Refinement of global ice microphysics using spaceborne active sensors

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2011jd015885, 2011 Refinement of global ice microphysics using spaceborne active sensors Kaori Sato 1 and Hajime Okamoto 1 Received 28 February 2011; revised 26 July 2011; accepted 27 July 2011; published 20 October [1] This work improved on the lidar and radar retrieval algorithm developed by Okamoto et al. to extend the applicability of the microphysical retrieval scheme from the cloud region with lidar radar overlap to lidar or radar only cloud regions with an available radar lidar overlap area in the vertical profile by use of the Levenberg Marqardt method. The algorithm was formulated to efficiently reflect the information from the lidar radar overlap region to the microphysical retrieval at the radar or lidar only region to avoid the use of a prescribed parameterization among the observables and cloud microphysics. The algorithm incorporated particle type discrimination before the microphysical retrieval, consistent with the theoretical treatment of two dimensional (2 D) and three dimensional (3 D) ice particle mixtures in the radar and lidar forward models and the combined use of three observables (the radar reflectivity Z e, the lidar backscattering coefficient b, and the depolarization ratio d) for the lidar or radar only cloud regimes. A full one to one comparison of the retrieved microphysical properties with the results of the previous algorithm revealed that r eff could be retrieved consistently within about 10% uncertainty, on average. The ice water content (IWC) retrieval also performed well, except for extreme cases, and the uncertainties of IWC as well as r eff were within about 40% for the radar only region, despite the depth of the radar only cloud layers. When considering only the cloud region with lidar radar overlap, the zonal mean profiles of r eff may be slightly larger and IWC may be slightly smaller when considering attenuation caused by the lidar only region, which occasionally occurs above the region of lidar radar overlap. Citation: Sato, K., and H. Okamoto (2011), Refinement of global ice microphysics using spaceborne active sensors, J. Geophys. Res., 116,, doi: /2011jd Introduction [2] Lidar and cloud profiling radar with multiple parameters provide valuable information on the cloud phase [Yoshida et al., 2010], ice particle geometry [Okamoto et al., 2010], particle size, ice water content (IWC), and in cloud vertical motion [Sato et al., 2009]. These cloud microphysical properties and cloud dynamics affect the falling velocity of particle ensembles and cloud duration time, as well as the optical properties of clouds, which are still critical parameters in models, especially with bulk cloud microphysics [Matrosov and Heymsfield, 2000; Heymsfield, 2003; Noel and Chepfer, 2010; Sato et al., 2010; Satoh and Matsuda, 2009]. Comprehensive use of such information should significantly increase our understanding of the mechanisms underlying the vertical distribution of ice microphysics and its interaction with cloud dynamics, which is still insufficient for future climate sensitivity studies using global models 1 Research Institute for Applied Mechanics, Kyushu University, Kasuga, Japan. Copyright 2011 by the American Geophysical Union /11/2011JD [Tsushima et al., 2006]. Today, combined observations from lidar and cloud profiling radar from space (i.e., CloudSat/ CALIPSO) [Stephens et al., 2002; Winker et al., 2003] provide a wide coverage of the vertical distribution of ice cloud microphysical properties over the globe because of the difference in their sensitivities to cloud ice. However, the ratio of the region of cloud with radar lidar overlap to all of the clouds observed from space by CloudSat/CALIPSO is estimated to be about 70% at high altitudes, decreasing to 20% below 5 km [Okamoto et al., 2010]. Thus, to assess the global statistics of ice cloud microphysics, it is necessary to develop schemes that consider the lidar or radar only regions [Delanoë and Hogan, 2010; Deng et al., 2010]. Additionally, it is now common knowledge that the global statistics of ice cloud microphysics are occasionally affected by strong specular reflection of the returned lidar signal from horizontally oriented ice crystals, characterized by a low lidar depolarization ratio d. These cases have demonstrated that the retrieval of ice cloud microphysics becomes extremely difficult (i.e., no solution can be found or a large error is produced in the solution) without the appropriate theoretical treatment of lidar b and d in the retrieval algorithm for mixtures of ice crystals with their maximum 1of20

2 dimension oriented parallel to the normal incident wave in two dimensional (2 D) space and randomly oriented in three dimensional (3 D) space [Iwasaki and Okamoto, 2001; Okamoto et al., 2010]. Low d values are thought to occur preferentially at lower altitudes with temperatures in the range 20 C to 5 C [Okamoto et al., 2010; Noel and Chepfer, 2010], which corresponds to the area where a large fraction of 2 D ice particles exist. However, earlier studies also pointed out that low d also occurs at higher altitudes with colder temperatures [Sassen and Zhu, 2009]. These studies suggest that it is important that the retrieval algorithm discriminate particle types (shape, orientation, and phase) and account for 2 D and 3 D ice mixtures to interpret the observables properly and to estimate cloud microphysics and ice particle types reliably. Recently, an algorithm that can handle cloud particle phase and type (2 D and 3 D ice mixtures) and thus specular reflection was developed (referred to as the O10 algorithm, from the work of Okamoto et al. [2010]). Using it, global statistics for the distribution of ice particle size (r eff ), ice water content (IWC), and mixing ratio of 2 D and 3 D ice particles (X) have been reported. This paper extends that study in two new directions: (1) it extends the applicability of the O10 algorithm from the cloud region of lidar radar overlap to lidar or radar only cloud regions using the Levenberg Marquardt algorithm, which can account for different particle habits (2 D and 3 D ice); and (2) it updates the global distribution of ice microphysical properties. The new scheme discriminates particle type before microphysical retrieval and provides consistent treatment of a nonspherical particle model between lidar and radar forward models, in which the scattering properties are calculated using the modified Kirchhoff method [Iwasaki and Okamoto, 2001] and the discrete dipole approximation (DDA) [Draine, 1988; Okamoto, 2002; Sato and Okamoto, 2006], respectively. [3] This paper is organized as follows. Section 2 describes the retrieval algorithm; the components and forward models of the method are explained in section 2.2.1, and the basic concept, equations, and assumptions to extend the lidar radar part of the algorithm to the radar or lidar only part are provided in section Here, a large portion is devoted to the procedure in which we used the information of the behavior of the radar and