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Keywords:

  • Remote sensing;
  • ice;
  • cloud

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Retrieval Algorithm
  5. 3. Differences From Previous Algorithm
  6. 4. Algorithm Performance
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References

[1] A new remote sensing retrieval of ice cloud microphysics has been developed for use with millimeter-wave radar from ground-, air-, or space-based sensors. Developed from an earlier retrieval that used measurements of radar reflectivity factor together with a priori information about the likely cloud targets, the new retrieval includes temperature information as well to assist in determining the correct region of state space, particularly for those size distribution parameters that are less constrained by the radar measurements. These algorithms have served as the ice cloud retrieval algorithms in Releases 3 and 4 of the CloudSat 2B-CWC-RO Standard Data Product. Several comparison studies have been performed on the previous and current retrieval algorithms: some involving tests of the algorithms on simulated radar data (based on actual cloud probe data or cloud resolving models) and others featuring statistical comparisons of the R04 2B-CWC-RO product (current algorithm) to ice cloud mass retrievals by other spaceborne, airborne, and ground-based instruments or alternative algorithms using the same CloudSat radar data. Comparisons involving simulated radar data based on a database of cloud probe data showed generally good performance, with ice water content (IWC) bias errors estimated to be less than 40%. Comparisons to ice water content and ice water path estimates by other instruments are mixed. When the comparison is restricted to different retrieval approaches using the same CloudSat radar measurements, CloudSat R04 results generally agree with alternative IWC retrievals for IWC < 1000 mg m−3 at altitudes below 12 km but differ at higher ice contents and altitudes, either exceeding other retrievals or falling within a spread of retrieval values. Validation and reconciliation of all these approaches will continue to be a topic for further research.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Retrieval Algorithm
  5. 3. Differences From Previous Algorithm
  6. 4. Algorithm Performance
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References

[2] Clouds have a strong and complex influence on the Earth's radiation budget and hydrological cycle and constitute the major source of uncertainty in predicting climate change and sensitivity [Intergovernmental Panel on Climate Change, 2001; Randall et al., 2007]. While the measurement of cloud occurrence and cloud properties at useful spatial and temporal scales is notoriously difficult [Stephens and Kummerow, 2007], the recent proliferation of new satellite platforms in the last few years [e.g., Eriksson et al., 2008; Stephens et al., 2002; Wu et al., 2009] is fostering a number of new approaches.

[3] This paper describes the development, structure, and performance of remote sensing retrievals of ice cloud properties designed for use with the Cloud Profiling Radar (CPR) on the CloudSat satellite, which was launched in April 2006. The CPR measures copolar radar reflectivity (with no Doppler information), so retrievals must be based on reflectivity data alone or in combination with non-CloudSat sources such as model data, climatological data, or observations from other instruments. A number of ice cloud retrievals have been reported in recent years, some using reflectivity alone [e.g., Sassen et al., 2002; Heymsfield et al., 2005; Sayres et al., 2008] and some adding temperature as an additional constraint [e.g., Liu and Illingworth, 2000; Hogan et al., 2006]. Many of these prescribe direct reflectivity–ice water content relations, usually in the form of a power-law relation, allowing measured reflectivity values to be converted directly to ice water content. An alternative approach, being used in the CloudSat retrievals, is one of using an optimal estimation algorithm to retrieve parameters of the particle size distribution (PSD). This approach was used in the early liquid and ice cloud retrievals developed for CloudSat [Austin and Stephens, 2001; Benedetti et al., 2003]. Once the PSD parameters are retrieved, ice water content, effective radius, and other moments of the distribution are easily calculated. The retrievals in the current paper follow this practice, improving on the earlier retrieval described by Benedetti et al. [2003] and modifying it to use radar without an independent measurement of visible optical depth.

[4] The current retrieval algorithm, using radar and temperature data, is described in section 2. Differences from the preceding algorithm (used for a provisional CloudSat product) follow in section 3. Algorithm performance is addressed in section 4. Discussion of various aspects of the algorithms and a sampling of CloudSat results follow in section 5, and conclusions follow in section 6.

2. Retrieval Algorithm

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Retrieval Algorithm
  5. 3. Differences From Previous Algorithm
  6. 4. Algorithm Performance
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References

[5] The earliest prelaunch versions of the CloudSat ice retrieval followed the algorithm described by Benedetti et al. [2003], modified to use radar alone (with no optical depth input). These represented the ice cloud particles as a distribution of ice spheres of fixed density whose size was modeled using a three-parameter modified gamma distribution. In the radar-only (RO) retrieval case, the state vector (containing the unknowns to be retrieved) was composed of an array of characteristic diameter values (one of the three size distribution parameters) corresponding to the cloudy bins of the measured radar profile. Thus for a measurement vector containing p cloudy bins, the retrieval would solve for p values of the characteristic diameter. The other two size distribution parameters (the particle number concentration and the distribution width parameter) were assigned fixed values and uncertainties (based on climatology, field data, or other criteria); these forward model parameters were constrained to be height-invariant. Once the elements of the state vector were determined, values of typical microphysical parameters such as effective radius and ice water content (IWC) were easily calculated in terms of the size distribution parameters. The remaining inputs to the retrieval consisted of an a priori vector and covariance matrix, corresponding to the best knowledge of the elements of the state vector before the measurement is made. These were determined in a manner similar to the forward model parameters. An augmented retrieval using a combination of radar plus visible optical depth (RVOD) in the measurements vector was constructed similarly. (This is in fact the case described by Benedetti et al. [2003].) This augmented version added the (height-invariant) particle number concentration to the state vector, allowing this parameter to be retrieved rather than prescribed.

2.1. Motivation for Improvements

[6] While these early retrieval versions showed promise and were straightforward to implement, there were some difficulties in their use. (Parallel difficulties were found in the early CloudSat liquid cloud retrieval, which had a similar structure and was under simultaneous development.) First, the retrieval occasionally failed to converge, because no combination of state vector elements and (fixed) forward model parameters could be found that were consistent with both the radar measurements and the a priori data throughout the cloud column. Second, the forward model parameters (number concentration and distribution width parameter) were poorly known and therefore had to be specified with large uncertainty. This reduced both the accuracy of the retrieval (for cases where the true values differed from the assigned fixed values) and the precision of the results (owing to the effect of the large parameter uncertainties propagating into the uncertainties of the results). Finally, calculations of uncertainty in derived products such as ice water content require knowledge of the covariance between variables that were part of the state vector (e.g., characteristic diameter, which was being retrieved) and those that were not (e.g., particle number concentration, which was held at a height-invariant fixed value and not being retrieved), but there was no source for this information. The retrieval process provides a covariance matrix, but this matrix contains only covariances between the elements of the state vector.

