Critical Assessment of Microphysical Assumptions within TRMM Radiometer Rain Profile Algorithm Using Satellite, Aircraft, and Surface Datasets from KWAJEX

Steven T. Fiorino Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio

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Eric A. Smith NASA Goddard Space Flight Center, Greenbelt, Maryland

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Abstract

The Tropical Rainfall Measuring Mission (TRMM) Microwave Imager precipitation profile retrieval algorithm (2a12) assumes cloud model–derived vertically distributed microphysics as part of the radiative transfer–controlled inversion process to generate rain-rate estimates. Although this algorithm has been extensively evaluated, none of the evaluation approaches has explicitly examined the underlying microphysical assumptions through a direct intercomparison of the assumed cloud-model microphysics with in situ, three-dimensional microphysical observations. The main scientific objective of this study is to identify and overcome the foremost model-generated microphysical weaknesses in the TRMM 2a12 algorithm through analysis of (a) in situ aircraft microphysical observations; (b) aircraft- and satellite-based passive microwave measurements; (c) ground-, aircraft-, and satellite-based radar measurements; (d) synthesized satellite brightness temperatures and radar reflectivities; (e) radiometer-only profile algorithm retrievals; and (f) radar-only profile or volume algorithm retrievals. Results indicate the assumed 2a12 microphysics differs most from aircraft-observed microphysics where either ground or aircraft radar–derived rain rates exhibit the greatest differences with 2a12-retrieved rain rates. An emission–scattering coordinate system highlights the 2a12 algorithm's tendency to match high-emission/high-scattering observed profiles to high-emission/low-scattering database profiles. This is due to a lack of mixed-phase-layer ice hydrometeor scatterers in the cloud model–generated profiles as compared with observed profiles. Direct comparisons between aircraft-measured and model-generated 2a12 microphysics suggest that, on average, the radiometer algorithm's microphysics database retrieves liquid and ice water contents that are approximately 1/3 the size of those observed at levels below 10 km. Also, the 2a12 rain-rate retrievals are shown to be strongly influenced by the 2a12's convective fraction specification. A proposed modification of this factor would improve 2a12 rain-rate retrievals; however, fundamental changes to the cloud radiation model's ice parameterization are necessary to overcome the algorithm's tendency to produce mixed-phase-layer ice hydrometeor deficits.

Corresponding author address: Eric A. Smith, Goddard Space Flight Center, Code 613.6, Greenbelt, MD 20771. Email: eric.a.smith@nasa.gov

Abstract

The Tropical Rainfall Measuring Mission (TRMM) Microwave Imager precipitation profile retrieval algorithm (2a12) assumes cloud model–derived vertically distributed microphysics as part of the radiative transfer–controlled inversion process to generate rain-rate estimates. Although this algorithm has been extensively evaluated, none of the evaluation approaches has explicitly examined the underlying microphysical assumptions through a direct intercomparison of the assumed cloud-model microphysics with in situ, three-dimensional microphysical observations. The main scientific objective of this study is to identify and overcome the foremost model-generated microphysical weaknesses in the TRMM 2a12 algorithm through analysis of (a) in situ aircraft microphysical observations; (b) aircraft- and satellite-based passive microwave measurements; (c) ground-, aircraft-, and satellite-based radar measurements; (d) synthesized satellite brightness temperatures and radar reflectivities; (e) radiometer-only profile algorithm retrievals; and (f) radar-only profile or volume algorithm retrievals. Results indicate the assumed 2a12 microphysics differs most from aircraft-observed microphysics where either ground or aircraft radar–derived rain rates exhibit the greatest differences with 2a12-retrieved rain rates. An emission–scattering coordinate system highlights the 2a12 algorithm's tendency to match high-emission/high-scattering observed profiles to high-emission/low-scattering database profiles. This is due to a lack of mixed-phase-layer ice hydrometeor scatterers in the cloud model–generated profiles as compared with observed profiles. Direct comparisons between aircraft-measured and model-generated 2a12 microphysics suggest that, on average, the radiometer algorithm's microphysics database retrieves liquid and ice water contents that are approximately 1/3 the size of those observed at levels below 10 km. Also, the 2a12 rain-rate retrievals are shown to be strongly influenced by the 2a12's convective fraction specification. A proposed modification of this factor would improve 2a12 rain-rate retrievals; however, fundamental changes to the cloud radiation model's ice parameterization are necessary to overcome the algorithm's tendency to produce mixed-phase-layer ice hydrometeor deficits.

Corresponding author address: Eric A. Smith, Goddard Space Flight Center, Code 613.6, Greenbelt, MD 20771. Email: eric.a.smith@nasa.gov

1. Introduction and background

Remotely sensed rainfall measurements, made by either ground-based radar networks or space-based radiometers and/or radars, offer the only reliable means of obtaining spatially continuous precipitation measurements at the global scale. However, despite the obvious finescale, volumetric, and continuous coverage advantages of remotely sensed rainfall, the lack of a complete characterization of the vertical distribution of the optical-radiative properties of precipitation-sized water and/or ice hydrometeors prevents such rainfall measurements from being accepted as fully verified. With the November 1997 launch of the Tropical Rainfall Measuring Mission (TRMM; all acronyms are listed together in appendix B for easy reference) satellite carrying both the multichannel passive microwave (PMW) TRMM Microwave Imager (TMI), which measures the integrated effects of liquid and ice along the instrument viewing paths, and the 13.8-GHz precipitation radar (PR), which measures detailed vertically resolved rain-rate profiles, important new retrieval products concerning the four-dimensional distribution of precipitation and latent heating in the Tropics have become available (Kummerow and Okamoto 1999; Kummerow et al. 2000). New initiatives and techniques for validating the TRMM retrievals have emerged concomitantly (Smith and Hollis 2002).

Quantitative and physical validations of the TRMM algorithms are an important research area because of the widespread use of TRMM retrievals in studies of climate, weather, and hydrometeorology.1 The main scientific objective of this study is to identify the foremost drawbacks in the assumed microphysics of the standard wide-swath/instantaneous TRMM rain profile algorithm—referred to as the level-2, radiometer-only 2a12 algorithm. This identification is made possible by intercomparing the cloud-radiation-model-generated microphysics of 2a12 with in situ aircraft (A/C) microphysical measurements acquired during the TRMM Kwajalein Atoll Field Experiment (KWAJEX) which took place during August–September of 1999 (Yuter et al. 2005). In doing so, we also suggest physically based modifications to the 2a12 algorithm (or similar such algorithms) that would improve its (their) retrieval performance.

In addition to 2a12, the other TRMM standard rain profile algorithms consist of 2a25 (the narrow-swath/instantaneous, radar-only, level-2 algorithm), and 2b31 (the narrow-swath/instantaneous, combined radar–radiometer, level-2 algorithm). The publications by Kummerow et al. (1996) and Kummerow (1998) describe the method for 2a12; those by Iguchi and Meneghini (1994), Iguchi et al. (2000), and Meneghini et al. (2000) describe 2a25; and those by Smith et al. (1997) and Haddad et al. (1997) describe 2b31. To date, validation approaches used with these algorithms have included rain gauge comparisons, ground radar comparisons, algorithm-to-algorithm comparisons, diagnostic moisture budget studies, and physical hypothesis testing. However, the most fundamental validation approach—direct comparison of the assumed microphysics with three-dimensional microphysical observations—has yet to be performed.

The 2a12 algorithm assumes cloud-model-generated microphysical profiles in the radiative transfer–controlled inversion process to produce rain profile retrievals. A main goal of five TRMM field campaigns (especially KWAJEX) was to acquire datasets that could be used to support microphysical analyses and physical verification studies of the TRMM standard algorithms, an objective particularly relevant to 2a12 because of its direct dependence on model-generated microphysical profile information. In fact, the main observational goal of KWAJEX was to acquire multiple, coincident datasets that could be used to directly falsify assumptions and simplifications embedded in any of the physically based TRMM precipitation algorithms. Identifying such deficiencies permits better understanding of algorithm uncertainties and guides improvements in describing the interplay during inversion between radiative transfer and microphysical parameterization, essential in generating reliable surface rain rates and rain-rate profiles. With that in mind, a foremost component of this research has been to generate merged and carefully matched microphysics–radiometer–radar datasets from the KWAJEX campaign to allow determination of error sources in the instantaneous rain retrievals by the level-2 TRMM radiometer algorithm related to oversimplified and/or invalid microphysical assumptions.

The mainstream benefit of this study is refinement of the TMI method for retrieving instantaneous rain profiles based on cloud modeling, noting that TMI is the principal TRMM instrument for producing the optimal rainfall sampling because of its wide-swath coverage. The PR's swath is ∼1/3 of the width of the TMI swath and is better suited to understanding the physics of rainfall, transferring to the extent possible this understanding to radiometer algorithms. These refinements are important because wide-swath TMI-generated precipitation data are needed to understand how the global–tropical water cycle at multiple scales accumulates from precipitation processes taking place at cloud scales (e.g., see Grabowski 2003), and to improve observationally based forcing of hydrometeorological models addressing such fundamental problems as flood forecasting and freshwater resources assessment.

Such studies address a core objective of TRMM—producing representative rain-rate fields and rainfall climatological descriptions from physically based and objectively validated retrieval algorithms. The direct relationship between vertically distributed rain rates and the vertical profile of latent heating enables instantaneous retrievals to improve weather prediction through data assimilation and climate dynamics through tropical–diabatic forcing of the general circulation. Also, improvements to the TRMM radiometer algorithm are applicable to the next-generation Global Precipitation Measurement (GPM) mission (Smith et al. 2005) in which a constellation of satellites, each carrying a microwave radiometer, will provide the main rainfall coverage.

The method used for the analysis is described in section 2. Section 3 identifies the required datasets and provides an in-depth discussion of the dataset merging and matching procedures. Results of the analysis and final conclusions are then presented in sections 4 and 5, respectively.

2. Method

Because the analysis involves multiple datasets and a battery of diagnostic tools, an explanation of the method is best presented by first describing the main processes in the analysis procedure. The procedure involves the following four basic steps:

  1. generation of merged and matched radiometer–radar–microphysics datasets from KWAJEX measurements, “synthesizing” additional TMI–PR measurements from A/C radiometer–radar measurements as necessary;

  2. identification of situations in which radar-derived rain rates and actual or synthesized TMI-retrieved 2a12 rain rates differ, establishing relationships between rain rates and especially rain-rate differences with respect to underlying microphysics within the PMW emission–scattering (ES) coordinate system;

  3. determination of differences between assumed 2a12 algorithm microphysics and observed in situ microphysics, followed by hypothesis testing focused on relating 2a12 algorithm weaknesses to inadequate microphysical assumptions; and

  4. specification of reformulation of retrieval procedure in 2a12 algorithm designed to mitigate exposed microphysical weaknesses.

The following sections provide detailed discussions, including graphical aids, for each of these four steps.

a. Merged and matched KWAJEX datasets

The dataset pool consists of 10 individual space- and time-coincident datasets collected during the KWAJEX field phase during the months of August and September of 1999. All datasets contain up to 40 140 instantaneous elements, which correspond to all raining (“wet”) brightness temperature (Tb) “superpixels” recorded during 28 National Aeronautics and Space Administration (NASA) DC-8 A/C flights that produced the main data envelope for this investigation. Three research aircraft, all equipped with microphysics-sensing equipment, were used during KWAJEX: 1) the NASA DC-8, 2) the University of North Dakota (UND) Citation, and 3) the University of Washington (UW) Convair-580. A Tb superpixel is the basic KWAJEX areal intercomparison unit for the different datasets. The superpixel spatial scale is defined by the NASA Marshall Space Flight Center Advanced Microwave Precipitation Radiometer (AMPR; i.e., the A/C prototype for the TMI), with each superpixel consisting of 20 full-resolution AMPR pixels (five along track; four cross track), describing an approximately 1.9 km × 1.5 km grid box (i.e., ∼3 km2 area).

