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  • View in gallery

    (a) Overview of the C3VP operational coverage area and related datasets. Range rings are provided in 50-km increments for the dual-polarization, C-band radar at King City. The 331° azimuth is shown, pointing in the direction of the CARE site located approximately 33 km northwest of the radar location. The portion of the CloudSat orbit described within the text is shown as a heavy dashed line. The flight track of the NRC Convair-580 is indicated with annotated flight segments referencing profiles described within the text. (b) As in (a), but with coverage limited to a range of 100 km and including the horizontally polarized radar reflectivity obtained from the 0.8° tilt angle at 0600 UTC. (c) As in (b) but for the radar reflectivity at 0630 UTC. (d) As in (b), but for the radar reflectivity at 0700 UTC.

  • View in gallery

    Observations of (a) air temperature, (b) relative humidity with respect to water, and (c) relative humidity with respect to ice, obtained from the aircraft profiles described in the text and shown in Fig. 1.

  • View in gallery

    (a) Paired values of IWCs measured by the aircraft CVI and estimated from the relationship of Heymsfield et al. (2007), as described within the text. (b) Histogram of the ratio of the calculated and measured IWCs at 20% intervals. (c) Vertical variability of ratios of calculated and measured IWCs.

  • View in gallery

    (a) Vertical profiles of the slope parameter (λs) for the inverse exponential size distribution, obtained from reliable fits to aircraft observations. (b) As in (a), but for the distribution intercept (Nos). (c) Scatterplot of the exponential size distribution parameters Nos and λs. (d) IWCs for each aircraft profile as measured by the CVI.

  • View in gallery

    Crystal images obtained from aircraft probes to represent of habits at various altitudes. The bottom two panels are from the 2D-P system, which better depicts the structure of the largest aggregates that begin to overwhelm the 2D-C probes at lower altitudes. The altitude and temperature for each panel were estimated by matching the time stamp to aircraft flight data.

  • View in gallery

    Range–height diagrams of the (a) horizontally polarized radar reflectivity and (b) differential reflectivity obtained from the King City radar at 0624 UTC along the 331° azimuth and in the direction of the CARE site.

  • View in gallery

    CloudSat 94-GHz radar reflectivity depicting snowfall occurring across the C3VP domain around 0600 UTC 22 Jan 2007. Observations were obtained from the orbital segment in Fig. 1.

  • View in gallery

    Single-scattering parameters for aggregates with fractal dimension df = 2.05, parameter f = 0.5, and incident radiation at 95 GHz, based upon Ishimoto (2008), and best-fit, least squares relationships parameterized as a function of the particle dimension: (a) radar backscattering cross section, (b) scattering cross section, (c) extinction cross section, and (d) asymmetry parameter.

  • View in gallery

    Single-scattering parameters among the various shape assumptions, including Mie spheres at air temperatures representative of the aircraft profile and with densities following the mass–diameter relationship of Heymsfield et al. (2007), the stellar dendrites of Liu (2008a), and aggregates simulated by Ishimoto (2008): (a) radar backscattering cross section, (b) scattering cross section, (c) absorption cross section, and (d) asymmetry parameter.

  • View in gallery

    Mass–diameter relationships for the various ice crystal shape assumptions used in the simulation of CloudSat reflectivity and described within the text.

  • View in gallery

    Average PSDs and temperatures within three 1-km layers and modified PSDs for each crystal assumption, representing processes used to conserve the total ice water among CloudSat reflectivity simulations. Total IWCs for each population are based upon values expected by the Heymsfield et al. (2007) mass–diameter relationship. The vertical dashed line represents the minimum size threshold for including Ishimoto (2008) aggregates.

  • View in gallery

    (a) CFAD and mean profile of the 94-GHz CloudSat reflectivity acquired from the vertical profiles shown in Fig. 7, along with mean, minimum, and maximum values acquired from simulations of ice crystals as Mie spheres. (b) As in (a), but based upon the hybrid scattering assumption. (c) As in (a), but derived from simulations of dendrites. In each panel, the CFAD of the CloudSat observations is shaded at intervals of 1%, 2.5%, 5%, 10%, and 25% using histogram binning intervals of 2 dBZ and 500 m.

  • View in gallery

    Fraction of the total IWC obtained from particles less than a given size, based upon mean PSDs within 1-km altitude layers and the mass–diameter relationship of Heymsfield et al. (2007). The 0.9-mm threshold for Mie resonance at 94 GHz is indicated, based upon the results of Lhermitte (1990). Average temperatures (Tavg) are provided for each layer, along with the total IWC, and the number (N) of PSDs averaged within each height interval.

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Incorporating Ice Crystal Scattering Databases in the Simulation of Millimeter-Wavelength Radar Reflectivity

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  • 1 Earth Science Office, NASA Marshall Space Flight Center, Huntsville, Alabama
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Abstract

The Canadian CloudSat/Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) Validation Project (C3VP) was designed to acquire aircraft, surface, and satellite observations of particle size distributions during cold season precipitation events for the purposes of validating and improving upon satellite-based retrievals of precipitation and the representation of cloud and precipitation processes within numerical weather prediction schemes. During an intensive observation period on 22 January 2007, an instrumented aircraft measured ice crystal size distributions, ice and liquid water contents, and atmospheric state parameters within a broad shield of precipitation generated by a passing midlatitude cyclone. The 94-GHz CloudSat radar acquired vertical profiles of radar reflectivity within light to moderate snowfall, coincident with C3VP surface and aircraft instrumentation. Satellite-based retrievals of cold season precipitation require relationships between remotely sensed quantities, such as radar reflectivity or brightness temperature, and the ice water content present within the sampled profile.

In this study, three methods for simulating CloudSat radar reflectivity are investigated by comparing Mie spheres, single dendrites, and fractal aggregates represented within scattering databases or parameterizations. It is demonstrated that calculations of radar backscatter from nonspherical crystal shapes are required to represent the vertical trend in CloudSat radar reflectivity for this particular event, as Mie resonance effects reduce the radar backscatter from precipitation-sized particles larger than 1 mm. Remaining differences between reflectivity from nonspherical shapes and observations are attributed to uncertainty in the mass–diameter relationships for observed crystals and disparities between naturally occurring crystals and shapes assumed in the development of ice crystal scattering databases and parameterizations.

