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  • View in gallery

    The ZeS relations for nonspherical ice particle models from Hong (2007), Kim et al. (2007), and Liu (2008b). The various colors indicate the following ice models: Liu (2008b) columns (LC1, LC2, and LC3), plates (LP1 and LP2), rosettes (LR3–LR6), and sector (LSS) and dendritic (LDS) snowflakes; Hong (2007) columns (HC1 and HC2), plates (HP), six-bullet rosettes (HR6), aggregates (HA), and droxtals (HD); and Kim et al. (2007) columns (KC), four-arm (KR4) and six-arm (KR6) rosettes. For each snow rate and ice model, corresponding radar reflectivities are calculated for an assumed temperature of −5°, −10°, and −15°C using the Field et al. (2005) ice PSD parameterization and are indicated by different symbols (plus sign, diamond, or asterisk) for each ice particle. A best-fit (black line) and corresponding 1-σ uncertainties (blue and red lines) are then determined based on these data points. Throughout the text, these three relationships will be referred to as upper, average, and lower ZeS relationships.

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    Normalized count of number of snow cases falling in each 1-dBZe bin, comparing the use of attenuation correction (dotted line) with the uncorrected method (solid line). The histogram includes about 6.1 × 106 cases and includes data from the entire CloudSat orbit (maximum latitude 81.8°), for the period July 2006–June 2007.

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    (a) CPR radar reflectivity, (b) CPR-derived IWP (black line; kg m−2) and CPR-derived (or AMSR-E in precipitating regions) LWP (gray line; kg m−2, and (c) two-way total columnar attenuation (dB) for a snowfall case in the southern Pacific Ocean.

  • View in gallery

    Reference plot for interpreting the difference plots presented below. Values are for the average ZeS relationship, with no vertical continuity test, a −10-dBZe threshold, and the use of attenuation correction. (top) The snow frequency (precisely, the percent of total CloudSat profiles in each bin considered to be snowing), and (bottom) the mean liquid equivalent snow rate (mm day−1).

  • View in gallery

    Difference in mean snow rate due to attenuation correction (mm day−1) (using average ZeS relationship, no vertical continuity test, and −10-dBZe threshold) for the (right) Northern and (left) Southern Hemispheres.

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    Normalized histogram (bin size of 0.01 mm) of AMSR-E derived LWP for precipitation cases with 2-m temperature less than 4°C (solid line), snowfall cases (surface temperature <0°C; dotted line), all mixed-precipitation cases (0°–4°C; dashed line), and all snow cases in the Southern Ocean latitude belt (66°–45°S; dash–dotted line). Only over-ocean and inland water cases are considered, and cases with LWP of greater than 0.5 mm were rejected for reasons of sea ice contamination.

  • View in gallery

    (top) Zonally averaged snowfall frequency. (bottom) Zonally averaged mean snow rate (mm day−1) for average ZeS relationship (thick line), with the uncertainty range as given by the upper and lower ZeS relationships shaded. Averages include a full year of data (cold and warm seasons).

  • View in gallery

    Difference in (top) snow frequency and (bottom) mean snow rate (mm day−1) due to vertical continuity (no test minus with test) for the (right) Northern and (left) Southern Hemispheres.

  • View in gallery

    As in Fig. 8, but differences are due to the choice of reflectivity threshold (−15-dBZe threshold minus −10-dBZe threshold).

  • View in gallery

    The method details discussed in sections 4a (dashed line), 4c (solid line), and 4d (dotted line) are compared by zonally averaging the effect of each. (top) The three effects are shown in terms of snow frequency (%). (bottom) The three effects are shown in terms of mean snow rate (mm day−1).

  • View in gallery

    Ratio of the number of profiles with near-surface mixed precipitation (2-m temperature of 0°–4°C) to the number of profiles with snow (<0°C) for the (right) Northern and (left) Southern Hemispheres. Bins with ratios that are greater than 1 are colored red, and bins with ratios equal to 0 are white.

  • View in gallery

    (bottom) For each 2-dBZe × 2-K bin, AMSR-E-derived LWP from all over-ocean and inland water precipitation cases is averaged to produce a mean LWP for that bin. Precipitation cases with LWP of more than 0.5 mm were excluded for reasons of sea ice contamination. The green vertical line is the freezing point, the red horizontal line is at approximately the most significant reflectivity in terms of frequency of occurrence (0 dBZe), and the blue horizontal line is at approximately the most significant point in terms of snowfall accumulation (6 dBZe). (top) Similar to the bottom panel, but showing the number of precipitation cases in each bin divided by 1000.

  • View in gallery

    Map of Canada showing locations of surface stations referenced in section 4g and its associated figures.

  • View in gallery

    For winter 2006/07, the total liquid equivalent snowfall is shown for 17 Canadian surface stations. The black columns show the observed snowfall total from the Canadian National Climate Data and Information Archive. The darkest-, medium-, and lightest-shaded areas represent the lower, average, and upper ZeS relationships, respectively, of CloudSat-derived snowfall accumulation totals (averaged over a 200 km × 200 km bin centered on each station) for the same time period.

  • View in gallery

    (top) For YRB, the monthly total percent of precipitating profiles (i.e., profiles meeting reflectivity criteria but with any surface temperature) containing mixed precipitation (ECMWF 2-m temperature of 0°–4°C; black circles) and snow (<0°C; gray circles). (second from top) Similar to Fig. 14 but showing the monthly breakdown (July–June) for YRB. (middle two panels) As in top two panels, but for YYZ. (bottom two panels) As in top two panels, but for YYT.

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Uncertainty Analysis for CloudSat Snowfall Retrievals

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  • 1 Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin
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Abstract

A new method to derive radar reflectivity–snow rate (ZeS) relationships from scattering properties of different ice particle models is presented. Three statistical Ze–i relationships are derived to characterize the best estimate and uncertainties due to ice habit. The derived relationships are applied to CloudSat data to derive near-surface snowfall retrievals. Other uncertainties due to various method choices, such as vertical continuity tests, the near-surface reflectivity threshold used for choosing snowfall cases, and correcting for attenuation, are also explored on a regional and zonally averaged basis. The vertical continuity test in particular is found to have interesting regional effects. Although it appears to be useful for eliminating ground clutter over land, it also masks out potential lake-effect-snowfall cases over the Southern Ocean storm-track region. The choice of reflectivity threshold is found to significantly affect snowfall detection but is insignificant in terms of the mean snowfall rate. The use of an attenuation correction scheme can increase mean snowfall rates by ∼20%–30% in some regions. The CloudSat-collocated Advanced Microwave Scanning Radiometer (AMSR)-derived liquid water path is also analyzed, and significant amounts of cloud liquid water are often present in snowfall cases in which surface temperature is below freezing, illustrating the need to improve the arbitrary model-derived surface temperature criterion used to select “dry” snowfall cases. Precipitation measurements from conventional surface weather stations across Canada are used in an initial attempt to evaluate CloudSat snowfall retrievals. As expected, evaluation with ground-based data is fraught with difficulties. Encouraging results are found at a few stations, however—in particular, those located at very high latitudes.