The 10 members of the merged–matched Kwajalein dataset consist of the following: 1) AMPR Tb, 2) coincident TMI Tb, 3) coincident PR reflectivity profiles, 4) coincident 13.8-GHz Airborne Rain Mapping Radar (ARMAR; i.e., NASA Jet Propulsion Laboratory's A/C PR prototype) reflectivity profiles, 5) Kwajalein S-band ground validation radar (GV radar) reflectivity volume scans, 6) synthesized TMI Tb based on a special “wet/dry” dataset of AMPR–TMI Tb matchups, 7) synthesized PR reflectivities based on a special wet/dry dataset of ARMAR–PR reflectivity profile matchups, 8) 2a12-algorithm rain-rate retrievals from synthesized TMI Tb along with underlying assumed microphysics parameters, 9) 2a25-algorithm rain-rate retrievals from synthesized PR reflectivity profiles, and 10) coincident in situ A/C microphysical measurements.

As noted for dataset members 6 and 7 above, two additional special datasets were needed, consisting of 7140-element rain and no-rain (i.e., wet/dry) datasets containing pairs of AMPR–TMI Tb and pairs of ARMAR–PR reflectivity profiles, respectively, acquired from all wet/dry superpixels within ±10 min of any TRMM overpass occurring during the KWAJEX A/C campaign. Further discussion of these datasets relevant to the analysis is provided in section 3.

In addition to rainfall information, the 2a12 algorithm produces microphysical information related to manipulation of selected microphysical profiles from within a cloud-radiation-model database guiding its Bayesian inversion scheme. To facilitate the intercomparison with the in situ A/C measurements, the assumed 2a12 and observed A/C microphysics are converted to bulk parameters. The bulk parameters consist of liquid and ice water contents (LWC/IWC), along with water droplet and equivalent ice sphere effective radii and effective variances for the underlying liquid–frozen hydrometeor size spectra. The reasoning behind and numerical formulations for these bulk parameters are addressed in section 2b, and are expanded upon in section 3 within the context of the analysis.

It is emphasized that the dataset pool incorporates synthesized TMI and PR data. The main reason KWAJEX collected coincident AMPR and ARMAR measurements stems from their prototype relationships to the TMI and PR instruments. Because TRMM overpasses coincident with significant rain conditions within the A/C and GV-radar-coverage domains were relatively rare events during KWAJEX, TMI/PR overpass syntheses based on AMPR and ARMAR measurements are used to produce more robust datasets of retrieved rain rates. Despite differences in resolution and swath width, viable methods to synthesize TMI and PR observations based on the coincident high-resolution A/C observations have been developed (see section 3).

b. Rain-rate-microphysics analysis within E–S coordinate system

Whereas the coincidence of A/C flights and TRMM overpasses was an infrequent event during KWAJEX, they exist in sufficient quantity to enable direct rain-rate-retrieval–microphysics analyses—see Fig. 1. During KWAJEX, the DC-8 generally flew at altitudes between 10 and 13 km, the Citation flew between 5 and 10 km (except during descent spirals as described by Heymsfield et al. 2002), and the Convair flew from near the surface up to 6 km. Each aircraft was equipped with state-of-the-art microphysical instrumentation, including suites of electro-optical probes: the 1) forward-scattering spectrometer probe (FSSP), 2) two-dimensional cloud probe (2DC), 3) two-dimensional precipitation probe (2DP), 4) high-volume particle sampler (HVPS), and 5) cloud-particle imager (CPI). The FSSP, 2DC, 2DP, HVPS, and CPI are all designed to sample increasingly larger sizes of hydrometeors with decreasing size resolution. In addition to the electro-optical probes, the Citation and Convair were equipped with King (hot wire) and Rosemount (icing) probes to detect cloud LWCs; see Kingsmill et al. (2004) for a more complete description of the TRMM Common Microphysics Products (CMP). A summary of the KWAJEX flights is provided in Yuter et al. (2005).

The three different aircraft altitude blocks, extending over most of the troposphere, allow generation of statistically composited and vertically distributed observed microphysical profiles for total-column intercomparisons. The assumed microphysics in the 2a12 a priori cloud-radiation database are implicit in the algorithm's LWC/IWC output quantities at 14 levels between 0.5 and 18 km. A Marshall–Palmer (M–P) drop size distribution (DSD) is assumed, permitting the calculation of bulk level-specific and total-column DSD parameters, including water/ice effective radii (rwate, ricee) and water/ice effective variances (υwate, υicee). The underlying M–P assumption also allows calculation of level-specific and/or total-column rwate and υwate and LWC parameters from the range-gated (height above surface) rain-rate output of 2a25. It is emphasized that an assumed effective variance factor—that is, a measure of the spread of a DSD—is constant because the assumed DSD distribution is an analytic expression bearing that property. Therefore, when assumed DSD parameters from 2a12 are directly compared with observed DSD parameters, observed–assumed υwate and υicee difference variations are produced entirely by the observations. Nonetheless, meaningful intercomparisons between observed and assumed microphysical parameters—level specific or total column—can be obtained when profile algorithm rain rates are related through a common framework to GV-radar-derived rain rates.

Such a link between radar measurements and microphysical parameters with respect to modeled radiation signatures exists empirically in the classical relationship between reflectivity Z–rain rate R: Z = aRb. An alternate physically based linkup that brings both radar and radiometer measurements into relationships with variables from the microphysical realm comes from casting reflectivity or rain-rate measurements into an ES coordinate system. The coordinate system is explained with an ES chart, which has x and y axes defined by a radiometer-based index of volume emission coordinate and an analogous index of volume scattering coordinate, respectively. Rain rates or reflectivities are linked to their respective E and S indices through space-/time-matched measurements situated on the chart's z axis.

Early passive microwave precipitation retrieval techniques generally relied on either purely emission based (e.g., Wilheit et al. 1977, 1991) or purely scattering based (e.g., Adler et al. 1994; Ferraro and Marks 1995) algorithms when determining precipitation; see Wilheit et al. (1994) and Smith et al. (1998) for overviews. Liu and Curry (1992, 1998) coupled emission and scattering signals to seek an index that was linearly proportional to rain rate, which would mitigate against low-frequency emission signal saturation at high rain rates and high-frequency scattering signal insensitivity at low rain rates. Transformation to reflectivity and/or rain-rate “surfaces” in a passive emission–scattering coordinate system allows the respective strengths of the radiometer (emission) and radar (scattering) to be combined for simultaneous analysis and graphical visualization. Addressing both emission and scattering effects together provides a full account of processes involved in cloud-radiation-model precipitation retrieval as employed with TMI Tb and the 2a12 algorithm, as well as with radar reflectivities and their associated rain-rate retrievals (e.g., from 2a25 or from a GV-radar Z–R relationship). This coordinate system is also effective in directly relating microphysical parameters to associated active or passive radiative signatures.

The ES indices used for the analysis are calculated from the KWAJEX AMPR four-channel superpixel Tb. The indices are normalized such that a 0.0 value indicates an absence of either emission or scattering and a 1.0 value indicates maximum emission or scattering. The indices are optimized for precipitation-sized hydrometeors over the range of AMPR Tb occurring during the DC-8 overflights. appendix A describes the formulation used for the ES index calculations while associated emission and scattering decision trees and idealized plots describing the procedure are shown in the accompanying figure. The top panel of Fig. 2 illustrates E-index and S-index values for all 40 140 KWAJEX wet superpixels, thus providing a measure of the relative amount of millimeter–centimeter microwave energy being emitted/scattered in each superpixel volume. Each point is further subdivided by a color code according to its 19.35- and 37.1-GHz saturation/depression characteristics. The color of each point coupled with its location in ES coordinate space allows for interpretation about the total-column microphysical properties of the absorbing/scattering layer during the time of measurement. For example, and in simple terms, a point with an S index larger than its E index and color coded for no 19.35-GHz saturation but for scattering at 37.1 GHz would be characterized by an environment containing numerous large ice particles and only moderate rain rates, whereas a point with an E index larger than its S index and color coded for 19.35-GHz saturation but for no scattering at 37.1 GHz would be characterized by an environment containing numerous large water drops (i.e., large rain rates), but few large ice particles.

The lower six panels of Fig. 2 illustrate how volume emission–scattering effects on radar reflectivity are readily apparent in ES coordinates. During KWAJEX, the ARMAR data provided 60-m-vertical-resolution reflectivity measurements at more than 75% of the AMPR superpixels. These quality-controlled ARMAR–AMPR matchups amount to approximately 31 000 superpixels and are referred to as “QC ARMAR–AMPR pairs.” In Fig. 2, the ARMAR reflectivities are averaged into 1-km layers and are plotted for selected layers between 1 and 10 km. In layers below 4 km, the reflectivity surfaces generally exhibit variation only along the emission axis—that is, reflectivities become larger with larger E-index values but show little change along the scattering axis. This effect is due to the emission effects of the primarily liquid precipitation at these levels. Above 6 km, the reverse is true—the variations are mainly along the scattering axis. At these levels, precipitation consists mainly of ice particles, which are mostly scatterers. The intervening 4–6-km layer is a mixed-phase region, containing differing amounts of both water and ice precipitation. Note that the ARMAR reflectivity surfaces respond to these mixtures as they vary along both emission and scattering axes.

Figure 3 graphically illustrates how ES coordinates and their transformation to total-column microphysical coordinates link radar, radiometer, and microphysics measurements so as to identify differences between what the 2a12 algorithm assumes and what is actually observed. As shown in Figs. 3a and 3b, GV-radar reflectivities are cast into ES space after conversion to rain rates through the appropriate Z–R relationship. Note that only high-quality (HQ) GV-radar points are used—that is, with range of less than 78 km and satisfying a high-interpolation-quality test. GV-radar rain rates can then be compared with 2a12 algorithm rain rates such that differences in ES space can be identified. The 2a12 rain rates are then recast into the transformed assumed–observed total-column microphysical coordinate systems—that is, Figs. 3d–f. Differences between assumed and observed microphysics are then examined as a function of rain rate—that is, Figs. 3g–i—thus relating back to rain-rate discrepancies between the 2a12 algorithm and the GV radar (or other radar sources). The results shown in Fig. 3 are discussed further in section 4.

c. Determination of algorithm discrepancies

As evident in Fig. 3, direct comparisons of 2a12 DSD properties with A/C measurements exhibit important differences. These differences are linked back to the GV-radar measurements and are shown to be greatest where the 2a12-retrieved rain rates differ most from the GV-radar-derived rain rates. As further elaborated in sections 3 and 4, the A/C microphysical observations were confined to “safe for aircraft” regions of clouds, typically areas of relatively lower reflectivities and surface rain rates. The total-column microphysical observations are even more limited because they require close coupling in time and space of at least two aircraft and HQ GV-radar measurements, and therefore analyses of level-specific algorithm discrepancies are also included in section 4. In the level-specific intercomparisons, it is found that the vertical resolution of the GV-radar products (i.e., for layers 1.5–3.0, 3.0–7.5, 7.5–9.0, and 9.0–12.0 km) is somewhat coarse for producing highly correlated relationships with A/C data. However, there are favorable comparisons at specific levels between A/C microphysics and more highly resolved ARMAR reflectivities/rain rates and synthesized 2a25 PR rain rates, as well as 2a12 microphysics.

