It has been long believed that the dominant microwave signature of snowfall over land is the brightness temperature decrease caused by ice scattering. However, our analysis of multiyear satellite data revealed that on most of occasions, brightness temperatures are rather higher under snowfall than nonsnowfall conditions, likely due to the emission by cloud liquid water. This brightness temperature increase masks the scattering signature and complicates the snowfall detection problem. In this study, we propose a statistical method for snowfall detection, which is developed by using CloudSat radar to train high-frequency passive microwave observations. To capture the major variations of the brightness temperatures and reduce the dimensionality of independent variables, the detection algorithm is designed to use the information contained in the first three principal components resulted from Empirical Orthogonal Function (EOF) analysis, which capture ~99% of the total variances of brightness temperatures. Given a multichannel microwave observation, the algorithm first transforms the brightness temperature vector into EOF space and then retrieves a probability of snowfall by using the CloudSat radar-trained look-up table. Validation has been carried out by case studies and averaged horizontal snowfall fraction maps. The result indicated that the algorithm has clear skills in identifying snowfall areas even over mountainous regions.
 During winter, a large portion of precipitation at high latitudes takes the form of snowfall [Levizzani et al., 2010], which not only causes potentially hazardous weather, but also has important implications to hydrological cycle and Earth's radiation balance [e.g., Barnett et al., 1989; Walsh, 1995]. However, routine observations of snowfall or snow accumulation have so far mostly been restricted to limited ground-based stations; their spatial distribution is spotty, and the duration of data record is short and station dependent [e.g., Walsh, 1996]. For large-scale weather monitoring and global climate studies, satellite observations have therefore become highly desirable. However, unlike satellite rainfall retrievals that have a history of several decades [e.g., Smith et al., 1998; Adler et al., 2001; Kummerow et al., 2001], satellite snowfall detection and retrieval are still in a very early stage, and until recently there have been very few space-borne sensors suitable for detecting falling snow.
 Space-borne active sensors that can be used to estimate both horizontal and vertical snowfall distributions have not been available until the Cloud Profiling Radar (CPR) on CloudSat [Stephens et al., 2002], which was launched in April 2006. The high sensitivity of the CPR (–25 dBZ) enables investigators to study the snowfall frequency and intensity based on measured radar reflectivity [e.g., Liu, 2008a; Matrosov et al., 2008; Kulie and Bennartz, 2009; Turk et al., 2011; Wood, 2011]. However, because CPR does not scan, it only measures a 1.5 km-wide strip on the Earth surface by each satellite pass, which largely limits its utility for weather monitoring and climate data collection. Passive satellite sensors such as high-frequency (>80 GHz) microwave radiometers have also been used in detecting snowfall events [Liu and Curry, 1997; Chen and Staelin, 2003; Kongoli et al., 2003; Ferraro et al., 2005; Skofronick-Jackson et al., 2004; Noh et al., 2006, 2009]. While most of these studies targeted moderate to heavy snowfall events under unfrozen or nonsnow-covered surfaces, the encouraging results from these studies offered a viable alternative to high-sensitivity space-borne radar for snowfall detection and retrieval. In particular, recently, there have been multiple satellites that carry high-frequency microwave sensors, such as Advanced Microwave Sounding Unit – B (AMSU-B), Microwave Humidity Sounder (MHS), Advanced Technology Microwave Sounder, Special Sensor Microwave Imager Sounder, and the future Global Precipitation Mission Microwave Imager, which offers unprecedented spatial and temporal coverage of the globe. Therefore, developing a snowfall detection and retrieval algorithm that maximizes the utility of these data will be highly beneficial to both weather and climate studies.
 Similar to the case of retrieving rainfall over land [Ferraro et al., 2005; Wang et al., 2009], the primary signature in the microwave spectrum for snowfall retrieval is believed to be the scattering by ice particles, which reduces the upwelling radiation emitted from surface and the lower atmosphere. The strength of the ice scattering signature has been examined using radiative transfer simulations by several investigators [e.g., Bennartz and Petty, 2001; Zhao and Weng, 2002; Bennartz and Bauer, 2003; Kneifel et al., 2010; Skofronick-Jackson and Johnson, 2011]. Aircraft observations over ocean by downward-looking microwave radiometers confirmed the brightness temperature depression caused by ice scattering. For example, Katsumata et al.  reported that brightness temperature at 89 GHz drops about 15 K over convective snowfall cells compared to their neighboring clear-sky region, and Noh et al.  found that brightness temperatures at 150 GHz are about 50 K lower than neighboring clear-sky regions for some snowing clouds. The minimum detectable signature by currently available and planned future sensors has been studied by radiative transfer model simulations (G. Skofronick-Jackson et al., personal communication, 2012) and by comparisons between satellite radiometer and surface radar observations (S. Munchak and G. Skofronick-Jackson, personal communication, 2012).