lidar signals among consecutive vertical grids to fill in the lack of information of the observables when only one of the instruments could be used. Section 3 characterizes the algorithm by comparing the microphysical properties derived by the new scheme and the O10 algorithm for singlegranule data from the CloudSat/CALIPSO merged data set. Section 4 tests the method using 1 month data. Finally, the results are summarized in Section Analysis Method 2.1. Components of the Algorithm [4] The algorithm consists of three parts: the cloud detection, the cloud phase or cloud particle classification, and the microphysical retrieval schemes. This study refined only the microphysical retrieval, and the first two components are the same as in the O10 algorithm (i.e., the cloud mask and the cloud phase or particle type classification follow Okamoto et al. [2007, 2008], Hagihara et al. [2010], and Yoshida et al. [2010], respectively). The cloud mask scheme for CALIOP by Hagihara et al. [2010] is different from the CALIPSO standard cloud mask (vertical feature mask, VFM) and is carried out in two steps at the original resolutions of CALIPSO level 1B data (i.e., threshold test for the attenuated total backscattering coefficient at mm, followed by a spatial continuity test) to avoid the contamination of noise and dense aerosols in clouds in an original way. The cloud phase or particle type classification scheme combined d with the ratio of b for two vertically consecutive cloud grids as a proxy of attenuation, which uniquely provided a vertically resolved (i.e., 240 m resolution) cloud particle type, e.g., 3 D or2 D ice with weak attenuation and high or low d, supercooled water with low d but strong attenuation. [5] The CloudSat/CALIPSO merged data set for the ice cloud used here was created by projecting the cloud masked CALIPSO data onto the CloudSat grid with the same vertical and horizontal resolutions (i.e., 83 vertical bins with 240 m vertical resolution in a single vertical profile), and then the cloud phase classification scheme is applied. If the cloud fraction for CloudSat/CALIPSO in a grid box exceeds 50%, the pixel is identified as a cloud pixel for CloudSat/CALIPSO Refinements in the Microphysics Retrieval Scheme [6] The algorithm extends the O10 microphysics scheme in two new ways: (1) It increases the applicability of the lidarradar overlap cloud region to the lidar or radar only cloud regions and (2) it gives an optimal estimation of the microphysics and their retrieval uncertainties with the Levenberg Marquardt algorithm [Marquardt, 1963]. The main feature of the algorithm is that it deals with a mixture of 2 D and 3 D ice particles when retrieving the microphysical properties (e.g., r eff and IWC) from three observables (Z e,obs, b obs, and d obs ). The definition of r eff is defined as follows throughout this paper: r eff ¼ R req;max r eq;min req 3 R req;max r eq;min dnðr eqþ dr eq dr eq ; ð1þ req 2 dnðr eqþ dr eq dr eq where r eq is the mass equivalent radius to a sphere and modified gamma function with the value of 2 for the dispersion is assumed for the size distribution [dn(r eq )]/dr eq. [7] In the following discussion, we first describe the input observables and retrieval outputs and the forward models that relate them to each other (section 2.2.1). Then, we discuss improvements 1 and 2 in sections and 2.2.3, respectively Forward Models [8] The basic equations that relate the input observables (b obs and d obs at 532 nm for CALIPSO and Z e,obs for CloudSat) to the outputs (r eff and IWC) at each lidar radar grid are Z e;obs ¼ Z e;r ð1 X ÞþZ e;h X IWC exp ð 2 ra Þ " # exp 2IWC ra;r ð1 X Þþ ra;h X DR 1 ; ð2þ 2IWC ra;r ð1 X Þþ ra;h X DR obs ¼ ½ r ð1 X Þþ h X ŠIWC expð2 li Þ " # exp 2IWC li;r ð1 X Þþ li;h X DR 1 ; ð3þ 2IWC li;r ð1 X Þþ li;h X DR 2of20

3 obs ¼ cr;rð1 X Þþ cr;h X IWC: ð4þ co;r ð1 X Þþ co;h X Equations (2), (3), (4) correspond to equations (7), (9), (10), respectively, of Okamoto et al. [2010]. The definitions of the symbols and equations are summarized at the end of this paper, and it is not necessary to follow the detail of the equations for the discussion provided in the following sections. Briefly, the equations show that d obs is characterized by the mass ratio of IWC for 2 D ice and 3 D ice to the total IWC (X and 1 X, respectively), which is determined by the difference in the backscattering efficiency of 2 D (b h ) and 3 D (b r ) ice particles for the same mass and effective radius. In this paper, X is set to 1 (100% 2 D ice) or 0 (100% 3 D ice) when d obs approaches 0% or when d obs 40%, respectively. For Z e,obs and b obs (equations (1),(2)), the attenuation of Z e and b on a lidar radar grid (the first two terms on the right hand side), which is due to r eff, IWC, and X of the upper grids and the current grid (last two terms on the right hand side), and the correction term h for multiple scattering are taken into account. Note that in this paper, the nonattenuated value of Z e,obs and b obs are denoted as Z e,obs,un and b obs,un, respectively. [9] The algorithm provides look up tables (LUTs) for Z e, b, and extinction coefficients for lidar (s li ) and radar (s ra ) of the current grid as a function of r eff with IWC = 1 g m 3 for both 2 D and 3 D ice particle models to retrieve r eff and IWC from Z e,obs, b obs, and d obs. The particle models of 2 D and 3 D ice are almost the same as the ones used in the O10 algorithm (sphere as an analog to a 3 D ice category and a 2 D plate category), with a few improvements. These improvements use a mixture of 50% column and 50% bullet rosettes (the CB50% model, which means mixture of 50% 2 D column and 50% 3 D bullet rosettes) for the 3 D ice category, and h = 0.7, as suggested by Okamoto et al. [2010], to reduce uncertainty in the retrieved microphysics. Based on these 2 D and 3 D ice particle geometries, b for the 2 D ice particles is estimated using the modified Kirchhoff method [Iwasaki and Okamoto, 2001] and b for the 3 D ice particles is estimated from b = s/s, where s and S are the extinction at 532 nm, estimated from the geometrical cross section of the particles, and the lidar ratio (here S = 25 sr), respectively [Okamoto et al., 2010]. For Z e, both the 2 D and 3 D ice particle types are calculated using the DDA [Sato and Okamoto, 2006; Sato et al., 2009; Okamoto et al., 2010]. These calculations are performed for single particles with r eq ranging from 1 to around 3500 mm. Z e and b for the assembly of ice particles with a certain combination of r eff,iwc,andx are then estimated [Sato and Okamoto, 2006] (Figures 1a and 1b). 3of20 Figure 1. (a) b at 532 nm and (b) dbz e at 95 GHz as functions of r eff for IWC = 1 g m 3. The lines expressing log 10 b 532 / r 1 eff,dbz e / r 3 eff, and dbz e / r eff are also shown in red. (c) Schematic of the b obs,i+2,un estimate for IWC = 1gm 3. The b profile changes from b obs,i+1,un to b obs,i+2,un along the red solid line in reality, while the algorithm estimates b i+2,un change along the red dashed line, which ideally coincide with b obs,i+2,un recalculated for d = 1% holding r eff and IWC the same, i.e., b obs,i+2,un.