Last, a difference analysis focusing on the high-emission/high-scattering areas not probed by the three KWAJEX A/C is performed on 2a12-retrieved LWCs and those derived from 2a25. This analysis highlights the main advantages offered by the synthesized PR rain rates: 1) availability at more than 75% of wet superpixels, 2) removal of attenuation effects that are present in original ARMAR reflectivities, which is particularly important at higher reflectivities, and 3) sufficient correlation with observed liquid water microphysical parameters to allow calculation of “proxy” in situ measurement (through assumed DSD) when A/C measurement is unavailable.

d. Algorithm reformulation

Because weaknesses in the 2a12-assumed microphysics are identified in section 4a, a suggested reformulation of the microphysical guidance within the 2a12 standard algorithm is offered in section 4b. The suggested modifications are particularly relevant for the mixed-phase layer where in situ–measured IWCs are found to be approximately 3 times the assumed IWCs in the 2a12 database. Because the suggested modifications are intended for improving the seven-category microphysical parameterization scheme used to generate the 2a12 cloud-radiation database, ice fraction and ice habit characteristics are calculated and included. The KWAJEX CMP (Kingsmill et al. 2004) provides for the identification of three ice habits in the A/C measurements, in addition to total IWC. Subtraction of IWCs associated with graupel, aggregate, and needle/column habits from total precipitation IWC yields a catchall fourth category: indeterminate ice particles. In the stratiform cases investigated, fractions for each of the three identifiable habits in relationship to the total IWC are calculated to aid in development of an alternative mixed-phase-layer ice mass transfer parameterization.

3. Required datasets

The initial step in the analysis procedure involves merging previously processed component datasets into a single merged–matched dataset, followed by generation of additional required dataset components (including synthesized TMI Tb and PR reflectivity profiles). Of the 10 wet datasets and two wet/dry datasets described in section 2a, seven were processed by colleagues and were ready for intercomparison within the merged dataset (including both wet/dry datasets). These seven—that is, the wet AMPR, the wet/dry AMPR, the GV radar, the wet ARMAR, the wet/dry ARMAR, the coincident overpass TMI Tb, and the coincident overpass PR reflectivities—are described in section 3a. Subsequent sections describe the following required datasets—section 3b: synthesized TMI Tb, section 3c: synthesized PR reflectivities, section 3d: 2a12 retrievals, section 3e: 2a25 retrievals, and section 3f: matched A/C microphysics.

a. Previously processed component datasets

The framework of the analysis is based on the four-channel AMPR Tb that were collected from approximately 12-km altitude aboard the NASA DC-8.2 This dataset establishes the basic temporal and spatial reference to which all other KWAJEX data components are matched and is thus the kernel of the merged–matched dataset. From the four-channel Tb, the basic superpixel spatial scale, ES indices, 19.35-GHz saturation and 37.1-GHz depression flags, modified convective/stratiform separation index, and synthesized TMI Tb are calculated.

As described previously, KWAJEX superpixels consist of 20 full-resolution AMPR pixels. The typical DC-8 A/C ground speed of ∼200 m s−1 and ∼12 km altitude, and AMPR scan period of 7 s, lead to a ground area for a five-scan by four-element superpixel of about 1.9 km × 1.5 km at 85.5 GHz. Because the 85.5-GHz channel is used to define the superpixel size, the lower-resolution, larger footprints for the 10.7-, 19-, and 37-GHz frequencies lead to those channels being purposefully oversampled for a given superpixel. Use of the superpixel dimension facilitates matching measurements from other KWAJEX instruments. Whereas a 1.9 km × 1.5 km superpixel size presents minor difficulties in synthesizing TMI Tb (section 3b) and in the execution of the 2a12 algorithm (section 3d), it is useful for the subsequent intercomparison analyses (all conducted at the superpixel scale). The primary purpose of the wet/dry datasets (identified by superpixels within ± 10 min of TRMM overpasses) is for the synthesis of TMI and PR values, as discussed in sections 3b and 3c.

Ground-truth rain rates for KWAJEX have been obtained from the reflectivity measurements of the Kwajalein S-band GV radar.3 Given a superpixel time tag and latitude/longitude position, the GV-radar matching algorithm first finds the closest radar volume that precedes but is within 10 min of a superpixel time. Because superpixels and radar pixels are only rarely matched exactly in time, and because the radar beamwidth is usually 2 km or less at the range of the DC-8, the matching algorithm calculates GV-radar quantities for the closest 2 km × 2 km radar pixel. The Z–R relationship used to obtain GV-radar rain rates is
i1558-8432-45-5-754-e1
where Z is reflectivity (mm6 m−3) and R is rain rate (mm h−1). This expression has been derived specifically for the KWAJEX radar using the method given in Hagen and Yuter (2003). The matched GV-radar data are divided into five height layers: 1) below 3.0 km (generally interpreted as 1.5–3.0 km), 2) 3.0–7.5-km layer (melting band), 3) 7.5–9.0-km layer (lower ice region), 4) 9.0–12.0-km layer (upper ice region), and 5) above 12.0 km (not used in analysis). Surface rain rates are calculated using reflectivities from the 1.5–3.0-km layer.

The 60-m-vertical-resolution ARMAR reflectivity measurements for KWAJEX were also collected aboard the NASA DC-8 A/C.4 The ARMAR reflectivity profiles were then matched to both the 40 140 superpixel wet dataset and 7140 superpixel wet/dry dataset.5 As with the GV radar, the ARMAR data were matched to the merged dataset by geolocating the ARMAR beams in time–space with each of the AMPR-defined superpixel positions and times. Because the DC-8 flight altitude of ∼12 km yields a nadir resolution of ∼800 m and the beams are spaced approximately 400 m apart, both along and across track, there are up to 15 beams per superpixel. Each of these beams was collected, and all radar data (including average vertical incidence angle) were averaged horizontally at each range gate position.

The 7140 superpixel AMPR and ARMAR wet/dry component datasets were created specifically for use in conjunction with coincident TMI and PR overpass measurements to synthesize additional TMI and PR observations. Coincident TMI Tb (TRMM algorithm 1b11) and PR reflectivities (TRMM algorithm 1c21) were then processed and matched to the merged dataset.6 As noted previously, “coincident” is taken to mean within at most a ±10-min time difference. Any AMPR superpixel occurring within the ±10-min TRMM coincidence window—regardless of the presence of clouds or precipitation—was included in the wet/dry datasets. The association of the AMPR (ARMAR) component datasets with the coincident TMI (PR) observations permits development of functional relationships between measurement pairs taken from the DC-8 aircraft and the TRMM spacecraft. As outlined in sections 3b and 3c, this ability enables synthesis of TMI Tb and PR reflectivities at the appropriate superpixel positions.

b. TMI synthesis

TMI observations for all KWAJEX superpixels are synthesized by first obtaining channel-specific linear regressions between the wet/dry AMPR measurements and the coincident TMI overpass measurements and then applying these regressions to the 40 140 AMPR Tb superpixels within the wet dataset to generate synthesized TMI Tb. The primary noise factor in the regressions is the time difference between the AMPR and satellite measurements. While maintaining sufficient dynamic range to include both wet and dry superpixels, the regressions are optimized by minimizing the maximum allowable time difference and maximizing the correlation coefficient of the scatter to the regression. In addition, the slope stability of the regression as compared with adjacent time difference windows is considered in some cases. All regressions result in optimal maximum time differences of less than 60 s—strong evidence of the small autocorrelation length scale of precipitation.

Both the horizontal and vertical channels of each of the TMI's four rain frequencies are projected from the four variably polarized AMPR channels. Figure 4 illustrates the synthesis plots of the vertically and horizontally polarized TMI regression curves for each of the four radiometer frequencies. Figure 5 shows the variation of the correlation coefficients and dynamic range with changes in maximum allowable time difference. The lower-right panel in Fig. 5 illustrates both the change in 85.5-GHz (vertical and horizontal) regression curve slope and the variation in correlation coefficient against changes in maximum allowable time difference.

One minor drawback to the above regression optimization procedure is that, for a small population of superpixels, the synthesized 37.0- and 85.5-GHz horizontally polarized Tb exceed the vertically polarized values (see the intersection points of regression curves at AMPR Tb value of ∼280 and ∼170 K in the lower-left and right-panels of Fig. 4). These “nonphysical” points amount to only 0.04% of 37.0-GHz cases and 0.7% of 85.5-GHz cases and are not used in subsequent analysis.

Because the difference between an observed Tb and a surrounding “clear air” Tb is an input variable to the 2a12 algorithm, clear-air or background Tb are also calculated for each AMPR channel at all 40 140 raining superpixels. These clear-air AMPR Tb are calculated from the AMPR wet/dry dataset by applying a linear regression to all 4923 completely nonraining pixels (i.e., no wet AMPR full-resolution pixels) over each channel's KWAJEX time series.

Using the synthesis equations shown in Fig. 4 and the clear-air calculations, vertically polarized and horizontally polarized TMI Tb are produced for all 40 140 wet cases. Important is that matching the synthesized TMI Tb with AMPR superpixels of resolution ∼3 km2 does not increase the resolution of the synthesized Tb. This fact ensures that the synthesized Tb do not violate resolution assumptions used in the 2a12 algorithm.

c. PR synthesis

To synthesize PR reflectivities from ARMAR measurements, a layer-by-layer calibration correction is found based on the reflectivity differences in the uncorrected 1c21 PR and ARMAR measurements. The layer-by-layer calibration corrections are then applied to the 40 140 superpixel wet ARMAR dataset to produce synthesized PR profiles. Because 1c21 measurements were all made within ±10 min of a PR overpass, the calibration correction must be made with data in the ARMAR wet/dry dataset, in which approximately 70% of the superpixel profiles are nonraining. As a consequence, there is a dearth of PR echoes for calibration comparisons at most of the 7140 wet/dry superpixels. To improve the statistical significance of the distribution of echoes in the layer comparisons, the 60-m-resolution ARMAR data and 250-m-resolution PR data are averaged into 1-km layers from the surface to 8 km for the calibration comparisons (the lowest layer is set at 0.5–1 km because of the cluttered nature of the surface returns). A sensitivity threshold of 14 dBZ is set in the ARMAR data so as to match more closely the PR's threshold as evidenced in the 1c21 data.

Similar to the procedure used for TMI synthesis, the primary variable used in optimizing the calibration between the PR and ARMAR data is the maximum allowable time difference between measurement times. As an example, the top two panels in Fig. 6 illustrate for the 3–4-km layer the variability of the mean and median distribution reflectivities and the change in population size of the matched distribution with respect to the variation in maximum time difference. For a given superpixel to qualify as “matched,” the reflectivity values of both radars have to exceed 14 dBZ. Note that, unlike the TMI synthesis cases, the optimum combination of matched distribution size and stability in the mean/median differences occurs at a time difference of approximately 6 min. This is the case for all layers up to 8 km, except the 0.5–1.0-km layer where using a time difference of 1 min limits the matched distribution enough to eliminate most of the surface-contaminated echoes, thus allowing a more refined determination of the calibration correction. The lower two panels of Fig. 6 illustrate the histogram distributions of the PR and ARMAR reflectivities in the 3–4-km layer. A weighted average of the mean and median differences—in which slightly more weight is given to the mean differences because of the non-Gaussian nature of the distributions—is used to establish the calibration corrections.