[7] In order to overcome these difficulties, an improved algorithm was devised, following the lead of the improved CloudSat liquid cloud retrieval by adding the height-invariant number concentration and distribution width parameter (still using the modified gamma distribution) to the state vector, thereby retrieving values of these parameters in accordance with the measurements, a priori data, and the uncertainties in each. While this change causes the seemingly awkward effect of making the state vector longer than the measurements vector (i.e., retrieving p + 2 quantities from p or p + 1 measurements), a state space diagram shows how a priori data provide the additional constraints necessary to achieve a unique solution (Figure 1). In Figure 1, representing an RO retrieval for a single-bin cloud, the three axes correspond to the three parameters of the particle size distribution. The curved surface grid represents the locus of points (derived from the size distribution parameters) that fit the radar measurement exactly. Note that this surface is not orthogonal to any of the three coordinate directions, so no PSD parameter is solely determined by the radar measurement, but it is fair to say that the exact measurement surface is most orthogonal to the characteristic diameter Dn. Thus one might say that the characteristic diameter is mostly determined by the radar measurement and the number concentration and width parameter are mostly determined by the a priori data, although both data sources contribute to all three parameters. The a priori data point is shown in Figure 1: the retrieval process selects a point in state space that is consistent with the measurements and the a priori data and the uncertainties in each. This illustrates the major improvement in the previous algorithm: the number concentration NT and width parameter ν coordinates of the solution point are free to vary in the neighborhood of the a priori point (depending on relative uncertainties), rather than being fixed to prescribed values.

image

Figure 1. Three-dimensional state space for a single-bin RO cloud retrieval (previous algorithm) with measured Ze = −20 dBZ. The set of points fitting the radar measurement exactly form a surface in state space represented by the blue mesh. The a priori point and uncertainty are shown by the red dot and ellipsoid.

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[8] The above improved algorithm served as the ice water content retrieval algorithm in version 5.0 of the CloudSat 2B-CWC-RO standard data product. This version first appeared in Release 3 (R03) of this product, which was designated a “beta” version and released to the science team and community on a limited basis. During the period from January to October 2007, a number of tests were performed on this product. One test whose results were particularly amenable to evaluation of the retrieval as a function of a number of variables was an ice cloud retrieval intercomparison study described by Heymsfield et al. [2008]. Evaluations using results from this intercomparison are discussed in section 4.

2.2. Height and Temperature Dependence

[9] The algorithm in the previous section was shown to perform well overall, but it suffered from bias when retrieving the particles at the coldest temperatures and lowest reflectivities and had a greater RMS error than would be preferred. It was believed that the use of the height-invariant number concentration and distribution width parameter was a factor in both of these shortcomings. If these parameters were allowed to vary with altitude (which seemed more realistic) and if a temperature dependence could be incorporated into the retrieval in some way, it seemed likely that the performance should improve.

[10] The key change in formulation in the current algorithm is the change to height-varying retrievals of all three size distribution parameters. This is accomplished by expanding the state vector to include complete profiles of each of the parameters, allowing other height-dependent information to be utilized.

[11] By changing the retrieval framework such that profiles of all three distribution parameters are retrieved, it became possible to include temperature dependencies by making the a priori data values dependent on temperature. Since temperature is one of the most important factors influencing cloud particle evolution, knowledge of the temperature (whether by measurement or modeling) should help narrow the part of the state space selected for consideration in the retrieval process. The most direct way to incorporate this information is to make the a priori data dependent on temperature. The a priori data represent our best knowledge of the state vector before the (radar) measurement is made. If we know the temperature of a particular cloudy region, then we have a better idea of the cloud properties than we would without this information.

[12] In order to determine useful temperature-dependent values of the size distribution parameters, a number of in situ 5-s average ice particle size spectra were examined, including 5796 measurements from four flights during the ARM 2000 Cloud IOP, 2727 measurements from one flight during the AIRS experiment (Canada), and 3709 measurements during ten flights during CRYSTAL-FACE. The spectra were specified in terms of the particle maximum dimension. A mass-dimension relation [Heymsfield et al., 2007] was used to convert the spectra to corresponding distributions of equivalent-mass spheres for use by the retrieval. (Direct measurements of IWC were used to constrain the mass-dimension relationships of Heymsfield et al. [2007].) Each converted particle spectrum was then fit by a three-parameter distribution function. The fits were weighted to place more emphasis on the points with D > 100 μm. Initially, a modified gamma function of the same type used in the prior retrievals was used for the fit, but this selection proved problematic, because the fit often resulted in a function that grew without bound as the size approached zero, making integrals over the size distribution diverge. Rather than enforcing a minimum particle size to the distribution and dealing with more complex mathematical expressions (due to the truncated distribution) and the issue of what the minimum size should be, it was decided to change to a lognormal size distribution (defined below in (4)). This choice had the advantage of better behavior in the small-particle limit (while retaining analytic expressions for moments of the distribution) and having the same form as the size distribution used in the corresponding liquid water retrieval, which may be of benefit in future crossover development. The choice of a lognormal form is also consistent with McFarquhar and Heymsfield [1997], who described a bimodal size distribution with a lognormal function representing the larger particles. (It should be noted that, while the semiinfinite lognormal distribution used in the following analysis extends to sizes both larger and smaller than the actual particle size distribution, the errors incurred by using the nontruncated spectra are inconsequential because the integrands are dominated by the 25- to 2000-μm size range.)

[13] Scatterplots of the three lognormal distribution parameters as a function of temperature are shown in Figure 2, together with linear least-squares fits. The resulting expressions for the fits are as follows:

  • equation image
  • equation image
  • equation image

with standard deviations in log NT, ω, and log Dg of 0.555, 0.235, and 0.226, respectively. (The notation “log” indicates the common logarithm; “ln” is used for the natural logarithm.) These expressions were obtained from the synoptic probe data: a separate fit process was performed on convective data, but the convective fits were not used in this version of the retrieval. The current retrieval algorithm is described in detail in sections 2.3 and 2.4.

image

Figure 2. Lognormal particle size distribution parameters from a large collection of cloud probe data plotted as a function of temperature. The solid lines indicate a linear least squares fit to each PSD parameter (resulting in expressions (1), (2), and (3)); the dashed lines indicate the assigned standard deviations.