4 Refinement 1: Application to the Radar or Lidar Only Region [10] There is thought to be more confidence in the microphysical properties retrieved for the cloud region with radar lidar overlap versus those obtained for radar or lidar only regions because of the number of independent observables. Here, the O10 method is extended to the lidaror radar only cloud region by making the most of the lidarradar observables from the overlapping region to avoid using a prescribed parameterization that relates observables to the microphysics. [11] Before details of the procedure of the method are given, the basic concept and configuration are provided. The basic concept behind the microphysics derivation for the radar only (lidar only) region was as follows. For the lidar radar overlapped region, the dependence of the ratio of Z e,obs,un (dz e,obs,un )orb obs,un (db obs,un ) for two vertically consecutive grids on those of r eff (dr eff ) and IWC (diwc) can be inferred from the relation between dz e,obs,un and db obs,un of the two grids (see equations (A9) and (A10) in Appendix A). For the radar only (lidar only) region, b (Z e ) is estimated by projecting such a relation between dz e,obs,un and db obs,un of the previous two grids for dz e,obs,un (db obs,un ) between the grid of interest and the previous grid. Once we obtain the vertical profiles of all observables (Z e, b, d) by estimating them at grids where they are not observed, it is possible to estimate the vertical profile of the microphysics. [12] Since the relation between b and Z e depends on the microphysical properties, the method adopted here essentially could be considered equivalent to a way of extrapolating the microphysical properties to the radar (lidar ) only region by using the behavior of the microphysical properties of the previous two grids, and the measurement is extrapolated, constrained by physical conditions, in this paper to account for the variation in microphysical properties. [13] In the following discussion, the procedure to estimate b for the radar only region is provided, but the method can also be applied to the lidar only region. Here we consider three consecutive vertical grids, i, i + 1, and i + 2, looking downward from the top, characterized by (Z e,obs,i, b obs,i, d obs,i, r eff,i, IWC i,, X i ), (Z e,obs,i+1, b obs,i+1, d obs,i+1, r eff,i+1, IWC i+1, X i+1 ), and (Z e,obs,i+2, b obs,i+2, d obs,i+2, r eff,i+2, IWC i+2, X i+2 ), respectively. b obs,i+2 and d obs,i+2 are unknowns because of a lack of sensitivity of the lidar to detect cloud layer i + 2, and r eff, IWC, and X are the unknown variables to be retrieved. For simplicity, first we discuss the case for 100% 3 D ice (constant d obs > 0.4, X = 0); the application of the method to other values of d obs is discussed at the end of this section. [14] The procedure is organized in three steps: step 1, the use of the information content of Z e and b of the previous range gates to assess the range of b obs,i+2,un ; step 2, initial estimate of b obs,i+2,un ; step 3, introduction of sensitivity thresholds for CALIPSO to update nonphysical estimates of b obs,i+2,un. In step 1, it is assumed that the relation among Z e,obs,un and b obs,un lies in the same microphysical category for three consecutive grids, where we introduce the IWC dominant category and the r eff dominant category. The IWC (r eff ) dominant category is defined as the case in which the contribution from diwc (dr eff )todz e is larger than that from dr eff (diwc). This can be distinguished by investigating whether dz e,obs,un and db obs,un were positively related or negatively related to each other at the lidar radar overlapped region because of the opposite or same dependence of Z e and b on particle size or the IWC [Okamoto et al., 2007] as follows: [15] 1. IWC dominant category: obs;i;un > obs;iþ1;un and Z e;obs;i;un > Z e;obs;iþ1;un ; then IWC iþ1 < IWC i ; obs;i;un < obs;iþ1;un and Z e;obs;i;un < Z e;obs;iþ1;un then IWC iþ1 > IWC i : [16] 2. r eff dominant category: obs;i;un > obs;iþ1;un and Z e;obs;i;un < Z e;obs;iþ1;un then r eff;iþ1 > r eff;i ; obs;i;un < obs;iþ1;un and Z e;obs;i;un > Z e;obs;iþ1;un then r eff;iþ1 < r eff;i : These criteria arose from the information content consideration, which is especially effective in reducing the range of microphysics to be retrieved among all the possibilities when fewer observables could be obtained compared with the number of unknowns. [17] Instep2,b obs,i+2,un is derived as follows. As assumed in step 1, for the IWC dominant category, dz e,obs,un is positively related to db obs,un (i.e., obs;iþ2;un : Z e;obs;iþ2;un ¼ k obs;iþ1;un : Z e;obs;iþ1;un Þ obs;iþ1;un Z e;obs;iþ1;un obs;i;un Z e;obs;i;un and therefore obs;iþ2;un ¼ K obs;iþ1;un obs;iþ1;un = obs;i;un Z e;obs;i;un Z e;obs;iþ2;un =Z 2 e;obs;iþ1;un ; ð5þ where K is a variable relating dz e,obs,un and db obs,un of the former two grids (i, i + 1) and the latter two grids (i +1, i + 2). [18] Similarly, for the r eff dominant category, dz e,obs,un and db obs,un are negatively related, and therefore, obs;iþ2;un ¼ K obs;iþ1;un obs;iþ1;un = obs;i;un = Z e;obs;i;un Z e;obs;iþ2;un : ð6þ Z 2 e;obs;iþ1;un In the algorithm, as the simplest assumption, K is set to a vertically constant value of 1 to obtain the initial value for b obs,i+2,un (note that the value of K can be improved in step 3, and the effect of the assumption K = 1 on the initial estimate of the microphysical properties is further discussed in Appendix A). The b obs,i+2,un estimated by equations (5) and (6) assuming initially K = 1 is hereafter denoted as b i+2,un to distinguish it from b obs,i+2,un, which will be observed with more penetrating lidar. [19] Finally, in step 3, the evaluation of b i+2,un is performed. That is, the attenuated b i+2,un should be beyond the detection threshold of the cloud mask for CALIPSO [Hagihara et al., 2010], which is provided for each vertical profile. If the attenuated b i+2,un is larger than the cloud mask threshold, then the K value is corrected so that b i+2,un becomes the cloud mask threshold value. The estimated b UN is successively used to derive b UN of the next radar 4of20

