Development of A Snowfall Retrieval Algorithm at High Microwave Frequencies

Transcription

1 Development of A Snowfall Retrieval Algorithm at High Microwave Frequencies Yoo-Jeong Noh 1, Guosheng Liu 1, Eun-Kyoung Seo 1, James R. Wang 2, and Kazumasa Aonashi 3 1. Department of Meteorology, Florida State University, Tallahassee, Florida, USA 2. NASA Goddard Space Flight Center, Greenbelt, Maryland, USA 3. Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Ibaraki, Japan Corresponding Author Address: Yoo-Jeong Noh Department of Meteorology Florida State University Tallahassee, FL USA (85) (85) (fax) yjnoh@met.fsu.edu (Revised and submitted to Journal of Geophysical Research Atmospheres, March 26)

2 Abstract A snowfall retrieval algorithm based on Bayes theorem is developed using high frequency microwave satellite data. In this algorithm, observational data from both airborne and surface-based radars are used to construct an a-priori database of snowfall profiles. These profiles are then used as input to a forward radiative transfer model to obtain brightness temperatures at high microwave frequencies. In the radiative transfer calculations, two size distributions for snowflakes and ten observed atmospheric sounding profiles are used with snowfall profiles from observations. In addition, the scattering properties of the snowflakes are calculated based on realistic nonspherical shapes using discrete dipole approximation. The algorithm is first verified by airborne microwave and radar observations and then applied to the Advanced Microwave Sounding Unit-B (AMSU-B) satellite data. The retrieved snowfall rates using AMSU-B data from three snowfall cases in the vicinity of Japan show reasonable agreement with surface radar observations with correlation coefficients of about.8,.6 and.96 for the three cases, respectively. The comparison results also suggest the algorithm performs better for dry and heavy snow cases, but is less accurate for wet and weak snow cases. 1

3 1. Introduction Passive microwave instruments on satellites, such as the Special Sensor Microwave Imager (SSM/I) and the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), have provided measurements of global rainfall over the past several decades. In particular, the accuracy of rainfall retrievals has greatly improved in the tropical regions with the success of TRMM [Kummerow et al., 21]. However, precipitation retrieval over the higher latitudes, particularly snowfall retrieval, has not received as much attention. Although falling snow is an important component of global precipitation in extratropical regions, an accurate satellite snowfall algorithm has not yet been developed. It is believed that there are two major reasons for this lag. First, the ice signature is indistinguishable from the liquid water signature at visible and infrared wavelengths, and the radiative signature of snow particles (scattering signature) is weak at low microwave frequencies (<9 GHz). This leaves high-frequency microwave as the best candidate for snowfall retrieval. But satellite observations with a reasonable spatial and temporal resolution at these frequencies were not available until recently when the Advanced Microwave Sounding Units B (AMSU-B) was launched onboard the NOAA-15 satellite. The second reason for this lag is the nonspherical shape of ice particles and snowflakes, whose radiative properties are much more complex than their liquid counterparts (water drops). Additionally, the thermal emission by water vapor and cloud liquid water has a masking effect on the snow scattering and reduces the snowfall signature [Liu and Curry, 1998]. Studies of the scattering signatures of snow particles by several investigators laid the foundation for us to develop a snowfall retrieval algorithm. Using the discrete-dipole approximation (DDA, [Draine and Flatau, 2]), Evans and Stephens [1995] and Liu [24] 2

4 studied the single-scattering properties of ice and snow particles at high microwave frequencies. They pointed out that the scattering properties of nonspherical ice and snow particles are substantially different from spherical particles of equal volume. Based on the results of DDA simulations, Liu [24] proposed parameterizations of the scattering and absorption cross-sections and the asymmetry parameters for rosettes, sector, and dendrite snowflakes. Weng and Grody [2] showed that the scattering due to ice clouds is strongly dependent on frequency, and unlike the emission process, the scattering process is very sensitive to the distribution of the ice particle size. After analyzing data observed over ocean by an airborne radiometer and radar, Katsumata et al. [2] reported that snow clouds can reduce upwelling brightness temperatures at 89 GHz by up to ~15 K while being hardly detectable by radiometers at frequencies lower than 37 GHz. By radiative transfer modeling, Bennartz and Petty [21] and Bennartz and Bauer [23] concluded that in the middle and high-latitudes, the frequent occurrence of frozen precipitation makes it necessary to utilize high-frequency channels (>1 GHz) that are more sensitive to scattering by precipitationsized particles. They pointed out that a channel around 15 GHz contains significant useful information for identification and retrieval of frozen precipitation at middle and high latitudes. The advantage of the scattering information, especially at high microwave frequencies (greater than 89 GHz), is that it is sensitive enough to be detectable by satellites for frozen phase particles like snowflakes; it also can provide information about precipitation over strongly emitting surfaces and hence is the primary basis for estimating precipitation rates over land. Using the ice scattering signature at high microwave frequencies, algorithms to retrieve cloud ice water path and snowfall have been developed by several investigators. Liu and Curry [1998] and Deeter and Evans [2] presented methods to retrieve ice water path using airborne millimeter-wave radiometer data at 89, 15, 183±1, 183±3, 183±7 and 22 3

5 GHz. Liu and Curry [2] and Zhao and Weng [22] developed ice water path algorithms using high frequency microwave data from the Special Sensor Microwave Water Vapor Profiler (SSM/T2) and the AMSU-B data. Skofronick-Jackson et al. [23] investigated the combined use of radar and radiometer data at high microwave frequencies to retrieve microphysical profiles in tropical convective cloud. Also, Skofronick-Jackson et al. [24] presented a physical method to retrieve snowfall over land using AMSU-B data, and they applied the algorithm to a blizzard case that occurred over the eastern United States in 21. The goal of this study is to develop a snowfall retrieval algorithm based on Bayes theorem using high frequency microwave satellite data. An important component of the Bayesian algorithm is the a-priori database that connects brightness temperatures to snowfall rates. In constructing this database, we used a large number of snowfall profiles observed from both airborne and surface radars for shallow snow convections in the vicinity of Japan. We related these profiles to brightness temperatures with a radiative transfer model [Liu, 1998]. Therefore, this algorithm is particularly applicable to snowfall associated with shallow convections. A new feature added to the radiative transfer model is single-scattering properties parameterized for nonspherical snowflakes [Liu, 24]. To diversify the microphysical properties in the database, several published particle size distributions and atmospheric soundings measured over Japan during 23 are used. In situ data are desirable to validate and improve satellite retrieval algorithms; therefore, the lack of observational data has been a serious problem hampering snowfall algorithm development. Recently, the Wakasa Bay 23 field experiment [Lobl et al., 25] was conducted to validate satellite retrieval products from the Advanced Microwave Scanning Radiometer EOS (AMSR-E). It provides both remotely sensed and in situ data of snowfall 4