Corresponding author address: Andrew Molthan, NASA Marshall Space Flight Center, 320 Sparkman Dr., Huntsville, AL 35802. Email: andrew.molthan@nasa.gov

Abstract

The Canadian CloudSat/Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) Validation Project (C3VP) was designed to acquire aircraft, surface, and satellite observations of particle size distributions during cold season precipitation events for the purposes of validating and improving upon satellite-based retrievals of precipitation and the representation of cloud and precipitation processes within numerical weather prediction schemes. During an intensive observation period on 22 January 2007, an instrumented aircraft measured ice crystal size distributions, ice and liquid water contents, and atmospheric state parameters within a broad shield of precipitation generated by a passing midlatitude cyclone. The 94-GHz CloudSat radar acquired vertical profiles of radar reflectivity within light to moderate snowfall, coincident with C3VP surface and aircraft instrumentation. Satellite-based retrievals of cold season precipitation require relationships between remotely sensed quantities, such as radar reflectivity or brightness temperature, and the ice water content present within the sampled profile.

In this study, three methods for simulating CloudSat radar reflectivity are investigated by comparing Mie spheres, single dendrites, and fractal aggregates represented within scattering databases or parameterizations. It is demonstrated that calculations of radar backscatter from nonspherical crystal shapes are required to represent the vertical trend in CloudSat radar reflectivity for this particular event, as Mie resonance effects reduce the radar backscatter from precipitation-sized particles larger than 1 mm. Remaining differences between reflectivity from nonspherical shapes and observations are attributed to uncertainty in the mass–diameter relationships for observed crystals and disparities between naturally occurring crystals and shapes assumed in the development of ice crystal scattering databases and parameterizations.

Corresponding author address: Andrew Molthan, NASA Marshall Space Flight Center, 320 Sparkman Dr., Huntsville, AL 35802. Email: andrew.molthan@nasa.gov

1. Introduction

The launch of the National Aeronautics and Space Administration (NASA) CloudSat mission provided the first orbiting cloud radar system, generating vertical profiles of 94-GHz radar reflectivity obtained slightly off of the nadir track while orbiting in line with other NASA A-Train instruments capable of remotely sensing cloud properties (Stephens et al. 2002). CloudSat has demonstrated value by obtaining a global survey of cloud occurrence and structure for model evaluation (Marchand et al. 2008; Shi et al. 2010), and is particularly suited to cases of snowfall. The CloudSat radar was designed for a minimum detectable signal of −28 dBZ, sensitivity to small particles by transmitting at a wavelength of approximately 3.2 mm, and reduced attenuation in environments where liquid water content is minimized (Stephens et al. 2008). CloudSat precipitation and reflectivity products have been examined in snowfall events and validated against terrestrial radar observations to demonstrate their consistency in remote sensing of the complete vertical profile and detection of surface precipitation (Hudak et al. 2008). These studies represent a subset of results demonstrating the effectiveness of CloudSat in the detection of clouds, their structure, and resulting precipitation.

One goal of the CloudSat mission is to evaluate the representation of clouds within high-resolution weather and climate prediction models (Stephens et al. 2002). To achieve this goal, satellite simulators have been developed to convert model output to an equivalent reflectance, brightness temperature, or radar reflectivity observed from current and future satellites (Matsui et al. 2009). By using a satellite simulator, remaining differences between satellite products and forecast model output are confined to errors in the assumed or modeled characteristics of hydrometeors, their size distributions, vertical profiles of liquid and ice water content (IWC), and assumptions related to radiative transfer. Application of a satellite simulator to forecast model output requires a faithful simulation of the radiative transfer processes between the model grid point and remote sensor. The satellite radar simulator of Matsui et al. (2009) treats each model column individually and assumes single-scattering processes, representing all hydrometeors as Mie scattering spheres. Single-scattering assumptions are best applied to cold season precipitation in the high latitudes and are applicable to over 80% of profiles measured over the global oceans (Battaglia et al. 2007), but multiple scattering effects on the order of 1 dB or more can occur when reflectivity exceeds 10–15 dBZ (Matrosov and Battaglia 2009).

When applied to cold season precipitation, the use of bulk, soft sphere-shaped representations are inadequate for representing scattering effects of ice crystals and their aggregates at a variety of frequencies ranging from 3 to 35.6 GHz (Botta et al. 2010). Liu (2004) demonstrated that crystal habits and their complex shapes produce scattering phase functions that differ from a spherical shape representation, leading to excessive forward scattering by spheres comprised of pure ice or a lower density ice and air mixture. The results of Liu (2004) led to the development of an ice crystal scattering database representing 11 unique crystal habits and their single-scattering properties at frequencies ranging from 13.5 to 340 GHz (Liu 2008a; hereafter SCATDB). The current version of SCATDB assumes random particle orientations, although natural crystals may have a preferred orientation that affects their radar backscattering cross section as they fall (Liu 2008a). By combining mass–diameter and terminal velocity–diameter functions with SCATDB habits, Liu (2008b) obtained relationships between CloudSat radar reflectivity and snowfall rate that varied depending on the assumed crystal habit.

Currently, SCATDB lacks entries for aggregates, which often form due to the variability in the size and dispersion in the fall speeds of individual crystals (Field and Heymsfield 2003; Heymsfield et al. 2007). The shapes of aggregates are complex, depending upon the shapes of their constituent crystals, ice crystal fragmentation, and further depositional or accretional growth. Ishimoto (2008) simulated aggregates via Monte Carlo experiments by assigning ice mass to a grid in a fractal nature, then obtained radar backscattering cross sections as a function of diameter for a 95-GHz radar, a frequency similar to that of CloudSat. Variability in particle orientation was included by averaging the characteristics of eight randomly defined aggregates with incident radiation oriented at six different directions along the Cartesian axes. Ishimoto (2008) demonstrated that radar backscatter and other scattering characteristics from aggregates differ from the resonance effects present for Mie scattering spheres by producing a steady increase in the radar backscatter cross section with aggregate maximum dimension. Parameterizations were developed to relate single-scattering properties of aggregates to their maximum dimension, allowing for rapid calculations and use within radiative transfer calculations.

