How TRMM precipitation radar and microwave imager retrieved rain rates differ

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L24803, doi: /2007gl032331, 2007 How TRMM precipitation radar and microwave imager retrieved rain rates differ Eun-Kyoung Seo, 1 Byung-Ju Sohn, 1 and Guosheng Liu 2 Received 12 October 2007; accepted 13 November 2007; published 19 December [1] Analysis of the collocated rain retrievals from Tropical Rainfall Measuring Mission s precipitation radar and microwave radiometer reveals that their difference depends on the intensity and the type of rain the radiometer-derived rain rates vary from higher to lower than the radar-derived ones as rain rate or convective fraction increases. To better understand how this difference occurs, the relations between the two leading EOFs (Empirical Orthogonal Functions) of the observed brightness temperatures and the radiometer- or radar-derived rain rates were examined for convective, mixed and nonconvective rain categories. In all types of rain, the two EOFs respond to the variation of the radiometer- and radar-derived rain rates in a similar fashion in low rain rates, while they respond quite differently in high rain rates. Citation: Seo, E.-K., B.-J. Sohn, and G. Liu (2007), How TRMM precipitation radar and microwave imager retrieved rain rates differ, Geophys. Res. Lett., 34, L24803, doi: / 2007GL Introduction [2] The Tropical Rainfall Measuring Mission (TRMM) satellite was launched in 1997 with the primary goal of measuring tropical rainfall [Simpson et al., 1988; Kummerow et al., 1998]. For the first time, a precipitation radar was on board a satellite together with a microwave radiometer, which provides the opportunity to intercompare rain retrievals from active and passive instruments. The radiometer algorithm [Olson et al., 1999; Kummerow et al., 2000; Kummerow et al., 2001] inverts the TRMM Microwave Imager (TMI) brightness temperatures (T B s) into rain rates by using a predefined database consisting of the relationship between cloud properties and upwelling radiation. The algorithm first converts T B s of TMI into attenuation/scattering indices and then inverts the indices to rain rates using Bayesian theorem. The attenuation and scattering indices are vertically integrated properties. Meanwhile, the Precipitation Radar (PR) measures the intensity of backscattered energy from hydrometeors within a defined vertical interval; therefore, rain rates may be estimated at different altitudes. Since the active PR and passive TMI retrieval algorithms are based on different underlying principles, one retrieval can be used as a comparative reference for the other [Olson et al., 2006]. 1 School of Earth and Environmental Sciences, Seoul National University, Seoul, Korea. 2 Department of Meteorology, Florida State University, Tallahassee, Florida, USA. Copyright 2007 by the American Geophysical Union /07/2007GL [3] It has been known that the zonally averaged TMI rain rates is 24% larger than the PR rain rates over tropical region for version 5 products [Kummerow et al., 2000]. For the most up-to-date version 6 products, it is reported that the TMI surface rain rate has, in general, less bias with respect to independent estimates [Yang et al., 2006; Yuter et al., 2006]. Bowman [2007] found that the bias between the gauges and the TMI retrievals is comparable to that between the gauges and the PR retrievals. However, how the TMI and PR estimates compare with each other has been unclear to date [e.g., Stout and Kwiatkowski, 2004; Yuter et al., 2006]. Dissimilar to other comparative studies of examining the difference of zonally or regionally averaged values between the two retrievals, we seek to study their difference over the spectra of rain rates and types. First, we examine how the TMI and the PR retrievals differ with respect to rain intensity and convective fraction using collocated pixel data. This exercise helps us understand what rain type/ intensity causes the largest mismatch between the two retrievals. To get further insight of the mismatch, we then examine the T B - rain rate relations separately as a function of the PR- and the TMI-derived rain rates. This exercise sheds lights on why the mismatch occurs. [4] The study focuses exclusively on oceanic areas because the oceanic branch of the TMI rain algorithm is more physically based. Over land, the TMI rain algorithm is largely based on empirical regression, which prevents from gaining physical insight through this comparative study. 2. Data [5] Datasets used in this study are TRMM TMI T B s and the version 6 products of TMI- and PR-derived rain rates over oceanic regions. The data duration is one year from 1 December 2004 to 30 November TMI measures radiation at 10.65, 19.35, 37.0, and 85.5 GHz with both horizontal and vertical polarizations and at 21.3 GHz with vertical polarization, covering the tropics and subtropics (35 S 35 N). Data are sampled at every 9 km along the scanning direction except for the 85.5-GHz samples at every 4.5 km. TMI rain retrieval algorithm has been documented by Olson et al. [2006]. The PR is a scanning radar operating at 13.8 GHz [Iguchi and Meneghini, 1994]. Its sensitivity is about 17 dbz, which corresponds to about 0.7 mm h 1 in rain rate. PR pixels have a horizontal resolution of 4.3 km at nadir and a vertical resolution of 250 m from the Earth surface to 20 km altitude. The vertical profiles of rain rate (R) are calculated from radar reflectivity (Z) profiles using a Z-R relationship. Radar reflectivity was corrected for attenuation based on a hybrid of the Hitschfeld-Bordan and the surface reference method [Iguchi and Meneghini, 1994; Iguchi et al., 2000]. Rainfalls are further classified L of6