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2.3. Forward Model (Current Algorithm)

[14] The forward model developed for the retrieval assumes a lognormal size distribution of ice crystals,

  • equation image

where NT is the ice particle number concentration, D is the diameter of an equivalent mass ice sphere, Dg is the geometric mean diameter, ln indicates the natural logarithm, and ω is the width parameter. The distribution in (4) is fully specified by three parameters: NT, Dg, and ω. The ice water content (IWC) and the effective radius re are defined in terms of moments of the size distribution,

  • equation image
  • equation image

where ρi is the density of ice (fixed at 917 kg m−3 in this version).

[15] For thin ice clouds, the cloud ice particles are sufficiently small to be modeled as Rayleigh scatterers at the CloudSat radar wavelength (3.2 mm) and sufficiently large that their extinction efficiency approaches 2 for visible wavelengths. These assumptions yield the following definitions of radar reflectivity factor ZRay and visible extinction coefficient σext:

  • equation image
  • equation image

Using (4) for the size distribution in (5) through (8) gives the following equations for the various cloud properties using the units denoted in bracketed subscripts,

  • equation image
  • equation image
  • equation image
  • equation image

All of these properties are functions of position in the cloud column; we can therefore write IWC(z), re(z), σext(z), and ZRay(z). Equations (9) through (12) express the intrinsic properties of the cloud as functions of the parameters of the assumed particle size distribution. The parameters IWC and re are the quantities we seek to retrieve, and values of Z are related to our measurements. We may also specify the ice water path (IWP),

  • equation image

[16] Because radar reflectivity in the Rayleigh regime is a function of the sixth power of the particle diameter, a significant error (overestimate in reflectivity) may be introduced by use of the Rayleigh approximation (7) on the large crystals that violate the Rayleigh criterion (even if these coarser particles are few in number). To compensate for this error, a procedure similar to that used by Benedetti et al. [2003] was used to obtain a correction function to account for non-Rayleigh scattering of large particles. The ratio of Mie to Rayleigh scattering was calculated for a range of distribution parameters and then fit with approximation functions to preserve differentiability. In order to better reflect the possible variety of distribution shapes, the fit for this algorithm was done in terms of two distribution parameters,

  • equation image

where

  • equation image
  • equation image
  • equation image

and the coefficients a01, a02, a03, a11, a12, a21, and a22 have values of 0.99, −0.965, 0.25, 0.9688, 0.02, 0.0625, and 0.000001, respectively. As before, this ratio is unity for small particle sizes and decreases with larger particles. (Benedetti et al. [2003] investigated the error introduced by the assumption of spherical particles and their similar fMie for various crystal habits as a function of effective diameter and found differences on the order of 10%.)

[17] The radar reflectivity factor ZRay in (11) is defined with respect to ice, but remote sensing radars (including the CPR) conventionally measure the equivalent radar reflectivity factor Ze (defined with respect to liquid water) [Smith, 1984],

  • equation image

where the dielectric factor K is defined in terms of the index of refraction m,

  • equation image

Calculating these values for liquid water and ice at the CloudSat frequency results in the following value for equation image (where the ice and liquid temperatures are assumed to be −20°C and 7°C, respectively):

  • equation image

Treating density as constant and including the conversion to equivalent radar reflectivity factor, the new forward model can be written as

  • equation image

2.4. Retrieval Algorithm

[18] The retrieval uses an approach described by Rodgers [1976, 1990], Marks and Rodgers [1993], and Rodgers [2000], where a vector of measured quantities y (here, reflectivities in cloudy radar resolution bins) is related to a state vector of unknowns x (size distribution parameters) by the forward model F,

  • equation image

where εy represents measurement errors. Rodgers [1976] described an optimal-estimation technique in which a priori profiles are used as virtual measurements, serving as a constraint on the retrieval. An a priori profile xa is specified on the basis of likely or statistical values of the state vector elements, together with an a priori covariance matrix Sa representing the variability or uncertainty of this profile and any known correlations among the profile values.

[19] The retrieval algorithm obtains the optimal solution by maximizing the a posteriori probability P(xy), where, from Bayes' theorem,

  • equation image

Assuming that the elements of x and y have joint Gaussian probability distribution functions, this is equivalent to minimizing a cost function Φ that represents a weighted sum of the state vector–a priori difference (from P(x)) and the measurement vector-forward model difference (from P(yx)),

  • equation image

The solution is obtained by iteration using successive estimates of the x vector and the K matrix (K = ∂F/∂x). These quantities are also used to provide information on convergence, the quality of the solution, and the amounts and sources of retrieval uncertainty. The iterative solution takes the following form:

  • equation image

where the superscripts i and i + 1 indicate the iteration number and equation image indicates an estimate or retrieved value of x.

2.4.1. State and Measurement Vectors

[20] The state vector x is the vector of unknown cloud parameters to be retrieved. For a cloud reflectivity profile consisting of p cloudy bins, the state vector will have n = 3p elements,

  • equation image

where Dg(zi), NT(zi), and ω(zi) are the geometric mean diameter, number concentration, and distribution width parameter for height z1 (where zi refers to the bin at cloud base). The units of Dg are millimeters and the units of NT are m−3; ω is dimensionless.

[21] A state space diagram for the current algorithm is shown in Figure 3. Again, the state space diagram gives a useful indication of the influence of a priori data versus measurements. As the measured radar reflectivity changes, the gridded surface expands or contracts. Thus retrieval coordinates orthogonal to this surface are determined by the measurement, while coordinates parallel to the surface are determined by the a priori values.

image

Figure 3. Three-dimensional state space for a single-bin RO cloud retrieval (current algorithm) with measured Ze = −20 dBZ. The Mie correction function fMie is set to unity for plotting purposes.

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[22] The measurement vector y is composed of m = p elements for a cloud profile of p cloudy bins,

  • equation image

where image is the measured radar reflectivity for height zi. The equivalent radar reflectivity factor Ze is specified in units of mm6 m−3. To reduce the large dynamic range of the reflectivity variable and to make the model more linear, Ze has been converted to a logarithmic variable image by the transform image = 10 log Ze, where image has units of dBZ. Because ice particle attenuation is small (compared to attenuation by liquid particles), ice particle attenuation effects are neglected in the retrieval.