Corresponding author address: Michael J. Hiley, Dept. of Atmospheric and Oceanic Sciences, University of Madison—Wisconsin, 1225 W. Dayton St., Madison, WI 53706. Email: hiley@wisc.edu

Abstract

A new method to derive radar reflectivity–snow rate (ZeS) relationships from scattering properties of different ice particle models is presented. Three statistical Ze–i relationships are derived to characterize the best estimate and uncertainties due to ice habit. The derived relationships are applied to CloudSat data to derive near-surface snowfall retrievals. Other uncertainties due to various method choices, such as vertical continuity tests, the near-surface reflectivity threshold used for choosing snowfall cases, and correcting for attenuation, are also explored on a regional and zonally averaged basis. The vertical continuity test in particular is found to have interesting regional effects. Although it appears to be useful for eliminating ground clutter over land, it also masks out potential lake-effect-snowfall cases over the Southern Ocean storm-track region. The choice of reflectivity threshold is found to significantly affect snowfall detection but is insignificant in terms of the mean snowfall rate. The use of an attenuation correction scheme can increase mean snowfall rates by ∼20%–30% in some regions. The CloudSat-collocated Advanced Microwave Scanning Radiometer (AMSR)-derived liquid water path is also analyzed, and significant amounts of cloud liquid water are often present in snowfall cases in which surface temperature is below freezing, illustrating the need to improve the arbitrary model-derived surface temperature criterion used to select “dry” snowfall cases. Precipitation measurements from conventional surface weather stations across Canada are used in an initial attempt to evaluate CloudSat snowfall retrievals. As expected, evaluation with ground-based data is fraught with difficulties. Encouraging results are found at a few stations, however—in particular, those located at very high latitudes.

Corresponding author address: Michael J. Hiley, Dept. of Atmospheric and Oceanic Sciences, University of Madison—Wisconsin, 1225 W. Dayton St., Madison, WI 53706. Email: hiley@wisc.edu

1. Introduction

Active spaceborne snowfall observations on a near-global basis have been possible since the launch of CloudSat (Stephens et al. 2002) and its W-band Cloud Profiling Radar (CPR; Tanelli et al. 2008) in 2006. The CPR’s sampling capabilities are somewhat limited by its fixed, near-nadir scanning strategy, but it has nonetheless provided the first active observations of snowfall in many remote, higher-latitude locations. Furthermore, the CPR’s excellent sensitivity allows it to observe very light snowfall events that commonly occur at higher latitudes. The CPR also provides useful snowfall information over most land (with the possible exception of complex terrain) and ice-covered surfaces that complicate passive-only snowfall retrievals. Numerous investigations have already been undertaken that demonstrate the feasibility and utility of CloudSat observations to study snowfall (e.g., Hudak et al. 2008; Liu 2008a; Matrosov et al. 2008; Kulie and Bennartz 2009), although active microwave snowfall retrievals—especially retrievals based on single frequencies—are currently hindered by various complexities, including 1) properly modeling the backscattering properties of a potentially diverse population of ice habits associated with snowfall events, 2) accurately characterizing the snowflake particle size distribution, 3) developing enhanced tools to better discriminate rain versus snow (or mixed precipitation) events, 4) improving absorption and scattering models of partially rimed and melting snow, and 5) validating snowfall retrievals with robust, independent measurements.

Despite the complications associated with CloudSat snowfall retrievals, innovative work on this topic has recently been accomplished. For instance, Liu (2008a) provided a first look at near-global snowfall distribution using CloudSat data. The retrieval method adopted by Liu (2008a) was derived through relationships between 94-GHz radar reflectivities and the snow rate (ZeS relationship) based on a least squares fitting of three nonspherical modeled snowflake shapes from Liu (2004, 2008b). By choosing a near-surface CloudSat radar bin and utilizing collocated European Centre for Medium-Range Weather Forecasts (ECMWF) temperature data, Liu (2008a) identified potential snowfall cases based on specific surface temperature and reflectivity threshold criteria. Then, for each snowfall case the near-surface CloudSat-observed radar reflectivity was converted to a snowfall rate using the previously determined ZeS relationship. When applied to the first year of CloudSat data (July 2006–June 2007), the result was a unique census of snowfall frequency, intensity, and typical vertical profiles of reflectivity related to snowfall events. Liu (2008a) also evaluated CloudSat-generated results for snowfall accumulations averaged over a large swath of Canada and found general agreement between historical surface observations and CloudSat-derived snowfall totals on an annual basis.

Kulie and Bennartz (2009) also similarly converted near-surface CloudSat reflectivities to snowfall rates for the first year of CloudSat data using ZeS relationships study reflectivity distributions associated with snowfall. A summary of key differences in method between Kulie and Bennartz (2009) and Liu (2008a) will be presented in section 3. Kulie and Bennartz (2009) also developed a proxy dual–frequency precipitation radar snowfall dataset that demonstrated potential snowfall detection efficacies of dry snowfall that could be expected for the upcoming Global Precipitation Measurement mission.

In an attempt to guide future snowfall retrieval improvements using spaceborne cloud radars, this work will highlight the implications of key differences in method in Liu (2008a) and Kulie and Bennartz (2009). The intention of this study is not to assess what method is most appropriate or correct but rather to highlight and quantify the uncertainties associated with snowfall retrievals that are evident due to the underlying methods employed in these previous studies. Furthermore, interesting scientific issues arise when the sensitivity of the results to certain methodological parameters is tested, and such issues will be highlighted in this study. In addition, to better investigate the sensitivity of retrievals to the ice particle model used as a proxy for snowflakes, a new scheme to derive ZeS relationships will be introduced. This scheme allows for the inclusion of all shapes from the Hong (2007), Kim et al. (2007), and Liu (2008b) backscattering databases, thus providing improved uncertainty ranges for derived snowfall rates due to uncertainty in the scattering properties of the assumed snowflake shape. An attenuation correction scheme for CloudSat radar reflectivity will be introduced and applied to the above method, allowing an initial study of the impact of attenuation on the ability to observe near-surface snowfall with the CloudSat 94-GHz radar.

Snowfall accumulation data for the winter of 2006/07 from various Canadian surface observation sites will be compared with CloudSat-derived snowfall amounts to expand upon the comparison with historical snowfall observations presented in Liu (2008a). The various issues involved in comparing surface snowfall measurements with CloudSat data will be discussed.

2. Data

This study utilized the level-2B cloud geometrical profile (2B-GEOPROF), level-2B radar-only combined water content (2B-CWC-RO), level-2C precipitation column (2C-PRECIP-COLUMN), and ECMWF auxiliary data (ECMWF-AUX) CloudSat products that are available from the CloudSat Data Processing Center (see online at http://www.cloudsat.cira.colostate.edu/). Vertical profiles of CPR radar reflectivity factor at 240-m range bins were obtained from the 2B-GEOPROF product, and useful auxiliary data—such as collocated liquid water path (LWP) and water vapor path retrievals from the Advanced Microwave Scanning Radiometer–Earth Observing System (AMSR-E); vertical profiles of model-generated pressure, temperature, and humidity; and cloud ice/water content retrievals from the CPR data—were taken from the 2C-PRECIP-COLUMN, ECMWF-AUX, and 2B-CWC-RO products, respectively. Detailed documentation of these products can be obtained from the CloudSat Data Processing Center. Further information about how these products are incorporated in this study will be provided in subsequent sections.