2 Table 1. Statistics of the TMI- and PR-Derived Rain Rates for Collocated Rainy Pixels Over TRMM Satellite Covered Global Tropics Number Fraction of Rainy Pixels, % Mean PR/TMI Mean Rain Rate Rain Rate, mm h 1 Difference, mm h 1 category / category / category / all categories / into three types: stratiform, convective and others [Awaka et al., 1998]. [6] The analysis of this study is conducted only to those oceanic pixels whose TMI-derived rain rates are greater than 0. TMI and PR pixels were collocated by averaging PR rain rates over a nominal footprint (14 km 14 km area) of TMI. Hereinafter, the PR-derived rain rate means the averaged one over a nominal footprint of TMI. The convective areal fraction (convf) is defined as the ratio of the number of convective PR pixels (in the range of of rain type in 2A23 products) to the total number of collocated PR pixels within the footprint. Based on the convf, rain pixels are classified into one of the following three categories: 8 < 1 0:7 < convf 1:0 category ¼ 2 : ; if 0:3 < convf 0:7 : 3 0:0 convf 0:3 Namely, categories 1, 2 and 3 constitute mostly convective, mixed, and non-convective rain, respectively. Table 1 lists the statistics of the collocated rainy pixels over the TRMM satellite covered global tropics. Of all the collocated rainy pixels, 11.6% are classified as category 1 (mostly convective), 11.4% as category 2 (mixed) and 77.0% as category 3 (non-convective). Particular attention should be paid on the signs of TMI PR rain rate difference negative for the first two categories and positive for the other category, which is further explored in the next sections. 3. Spectral Difference Between PR and TMI Rain Rates [7] Using the one year collocated rain pixels, we compared the TMI- and PR-derived rain rates; their averaged difference in each 1 mm h 1 PR rain rate and 0.1 convf bin is plotted in Figure 1 along with frequency of occurrence of rain pixels in each bin. The magnitude and sign of the TMI minus PR rain rate present a distinct dependence on rain intensity, as well as on convective fraction to a less extent. TMI rain rates are higher than PR rain rates at low rain intensity while lower at high rain intensity; the transition from positive to negative difference occurs around 1 to 6mmh 1 PR rain rate. On the other hand, given the same PR rain rate, the TMI rain rates are generally higher than PR-derived rain rates when convf is low while lower when convf is high. This feature is more clearly shown in the PDF (probability density function) plot of the co-occurrence Figure 1. The difference (color pixels) in mm h 1 between TMI- minus PR-derived rain rate as a function of PR rain rate and convf. Contours represent occurrence frequency of rain pixels in % at the intervals of 0.005, 0.01, 0.1, 0.5, 1, 2, 4, 6, 8, 10. 2of6

3 3of6 of TMI- and PR-derived rain rates, separated into the three categories (Figure 2). As shown earlier in Table 1, the average difference of TMI minus PR rain rates are 2.28, 1.26 and 0.55 mm h 1, for rain categories 1, 2, and 3, respectively. [8] In summary, the radiometer and radar rain estimates systematically differ depending on the rain intensity and the rain type (convective fraction), although their mean values over entire rain spectrum are quite similar (see Table 1). This spectral difference implies that some physical assumptions used in the algorithms need to be reexamined. In the next section, we examine the relations between T B s and TMI- and PR-derived rain rates in an effort to shed light on the inner-working of the rain retrieval algorithms. 