5 Table 1. Summary of the Magnitude of the Uncertainties in Interpreting b and Z e Because of Measurement Bias Error, Those Associated With the Assumption in the Particle Model and Multiple Scattering Correction, and Those That Arise From the Uncertainties in the Estimated b (Z e ) in the Radar Only (Lidar Only) Region a Observable Measurement Bias Error (%) Particle Model Error (%) d obs d r 3 D Ice S Ratio Error in Multiple Scattering Correction (%) Error in b/z e Estimation for the Radar /Lidar Only Region (%) b Z e a The impact of each component is provided by the percentage of error relative to the magnitude of b and Z e ; d r is the the threshold value of d obs, which determines X 0. A dash indicates no contribution or low contribution. only grid to fill in the vertical profile of all observables (Z e, b, d). [20] Since b obs,i+2,un and d obs,i+2 are not observed, the algorithm uses b i+2,un and d i+2 with Z e,obs,i+2,un to reduce the range of probability of the microphysics (r eff,i+2 and IWC i+2 ) retrieval in the radar only region within the range of their uncertainties (see section 3 for further discussion). Here, d i+2 is set to the same value with grid i +1(d i+2 = d obs,i+1 ). [21] It is noted that the same treatment discussed above can be also made for 2 D and 3 D ice mixtures (i.e., d obs,i < 0.4 or d obs,i+1 < 0.4 or d obs,i+2 < 0.4). For a constant X, the dependence of b on r eff has the opposite tendency for 2 D and 3 D ice [e.g., Okamoto et al., 2010, Figure 3b]. In contrast, for a constant d, b for 3 D ice and 2 D and 3 D ice mixtures has a similar dependence on r eff (Figure 1a). In the algorithm, d i+2 is set to d obs,i+1 ; thus equations (5) and (6) can be directly used also for the 2 D and 3 D ice mixture cases, and the retrieval proceeds in the same way as for the 100% 3 D ice case. Figure 1c illustrates the situation in which r eff,i+1 =30mm, IWC i+1 =1gm 3, d obs,i+1 = 0.01 and r eff,i+2 = 100 mm, IWC i+2 =1gm 3, d obs,i+2 = 0.1 at grids i + 1 and i +2, respectively. In the algorithm, d i+2 = d obs,i+1 = Thus, for the 2 D and 3 D ice mixture cases, the estimated b i+2,un provides a good estimate of r eff,i+2 and IWC i+2 when b obs,i+2,un is equivalent to b calculated for r eff,i+2, IWC i+2, and d i+2 (hereafter b obs,i+2,un ) and not to b obs,i+2,un itself. [22] It is straightforward to obtain a formulation analogous to equations (5) and (6) for the lidar only cloud region, where Z e,i+2,un is estimated by transposing Z e,obs,i+2,un to the left hand side of equations (5) and (6) to rewrite them as a function of Z e,obs,i+2,un, and the cloud mask for CloudSat is used to improve the K value in step 3. Equations (5) and (6) also hold for situations in which the radar only region (layer i + 2) exists above the lidar radar overlap region (layers i, i + 1) Refinement 2: The Optimal Estimation Framework [23] The Levenberg Marquardt algorithm is used to estimate the optimal solution of r eff,i, IWC i (i =1,nth grid) for each vertical profile, which minimizes the cost function ¼ Xi¼1;n i¼1 X j¼3 j¼1 y i;j x 2 i;j ; s i;j where y, x, s, and j are the input observables, the forward model outputs, the total errors in y and x, and the number of observables at each cloud grid i, respectively. The uncertainties of the retrieved microphysical properties are estimated by considering possible error sources in the observables and forward models (Table 1). The s 2 i,j is obtained by multiplying y 2 i,j by the sum of the squares of the each error sources in Table 1. The uncertainty in d is incorporated through its effect on b. The value for the measurement bias errors was adopted from Okamoto et al. [2010]. The effect of these measurement bias errors to the retrieved microphysical properties is discussed for an ideal cloud case in Appendix B. Figure 2. Joint histograms of the percentage of change in (a) r eff and IWC and (b) dr eff and diwc, estimated from the microphysical properties obtained from the R/V Mirai cruise MR01K05 radar lidar data. The frequency of occurrence of the combination of (r eff,iwc),(dr eff,diwc)are indicated in colors. 5of20

6 Figure 3. The magnitudes of the uncertainties in (a) b obs,un, h (b obs,un b obs,un )/b obs,un i, and (b) Z e,obs,un, h (Z e,obs,un Z e,obs,un )/Z e,obs,un i, as functions of cloud layer depths, derived from the microphysical properties obtained from the R/V Mirai cruise MR01K05 radar lidar data Forward Model Error [24] The forward model errors in Z e and b in Table 1 were estimated using shipborne radar lidar data obtained for the R/V Mirai cruise MR01K05 and the ice microphysical properties derived from them [Sato et al., 2010], as follows. First, the running average of the microphysical properties derived for the radar or lidar region every minute with a vertical resolution of 82.5 m was used to convert the data to the horizontal and vertical resolutions of CloudSat, and a threshold of dbz e > 30 dbz was applied. Then, a histogram combining r eff and IWC was created. Considering the frequency of occurrence of the joint histogram of r eff and IWC, the mean uncertainties that were due to the particle model and multiple scattering correction were estimated. The particle model errors have three components: (1) the uncertainty of setting X = 0 for d obs > 0.4, (2) the uncertainty that is due to the use of the CB50% model to represent the 3 D ice particle type, and (3) the uncertainty that is due to assuming S = 25 sr. To assess issue (2), different types of 3 D ice particles, such as 3 D plates, were considered against the CB50% model (details of other geometries can be found in section of Okamoto et al. [2010]). To