6 events. The current study takes full advantage of this rich dataset for the purpose of snowfall retrieval algorithm development and validation. The rest of this paper is arranged as follows. Section 2 describes the dataset used for the study. Description of the a-priori database is given in section 3. The Bayesian retrieval algorithm is presented in section 4. In section 5, the algorithm is applied to AMSU-B data for snowfall events observed in the vicinity of Japan, and the results are compared with ground based radar-raingauge network data. Conclusions are given in section Data In this study, the Wakasa Bay and its surrounding areas (Fig. 1) near the Sea of Japan are the main focus. In order to construct a database for snowfall retrievals, data collected during the Wakasa Bay 23 field experiment [Lobl et al., 25] are used. This field experiment was carried out near Japan for: validating precipitation products from AMSR-E, examining the AMSR-E s shallow rainfall and snowfall retrieval capabilities, and understanding the precipitation structures through new remote sensing technology. Of the various datasets collected in the experiment, the data from the following two remote sensors onboard a C-13 aircraft are analyzed: the Millimeter-Wave Imaging Radiometer (MIR) and the dual frequency Precipitation Radar (PR-2). The MIR is a total power, cross-track scanning radiometer that measures radiation at seven frequencies: 89, 15, 183.3±1, 183.3±3, 183.3±7, 22, and 34 GHz [Racette et al., 1996]. The sensor has a 3-dB beam width of 3.5 at all channels. It can cover an angular swath up to ±5 degrees with respect to nadir. Each scan cycle is about three seconds [Wang, 23]. The PR-2 operates at 13.4 GHz (Ku-band) and 35.6 GHz (Ka-band), and uses a deployable 5.3-m electronically scanned membrane antenna 5

7 [Im, 23]. Besides the airborne remotely sensed data, nine upper air sounding profiles and in situ particle size distributions (explained in detail in section 3.2) observed at Fukui airport (36.14 N, E) during the Wakasa Bay 23 field experiment are used. Data from a 3.2 cm Doppler radar were also used to build the a-priori database. The radar was operated at Obama (35.55 N, E) in the coastal area of the western Japan from 2 to 17 February 21. To convert the equivalent radar reflectivity (Z e ) of this radar to snowfall rate (S), we used the Z e -S relationship of Aonashi et al. [23], which is derived by comparing the near surface radar reflectivity of this radar with the reading of a weighing snow gauge. The snowfall retrieval algorithm is applied to the NOAA-16 AMSU-B data. The AMSU-B has five channels: 89, 15, 183.3±1, 183.3±3, and 183.3±7 GHz [Zhao and Weng, 22]. The AMSU-B scans crosstrack ± 47 from nadir, thereby covering approximately a 2 km wide swath. The spatial resolution at nadir is ~16 km. Five of the seven MIR channels operate at the same frequencies as the AMSU-B. Finally, to validate the retrieved results, the AMeDAS (Automatic Meteorological Data Acquisition System) radar precipitation data are used. The AMeDAS [Makihara et al. 1995; Oki et al., 1997] consists of radar and automatic rain gauge stations located all over Japan. The radar-amedas data are 1-hr accumulated precipitation observations from gaugecalibrated radars. The data cover all of Japan and its coastal area. The spatial resolution is approximately 5 km x 5 km. 3. Building the a-priori Database 6

8 An important component of a Bayesian retrieval algorithm is the a-priori database that connects the observations (brightness temperatures) with the parameters to be retrieved (snowfall rates); the probability density of a snowfall rate in the database should be consistent with the likelihood of the same snowfall rate occurring in actual snow events. To build such a database, we collect snowfall data from airborne and surface based radars. The radar reflectivity is converted to snowfall rate, and a radiative transfer model is used to link the snowfall rate to microwave brightness temperatures. In an effort to accurately calculate the scattering parameters of snowflakes in radar equations and radiative transfer models, we performed DDA simulations using realistic snow particle shapes. The DDA [Draine and Flatau, 2] is a general method for computing the scattering and absorption of arbitrarily shaped particles. It is useful in studying the scattering caused by complex particles like dendrites. Two types of snowflakes are considered in the DDA computations as shown in Fig. 2. The ice volume is concentrated in the six main branches in type-a (sector snowflake) and more uniformly spreads across the basal plane in type-b (dendrite snowflake). Both types of snowflakes obey the following relations derived by Heymsfield et al. [22]: A =.261D r ρ =.15A e.377 max 1.5 r D 1. max, (1) where D max is the maximum dimension of the snowflakes, A r is the area ratio (the projected area of a snowflake normalized by the area of a snowflake with diameter D max ), and ρ e is the effective density defined as the mass divided by the volume of a circumscribed sphere. 3.1 Conversion of Radar Reflectivity to Snowfall Rate 7

9 Vertical snowfall rate profiles are derived from both the surface Doppler radar and the PR-2. These are used for building the a-priori database. To convert equivalent radar reflectivity of the surface Doppler radar to snowfall rate, a Z e -S relationship empirically derived by Aonashi et al. [23] is used. It was derived by comparing simultaneous observations of the near surface Doppler radar reflectivity to the snowfall rate of a weighing snow gauge. However, since there are no simultaneous Z e and S observations for PR-2, we derive the Z e -S relations for PR-2 based on theoretical calculations. The backscatter cross sections calculated from the discrete-dipole approximation (DDA) for snowflakes is used to develop the Z e -S relationships. For the snowfall rate calculation, the following equation by Rutledge and Hobbs [1983] for terminal velocity near ground is employed: v ( D) = D, (2).11 max where D max is the maximum dimension of snowflakes in m. Figure 3 shows the so-derived Z e -S relationships by symbols for three frequencies (13.4, 35.6, and 94 GHz) together with several other relations published in the literature for comparison. The Z e -S relations derived in this study are generally within the envelope of previously published ones. It appears that the difference of the Z e -S relations between the two snowflake types is small compared to the difference among different frequencies. Therefore, we take the averaged relation of the two snowflake types, but use separate equation for each of two PR-2 frequencies, i.e., 1.83 Z e = 25S at 13.4 GHz (3a) 1.4 Z e = 88.97S at 35.6 GHz (3b) where Z e is the equivalent radar reflectivity in mm 6 m -3, and S is the snowfall rate in mm h -1. 8