3. Methods

The method used to develop a CloudSat snowfall dataset in this study largely follows Kulie and Bennartz (2009), although note that the latitudinal boundaries in this study are extended to the maximum allowed by the orbit of CloudSat (81.8°N/81.8°S), which is higher than what was chosen by Kulie and Bennartz (2009). The method of Kulie and Bennartz (2009) differed from Liu (2008a) in several ways that emphasize the inherent uncertainty associated with snowfall retrievals using CloudSat data. The following is a summary of those differences:

  1. Choice of near-surface bin: Liu (2008a) considered the near-surface bin to be the fifth bin above the surface bin (as specified by the official CloudSat product) for ocean profiles and to be the sixth bin for land profiles. Kulie and Bennartz (2009) simply chose the sixth bin as the near-surface bin (∼1.3 km above the ground).

  2. Reflectivity threshold: In choosing snow profiles, Kulie and Bennartz (2009) required a near-surface reflectivity of −15 dBZe for snowfall cases; Liu (2008a) required −10 dBZe.

  3. Vertical continuity test: In an attempt to exclude nonprecipitating cloud and reduce ground clutter contamination, Kulie and Bennartz (2009) included an ad hoc requirement that the reflectivity must exceed −15 dBZe in the five bins above the near-surface bin for a profile to be considered as snowing.

  4. Particle size distribution: Liu (2008a) used exponential particle size distributions (PSD) from previous snowfall observations to derive ZeS relationships, whereas Kulie and Bennartz (2009) computed the PSD for a range of snowfall rates by using the Field et al. (2005) ice PSD parameterization.

  5. Temperature threshold: Liu (2008a) required a snowfall case to have an ECMWF 2-m temperature below 2°C. This criterion was based on land- and ship-based observations that showed approximately one-half of the precipitation at this temperature to be solid. Kulie and Bennartz (2009) reduced this threshold to 0°C so as to consider only “dry snowfall,” in an attempt to better match the ice particle models used and to reduce the overestimation of snowfall rates due to brightband effects from partially melted precipitation.

  6. Snowflake shapes used in ZeS derivation: Kulie and Bennartz (2009) considered an additional ice particle backscattering database from Hong (2007), as well as Liu (2008b). To investigate the sensitivity of these results due to snowflake shape, three ice particle models that serve as possible proxies for snowflakes were chosen for the analysis—aggregates from Hong (2007), a three-bullet rosette from Liu (2008b), as well as a spherical snowflake model from Surussavadee and Staelin (2006).

Section 4 will discuss the implications and regional effects of several of these choices of method.

A new piece of methodology in this study is the use of a different scheme for deriving ZeS relationships. Kulie and Bennartz (2009) utilized three different ice particle models from Surussavadee and Staelin (2006), Hong (2007), and Liu (2008b), combined with the Field et al. (2005) ice PSD, to generate ZeS relationships and to study the uncertainty in snowfall retrievals due exclusively to the assumed ice particle shape. Instead of selecting individual ice particle models, though, this study defines an average ZeS relationship based on almost 20 nonspherical ice particle models. For a given array of input snowfall rates, radar reflectivity is calculated for each ice particle shape using the modeled backscatter properties from Kim et al. (2007; hexagonal columns and rosettes), Hong (2007; plates, columns, rosettes, aggregates composed of bullets, and droxtals), and Liu (2008b; plates, columns, rosettes, and sector and dendritic snowflakes) with the Field et al. (2005) ice PSD parameterization for three different assumed temperatures [see Kulie and Bennartz (2009) for more details], and a best-fit line (in logarithmic space) is defined for the entire dataset of nonspherical ice particle models. Ice particle mass–particle size and fall speed–particle size relationships are defined in fashion similar to that in Kulie et al. (2010).

Figure 1 illustrates this best-fit ZeS relationship (Ze = 21.6S1.2; henceforth the “average” ZeS relationship) that will be applied to CloudSat near-surface reflectivity data, as well as the 1-standard-deviation (1 σ) uncertainties in the ZeS relationships (i.e., Ze = 61.2S1.1 and Ze = 7.6S1.3; henceforth the “upper” and “lower” ZeS relationships, respectively) to better study the possible errors in retrieved near-surface snowfall rates. Note that the use of the terms upper and lower does not imply that these relationships provide an absolute bound on uncertainty in derived snowfall rates; they are only used as a convenient way of describing these relationships. The variability in the ZeS relationships shown in Fig. 1 is due largely to the backscatter properties of the different ice particle models. Note, however, that some PSD variability effects are also included in the ZeS relationships by assuming three different temperatures for each ice particle model when calculating the ZeS relationships. The Field et al. (2005) PSD parameterization is temperature dependent and thus enables first-order PSD variability to be incorporated into the method (i.e., the characteristic particle size decreases with decreasing temperature using this parameterization). Further PSD variability arises that is due to the particle shape, because the Field et al. (2005) moment conversion scheme will produce different underlying PSDs because of each particle shape’s unique mass and/or fall speed–particle size relationship (e.g., Kulie et al. 2010). In addition, the Field et al. (2005) parameterization is based on over 9000 measured PSDs in the vicinity of the British Isles and provides a statistically robust method to retrieve the PSD. Further variability in the ZeS relationships is possible because of regional PSD differences and is left for further investigation, although the tacit postulation employed in this study assumes that the scattering properties of the ice models play the most important role in the overall modeled ZeS variability and uncertainty.

In addition, Fig. 1 indicates that it is difficult to match individual ice models with the best-fit average line generated from the entire ensemble of ice models. The Liu (2008b) three-bullet rosette (LR3) and Hong aggregate (HA) models compare favorably, but not perfectly, to the best-fit average line throughout most of the snowfall rate range indicated in Fig. 1 because of the combination of PSD and backscatter properties of the respective habits. Other particle models compare well to the best-fit line at higher snowfall rates but not at lower snowfall rates (e.g., the LSS and LDS shapes). A few particles—mostly plates (LP2), columns (LC1), and droxtals (HD)—display tendencies that are similar to the (blue) line denoting +1 σ. Other particles—mostly various versions of bullet rosettes (LR4, HR6, KR6)—match more favorably with the (red) line denoting −1 σ. Habits such as plates, columns, and droxtals are admittedly not very realistic renditions of most precipitating frozen particles. These particles are currently included, however, because they produce realistic microwave radiative signatures when used with the Field et al. (2005) PSD parameterization (Kulie et al. 2010). Future research may ultimately discount such particles, and the ZeS uncertainty range would correspondingly be narrowed if some of these habits were not included in the analysis.

4. Results

a. Attenuation correction

The attenuated equivalent radar reflectivity can be written as
i1558-8432-50-2-399-e1
where kext is the extinction coefficient, the exponential term in parentheses is the two-way attenuation along the total radar beam path s from the near surface to the top of the atmosphere (TOA), λ is the radar wavelength, K is related to the dielectric constant of the scattering medium (by convention, assumed to be water), σb is the backscatter cross section for an individual ice particle, and N(D) dD is the particle concentration within the size bin D. Attenuation by snowflakes or other low-density frozen particles does not usually significantly degrade the signal for W-band cloud radars unless the snowfall is sufficiently intense with extensive vertical depth (e.g., Matrosov 2007). The CloudSat 94-GHz radar signal, however, can also be severely attenuated as a result of liquid precipitation (not applicable to snowfall), melting precipitation, elevated cloud liquid water contents (e.g., supercooled cloud droplets coexisting with snowfall), and large columnar water vapor amounts (generally not a concern at higher latitudes during the winter). Thus, under certain circumstances appropriate attenuation corrections might have to be applied. When considering snowfall, however, Kulie and Bennartz (2009) ignored attenuation under the assumption that the conditions necessary for attenuation to play a significant role would be insignificant for dry snowfall cases—a potentially inadequate assumption if snowfall and elevated supercooled cloud liquid water amounts coexist. In this section, an attenuation correction scheme will be applied to test the degree to which attenuation affects snowfall retrievals.