4. Multivariate Relations of Radiance Indices to Rain Rates [9] The TMI algorithm uses attenuation and scattering indices [Petty, 1994] instead of the nine T B s to estimate rain rates. The attenuation index (P) is a normalized polarization difference, ranging from 0 and 1, with small value of P denoting opaque liquid cloud. Compared to T B s, P is insensitive to the scattering by ice particles and depends primarily on the liquid hydrometeors [Petty, 1994]. The other radiance index, scattering index S, represents volume scattering associated with frozen precipitation aloft. Large value of S corresponds to strong ice scattering. [10] In the following, we modified the Petty s P and S slightly as follows. The new P is redefined as 100(1-P 0 ) and the S is redefined as S 0, where P 0 and S 0 are those originally defined by Petty [1994]. The new P and S will have the same order of magnitude. In addition, greater values of the new P and S correspond to larger liquid volume (attenuation) and smaller ice volume (scattering), respectively, a similar trend to TMI low and high frequency T B s. [11] The radiance indices derived from TMI do not vary independently with each other since they all reflect the integrated properties of hydrometeors in the radiometer s field of view. To simplify the representation of observed signatures while capturing the major features, in this study, Empirical Orthogonal Function (EOF) analysis for five radiance indices (i.e.: P 10,P 19,P 37,P 85, and S 85 ; subscripts denote the frequency of TMI channels) is employed. Let I i represent a vector of the anomaly of the above five indices for the ith data point. These anomalies can be expressed with respect to EOFs, e j,asi i = P N j¼1 a i,je j, where a i,j is the amplitude for the jth EOF at point i and N is the number of EOFs. For TMI data over the TRMM covered tropical ocean, the EOF analysis showed that the first and second leading EOFs can explain about 76% and 13% of the total variance of the radiance indices, respectively. In other words, about 90% of total variance in the multivariate radiance indices can be explained by only two major EOFs. Or, the radiance index vector can be expressed with a good approximation by the two major EOFs. Figure 2. Occurrence frequency (%) of rain pixels in each 1mmh 1 TMI- and PR-derived rain rate bin at the intervals of 0.001, 0.02, 0.04, 0.06, 0.08, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.5, 5.0, 5.5, 6.0.

4 Figure 3. (a, b, c) The first (solid) and second (dotted) EOFs of radiance indices. (d, e, f) Occurrence frequency (%) in each bin size of 10 in the two leading EOF amplitudes. (g, h, i) PR-derived rain rate (mm h 1 ). (j, k, l) TMI-derived rain rate (mm h 1 ) in the EOF space. [12] In Figure 3, the two leading EOFs are shown separately for category 1, 2, and 3 rain pixels. The first EOF pattern has positive values for the attenuation indices and negative value for the scattering index, implying a tendency of the increase of liquid hydrometeors jointly with the increase of ice hydrometeors aloft. The second EOF pattern has, in general, positive values for all radiance indices except for a negative value for the attenuation index of 85 GHz for category 3, implying mostly liquid (positive amplitude) or ice (negative amplitude) only hydrometeors. Hence, the first and second EOF patterns represent a vertically-coupled tall and a liquid-dominant (or ice-dominant) cloud, respectively. [13] Using the amplitudes of the two leading EOFs as abscissa and ordinate, we may plot the occurrence frequency of rain pixels and the PR- or TMI-derived rain rates in EOF space (Figure 3). The characteristics of them are examined in the following. Because category 2 rain events have the 4of6

5 mixed features of categories 1 and 3, our discussion will focus on categories 1 and 3. [14] The left panel of Figures 3d, 3e, 3f, 3g, 3h, 3i, 3j, 3k, and 3l shows the frequency of rain pixel occurrence, mean rain rate derived from PR and mean rain rate derived from TMI for the category 1 (convective) rain events. While the increase of PR rain rates correspond to the increase of both the first and the second EOFs amplitude, the high values of TMI-derived rain rate are clustered mostly at the lower-right corner of the diagram highly positive for the first EOF amplitude and highly negative for the second EOF amplitude. This implies that for a high rain rate the PR retrieval corresponds to a rain profile of relatively balanced highliquid and high-ice hydrometeor profile while the TMI retrieval corresponds to a hydrometeor profile with excessive ice (highly negative second EOF amplitude). If we assume that the PR retrievals are closer to the truth, this above inconsistency may point to a problem of the excessive ice hydrometeors in the predefined TMI algorithm database as discussed by Seo et al. [2007a]. Furthermore, there is another significant difference: the TMI-derived rain rates (Figure 3j) in particular for heavy rain events are much smaller than PR-derived rain rates (Figure 3g). The TMI-derived mean rain rate does not exceed about 35 mm h 1, while the PR-derived mean rain rate can be as high as 80 mm h 1.If we assume that the PR retrievals are more close to the truth, the underestimation by TMI may be attributed to the following problems: (1) the excessive ice hydrometeors in the predefined database, (2) inadequate treatment of the beam-filling problem, which is quite significant for TMI observations of convective rain events as pointed out by Varma et al. [2004], and (3) the lack of high rain rates (>60 mm h 1 ) in the predefined database itself. [15] The right panel of Figures 3d 3l shows the frequency of rain pixel