The smoothed variation with height of the ARMAR-to-PR corrections for all eight layers yields differences that are less than 1 dBZ, suggesting that the two instruments were accurately calibrated before KWAJEX and that they were interrogating the same microphysical phenomena despite the up-to-6-min differences in observation times. The 60-m-vertical-resolution wet ARMAR dataset is then averaged to 250-m resolution with the smoothed ARMAR-to-PR calibration corrections applied to produce the synthesized wet PR dataset. In addition, a high-resolution 60-m wet PR component dataset and 60- and 250-m PR component datasets consisting of clear-air profiles only (for path-integrated attenuation calculations) are produced.

d. 2a12 retrieval synthesis

The 2a12 retrievals used for analysis are the product of a modified version of the version-5 operational algorithm. Modifications are necessary to accommodate the format of the inputs, the lack of a water vapor channel input, and the limited field of view (FOV) of the superpixel areas where unique retrievals are desired.7 With the exception of 22.3-GHz-channel Tb, the primary input parameters to the modified 2a12 algorithm are the same as in the operational version, that is, TMI Tb, TMI background Tb, and a convective fraction parameter. An explanation of the differences in how these input parameters are obtained follows.

Synthetic TMI Tb and background (clear air) TMI Tb are obtained as outlined in section 3b. The 22.3-GHz water vapor channel input to the operational 2a12 algorithm is mainly used to distinguish between raining and nonraining areas within the TMI FOV. Because ES indices are used to determine all 40 140 superpixels in the wet datasets as raining, and background Tb are synthesized separately using ES determined dry superpixels, the 22.3-GHz Tb input is not necessary for this study. Because of the limited FOV and somewhat independent nature of each of the superpixels (a given superpixel may be seconds or days separated from adjacent superpixels in the intermittent time series), calculation of convective fraction values for each superpixel requires a different approach than is done operationally.

Similar to what is used in the operational 2a12 algorithm, an AMPR-based convective–stratiform index (CSI) is developed that determines convective fraction from an integration of CSI values for convective or stratiform superpixels as determined by the GV radar. The technique to calculate a CSI and derive from it convective fraction is an adaptation of a similar scheme detailed in Hong et al. (1999). To calculate the CSI for each superpixel, a combination of E and S indices weighted by scattering information in the 85-GHz channels is used:
i1558-8432-45-5-754-e2
where w is defined as
i1558-8432-45-5-754-e3
and Tb85bg is the background (clear air) AMPR Tb. As a result of using ES indices, the CSI values are automatically normalized to a range of 0–1.

Once the CSIs are calculated for all 40 140 superpixels, any superpixels characterized as convective or stratiform by the GV-radar convective–stratiform map [adapted from Steiner et al. (1995) and Yuter and Houze (1997) as tuned for KWAJEX] are divided into 10 CSI bins of 0.1-CSI width (i.e., 0–0.1, 0.1–0.2, 0.2–0.3, etc.). The fraction of superpixels designated as “convective” by the GV radar (convective fraction values) for each of the CSI bins is then calculated and is plotted versus CSI. The upper-left panel in Fig. 7 depicts the spread of convective, stratiform, and mixed superpixels by CSI and superpixel sequence number. Superpixels designated as stratiform by the GV radar are generally confined to CSI values less than 0.3; this is apparent in the CSI-derived convective fraction diagram (upper-right panel of Fig. 7) where the 50% convective fraction threshold is crossed at a CSI of ∼0.31. Convective fraction values for all CSIs are calculated by interpolation, and thus each of the 40 140 wet superpixels is assigned a convective fraction value unique to its CSI value. By identifying which superpixels are more than one-half convective, a significantly more distinct convective–stratiform separation in ES space is achieved as illustrated in the lower panels of Fig. 7 with the contrasting GV-radar convective/stratiform mapping (lower-left panel) and CSI-derived mapping (lower-right panel).

The validity of the CSI-derived convective fraction values, as determined above, is predicated upon several assumptions. Most important, the CSI-derived convective fraction procedure assumes spatial and temporal homogeneity in the convective–stratiform “texture” within the KWAJEX radar domain during the KWAJEX field phase—a reasonable supposition given that KWAJEX took place in the tropical Pacific Ocean in late summer without a tropical cyclone passage. Also, the width dimension of the KWAJEX radar domain cylinder is taken as the same order as the width dimension of the TMI swath while the fractional number of convective superpixels within the radar domain is assumed to be analogous to convective fractional area.

Derived parameters from the modified 2a12 algorithm include surface rain rates (total and convective portion), precipitation LWCs/IWCs, and cloud LWCs/IWCs at 14 levels from 0.5 to 18 km. Only the total surface rain rate and precipitation LWC/IWC profiles are used in this analysis. A superpixel-by-superpixel comparison of the 2a12 rain rates versus HQ GV-radar rain rates, as shown in the upper-left panel of Fig. 8, indicates that the approaches generally produce rain rates similar in magnitude at the same times and locations. However, the scatter diagram and histograms of Fig. 8 also indicate that 2a12 rain rates often exceed GV-radar values by ∼60%–70% at magnitudes greater than 7 mm h−1 and often underestimate GV-radar values by ∼50% below 7 mm h−1. In addition, maximum 2a12 rain rates are “capped” at about 35 mm h−1.

To calculate the cloud-radiation-model-based DSD shape parameters shown in Fig. 3 and described previously in section 2b, the rwate/ricee and υwate/υicee values are derived from the LWCs/IWCs assuming a Marshall–Palmer distribution (Marshall and Palmer 1948), where
i1558-8432-45-5-754-e4
and n0 = 8000 m−3 mm−1. Pruppacher and Klett (1997) further show that Λ is related to LWC by
i1558-8432-45-5-754-e5
with the following units: Λ (mm−1), LWC (g m−3), and ρw (water density; g cm−3). Because the inverse of Λ is the DSD's characteristic diameter D0 and the effective diameter is Deff = 3D0 (Flatau et al. 1989), the liquid water effective radius rwate (mm) is defined by
i1558-8432-45-5-754-e6

A similar approach is taken to calculate the ice effective radius ricee, where the water density is replaced by an ice density ρice = 0.25 g cm−3 and LWC is replaced by IWC. This approach assumes a precipitation ice distribution with fairly dense spherical ice particles characterized by number concentrations that are nearly the same as those of liquid precipitation. This assumption is supported by the high concentrations of graupel particles found in the in situ observations (described in sections 3f and 4b) and in the observed minus assumed effective radii comparisons of Fig. 3h in which the ricee differences are similar in magnitude to the rwate differences.

As noted in section 2b, the assumed effective variances based on the 2a12 retrievals are constant because of the analytical nature of the assumed DSD. In the case of the full (nontruncated) Marshall–Palmer DSD applied in this analysis, the analytical solution for effective variance reduces to a value of 1/3. Thus, because the absolute observed minus assumed effective variance differences shown in Fig. 3g are based on variations in the observed values only, the analyses presented in section 4 assume an effective variance of 0.33.

e. 2a25 retrieval synthesis

Rain-rate retrievals are produced from synthetic PR reflectivity profiles using version 6.32 of the 2a25 algorithm modified specifically for the merged KWAJEX dataset.8 As with the 2a12 synthesis, modifications to the 2a25 algorithm are first required to accommodate the format of the input data. Further modifications are needed because synthetic surface reflectivities are too contaminated to be usable. Without reliable surface cross-sectional measurements, techniques that could be employed by the version-6.32 algorithm to estimate path-integrated attenuation (PIA), such as the surface reference technique of Meneghini et al. (2000) or a simpler adjacent clear-air PIA profile scheme, are untenable. Also, contaminated surface returns hinder the algorithm's convective–stratiform mapping. Thus, two 40 140 element datasets are generated—one assuming all superpixels are convective, and the other assuming all are stratiform. This process is accomplished by estimating PIAs for each profile based on measured reflectivity and DSD parameters obtained from the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment. The remainder of this section addresses how the convective–stratiform data are blended for subsequent intercomparison and analysis and how liquid microphysical data are obtained from modified 2a25 rain-rate retrievals.

The convective and stratiform 2a25 outputs are blended into a single 40 140-element dataset using the CSI-based convective–stratiform separation technique discussed in section 3d. For reasons explained, superpixels with a CSI > 0.31 are assigned the Z–R relationship for convective precipitation whereas superpixels with a CSI value ≤ 0.31 are assigned the stratiform relationship. The lowest range gates of the 2a25 retrievals—that is, surface, 250 m, and 500 m—are too contaminated for subsequent analysis. The five 250-m range gates over the 1–2-km layer actually compose the least noisy, lowest layer. Therefore, in comparisons with 2a12 surface rain rates, an average for range gates over the 1–2-km layer is used. In comparisons with the GV radar, which approximately samples the 1.5–3.0-km layer at its lowest elevation angle, using a 2a25 rain-rate average over the 1–2-km layer naturally yields a closer comparison. Averages of rain rates over the 1–2-km layer are also used for 2a25–ARMAR rain-rate comparisons.

Figure 9 illustrates matched superpixel and scatter-diagram comparisons of 2a25 rain rates versus GV-radar, 2a12, and ARMAR rain rates. In the GV-radar matchup (top panels), only HQ GV-radar superpixels are used, resulting in ∼8000 matches. The 2a25 rain rates significantly exceed GV-radar rain rates between matched superpixels from 2000 to 4000, but overall the scatter is evenly distributed around the 1-to-1 line. The comparison with the 2a12 rain rates results in about 21 000 matches. The matched superpixel diagram of the 2a25 and 2a12 rain rates (lower-left panel) indicates good agreement in terms of the timing and proportional magnitudes of the rain-rate changes, perhaps even better agreement than is seen in the GV-radar–2a25 matched superpixel diagram. However, close inspection of the 2a12–2a25 scatter diagram (lower-right panel) suggests that, similar to the comparison between 2a12 and GV-radar retrievals (Fig. 8), 2a12 rain rates overestimate 2a25 rain rates by 60%–70% at magnitudes greater than 7 mm h−1 and underestimate 2a25 rain rates by ∼50% below 7 mm h−1. For 2a12 rain rates greater than 2 mm h−1, the average 2a12 overestimate of 2a25 rain rates is ∼25%.

To make limited microphysical comparisons between 2a25, 2a12, and the in situ aircraft measurements, an M–P distribution assumption is applied to derive liquid water microphysical parameters from 2a25 rain-rate retrievals. Only liquid water parameters are derived because the 2a25 algorithm does not provide IWC values. Liquid water content values are obtained from the rain rates using the standard relationship (Pruppacher and Klett 1997), that is,
i1558-8432-45-5-754-e7
with the following units: rain rate R: mm h−1, LWC: g m−3, and water density ρw: g cm−3, and n0 is defined as 8, 000 m−3 mm−1. Effective water radius rwate can be obtained from LWC values using Eq. (6), and effective water variance υwate ≈ 0.33 for the M–P DSD as explained previously.