For all identified snowfall cases, the total columnar two-way attenuation (from the near surface to the TOA) was calculated for three atmospheric constituents: water vapor from collocated ECMWF data, cloud liquid water from either over-ocean 2B-CWC-RO retrievals or AMSR-E observations (see below for further explanation), and frozen hydrometeors using the three-bullet rosette ice particle model from Liu (2008b). The three-bullet rosette from Liu (2008b) was chosen for first-order attenuation correction calculations due to frozen hydrometeors since its modeled backscatter properties can be considered to be a plausible average value within the larger ensemble of ice models (e.g., Fig. 1 from Kulie and Bennartz 2009). If a truly ensemble approach were adopted, the two-way attenuation shown in Fig. 3 (discussed later in this section) for the snowfall-only regions would be altered by ±0.4 dB if the standard deviation of the backscatter properties for the entire ensemble of ice models is used. Note that AMSR-E cloud LWP retrievals were used in precipitating regions to augment the CPR-derived 2B-CWC-RO retrievals that diverge—and are thus flagged as unusable—when precipitation-sized particles are present. The AMSR-E LWP values (over ocean only) were evenly distributed in the data bins that contained divergent liquid water content solutions in the 2B-CWC-RO product as a plausible estimate of the cloud liquid water profile. Further details regarding the distribution of cloud liquid water can be found in Kulie et al. (2010).

As shown in Fig. 2, which mimics the near-surface snowfall reflectivity histogram shown in Kulie and Bennartz (2009), the cumulative effects of attenuation corrections on reflectivity distributions associated with snowfall are noticeable but arguably insignificant when considering the other potential sources of uncertainty that accompany snowfall retrievals. There is a discernable shift in the near-surface reflectivity histogram to larger values—especially above about the 8-dBZe bin where counts are consistently higher—when attenuation corrections are applied, but the overall results for many of the lighter snowfall cases are not grossly altered. Therefore, it is perhaps more instructive to study snowfall attenuation effects on a case-by-case or regional basis to investigate the true potential benefits of using attenuation corrections.

Figure 3 highlights a few notable attenuation features associated with a sample snowfall case that occurred on 6 August 2006 over the Southern Hemispheric Pacific Ocean north of Antarctica. All radar returns for this case are assumed to be associated with frozen hydrometeors because of cold near-surface temperatures, because the ECMWF-derived 2-m temperature for the entire domain shown in Fig. 3 does not exceed 0°C (not shown). Moving from south (left) to north (right), a limited attenuation due to water vapor in regions devoid of CPR echoes can be noted. The total columnar water vapor path (not shown) increases from south (∼4.4 kg m−2) to north (∼9.5 kg m−2), and the corresponding background gaseous attenuation due to water vapor increases slightly from 0.47 to 0.6 dB. Any increase in attenuation above these levels in cloudy and precipitating regions can therefore be attributed to cloud liquid water and/or frozen hydrometeors. Numerous attenuation peaks between 1.0 and 2.0 dB are evident between about 57.5° and 57.0°S and coincide with pronounced LWP maxima exceeding 1 kg m−2 that are associated with shallow convective clouds laden with supercooled water. Except for a small LWP maximum located near 56.5°S that produces a slight attenuation increase in a region of decreasing ice water path (IWP), the total two-way attenuation nicely tracks the columnar IWP (derived from the 2B-CWC-RO product) between about 57° and 54.7°S, suggesting the attenuation exceeding the background value due to water vapor largely results from frozen hydrometeors in this region. Note that the attenuation gradually increases from about 0.6 to about 1.5 dB in this zone and that attenuation maxima coincide with IWP maxima. The pronounced effect of LWP is again observed northward of about 54.7°S. The IWP maximum near 54.6°S exceeds the IWP maximum near 54.5°S, yet the attenuation values near the 54.5°S IWP peak are greatly amplified by the presence of supercooled water. Attenuation clearly should not be discounted in this snowfall case, especially when cloud liquid water is present. It should be acknowledged that recent modeling studies suggest that multiple-scattering effects act to enhance radar reflectivity and can largely counteract attenuation in dry snowfall (Matrosov and Battaglia 2009), and therefore attenuation corrections between 57° and 54.7°S might actually introduce unintended biases in near-surface snowfall retrievals. This topic will be discussed in greater detail in the concluding remarks.

Figure 4 shows the snowfall frequency (defined as the percentage of CloudSat profiles that meet snowfall criteria) and mean snow rate derived from CloudSat using the average ZeS relationship, no vertical continuity test, and a −10-dBZe reflectivity threshold to provide a reference for interpreting the following regional difference plots. Figure 5 provides a quantitative view of how the attenuation correction scheme affects these retrieved mean snowfall rates on a regional basis. Based on these results, attenuation appears to have a nonnegligible effect on mean snow rate in many regions. The mid- to high-latitude Southern Hemisphere storm-track region north of Antarctica is particularly sensitive to the attenuation correction scheme as the mean snow rate increases between 0.15 and 0.3 mm day−1 in many areas within this latitude belt—a roughly 20%–30% increase relative to retrieved snowfall rates without attenuation corrections. Cloud liquid water is apparently a large contributing factor to the attenuation corrections in this region. As shown in Fig. 6, the snowfall cases in the southern Pacific Ocean systematically contain higher retrieved LWP values in comparison with the entire snowfall dataset. As will be discussed in section 4f, even higher LWP amounts are typically associated with the mixed-precipitation category indicated in Fig. 6.

The effect of the attenuation scheme is somewhat less significant in the Northern Hemisphere, with mean snow rate increasing generally in the range of 0.05–0.1 mm day−1 throughout Siberia, Canada, and the Arctic Ocean. Two exceptions to this Northern Hemispheric trend are the western coast of Canada and the eastern coastal region (both land and ocean) of Greenland, which experience mean snowfall rate increases similar to those of the Southern Hemisphere. It must be emphasized, though, that continental regions like Siberia and Canada only contain attenuation corrections due to water vapor and frozen hydrometeors if the CloudSat 2B-CWC-RO product does not provide valid estimates of cloud liquid water (a common occurrence under precipitating conditions) since no independent cloud liquid water observations are readily available; thus, the attenuation correction is potentially underestimated in these regions. It is also important to note that clutter from elevated, complex terrain affects isolated data points in this area of Greenland (Kulie and Bennartz 2009) and most likely affects some data points in western Canada.

The effect of attenuation is significant enough in certain locales that we consider attenuation correction to be a useful addition to the method for determining snowfall rates from CloudSat. Therefore, in the remaining sections of this paper, the attenuation correction will be applied. Further modeling studies are required to clarify the sensitivity of the calculated two-way attenuation used in this study to such factors as ice particle size distribution, ice habit, temperature, and the assumed cloud liquid water profile and will be considered in follow-on studies.

b. Sensitivity to ice particle model

In section 2, various ice models from three microwave optical property databases were averaged, resulting in three ZeS relationships that represent the average of these models as well as so-called upper and lower relationships, which this section will consider as an estimate of the amount of uncertainty in derived ZeS relationships due to the ice model chosen.