[23] The measurement error covariance matrix Sε gives a measure of the uncertainties in the measurement vector and of correlations between the errors of the individual elements. In the present retrieval, it is assumed that the elements of y have independent errors; therefore Sε takes the form of a diagonal matrix with elements image representing the standard deviations of the measured radar reflectivity factor in dBZ (i.e., the uncertainty in the measured radar reflectivity values from whatever source: noise, calibration error, etc.). In the intercomparison study discussed in section 4.1, image was set to a fixed value of 1.0 dBZ in all bins. In the CloudSat R04 retrievals, image varied according to the reflectivity to represent the large effect of noise on weak signals and the reduced effect on strong signals.

2.4.2. Forward Model

[24] The forward model F(x) relates the state vector x to the measurement vector y. F therefore has the same dimension as y,

  • equation image

where the individual elements are given by the following expression:

  • equation image

The subscript FM is a reminder that these quantities are calculated from elements of x according to the forward model equation (29), as opposed to the elements of the y vector, which are measured quantities.

2.4.3. A Priori Data and Covariance

[25] A priori data for the retrieval help prevent outliers in the solution and constrain the solution where the measurements cannot. The a priori vector xa is specified as follows:

  • equation image

We also specify an a priori error covariance matrix Sa,

  • equation image

where all the off-diagonal elements are set to zero. In all likelihood, there probably are correlations between the elements of the cloud column that should be represented in (31), but such information is less readily available than mean and variance statistics and was therefore not included, consistent with the Rodgers [2000] description of a maximum entropy retrieval in which the solution is constrained as little as possible consistent with the available parameters and avoiding issues of reliability and sampling of covariance data. The impact of omitting off-diagonal values from Sa was examined in a synthetic data case for a similar liquid water retrieval and was found to be minimal, but there are a number of ways that covariance information might be utilized, so this is a topic for future research.

[26] Adjustment of the a priori parameters xa and uncertainties Sa allows customization of the retrieval for different cloud types, generation regimes, and geographic areas (tropical, midlatitude, etc.). Initial tests of the current improved algorithm used the temperature-dependent expressions (1), (2), and (3) for the a priori values of the size distribution parameters. While this scheme worked in a large fraction of test cases, the retrieval was occasionally unable to converge. Closer inspection showed that the measured radar reflectivity in these cases differed markedly from the value associated with the a priori size distribution parameters characteristic to that temperature. For example, the a priori parameters corresponding to the temperature in a particular bin might imply a reflectivity of +15 dBZ, while the radar measurement was −25 dBZ, a difference of 40 dBZ. (The reflectivities corresponding to the individual samples of the microphysical database are shown in Figure 4, together with a curve representing the reflectivity corresponding to the distributions specified by the temperature-dependent parameter expressions (1), (2), and (3). The range of Ze values covered by a variation of ±1 standard deviation in each of the PSD parameters is also shown.)

image

Figure 4. Radar reflectivity factor values corresponding to the particle size distribution parameters plotted in Figure 2. The solid line represents the reflectivity obtained using the temperature-dependent expressions (1), (2), and (3) for the PSD parameters; the dashed line shows the range of Ze for ±1 standard deviation in each of the three parameters.

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[27] Obviously, the microphysical state of a cloud is dependent on factors other than temperature, such as the availability of moisture and ice nuclei and convective intensity. Because knowledge of the temperature alone cannot account for this wide variation in Ze, a procedure was adopted whereby the temperature-dependent expressions (2) and (3) were used to determine the a priori values of Dg and ω, but the a priori number concentration NTa was determined by a method taking advantage of a Ze-IWC relationship from Liu and Illingworth [2000]. (A similar technique was used in the previous retrieval.) Specifically, equations (9), (11), and (21) were combined and solved for NT,

  • equation image

The Liu and Illingworth [2000] expression for IWC was then used to write the IWC term in terms of Ze. A value of NT was then obtained for each cloudy bin using the prescribed Dga and ωa values, and these NT values were then averaged to obtain an NTa value for the column. In this way, both temperature and reflectivity information contribute to the selection of a priori values.

[28] A priori uncertainties (diagonal terms in (31)) were set to the standard deviations of the fits of the three distribution parameters given in (1), (2), and (3) and shown in Figure 2. The uncertainty of the width parameter was reduced by 50% to reduce the bias of the retrieval based on performance tests and following the example of Benedetti et al. [2003], which had a tightly constrained width parameter.

2.4.4. Convergence and Uncertainties

[29] The state vector equation image is obtained by iteration. The a priori values xa are used as the initial value of equation image. Convergence of the solution is determined using a test with the following form [Marks and Rodgers, 1993]:

  • equation image

where n is the dimension of the equation image vector (n = 3p) and Δequation image is the change in the state vector between two consecutive iterations. The error covariance matrix Sx of the retrieved state vector equation image is given by

  • equation image

Elements of the Sx matrix give the covariance between elements of the retrieved state vector equation image; diagonal elements of Sx are variances in the elements of equation image and give a measure of the uncertainty in the retrieval. For this retrieval, we specify the criterion for “much less than” in (33) such that

  • equation image

[30] Random error components in the derived quantities re, IWC, and IWP are given by the customary expressions of error propagation,

  • equation image
  • equation image
  • equation image

Analytical expressions for the partial derivatives are easily derivable from (9), (10), and (13). The variance and covariance terms are all available in the solution matrix Sx.

[31] The above expressions describe the random components of uncertainty in the retrieval output given the stated uncertainties in the inputs and the assumptions used in constructing the retrieval. Biases not accounted for in the retrieval formulation (systematic uncertainties) are discussed in section 5.

2.5. CloudSat 2B-CWC-RO Release 4

[32] The current algorithm served as the ice water content retrieval algorithm in version 5.1 of the CloudSat 2B-CWC-RO standard data product. This version first appeared in Release 4 (R04) of this product, which was released to the science community in October 2007.

[33] A number of assessments and comparisons of the R04 product have been completed. Some of these are described in section 4.

3. Differences From Previous Algorithm

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Retrieval Algorithm
  5. 3. Differences From Previous Algorithm
  6. 4. Algorithm Performance
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References

[34] The previous algorithm (used in the beta R03 CloudSat products and evaluated by Heymsfield et al. [2008]) was predecessor to the current algorithm and was similar in structure. There were three principal differences between the previous and current retrievals: the assumed form of the particle size distribution, the structure of the state vector, and the source of a priori data values.