As a check on the validity of LWC calculations made from 2a25 rain-rate profiles, 1-km-layer averages of 2a25 rain rates and derived LWCs are compared with matched in situ measurements. The top panels in Fig. 10 depict matched superpixel comparisons of average 2a25 rain rates and derived LWCs with Convair-derived rain rates and LWCs at matched superpixels in the 2–3-km layer. Comparisons shown in the top panels of Fig. 10 demonstrate the sensitivity of the near-vertical-looking ARMAR and its derived/synthetic PR datasets to small-scale microphysical fluctuations, despite a sampling volume of at least six orders of magnitude greater than that of the Convair. At rain rates below 4 mm h−1 and LWCs less than 0.25 g m−3, the agreement between the 2a25 and Convair values is close despite mostly different environmental conditions in which the measurements were made. At higher rain rates, 2a25 values underestimate Convair values, possibly because of the inadequacy of the fallout equations used in calculating Convair rain rates from measured particle spectra. However, Convair LWC values are calculated without any gravitational assumptions, and 2a25 LWC values remain slightly underestimated for LWCs > 0.25 g m−3. The assumptions, conversions, and calculations necessary to obtain the Convair rain rates and LWCs are addressed in the next section.

f. Matched aircraft microphysics

As discussed in section 2b, in situ microphysical measurements were collected from three different research aircraft during KWAJEX. Four research groups took part in processing raw measurements into final microphysical products, compiling the common microphysical product data by priority flight legs composed of varying numbers of 1-km length segments of flight path.9 These “priority leg” segments of data are matched in time and space to the merged KWAJEX dataset superpixels for intercomparison and analysis. Subsequent discussion in this section describes the priority leg–matching methods, the calculations required to obtain derived microphysical data such as effective radii and variances, the adjustments and recalculations made to the lower-level Convair data, and some intercomparisons between size-spectra-derived reflectivity and reflectivity measured remotely by ARMAR.

To match aircraft microphysical data to times and geolocations of the AMPR superpixels, a maximum time difference of ±5 min and maximum latitude–longitude differences of ±0.01° between the priority leg segment center and the superpixel center are used as matching criteria. The ±5-min time difference is chosen because it falls between the 30- and 45-s satellite/aircraft instrument time differences used for synthesizing TMI Tb and the up-to-6-min satellite/aircraft instrument time differences used in synthesizing PR reflectivity profiles. This time difference is also consistent with the use of HQ GV-radar data, which are predominantly restricted to superpixel/radar time differences of less than 6 min. For locations near the equator as is the case for KWAJEX, a latitude–longitude difference of 0.01° results in a maximum difference between priority leg segment center and matched superpixel center of ∼1100 m in either east–west or north–south directions. This ensures that matched centers are never more than 1.5 km apart and are generally within 1 km of one another and that geolocation differences are essentially the size of or smaller than the flight segment length and/or superpixel dimensions (1.9 km × 1.5 km).

The matching of aircraft microphysics data to superpixels results in 1012 DC-8, 496 Citation, and 450 Convair matches. A diagram of the matched aircraft points in ES coordinate space is shown in the top panel of Fig. 11. It is evident that most of the matched measurements take place at low emission/low scattering, which is typical of stratiform conditions. Only the DC-8 measurements denote instances in which AMPR superpixels indicate 19.35-GHz saturation (generally points with E index > 0.6), noting that these measurements are taken at altitudes above 10 km where virtually no liquid water is present. The reason the aircraft data appear restricted to predominately light rain and stratiform conditions is aircraft safety considerations (thunderstorm avoidance) that were practiced during KWAJEX. To produce total-column microphysical profiles from the aircraft data, the in situ measurements have to be combined to represent adequately both liquid water path (LWP) and ice water path. Because only the Convair sampled at levels with enough water to characterize a tropical LWP, superpixels with adequate matched total-column microphysics are further restricted to points with Convair plus Citation and/or DC-8 data. The limitation in cases of matched superpixels with total-column microphysics is evident in the bottom panel of Fig. 11.

In addition to the superpixel time tag and latitude–longitude position, 19 flight and microphysical parameters are obtained for each superpixel in the matching process. Fifteen of these are extracted directly from the CMP-format priority leg segment data, and four are calculated from particle size spectra for each segment and then subsequently matched. The 19 parameters, plus two additional Convair-only variables (explained below), are given in Table 1. Water and ice effective radii are calculated from the particle spectra using the relationship
i1558-8432-45-5-754-e8
where ni is the particle concentration per bin per bin width (L−1 μm−1), ΔDi is bin width (μm), and Di is maximum particle dimension (μm), which, with the assumption for this calculation that all water and ice particles are spheres, becomes diameter. Actual bin widths vary over the measured particle size range from 5 μm to 25 mm and are listed in the TRMM CMP (Kingsmill et al. 2004) as follows: 5–40-μm range with 5-μm bin width (7 bins), 40–150-μm range with 10-μm bin width (11 bins), 150–1000-μm range with 50-μm bin width (17 bins), and 1–25-mm range with 400-μm bin width (60 bins). Ice particle concentrations are summed from the individual ice habit concentrations—graupel, aggregates, needle/columns, and indeterminate ice particles. Water and ice effective variances are similarly calculated using
i1558-8432-45-5-754-e9

Water effective radii and variances for the DC-8 are set to zero because it flew too high to sample liquid water meaningfully. At temperatures above +5°C, the Convair rwate/ricee and υwate/υicee values are summed using water and ice particle concentrations recalculated after the conversion of ice artifacts into water spheres. The reasoning for this conversion and how it is performed are explained below.

At levels below ∼4 km, the Convair microphysical data derived directly from the priority leg CMP exhibited an unexpectedly high amount of IWC. After the matching process, there remained superpixels where precipitation IWCs exceeded coexisting precipitation LWCs at levels with temperatures as high as 10°–25°C. The warm-layer precipitation IWCs were due to “ice artifacts” caused by drop splashing resulting from the impact of large rain drops on the aircraft instrumentation (P. Hobbs 2002, personal communication). Because the TRMM microphysics software used to produce the CMP data identified ice and ice habits by particle shape without reference to temperature, the fragmented raindrops evidently appeared nonspherical and were classified as ice (D. Kingsmill 2002, personal communication).

Whereas the warm-layer ice artifacts led to IWCs that were insignificant as compared with the IWCs measured by the Convair at higher levels and overall, the erroneous ice classifications caused gross underrepresentation of LWCs in the layer with temperatures above +5°C. To recover more representative precipitation LWC values in the warm layer, a procedure was developed and later confirmed by the principal investigator of the Convair A/C (P. Hobbs 2002, personal communication) in which ice artifacts were converted to equivalent-sized liquid water spheres. A detailed description of this conversion process can be found in Fiorino (2002). The converted LWCs, reflectivities, effective radii/variances, and derived rainrates are calculated for all Convair CMP segments and then are subsequently matched within the merged dataset for intercomparison.

Validation of the ice artifact conversion process outlined above is best represented by the Convair versus 2a25 rain rate and LWC diagrams presented in the top panels of Fig. 10. The comparisons would not have been nearly as favorable without ice artifact conversion given that the original matched Convair LWC values were generally two orders of magnitude smaller than the converted values. As a further check of both raw CMP and recalculated Convair values, calculated reflectivities for both the Citation and Convair data are compared with ARMAR measurements in two layers. The lower six panels of Fig. 10 illustrate scatter diagrams and histograms of layer-averaged ARMAR versus aircraft microphysics-derived reflectivity in the 2–3-km layer (Convair) and 6–7-km layer (Citation). Despite the attenuating effects present in the ARMAR data—which are negligible in the 6–7-km-layer comparison and are fairly small in the 2–3-km layer—the agreement is close given the nearly 1-to-1 relationships in the scatter diagrams and similar shapes and peaks in the histograms. The 6–7-km-layer comparison using reflectivity directly from the CMP suggests the Citation ice concentrations are not contaminated by drop splashing. The ARMAR values slightly exceed the Citation values in the 6–7-km layer and slightly underestimate the Convair values in the 2–3-km layer; this result is attributed to the attenuating effects on the ARMAR measurements noted above.

4. Results of analysis

In accordance with the method described in sections 2c and 2d, the following results are divided along two lines of inquiry: 1) identifying algorithm discrepancies, and 2) deducing appropriate algorithm reformulations. Differences between assumed and observed microphysics that demonstrate hypothesis validity are discussed in section 4a. Section 4b offers two approaches for mitigating weaknesses noted in the model-derived microphysics.

a. Algorithm discrepancies

As noted in the method section, observed minus assumed microphysical differences are investigated as both total-column and level-specific differences. The observed minus assumed total-column microphysical differences indicate that the A/C-observed LWC/IWC values are not only generally greater than the 2a12 assumed values (Fig. 3i), but are also significantly more variable (Fig. 3g). The total column matchups are further explored by considering differences between algorithm and GV-radar rain rates at those points.

Inspection of 2a12 rain rates plotted versus GV-radar rain rates at the 142 matched total-column superpixels (center plot of Fig. 12), reveals that while 2a12 rain rates generally underestimate GV-radar rain rates, a rain-rate difference of 2 mm h−1 or more was exceeded at only 23 of the matchups. Restricting the rain-rate difference analysis to these points highlights the expected trend of increasing observed–assumed microphysical differences with respect to increasing radar–algorithm rain-rate difference. Absolute observed–assumed column-averaged microphysical differences versus radar–algorithm rain-rate differences are plotted for the six column-averaged microphysical parameters in the panels surrounding the central scatter diagram of Fig. 12. The linear regression trend lines included in the diagrams indicate a hypothesis-supporting, positive slope in the microphysical-versus-rain-rate difference relationship, except in the case of effective water variance, for which the relationship is virtually constant. Nonetheless, this result for total-column microphysical points alone cannot be considered conclusive, given that the matched points cover only a restricted portion of the ES space under consideration and make up less than 0.5% of the total number of KWAJEX superpixels.

Figure 8 indicates situations in which 2a12 and GV-radar rain-rate differences greatly exceed 2 mm h−1—by as much as 15 mm h−1 for significant numbers of superpixels. By mapping the GV-radar, synthesized 2a25, and synthesized 2a12 rain-rate surfaces into ES coordinate space, rain-rate discrepancies beyond just magnitude differences become apparent. The top panels of Fig. 13 illustrate smoothed surfaces of near-surface rain rates derived from the GV-radar and synthesized 2a25 and 2a12 algorithms. Although all three rain-rate surfaces are similar in the approximate ES region where most aircraft in situ measurements occur, and the GV-radar and 2a25 surfaces are similar throughout ES space, the 2a12 rainrates deviate significantly from the radar rainrates at high emission superpixels. This algorithm deviation takes the form of positive GV-radar minus 2a12 rain-rate differences at high-emission, high-scattering points and strongly negative differences at high-emission, low-scattering points. Before postulating why the 2a12 algorithm seems unable to match Tb exhibiting high-emission/high-scattering characteristics to high-rain-rate profiles while producing profiles with too much rain for high-emission/low-scattering Tb, microphysical differences in the areas of significant rain-rate differences are first examined.