As expected, the derived mean snowfall rates are extremely sensitive to this assumption (Fig. 7). For example, in the Southern Hemisphere along the midlatitude storm-track region, the zonally averaged mean snowfall rate peaks at about 65°S. Depending on whether upper or lower uncertainty estimates for the ZeS relationships are chosen, the snow rate at this latitude can vary by almost an order of magnitude, from about 0.25 to just above 2 mm day−1. In the midlatitudes of the Northern Hemisphere, mean snow rate varies from about 0.3 to about 0.8 mm day−1 depending on the choice of ZeS relationship. Recall these snow rates are given in units of millimeters per day; therefore, when applied to an entire year, this source of uncertainty can result in a yearly liquid equivalent snowfall estimate ranging anywhere from 100 to 300 mm day−1 in this region.

The choice of ice model is clearly a very large source of uncertainty in this method. As with ZR relationships, no universally correct answer is likely to be found, and the best choice of ZeS relationship will certainly depend on the specific situation, based on regional and snowfall-type considerations. These results provide useful initial uncertainty estimates for CloudSat-derived snowfall rates, however.

c. Sensitivity to vertical continuity tests

Kulie and Bennartz (2009) developed an ad hoc vertical continuity test for inclusion of reflectivity observations into the snowfall dataset that required reflectivity to be greater than −15 dBZe from the 6th to the 11th CPR bins above the surface (∼1.3–2.5 km) to help to eliminate ground-clutter contamination and exclude nonprecipitating clouds, although it was noted that this requirement possibly eliminates shallow snowfall cases in which significant reflectivity does not extend above 1.3 km. Liu (2008a) also mentioned the possibility of excluding shallow snowfall cases, but no results were presented in either Liu (2008a) or Kulie and Bennartz (2009) to illustrate where this problem might be prevalent.

Figure 8 depicts the effect of this vertical continuity test on snow frequency and mean snow rate and pinpoints where the influence of this requirement is most prominent. By removing the continuity test, some polar regions experience an increase in snow frequency of 10%–15%, particularly the Southern Oceanic latitudes and the Arctic Ocean east of Greenland, as well as Siberia and Greenland itself. The increase observed over the oceans is not surprising, because winter cold-air outbreaks commonly produce shallow “lake effect” snowbands over the relatively warm ocean and large lake surfaces and can produce substantial snow (e.g., Katsumata et al. 2000; Aonashi et al. 2007). Thus, mean snowfall rates are impacted significantly in some of these areas as well; in particular, much of the Southern Ocean experiences an increase of 0.1 mm day−1 (i.e., a 36.5-mm increase in annual snowfall) due to the removal of the test. The difference is even larger over oceanic areas to the east and west of Greenland, and south of the Kamchatka Peninsula: around 0.2 mm day−1. These results indicate that excluding such shallow snowfall cases would be detrimental to snowfall datasets, and therefore every effort should be made to include them. The frequency increase over large continental expanses like Siberia is more puzzling, although it is most likely indicative of including shallow boundary layer clouds that may not be precipitating. This seems like a plausible scenario, because mean snowfall rates over regions like Siberia and inland Greenland do not experience as dramatic an increase when the vertical continuity test is removed. Note, however, that a few isolated pixels on the coast of Greenland experience tremendous increases in mean snowfall rate when the vertical continuity test is removed—an obvious clutter feature due to complex terrain that was highlighted in Kulie and Bennartz (2009).

Based on these results, it appears that a better method would be to retain the vertical continuity test over land but not to use it over oceanic areas. Clutter contamination in the near-surface reflectivity data used in this study is not an issue over the ocean—and actually seems limited to a handful of pixels in complex terrain such as coastal Greenland and the Andes Mountains—so that the increase in precipitation due to removal of the vertical continuity test likely corresponds to a real feature over oceanic areas. It remains unclear, however, whether it is accurate to assume that light snow rates at an altitude above 1 km are in fact reaching the ground.

d. Sensitivity to reflectivity threshold

The choice of a near-surface reflectivity threshold for differentiating between precipitating and nonprecipitating CloudSat profiles is somewhat arbitrary, although a −15-dBZe threshold is often used to differentiate between suspended cloud droplets and drizzle in rainfall algorithms. Liu (2008a) used a near-surface reflectivity threshold of −10 dBZe; Kulie and Bennartz (2009) used a −15-dBZe threshold.

Analysis by Kulie and Bennartz (2009) showed that, for the year of CloudSat data considered, snow rates of less than 0.1 mm h−1 (∼−8 dBZe) contribute very little to snowfall accumulation despite a significant number of snowfall cases occurring below this snow rate. The exact reflectivity corresponding to this snowfall rate, of course, depends on the whole range of previously mentioned assumptions about snowflake shape, PSD, and so on; it suggests, however, that at some point decreasing the reflectivity threshold further should begin to affect snowfall frequency only, with little effect on snowfall accumulation.

This is supported by Fig. 9, in which the effect of changing the reflectivity threshold from −10 to −15 dBZe is isolated using the average ZeS relationship. As expected, decreasing the threshold to −15 dBZe results in increased snow frequency of 5%–10% in polar regions but has almost no effect on mean snow rate.

e. Summary of sensitivity tests

The results of sections 4a, 4c, and 4d are summarized in Fig. 10 in which the differences in snow frequency and mean snow rate due to the various choices of method discussed are averaged zonally. In terms of snow frequency, the use of a vertical continuity test has the most significant effect, followed by reflectivity threshold. Attenuation correction has a noticeable but comparatively small effect on snow frequency. In terms of mean snow rate, differences due to vertical continuity test and attenuation correction are generally very similar while the choice of reflectivity threshold has a small but noticeable effect.

f. Temperature thresholds/mixed precipitation

The most convenient method to discriminate between rain and snow events is to use near-surface temperature thresholds. Liu (2008a) counted 2-m temperatures of less than 2°C as “cold” observations that were considered to be snowfall cases if the CPR reflectivity exceeded the threshold discussed in the previous section. This criterion was chosen on the basis of land- and ship-based observations that indicated a 50% snowfall occurrence probability at this temperature. To sample predominantly “dry” snowfall and avoid rimed or partially melted snow, Kulie and Bennartz (2009) used a more stringent 0°C temperature threshold, although this assumption is most likely not a sufficient criterion to eliminate all instances of “wet” snowfall.

In an attempt to highlight regions that are most susceptible to mixed precipitation or snowfall that is partially melted and/or more likely to be rimed, precipitation occurrences for cases with 2-m temperatures of 0°–4°C in comparison with subfreezing temperatures are shown in Fig. 11. Since the ice particle models used in this study are probably not a realistic rendition of heavily rimed snowfall and/or partially melted snowflakes, this study does not attempt to estimate the contribution of mixed precipitation to annual liquid-equivalent precipitation amounts. Nevertheless, it is instructive to study where mixed precipitation is more likely for future snowfall retrieval algorithm development. Figure 11 shows that, from a frequency of occurrence perspective, precipitation in the mixed category can be as much or more important over the northern Pacific Ocean, over the Atlantic Ocean off the east coast of Canada, over much of the United States, and over the entire Southern Ocean. Over northern Canada and Siberia, however, mixed precipitation becomes less frequent, occurring at a frequency of only 10%–25% of snowfall. Mixed precipitation is insignificant over Antarctica according to these results.