[35] The previous algorithm followed Benedetti et al. [2003] in assuming a modified gamma distribution of ice crystals,

  • equation image

where NT is the ice particle number concentration, Γ represents the gamma function [Abramovitz and Stegun, 1974], D is the diameter of an equal-mass ice sphere, Dn is the characteristic diameter, and ν is the width parameter. (This form of the gamma distribution was selected because the quantities that are raised to powers or that are arguments to the exponential function are nondimensional ratios.) The various cloud properties (9) to (12) were therefore defined in terms of NT, Dn, and ν. A similar fMie correction was defined as by Benedetti et al. [2003].

[36] The state vector in the previous retrieval was more similar to that used by Benedetti et al. [2003] than to (26). While it contained all components of the particle size distribution, two of the components (NT and ν) were constrained to be height-invariant. The state vector was given by

  • equation image

where Dn(zi) is the characteristic diameter for height zi and NT and ν are the number concentration and distribution width parameter for the entire profile. The a priori vector xa and a priori covariance matrix Sa had a corresponding structure. The measurements vector y was unchanged in the previous retrieval.

[37] A priori values and uncertainties were less sophisticated in the previous retrieval in that they did not incorporate any dependence on temperature. The a priori characteristic diameter was set to 50 μm (log image = −1.301 ± 0.65) and the width parameter to νa = 2.0 ± 0.05, following Benedetti et al. [2003]. The a priori number concentration parameter was set using a procedure similar to that of the current retrieval in which the Ze-IWC relation of Liu and Illingworth [2000] was used to make the height-invariant parameter dependent on reflectivity with the intent of preselecting the proper region of the state space. An uncertainty of 20% was applied as a working value with good convergence characteristics.

4. Algorithm Performance

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Retrieval Algorithm
  5. 3. Differences From Previous Algorithm
  6. 4. Algorithm Performance
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References

[38] While there is no all-encompassing test of the performance of the two ice retrieval algorithms, several assessments and comparisons have been performed that give some insight.

4.1. Intercomparison Study

[39] Heymsfield et al. [2008] compared a number of ice cloud microphysical retrieval algorithms by using simulated remote sensing measurements (radar reflectivity, optical depth, Doppler velocity, etc.) generated from a large database of cloud probe data. Because the remote sensing data were directly based on the particle data, this method allowed various retrievals to be compared without complications owing to instrument sampling. It was also possible to examine the performance of the various retrievals as a function of associated variables, such as the magnitude of the reflectivity, the temperature, the ice water content, and the optical depth.

[40] The previous algorithm described in this paper was included in the Heymsfield et al. [2008] study (it was denoted as method “1a” in Table 2 of that study), but few results of that algorithm were shown in that paper because the related radar-visible optical depth (RVOD) retrieval was considered more advanced. (A corresponding 2B-CWC-RVOD product is planned for release in 2008, but that retrieval is outside the scope of this paper.) The current retrieval described in this paper was not considered in the Heymsfield et al. [2008] study, as it was not yet available.

[41] In order to have a common basis for comparison, the current and previous retrievals described in this paper were run on the same data sets used by Heymsfield et al. [2008]. Plots of the ratio of retrieved to measured IWC (r = IWCretr/IWCmeas) are shown in Figures 5, 6, 7, and 8, where the previous algorithm is denoted “R03” and the current is denoted “R04.” The plots show individual retrievals as small dots, with mean and standard deviation values for a given parameter range plotted as a large black dot and horizontal line, respectively.

image

Figure 5. Ratio of retrieved to measured IWC for data from the intercomparison study described by Heymsfield et al. [2008], plotted as a function of radar reflectivity Ze, for (a) the previous algorithm “R03” and (b) the current algorithm “R04.” Small points represent the individual measurements, while the circles and horizontal lines represent the mean and standard deviation of values in a given parameter range.

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image

Figure 6. As in Figure 5, but plotted as a function of IWC.

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image

Figure 7. As in Figure 5, but plotted as a function of temperature.

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image

Figure 8. As in Figure 5, but plotted as a function of optical depth.

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[42] Figures 58 show that the current algorithm (R04) generally performs better than the previous, but there are situations where the opposite is true. In Figure 5, the R04 algorithm is seen to have less low bias at low Ze values (ignoring Ze below the −30 dBZ minimum detectable signal of CloudSat) at a cost of more low bias at high Z values. In Figure 6, the R04 algorithm performance is more uniform overall and has less high bias for low IWC values. Figure 7 shows that both the R03 and R04 algorithms have biases at the highest and lowest temperatures, although the details are different. (This in spite of the fact that R04 uses temperature information.) Figure 8 shows that R04 has less bias at the extremes of optical depth, but perhaps more at intermediate values.

[43] Retrieval data from the intercomparison data sets were also used to examine the tendency of the retrieval to converge on the a priori data values, due to limited measurement information. For all successful R04 retrievals in these data sets, a normalized retrieval–a priori difference was calculated for each state vector element,

  • equation image

The mean normalized differences over the entire data set were determined to be equation imagelog image = 0.55, equation imagelog image = 0.23, and equation imageω = 0.33. From prior experience and familiarity with the state space, it was expected that the log Dg and log NT elements would show the largest departure from a priori values, because changes in measured reflectivity move the solution surface mostly along these coordinates in the solution space. The log Dg component's mean difference was indeed the largest, but the log NT component was the smallest, most likely owing to the use of the Ze-IWC relation to set the a priori value of NT. Note that none of the parameters had a mean difference of zero, as would result if the parameters simply took the a priori values.

4.2. Other Comparison Studies

[44] Results from the 2B-CWC-RO product are being compared to retrievals using other platforms and algorithms, ground-based retrievals, and modeling results in order to better understand the relationships between them. Wu et al. [2009] compare global statistics of cloud ice from the Microwave Limb Sounder (MLS), CloudSat R04 data, and other data. (A previous study [Wu et al., 2008] had compared MLS and CloudSat R03 data.) They find that the CloudSat R04 IWC values generally agree with alternative IWC retrievals using CloudSat reflectivities [Sayres et al., 2008; Hogan et al., 2006] (hereinafter S08 and H06, respectively) for IWC < 1000 mg m−3 but differ as IWC increases above this level, with H06 > R04 > S08. Comparing normalized probability functions (PDFs) of CloudSat and MLS IWC, Wu et al. [2009] find relative differences of less than 50% over the range where the instrument sensitivities overlap, but CloudSat R04 IWC exceeds MLS IWC in the 14- to 17-km zone. Wu et al. [2009] also include comparisons to ECMWF, GEOS, ARM, CRYSTAL-FACE, and CEPEX data.