To obtain microphysical observations in the ES regions that the aircraft tracks avoided and where the greatest radar–algorithm rain-rate differences exist, proxy in situ LWC profiles are created using the well-correlated synthesized PR-to-Convair microphysics relationship described in section 3.5 (see Fig. 10, top panels). The 1–2-km-layer average LWC values obtained from applying a M–P distribution to the 2a25 reflectivity/rain-rate profiles are compared with the matching 1–2-km-layer average 2a12 LWC values. (IWCs are not calculated because additional assumptions would be required to produce such quantities from rain-rate profiles alone.) In a manner similar to that used for the total-column microphysical comparisons (Fig. 12), absolute LWC differences are plotted versus matched near-surface GV-radar minus 2a12 rain-rate differences for high-emission/high-scattering points with rain-rate differences >2 mm h−1 and for high-emission/low-scattering points with >5 mm h−1 rain-rate differences. These two diagrams, plus diagrams of the associated 2a12 versus 2a25 LWCs in the two ES quadrants under study (E index > 0.5 and S index > 0.5; E index > 0.5 and S index < 0.5), are depicted in Fig. 14. The LWC–rain-rate difference analysis diagrams (left panels in Fig. 14) exhibit increasing LWC differences with increasing rain-rate differences. As would be expected from the rain-rate differences shown in Fig. 13, the right panels of Fig. 14 indicate that the 2a25 LWCs exceed the 2a12 LWCs in the high-emission/high-scattering quadrant, with the opposite being true in the high-emission/low-scattering quadrant. The results illustrated in Fig. 14, coupled with the earlier results appearing in Fig. 12, are taken as conclusive evidence of the validity of the hypothesis of observed–assumed microphysical differences being positively correlated to the GV-radar minus 2a12 rain-rate differences.

To provide a better understanding of why the 2a12 high-emission rain rates appear to overemphasize low-scattering areas and suppress rain rates in high-scattering regions, observed and assumed LWC and IWC profiles are matched, plotted, and compared. Figure 15 illustrates assumed 2a12 and aircraft-measured LWCs/IWCs plotted at aircraft altitudes and matched to the closest 14 model profile levels. The curves running through the data scatter in the top and middle diagrams are layer-by-layer averages, smoothed by cubic-spline interpolation, and represent the composite assumed and observed profiles shown in the bottom diagram of Fig. 15. The most salient feature in the composite profiles of Fig. 15 is the significantly greater liquid and ice hydrometeor masses in the observed profiles below 10 km. Above 10 km, the assumed IWCs slightly exceed the values observed by the DC-8, although it is not understood why these systematic differences switch signs at high altitude. Also of note is the existence of a small but significant concentration of presumably supercooled liquid precipitation hydrometeors as high as 9.5 km (measured only by the Citation). Stith et al. (2002) and Kingsmill et al. (2004) also reported small but persistent supercooled water concentrations in the Citation KWAJEX measurements.

The consequence of additional mixed-phase-layer ice in the observed composite profile is the greater scattering of upwelling microwave radiation than what is being produced in the cloud-radiation-model database. Although the observed composite IWC profile results from predominately stratiform (low emission/low scattering) superpixels, if the same “factor of three” IWC underestimate is assumed for the 2al2 high-emission/high-scattering points, an explanation of why the algorithm matches highly scattered Tb to high-emission/low-scattering and thus high-rain-rate profiles can be offered. The presumption that the cloud-radiation-model database's underestimate of mixed-phase-layer ice at low-emission superpixels can be assumed for the high-emission superpixels where no in situ measurements were made is supported by the variation of 2a12 rain rates in the low-emission region. Because 2a12's rain rates decrease as scattering increases in the high-emission region, one would expect a decrease in algorithm rain rates with increasing scattering in the low-emission (E index < 0.5) region as well if the aircraft-documented lack of 2a12 mixed-phase-layer ice is truly a contributor to the inverse rain-rate relationship. Inspection of the 2a12 rain-rate surface shown in the top-right panel of Fig. 13 indicates low-emission rain rates actually increase with increased scattering. However, this is more a result of the convective fraction specification (see section 3d) than the actual output of 2a12's Tb matching and profile selection process.

The bottom panels of Fig. 13 show how 2a12's unmodified rain rates are modified by the convective fraction specification. The lower-middle panel in Fig. 13 shows the convective fraction surface plotted in ES coordinates—note that the values are nearly constant across all scattering values and are near maximum in high-emission areas while they increase dramatically from near 0 to 1 from low to high scattering in the low-emission region. Thus, in high-emission regions the convective fraction acts to increase rain rates across all scattering values but not to reverse the reduction in rain rates from low to high scattering values. In the low-emission region, rain rates are increased at high scattering values but are left nearly unchanged at low scattering values—an effect that could reverse a rain-rate reduction from low to high scattering to an increase. The lower-left panel in Fig. 13 is the 2a12 rain-rate surface before modification by the convective fraction (S. Yang 2002, personal communication). Note that low-emission rain rates do decrease slightly from low to high scattering values as expected given analyzed mixed-phase-layer ice discrepancies.

In summary, 2a12 algorithm rain rates derived from synthesized KWAJEX TMI Tb underestimate GV-radar and synthesized PR rain rates by ∼50% at rain rates <7 mm h−1 and overestimate GV-radar and PR rain rates by nearly 67% at rain rates ≥7 mm h−1. Examination of the 2a12 rain rates in ES coordinates reveals most of the overestimation occurs at high-emission/low-scattering superpixels, whereas the radar-derived rain rates indicate that 2a12 significantly underestimates rain rates at convective high-emission/high-scattering points. This suggests underproduction of ice, particularly larger ice hydrometeor, by the cloud-radiation model underlying the algorithm, particularly in the mixed-phase layer, thus suppressing the number of high-scattering, high-rain-rate profiles contained in 2a12's database. In turn, this creates deficient a priori Bayesian probabilities and, more important, forces the algorithm's Bayesian weighting scheme to underrepresent high-emission/high-scattering profiles (characterized by saturated or nearly saturated low-frequency channels and depressed high-frequency channels) in favor of high-emission/low-scattering profiles (characterized by highly saturated low-frequency channels but nondepressed high-frequency channels). This is a physical deficiency in the algorithm given that centimeter–millimeter-wavelength Tb in precipitating clouds are highly sensitive to the balance between large ice and mixed-phase hydrometeors within and above the rain layer's all-liquid layers.

b. Algorithm reformulation

Two possible modifications to the 2a12 algorithm are suggested to mitigate the effects of the mixed-phase-layer ice hydrometeor shortage in the cloud-radiation model database profiles. A straightforward procedure involves modification of the convective fraction specification, whereas a more microphysically satisfying but also more demanding procedure addresses possible flaws contained in the ice parameterization scheme used in 2a12's cloud model.

As illustrated in Fig. 13, the convective fraction specification has a profound effect on 2a12 rain-rate retrievals. The algorithm convective fraction specification not only enhances rain rates in proportion to its fractional value at individual pixels, but also augments the profile microphysics. Because the rain rate for a given superpixel is nonlinearly related to a collection of microphysical database profiles that best represent the microwave Tb viewed from space (Kummerow 1998), adjusting the microphysical profiles in proportion to changes in the surface rain rate provides a robust path for modifying the algorithm's behavior. By the same token, this approach introduces microphysical properties inconsistent with the cloud model that supports the algorithm. Nonetheless, one can see that by adjusting the convective fraction surface to deemphasize the enhancement at low scattering (S index < 0.5) while augmenting the enhancement in high-scattering areas would bring the 2a12 surface rain rates more in line with the GV-radar and 2a25 rain rates in ES space. In mathematical terms, the convective fraction values could be reduced at high-emission values by modifying the emission input to the CSI in Eq. (2). Such an adjustment would do little to correct the mixed-phase-layer ice hydrometeor deficit in the profile database, but it would offer some improvement to the low-level LWC values and would circumvent having to reparameterize the cloud-radiation model ice physics, thus requiring repopulation of the algorithm's microphysical profile database and associated Tb vectors.

The more microphysically satisfying modification would improve the multihydrometeor microphysics parameterization scheme used for generating the 2a12 cloud-radiation database. In such parameterizations, up to six basic hydrometeor categories have been represented (i.e., cloud droplets, precipitating water drops, pristine ice crystals, snowflakes, ice aggregates, and graupel/hail particles), as well as water vapor. As is evident in Fig. 15, both liquid and ice water contents are underrepresented at levels below 10 km in 2a12's cloud-radiation model database. In qualitative terms, this suggests that the mass transfer of vapor into the various allowed hydrometeor categories is a more significant microphysics parameterization problem in generating 2a12's database than the mass transfers between specific ice habits and liquid water categories.

That there are intrinsic weaknesses to all current bulk microphysical parameterization schemes involving multiple ice categories is well known to the cloud-modeling community. A major weakness has been the somewhat arbitrary definition of a fixed number of ice habit categories whose size distributions and concentrations are determined diagnostically using unverified mass transfer equations and lacking any type of model history governing the evolution of the given hydrometeor populations (G. Tripoli 2003, personal communication). With that as a backdrop, it is not surprising that there are microphysical deficiencies in precipitation retrieval algorithms based on microphysical databases generated by cloud models.

It is almost tautological to declare that any detailed radiative transfer technique used to generate Tb associated with a microphysical profile database is sensitive to specific ice habits and ice water paths. This is particularly so for large frozen or partially frozen hydrometeors. Therefore, any improvements to a microphysical parameterization scheme used for precipitation retrieval must include emphasis on graupel production throughout all relevant mass transfers leading to graupel particle concentrations and size distributions. The in situ aircraft measurements analyzed here indicate that graupel is the dominant ice habit in the mixed-phase layer. This finding is emphasized in Fig. 16, which illustrates the variation in height of the total IWC fraction of the various aircraft-measured ice habits, with graupel being the largest fraction below 9.5 km and making up nearly 70% of the total IWC in the 1500-m layer above the melting layer. Later analyses of the KWAJEX CMP data, such as those found in Kingsmill et al. (2004), support the finding that graupel is the dominate ice category, even in stratiform environments. The Kingsmill et al. (2004) analysis also suggests that a significant portion of water content categorized as indeterminate in Fig. 16 may be more correctly classified as aggregates.

5. Conclusions

This investigation finds that differences between in situ–measured microphysics and 2a12 algorithm–assumed microphysics are greatest where the algorithm's surface rain rates differ most from rain rates derived from the KWAJEX ground validation radar rain rates and synthesized 2a25 rain rates. In addition to verifying the hypothesis motivating this research, the analysis also accomplishes the following: 1) it demonstrates the efficacy of a two-dimensional emission–scattering coordinate system in intercomparing radar- and radiometer-derived microphysics and rain measurements, 2) it identifies and quantifies ice deficiencies in the current version (5) of the 2a12 algorithm, 3) it proposes modifications to the 2a12 algorithm that would mitigate its shortcomings vis-à-vis microphysical assumptions, 4) it diagnoses the strengths of a downward-looking radar in validating a radiometer rain algorithm, and 5) it quantifies the limitations in using crewed aircraft for exploring the complete microphysical domain of precipitating clouds.

The ES coordinate system proves effective in uncovering the tendency of the 2a12 algorithm to match high-emission/high-scattering brightness temperature signatures with high-emission-/low-scattering-assumed cloud-radiation-model-generated database profiles. The ES coordinate diagrams show clearly the similarity between the GV-radar-derived and synthesized PR-derived rain-rate surfaces in ES space and provide helpful contrasting depictions of the concomitant 2a12 rain-rate surfaces for isolating differences. In general, the ES coordinate system is more effective than a combination of matched superpixel plots, scatter diagrams, and histograms for isolating algorithm problems in conjunction with the assumed microphysics.

The mismatching by 2a12 of high-rain-rate/high-scattering microphysical profiles into high-emission/low-scattering profiles is traceable to an apparent deficiency of scattering mixed-phase-layer ice hydrometeors in the cloud-radiation-model simulations used to populate the algorithm database. Analysis of the in situ observations indicates that the assumed profile mixed-phase-layer IWCs and low-level LWCs are too low by as much as a factor of 3 in generally stratiform cases, that is, those cases that the aircraft largely interrogated. That the assumed profile ice and liquid water contents are both underestimated suggests that the most significant model parameterization problem may be the transfer of water vapor into the various allowed hydrometeor categories rather than the mass transfers between specific ice habits and liquid water categories. The aircraft measurements additionally show that graupel hydrometeors make up nearly 70% of the IWC in the lowest regions of the mixed-phase layer where the greatest observed-minus-assumed IWC differences occur.