Previous studies by Liu (2008a) and Ishimoto (2008) provide varying assumptions of crystal shapes that could be applied in a satellite simulator with applications in weather forecast and climate model evaluations. In this study, SCATDB entries and parameterizations derived from Ishimoto’s (2008) aggregates are compared to results from Mie scattering spheres to determine their relative success in reproducing observations from CloudSat. Given the use of satellite simulators in weather forecast and climate model validation and their potential future use in the development of satellite-derived retrievals of precipitation and cloud properties, it is important to consider the impacts of ice crystal scattering characteristics on inferences drawn from CloudSat observations. Herein, CloudSat radar reflectivity is simulated from aircraft-measured particle size distributions obtained during a widespread snowfall event in southern Ontario, Canada, sampled during the 22 January 2007 intensive observation period of the Canadian CloudSat/Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) Validation Project (C3VP). Various assumptions of ice crystal shape are explored to determine techniques capable of reproducing the general features within the CloudSat observations.

2. The Canadian CloudSat/CALIPSO Validation Project

C3VP was an international collaboration between the CloudSat/CALIPSO and NASA Global Precipitation Measurement (GPM) science communities, designed to obtain aircraft and surface measurements of cold season particle size distributions and other in situ data. Field campaign observations are useful for the evaluation and improvement of satellite-based precipitation retrieval algorithms and cloud microphysical processes simulated within weather and climate prediction models (Shi et al. 2010; Molthan et al. 2010). Numerous observational assets were available with deployments managed at the Centre for Atmospheric Research Experiments (CARE) site in Egbert, Ontario. The operational, C-band, dual-polarization radar at King City, Ontario, provided real-time analysis of precipitation occurring over the region and allowed for some inference of cloud microphysical processes. Standard surface weather data were provided by an experimental U.S. Climate Reference Network station established at the CARE site. The National Research Council Canada (NRC) Convair-580 instrumented research aircraft was deployed to measure particle size distributions, temperature, relative humidity, and total ice or liquid water content. Aircraft data obtained during the C3VP intensive observation period of 22 January 2007 were used to determine the sensitivity of the simulated CloudSat reflectivity to varied ice crystal shape and scattering assumptions.

3. Aircraft and radar observations on 22 January 2007

The C3VP observation period of 22 January 2007 sampled snowfall associated with a midlatitude cyclone tracking along the U.S.–Canadian border between 0000 and 1200 UTC. Radar reflectivity from the King City radar indicated the widespread coverage of precipitation over the C3VP domain during aircraft flight operations (Fig. 1). The research aircraft flight track was partitioned into periods of climb and descent to represent vertical profiles of particle size distribution and atmospheric state variables. The first profile was obtained from a descending spiral near the CARE site from 0600 to 0624 UTC. The second profile was obtained between 0642 and 0709 UTC as the aircraft departed the CARE site and began an ascent toward the east-southeast. Temperatures ranged from −10° to −15°C in the lowest 3 km and included a weak temperature inversion near 1.5 km due to warm air advection near the frontal boundary (Fig. 2a). Persistent upward motion in the vicinity of the cyclone and frontal boundary maintained saturation (supersaturation) with respect to water (ice) throughout the majority of the vertical column (Fig. 2b), within a temperature range supporting the development of sector plates and dendrites, except for a region favorable for needle habit growth near cloud top (Pruppacher and Klett 1978).

Data from Particle Measuring Systems (PMS) 2D-C (15 μm–0.96 mm) and 2D-P (0.2–6.4 mm) probes were used to construct particle size distributions (PSDs), accommodating the overlap between probe size ranges while eliminating the erroneous contributions of small crystals resulting from larger crystals shattering on probe housings. The resulting size distributions were made available at 5-s increments, coincident with aircraft measurements of temperature and relative humidity. Ground-relative air speeds during the aircraft profiles ranged from 85 m s−1 near cloud base to 125 m s−1 near cloud top, corresponding to 5-s coverage areas ranging from 0.45 to 0.6 km. Although these represent samplings on scales smaller than the 1.7-km along-track resolution of CloudSat, aircraft measurements represent the general characteristics sampled by the CloudSat radar. Measurements of total ice water content were obtained from a counterflow virtual impactor (CVI; Twohy et al. 1997) with expected errors of 11% (23%) for actual values of 0.2 g m−3 (0.01 g m−3), as reported by Heymsfield et al. (2005). Although light riming of some crystals was apparent in photographs obtained at the surface, no significant amount of cloud liquid water was detected in the Convair-580 profile, resulting in CVI estimates being attributed to ice.

To partition the total ice water content among contributions from particles of varying size, a mass–diameter relationship must be derived or assumed. Heymsfield et al. (2007) reviewed several previous mass–diameter relationships in power-law form:
i1520-0426-28-3-337-e1
where values of bm range from 1.5 to 3 for dendrites and pure ice spheres, respectively. Observed values of am spanned orders of magnitude with greater variability than bm, the mass–diameter exponent. Heymsfield et al. (2007) continued their analysis by deriving several mass–diameter relationships for ice crystals observed within large-scale ascent or those associated with convective storms. Heymsfield et al. (2007) determined functions of am(T) for fixed values of bm ranging from 1.5 to 2.3, allowing for the use of temperature-dependent relationships in a linear form:
i1520-0426-28-3-337-e2

Five Heymsfield et al. (2007) relationships of am(T) and bm were considered, along with the Heymsfield et al. (2004) mass–diameter relationship of am = 0.077 and bm = 2.05, to determine which combination of mass–diameter relationship and measured particle size distributions produced the best fit to in-flight estimates of total IWC measured from the onboard CVI. Ratios of calculated and observed (CVI) total ice water content were determined from paired observations, restricted to CVI reports of at least 0.01 g m−3 (Fig. 3). Although shattered crystals were excluded in the final, merged particle size distributions, remaining counts of particles less than 50 μm in their maximum dimension were unreliable, and analyses herein are limited to particle number concentrations from bin centers of 90 μm or larger.