10 3.2 Radiative Transfer Modeling of the Observed Snow Events Since the a-priori database linking the brightness temperatures and snowfall rate will be constructed by radiative transfer calculations, it is essential that the radiative transfer model can produce brightness temperatures consistent with observations. This step is particularly important for the radiative transfer modeling of snowfall because the scattering properties of nonspherical snowflakes are not as well understood as those of raindrops. In this section, we simulate and compare the model brightness temperatures with those observed by MIR during the Wakasa Bay 23 field experiment to ensure the validity of the radiative transfer model. The radiative transfer model used in the study solves the radiative transfer equation using the discrete ordinate method [Liu, 1998] and calculates the single-scattering properties of nonspherical snowflakes using the DDA based parameterization described by Liu [24]. It assumes the snowflakes are composed equally (by mass) of sector and dendrite particles with random orientations. On 29 January 23, strong northwesterly flow was dominant over the Sea of Japan, and extensive areas of snowfall were reported along the west coast of the main island of Japan. An aircraft flight observed the snowfall over ocean along several different flight legs; Figure 4 shows the well-developed convective cells, with echo tops up to 4 km, observed on the first flight leg by the airborne radiometer MIR and the PR-2 radar. Aircraft nadir observations of the brightness temperature depressions ( T B = T B - T B, where T B and T B are the cloudy and clear-sky brightness temperatures, respectively) and the time-height cross section of snowfall rate converted from PR GHz and 35.6 GHz radar reflectivity are presented in the figure. The clear-sky brightness temperatures are derived from locations where no radar echo was 9

11 observed. The depression of MIR brightness temperatures is a response to the convective snow cells, although the sign and the amplitude of the variation are channel-dependent. The depressions of brightness temperatures are significantly greater at 22 and 34 GHz than the other channels, and they reach about 8 K for the first cell. Among the three 183-GHz water vapor channels, 183±7 GHz is the most sensitive to the snowfall cells. It is notable in Fig. 4a that the 89-GHz brightness temperatures in some convective cells are higher than clear-sky values; this implies rich cloud liquid water exists in these cells, which is a result consistent with Katsumata et al. [2] who studied snow clouds in the same region. While the increase in brightness temperature occurs at 15 GHz as well, the overall signature in this channel is of a depression corresponding to a snow cell. To take into account the emission from cloud liquid water, a layer of cloud liquid water is assumed between 3 and 3.5 km. The liquid water path (LWP, g m -2 ) is determined by the brightness temperature increase at 89 GHz using the equation (4) that is derived by regressing radiative transfer model simulation results. LWP = T. (4) 2.52( B89 ) Due to the uncertainties for input variables such as atmospheric water vapor profiles and snow particle size distributions, we choose to vary these variables in the radiative transfer model simulations. One of the most commonly used particle size distributions for snowflakes is in an exponential form: N( D) = N exp( ΛD). (5) The parameters N and Λ may be expressed either as constants or as functions of snowfall rate. In the radiative transfer simulations, we used the same form of the particle size distribution as (5), but with two different parameterizations of the N and Λ. First, the distribution of Sekhon 1

12 and Srivastava [197] was used, with N and Λ parameterized as functions of S. The second size distribution was derived from data by Dr. Muramoto s research team at Kanazawa University ( referred to as the Muramoto size distribution hereafter.), who analyzed images of snow particles observed at Fukui Airport every 1 minutes from 16 LST 28 January to 8 LST 29 January 23. In Fig. 5, some examples of the observed particle size distributions and their corresponding precipitation rates are presented. The parameters for the exponential distribution equation are obtained from curve-fittings of these observations. The Muramoto size distribution is used in the radiative transfer simulation together with the size distribution of Sekhon and Srivastava [197]. Simulations are conducted to examine the radiative transfer model and the specification of the input parameters. In Fig. 6, the model results are shown for the 29 January 23 snow case (Fig.4). The x-axis represents the MIR observations and the y-axis the model results. The black circles represent the results of using the Muramoto size distribution (from observations) and one Fukui sounding profile with the surface wind speed of 8 ms -1 (averaged from observations); the red triangles show the Sekhon and Srivastava size distribution and the US standard winter mid-latitude atmosphere; the blue triangles represent the Sekhon and Srivastava size distribution and one Fukui sounding profile. Considering all the uncertainties related to the model inputs, the modeled T B s generally agree with the MIR observations. However, the modeled result at 34 GHz has a larger depression than observed. While 22 and 34 GHz channels are not used in the satellite retrievals at this stage because no satellite has theses channels, disagreements at these two frequencies should be improved through future works using more detailed bias analyses as done by Bauer and Mugnai [23]. As expected, 89 GHz responds more sensitively to liquid water compared to the other channels; this results in positive T B values in Fig. 6. From the other test simulations (not shown here), 11

13 the surface temperature change (from 273 K to 267 K) in the model does not have any measurable effect on the brightness temperature depressions. In spite of the fair agreements between the model and observations, there are still uncertainties in perfectly simulating the real atmosphere by the radiative model. To reduce possible biases in modeling, various combinations of input conditions will be used to generate the database. 3.3 Constructing the Database Now that the radiative transfer model produces reasonable brightness temperatures, we next use this model to link snowfall rate with brightness temperatures at high microwave frequencies. The snowfall profiles in the database are made using two sources: PR-2 data from the 23 Wakasa Bay experiment and surface radar data from February 21. The PR-2 snowfall rate profiles are derived from PR-2 observations made on 29 January 23. Radar reflectivity is converted to snowfall rate using (3), and a liquid water cloud layer is inserted between 3 and 3.5 km with liquid water path using (4) calculated from 89 GHz T B. A total of 221 snow profiles are generated from the PR-2 dataset. Surface radar data from two snowy days, February 21, are also used to enrich the database. Radar reflectivity was converted to snowfall rate using the Aonashi et al. [23] empirical Z e -S relationship. As mentioned earlier, the snow clouds in this region are rich in liquid water. However, the surface radar observations do not contain information on cloud liquid water because of the small size of cloud liquid water droplets. To obtain realistic snow cloud profiles for radiative transfer modeling, we add a liquid water cloud layer to the snowfall profiles derived from surface radar. To determine how much liquid water to include in each snowfall profile, we conducted an Empirical Orthogonal Function (EOF) analysis on 12

