LWP

Fig. 18. Same as Fig. 16, except that the absolute calibration G0.4% G8% G0.1% markers indicate the proﬁles based on inter-calibration G49% G34% G20% G G G the cloud model with the indicated assumption ðmwatÞ 0.4% 6% 0.1% amount of biases in mwat. TOTAL G49% G34% G20%

sumed one (e.g., upper triangle in Fig. 21). Al- clouds, and thus the fixed value of reff ; wat (i.e., though the retrieved LWC profiles have large 10 mm) does not affect the retrieval micro- errors, estimated errors in LWP are approxi- physical profiles. Also, the difference of mwat, mately the same as those of pure-water clouds which can be considered as the change in case. However, these LWC errors make the re- reff ; wat (see section 4.2), has no effects on the retrieval errors in IWC and reff ; ice large through trieval results. Figure 22 shows the assumed the attenuation correction process. The esti- and retrieved microphysical profiles with the G mated errors in LWC, LWP, IWC, and reff ; ice, biases of 1onmice of mixed-phase cloud due to the inter-calibration errors, are G203%, models. As well as the results of the absolute G24%, G53%, and G37%, respectively. calibration errors for mixed-phase sub-layers, Next, the effects of some assumed parame- characteristics of the retrieved profiles of IWC ters in the retrieval algorithm is investigated. and reff ; ice are almost the same as those for The assumed parameters are reff ; wat, mwat, and pure-ice sub-layers, and the retrieved LWC pro- mice in the retrieval procedure of the mixed- file shows large fluctuations. The retrieval er- phase sub-layer. It is clear from Fig. 6 and Fig. rors due to the assumptions in the retrieval al- 7thatreff ; wat hardly affects Zobs for mixed-phase gorithm on LWC, LWP, IWC, and reff ; ice are 1024 Journal of the Meteorological Society of Japan Vol. 84, No. 6

Fig. 20. Examples of the vertical profiles of retrieved microphysical parameters: (a) LWC,(b)IWC, (c) reff ; ice, and (d) D/L for the assumed mixed-phase cloud models. The shaded bars indicate the assumed profile, and the markers indicate the profiles retrieved from the radar signals of Zobs with the indicated biases.

G167%, G9%, G105%, and G36%, respectively. 5. An application to the observational Summing up all of the above-mentioned er- data rors, the retrieval errors of LWC, IWC, and reff ; ice are about G319%, G75%, and G35%, re- 5.1 Description of the observation spectively; while, the retrieval errors in LWP An intensive experiment, named Vertically and IWP are estimated to be about G19% and Pointing Measurements, Tsukuba, 2001 (abbre- G30%, respectively (see Table 3). viated as VPM_TKB01) was conducted by From the sensitivity studies mentioned utilizing the ground-based triple-band multi- above, a mislabeling of the mixing condition parameter radar system and a microwave- and/or D/L tends to make large retrieval errors radiometer at the National Research Institute in this retrieval algorithm. Additional informa- for Earth Science and Disaster Prevention tion, such as size and/or shape of cloud par- (NIED), located at 36.12N and 140.09Ein ticles, which can be estimated from Doppler Tsukuba, Japan, during June 12 to July 8, velocity or polarization observed by radar, is 2001. This was the ﬁrst experiment to use the helpful in identifying the mixing condition triple-band radar system in Japan. Table 4 and/or D/L, and minimizing the retrieval er- shows the main speciﬁcations of the NIED mul- rors. tiparameter radar system (refer to Iwanami December 2006 Y. YOSHIDA et al. 1025

Fig. 21. Same as Fig. 20, except that the markers indicate the profiles retrieved from the radar signals containing the inter-calibration errors. et al. (2001) for details). The objectives of the tegration is 256. In the algorithm, the vertical VPM_TKB01 are: (1) to understand the micro- resolutions of the Ka-band and W-band data physical structures of the cloud and precipita- (i.e., 50 m) are corrected to be 100 m before the tion system from observation at different radar- retrieval of cloud microphysical profiles. wavelengths; (2) to develop the method of esti- After the VPM_TKB01 experiment, that was mation for cloud and precipitation parameters, the first one done by NIED multiparameter such as LWC, IWC, size distribution, thermody- radar system, the range differences of the order namic phase of cloud particles, and rain rate; of several ten meters among the three radars, and (3) to understand the cloud formation and caused by insufficient range-zero tuning, are precipitation processes from their initial stage found from the observed data. They are cor- of water vapor convergence, through cloud for- rected by using the heights of reflectivity max- mation and precipitation, to dissipation. Three ima in clouds. The X-band radar could not al- radars continuously measured vertical profiles ways detect small particles, which are usually of clouds with the antennas vertically pointing found in the pure-water clouds, and/or near and horizontally scanning. The vertical resolu- the cloud-top of pure-ice clouds. The inter- tion is 100 m for X-band, and 50 m for Ka-band calibration is conducted with some difficulties and W-band radars, and the number of pulse in- as described in the next subsection. 1026 Journal of the Meteorological Society of Japan Vol. 84, No. 6

Fig. 22. Same as Fig. 20, except for the markers indicate the proﬁles based on the cloud model with the indicated amount of biases in mice.