assess issues (1) and (3), the threshold value of d obs that determine X 0 and S were varied over the range d obs = and S = sr, respectively. For the uncertainty of forward modeling of b that is due to the multiple scattering correction, h was varied in the range , as in the work by Okamoto et al. [2010]). The effect of multiple scattering on Z e was not considered here because it is usually smaller than about 1 db for the ice phase when dbz e < 15 db [Matrosov and Battaglia, 2009] Z e,un and b UN [25] To estimate the uncertainties of Z e,un and b obs,un obtained from equations (5) and (6), the joint histograms of the percentage of change of r eff and IWC for three consecutive vertical grids, dr eff,i+1,i /r eff,i and diwc i+1,i /IWC and dr eff,i+2,i+1 /r eff,i+1 and diwc i+2,i+1 /IWC i+1 (Figures 2a and 2b) were created where dr eff,i+1,i = r eff,i+1 r eff,i and diwc i+1,i = IWC i+1 IWC i. Then, looking downward as if from a satellite, Z e,un (b UN ) at the third grid was estimated from Z e, obs and b obs of the first two grids, pretending that Z e,obs (b obs ) at the third grid was unknown. Finally, by using the frequency of occurrence of r eff, IWC, dr eff,i+1,i /r eff,i, diwc i+1, i/iwc i, and dr eff,i+2,i+1 /r eff,i+1 dr eff,i+1,i /r eff,i, diwc i+2,i+1 / IWC i+1 diwc i+1,i /IWC i, the uncertainty of Z e,un (b UN ) was calculated. Because the uncertainty of Z e,un (b UN ) may increase with increasing depth of the lidar only (radaronly) region, their dependence on the layer depth from the cloud base of the lidar radar region was also estimated (Figures 3a and 3b), i.e., if Z e,un (b UN ) of the fourth grid was estimated using the estimate for the third grid, then the uncertainty in Z e,un (b UN ) of the fourth grid may be larger than that of the third grid. However, the uncertainties were not so sensitive to the layer depths, where maximum penetration depths of about 5 km were considered, and did not exceed about 40% and 80% for Z e,un and b UN, respectively. [26] Because the algorithm searches for two microphysical properties from three observables, Z e,obs (or Z e,un ), b obs (or b UN ), and d obs (or d), the retrieval performed with the Levenberg Marquardt method is less sensitive to the initial values of r eff and IWC used to start the iteration. To reduce the time required for the algorithm to converge, here, the initial value of r eff,i was set to a value close to the positive root of the following polynomial: Z eðobsþ;i;un Derr Ze;i log 10 X 4 ðobsþ;i;un Derr ak ð Þ log k1 k¼1 10 r eff ;i ¼ 0; ð7þ i where a(k) are coefficients based on the LUTs (section 2.2.1) for Z e and b and depend on the size range and d. Derr bi and Derr Ze,i are ranged from 0 to s i,b(obs),i,un and s i,ze,obs,i,un, which are the total errors in b (obs),i,un and in Z e,(obs),i,un for grid i 6of20

7 a) b) c) Figure 4. Time height cross sections of (a) dbz e,m, (b) b m, and (c) d m for a cloud observed on 8 October 2006 (granule 23650) by CloudSat/CALIPSO in the latitude range 30 to 50. The boundary of the virtual lidar radar overlap region and the virtual radar only region is indicated by the pink line. 7of20

8 Figure 5. (a) Frequency distribution profiles of Z e for the virtual regions of lidar radar overlap and radar only for the one granule data and that for the real lidar radar overlap and radar only regions detected from the cloud mask scheme for 1 month data. (b) Frequency distribution profiles of Z e for the one granule data sorted by the cases d obs >5% and d obs < 5%. defined at the beginning of this section, respectively. The initial value of IWC i is defined as follows: IWC i ¼ Z e; ðobsþ;i;un =Z e r eff;i ; IWC ¼ 1gm 3 ; ð8þ where Z e is calculated for r eff,i derived from equation (7) at IWC = 1 g m Characterization of the Algorithm With Observation Data 3.1. Retrieval From Satellite Data: Comparison With the O10 Algorithm [27] Here, the algorithm and the inherent assumption were tested using the ice phase cloud data of the merged CloudSat/CALIPSO data set collected on 8 October The full height time cross section of the microphysics retrieved using the new scheme was compared against values obtained from the O10 algorithm to characterize the new scheme. The uncertainty of the retrieved microphysics obtained by the O10 algorithm with a nonspherical ice particle model relative to in situ measurements has low bias and standard deviation, i.e., about +3% ± 43% and 1% ± 14% for IWC and r eff, respectively [Heymsfield et al., 2008; Okamoto et al., 2010]. Therefore, evaluation of the method conducted in this section in comparison with the O10 results is considered to provide a reasonable estimate of the mean value and a slightly smaller standard deviation of the relative errors in IWC and r eff. The comparison is outlined in the following paragraphs. [28] First, the CloudSat/CALIPSO overlap cloud region was extracted from the data set. The O10 algorithm was applied to this extracted data to retrieve the reference r eff and IWC profiles (hereafter denoted by r eff,o10 and IWC O10 ). Next, for each vertical profile of the extracted data, b observed for the cloud layers corresponding to twothirds of the lowest cloud layers was artificially replaced with a deficit (i.e., two thirds of the cloud region for the lidar radar overlap was artificially changed into a virtual radar only cloud region). The algorithm developed was applied to this artificial data to compare the retrieved microphysics (hereafter denoted by r eff,s11 and IWC S11 ) with the reference case. Figure 4 shows examples of time height cross sections of the observables, which are part of the comparison. For this case, dbz e (Figure 4a) increases steadily from the cloud top to the cloud base, while d and b take a variety of values, especially near the cloud base (Figures 4b and 4c). These tendencies in d and b at the virtual radar only region (i.e., the region below the