14 the database from the Wakasa Bay 23 field experiment, in which both snowfall profile and liquid water amount are available. The EOF method, as described by Biggerstaff et al. [26] and von Storch and Zwiers [1999], relates the one-dimensional variable of snowfall profiles to the scalar variable of liquid water content. Using this method, the dimensionality of each snowfall profile can be reduced to the scalar values of the EOF coefficients. Using these coefficients, the relationship between the vertical distribution of liquid water contents and snowfall profiles was obtained. The derived liquid water contents of each snowfall profile in 21 are combined with surface radar data to construct about 1 snow cloud profiles. The a-priori database is then constructed through radiative transfer model simulation using all possible combinations of: 221 Wakasa Bay (23) snow cloud profiles, about 1 surface radar (21) snow cloud profiles, a total of 1 atmospheric sounding profiles (from observations at Fukui and the US standard mid-latitude winter atmospheric profile), and two types of particle size distributions. The total number of datum points in the database is about Bayesian Retrieval Algorithm A retrieval algorithm based on Bayes theorem can be stated mathematically as follows [e.g., Olson et al., 1996; Evans et al., 1995, 22]. Let vector x represent snowfall rate profiles, and vector y represent available observations. In general, the best estimate of x, given the observations y, is assumed as the expected value, E( x y ) =... x P ( x) d x. (6) In Bayes theorem, the probability density function, P(x), is written as P x) P( y = y x = x ) P( x = x ) P [ y y ( x)] P ( ), (7) ( true true OS s a x 13

15 where P OS is the probability equivalent to the distance between observation y and simulations y s (x) for the atmosphere state x. P a is the a-priori probability that x is true. If we assume that the errors in the observations and the simulations are Gaussian and uncorrelated, then P OS can be written as POS T 1 [ y y s ( x)] exp{.5[ y y s ( x)] ( O + S) [ y y s x ( )]}, (8) where O and S are the observation and simulation error covariance matrices, respectively. For a sufficiently large database, the integral in (6) can be approximated by the summation for all x j. If we assume that the profiles in the database occur with the same relative frequency as those in nature, or at least with the same frequency as those found in the region where the retrieval method is applied, then the weighting by P a is represented simply by the relative number of occurrences of a given profile type x j. Then (6) may be written as exp{.5[ y y ( x ( O + S) [ y T 1 ˆ s j E( x y ) = x j j  where the normalization factor is )] y ( x s j )]}, A ˆ T 1 = exp{.5[ y y ( x )] ( O + S) [ y y ( )]}. (1) j s j s x j In the present study, the error covariance matrices, O and S, are set as follows similar to Olson et al. [1996]. The error covariance matrix, S, has no contribution if the model simulation, y s (x), is assumed to be true. The observation error variances are set equal to the instrument error variances with an assumption of zero-mean Gaussian distributed noise with a standard deviation of 1.5 K to each channel except for.6 K to 15 GHz and 183±7 GHz. Due to a lack of information on the correlation of errors between channels, only the diagonal terms of the matrix O are estimated here, and off-diagonal terms are set to zero. The matrix (9) 14

16 (O+S) -1 for any in a model database is inversely proportional to the value of a diagonal term of the error variance, which determines the width (or spread) of the weighting function in terms of brightness temperature distance. In the retrievals, we use [3 K, 1.2 K, 3 K, 3 K, 1.2 K] for TB 15 K and [4.5 K, 1.8 K, 4.5 K, 4.5 K, 1.8 K] for TB 15 K, respectively, as observation plus simulation uncertainties for each frequencies for AMSU-B. The algorithm is then applied to the case of 29 January 23 as an assessment of the algorithm s performance. Figure 7 shows the retrieved snowfall by applying the algorithm to MIR data measured for two different flight legs. The observed snowfall from PR-2 35 GHz (the upper panels) is compared with the retrievals. It appears that the retrieval algorithm captures the basic features of the snow cloud cells, although differences exist in details between the observed and retrieved structures. In Fig. 7b, the retrieved snowfall rates are underestimated particularly around the fifth cell compared to the observations. This problem may also have been partly caused by the following reason: since MIR data at 34 and three 183 GHz channels had noises around the fifth cell, data from these frequencies were not utilized in the retrieval algorithm. 5. Application of AMSU-B Snowfall Retrieval to Snowfall Over the Sea of Japan The snowfall retrieval algorithm is applied to the AMSU-B satellite data. Since there are no 22 and 34 GHz channels in AMSU-B, the AMSU-B version of the retrieval algorithm only uses data from five channels with frequencies from 89 to 183±7 GHz. Three snowfall cases are studied from 14, 16 and 27 January 21. These were located over Japan and its surrounding areas, and coincided with the field experiment Winter MCSs Observations over the Japan Sea - 21 [Murakami et al., 21a, 21b; Yoshizaki et al., 15

17 21]. During 12 to 19 of January, the cold airmass with air temperature lower than 35 C at 5 hpa stayed quasi-stationary over the Japan Sea. Heavy snowfalls occurred on the western coastal areas of the Japan Islands. The snowfall was mainly induced by quasi-stationary bandshaped snowfall systems elongated east and west along the southern coast of Japan. Meanwhile, on 27 January a synoptic cyclone developed and brought heavy snowfalls over the Kanto plain. For 14, 16, and 27 January 21, Figures 8 through 1 show the brightness temperature depressions at four of the five AMSU-B frequencies, the retrieved snowfall rates at 1.5 and 2.1 km, the hourly-accumulated snow amount from the AMeDAS radar data, and the GMS infrared (IR) cloud top temperatures. Note that the AMeDAS radar snow amount is the hourly-accumulated snow (in mm) averaged for 3 hours around the nearest time to the satellite passage or 1-2 hours after satellite passage, not instantaneous snowfall rate. Heavy snow bands are observed in the Wakasa Bay area on 14 and 16 January from the AMSU-B observations (Fig. 8a-d and 9a-d). As stated by Bennartz and Bauer [23], the reduction of brightness temperature due to the scattering of snow appears much stronger at 15 GHz than at 89 GHz. The snow bands are also clearly resolved at 183±7 GHz frequency. On 14 January 21, the retrievals near the surface (Fig. 8e) are in good agreement with the AMeDAS radar observations. In particular, strong snow bands northeast of the Wakasa Bay are clearly reproduced in the retrievals. Despite the difficulty of direct quantitative comparison between surface radar data and retrievals from the satellite, the maximum snowfall region shows a similar magnitude and pattern. Meanwhile, in Fig. 8h IR signals for snowfall are not clearly distinguishable; there is just an exceedingly blurred pattern of clouds. It is noteworthy that the broad distribution of the depressions of brightness temperatures at 183±1 GHz is very similar to that of low IR cloud top temperatures. 16