[45] Turning to ice water path (IWP), Wu et al. [2009] find that MODIS and AMSU-B show a high bias compared to CloudSat R04 for values between 10 and 500 g m−2. Comparisons of CloudSat partial IWP statistics against MLS IWP values from specific channels show generally good agreement over ranges of overlapped sensitivity. Many of these comparisons are summarized schematically in Figure 9 for IWC and Figure 10 for IWP; refer toWu et al. [2009] for details and comparisons based on location.

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Figure 9. Schematic summary of comparisons of CloudSat IWC retrieval algorithm to other algorithms and instruments as reported by Wu et al. [2009] and Eriksson et al. [2008] (italicized labels). Solid bars indicate comparable results, while hatched bars indicated markedly different results for ice water path from the top of the atmosphere down to the altitude indicated by a given bar.

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image

Figure 10. Schematic summary of comparisons of CloudSat IWP retrievals to other algorithms and instruments as reported by Wu et al. [2009] and Eriksson et al. [2008] (italicized labels). Solid bars indicate comparable results, while hatched bars indicated markedly different results.

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[46] Eriksson et al. [2008] compare partial ice water columns retrieved by CloudSat, MLS, and Odin-SMR retrievals and find that CloudSat R04 partial IWP values exceed those of both MLS and Odin-SMR. Agreement of the distribution of measured values is better at partial IWP values below 100 g m−2. SMR results can be brought much closer to those from CloudSat R04 by the use of a cloud inhomogeneity correction, although the R04 values remain higher. Eriksson et al. [2008] also examined the effect of differing particle size distribution representations by applying methodologies based on work by Liu and Illingworth [2000] (LI00) and McFarquhar and Heymsfield [1997] (MH97) to CloudSat radar reflectivities; they found that CloudSat R04 results were comparable to LI00 and MH97 at 11 km, but the PDFs showed that R04 > MH97 > LI00 at higher altitudes. These results are included in the schematic summaries in Figures 9 and 10.

[47] An additional investigation [Woods et al., 2008] has examined the previous and current retrievals (used in the CloudSat R03 and R04 products) by applying the algorithm to profiles of simulated clouds generated by a cloud-resolving numerical model. The study shows the sensitivities of the retrievals to assumptions of various properties of the ice particles (e.g., shape, density) and showed how known dependencies of these properties might be utilized to improve the retrieval.

5. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Retrieval Algorithm
  5. 3. Differences From Previous Algorithm
  6. 4. Algorithm Performance
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References

[48] The current retrieval algorithm (section 2) was implemented as the ice retrieval algorithm in the CloudSat 2B-CWC-RO product beginning with Release 4 (R04) in October 2007. Since that time, R04 2B-CWC-RO data have been processed and released for the entire mission to date (mid-June 2006 to mid-August 2008), with a given product file generally available within two weeks of the satellite observation (and often within one week). The store of available data is now of sufficient length to allow some analysis of statistics.

5.1. Liquid-Ice Partition

[49] Before reporting statistical results of retrieved ice water content, it is necessary to explain the liquid-ice partition that is employed in the 2B-CWC-RO product. The original list of CloudSat standard data products included separate products for liquid water content and ice water content. Because there was no independent means of determining the cloud phase in any given radar resolution bin, the plan was to run the liquid and ice retrievals separately on the entire radar profile, resulting in a set of liquid microphysical parameters for each cloudy bin and a corresponding set of ice microphysical parameters for each cloudy bin. The user would then select which answer would be more appropriate or combine the two in some way. No attempt would be made to partition the measured reflectivity between the liquid and ice phases: each solution would assume the entire radar signal was due to a single phase of water.

[50] As the retrievals were further developed and the time approached for the first postlaunch data releases, it became clear that this approach would be overly confusing and would likely result in “double counting” of the cloud water content: users interpreting each cloudy bin as containing both liquid and ice water content. To avoid this confusion, a new combined cloud water content product (2B-CWC) and algorithm were developed. In the new algorithm, the liquid and ice retrievals are run separately on the entire radar profile (as before, although the portion of the cloud warmer than 1°C was omitted from the ice retrieval in R04 because the temperature-dependent a priori data values do not make sense for warmer clouds), but the two resultant profiles are then combined into a composite profile using a simple scheme based on temperature. In this scheme, the portion of the profile cooler than −20°C is deemed pure ice, so the ice retrieval solution applies there. Similarly, the portion of the profile warmer than 0°C is considered pure liquid, so the liquid solution applies there. In between these temperatures, the ice and liquid solutions are scaled linearly with temperature (by adjusting the ice and liquid particle number concentrations) to obtain a profile that smoothly transitions from all ice at −20°C to all liquid at 0°C while matching the radar measurements over the whole range.

[51] This scheme gives a very basic partition of the radar measurements into ice and liquid phases. The 2B-CWC-RO data product files contain both the composite profiles (which most users will want to use) and the single-phase retrieval profiles (which may be of interest to some investigators). The output data from the R04 ice cloud retrieval from section 2 (which interprets all cloud as ice from the +1°C contour to the stratosphere) is found in fields with names starting with IO_RO_ (for “ice-only” and “radar-only”). Corresponding outputs from the liquid cloud retrieval have names starting with LO_RO_. The fields representing the combination of these into composite profiles have names beginning with RO_ice_ and RO_liq_; the statistics presented in this section are based on these composite profiles unless noted otherwise.

5.2. Sensitivity

[52] The range of detectable IWC values is a function of the radar parameters and the data processing procedure. For CloudSat, the minimum detectable reflectivity is approximately −30 dBZ, which corresponds to an ice water content of roughly 1–5 mg m−3, depending on the particle size distribution parameters (ignoring variations within a radar resolution bin). Bins with radar signals near the noise floor may or may not be included in retrieval calculations depending on the cloud mask value assigned in the 2B-GEOPROF product [Mace et al., 2007].

[53] The upper limit of retrieved IWC has not been determined. As particle size increases, radar scattering at the CPR wavelength moves into the Mie scattering regime, reducing the magnitude of the measured Ze. CloudSat data contain very few instances of Ze > 20 dBZ, and PDFs of Ze show a noticeable downturn above 15 dBZ [e.g., see Wu et al., 2009]. Particles of large size violate the assumed PSD but are partially compensated for by the fMie correction. Further research is necessary to establish the accuracy of retrieved IWC for very high Ze values.

5.3. Geographic Distribution

[54] Figure 11 shows 3-month averages of R04 IWP for all cloud types. Individual profile values were averaged over 2° × 2° latitude/longitude boxes, with most boxes having over 2000 profiles during the 3-month period (and none having fewer than 880). The seasonal dependence is perhaps most visible over southern Africa and South America between 0° and 30° south latitude.