The linear relationship (2) of am(T) and fixed value of bm = 1.9 was selected from Heymsfield et al. (2007) for use with C3VP data, based upon the minimization of the calculated and observed IWC ratio and a median ratio near unity. Coefficients and applicable ranges of temperature for (2) are listed in Table 1. Ratios were concentrated within 50% of the CVI-estimated value (Fig. 3a), but calculated values tended to overestimate (underestimate) CVI values between 4 and 6 km (0.5 and 2 km). The median ratio of calculated and observed ice water content was 0.90, with a right-skewed distribution accounting for relatively infrequent but large ratios near cloud top (Fig. 3b). The standard deviation (σ) for the IWC ratios was 0.46, greater than values reported by Heymsfield et al. (2004) or Heymsfield et al. (2007). The Heymsfield et al. (2007) relationship (2) was selected for its ability to provide a plausible range of calculated IWC values while representing flexibility in M(D) with crystal habit and type attributable to ambient temperature and the aggregation of crystals within the sampled environment.

In addition to the mass–diameter relationship, particle size distributions can be characterized in terms of parameters acquired from the fitting of functions chosen to represent their general shape. The inverse exponential distribution for snow was proposed for surface snowfall by Gunn and Marshall (1958) and is used within various single-moment, bulk water microphysics schemes (Lin et al. 1983; Hong et al. 2004; Tao et al. 2003):
i1520-0426-28-3-337-e3

The first and second moments of the measured particle size distributions were used in the moment-fitting method of Heymsfield et al. (2002) to estimate the intercept (Nos) and slope parameter (λs) of an inverse exponential distribution (3), based upon particle number concentrations and their maximum dimension. Parameter estimates were retained if they were strongly correlated (R2 ≥ 0.8) to observed distributions.

Changes in the distribution intercept reflect the increase or decrease in number concentrations of small particles, while the distribution slope is inversely proportional to the arithmetic mean size of the population (D = λs−1). In each of the aircraft profiles, crystal probes sampled size distributions where λs and Nos decreased from cloud top toward cloud base (Fig. 4). This vertical trend in the paired values of λs and Nos corresponds to growth by aggregation (Lo and Passarelli 1982) and is characterized by an increase in mean particle size (λs−1), a decrease in the number concentration of small particles (Nos), and a decrease in the total number concentration (Nos/λs) (Fig. 4c). Depositional growth in the water-saturated and ice-supersaturated environment combined with aggregation to increase the mean particle size and total ice water content (Fig. 4d).

Crystal probe imagery corroborated size distribution inferences by depicting the rapid transition from individual crystals to aggregates, with some aggregates appearing as high as 5 km (Fig. 5). Aircraft observations of aggregation were supplemented by dual-polarization variables obtained from the King City radar around the time of the aircraft’s descending spiral. Analysis of King City radar reflectivity at the spiral base indicated a narrow, isolated band of enhanced reflectivity approximately 20 km wide and 1 km deep, perhaps the result of mesoscale processes that enhanced aggregation and mean particle size for a short period of time (Fig. 6a). The descending spiral produced minimum distribution slope values near 0.5 mm−1 coinciding with a sharp decrease in Nos. This isolated increase in mean particle size was surrounded by dual-polarization observations of a broader aggregation zone, marked by a steep increase (decrease) in radar reflectivity (differential reflectivity) at 2 km as individual, horizontally oriented crystals formed aggregates with no preferred orientation (Fig. 6b).

4. Simulating CloudSat reflectivity

In their development of a comprehensive satellite simulator, Matsui et al. (2009) included equations developed by Masunaga and Kummerow (2005) to simulate radar reflectivity profiles from forecast model outputs, including the effects of attenuation both along the path and within a specific model grid volume. The radar simulator developed by Matsui et al. (2009) was used here to obtain nonattenuated values of CloudSat reflectivity, based upon the ice crystal scattering database of Liu (2008a), a parameterization of scattering by aggregates based upon the results of Ishimoto (2008), and Mie scattering spheres. Results were compared against a mean profile and distribution of CloudSat observations acquired within comparable snowfall sampled around 0600 UTC (Fig. 7).

Given the temporal variability among the various datasets acquired during the C3VP intensive observation period, radar reflectivity from the King City radar was examined from 0600 to 0700 UTC to evaluate precipitation trends during the CloudSat orbital time and aircraft flight profiles of interest (Fig. 1). Light to moderate precipitation occurred over the CARE site and within the flight area between 0600 and 0630 UTC with typical, hourly precipitation rates near 0.4 mm h−1 (Molthan et al. 2010), then began to dissipate in coverage and shift eastward through 0700 UTC. Although precipitation rates varied at the surface, the storm is considered steady state for the purposes described herein. Profiles of particle size distribution parameters, temperature, and relative humidity were similar throughout the bulk of the two aircraft profiles. Since the descending spiral data appear to have sampled a short-lived, mesoscale band of enhanced reflectivity and larger aggregate sizes below 2 km (Fig. 6), subsequent CloudSat reflectivity simulations are based upon the ascending aircraft profile, chosen to represent average conditions expected throughout the broader region of snowfall.

a. Selection of particle scattering assumptions

Simulated reflectivity profiles assume either Mie scattering spheres, the stellar dendrites of SCATDB, or a hybrid combination of Mie spheres and fractal aggregates simulated by Ishimoto (2008). Mie spheres represent the spherical shapes frequently used to approximate ice crystals and their aggregates within single-moment, bulk water, cloud microphysics schemes (Lin et al. 1983; Hong et al. 2004; Tao et al. 2003), and have been used previously in simulations of CloudSat reflectivity (Matsui et al. 2009; Shi et al. 2010). The effective density (ρe) of a Mie sphere can be described as the ratio of the pure ice mass and the total volume of an equivalent diameter sphere. Given that the selected Heymsfield et al. (2007) mass–diameter relationship (2) varies with temperature, values were obtained from the aircraft profile to determine effective densities of simulated Mie spheres. Scattering properties of Mie spheres assume the complex refractive index of ice based upon aircraft measurements of air temperature. Dielectric properties were obtained from a Maxwell–Garnett dielectric function assuming a two-component inclusion of ice and air (Bauer and Schluessel 1993; Olson et al. 2001), where the volume fraction of ice inclusion is obtained from the ratio of ρe to that of pure ice.