18 For the 16 January 21 case, our retrieval algorithm exactly detects two strong stationary snow bands shown in Fig. 9b and 9d, although the maximum snowfall appears slightly behind in the west side of the Wakasa Bay. The snow band in the 16 January case is a continuation of the snow band shown earlier on 14 January, which lasted several days. However, the pattern of brightness temperature depressions at 89 and 183±1 GHz channels become less similar to that of 15 and 183±7 GHz channels and differ significantly from the IR image. It is inferred that the characteristics of these snow bands, including the composition of liquid and ice/snow in the clouds, have changed during 14 to 16 January. In contrast to snow bands in the previous two cases, an organized snow cloud system associated with a polar low on 27 January was observed. In the GMS IR image (Fig. 1h), we can see that clouds covered most of central Japan. The intense echo area was circular/spiral in shape and corresponded to the maximum depression of brightness temperature of about 7 K at 15 GHz (Fig. 1b). The AMSU-B snowfall retrievals show broad snow coverage over central Japan that compares well with AMeDAS snow accumulation about 2 hours after satellite passing time. Next, we examine the algorithm s performance in a more quantitative manner using a scatterplot of satellite retrieved snowfall rate versus AMeDAS radar observed hourly snowfall accumulation (Fig. 11). The data pairs in the scatterplot are generated by averaging the satellite retrievals and the AMeDAS radar hourly snowfall accumulations to a 1 x 1 grid over the same area of Fig In addition, for a satellite retrieval AMeDAS hourly snowfall accumulations (3-hr averaged to the center time) from 3 time periods are compared: the nearest hour to the satellite passage, 1 hour after, and 2 hours after satellite passage. The correlation coefficients between satellite retrievals and AMeDAS data at these times are, respectively:.796,.834, and.79 for the 14 January 21 case;.625,.634, and

19 for the 16 January 21 case; and.915,.96, and.971 for the 27 January 21 case. Although the correlation coefficients for the January 16 case are relatively lower than the other cases, the highest correlation between the satellite retrievals and surface radar measurements occurs about 1 or 2 hours after the satellite passage. This phenomenon may reflect the fact that satellite-measured quantities are snow particles floating in the atmosphere; it takes time for the low-terminal-velocity snowflakes to reach surface. The correlation coefficients shown above for the three cases are very different, ~.8 for the January 14 case, ~.6 for the January 16 case, and ~.96 for the January 27 case. To get insight into this difference, we investigate how brightness temperatures at each frequency contributed to the retrieval. Figure 12 shows the brightness temperature depressions at different channels versus snowfall rate retrievals. The correlation coefficients at each frequency for three cases are summarized in Table 1. For all the cases, the correlations are higher at 15 GHz and 183±7 GHz except for 15 GHz of 16 January case. Since they are more sensitive to ice/snow scattering, a higher weighting has been given to these two channels in our algorithm. It is interesting to notice that for the January 27 case the correlation coefficients between snowfall rate and brightness temperature at all channels are high, and the brightness temperature depressions are large. The strong scattering signature leads the algorithm to perform the best. On the other hand, on January 16 the brightness temperature depressions are small, and the correlation for 89 GHz is even close to zero. It is interpreted that rich cloud liquid water exists in this case, and the algorithm performs not as well under such conditions. For these snowfall cases, the coverage of the a-prior database is examined by an EOF analysis to the brightness temperatures of the AMSU-B data and the database [Bauer, 21; Seo and Liu, 25]. Figure 13 shows the multi-channel coverage of the database (shaded 18

20 contours) projected onto the EOF domain of the AMSU-B observations (line contours with intervals of.5). The first and second EOFs represent about 98% of total variance of brightness temperatures in our database. In Fig. 13, although the maximum occurrence is not perfectly matched, it is shown that most of the observed cases are covered by the database. 6. Conclusions A snowfall retrieval algorithm has been developed based on Bayes theorem using high frequency microwave radiometry observations. The a-priori database of the Bayesian algorithm is constructed using airborne and surface based radar measurements of snowstorms in the vicinity of Japan Sea. The relations between brightness temperatures and snowfall rates in the database are established by radiative transfer modeling. The algorithm is subsequently applied to airborne MIR and satellite AMSU-B measurements of snowfall near the Japan Sea, and the retrieved snowfall rates are compared with surface radar observations. Since the a-priori database is an essential component of the Bayesian retrieval algorithm, special attention has been paid in this study to its construction. First, the backscattering of radar reflectivity and the single-scattering properties used in the radiative transfer model are calculated using a discrete dipole approximation for realistic nonspherical ice particles. Using the scattering properties from nonspherical particles, snowfall rates derived from radar reflectivities and brightness temperatures derived from radiative transfer models are expected to be more accurate than those computed from (so far) widely used spherical approximations. The radiative transfer model that is used to compute brightness temperatures for given snowfall rate profiles was tested against airborne microwave radiometer data. Given the uncertainties in input variables, it appears that the model results 19