 Despite these early successes in snowfall detection and retrievals, mostly for cases of intense snowstorms, many obstacles still remain in the development of a globally applicable snowfall algorithm. Particularly, over snow-covered surfaces, separation of signatures of snow in the air and on the ground is still very challenging. In a study by Noh et al. , the investigators attempted to retrieve snowfall in the Great Lakes region for an entire winter season by combining satellite microwave observations and surface emissivity estimates. They found that the satellite retrievals compared reasonably well with surface radar network measurements in the early winter season when there is no accumulated snow on the ground. However, for the late winter season when snow constantly covers the ground, the snowfall retrievals become very noisy and even the horizontal pattern of the snowfall retrievals does not match with that observed by ground-based radars. As pointed by Liu and Curry , under very cold environment, the strongest signature of a snowstorm may not necessarily be the brightness temperature reduction due to scattering by snowflakes; a brightness temperature increase due to liquid water emission and surface warming also occurs, which further complicates the readily challenging snowfall detection and retrieval problems. Thermal emission from cloud liquid water has a masking effect to the snow scattering and thus reduces the snow signature in observed microwave radiances. In some cases, the influence of liquid water in snowing clouds becomes so strong that the snowstorm causes a warming (like rainfall over ocean) in microwave brightness temperatures (Y. Wang et al., personal communication, 2012). In addition, unlike raindrops that are (nearly) spheres with a known density of 1 g cm–3, snowflakes are highly nonspherical, and their density varies with particle size and shape. Modeling snowflakes with realistic shapes and their scattering properties are still needed for quantitatively estimating snowfall rate from satellite-observed radiances [Liu, 2004; 2008b; Petty and Huang, 2010].
 Because of these complications that involve surface emissivity, cloud liquid water, and nonspherical ice scattering by snowflakes, to develop a physically based snowfall detection and retrieval algorithm still faces many challenges. In this study, we take an alternative approach, i.e., to explore the possibility to detect snowfall using an empirical algorithm. The algorithm takes the advantage of coincident observations of CloudSat CPR and NOAA AMSU-B/MHS, using CloudSat radar observations as “truth” to train an algorithm that uses passive microwave data as input. To reduce the dimensionality of the independent variables while retaining most of the information contained in the observed multiple channel brightness temperatures, the algorithm's training and execution are carried out in Empirical Orthogonal Function (EOF) space. The main goal of this study is to examine the validity and effectiveness of such an approach in detecting snowfall over complicated surfaces. The rest of the paper is arranged as follows. In section 2, data and collocation procedures are explained. In section 3, we examine how multichannel brightness temperatures vary when influenced by surface and atmospheric variables. The proposed algorithm is explained in section 4, and its validation is conducted in section 5. Finally, conclusions are given in section 6.
 The primary data for this study are from CPR of CloudSat, and MHS and AMSU-B from NOAA satellites. While the method described in later sections can be applied to any regions, we will focus the land region of 40° to 65°N and 50° to 170°W in North America. The CPR is a 94 GHz nadir-looking radar that measures the power backscattered by cloud and precipitating particles as a function of distance from the radar. The standard CloudSat product 2D-GEOPROF (Release version 4) [Mace, 2007] is used, which includes radar reflectivity in 150 bins in the vertical with a bin size of about 240 m. The footprint size of radar reflectivity profiles is 1.4 km (cross-track) and 1.7 km (along-track). To avoid surface contamination, data in the lowest four bins near the surface (~1 km deep) were excluded in the data analysis. All near-surface results derived in this study are based on radar observations at the fifth bin, which may have caused some shallow snowfall events being missed. In the following, the radar reflectivity at the fifth bin is called “near-surface reflectivity.”