5.2 Calibration of the radar signals gions, they are inter-calibrated by the above- The calibration constant (see Eq. (2)) of the mentioned ordinary method. Next, a pure-ice X-band radar is determined by the ZPHI cloud layer, which was detected by all of the method (Testud et al. 2000; Testud et al. 2001), radars, is used. Under the assumption that as well as by the self-consistency method (Vive- the ice cloud consists of ice-particles with kanandan et al. 2003; Park et al. 2005). The D/L ¼ 1/3, DWRKa/W can provide reff ; ice, and calibration constants estimated by the two Zobs; X can give IWC. This estimation procedure methods agree with each other. The Ka-band is the same as the one mentioned in section 3 and W-band radars are inter-calibrated pre- for pure-ice clouds, except that the fixed value cisely based on the X-band radar signals. Usu- of D/L ¼ 1/3 is used here. Then, we can esti- ally, the relative calibration of two different mate the more accurate calibration constants wavelength radars is conducted by using radar for the Ka-band and W-band radars, from the signals from Rayleigh-scatterers, which are radar reflectivity factor calculated based on the often seen in the upper part of cirrus clouds estimated reff ; ice and IWC. The pure-ice cloud (e.g., Wielicki et al. 1990; Francis et al. 1994). used in this calibration is relatively thin and But, unfortunately, the NIED X-band radar shows small DWRKa/W values, and thus the as- could not detect such regions of small signals. sumption of D/L value to some fixed value We try to calibrate the Ka-band and W-band makes no difference in the estimated calibra- radars by another method. First, since they tion constant. However, the relative error be- could detect the same Rayleigh-scattering re- tween the Ka-band and W-band radars is esti- December 2006 Y. YOSHIDA et al. 1027

Table 3. Summary of the error analyses of the algorithm for mixed-phase cloud case. mixed-phase cloud LWC IWC reff ; ice LWP IWP absolute calibration G109% G33% G12% G18% G29% inter-calibration G203% G53% G37% G24% G38% G G G G G assumption ðmwat; reff ; wat; miceÞ 167% 105% 36% 9% 35% TOTAL G319% G75% G35% G19% G30%

Table 4. Speciﬁcations of NIED multiparameter radar system. X-band Ka-band W-band Frequency 9.375 GHz 35.35 GHz 95.13 GHz Antenna Type Circular Parabola, 2.1 mf Cassegrain, 2.1 mf Scan Range (Scan Rate): AZ Full Circle (a 36 deg/s) Full Circle (a 24 deg/s) EL 2toþ92 deg (a 18 deg/s) 2toþ182 deg (a 12 deg/s) Antenna Gain 41.6 dB 54.0 dB 58.7 dB Beam Width 1.3 deg 0.3 deg 0.1 deg Transmitter Tube Magnetron Magnetron Klystron (EIA) Peak Power 50 kW 100 kW 1.75 kW Pulse Length 0.5 ms 0.5 ms 0.25 to 2.0 ms Pulse Repetition Frequency a1,800 Hz 400/4,000 Hz a20 kHz Polarization H and VHHor V Doppler Processing PPP, FFT PPP PPP, FFT Noise Figure 2.5 dB 3.5 dB 7.5 dB Observation Range 80 km 30 km 30 km Outputs Z, V, W, ZDR, rhv, FDP, KDP Z, V, WZ, V, W, ZDR, rhv, FDP, KDP

mated to be about G0.6 dB, and the calibration Figure 23 shows the vertical-time profiles of constant errors for the Ka-band and W-band ra- the radar reflectivity factors observed by the dars are estimated to be about G2dB. triple-band radar system for the time period from 20:30 to 22:30 JST on 21 June, 2001. As 5.3 Results of application mentioned above, the X-band radar could not Developed algorithm requires the use of detect optically thin regions. The regions, for triple-band radar with high sensitivity and ac- which the present algorithm is applicable, are curacy to show its full performance, especially restricted only to the limited parts shown in for mixed-phase cloud, as mentioned in section Fig. 24. The observed cloud layer was shown to 4. Nevertheless, errors arisen from insufficient be in pure-ice condition with no LWP by the range-zero tuning and difficulties in calibra- microwave-radiometer observation. Further, we tion are unfortunately found in the triple-band show the equivalent reflectivity factor Ze in Fig. radar dataset of VPM_TKB01 experiment. 24, instead of the observed reflectivity factor Therefore, in this study, we have applied the Zobs shown in Fig. 23. The differences between retrieval algorithm only to the observational Figs. 23 and 24 are mainly due to the large at- data for a pure-ice cloud layer by assuming a tenuation by gaseous absorption. In this case, fixed ice-particle shape of D/L ¼ 1/3. The radio- the attenuation effects by scattering of ice- sonde profile measured at the JMA Tateno particles are small, because the retrieved Aerological Observatory (36.05 N, 140.13 E) at values of IWC with large reff ; ice are very small, 21:00 JST on the same day is used for the cor- as shown in Fig. 25. Figure 25 shows the corre- rection of the attenuation by gaseous absorp- sponding profiles of the retrieved reff ; ice and tion. IWC by the present algorithm. The ranges of 1028 Journal of the Meteorological Society of Japan Vol. 84, No. 6