Two algorithm modifications are proposed to reduce the observed–assumed rain-rate and microphysical differences. First, a straightforward modification involving a change to the current 2a12 convective fraction specification is suggested. This modification would improve the rain-rate matchup in magnitude and ES space. By the same token, it would do little to rectify underlying ice microphysics problems in the cloud-radiation-model simulations. The second more physically based, and more demanding to implement, modification requires that the microphysical parameterization scheme of the cloud model be improved to characterize liquid and ice water contents better for levels below 10 km—especially IWCs within the mixed-phase layer resulting from graupel. Such a modification would then require an updated 2a12 cloud-radiation-model database to be compiled. (A version-6 2a12 algorithm with a new cloud-radiation database has been developed, but without substantive changes to the cloud model.)

Analysis of the KWAJEX data reveals that aviation safety concerns resulting from using crewed research aircraft have been, and will continue to be, a major limitation in the collection of in situ microphysical measurements across the full spectrum of precipitation phenomena. Although the KWAJEX aircraft priority-leg microphysical data analyzed for this research could not have been obtained effectively by other means and thus are invaluable to the conclusions that have been drawn, they represent limited flight-track information given that the strong action zones of precipitating clouds are currently off limits because of safety concerns. Therefore, barring the development of slow-flying armor-plated research aircraft, it is recommended that future campaigns examine new ways to equip and utilize remotely controlled drone aircraft, other uncrewed aerial vehicles, and elevated mountain terrains to collect in situ microphysical data for intense precipitation conditions. Crewed aircraft that cannot safely penetrate strong convective turrets and supercooled water regions simply cannot gather the full spectrum of microphysics needed for a thorough study of precipitation. Future field experiments addressing intense rainfall microphysics will need to address this issue in the a priori planning and strategizing stages.

These last remarks are not a wholesale criticism of using crewed aircraft for probing the microphysics of precipitating clouds. Whereas Fig. 13 shows clearly that the KWAJEX aircraft tracks are restricted to only one of the four quadrants of microphysical ES space, that is, the low-emission/low-scattering quadrant, it is that quadrant in which much of the mid- to light rainfall occurs. As past studies have noted, this is perhaps the most difficult of the retrieval regimes for both space-viewing radiometers and radars (Smith et al. 1998; Meneghini et al. 2000). Therefore, it is stressed that the major role for crewed aircraft in studies of precipitation microphysics and in validation campaigns for precipitation algorithms is within the low mid- to light-rain regimes where algorithms have difficulty detecting precipitation and quantifying rain rates.

As noted initially, the kind of analysis presented here offers a fundamental, physically based validation of the TRMM radiometer-only standard algorithm, that is, a detailed three-dimensional intercomparison of the algorithm's assumed profile microphysics. The analysis has exposed various prominent weaknesses—the ice water content within the mixed-phase layer and inconsistencies concerning the specification of convective fraction in conjunction with implied rain rates and microphysical properties. Notwithstanding the possibility that the analysis procedures contain their own microphysical weaknesses, the research has arrived at conclusions that justify modifications in specific components of the 2a12 algorithm that are suspect by its principal producer (C. Kummerow 2002, personal communication) and others (e.g., Lang et al. 2003). It is emphasized that the results shown in Fig. 15 exhibit discrepancies between microphysical observations and algorithm assumptions that deserve careful scrutiny. Furthermore, the results shown in Fig. 13 quantify how sensitive 2a12 retrievals are to the specification of convective fraction—a parameter directly linked to the algorithm's underlying microphysical assumptions and thus directly to the algorithm's rainfall outcomes.

One could question the validity of drawing the above conclusions based on the results of a modified 2a12 algorithm using synthesized inputs matched to a superpixel resolution finer than that assumed by the algorithm. However, it is noted that, despite being matched to the approximately 2 km × 2 km AMPR superpixels, the synthesized TMI Tb maintain the resolution of the observed TMI Tb (∼14 km × 14 km) because the regression analysis that produced them cannot alter the resolution from the observed values. Furthermore, inspection of the rain-rate comparisons in Figs. 8 and 9 (lower panels) reveals consistency with the observed 1998 zonally averaged rain rates shown in Fig. 4 of Kummerow et al. (2000). They conclude that version 5 of 2a12 overestimates version 5 of 2a25 by 24% in the Tropics. This research finds a 2a12 overestimate of 60%–70% at rain rates above 7 mm h−1 and an underestimate of 50% below 7 mm h−1 but a similar overall average overestimate of ∼25% for rain rates above 2 mm h−1. Thus, the synthesized 2a12 retrievals and conclusions that are drawn are deemed valid and should be considered in future improvements of the TRMM 2a12 standard algorithm and any similar cloud-model-based radiometer algorithm.

The principle expected benefits of any physically based future improvements to the TRMM level-2 radiometer algorithm will be the generation of more accurate, instantaneous retrievals of rain rates and associated microphysical profiles. Such a result will provide a better understanding of how tropical/subtropical water budgets at large scales build up from micro- and mesoscale cloud and precipitation processes (see Hou et al. 2000). Such results address the core objective of TRMM, that is, producing a highly representative tropical rainfall climatological description from physically based and objectively validated retrieval algorithms. The successor GPM mission will consist of a globe-encircling fleet of satellites—each carrying a passive microwave radiometer. With enhanced physical retrieval algorithms, the GPM constellation could conceivably provide complete and continuous coverage of one of the atmosphere's most important meteorological variables at degrees of accuracy and precision that will enable an evolution from rainfall climatological descriptions to rainfall climate dynamics.

Acknowledgments

The authors acknowledge the generous and professional assistance provided by a number of colleagues in creating the various datasets essential to the analysis. We are extremely grateful to 1) Ms. Robbie Hood and Mr. Frank LaFontaine for preparation of the AMPR dataset; 2) Dr. Sandra Yuter for preparation of the Kwajalein GV-radar dataset and coordination of the KWAJEX aircraft priority-leg analysis; 3) Drs. Steve Durden, Eastwood Im, and Joseph Turk for preparation of the ARMAR dataset; 4) Dr. David Kingsmill for preparation of the NASA DC-8 microphysics dataset and coordination of the CMP definition; 5) Drs. Anthony Grainger, Julie Haggerty, and Jeffery Stith for preparation of the UND Citation microphysics dataset; 6) Prof. Peter Hobbs and Mr. Arthur Rangno for preparation of the UW Convair microphysics dataset; 7) Dr. Ziad Haddad for preparation of the synthesized 2a25 dataset; and 8) Dr. Song Yang for KWAJEX merged–matched dataset coordination and preparation of the synthesized 2a12 dataset. The collective efforts of these individuals have produced a unique and valuable multiplatform dataset that was central to this research project and will be valuable to others for future research on interrelationships among microwave radiative transfer, microwave remote sensing, and precipitation microphysics. The authors also thank the three reviewers of an early manuscript of this paper. Their critical insights, comments, and encouragement significantly improved the published product.

Portions of the contents herein represent material from the first author's Ph.D. dissertation research. Part of his research support was provided by the Air Force Institute of Technology. The additional research support was provided by the National Aeronautics and Space Administration through a research grant awarded to The Florida State University and directed by the second author (Grant NAG5-4752), under the auspices of the Tropical Rainfall Measuring Mission (TRMM) Research Office. The views expressed in this research are those of the authors and do not reflect the official policy or position of the U.S. Air Force, U.S. Department of Defense, or the U.S. government.

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APPENDIX A

Description of E–S Coordinate System

The first requirement in setting up the ES coordinate system is to establish threshold definitions for its two axes. To maximize the spread of ES points, maximum emission channel Tb thresholds at 10.7 and 19.35 GHz are set just below the maximum Tb measured in the AMPR dataset under consideration. The minimum emission channel Tb threshold is set just above the 10.7- and 19.35-GHz Tb brightness temperature distribution peaks; this defines the E index for precipitation-sized hydrometeors. In addition, minimum and maximum scattering-channel (37.0 and 85.5 GHz) Tb thresholds are set close to the minimum and maximum Tb measured in the dataset for those particular channels. There are then three steps in making an emission-index (10.7- and 19.35-GHz Tb) calculation, as follows.

  1. Calculate the initial E index based on the 10.7-GHz warming.

  2. Calculate the E index enhancement multiplier based on the 19.35-GHz warming.

  3. Assume there is 19.35-GHz saturation if Tb10.7 or Tb19 > 275 K.

In addition, there are three steps in making a scattering-index (37.0- and 85.5-GHz Tb) calculation, with step 1 having four conditions:
  1. Calculate the initial S index based on the relative relationship between 19.35- and 37.0-GHz Tb, in which there are the following four possibilities: (i) no scattering (low Tb19/low Tb37), (ii) low-level scattering (low Tb19/Tb37 warms), (iii) moderate scattering (Tb19 warms/Tb37 > Tb37MIN), and (iv) heavy scattering (Tb19 warms/TB37 < Tb37MIN).

  2. Calculate the S index enhancement based on the depression in Tb85.

  3. Assume there is 37.0-GHz depression if Tb19 and Tb37 < 260 K.

Figure A1 provides graphical schematics in the form of emission-index and scattering-index decision trees that summarize the definitions and calculations described above.

APPENDIX B

List of Acronyms, Symbols, and Abbreviations

  • 1b11  Level-1 TMI radiance (brightness temperature) data

  • 1c21  Level-1 PR (uncorrected attenuation) reflectivity data

  • 2a12  TRMM level-2 radiometer rain profile algorithm

  • 2a25  TRMM level-2 radar-only rain profile algorithm

  • 2b31  TRMM level-2 radar–radiometer combined algorithm

  • 2DC  Two-dimensional cloud probe

  • 2DP  Two-dimensional precipitation probe

  • A/C  Aircraft

  • AMPR  Advanced Microwave Precipitation Radiometer

  • ARMAR  Airborne Rain Mapping Radar

  • CMP  Common Microphysics Products

  • CPI  Cloud particle imager

  • CSI  Convective–stratiform index

  • DSD  Drop size distribution

  • E index  Emission index

  • S index  Scattering index

  • ES  Emission–scattering

  • FSSP  Forward-scattering spectrometer probe

  • FOV  Field of view

  • GMU  George Mason University

  • GPM  Global Precipitation Measurement mission

  • GSFC  Goddard Space Flight Center

  • GV radar  Kwajalein ground validation radar

  • HQ  Highest-quality GV-radar data (range <78 km; interpolation quality = 8)

  • HVPS  High-volume particle imager

  • IWC  Ice water content

  • KWAJEX  Kwajalein Atoll (Republic of Marshall Islands) Field Experiment

  • LWC  Liquid water content

  • LWP  Liquid water path

  • M–P  Marshall–Palmer

  • NASA  National Aeronautics and Space Administration

  • NCAR  National Center for Atmospheric Research

  • υicee  Ice effective variance

  • υwate  Water effective variance

  • PIA  Path-integrated attenuation

  • PMW  Passive microwave

  • PR  TRMM precipitation radar

  • QC  Quality-controlled ARMAR–AMPR superpixel matches (∼31 000)

  • ricee  Ice effective radius

  • rwate  Water effective radius

  • Tb  Brightness temperature

  • TMI  TRMM Microwave Imager

  • TRMM  Tropical Rainfall Measuring Mission

  • UND  University of North Dakota

  • UW  University of Washington (e.g., UW Convair-580)

  • ZR  Empirical reflectivity–rain-rate relationship

Fig. 1.
Fig. 1.