21 agree reasonably well with observations except for the very high frequency 34 GHz channel. Second, the snowfall rate profiles used for building the database are from actual radar observations. The use of observational data instead of numerical model outputs ensures that the statistics of snowfall rate profiles in the database are consistent with those occurring naturally. To enrich the database, we included profiles from airborne radar and surface radar observations. Third, the diversity of the database is further enhanced by using two different types of particle size distributions: the widely used Sekhon and Srivastava [197] distribution and the Muramoto distribution that was derived in the Japan Sea region using in situ ice particle measurements. Furthermore, embedded cloud liquid water layers and ten atmospheric sounding profiles are used as input for computing brightness temperatures with a radiative transfer model. The Bayesian snowfall retrieval algorithm was applied to satellite microwave AMSU- B data for three snowfall cases during January 21 in the vicinity of the Japan Sea. The retrieved results are compared with the AMeDAS surface radar observations. Overall, the algorithm produces snowfall patterns in agreement with the radar data, especially within 1-2 hours after the satellite passage. The correlation coefficients between 1 x1 gridded results of retrieved snowfall rate and AMeDAS radar snow accumulation varies from ~.6 for a relatively light snowfall case of snow bands with smaller scales to ~.96 for a heavy snowfall case associated with a low-pressure system. It appears that the snow particles are relatively wet for the low correlation case with rich cloud liquid water, but the snow particles are dry for the high correlation case, in which all AMSU-B channels show appreciable scattering signatures. Therefore, further characterizing the vertical structure of hydrometeors through inclusion of cloud liquid water layers, through observation, and through development 2

22 of the a-priori database accordingly are highly desirable for improvement of the accuracy of wet snowfall retrieval in the future. A further note is that the database developed in this study is based on observations of snowfall events near the Japan Sea for the sole reason of data availability. Therefore, our algorithm is considered best suited for snowfall in this region. However, as more snowfall radar observations become available in the future, for example by CloudSat radar [Stephens et al., 22], a global database can be constructed in a similar fashion, and the algorithm may be applied globally. Acknowledgements. The authors thank all team members of the Wakasa Bay 23 field experiment for providing radar, radiometer, in situ, and upper air sounding data. This research has been supported by NASA grants NAG and NNG4GB4G. 21

23 References Aonashi, K., Y. Shoji, H. Fujii, T. Koike, S. Shimizu, K. Nakamura, Y.-J. Noh, and G. Liu (23), The structural and microphysical characteristics of solid precipitation derived from Wakasa Bay field experiment, Preprints of 22 Fall Meeting of the Meteorological Society of Japan. Bauer, P. (21), Over-Ocean rainfall retrieval from multisensor data of the Tropical Rainfall Measuring Mission. Part I: Design and evaluation of inversion databases, J. Atmos. Oceanic Technol., 18, Bauer, P., and A. Mugnai (23), Precipitation profile retrievals using temperature-sounding microwave observation, J. Geophys. Res., 18, D23, doi:1.129/23jd3572. Bennartz, R., and P. Bauer (23), Sensitivity of microwave radiances at GHz to precipitation ice particles, Radio Sci., 38, D875, doi:1.129/22rs2626. Bennartz, R., and G. W. Petty (21), The sensitivity of microwave remote sensing observations of precipitation to ice particle size distributions, J. Appl. Meteor., 4, Biggerstaff, M. I., E.-K. Seo, Hristova Veleva, and K.-Y. Kim (26), Impact of cloud model microphysics on passive microwave retrievals of cloud properties. Part I: Model comparison using EOF analyses, J. Appl. Meteor., In press. Boucher, R. J., and J. G. Wieler (1985), Radar determination of snowfall rate and accumulation, J. Climate Appl. Meteor., 24, Carlson, P. E., and J. S. Marshall (1972), Measurement of snowfall by radar, J. Appl. Meteor., 11,

24 Deeter, M. N., K. F. Evans (2), A novel ice-cloud retrieval algorithm based on the Millimeter-Wave Imaging Radiometer (MIR) 15- and 22-GHz Channels, J. Appl. Meteor., 39, Draine, B. T., and P. J. Flatau (2), User Guide for the Discrete Dipole Approximation Code DDSCAT (Ver. 5a1), Available at http//arxiv.org/abs/astro-ph/8151v4, Evans, K. F., J. Turk, T. Wong, and G. L. Stephens (1995), A Bayesian approach to microwave precipitation profile retrieval, J. Appl. Meteor., 34, Evans, K. F., S. J. Walter, A. J. Heymsfield, and G. M. McFarquhar (22), Submillimeterwave cloud ice radiometer: Simulations of retrieval algorithm performance, J. Geophys. Res., 17, D3, doi:1.129/21jd79. Fujiyoshi, Y., T. Endoh, T. Yamada, K. Tsuboki, Y. Tachibana, and G. Wakahama (199), Determination of a Z-R relationship for snowfall using a radar and high sensitivity snow gauges, J. Appl. Meteor., 29, Giraud, V., J. C. Buriez, Y. Fouquart, F. Parol, and G. Seze (1997), Large-scale analysis of cirrus clouds from AVHRR data: Assessment of both a microphysical index and the cloud top temperature, J. Appl. Meteor., 36, Hayashi, S., M. Yoshizaki, T. Kato, H. Eito WMO-1 Observation Group (21), A polar low observation over the Japan Sea on 27 January 21(1). -Observed structures and numerical results (in Japanese), Preprints of Autumn Meeting of Japan Meteor. Soc., 8, 28. Heymsfield, A. L., S. Lewis, A. Bansemer, J. Iaquinta, L. M. Miloshevich, M., Kajikawa, C. Twohy, and M. R. Poellot (22), A general approach for deriving the properties of cirrus and stratiform ice cloud particles, J. Atmos. Sci., 59,

25 Im, E. (23), APR-2 Dual-Frequency Airborne Radar Observations, Wakasa Bay. Boulder, CO: National Snow and Ice Data Center, Digital media. Available at Imai, J. (196), Raindrop size distributions and the Z-R relationship, Proc. 8 th Weather Radar Conference, Boston, MA, Katsumata, M., H. Uyeda, K. Iwanami, and G. Liu (2), The response of 36- and 89-GHz microwave channels to convective snow clouds over ocean: observation and modeling, J. Appl. Meteor., 39, Kingsmill, D. E., S. E. Yuter, A. J. Heymsfield, P. V. Hobbs, A. V. Korolev, S. Jeffrey L, A. Bansemer, J. A. Haggerty, and A. L. Rangno (24), TRMM Common microphysics products: A tool for evaluating spaceborne precipitation retrieval algorithms, J. Appl. Meteor., 43, Kongoli, C., R. R. Ferraro, P. Pellegrino, and H. Meng (25), Snow microwave products from the NOAA s Advanced Microwave Sounding Unit, paper presented at 19th Conference on Hydrology, San Diego, CA, 8-14 January 25. Kummerow, C., Y. Hong, W. S. Olson, S. Yang, R. F. Adler, J. McCollum, R. Ferraro, G. Petty, D.-B. Shin, and T. T. Wilheit (21), The evolution of the Goddard Profiling Algorithm (GPROF) for rainfall estimation from passive microwave sensors, J. Appl. Meteor., 4, Liu, G. (1998), A fast and accurate model for microwave radiance calculations, J. Meteor. Soc. Japan, 76, Liu, G. (24), Approximation of single scattering properties of ice and snow particles for high microwave frequencies, J. Atmos. Sci., 61,