Fig. 23. Vertical-time proﬁles of the Fig. 24. Same as Fig. 23, except that it attenuated radar reﬂectivity factors ob- only shows the region where the pres- tained by the NIED multiparameter ent retrieval algorithm is applied. radar system at (a) X-band, (b) Ka- band, and (c) W-band on 21 June, 2001.

the retrieved reff ; ice and IWC are reasonable as radar signals with accurately tuned ranging at compared with other studies (e.g., Heymsfield all wavelengths. The triple-band multipara- et al. 1990; Matrosov et al. 1995). The retrieved meter radar system of NIED may have a capa- particle sizes reff ; ice became larger gradually bility to satisfy these requirements. Further ob- from the upper part to the lower part of the servations are scheduled for the near future. cloud layer, and this feature is consistent with 6. Summary the Doppler velocity profile observed by X-band radar (Fig. 26), as well as the ice cloud micro- We have developed the algorithm to retrieve physical structures known from previous in- microphysical profiles of pure-water, pure-ice, situ observations (e.g., Heymsfield et al. 1990). and mixed-phased non-precipitating clouds On the other hand, the IWC profile shows from the surface observation by utilizing the more complex features, possibly reflecting the triple-band radar system and the microwave- cloud formation and growing processes. With- radiometer. A set of X-band (9.4 GHz), Ka- out simultaneous in-situ observation, however, band (35 GHz), and W-band (95 GHz) radars is we cannot directly validate the estimated re- a suitable selection for observing cloud vertical sults. We have to examine further the perfor- structures. To precisely treat the scattering of mance of the algorithm by applying it to more radar waves, non-sphericity effect and radar suitable data sets, which are of high sensitivity wave attenuation by non-spherical ice-particles December 2006 Y. YOSHIDA et al. 1029

lated using DDA. The algorithm can detect any mixing conditions of water-droplets and ice- particles in the cloud layer by using radar signals and microwave brightness temperatures. For pure-water and pure-ice conditions, the retrieval procedure of microphysical parameters is similar to those of the previous dual- wavelength techniques, except that this algorithm can be further estimated for the equivalent aspect ratio of ice-particles. For mixed-phase condition, the algorithm can retrieve profiles of cloud microphysical parameters with the iteration procedures by changing the ice-particle shape parameter D/L in each sub-layer, until the retrieved profiles satisfy the observed radar signals and microwave brightness temperatures. From the sensitivity studies for the assumed cloud microphysical profiles, the uncertainty of this algorithm is estimated to be about G49% and G34% for the retrieval of LWC and reff ; wat of pure-water clouds, G53% and G24% for IWC and reff ; ice of pure-ice clouds, and G319%, G75%, and G35% for LWC, IWC, and reff ; ice of mixed-phase clouds, respec- Fig. 25. Vertical-time profile of (a) IWC tively. and (b) reff ; ice retrieved by this algo- The algorithm is also applied to the observa- rithm. tional data obtained by the triple-band multiparameter radar system in the VPM_TKB01 experiment, which was conducted at the NIED, located at 36.12N and 140.09E in Tsukuba, Japan, during June 12 to July 8, 2001. Due to the unsatisfactory observed radar data, we could apply the retrieval algorithm only to pure-ice cloud layer, with an additional assumption of the fixed D/L ¼ 1/3. The retrieved microphysical profiles show reasonable features, as compared with the observed features by the previous studies (Heymsfield et al. 1990; Matrosov et al. 1995). Further verification of the algorithm is needed, with more precise radar observations, together with in-situ observa- Fig. 26. Vertical-time profile of the Dop- tions of cloud microphysical parameters. A fur- pler velocity observed by the NIED X- ther improvement of the algorithm is needed to band multiparameter radar. detect more realistic cloud parameters such as ice-particle shapes and size distribution functions. To improve the identification of the mix- are taken into account, which are sometimes ing condition or D/L, which are main causes of neglected in the previous studies. In order to retrieval errors in this algorithm, additional account for non-sphericity, hexagonal shaped radar information such as Doppler velocity and ice-particles with several aspect ratios polarization may be helpful, because these pa- (D/L ¼ 1/3; 1/4; 1/5; 3/1; 4/1, and 5/1) are used, rameters are sensitive to sizes and/or shapes and the single scattering properties are calcu- of cloud particles. 1030 Journal of the Meteorological Society of Japan Vol. 84, No. 6

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