 MHS is a revised version of AMSU-B [NOAA, 2007]; both instruments are cross-track scanning radiometers with five channels, but have slight differences in frequency and polarization arrangement. The center frequencies for MHS are 89, 157, 183.3 ± 1, 183.3 ± 3, and 190.3 GHz, while they are 89, 150, 183.3 ± 1, 183.3 ± 3, and 183.3 ± 7 GHz for AMSU-B. MHS's polarization is also slightly different from that of AMSU-B. For AMSU-B, all channels are vertically polarized at nadir, while for MHS, the 89, 157, and 190 GHz channels are vertically polarized at nadir, and the 183 ± 1 and 183 ± 3 GHz channels are horizontally polarized at nadir. The antenna beamwidth is 1.1 degrees (at the half power point), and the horizontal resolution varies with the viewing angle. The resolution at nadir is nominally 16 km and increases as the radiometer scans away from nadir. Ninety contiguous cells in each scan line are sampled in a continuous fashion covering ±48.95° from nadir. The MHS and AMSU-B brightness temperature data are provided by NOAA Comprehensive Large Array-Data Stewardship System.
 A matchup dataset has been created in this study by matching the closest CPR and MHS/AMSU-B pixels. Since the distinct difference in footprint sizes between MHS/AMSU-B and CPR, there is no right way to make a good match spatially for their collocation. In this study, we simply match each CloudSat pixel with the closest MHS or AMSU-B pixel, and the search in the matching is limited to those pixels with centers less than 25 km away and observation times less than 15 min apart from CPR's. For testing purposes, we have also conducted an alternate way for the matchup, i.e., averaging all CPR observations within a MHS/AMSU-B field of view. Comparisons have been made between retrieval results based on the two methods of conducting matchup. However, it is found that the second method does not provide a better outcome. It should be mentioned that due to the mismatch of the pixels sizes, large uncertainties would certainly be introduced, particularly for those clouds with large horizontal variability. When interpreting the outcome of our algorithm, we need always to keep this deficiency in mind. Additionally, due the close orbit formation of CloudSat and NOAA-18 satellites, the passive microwave data in the matchup dataset are overwhelmingly dominated by MHS data, which results in insufficient datum points for performing data analysis and creating look-up tables for CloudSat–AMSU-B matchups if AMSU-B data are handled separately. Therefore, in this study, we did not make distinction between AMSU-B and MHS for data analysis. Since the look-up table generated in later section is largely based on CloudSat and MHS matchups, retrievals from both MHS and AMSU-B observations are effectively based on training data of the CloudSat–MHS matchups.
 Surface air (2 m) temperature is used to determine whether surface precipitation is rainfall or snowfall. Using multiyear shipboard and ground-based weather report, Liu [2008a] found that the transition between snow and rain commonly occurs within the air temperature range of 4°C to −1°C, with the 50% transition probability occurring at 2°C. A stricter threshold of 2 m temperature less than 0°C is used in this study to make the threshold more conservative, which corresponds to a 90% rain to snow transition probability based on the weather station and shipboard data. For matchup pixels, the 2 m temperature in CloudSat ECMWF-AUX data product [Partain, 2007] is used. The ECMWF-AUX product contains atmospheric variables from European Center Medium-range Weather Forecasting (ECMWF) model analysis, interpolated to the location of CPR bins. Note that only a small fraction of MHS/AMSU-B data can be matched with CloudSat observations. The 2 m temperature in Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalysis dataset [Rienecker et al., 2011] is used when conducting retrievals for MHS/AMSU-B pixels that are not matched with CloudSat data. The MERRA data are archived hourly with a resolution of 1/2 and 2/3 degrees in the latitudinal and longitudinal directions, respectively. Our limited comparison between the ECMWF and MERRA 2 m temperatures showed that they agree within 0.4°C on average with a 4.4°C standard deviation for the region investigated in this study.
3 Brightness Temperature Variations Over Snowing Clouds
 For extracting ice and snow signatures from microwave observations, the conventional wisdom is to examine the reduction of brightness temperature caused by ice scattering. This approach has been used for both ice water path [e.g., Zhao and Weng, 2002; Seo and Liu, 2005] and rainfall [e.g., Ferraro and Marks, 1995; Gopalan et al., 2010] retrievals. Kongoli et al.  investigated this ice scattering signature for snowfall detection, and it appears to be successful for many cases. To further explore this possibility, here we study the brightness temperature change from background values using data observed by MHS on NOAA-18 satellite. The duration of the data is June 2006 through December 2010, and the region chosen for the study is the land area in the domain of 40° to 65°N and 50° to 170°W. The background values of brightness temperatures are calculated monthly by averaging brightness temperatures at nonprecipitation scenes (near-surface CPR radar reflectivity less than –15 dBZ) at every 2.5° (latitude) by 2.5° (longitude) grid.