Although the SCATDB provides 11 ice crystal habits, only the stellar dendrite class was investigated here. The selection of dendritic snowflakes was based upon crystal growth in an environment saturated (supersaturated) with respect to water (ice); environmental temperatures favoring their development (Pruppacher and Klett 1978); the suggestion of branched structures in aircraft crystal probe imagery (Fig. 5); and aggregates composed of individual, branched crystals in photographs obtained at the surface (Petersen et al. 2007). The SCATDB provides scattering characteristics for dendrite snowflakes ranging from 75 μm to 12.454 mm in particle maximum dimension and from temperatures of 0° to −40°C by interpolating between anchor points of varying size, temperature, and frequency. In support of CloudSat reflectivity simulations, the SCATDB uses 94 GHz as an anchor point so that interpolations are limited to crystal diameter and temperature. To approximate various populations of ice crystals, SCATDB calculations assume random orientations without account of the orientations preferred by falling crystals. As incident frequency increased, backscattering cross sections were sensitive to the sample size of the simulated orientations, but differences in orientation did not significantly impact the absorption or scattering cross sections (Liu 2008a).

Currently, the SCATDB lacks aggregates, which frequently occur in snowfall and were present throughout the aircraft profile observed on 22 January 2007. Simulation of reflectivity from aggregates is obtained using single-scattering properties of Ishimoto’s (2008) fractal aggregates, constructed as a randomly generated ice lattice. Although the results of Ishimoto (2008) are based upon a frequency of 95 GHz, which differs slightly from the 94-GHz CloudSat radar, the results at 95 GHz are used here to examine the potential benefits of representing crystals as aggregate shapes rather than individual crystals or spheres. Characteristics of fractal aggregates were described in terms of their fractal dimension, related to the aggregation process. Ishimoto (2008) determined that aggregates with a fractal dimension (df) of 2.1 were comparable to aggregates observed by Heymsfield et al. (2002) and simulations of aggregation by Westbrook et al. (2004). The total mass of a single aggregate is the product of the pure ice density (ρi), the number of ice lattice points occupied by constituent ice crystals (N), the volume of a single lattice grid point (δ3), and the parameter f = dV/δ3, which represents the ratio of ice crystal volume (dV) to the volume of the ice lattice point. The effective bulk density of an aggregate can be determined from the ratio of aggregate mass to an equivalent diameter sphere.

Here, simulated aggregates derived from ice constituents with f = 0.5 and df = 2.1 were selected to represent shapes comparable to those in Heymsfield et al. (2002) and the mass–diameter relationship selected from Heymsfield et al. (2007) (Fig. 10). Although Ishimoto (2008) provided the calculation of the radar backscattering cross section (σbs), H. Ishimoto (2009, personal communication) provided the remaining data for the scattering cross section (σsca), absorption cross section (σabs), asymmetry parameter, and the radius of an equivalent, pure ice sphere (req) for aggregates, assuming incident radiation at 95 GHz (Fig. 8). Cross-section parameters were fit to power-law forms through least squares minimization, but the asymmetry parameter was fit by a quadratic equation and a linear segment to accommodate the rapid change near 3.5 mm (Tables 2 and 3).

Differences in the scattering characteristics of Mie spheres, Liu (2008a) stellar dendrites, and Ishimoto (2008) aggregates are shown in Fig. 9. Trends in the radar backscattering cross sections (σbs) differ for crystal sizes larger than 0.9 mm, a threshold used by Lhermitte (1990) to define Rayleigh and Mie scattering regimes at 94 GHz. Trends and values of σbs among the crystal scattering assumptions are similar for sizes less than 0.9 mm and suggest that Rayleigh assumptions are sufficiently accurate for this application. Beyond 0.9 mm, Mie spheres are characterized by resonance effects, where σbs oscillates between local maxima and minima with continued increases in diameter. Resonance in σbs is similar among spheres of different density, although a slight increase in σbs occurs for spheres at warmer temperature and greater mass.

Stellar dendrites from SCATDB produce a peak in σbs near 2.0 mm, followed by a local minimum near 3.5 mm and a continued increase in σbs for particles with maximum dimensions as large as 10 mm. Radar backscattering cross sections from stellar dendrites exceed variable density Mie spheres. Populations of crystals in this portion of the size spectrum would produce an increase in radar reflectivity versus a spherical representation. The power-law parameterization of σbs for aggregates avoids the resonance effects of Mie spheres or the local minima in backscatter from Liu (2008a) dendrites, but the raw data suggest a slight decrease in σbs for aggregates with maximum dimensions near 4 mm. The power-law representation in the final parameterization omits this isolated decrease and σbs increases steadily with increases in maximum dimension for the valid size range from 1.1 to 20.2 mm. Due to the limited number of observation points, it is unclear whether the isolated reduction in σbs at 4 mm is physically based or an effect of random construction and particle orientations developed by Ishimoto (2008).

Other scattering parameters exhibit differences varying with shape representation, but to a far lesser degree than the Mie resonance oscillations present within radar backscattering cross sections. Scattering and absorption cross sections increase uniformly for diameters less than 0.9 mm with greater spread at larger diameters. Scattering cross sections of aggregates follow the trend for stellar dendrites but exceed dendrite values, implying that simulated aggregates produce a larger cross-sectional area than dendrites or spheres of equivalent maximum dimension. The absorption cross sections of Liu (2004) and Ishimoto (2008) aggregates are comparable for maximum dimensions as large as 5 mm, but σabs for aggregates exceeds that of stellar dendrites for larger particles. The greatest differences in scattering characteristics occur in the asymmetry parameter. Dendrites minimize forward scattering, while the Mie spheres produce strong forward scatterers. The aggregates of Ishimoto (2008) approximate an average asymmetry parameter obtained from Mie spheres and SCATDB dendrites.