pink lines in Figure 4) cannot be fully inferred from the virtual lidar radar overlap region (i.e., the region above the pink lines in Figure 4). During this orbit, specular reflection of the returned lidar signal was often observed (i.e., indicated in part by the low d obs < 5% in Figure 5a), and the vertical depth of the virtual radar only region created in this way ranged up to 5 km (Table 2). This provided a clear difference in the frequency distribution profiles of Z e for the virtual region of lidar radar overlap and that for the virtual radar only region (Figure 5b). As a result, the frequency distribution profiles of Z e for the virtual region of lidar radar overlap and for the virtual radar only region data covered most of the Z e range observed in the real lidar radar overlap and radar only regions for the same month, which was simply obtained from applying the cloud mask scheme for CALIPSO and CloudSat to the 1 month data (Figure 5b). As seen in Figure 5b, CALIOP samples a wide range of cloud portions with various Z e values. Validation of the lidar radar method (from the work of Okamoto et al., 2003, hence the Table 2. Distribution of the Cloud Geometrical Thickness of the Virtual Radar Only Region Geometrical Thickness (km) Number of Vertical Profiles of20

9 Figure 6. Same as Figure 4 but for (a) attenuated b UN, and (c) attenuated b obs,un. O10 method) against in situ measurements showed that the lidar radar method would have the same level of accuracy at higher optical depths up to 50 and also for a variety of Z e values if the lidar could penetrate [Heymsfield et al., 2008]. This implies that validation of the developed algorithm against the O10 algorithm is essentially independent of the cloud portion investigated. In this sense, this test case is a good one to characterize the algorithm performance at the radar only cloud region, but simultaneously these sample data may be considered to be a rather difficult case for retrieving the right microphysical properties [Okamoto et al., 2010], since they are not able to speculate on the existence of 2 D ice in the virtual radar only region from the observables for the virtual regions of the lidar radar overlap (b obs, d obs, Z e,obs ) or radar only (Z e ) (Figure 4a). For example, an increase in the low d obs (<5%) fraction from the virtual regions of lidar radar overlap to the radar only region shown in Figure 5b cannot be directly inferred from d obs for the virtual lidar radar overlap region, and also it cannot be inferred from Z e for the virtual radar only region alone, since the range of Z e where the low d obs values (<5%) reside overlaps with that of d obs > 5%. [29] The performance of the algorithm for the radar only region is especially emphasized here and was investigated because the ice cloud fraction of the lidar only region is not very large compared with the ice cloud fraction of the radaronly region [Hagihara et al., 2010] Results [30] The b UN (Figure 6a) estimated to retrieve the microphysical properties for the virtual radar only region provides a good estimate of the microphysical properties when it equals b obs,un (Figure 6b). As explained earlier in section 2 (Figure 1c), b obs,un is obtained by converting b obs,un from the case with d obs to the case with the estimated d, keeping r eff and IWC the same with the reference values. Both b UN and b obs,un, shown in Figure 6, are converted to attenuated values because of the microphysical properties at all of the cloud layers above, similarly to b obs (Figure 4b). Note that the time height cross section of the attenuated b obs,un has fewer data points than that of the attenuated b UN near the cloud base. This is because the attenuated b obs,un is reestimated from r eff and IWC retrieved by the O10 algorithm for the estimated d, and there are 9of20

10 Figure 7. scheme. Same as Figure 4 but for r eff and IWC retrieved by (a, c) the O10 algorithm and (b, d) the new 10 of 20

11 Figure 8. Scatterplot of (a) r eff and (b) IWC between those obtained from the O10 algorithm and the new scheme. The 1:1 line is also shown. few portions where the algorithm cannot find a solution for the microphysical properties within the retrieval accuracy they require. Since the attenuated b UN (Figure 6a) does not necessarily have to be equivalent to b obs, it is larger than the observed b obs (Figure 4b) where d d obs < 0.05 (e.g., latitude around 40.5 ), while it is smaller than the observed b obs where d > d obs (e.g., latitude around 44 ). The attenuated b obs,un (Figure 6b) becomes larger (smaller) than b obs when the estimated d d obs (d > d obs ) (e.g., Figure 1c). Consequently, b UN has better agreement with b obs,un than with b obs, i.e., b UN overestimates the b obs,un within 40% when d obs > 15% and 100% when d obs < 15%. The less fine structure observed in the b UN profile compared with that of b obs,un is attributed to the less fine structure in the Z e profile compared with b obs. Figure 7 shows examples of timeheight cross sections of the retrieved physical parameters corresponding to the same scene as that of Figures 4 and 6. The values of r eff,s11 and IWC S11 (Figures 7b and 7d) show profiles similar to those of the reference ones (Figures 7a and 7c) at the virtual region of radar lidar overlap. The microphysical retrieval successfully extends the microphysical profile to the radar only region as the reference profile, though the vertical profile is slightly monotonous with a less fine structure compared with the reference one reflecting the vertical profile of b UN (Figures 7b and 7d). [31] Figures 8a and 8b show the one to one comparison of the microphysical properties retrieved by the developed method and those of the reference values for the virtual radar only region for the one granule data. The correlation coefficient between the retrieved and reference values of r eff and IWC were 0.81 