26 Liu, G., and J. A. Curry (1996), Large-scale cloud features during January 1993 in the North Atlantic Ocean as determined from SSM/I and SSM/T2, J. Geophys. Res., 11, Liu, G., and J. A. Curry (1997), Precipitation characteristics in Greenland-Iceland-Norwegian Seas determined by using satellite microwave data, J. Geophys. Res., 12, Liu, G., and J. A. Curry (1998), An investigation of the relationship between emission and scattering signals in SSM/I data, J. Atmos. Sci., 55, Lobl, E., K. Aonashi, B. Griffith, C. Kummerow, G. Liu, M. Murakami, T. Wilheit (25), Wakasa Bay An AMSR Precipitation Validation Campaign ( Wakasa Bay Experiment ), Bull. Amer. Met. Soc., submitted. Makihara, Y., N. Kitabatake, and M. Obayashi (1995), Recent developments in Algorithms for the JMA nowcasting system Part I: Radar echo composition and radar-amedas precipitation analysis, Geophys. Mag. Series 2, 1, Murakami, M., M. Hoshimoto, N. Orikasa, H. Horie, H. Okamoto, H. Minda, WMO-1 Aircraft Observation Group (21a), Aircraft observation of inner structures in Japan Sea Polar-airmass Convergence Zone (in Japanese), Preprints of Spring Meeting of Japan Meteor. Soc., 8, 24. Murakami, M., N. Orikasa, M. Hoshimoto, H. Horie, H. Okamoto, H. Minda, WMO-1 Aircraft Observation Group (21b), Inner structures of meso-low (polar-low) over the Japan Sea based on research aircraft observation (preliminary results) (in Japanese), Preprints of Spring Meeting of Japan Meteor. Soc., 79, 158. Ohtake, T., and T. Henmi (197), Radar reflectivity of aggregated snowflakes, Preprints of 14 th Conference on Radar Meteorology, Tucson, AZ, Oki, R., A. Sumi, and D. A. Short (1997), TRMM sampling of radar-amedas rainfall using the threshold method, J. Appl. Meteor., 36,

27 Olson, W. S., C. D. Kummerow, G. M. Heymsfield, and L. Giglio (1996), A method for combined passive-active microwave retrievals of cloud and precipitation profiles, J. Appl. Meteor., 35, Puhakka, T. (1975), On the dependence of Z-R relation on the temperature in snowfall, Preprints of 16 th Radar Meteor. Conference, Houston, TX, Racette, P., R. F. Adler, J. R. Wang, A. J. Gasiewski, D. M. Jackson, and D. S. Zacharias (1996), An airborne Millimeter-wave Imaging Radiometer for cloud, precipitation, and atmospheric water vapor studies, J. Atmos. Oceanic Technol., 13, Rutledge, S. A., and P. V. Hobbs (1983), The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. Part VIII: A model for the seeder-feeder process in warm-frontal rainbands, J. Atmos. Sci., 4, Seo, E., and G. Liu (25), Retrievals of cloud ice water path by combining ground cloud radar and satellite high-frequency microwave measurements near the ARM SGP site, J. Geophys. Res., 11, D1423, doi:1.129/24jd5727. Sekhon, R. S., and R. C. Srivastava (197), Snow size spectra and radar reflectivity, J. Atmos. Sci., 27, Skofronick-Jackson, G. M., J. R. Wang, G. M. Heymsfield, R. Hood, W. Manning, R. Meneghini, and J. A. Weinman (23), Combined radiometer radar microphysical profile estimations with emphasis on high-frequency brightness temperature observations, J. Appl. Meteor., 42, Skofronick-Jackson, G. M., M. J. Kim, J. A. Weinman, D. E. Chang (24), A physical model to determine snowfall over land by microwave radiometry, IEEE Trans. Geosci. Remote Sens., 42,

28 Stephens, G., D. G. Vane, R. J. Boain, G. G. Mace, K. Sassen, Z. Wang, A. J. Illingworth, E. J. O'Connor, W. B. Rossow, S. L. Durden, S. D. Miller, R. T. Austin, A. Benedetti, C. Mitrescu, and The CloudSat Science Team (22), THE CLOUDSAT MISSION AND THE A-TRAIN: A new dimension of space-based observations of clouds and precipitation, Bull. Amer. Met. Soc., 83, Stubenrauch, C. J., R. Holz, A. Chedin, D. L. Mitchell, and A. J. Baran (1999), Retrieval of cirrus ice crystal sizes from 8.3 and 11.1 micron emissivities determined by the improved initialization inversion of TIROS-N operational vertical sounder observations, J. Geophys. Res. 14, D24, von Storch, H., and F. W. Zwiers (1999), Statistical Analysis in Climate Research, 484 pp., Cambridge University Press. Wang, J. (23), Millimeter-wave Imaging Radiometer (MIR) Brightness Temperatures, Wakasa Bay, Japan, Boulder, CO: National Snow and Ice Data Center. Digital media. Weng, F., and N. C. Grody (2), Retrieval of ice cloud parameters using a microwave imaging radiometer, J. Atmos. Sci., 57, Yoshizaki, M., T. Kato, H. Eito, A. Adachi, M. Murakami, S. Hayashi, and WMO-1 Observation Group (21), A report on Winter MCSs (mesoscale convective systems) observations over the Japan Sea in January 21 (WMO-1) (in Japanese), Tenki, 48, Zhao, L., and F. Weng (22), Retrieval of ice cloud parameters using the Advanced Microwave Sounding Unit, J. Appl. Meteor., 41,

29 Table captions Table 1. Correlation coefficients between snowfall retrievals and AMSU-B channels.

30 Table 1. Correlation coefficients between snowfall retrievals and AMSU-B channels. Channels 14 January January January GHz GHz ±1 GHz ±7 GHz