The LWP histograms presented earlier in Fig. 6 highlight the consistently larger LWP (retrieved from AMSR-E) associated with CPR observations in the mixed-precipitation category. Related to this is Fig. 12, which illustrates the mean LWP associated with a given near-surface CPR reflectivity and ECMWF 2-m temperature, as well as the number of precipitation cases associated with each reflectivity–temperature bin. The two horizontal lines in the bottom panel of Fig. 12 highlight both the peak in the near-surface reflectivity histogram near 0–1 dBZe from Fig. 2 and the reflectivity threshold near 5–6 dBZe that contributes most to the total snowfall accumulation (see Kulie and Bennartz 2009). Figure 12 shows distinctive trends in mean LWP and precipitation event frequency of occurrence as a function of reflectivity and temperature. Higher LWP values are more commonly associated with elevated temperatures, especially when near-surface reflectivities exceed about 10 dBZe, although there are elevated LWP values associated with lower-reflectivity–lower-temperature bins that are probably related to shallow convective, lake-induced snowfall. An obvious LWP maximum exceeding 0.2 kg m−2 exists near the 17-dBZe–3°C bin, but observations in this data bin occur infrequently and are probably more indicative of rain than snow. The maximum frequency of occurrence is located near the 6-dBZe–1°C bin, and frequency of occurrence increases steadily between 0° and 1°C up to about the 10-dBZe reflectivity level. Therefore, increasing the temperature threshold from 0° to 1°C to include a CPR observation in the snowfall dataset greatly increases the number of total observations—and higher attendant LWP values—included in the snowfall category. Even if a 0°C temperature threshold is used, however, LWP values can become large at higher reflectivities and cannot be discounted at the lowest reflectivities. Observations in the ∼4–10-dBZe reflectivity range at temperatures below about −1°C coincide with lower LWP values, and therefore these observations that contribute significantly to total snowfall amounts may not be as susceptible to riming. Overall, Fig. 12 clearly shows that using only a temperature threshold to rigidly define when a CloudSat observation should be classified as “snow,” especially if the temperature threshold exceeds 0°C, potentially complicates snowfall retrievals because of the presence of cloud liquid water.

g. Comparison with independent snowfall datasets

Comparison of radar snowfall retrievals by independent measurements is a tremendously difficult task. Not only are there spatiotemporal sampling issues that make CloudSat snowfall retrieval comparisons with ground-based snowfall measurements difficult, but measuring snowfall at the surface with precipitation gauges is potentially fraught with errors (e.g., Knuth et al. 2010; Lundberg and Halldin 2001; Matrosov et al. 2008), and robust snowfall accumulation datasets are a scarce commodity. In an attempt to provide an initial analysis of whether CloudSat-derived snowfall rates are in a reasonable range, Liu (2008a) provided comparisons of CloudSat-derived accumulations over a large section of Canada with long-term snowfall accumulation surface measurements. The CloudSat-derived accumulations were found to be “generally in the ballpark of climatology” when compared with averages of multiple Canadian surface snowfall gauges since 1891 (Groisman and Easterling 1995).

In an attempt to expand upon the initial comparison made by Liu (2008a) by utilizing additional independent snowfall datasets, qualitative comparisons were made over Antarctica with the climatological, model-derived snowfall accumulations reported by Bromwich et al. (2004). Taking into account the data gap at the highest latitudes in Fig. 4 due to the limits of the CloudSat orbit, the spatial distribution and overall snowfall accumulation pattern from CloudSat data for 1 yr were encouragingly similar to the Bromwich et al. (2004) results (not shown). Snowfall accumulation magnitudes also compared reasonably well. For example, comparing the CloudSat snowfall retrievals using the average ZeS relationship shown in Fig. 4 with Fig. 11 of Bromwich et al. (2004) and multiplying the values in Fig. 4 by 365 to obtain snowfall accumulation in millimeters per year reveals that the snowfall generally ranges from about 400 to 500 mm yr−1 near the coast and decreases steadily to zero toward the center of the continent in both studies. Note that the results in Bromwich et al. (2004) are not limited to snowfall only, and so comparisons outside the continent of Antarctica are not useful because of the inclusion of liquid precipitation.

Since comparison of CloudSat snowfall retrievals with climatological, model-derived, accumulations is admittedly not an optimal method of analyzing CloudSat retrievals, further comparisons were made with a geographically diverse array of Canadian ground stations (Fig. 13). Using the first year of CloudSat data (July 2006–June 2007), any CloudSat profile occurring within a 200 km × 200 km box around one of these stations was averaged into the statistics for that corresponding station. The criteria for determining which of these profiles were snowing required the near-surface bin to have a reflectivity greater than −10 dBZe with no vertical continuity test, with an ECMWF surface temperature of less than or equal to 0°C. For profiles meeting these criteria, reflectivity was converted to snow rate using each of the ZeS relationships discussed in section 3. The choice of a 200-km bin size is arbitrary but must be both sufficiently large to include a large number of CloudSat profiles in the averages and small enough to avoid including weather systems far removed from the station being considered. Extensive testing with 100-, 200-, and 300-km bin sizes showed 200 km to be an acceptable compromise between these two effects.

For each station, snow rates from these profiles were totaled to determine a mean snowfall rate for the year, which provides an estimate of that year’s snowfall accumulation suitable for comparison with snow gauge data from the Canadian National Climate Data and Information Archive (see online at http://www.climate.weatheroffice.ec.gc.ca/climateData/canada_e.html). The choice of stations was limited primarily by which stations had complete data for the year-long period being considered. These stations utilize the simplistic technique of ruler-based snowfall measurement with a set snow-to-liquid ratio (SLR) of 10:1 [see the Meteorological Service of Canada’s Manual of Climatological Observations (MANCLI) available online at http://www.msc.ec.gc.ca/msb/manuals/mancli/chap3_e.html#3_5__e]. This is a significant source of error in this study because the SLR can vary widely depending on meteorological conditions and various microphysical factors (Baxter et al. 2005); in addition, the SLR climatological data over the United States in Baxter et al. (2005) suggest that 15:1 would be more accurate for stations along the U.S.–Canadian border. Another complicating factor is that certain Canadian stations do explicitly measure liquid content of snowfall by manually melting snow trapped in a container (see MANCLI, section 3.8.1); information on which specific stations use this method is not readily available, however (C. Barnes, Meteorological Service of Canada, 2009, personal communication).

The results for each station are summarized in Fig. 14 and are compared with each of the three ZeS relationships derived in section 3. In broad terms, CloudSat-derived snow rates are underestimated at lower latitudes with the average ZeS relationship becoming a better estimate at higher latitudes when considering year-long totals. To be more specific, four of eight Canadian stations located south of 50°N are underestimated even by the upper ZeS relationship [Montreal, Quebec (YUL); Fredericton, New Brunswick (YFC); Vermilion, Alberta (YVG); and St. John’s, Newfoundland (YYT)] whereas for four of the eight stations [Calgary, Alberta (YYC); Kindersley, Saskatchewan (YKY); Norman Wells, Northwest Territories (YVQ); and Resolute, Nunavut (YRB)] located north of 50°N the average ZeS relationship is within 20 mm of the observed amount and three more [Edmonton, Alberta (YEG); Prince George, British Columbia (YXS); and Mayo, Yukon (YMA)] are located between the average and upper ZeS relationships.