5. Simulation of CloudSat reflectivity

Three simulations of CloudSat reflectivity were performed, each exploring the use of a different ice crystal scattering assumption. In the first experiment, ice crystals were assumed to be Mie scattering spheres with an effective density determined by a mass–diameter relationship provided by (2) and Table 1. As particle sizes increase, their effective densities decrease. In the second experiment, ice crystals were simulated as SCATDB stellar dendrites. The third experiment combined the Ishimoto (2008) parameterization of backscatter from low-density aggregates (df = 2.05). The Ishimoto (2008) parameterizations are valid for sizes ranging from 1.13 to 20.2 mm, requiring an accommodation for the numerous observed particles with sizes less than the minimum diameter. Comparing the parameterized values of σbs from Ishimoto (2008) aggregates and variable density Mie spheres, the trend in σbs is similar for particles with maximum dimensions less than 1.13 mm due to their proximity to the Rayleigh and Mie scattering threshold of 0.9 mm (Fig. 9). To accommodate the use of Ishimoto (2008) aggregate parameterizations across the full range of sizes, the third experiment used a hybrid approach, where variable-density Mie spheres provided backscatter from particles less than 1.13 mm, and Ishimoto (2008) aggregates composed the remainder of the size distribution.

Each experiment implied a unique mass–diameter relationship, which must be accounted for to ensure that all simulations were based upon an equivalent ice water content. The mass–diameter relationship for Ishimoto (2008) aggregates produces particles with greater mass than spheres derived from the relationship of Heymsfield et al. (2007). Meanwhile, the mass of a SCATDB dendrite is less than the mass of a Mie sphere with the same maximum dimension (Fig. 10). To ensure that profiles of simulated CloudSat reflectivity are attributed to an equivalent ice water content, number concentrations of particles within each bin of the measured particle size distribution are scaled to produce the ice mass based upon (2). The effects of scaling each PSD are shown in Fig. 11, using average PSDs within 1-km layers to demonstrate the expected impacts on particle number concentrations used within each scattering assumption. Since each aggregate (dendrite) of a given diameter represents a total mass greater (less) than the mass of a Mie sphere acquired from (2), the number concentrations are reduced (increased) to total the IWC expected from the aircraft-measured particle size distribution. In the hybrid approach for aggregates, particles with maximum dimension less than 1.13 mm are treated as Mie spheres and no adjustment in number concentration is required. When the approach is applied to dendrites, their mass–diameter relationship begins to approach that of Mie spheres for sizes less than 0.5 mm and modifications to the aircraft-measured PSDs are reduced.

Analysis herein uses the nonattenuated value of the simulated CloudSat reflectivity, focusing on profile sensitivity to the characteristics of σbs(D) among the various assumptions. Attenuation of the radar signal by ice is much less than attenuation by water (Stephens et al. 2008), but aircraft probes did not detect the presence of measurable quantities of cloud liquid water and no significant attenuation is expected. These assumptions allow for the examination of simulated profiles representing an equivalent amount of ice mass and focus the analysis on their ability to represent the CloudSat reflectivity obtained during the 22 January 2007 event.

a. Comparisons of simulated and observed CloudSat profiles

Aircraft particle size distributions and atmospheric state data were available at 5-s increments and with variable resolution in altitude. Mean profiles of simulated reflectivity were computed with a running, arithmetic mean (boxcar) filter of linear values within 500-m bins, centered 250 m apart, then converted to decibels. Bins for each mean value averaged 13 observations per bin, with counts generally increasing from 5–8 at cloud top (4–6 km) to 15–20 at lower altitudes (1–3 km). Minimum and maximum values were tracked to represent the variability in simulated values acquired from aircraft data.

CloudSat reflectivity profiles were obtained from the 2B-GEOPROF product for the orbital segment shown in Fig. 7 with instrument noise and surface returns removed through the application of product quality indicators. Variability in CloudSat reflectivity along the cross section is displayed as a contoured frequency with altitude diagram (CFAD; Yuter and Houze 1995) based upon a joint histogram of reflectivity and height with bin intervals of 2 dBZ and 500 m. Use of the CFAD for CloudSat observations demonstrates the range and relative frequency of reflectivity values with height for comparison to mean profiles acquired from aircraft sampling data (Fig. 12).

Comparisons can be made by characterizing the profile as three layers: cloud top (4–6 km), midcloud (2–4 km), and cloud base (0–2 km). Simulated values of CloudSat reflectivity are then assessed within the context of their varied assumptions and the contributions of particle size intervals to the total ice water content. At cloud top, the dominance of small particles is apparent with 90%–100% of the total ice water content acquired from particles less than 0.9 mm, the Lhermitte (1990) size threshold for Mie scattering (Fig. 13). Simulated values of 94-GHz reflectivity from Mie spheres produce a mean profile similar to the CloudSat observations (Fig. 12a). Since the hybrid approach incorporates Mie calculations for sizes less than 1.1 mm, it provides a good fit to cloud-top reflectivity. The influence of Ishimoto (2008) aggregates begins below 5 km, where particles larger than 0.9 mm appear in the particle size distributions (Fig. 12b). Mie resonance effects occur at these larger sizes, with a reduction in σbs for increasing maximum dimension, whereas the parameterizations of Ishimoto (2008) continue the increase in σbs with particle size. Reflectivity from the hybrid approach follows the increase in observed reflectivity in the transition to midcloud, while resonance effects in the Mie simulation reduce the reflectivity and do not follow the trend in the CloudSat observations. The simulation using SCATDB dendrites produces mean values of reflectivity greater than CloudSat, but also benefits from avoiding resonance effects as particle sizes increase (Fig. 12c). Some of the excess in reflectivity within the dendrite simulation is likely attributable to an overestimate of IWC near cloud top (Fig. 3c) and the resulting scaling of measured particle size distributions (Fig. 11).