 The brightness temperature depression, ΔTB = TB−TB0, averaged over the 4.5 years, is shown in Figure 1 as a function of near-surface CPR radar reflectivity and 2 m temperature, where TB is the MHS observed brightness temperature (regardless weather conditions) and TB0 is the background brightness temperature computed from nonprecipitation scenes for the corresponding month and grid. In this diagram, incidences of 2 m temperature lower than 0°C and near-surface radar reflectivity greater than –15 dBZ may be considered as snowfall cases, and a negative value of ΔTB indicates brightness temperature decrease from the nonprecipitation background. As shown in Figure 1, for snowfall conditions (i.e., 2 m temperature lower than 0°C), ΔTBs at 157 and 190 GHz for snowfall conditions do not turn to negative until near-surface radar reflectivity becomes greater than about 15 dBZ, i.e., under relatively heavy snowfall conditions. ΔTBs at almost all the MHS channels are more likely to be greater than 0 even under the snowfall conditions (>–15 dBZ). In other words, brightness temperatures are more likely warmer under snowing than under nonsnowing conditions, which is particularly evident at 89 GHz. Therefore, the brightness temperature reduction by ice scattering is not the dominant signature for over-land snowfall events, except for medium to heavy snowfalls. For light snowfall conditions, the dominant signature is rather the increase in brightness temperature. Liu and Curry  and Y. Wang et al., (personal communication, 2012) discussed this “warming” signature over cloudy skies during cold seasons and attributed its cause, at least partially, to the emission of microwave energy by liquid water drops in the snowing clouds. In the study of Y. Wang et al., (personal communication, 2012) for over-ocean snowing clouds, they found that some 75% of snowing clouds contain cloud liquid water measurable by satellite microwave radiometers.
 The seemingly surprising behavior of brightness temperature change due to snowing clouds can also be demonstrated by a case on January 22, 2007. Shown in Figure 2 are (a) infrared brightness temperature at Advanced Very High Resolution Radiometer (AVHRR) 11 µm channel, (b) brightness temperature depression ΔTB at MHS/AMSU-B 157/150 GHz channel, and (c) CloudSat CPR radar reflectivity time–height cross section. The AVHRR and MHS/AMSU-B images are composites from two orbits from 0500Z to 0800Z, and the CloudSat data are taken around 0700Z. The lines in Figures 2a and 2b denote the ground track of CloudSat radar measurement that is shown in (c). Snowfall events were observed by CloudSat CPR from 41° to 53°N with the heaviest snowfall occurred around 45°N. However, the 157/150 GHz ΔTB map showed that most of the snowing area has positive values of ΔTB; negative values within the snowing area can be found only around the heaviest snowfall area around 45°N. Furthermore, it is seen that the greatest negative values of ΔTB occur from 53° to 60°N, where CloudSat indicates no precipitation at all. Infrared data shown in Figure 2a indicate cold brightness temperatures between 53° and 60°N along the CloudSat track, suggesting that the microwave radiometer data are responding to cold surfaces probably covered by snow. Clearly, a threshold method to detect snowfall based on the principle that ice scattering reduces upwelling brightness temperatures will fail in this case.
 As shown above, it is difficult to link the brightness temperature variation at any single channel to the intensity of snowfall since the “cooling” signature due to ice scattering may well be swallowed by the “warming” signatures caused by cloud liquid water; even we know perfectly the surface emissivity. In searching for a way to detect snowfall, we investigate next whether the multichannel brightness temperatures as a whole collectively contain any snowfall signature. In Figure 3, we show the root-mean-square (rms) differences of the 5 MHS brightness temperatures taken from the domain of 40° to 50°N and 75° to 85°N during winter months (December, January, and February) of 2006 to 2010 and when 2 m air temperature is lower than 0°C, as a function of the collocated CPR reflectivity near surface, which is a proxy of snowfall rate [Liu, 2008a]. While there is no clear correspondence between the two quantities (if there were, we may simply use the former to derive the latter statistically), we do observe that many pixels have high values of rms difference when no snowfall is occurring, e.g., near-surface radar reflectivity lower than –20 dBZ. In addition, if we only observe the highest values of the rms differences at each near-surface radar reflectivity bin, those values seem to decrease with the increase of near-surface radar reflectivity. In other words, the vector comprised by the five brightness temperatures seems to contain information on snowfall intensity. In the next section, we attempt to use this information to develop a snowfall detection algorithm over land.