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Figure 11. Maps of average CloudSat 2B-CWC-RO (R04) ice water path (IWP) including all cloud types for four 3-month seasonal periods. Grid boxes measure 2° latitude by 2° longitude.

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[55] Figure 12 shows a different mapping of IWP data. The eight data maps show the mean IWP for the 12-month period December 2006 to November 2007, partitioned into the eight cloud types reported in the CloudSat 2B-CLDCLASS product. (The 2B-CLDCLASS assigns a cloud type to each cloudy radar bin, so clouds in a single radar profile may be partitioned into several types, contributing to several different IWP maps.) These distributions provide rich information about the distribution of ice in the atmosphere and the types of clouds that define these distributions. The largest IWP values are associated with altostratus, nimbostratus, and deep convective clouds with the heaviest burdens occurring in regions of convection and midlatitude storm tracks associated with synoptic weather systems. The contribution by cirrus clouds to the global ice amount is small.

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Figure 12. Maps of average CloudSat 2B-CWC-RO (R04) ice water path (IWP) for the 12-month period starting in December 2006, sorted according to the 2B-CLDCLASS cloud type. Grid boxes measure 2° latitude by 2° longitude. (Note the change in scale for the last two categories.)

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5.4. Systematic Errors

[56] The uncertainty values reported in the 2B-CWC-RO data products (described in section 2.4.4) describe the random components of uncertainty in the various retrieval outputs (those that may be reduced by averaging) given the stated uncertainties in the inputs and the assumptions used in constructing the retrieval. Biases or systematic errors are not included in these values, but are likely to be the dominant component of uncertainty in global statistics of ice mass due to the large number of samples being averaged. Because the systematic error is due to factors unaccounted for in the retrieval formulation, it can only be estimated by independent evaluations of the bias in the retrieved values.

[57] The comparison studies discussed in section 4 were considered as sources of information for an estimate of the bias of the R04 algorithm. Two of the studies [Eriksson et al., 2008; Wu et al., 2009] compared CloudSat data with other remote sensing retrievals and were therefore considered more useful as consistency checks and illustrations of the differences between algorithms, because they do not provide an absolute measurement for comparison. The other study, the algorithm intercomparison described by Heymsfield et al. [2008], seemed more useful as a quantitative reference. In that study, a variety of cloud probe data were used to generate simulated remote sensing measurements. Remote sensing retrievals were then performed on the simulated measurements, and the retrieval outputs could then be compared directly to the original cloud fields used to generate the simulated measurements, avoiding the sampling issues (mismatch of in situ and remote sensing data) that make validation so challenging. While this technique still has assumptions and limitations of its own, it seems the best available source of information on retrieval biases until other validation studies become available.

[58] Results of the Heymsfield et al. [2008] process were discussed in section 4.1. The mean values of the ratio r of retrieved to measured IWC in Figures 5, 6, 7, and 8 show the estimated bias over the ensemble of retrievals as a function of various variables. Most of the mean values are inside the indicated ±25% range for the R04 retrieval, but a few do exceed this range. On this basis, it was felt that a conservative estimate would place the bias for a given measurement at 40% or less. Obviously this value is somewhat subjective, but it at least provides some basis for the calculation of uncertainties until more extensive validation studies are performed.

5.5. Global Statistics

[59] Various global statistics of IWP are given in Figures 1315. In Figure 13, the mean global IWP over the 12-month period December 2006 to November 2007 is partitioned (on a bin-by-bin basis) into the eight cloud types reported by the CloudSat 2B-CLDCLASS product (Figure 13, top) and as nonconvective, convective, and total IWP (Figure 13, bottom), where the convective category includes 2B-CLDCLASS types “cumulus” and “deep convection,” and the nonconvective includes everything else. (It should be noted that CloudSat does not sample clouds poleward of roughly 82° latitude, so this “global” average omits a small region around each pole. CloudSat also does not sample the diurnal cycle, because it is in a sun-synchronous orbit.) Each of these values are averages of hundreds or thousands of individual profiles, resulting in random uncertainties that are miniscule owing to averaging. The error bars are therefore solely due to the assumed systematic uncertainty of 40% that propagates from the individual profile right up to the global mean. Statistics like these are of particular interest for comparisons to global climate models [Stephens et al., 2008].

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Figure 13. Global Mean IWP from the 2B-CWC-RO (R04) product over the 12 months from December 2006 to November 2007, partitioned (top) into the eight 2B-CLDCLASS cloud types and (bottom) into categories of convective (cumulus and deep convection) and nonconvective (all other types), together with the sum of the two (lower panel). Error bars show the estimated systematic uncertainty.

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Figure 14. Global mean IWP from the 2B-CWC-RO (R04) product over the 12-month period from December 2006 to November 2007, partitioned into temperature ranges for individual seasons and the full year (all cloud types).

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Figure 15. Global mean IWP from the 2B-CWC-RO (R04) product over the 12-month period from December 2006 to November 2007, partitioned into temperature ranges, for the top three cloud types by mass (altostratus, nimbostratus, and deep convection).

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[60] The IWP statistics can also be shown as a function of temperature using the ECMWF model temperature data used in CloudSat processing (the CloudSat ECMWF-AUX product). Because an ECMWF temperature may be assigned to each radar bin containing cloud, we can partition the integrated ice water content into temperature ranges instead of cloud types. Figure 14 shows global mean IWP as a function of temperature for the same 12-month period and also for seasonal 3-month periods during the same year. The temperature distribution seems to have little seasonal variation at the global scale. It must be noted that the rapid falloff between −20° and 0°C is at least in part due to the partitioning of the radar backscatter between the liquid and ice phases, as described in section 5.1.

[61] Figure 13 confirmed that the majority of atmospheric ice mass is classified by 2B-CLDCLASS as altostratus, nimbostratus, and deep convection (also implied by Figure 12). Figure 15 shows the distribution of ice in these three types as a function of temperature for the same 12-month period considered above.