31 Figure captions Figure 1. Map of the Wakasa Bay and surrounding areas. Figure 2. Two types of snowflakes used in the DDA computation. Figure 3. Z e -S relationships for snow from calculations using DDA and several previous studies. Figure 4. Brightness temperature depressions from MIR and snowfall rate from PR-2 (c) 14 GHz and (d) 35 GHz at nadir along the flight track from 319 UTC to 333 UTC on 29 January 23. Figure 5. Snow particle size distribution and precipitation from ground observations at Fukui airport during Wakasa 23 Field experiment. Figure 6. Comparisons of brightness temperature depressions between MIR observations and the radiative model results. Figure 7. Comparisons of PR-2 observations at 35 GHz (upper) and retrieved snowfall rate (lower) along (a) leg1 and (b) leg3. Figure 8. Comparisons of observations and retrieved results on 14 January 21. (a-d) Brightness temperature depressions from the AMSU-B at 89, 15, 183+3, and GHz, (e-f) retrieved snowfall at 1.5 km and 2. km from the surface, and (g) hourly accumulated snow data (3-hr averaged) from the AMeDAS radar data and (h) GMS IR cloud top temperatures. Figure 9. Same as Fig. 8, but for 16 January 21. Figure 1. Same as Fig. 8, but for 27 January 21. Figure 11. Comparisons between retrieved snowfall rates and 3-hr averaged hourly accumulated surface radar snow amounts at the nearest corresponding time, after 1 hour, and after 2 hours respectively for 14, 16, and 27 January 21. Figure 12. Comparisons between retrieved snowfall rates and AMSU-B brightness temperature depressions at each frequency respectively for 14, 16, and 27 January 21. Figure 13. Multi-channel relationship of brightness temperature departures between the a-priori database and AMSU-B observations in EOF space. Projected are shaded contours of occurrences in the database onto the EOF domain of AMSU-B observations (line contours).

32 N E Figure 1. Map of the Wakasa Bay and surrounding areas.

33 (a) Type-A (Sector Snowflake) (b) Type-B (Snowflake) Figure 2. Two types of snowflakes used in the DDA computation.

34 Ze (mm 6 m -3 ) Snowfall Rate (mm/h) Sector Snowflake-13.4GHz Sector Snowflake-35.6GHz Sector Snowflake-94.GHz Snowflake-13.4GHz Snowflake-35.6GHz Snowflake-94.GHz Wakasa snow (Aonashi,23) Snow_dry (Puhakka,1975) Snow (Sekhon & Srivastaya,197) Snow_dry (Imai,196) Snow_plate, column (Ohtake & Henmi,197) Single crystals (Carlson & Marshall,1972) Snow_dry (Fujiyoshi et al.,199) Snow (Boucher & Wieler,1985) Figure 3. Z e -S relationships for snow from calculations using DDA and several previous studies.

35 T B (K) T B (K) (a) (b) (c) (d) Figure 4. Brightness temperature depressions from MIR and snowfall rate from PR-2 (c) 14 GHz and (d) 35 GHz at nadir along the flight track from 319 UTC to 333 UTC on 29 January 23.

36 Number (m -3 mm -1 ) Number (m -3 mm -1 ) Number (m -3 mm -1 ) Number (m -3 mm -1 ) Jan 28 18:-18:59-9 min 1-19 min 2-29 min 3-39 min 4-49 min 5-59 min Jan 28 22:-22:59 Jan 29 4:-4:59 Jan 29 6:-6: Diameter (mm) Precipitation (mm/h) Precipitation (mm/h) Precipitation (mm/h) Precipitation (mm/h) Jan 28 18:-18:59 Jan 28 22:-22:59 Jan 29 4:-4:59 Jan 29 6:-6:59 6: 6:2 6:4 7: Time (min) Figure 5. Snow particle size distribution and precipitation from ground observations at Fukui airport during Wakasa 23 Field experiment.

37 GHz 3 15GHz Model T B S-S & Standard winter S-S & Fukui Muramoto & Fukui GHz GHz Model T B GHz 3 34GHz Model T B MIR T B MIR T B Figure 6. Comparisons of brightness temperature depressions between MIR observations and the radiative model results. : Sekhon and Srivastava distribution with US standard atmosphere winter profile : Sekhon and Srivastava distribution with a Fukui radiosonde sounding : Muramoto distribution with a Fukui radiosonde sounding

38 (a) Figure 7. Comparisons of PR-2 observations at 35 GHz (upper) and retrieved snowfall rate (lower) along (a) leg1 and (b) leg3. (b)

39 (a) (b) (c) (d) (e) (f) (g) (h) Figure 8. Comparisons of observations and retrieved results on 14 January 21. (a-d) Brightness temperature depressions from the AMSU-B at 89, 15, 183+3, and GHz, (e-f) retrieved snowfall at 1.5 km and 2. km from the surface, and (g) hourly accumulated snow data (3-hr averaged) from the AMeDAS radar data and (h) GMS IR cloud top temperatures.

40 (a) (b) (c) (d) (e) (f) (g) (h) Figure 9. Same as Fig. 8, but for 16 January 21.

41 (a) (b) (c) (d) (e) (f) (g) (h) Figure 1. Same as Fig. 8, but for 27 January 21.

42 2. (a) 14 Jan 21 Observations (mm) time=hr time=+1hr time=+2hr Retrievals (mm/h) (b) 16 Jan 21 Observations (mm) Retrievals (mm/h) (c) 27 Jan 21 5 Observations (mm) Retrievals (mm/h) Figure 11. Comparisons between retrieved snowfall rates and 3-hr averaged hourly accumulated surface radar snow amounts at the nearest corresponding time, after 1 hour, and after 2 hours respectively for 14, 16, and 27 January 21.

43 1 5 (a) 14 Jan 21 T B (K) GHz 15GHz GHz 183+7GHz Retrievals (mm/h) (b) 16 Jan 21 T B (K) Retrievals (mm/h) 2 (c) 27 Jan 21 T B (K) Retrievals (mm/h) Figure 12. Comparisons between retrieved snowfall rates and AMSU-B brightness temperature depressions at each frequency respectively for 14, 16, and 27 January 21.

44 Figure 13. Multi-channel relationship of brightness temperature departures between the a-priori database and AMSU-B observations in EOF space. Projected are shaded contours of occurrences in the database onto the EOF domain of AMSU-B observations (line contours).