4 Snowfall Detection Algorithm
 Since the brightness temperatures from the 5 MHS channels seemed to contain signatures on snowfall over land, the task of our algorithm development is then to extract this signature and convert it to snowfall probability or snowfall rate. One possible approach may be to configure a brightness temperature combination from the five channels, so that this channel combination is the most sensitive to snowfall and not sensitive to variations of other geophysical parameters, such as surface emissivity, atmospheric water vapor, etc. However, how to configure this channel combination, or even whether there would be such a channel combination, is unclear. Therefore, in this study, we take an approach that relates the dominant components in brightness temperature variations statistically to the snowfall probability as observed independently by CloudSat. We evaluate the dominant brightness temperature variations using EOF analysis. Haddad and Park  have also explored the idea to relate the principal components in EOF analysis to snowfall over polar regions. Their results showed that one of the principal components contains information of snowing clouds. Using Tropical Rainfall Measuring Mission precipitation radar measurements as truth for rain intensity, (G. Petty and K. Li, Improved passive microwave retrievals of rain rate over land and ocean, submitted to Journal of Atmospheric and Oceanic Technology, 2012 proposed a rain retrieval method that uses EOFs of clear-sky passive microwave brightness temperatures to separate rain/no-rain pixels and then to retrieve rain rate using the departure of rainy scene EOFs to those of clear-sky scenes.
 We mainly concern the variations of brightness temperatures; their mean values (mean of all pixels with 2 m temperature lower than 0°C) in the study area (40° to 65°N, 50° to 170°W, land area only) are removed first before EOF analysis is conducted. In addition, since MHS (or AMSU-B) is a cross-scanning radiometer, its Earth-viewing angle varies with scan position. Ideally, the EOF analysis should be done for data having the same scan position. However, dividing data to so many subgroups largely reduces the number of samples for the EOF analysis using the MHS-CloudSat matchup data and makes the results unstable. As a compromise, we grouped data of neighboring 10 scan positions (about 11° across) as one subgroup for the EOF analysis, and subsequently for creating look-up tables in the snowfall probability retrievals.
 In Figure 4 are shown the amplitudes of the first three leading principal components resulted from the EOF analysis of the MHS brightness temperatures over North America land areas under the condition of 2 m temperatures lower than 0°C. Note that we re-order the channels as 89, 157, 190, 183±3, and 183±1 GHz, so that their sensitivity to surface emission varies in descending order. The first three EOFs explain 98.9% (88.6%, 8.2%, and 2.1%, respectively) of the total variances in the observed brightness temperatures. The first EOF has the greatest response to TBs at window channels (89 and 157 GHz) and the smallest response to TB near the water vapor absorption line center, implying that this EOF responds mostly to the variation of surface characteristics. The second and the third EOFs display an opposite pattern in Figure 4, presumably one responding to the “warming” by liquid water and/or water vapor and the other to the “cooling” by ice scattering. The linear correlation coefficients calculated between vertically integrated CPR reflectivity (a proxy of ice water path) and the TB projection on the three EOFs are –0.17, 0.05, and 0.39, respectively, indicating that the third EOF probably contains the most ice scattering information. Therefore, it is important to retain the third EOF component in the snowfall retrieval algorithms. While the first two EOFs seem to have less (little) direct information on ice scattering, they help situate the conditions under which the snowfall detection and/or retrieval will be conducted. Therefore, in our snowfall detection algorithm, we will use all the three leading EOFs.