5.6. Comparison to Ze-IWC Relations

[62] Many if not most radar remote sensing retrievals of ice water content [e.g., Liu and Illingworth, 2000; Sassen et al., 2002; Heymsfield et al., 2005; Sayres et al., 2008] use a Ze-IWC relation in the form of a power law,

  • equation image

It is therefore logical to ask what form the Ze-IWC relation takes in the retrievals described in this paper. The answer is that neither the previous nor the current algorithms described here take a single expression of form given by (42). This is best illustrated (for the R04 case) by combining (9), (11), and (21) and solving for IWC,

  • equation image

If NT and ω were fixed to assigned values, then (43) would come close to the form of (42). (The fMie term would still complicate matters somewhat.) In the current retrieval algorithm, however, NT and ω (and Dg) are variable, being partially determined by a priori values that are themselves functions of temperature and (for NT) reflectivity. As a consequence, the relation between Ze and IWC cannot be written in the form of (42).

[63] In the absence of a simple Ze-IWC relation, it is instructive to plot the distribution of data points on a Ze-IWC scatter plot. Figure 16 shows scatter plots for one orbit (3229 on 6 December 2006) of 2B-CWC-RO (R04) data, one for each 2B-CLDCLASS cloud type. The horizontal coordinate of each point is the radar reflectivity Ze corrected for gaseous attenuation (both quantities are available in the 2B-GEOPROF product). The red points represent the IWC value retrieved by the R04 algorithm assuming ice only (the IO_RO_ice_water_content field of 2B-CWC-RO), while the black points represent the IWC after the LWC-IWC temperature-based partition (which only affects points warmer than −20°C). Ze-IWC relations from four other studies [Liu and Illingworth, 2000; Sassen et al., 2002; Heymsfield et al., 2005; Sayres et al., 2008] are overlaid as lines on the data. The data take discrete values in the vertical coordinate because the 2B-CWC-RO product reports IWC to a precision of 1 mg m−3.

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Figure 16. Scatterplot of a single granule of 2B-CWC-RO (R04) ice water content versus 2B-GEOPROF (R04) radar reflectivity factor plus gaseous attenuation correction, sorted according to 2B-CLDCLASS cloud type. Ze-IWC relations from four other studies [Liu and Illingworth, 2000; Sassen et al., 2002; Heymsfield et al., 2005; Sayres et al., 2008] are overlaid on each plot. Red points represent the solution of the R04 ice-only retrieval; black points are the final values reported following the IWC-LWC partition. (As and Ns are sampled to reduce number of points.)

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[64] The plots in Figure 16 show how a single value of radar reflectivity maps to a range of possible IWC values, owing to the factors cited earlier. They also illustrate how R04 values are often higher (particularly for low IWC values) than those prescribed by the displayed Ze-IWC relations. (For example, cirrus values of R04 are often greater than those predicted by Liu and Illingworth [2000], as reported above 14 km in Figure 9.) The R04 values in red do seem to roughly span the range of IWC values predicted by the different Ze-IWC relations, although they exceed the range both below and above.

[65] Figure 17 shows a compilation Ze-IWC plot for all cloud types for the same orbit as Figure 16 in which the data points are stratified by temperature. Figure 17 (top) shows the ice-only retrieval solutions, while Figure 17 (bottom) gives the same cases following the LWC-IWC partition. It should be noted that each temperature range is plotted successively from coldest to warmest, so some of the colder points are hidden behind the warmer points. For purposes of comparison, contours of Ze-IWC for temperatures ranging from −60°C to −10°C from a temperature-dependent Ze-IWC relation from Hogan et al. [2006] are overlaid on Figure 17 (top). Again, the plot confirms some of the differences between the R04 and Hogan et al. [2006] results in Figure 9.

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Figure 17. Scatterplot of a single granule of sampled 2B-CWC-RO (R04) ice water content (all cloud types) versus 2B-GEOPROF (R04) radar reflectivity factor plus gaseous attenuation correction, in which each point is color-coded according to the ECMWF model temperature. Ze-IWC relations from Hogan et al. [2006] are overlaid for six different temperatures. (top) Solution of the R04 ice-only retrieval. (bottom) Final values reported following the IWC-LWC partition.

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6. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Retrieval Algorithm
  5. 3. Differences From Previous Algorithm
  6. 4. Algorithm Performance
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References

[66] A new remote sensing retrieval of ice cloud microphysics has been developed for use with millimeter-wave radar from ground-, air-, or space-based sensors. Developed from an earlier retrieval that used measurements of radar reflectivity factor together with a priori information about the likely cloud targets, the new retrieval includes temperature information as well to assist in determining the correct region of state space, particularly for those size distribution parameters that are less constrained by the radar measurements. Both retrievals are cast in an optimal estimation framework and may be considered as descendants of the algorithm reported by Benedetti et al. [2003]. The previous and current algorithms described in this paper have served as the ice cloud retrieval algorithms in Releases 3 and 4 (respectively) of the CloudSat 2B-CWC-RO Standard Data Product. Release 3 was a provisional product released on a limited basis; Release 4 was produced for the entire mission and is the current version at the time of this writing.

[67] Several comparison studies have been performed on the previous and current retrieval algorithms: some involving tests of the algorithms on simulated radar data (based on actual cloud probe data or cloud resolving models) and others featuring statistical comparisons of the R04 2B-CWC-RO product to ice cloud mass retrievals by other spaceborne, airborne, and ground-based instruments or alternative algorithms using the same CloudSat radar data. Comparisons involving simulated radar data based on a database of cloud probe data showed generally good performance with bias errors estimated to be less than 40%. Comparisons to ice water content and ice water path estimates by other instruments are mixed, with the R04 CloudSat results sometimes lower but more often higher than other platforms, although the relative comparison changes with altitude, temperature, ice water content, and other factors. When the comparison is restricted to different retrieval approaches using the same CloudSat radar measurements, the various approaches sometimes are comparable and sometimes take a spread of values: sometimes the R04 results are at one extreme of the spread, and sometimes they are in the middle. Validation and reconciliation of all these approaches will continue to be a topic for further research. One area of particular emphasis for the retrievals described in this paper will be potential improvement by more accurate a priori data and uncertainties.

[68] CloudSat Release 4 2B-CWC-RO data (using the second algorithm) were released to the community in October 2007. Data are available for the entire mission from June 2006 to date (27 months so far), allowing statistical analysis of measurements through a complete annual cycle. A sample of such analyses are included in the present paper.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Retrieval Algorithm
  5. 3. Differences From Previous Algorithm
  6. 4. Algorithm Performance
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References

[69] This research was supported by the Office of Science (BER), U. S. Department of Energy, grants DE-FG02-05ER63961 and DE-FG03-94ER61748, and by NASA grant NAG5-13640.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Retrieval Algorithm
  5. 3. Differences From Previous Algorithm
  6. 4. Algorithm Performance
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References