In Table 1, snowfall totals were partitioned by month and only the average ZeS relationship was considered to allow the application of standard statistical measures such as bias, root-mean-square error (RMSE), and correlation. The higher-latitude stations YRB and YMA show particularly good results, with high correlation and low bias and RMSE. Note that because of YRB’s high-latitude location and the nature of the CloudSat orbit almost 2 times more CloudSat overpasses occurred within this station’s bin than within the bin of any other station being considered. Many stations show far less encouraging results, with 7 of the 18 stations showing a correlation of less than 0.5.

In addition, snowfall totals are broken down on a monthly basis for a representative selection of these stations and are shown in Fig. 15, with YRB representing a station with excellent correlation; Toronto, Ontario (YYZ), representing a station with moderate correlation; and YYT representing a station with poor correlation. As expected from its high correlation, monthly observed snowfall totals at YRB closely follow CloudSat-derived amounts. At YYZ, the average ZeS relationship is generally good except for March of 2007 for which month the CloudSat-derived snowfall is zero. The problem of severe underestimation of observed snowfall by CloudSat-derived totals is more widespread at YYT, where the upper ZeS relationship underestimates the observed amount by more than 30 mm in both January and February of 2007.

It is possible that a large contributor to these underestimates of snowfall is the choice of temperature threshold. Frozen precipitation is still possible when the surface temperature is above freezing, and so by excluding any CloudSat profile with 2-m temperatures greater than 0°C, cases that at a surface station would still be considered to be snowfall will be excluded from CloudSat-derived snowfall statistics. To investigate this effect, Fig. 15 also shows the ratio of precipitating CloudSat profiles that are in the mixed-precipitation category (0°–4°C) based on surface temperature. For example, at YRB, a station where CloudSat snow rates correlate well with ground observations, there is little precipitation with surface temperature in the 0°–4°C range. At YYZ and YYT, where CloudSat underestimation is a significant issue, precipitation in the mixed category is more common. For example, at YYT for January and February of 2007, mixed-precipitation profiles constitute 27% and 12% of the total number of precipitation profiles, respectively, supporting the hypothesis that frozen precipitation when the surface temperature is above 0°C is a significant contributor to the underestimation in CloudSat-derived snowfall statistics. Simply increasing the temperature threshold to 1° or 2°C does improve the year-long results for underestimated stations because of the inclusion of more precipitation cases, but note that these precipitating profiles are more likely to contain rimed or liquid precipitation, which are not described by the ice models used in this method. This likelihood is supported by data showing that monthly correlations generally decrease when the temperature threshold is raised above 0°C (not shown).

Overall, the results from this section are difficult to interpret because of the large number of uncertainties and sources of error in both data sources. Nevertheless, the comparisons are insightful whether or not they are conclusive, and they will be discussed further in section 5.

5. Conclusions

The various tests presented in this work demonstrate the sensitivity of snowfall retrievals to several key underlying retrieval assumptions in deriving snowfall rates using CloudSat data and provide necessary guidance on plausible retrieval uncertainty estimates due to methodological differences. Since W-band radars can be susceptible to attenuation, the sensitivity of retrieved snowfall rates to an attenuation correction scheme is presented. The attenuation correction scheme does not significantly alter the overall radar reflectivity histogram of near-surface snowfall derived from CloudSat data, but distinct regional effects are noted. For instance, retrieved snowfall increases by 20%–30% over many regions of the Southern Hemisphere oceanic storm-track region when an attenuation correction is applied, and increases of similar magnitude occur over isolated oceanic regions in the Northern Hemisphere (e.g., coastal Greenland). The attenuation correction scheme is thus deemed a useful upgrade to the snowfall retrieval method, but two open related issues remain: 1) overland attenuation corrections in this study are probably underestimated because no independent cloud liquid water estimate was available from concurrent passive microwave observations and 2) multiple-scattering effects need to be accounted for. The attenuation correction scheme appears to be beneficial, but it should be acknowledged that recent studies suggest multiple-scattering effects can counteract attenuation in dry snowfall (Matrosov and Battaglia 2009). Therefore, attenuation corrections might actually introduce unintended biases in near-surface snowfall retrievals, and additional work must be undertaken to clarify this effect under typical real-world snowfall conditions.

Two additional ad hoc methodological components used by Kulie and Bennartz (2009) to retrieve snowfall were 1) vertical reflectivity continuity tests to avoid nonprecipitating clouds and to help to mitigate ground clutter and 2) minimum reflectivity thresholds for inclusion of a CloudSat observation into the snowfall dataset. The vertical continuity test, however, likely eliminates valid snowfall cases primarily over ocean and should probably only be employed only over land. The choice of reflectivity threshold (−15 vs −10 dBZe) is only significant in terms of snowfall frequency and not snowfall accumulation. The vertical continuity sensitivity tests are also useful to highlight regions that are frequently affected by low-topped, lake-effect snowfall events. This knowledge will be extremely beneficial for future snowfall algorithm development by identifying where lake-effect snow preferentially occurs.

Another large source of snowfall retrieval uncertainty is modeling the backscatter properties of frozen hydrometeors. By using average ZeS relationships derived from an ensemble of nonspherical ice particle models—plus bounding uncertainty estimates from this same ensemble, strong latitudinal variation in snowfall rates is shown, with large corresponding uncertainties of near 100%. Reducing this uncertainty will be a crucial next step. It is hoped that certain ice particle models can be eliminated as plausible options, possibly by assessing the ice particle models’ response to combined active and passive response of snowfall, to further constrain the ZeS relationships. The concurrent development of more realistic models for aggregate-type snowflakes is also a high priority item for improved retrievals. Promising recent work by Petty and Huang (2010), who have developed numerous aggregate snowflake models with more shape complexity and realism than the models used in this study, should be implemented in future work.

Snowfall retrievals are also currently hindered by the use of simple NWP-derived near-surface temperature thresholds to discriminate between rain and snow events. To emphasize the complications of using a temperature threshold above 0°C, a “mixed precipitation” category was created in this study to investigate CloudSat precipitation observations associated with a near-surface temperature bin of 0°–4°C. This study highlights that numerous regions around the globe receive a nonnegligible fraction of cold-season precipitation in this category. A distinct complicating factor associated with the mixed-precipitation category, however, is the elevated amounts of liquid water path that accompany such events. Consistently higher LWP indicates the potential for enhanced riming, and the ice particle models used in this study might not be appropriate to describe the scattering and absorption properties of rimed frozen hydrometeors. The importance of correcting for attenuation is also magnified with higher LWP values. A natural recommendation from these results is to create a separate cold precipitation category for observations slightly above freezing to highlight the increased uncertainty currently associated with such precipitation retrievals and to motivate the development of more-sophisticated hydrometeor models for rimed or melted snow. Another possible method to reduce snowfall retrieval uncertainties is to introduce a threshold based on AMSR-derived LWP. To ensure the validity of the dry-snowfall assumption, snowfall cases exceeding a certain amount of supercooled cloud liquid water could be eliminated from consideration.