 The CPR radar reflectivity gives the indication of the amount of cloud and precipitation particles in the observed volume. Using simulated backscattering cross sections for several types of nonspherical snowflakes [Liu, 2004; 2008b] and particles size distribution published by several investigators [Braham, 1990; Lo and Passarelli, 1982], Liu [2008a] proposed a radar reflectivity to snowfall rate conversion relation, Ze = 11.5S1.25, where Ze and S denote the effective radar reflectivity factor (in mm6 m–3) and snowfall rate (in mm h–1, liquid water equivalent). For snowfall detection, we need to define a threshold by the CPR radar reflectivity for snowfall onset. Several investigators have so far proposed “precipitation threshold” [e.g., Haynes et al., 2009; Liu, 2008a; Sauvageot and Omar, 1987; Matrosov et al., 2004; Frisch et al., 1995; Baedi et al., 2002; Mace and Sassen, 2000; Kato et al., 2001; Kogan et al., 2005; Wang and Geerts, 2003], mostly for drizzle, with radar reflectivity generally between –20 and –10 dBZ. To be consistent with these previous studies, we define –15 dBZ as the snowfall threshold, which corresponds to about 0.01 mm h–1 snowfall rate based on the Liu [2008a] conversion formula.
 The proposed snowfall detection algorithm is based on a look-up table of snowfall probability in the three-dimensional EOF space (the first three EOFs). In each EOF axis, 20 equally spaced bins are placed according to the possible values of the brightness temperature projection onto the EOF vector. With the first three EOFs being used in this study, there are 8000 cells (20×20×20) in the EOF space. Then, using the collocated MHS/AMSU-B and CloudSat data of 4.5 years, the probability of snowfall is calculated in each EOF cell. The probability of snowfall is defined by the number of observations that have the CPR radar reflectivity greater than –15 dBZ divided by the total number of observations. The distribution of so-derived snowfall probability for the subgroup of the 10 near-nadir pixels is shown in Figure 5. It is seen that probability values are high in one part of (upper left in this figure) of the diagram and decrease gradually toward other directions. The orderliness of the probability values in the diagram indicates the possibility of stable retrievals as we use it as a look-up table. While not shown, diagrams for other scanning positions show a similar behavior.
 It is noted that in Figure 5, there are some random cells with high-probability values in otherwise low-probability neighborhood. Probability values in these cells are probably not reliable due to inadequate number of observations within it. In creating the look-up table, we required at least five datum points in each cell for computing a value of probability. Using five datum points as the minimum is intended to screen out some outliers while not excluding too many legitimate datum points. To create the look-up table in this study, we have used all available matchup data before CloudSat suffered a battery problem in early 2011. To increase the reliability of the look-up table, more satellite radar observations are highly desirable.
 Using the so-derived look-up table, the detection algorithm works as follows: For an observed set of MHS (or AMSU-B) brightness temperatures, , it is first projected onto the first (), second (), and third EOF () by , where i = 1, 2, or 3 and ai denotes the projected amplitude to the ith EOF. The parameter ai then becomes the new “channel” in EOF space, and the snowfall probability can be found in its corresponding cell of the look-up table derived using the MHS/AMSU-B and CloudSat matchup data.
5.1 Case Studies
 Let us first revisit the case shown in Figure 2, in which brightness temperature from any single channel seemed unable to identify the area of snowfall. The retrieved snowfall probability map using the look-up table described in previous section is shown in Figure 6, together with the snowfall probability along the CloudSat track in Figure 2d. Retrievals were not conducted for ocean and lake areas, nor were done where 2 m air temperature is higher than 0°C. Compared to the CloudSat radar reflectivity cross section in Figure 2c, it is found that the retrieved snowfall probability is remarkably consistent to the CloudSat observations. For example, the highest snowfall probability occurs near 45°N; the area with probability greater than 40% extends from 42° to 53°N; and in the area where MHS 157 GHz brightness temperature showed the greatest depression (~55°N), the retrieved snowfall probability is lower than 10%, consistent with the CloudSat CPR's indication of clear sky.
 For the second case, we show the composite data observed on 14 January 2007 during the time period of 1630Z to 2030Z, during which CloudSat passed the study area three times. In Figure 7 are shown the horizontal distribution of retrieved snowfall probability and the 3 CloudSat passes — their tracks, radar reflectivity latitude–height cross sections, and snowfall probability along the tracks. In the portion of the first CloudSat track (Figure 7b) south of 44°N, the 2 m air temperature is warmer than 0°C, no snowfall probability retrieval is conducted. In the region north of 44°N, a snowfall cell and some high clouds are detected by the CPR; the retrieved snowfall probability is higher than 40%. The retrieval algorithm misidentified the high clouds near 49°N as snowfall and missed the weak shallow snowfall near 57°N. Corresponding to the second CloudSat track (Figure 7c), the algorithm correctly identified all the snowfall features except for the weak shallow snowfall cell near 65°N. Low-probability values are retrieved for regions where CloudSat shows no clouds and precipitation. The third CloudSat track (Figure 7d) corresponds to mountainous regions where we did not expect that the algorithm would perform well. However, interestingly, the retrieval algorithm shows reasonably good skill in this region, i.e., high snowfall probability in regions where the CPR shows precipitation.