Within the midcloud portion, particle size distributions extend to greater number concentrations of non-Rayleigh scatterers. Departures occur between profiles acquired from assumptions using Mie spheres and either dendrites or aggregates. In the 2–4-km range, 30%– 60% of the total ice water content is obtained from particles less than 0.9 mm (Fig. 13). Mie scattering assumptions produce a stagnant profile with values 3–4 dB less than the mean profile of observations and do not represent the continued, downward increase in CloudSat reflectivity. Here, particles with diameters within Mie resonance backscatter minima reduce the total contribution to the radar backscatter. Simulations with stellar dendrites and aggregates continue the downward increase in reflectivity although each assumption exhibits a positive bias. Crystal probe imagery in the 2–4-km layer depicts individual crystals and some clustering into aggregates that occurred as high as 5 km (Fig. 5). The measured size distributions were likely a mix of large, individual crystals and aggregates. Although the simulated profiles do not include a mixture of these particle types, reflectivity from dendrites is comparable to aggregates and remains approximately 2–3 dB greater than the CloudSat mean profile.

Approaching cloud base, more than 85% of the total ice water content is partitioned among particles larger than 0.9 mm. Crystal probe imagery (Fig. 5) is dominated by the large aggregates apparent within surface photographs (Petersen et al. 2007) and inferred from dual-polarization radar parameters (Fig. 6). Reflectivity simulated from Mie scattering assumptions is nearly constant at −4 dBZ in the lowest 2 km, while the mean CloudSat reflectivity profile continues to increase (Fig. 12). Although the mean profile from the Ishimoto (2008) aggregates steadily increases toward the surface, mean reflectivity values in the lowest 2 km of the dendrite simulation exhibit a marked reduction. In Fig. 8, a general decrease in σbs occurs for simulated dendrites with maximum dimensions between 2 and 4 mm. In the 1–2-km altitude range, 70% of the total ice water content is accounted for by crystals less than 2 mm, leaving the remainder to be distributed among dendrites within a local backscatter minimum. Similar to the case of Mie scattering spheres, the reduction in backscatter from this portion of the size distribution contributes to the decrease in the total backscatter and reduced values of the simulated CloudSat reflectivity.

Although reflectivity acquired from dendrites or aggregates represents the general shape of the mean CloudSat profile below 5 km, each assumption produced a positive bias. This positive bias is attributable to differences in the scattering characteristics of naturally occurring and simulated crystals and the use of nonattenuated values in an environment where the CloudSat signal will attenuate. Estimates of ice water content generated by (2) and the measured particle size distributions imply that simulated reflectivity is acquired from an amount of mass that may exceed the CVI measurements, or the amount of ice water present for contributing to the total CloudSat radar backscatter. Although SCATDB dendrites minimized this positive bias in the lowest 1–2 km, IWC estimates acquired from particle size distributions consistently underestimated CVI measurements at these altitudes, resulting in a simulated reflectivity acquired from less mass than was observed. In each of the particle-type experiments, assumptions of shape and particle orientation were made to accommodate the simulation of single-scattering characteristics for either 94 or 95 GHz. Differences in the simulated and observed reflectivities may also relate to assumptions of particle orientation since some crystal shapes will acquire a preferential orientation as they precipitate.

6. Summary and conclusions

Aircraft observations acquired during the C3VP intensive observation period of 22 January 2007 were used to simulate CloudSat reflectivity from snowfall, exploring sensitivities in simulated reflectivity profiles based upon scattering assumptions assigned to ice crystals. Three scattering assumptions were investigated using variable-density Mie scattering spheres, dendrites within the ice crystal scattering database of Liu (2008a), and parameterizations fit to properties of fractal aggregates provided by Ishimoto (2008). Each simulated profile was based upon aircraft-measured particle size distributions within moderate snowfall, generated in advance of a warm frontal boundary and an area of surface low pressure, an event comparable to numerous storms that generate cold season precipitation in the midlatitudes.

Simulations of CloudSat reflectivity near cloud top were reasonably approximated by Mie scattering assumptions when populations of crystals were dominated by sizes less than 0.9 mm. As crystals continued their growth and formed aggregates with maximum dimensions greater than 0.9 mm, CloudSat reflectivity was best represented by applying the scattering characteristics of the Liu (2008a) dendrites or a hybrid approach combining the Ishimoto (2008) aggregates with Mie spheres that accommodate particles with maximum dimensions less than the applicable range of aggregate parameterizations. The Mie scattering spheres used here were insufficient for approximating the CloudSat reflectivity from the particle size distributions dominated by particles with maximum dimensions greater than 0.9 mm. These larger particles and their number concentrations were located within radar backscatter minima and reduced the total radar backscatter. Simulations of reflectivity using the Liu (2008a) dendrites or the Ishimoto (2008) aggregates reproduced the overall trend in CloudSat observations but consistently overestimated the observed reflectivity values. This overestimate occurred despite the tendency of the Heymsfield et al. (2007) mass–diameter relationship to underestimate IWC within the aggregate zone, suggesting that the backscatter of simulated crystals may exceed natural crystals due to assumptions of their shape, composition, or assumed orientation.

Several mass–diameter relationships were investigated for application to the C3VP dataset, and although the Heymsfield et al. (2007) results provided a reasonable fit, all crystal scattering assumptions imply a unique mass–diameter relationship that may not fit an observed case. Future studies seeking to develop a mass–diameter relationship for both aircraft observations and simulated scatterers would alleviate the need to scale particle size distributions, which is currently necessary for the conservation of ice water contents measured by the CVI. By improving the representation of ice water content from particle size distributions and crystal database entries, greater emphasis can be placed upon the sensitivities of results to assumed single-scattering characteristics related to particle shape and orientation. Attenuation will be affected by the amount of ice mass and liquid water present, and the aforementioned positive bias in simulated values could be reduced by including their effects.

Currently, efforts are under way to evaluate weather and climate model forecasts via satellite simulators that translate model output to an equivalent satellite product (Matsui et al. 2009), a strategy that avoids discrepancies between retrieval and forecast model assumptions. Observations from the C3VP campaign, combined with ice crystal scattering databases, demonstrate that simulated satellite products will be sensitive to the assumed characteristics of ice crystals and aggregates, and that spherical representations are incapable of reproducing the general, vertical trend in CloudSat reflectivity when large particles are present. Radiative transfer codes and future satellite simulators would benefit from future studies examining the scattering characteristics of ice crystals and aggregates over a broad range of frequencies, benefiting retrieval development for orbiting or proposed future instruments, such as the NASA Global Precipitation Measurement mission.