and 0.6, respectively. The errors in r eff and IWC are smaller than the uncertainty in b UN probably because the error in b UN was divided into those of the two microphysical properties. The mean relative error for r eff h(r eff,s11 r eff,o10 )/r eff,o10 i, was smaller than about 10%, which is independent of d obs. In the case of IWC, the relative error is generally smaller than 20%, except for a few cases in which the estimated d was significantly larger than the value of d obs when d obs < 5%. These cases indicate that retrieval of IWC may become difficult when 2 D ice scenes are retrieved as 3 D ice scenes and the importance of the information on d obs for IWC retrieval when a large mass fraction of 2 D ice exists. In the real situation, it is thought that the uncertainty in the retrieved IWC will be reduced compared with the case considered here since the information on d obs where 2 D ice exists will be obtained more often because of specular reflection. The scatter around the truth is larger for the IWC case than that for r eff, reflecting that for b UN (figures not shown). The rather wide standard deviation for IWC is common for Z e only retrieval algorithms because of the insufficient number of observables relative to the number of parameters to be retrieved [Austin et al., 2009]. [32] In order to assess the applicability of the algorithm to the radar only cloud region, the mean error and standard deviation of the retrieved r eff and IWC were investigated as functions of dbz e.atdbz e < 17.5 db/dbz e > 17.5 db, the retrieved r eff tends to be underestimated/overestimated and the error increases gradually as dbz e increases (Figure 9a). The absolute value of the estimated retrieval error with the algorithm is also plotted in Figure 9a with the actual difference between the retrieved and reference profiles for the one granule data. The estimated retrieval error of r eff is comparable to the actual error when dbz e is small. It increases gradually with dbz e, but the change is insufficient, resulting in an underestimation of the actual error for dbz e > 12.5 db. The actual error of IWC is larger for smaller dbz e (Figure 9b). Compared with the actual error, the estimated error bar for IWC is rather independent of dbz e, and the algorithm tends to underestimate the average magnitude of the error of IWC when dbz e < 17.5 db. It is noted that the uncertainty of the O10 algorithm as a function of Z e, which was estimated based on previous papers using in situ data, is about 7.5% ± 50% for IWC and 2.5% ± 16% for r eff around dbz e = 25 db, which decrease with increasing Z e to about 2.5% ± 5% for IWC and 0.8% ± 1.6% for r eff around dbz e =15dB[Heymsfield et al., 2008; Okamoto et al., 2010]. The dependence of the retrieval uncertainty on the geometrical thickness of the cloud layers in the radar only region was also investigated. It was found that the retrieval errors of r eff and IWC do not show clear dependence on the distance from the lidar radar overlap 11 of 20

12 Figure 9. Mean errors h(r eff,s11 r eff,o10 )/r eff,o10 i, h(iwc S11 IWC O10 )/IWC O10 i and their standard deviations as a function of dbz e,obs. Extreme cases correspond to a few cases in which the estimated d was significantly larger than the value of d obs when d obs < 5%. The standard deviations of h(r eff,s11 r eff,o10 )/r eff,o10 i and h(iwc S11 IWC O10 )/IWC O10 i including and not including the few extreme cases are indicated by bold bars and not bold bars, respectively. The absolute value of the retrieval error estimated by the algorithm is also plotted. cloud region (i.e., the error does not accumulate with cloud depth), which is smaller than 10% for r eff and smaller than 50% for IWC for the majority (figure not shown). [33] Finally, the frequency distribution of r eff and IWC between the values retrieved by the developed algorithm for the virtual radar only region and those obtained with the O10 algorithm is compared in Figures 10a and 10b. The frequency distribution profile of the retrieved IWC is shifted slightly to smaller values compared with the reference, but, overall, the peaks and widths of the frequency distributions are similar and are in good agreement with each other for both r eff and IWC. [34] In conclusion, the retrieval algorithm can retrieve r eff stably also for cases when only Z e is available. Additionally, a good performance for IWC is expected in the Z e only region. Both r eff and IWC have less dependence on cloud depths, and the overall dependence of the microphysical retrieval on dbz e indicates that the retrieval of r eff and IWC for large dbz e, which often occurs in the radar only region, will be accomplished within an approximate 40% error. Point by point comparison of the retrieved and true microphysical properties may show some degree of scatter, but the retrieval is able to capture the features of the frequency distributions of r eff and IWC of the true profiles sufficiently well, and the retrieval results are sufficiently applicable for statistical use. Although it is considered that evaluation of the algorithm by O10 algorithm is not essentially affected by the cloud scene considered, direct evaluation of the algorithm at the real radar only region may still be important to further assess the ambiguity of the evaluation of the algorithm at the radar only cloud region and further improve the assumption made for the K value. 