 Similarly, in Figure 8, we show a case on 11 January 2009 during the time period of 0630Z to 0930Z. In this case, the relatively shallow snowfall cell in Figure 8c and the snowfall cells over mountainous areas in Figure 8d are clearly identified. Again, the algorithm seems to have difficulties to separate clouds with and without precipitation reaching to the surface (Figure 8b). In other words, the algorithm is responding rather to integrated condensates in the atmospheric column, than to the condensates in the level near the surface. This is a common problem to algorithms using passive sensors, and the performance of such algorithm will ultimately depend on the correlative relation between column integrated water and precipitation near surface [You and Liu, 2012].
5.2 Mean Snowfall Pattern
 Using the collocated CloudSat and MHS data, the mean relation between CloudSat near-surface radar reflectivity and MHS-derived probability of snowfall is investigated and shown in Figure 9 as probability density function, normalized so that the summation of values at each MHS-derived snowfall probability category is 100%. In producing this figure, matchup data are first assigned to a two-dimensional bin with a size of 10 dBZ of near-surface CloudSat radar reflectivity by 10% of MHS-derived probability of snowfall. The number of observations in each bin is then counted and normalized by the total number of observations for those bins with the same snowfall probability. Clearly, the MHS-retrieved snowfall probability is positively in correspondence to the near-surface radar reflectivity (a proxy of snowfall rate near surface), implying that heavier snowfall events are more likely to be identified by algorithm as “snowing.”
 Figure 10 shows the Heidke skill score [e.g., Wilks, 2005] distribution calculated from CloudSat–MHS data pairs when assuming various snowfall onset threshold values by near-surface reflectivity and MHS snowfall probability. The ridge in the distribution as shown by dots indicates the best correspondence between a threshold of radar reflectivity and a threshold of MHS snowfall probability. For example, if we believe that CloudSat reflectivity of –15 dBZ is the best threshold for snowfall, the most appropriate threshold when using MHS-derived snowfall probability will be ~40%. Using this pair of thresholds, the number fractions of (a) snowing MHS pixels and (b) CloudSat pixels in every 1°×1° grid over the study area are calculated using data of 4.5 years, and the results are shown in Figure 11. The averaged bias and rms difference between the two fractions are 0.4% and 6.3%, and their correlation coefficient is 0.67. While there are differences in details, the two distribution maps show a great similarity in general, which further confirms the skill of the snowfall detection algorithm.
 Finally, the snowfall detection algorithm's skill is investigated against 2 m temperature, and the results as presented by Heidke skill score is shown in Figure 12. In this investigation, all matchup data are divided into subsets of 5°C bins of 2 m temperature. Within each subset, Heidke skill score is computed using CloudSat near-surface radar reflectivity greater than –15 dBZ and retrieved snowfall probability greater than 40% as snowfall thresholds. As shown in Figure 12, the skill scores decreases as 2 m air temperature becomes colder, from 0.4 near 0°C to 0.1 near –45°C. There are a number of factors probably responsible for this algorithm skill score's dependence on air temperature. First, as temperature lowers, surface is more likely covered by snow, which may confuses the algorithm since scattering signatures by snow on the ground and in the air have similar effect on upwelling microwave radiation. Additionally, snow-covered surfaces are more reflective than bare ground, which enhances the warming effect induced by cloud liquid water and water vapor. Last, under colder environments, snowflakes are generally small in size, which in turn produces weaker scattering signatures.