occurrence, mean rain rate derived from PR and mean rain rate derived from TMI for the category 3 (nonconvective) rain events. In this category, the PR- (Figure 3i) and TMI-derived (Figure 3l) rain rates have similar range (0 to 40 mm h 1 ). However, the relationship between TMI radiance and rain rates has the similar trend to that for category 1. That is, the excessive ice hydrometeors in the predefined database seem to be problematic in high rain rates even for category 3. In low rain rate (<10 mm h 1 )for category 3, the TMI rain rates are higher than the PR rain rates, which is largely responsible for overall positive difference of TMI minus PR rain retrievals because of the large population of pixels in this range. While the definite reason to this difference needs to be investigated in the future, the possibilities can be as follows: (1) the insensitivity of the PR to rain rates lower than 0.7 mm h 1, (2) the uncertainty in determining no-rain background TMI T B s, and (3) the lack of data points with zero rain rates in the predefined database of the Bayesian-type TMI retrieval algorithm. In relation to the last point, a realistic prior PDF, P(x 0), having all zero rain rates as well as rain events might decrease the difference by lowering TMI rain rates in very light rain rate. Details on this improvement are given by Seo et al. [2007b]. 5. Conclusions [16] TRMM rain rates (version 6) derived from the TMI and the PR were compared to investigate how they differ from each other as a spectral function of rain type and intensity. It is found that when averaging all the collocated TMI and PR pixels the difference between TMI- and PR-derived rain rate is small (0.02 mm h 1 ). However, when examining their difference as a function of rain intensity and type, it is found that their difference is systematic, i.e., TMI algorithm underestimates (overestimates) rain rates over PR algorithm for heavy (light) and more (less) convective rain event. The small difference is the result of the cancellation of underestimation at one end while overestimation at the other end of the rain spectrum. [17] Using the corresponding relations between retrieved rain rates and the leading EOFs of observed T B s, we attempt to get further insight of the difference between the PR and the TMI retrievals. In the convective rain category, TMIderived rain rates are systematically lower than those derived by the PR when the attenuation and scattering signals become stronger. In the non-convective rain cloud category, TMI-derived rain rates are higher than the PR-derived ones when the attenuation and scattering signals are weak (rains are lighter), which is primarily responsible for the overall positive bias (however small) of the TMIminus the PR-derived rain rates due to the large population of rain pixels in the rain rate range and category. At high rain rates of all the categories, high PR-derived rain rates correspond to strong attenuation and scattering microwave signatures, implying hydrometeor profiles of relatively balanced amount of both liquid and ice. In comparison, high TMI-derived rain rates correspond to excessive ice scattering microwave signatures. [18] This comparative study does not answer the question whether the PR or the TMI retrieval algorithm performs better. Rather, it tries to answer how the two differ, in an attempt to find the weakness of the algorithms. If we assume that the PR s retrieval is closer to the truth, the low bias of TMI retrievals in the convective category may indicate that an improvement in handling the beam-filling of the TMI algorithm is needed [Varma et al., 2004]. Similarly, the excessive ice scattering signature may indicate that the cloud resolving model based TMI database needs to be improved [Seo et al., 2007a]. Inversely, if we assume that the TMI s retrievals are closer to the truth especially in low rain rates, the PR s low sensitivity may prove to be an important problem for deriving long-term rain climatology, and its algorithm s handling of drop size distribution may need to be revisited (for example, adopting rain type based drop size distributions). Keeping the above possible weaknesses of each algorithm in mind, particular attentions should be paid in these areas in future algorithm development. In addition, the finding of this study posts a challenge to future algorithm validation field experiments. That is, an overall averaged surface rain measurement is not a sufficient ground truth required for validating an algorithm. To better validate the physics that goes into the algorithm, the ground truth data need to be stratified by rain intensity and type. [19] Acknowledgments. This work was funded by the Korea Meteorological Administration Research and Development Program under grant CATER The first author was supported by the BK21 Project of the Korean Government through the School of Earth and Environmental Sciences, Seoul National University in of6

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