4. Refinements in the Global Ice Microphysical Properties [35] For 1 month data from the CloudSat/CALIPSO merged data set for October 2006, the microphysical properties obtained using the O10 algorithm for the cloud region with lidar radar overlap and those obtained by the new algorithm for the radar or lidar only regions are compared in Figures The zonal mean profiles of the microphysical properties are similar for the region of lidar radar overlap for both profiles, but the mean value of the IWC around 10 km is slightly smaller for the O10 case. This is thought to be due to the attenuation of the lidar signal in the lidar only region, which is located above the cloud region of lidar radar overlap and considered only in the new algorithm. Less attenuation correction leads to a smaller estimate of the nonattenuated b obs, which further results in the retrieval of larger r eff and smaller IWC (e.g., Figures 11a, 11b, 12a, 12b, 13a, and 13b). The IWC has a bimodal structure, with larger IWCs around 6 and 17 km, when only microphysical properties from the cloud region with lidarradar overlap are considered (Figures 11b and 12b). This is considered to be due to the events of deep convection [Okamoto et al., 2010]. However, this structure is masked when IWC and r eff are averaged for all regions (i.e., the lidar only, lidar radar, and radar only regions; Figure 12d). The contrast between the zonal mean profile of IWC for the all cloud regions case and the lidar radar cloud region is 12 of 20

13 that increased the applicability of the algorithm to the lidaror radar only cloud region with the Levenberg Marquardt algorithm when the radar lidar overlap area was available in a vertical profile. The algorithm features the same cloud particle type detection scheme and the same theoretical treatment of 2 D and 3 D ice particle mixtures for the radar and lidar forward models as in the O10 algorithm and uses the combination of Z e, b, and d for every regime (i.e., the lidar only, lidar radar, and radar only regimes). [37] 2. A unique way to deal with the microphysical property retrieval at the radar or lidar only cloud layers with an insufficient numbers of observables was developed, where the possible range of the percentage of change of r eff and IWC from one grid to the other was estimated within a certain range of accuracy from the differential of b (Z e ) among three consecutive vertical cloud grids in the radar or lidar only cloud region. The method can be applied to any case (i.e., cloud layers consisting of 2 D ice, 2 D and 3 D ice mixtures, or 3 D ice). [38] 3. The retrieved microphysical properties were characterized. This revealed that r eff has stable accuracy and the algorithm provides a good estimate of the frequency distribution of r eff. The IWC retrieval also performed well, though the error had a wider standard deviation compared a) Figure 10. The frequency distribution of (a) r eff and (b) IWC retrieved with the new scheme and the O10 algorithm for the virtual radar only region. b) due to the fraction of large IWC for the optically thick clouds of the radar only regions, which drags the mean value up, and the small IWC for the optically thin clouds of the lidar only regions located at high altitudes. The frequency distribution characterizes the peak r eff for the lidaronly, lidar radar, and radar only regions to be around 20 mm, 40 mm, and 60 mm, respectively (Figure 13a). The peak IWC for the lidar only, lidar radar, and radar only regions is shown to be around g m 3, g m 3, and between and g m 3, respectively (Figure 13b). 5. Summary [36] 1. Refinements of the microphysical retrieval scheme (the O10 algorithm) of Okamoto et al. [2010], which can handle the specular reflection of the lidar return, were made Figure 11. The zonal mean profiles for (a) r eff and (b) IWC obtained at the cloud region of the lidar radar overlap using the O10 algorithm from the 1 month merged CloudSat/ CALIPSO data set for October of 20

14 Figure 12. Zonal mean profiles for (a) r eff and (b) IWC obtained for the lidar radar overlap cloud region and (c) r eff and (d) IWC obtained for the lidar or radar cloud region using the new algorithm. The observation data used are the same as in Figure 11. with that for the case for r eff. The accuracy of r eff and IWC retrieval depended little on the cloud depth of the radar only region, and the retrieval was within about 40% uncertainty for the radar only region. [39] 4. The zonal mean profiles of r eff and IWC indicate that the microphysical properties that account only for the lidar radar overlap cloud regime may provide slightly larger/smaller r eff /IWC because of the attenuation in the lidar beam caused at the lidar only region, which was occasionally observed above the cloud region of lidar radar overlap. Because of the difference in the observed cloud system among the cloud scenarios, the bimodal structure of r eff and IWC observed for the cloud region of lidar radar overlap is masked when the microphysical properties from all cloud scenarios are considered in the mean profile. Appendix A: Implication of Equations (5) and (6) for the Estimation of Microphysical Properties [40] Based on the relation among Z e and b observed in cloud layers where lidar and radar overlap, the algorithm proposed a method to divide the differential of Z e,obs,un (b obs,un ) between consecutive cloud grids into the contribution from dr eff and diwc for the radar (lidar ) only cloud region. However, without a retrieval, it is usually not able to provide quantitative estimates of the magnitude of diwc and dr eff. By a simple approach, here we discuss how diwc and dr eff were expressed in term of the differentials of Z e and b between cloud grids for cases in which both Z e and b were observed and in which b was estimated through equations (5) or (6). Such a comparison of the expressions for diwc and dr eff provide better insight into the assumptions underlying the retrieved microphysical properties when equations (5) and (6) are used. [41] For simplicity, we first discuss the case for constant IWC = 1 g m 3.dBZ e can be expressed as a function of r eff as and therefore dbz e ¼ A 0 þ A 1 log 10 r eff Z e ¼ 10 ð0:1a0þ r 0:1A1 eff ¼ C 0 r C 1 eff ða1þ ða2þ where A 0, A 1, C 0 =10 (0.1A0), and C 1 = 0.1A 0 are constants for a certain size range. In the Rayleigh regime, A 1 30 and C 1 3, 14 of 20