 The conventional wisdom for detecting snowfall by high-frequency passive microwave observations has been to extract the scattering signature resulting from ice particles, which corresponds to a brightness temperature decrease in respect to nonsnowfall conditions. However, our analysis of multiyear satellite brightness temperature data over land has revealed that on most occasions brightness temperatures are rather higher under snowfall than nonsnowfall conditions. The possible causes for this “warming” have been discussed previously by Liu and Curry  and (Y. Wang et al., personal communication, 2012) and are largely attributed to the emission of cloud liquid water in the snowing clouds, among several other factors such as radiative warming of underlying surface. Regardless the detailed partition among the contributing factors, the very fact of rising brightness temperature complicates the snowfall detection problem, because the scattering signature that is the most directly related to snowflakes has been masked. In this study, instead of attempting to directly extract the scattering signature, we take the advantage of having coincident observations by an active sensor (CloudSat radar) with the high-frequency microwave passive sensors (MHS and AMSU-B) and proposed a statistical approach to the snowfall detection problem. Specifically, we use the cloud radar to train the radiometer observations and to develop a statistical detection algorithm. The statistical algorithm does not depend on ice scattering alone. Rather, it seeks to differentiate the joint variations of brightness temperatures at all MHS/AMSU-B channels, i.e., the brightness temperature vector, under snowfall and nonsnowfall conditions. In other words, even the brightness temperature warming due to cloud liquid water can also be used in the detection algorithm, if this signature acts differently in changing the brightness temperature vector between snowfall and nonsnowfall conditions.
 To capture the variations of brightness temperature vector, we first carried out EOF analysis of brightness temperatures over the study region of 40° to 65°N and 50° to 170°W (land areas only). It is found that the first three EOFs capture most (~99%) of the variances of the brightness temperatures and the third EOF has the highest correlation with radar reflectivity. The detection algorithm is then designed using the information contained in the first three EOFs. Specifically, assuming near-surface CloudSat radar reflectivity of –15 dBZ as snowfall threshold and using the collocated CloudSat and MHS data, a look-up table of snowfall probability, defined as the number ratio of snowfall pixels to all observed pixels, is made in the three-dimensional EOF space. Constructing the look-up table can be considered to be the training phase of the detection algorithm. In the retrieval phase, the five observed brightness temperatures are first projected on to the three EOFs, and the amplitudes of their projections are then used to find the snowfall probability in the look-up table. Therefore, this detection algorithm gives a snowfall probability for every radiometer observation. If one prefers a binary decision of the presence of snowfall, our analysis using Heidke skill scores indicates a snowfall probability of 40% corresponds the best to the –15 dBZ CloudSat snowfall threshold. Due to the lack of independent validation data, the validity of the detection algorithm is examined by coincident CloudSat radar observations primarily through case studies. For all the cases examined, there is a clear positive response of retrieved snowfall probability to CloudSat radar reflectivity, even over mountainous regions, which affirms the skill of this approach. However, as for all radiometer observations, the algorithm lacks the ability to distinguish hydrometers near the surface and high above, which leads to snowfall false alarms when hydrometeors do not reach surface.
 While the results as shown in the validation section are encouraging, this study is of many shortcomings primarily due to the limitation of the datasets. First, CloudSat radar covers a narrow (1.5 km) path, and the satellite is in a different orbit from those satellites carrying MHS/AMSU-B sensors, which limits the number of coincident sample even we use all available data. Because of the statistical nature of the look-up-table detection algorithm, this limitation may particularly cause inaccuracy to the cells in the table that corresponds to “rare events” (mostly likely heavy snowfall events). Second, the size of CloudSat pixels is much smaller than the MHS/AMSU-B pixel size. While the error caused by this mismatch is random, its magnitude can be big. In this study, besides matching two pixels with the closest centers, we also tried averaging all CloudSat pixels within the MHS/AMSU-B field of view. Since the pixel sizes of the two sensors are so different, the two matching approaches do not change the final result large enough to alter our conclusions. We suspected that this pixel size mismatch is the major source of random error in this algorithm. The GPM core satellite is scheduled to launch in 2014, carrying high-frequency radiometers with spatial resolution better than 5 km and a dual-frequency radar [Hou et al., 2008]. The mismatch problem can be largely mitigated when applying the same approach to the GPM sensors. Last, the validation performed in this study is based on CloudSat data that are also used for producing look-up tables. Validations using independent measurements other than CloudSat's, such as those from surface radars, are highly desirable in the future.
 This research has been supported by NASA grants NNX10AG76G and NNX10AM30G. EKS's participation of this research has been supported by the Korea Meteorological Administration Research and Development Program under grant CATER 2012–2062 and the research grant of the Kongju National University in 2011.