Acknowledgments

Petersen acknowledges funding from the NASA Precipitation Measurement Mission via Dr. Ramesh Kakar, and the Global Precipitation Mission Science Project Scientist (Dr. Arthur Hou) and Project Offices (Dr. Mathew Schwaller). Prime funding for aircraft studies during the Canadian CloudSat/CALIPSO Validation Project was provided by the Canadian Space Agency. The lead author was supported in part by the Cooperative Education Program at NASA Marshall Space Flight Center, and thanks three anonymous reviewers for constructive comments that improved the clarity of the final published manuscript.

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Fig. 1.
Fig. 1.

(a) Overview of the C3VP operational coverage area and related datasets. Range rings are provided in 50-km increments for the dual-polarization, C-band radar at King City. The 331° azimuth is shown, pointing in the direction of the CARE site located approximately 33 km northwest of the radar location. The portion of the CloudSat orbit described within the text is shown as a heavy dashed line. The flight track of the NRC Convair-580 is indicated with annotated flight segments referencing profiles described within the text. (b) As in (a), but with coverage limited to a range of 100 km and including the horizontally polarized radar reflectivity obtained from the 0.8° tilt angle at 0600 UTC. (c) As in (b) but for the radar reflectivity at 0630 UTC. (d) As in (b), but for the radar reflectivity at 0700 UTC.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 2.
Fig. 2.

Observations of (a) air temperature, (b) relative humidity with respect to water, and (c) relative humidity with respect to ice, obtained from the aircraft profiles described in the text and shown in Fig. 1.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 3.
Fig. 3.

(a) Paired values of IWCs measured by the aircraft CVI and estimated from the relationship of Heymsfield et al. (2007), as described within the text. (b) Histogram of the ratio of the calculated and measured IWCs at 20% intervals. (c) Vertical variability of ratios of calculated and measured IWCs.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 4.
Fig. 4.

(a) Vertical profiles of the slope parameter (λs) for the inverse exponential size distribution, obtained from reliable fits to aircraft observations. (b) As in (a), but for the distribution intercept (Nos). (c) Scatterplot of the exponential size distribution parameters Nos and λs. (d) IWCs for each aircraft profile as measured by the CVI.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 5.
Fig. 5.

Crystal images obtained from aircraft probes to represent of habits at various altitudes. The bottom two panels are from the 2D-P system, which better depicts the structure of the largest aggregates that begin to overwhelm the 2D-C probes at lower altitudes. The altitude and temperature for each panel were estimated by matching the time stamp to aircraft flight data.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 6.
Fig. 6.

Range–height diagrams of the (a) horizontally polarized radar reflectivity and (b) differential reflectivity obtained from the King City radar at 0624 UTC along the 331° azimuth and in the direction of the CARE site.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 7.
Fig. 7.

CloudSat 94-GHz radar reflectivity depicting snowfall occurring across the C3VP domain around 0600 UTC 22 Jan 2007. Observations were obtained from the orbital segment in Fig. 1.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 8.
Fig. 8.

Single-scattering parameters for aggregates with fractal dimension df = 2.05, parameter f = 0.5, and incident radiation at 95 GHz, based upon Ishimoto (2008), and best-fit, least squares relationships parameterized as a function of the particle dimension: (a) radar backscattering cross section, (b) scattering cross section, (c) extinction cross section, and (d) asymmetry parameter.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 9.
Fig. 9.

Single-scattering parameters among the various shape assumptions, including Mie spheres at air temperatures representative of the aircraft profile and with densities following the mass–diameter relationship of Heymsfield et al. (2007), the stellar dendrites of Liu (2008a), and aggregates simulated by Ishimoto (2008): (a) radar backscattering cross section, (b) scattering cross section, (c) absorption cross section, and (d) asymmetry parameter.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 10.
Fig. 10.

Mass–diameter relationships for the various ice crystal shape assumptions used in the simulation of CloudSat reflectivity and described within the text.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 11.
Fig. 11.

Average PSDs and temperatures within three 1-km layers and modified PSDs for each crystal assumption, representing processes used to conserve the total ice water among CloudSat reflectivity simulations. Total IWCs for each population are based upon values expected by the Heymsfield et al. (2007) mass–diameter relationship. The vertical dashed line represents the minimum size threshold for including Ishimoto (2008) aggregates.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 12.
Fig. 12.

(a) CFAD and mean profile of the 94-GHz CloudSat reflectivity acquired from the vertical profiles shown in Fig. 7, along with mean, minimum, and maximum values acquired from simulations of ice crystals as Mie spheres. (b) As in (a), but based upon the hybrid scattering assumption. (c) As in (a), but derived from simulations of dendrites. In each panel, the CFAD of the CloudSat observations is shaded at intervals of 1%, 2.5%, 5%, 10%, and 25% using histogram binning intervals of 2 dBZ and 500 m.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Fig. 13.
Fig. 13.

Fraction of the total IWC obtained from particles less than a given size, based upon mean PSDs within 1-km altitude layers and the mass–diameter relationship of Heymsfield et al. (2007). The 0.9-mm threshold for Mie resonance at 94 GHz is indicated, based upon the results of Lhermitte (1990). Average temperatures (Tavg) are provided for each layer, along with the total IWC, and the number (N) of PSDs averaged within each height interval.

Citation: Journal of Atmospheric and Oceanic Technology 28, 3; 10.1175/2010JTECHA1511.1

Table 1.

Parameterization of am(T) described in Heymsfield et al. (2007), with relevant constants and temperature range, based upon a linear equation with parameters am(kg mbm) = C0 + C1 T and bm = 1.9.

Table 1.
Table 2.

Parameterizations developed for 95-GHz crystal aggregate scattering characteristics in accordance with Ishimoto (2008) for fractal aggregates with df = 2.1, f = 0.5, and maximum crystal maximum diameter (mm).

Table 2.
Table 3.

Values of coefficients and exponents used in Ishimoto’s (2008) parameterizations of single-scattering properties for aggregates at 95 GHz.

Table 3.
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