CloudSat-derived snowfall accumulation comparisons with conventional snowfall gauges demonstrate the difficulty of comparing CloudSat-derived snowfall with the ground-based observations. The variety of sources of error and the lack of correlation at many stations make it difficult to make any generalizations about the accuracy of one ZeS relationship relative to another, although, as with radar-estimated rainfall, one should not expect to find any globally accurate ZeS relationship. One initial finding suggested by this study is that the CloudSat-derived results may be more useful at higher latitudes where temporal sampling is greater and mixed precipitation (or frozen precipitation when the surface temperature is greater than 0°C) is less of an issue. In addition, this work accentuates the need for more robust and sophisticated ground validation networks for comparison with CloudSat-derived snowfall estimates.

Acknowledgments

The authors acknowledge the CloudSat Science Team and the CloudSat Data Processing Center. This research was partially funded by Wisconsin Space Grant and University of Wisconsin Hilldale Fellowships to M. Hiley and from NASA Grant NNX07AE29G. Also, thanks are given to the Meteorological Service of Canada for climate data, as well as to Caroline Barnes of the Data Analysis and Archives Division for her assistance with interpreting these data. This manuscript also benefited greatly from the constructive comments of three anonymous reviewers.

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Fig. 1.
Fig. 1.

The ZeS relations for nonspherical ice particle models from Hong (2007), Kim et al. (2007), and Liu (2008b). The various colors indicate the following ice models: Liu (2008b) columns (LC1, LC2, and LC3), plates (LP1 and LP2), rosettes (LR3–LR6), and sector (LSS) and dendritic (LDS) snowflakes; Hong (2007) columns (HC1 and HC2), plates (HP), six-bullet rosettes (HR6), aggregates (HA), and droxtals (HD); and Kim et al. (2007) columns (KC), four-arm (KR4) and six-arm (KR6) rosettes. For each snow rate and ice model, corresponding radar reflectivities are calculated for an assumed temperature of −5°, −10°, and −15°C using the Field et al. (2005) ice PSD parameterization and are indicated by different symbols (plus sign, diamond, or asterisk) for each ice particle. A best-fit (black line) and corresponding 1-σ uncertainties (blue and red lines) are then determined based on these data points. Throughout the text, these three relationships will be referred to as upper, average, and lower ZeS relationships.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 2.
Fig. 2.

Normalized count of number of snow cases falling in each 1-dBZe bin, comparing the use of attenuation correction (dotted line) with the uncorrected method (solid line). The histogram includes about 6.1 × 106 cases and includes data from the entire CloudSat orbit (maximum latitude 81.8°), for the period July 2006–June 2007.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 3.
Fig. 3.

(a) CPR radar reflectivity, (b) CPR-derived IWP (black line; kg m−2) and CPR-derived (or AMSR-E in precipitating regions) LWP (gray line; kg m−2, and (c) two-way total columnar attenuation (dB) for a snowfall case in the southern Pacific Ocean.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 4.
Fig. 4.

Reference plot for interpreting the difference plots presented below. Values are for the average ZeS relationship, with no vertical continuity test, a −10-dBZe threshold, and the use of attenuation correction. (top) The snow frequency (precisely, the percent of total CloudSat profiles in each bin considered to be snowing), and (bottom) the mean liquid equivalent snow rate (mm day−1).

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 5.
Fig. 5.

Difference in mean snow rate due to attenuation correction (mm day−1) (using average ZeS relationship, no vertical continuity test, and −10-dBZe threshold) for the (right) Northern and (left) Southern Hemispheres.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 6.
Fig. 6.

Normalized histogram (bin size of 0.01 mm) of AMSR-E derived LWP for precipitation cases with 2-m temperature less than 4°C (solid line), snowfall cases (surface temperature <0°C; dotted line), all mixed-precipitation cases (0°–4°C; dashed line), and all snow cases in the Southern Ocean latitude belt (66°–45°S; dash–dotted line). Only over-ocean and inland water cases are considered, and cases with LWP of greater than 0.5 mm were rejected for reasons of sea ice contamination.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 7.
Fig. 7.

(top) Zonally averaged snowfall frequency. (bottom) Zonally averaged mean snow rate (mm day−1) for average ZeS relationship (thick line), with the uncertainty range as given by the upper and lower ZeS relationships shaded. Averages include a full year of data (cold and warm seasons).

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 8.
Fig. 8.

Difference in (top) snow frequency and (bottom) mean snow rate (mm day−1) due to vertical continuity (no test minus with test) for the (right) Northern and (left) Southern Hemispheres.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 9.
Fig. 9.

As in Fig. 8, but differences are due to the choice of reflectivity threshold (−15-dBZe threshold minus −10-dBZe threshold).

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 10.
Fig. 10.

The method details discussed in sections 4a (dashed line), 4c (solid line), and 4d (dotted line) are compared by zonally averaging the effect of each. (top) The three effects are shown in terms of snow frequency (%). (bottom) The three effects are shown in terms of mean snow rate (mm day−1).

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 11.
Fig. 11.

Ratio of the number of profiles with near-surface mixed precipitation (2-m temperature of 0°–4°C) to the number of profiles with snow (<0°C) for the (right) Northern and (left) Southern Hemispheres. Bins with ratios that are greater than 1 are colored red, and bins with ratios equal to 0 are white.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 12.
Fig. 12.

(bottom) For each 2-dBZe × 2-K bin, AMSR-E-derived LWP from all over-ocean and inland water precipitation cases is averaged to produce a mean LWP for that bin. Precipitation cases with LWP of more than 0.5 mm were excluded for reasons of sea ice contamination. The green vertical line is the freezing point, the red horizontal line is at approximately the most significant reflectivity in terms of frequency of occurrence (0 dBZe), and the blue horizontal line is at approximately the most significant point in terms of snowfall accumulation (6 dBZe). (top) Similar to the bottom panel, but showing the number of precipitation cases in each bin divided by 1000.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 13.
Fig. 13.

Map of Canada showing locations of surface stations referenced in section 4g and its associated figures.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 14.
Fig. 14.

For winter 2006/07, the total liquid equivalent snowfall is shown for 17 Canadian surface stations. The black columns show the observed snowfall total from the Canadian National Climate Data and Information Archive. The darkest-, medium-, and lightest-shaded areas represent the lower, average, and upper ZeS relationships, respectively, of CloudSat-derived snowfall accumulation totals (averaged over a 200 km × 200 km bin centered on each station) for the same time period.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Fig. 15.
Fig. 15.

(top) For YRB, the monthly total percent of precipitating profiles (i.e., profiles meeting reflectivity criteria but with any surface temperature) containing mixed precipitation (ECMWF 2-m temperature of 0°–4°C; black circles) and snow (<0°C; gray circles). (second from top) Similar to Fig. 14 but showing the monthly breakdown (July–June) for YRB. (middle two panels) As in top two panels, but for YYZ. (bottom two panels) As in top two panels, but for YYT.

Citation: Journal of Applied Meteorology and Climatology 50, 2; 10.1175/2010JAMC2505.1

Table 1.

Bias, RMSE, and correlation for monthly snowfall totals of Canadian surface stations in comparison with CloudSat-derived estimates using the average ZeS relationship. Here, avg mixed precip ratio is the ratio of mixed precipitation (0°–4°C 2-m temperature) to the total number of precipitation profiles, and avg snow ratio is the ratio of snow profiles (<0°C) to the total number of precipitation profiles.

Table 1.
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