Example PR overpasses of Kwajalein ground radar domain during KWAJEX. There was a total of 31 PR overpasses for which some portion of PR FOV intersected the GV-radar domain during the experiment period (26 Jul–14 Sep 1999). Ten examples show representative cases of heavy rain, weak rain, and no-rain events.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 2.
Fig. 2.

(top) The ES diagram depicting E- and S-index values for all 40 140 AMPR-derived wet superpixels from 28 KWAJEX DC-8 flights, with each point characterized by color coding indicating 19.35-GHz saturation and/or 37.1-GHz depression properties. (bottom) ARMAR reflectivity surfaces in matched ES space that have been smoothed by 11 × 11 filter for each of the six layers shown (QC ARMAR–AMPR matchups).

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 3.
Fig. 3.

Three-dimensional charts and histograms depicting (top) relationships among reflectivity–rain-rate surfaces in ES space, (middle) rain-rate surfaces in total-column microphysical parameter space, and (bottom) observed–assumed difference histograms, where (a)–(f) are smoothed using 11 × 11 filter. Individual panels show (a) GV-radar reflectivity (HQ values), (b) GV-radar rain rate (HQ values), (c) 2a12 rain rate (QC values), (d) 2a12 rain rate in assumed total-column LWC–IWC space, (e) 2a12 rain rate in assumed total-column water–ice effective radius space, (f) 2a12 rain rate in observed total-column water–ice effective variance space (note assumed coordinates would be constant at 1/3), and (g)–(i) histograms of observed–assumed total-column microphysical parameter differences.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 4.
Fig. 4.

TMI synthesis regression curves. Regression curves are extrapolated to include full range of AMPR Tb in 40 140–superpixel KWAJEX wet dataset.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 5.
Fig. 5.

TMI synthesis optimization diagrams plotted as correlation coefficient with respect to AMPR–TMI overpass time difference. (bottom right) The 85.5-GHz synthesis requires a slope optimization analysis to identify optimum time difference window.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 6.
Fig. 6.

The 3–4-km-layer ARMAR to PR distribution (top) median and (second from top) mean matchup number (plotted in number × 10−1) sensitivity to observation time difference, and 3–4-km-layer (third from top) PR and (bottom) ARMAR matched distribution histograms.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 7.
Fig. 7.

(top left) The GV-radar convective–stratiform mapping plotted by CSI vs superpixel number, (top right) variation of convective superpixel fraction with changes in CSI as calculated from distribution of GV-radar-derived convective–stratiform–weak echo superpixels shown in top left panel, (bottom left) GV-radar convective–stratiform mapping plotted in ES space, and (bottom right) ES space separation of convective and stratiform superpixels using convective fraction values > 0.5 = convective (or CSI > 0.31 = convective).

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 8.
Fig. 8.

(top left) The 2a12 (solid) and GV-radar (dashed) rain rates at matched HQ GV-radar superpixels are compared [HQ indicates high-resolution range (range < 78 km) and best interpolation quality (interpolation quality = 8)]. (top right) The corresponding scatter diagram of 2a12 and GV-radar rain rates. (bottom) The individual histograms.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 9.
Fig. 9.

Comparisons involving 2a25 rain rates with respect to (top left) GV radar and (bottom left) 2a12. (right) The corresponding scatter diagrams.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 10.
Fig. 10.

(top left) Rain rate and (top right) liquid water content intercomparisons for synthesized 2a25-derived vs Convair-derived values in 2–3-km layer. Convair rain rates and LWCs are recalculated from particle size spectra after conversion of ice artifacts to liquid water spheres. Synthesized 2a25 LWCs are calculated from rain rates assuming M–P distribution. (bottom six) The scatter diagram and histogram comparisons of reflectivity calculated from aircraft particle spectra vs ARMAR, displayed for (left) ARMAR vs Convair in the 2–3-km layer and (right) ARMAR vs Citation in the 6–7-km layer.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 11.
Fig. 11.

(top) The ES diagram of all merged–matched aircraft priority-leg microphysical measurements. (bottom) The ES diagram of only those superpixels in which Convair observations match up with one or both of the other aircraft observations; these points are used to produce total-column microphysical profiles. Lighter shaded symbols indicate points with a 37.1-GHz depression but no saturation at 19.1 GHz. Darker symbols are predominately those points with no 19.1-GHz saturation or 37.1-GHz depression. Squares indicate data from the Convair, circles are from the Citation, and plus signs are from the DC-8.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 12.
Fig. 12.

(left and right) The observed minus assumed column-averaged microphysical parameter differences vs GV-radar minus 2a12 rain-rate differences with respect to liquid and ice. (center) Scatter diagram of 2a12 vs GV-radar rain rate, highlighting 23 points with the greatest rain-rate differences used for outside diagrams. Black lines in the outside diagrams are linear least squares fit lines to indicate a general trend with respect to increasing rain-rate difference.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 13.
Fig. 13.

(top) Three-dimensional depictions of KWAJEX rain-rate surfaces derived from GV radar, synthesized 2a25, and synthesized 2a12. Surfaces are smoothed using an 11 × 11 averaging filter. White enclosed areas in low-emission/low-scattering regions of each surface indicate the approximate area of matched-up aircraft microphysical data (i.e., in ES coordinate space). (bottom) Three-dimensional illustration of how convective fraction specification to (middle) 2a12 algorithm changes (left) original unmodified rain-rate profiles to (right) final modified profiles at high-emission/high-scattering points. Surfaces are smoothed using 11 × 11 averaging filter. Lower color-coded rain-rate scale applies to lower-left panel only. Top color-coded rain-rate scale applies to all three top panels and lower-right panel.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 14.
Fig. 14.

(top left) The observed minus assumed LWC difference vs GV-radar minus 2a12 rain-rate difference at the E and S index > 0.5. (bottom left) The same for E index > 0.5 and S index < 0.5. (right) Assumed (2a12 derived) vs observed (2a25 derived) LWCs at same points and same ES regions as shown on the left.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 15.
Fig. 15.

(top) Composite profile of matched KWAJEX aircraft and 2a12 IWC data with cubic-spline-smoothed average curve fits (black/gray lines). (middle) The same for LWC. (bottom) Composite-averaged altitude vs liquid and ice water content profiles of aircraft- and 2a12-derived LWC and IWC. Profiles are equivalent to those shown in top two panels except for individual data points being removed and abscissa scales being reduced.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Fig. 16.
Fig. 16.

(top) Averaged IWC profiles composited over all superpixel-matched microphysical A/C measurements for four ice habits (graupel, aggregates, needle/columns, and indeterminate ice particles). Note that the needle/column profile lies very close to the altitude axis. (bottom) Similar profiles, except in terms of the fraction of total ice water content.

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

i1558-8432-45-5-754-fa01

Fig. A1. Idealized curves of brightness temperature vs rain rate and decision trees for (top) E index and (bottom) S index calculations. (left) Plot locations of the brightness temperature thresholds (TB10MIN, TB19MIN, TB37MAX, etc.) that are referenced in (right) the decision trees. Curves of idealized brightness temperature vs rain rate are closely related to those from Spencer et al. (1989).

Citation: Journal of Applied Meteorology and Climatology 45, 5; 10.1175/JAM2336.1

Table 1.

Aircraft component of matched–merged microphysics dataset.

Table 1.

1

The three following TRMM special issues published by the American Meteorological Society help to emphasize this point: 1) Journal of Applied Meteorology (2000, Vol. 39, No. 12), 2) Journal of Climate (2000, Vol. 13, No. 24), and 3) Meteorological Monographs (2002, No. 59).

2

The original, processed AMPR component dastaset was produced by Ms. Robbie Hood and Mr. Frank LaFontaine of the NASA Marshall Space Flight Center/University of Alabama Huntsville Global Hydrology and Climate Center, National Space Science and Technology Center in Huntsville, Alabama.

3

The original, processed GV-radar and matched, wet component datasets were produced by Dr. Sandra Yuter of the Department of Atmospheric Sciences, University of Washington, in Seattle, Washington.

4

The original, processed ARMAR component dataset was produced by Drs. Steve Durden and Eastwood Im of the NASA Jet Propulsion Laboratory/California Institute of Technology, in Pasadena, California.

5

The matched, wet and wet/dry ARMAR component datasets were produced by Dr. Joseph Turk of the Naval Research Laboratory, in Monterey, California.

6

The original, processed coincident TMI and PR component datasets were produced by Dr. Song Yang of George Mason University (GMU)/NASA Goddard Space Flight Center (GSFC) in Greenbelt, Maryland.

7

The necessary modifications to the 2a12 algorithm were provided by Dr. Song Yang (GMU/NASA GSFC) and Dr. William Olson of the Joint Center for Earth Systems Technology of University of Maryland, Baltimore County/NASA GSFC in Greenbelt, Maryland.

8

The necessary modifications to the 2a25 algorithm were provided by Dr. Ziad Haddad of NASA Jet Propulsion Laboratory/California Institute of Technology in Pasadena, California.

9

The UW Convair-580 data were collected, compiled, and processed for the KWAJEX CMP dataset by the Cloud and Aerosol Research Group led by Dr. Peter Hobbs at the University of Washington Department of Atmospheric Science. The UND Citation data were collected, compiled, and processed under the direction of Drs. Jeffery Stith [National Center for Atmospheric Research (NCAR)], Julie Haggerty (NCAR), and Anthony Grainger (UND). The NASA DC-8 microphysical data were prepared for distribution by Dr. David Kingsmill of the Desert Research Institute at the University of Nevada in Reno, Nevada.

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  • Fig. 1.

    Example PR overpasses of Kwajalein ground radar domain during KWAJEX. There was a total of 31 PR overpasses for which some portion of PR FOV intersected the GV-radar domain during the experiment period (26 Jul–14 Sep 1999). Ten examples show representative cases of heavy rain, weak rain, and no-rain events.

  • Fig. 2.

    (top) The ES diagram depicting E- and S-index values for all 40 140 AMPR-derived wet superpixels from 28 KWAJEX DC-8 flights, with each point characterized by color coding indicating 19.35-GHz saturation and/or 37.1-GHz depression properties. (bottom) ARMAR reflectivity surfaces in matched ES space that have been smoothed by 11 × 11 filter for each of the six layers shown (QC ARMAR–AMPR matchups).

  • Fig. 3.

    Three-dimensional charts and histograms depicting (top) relationships among reflectivity–rain-rate surfaces in ES space, (middle) rain-rate surfaces in total-column microphysical parameter space, and (bottom) observed–assumed difference histograms, where (a)–(f) are smoothed using 11 × 11 filter. Individual panels show (a) GV-radar reflectivity (HQ values), (b) GV-radar rain rate (HQ values), (c) 2a12 rain rate (QC values), (d) 2a12 rain rate in assumed total-column LWC–IWC space, (e) 2a12 rain rate in assumed total-column water–ice effective radius space, (f) 2a12 rain rate in observed total-column water–ice effective variance space (note assumed coordinates would be constant at 1/3), and (g)–(i) histograms of observed–assumed total-column microphysical parameter differences.

  • Fig. 4.

    TMI synthesis regression curves. Regression curves are extrapolated to include full range of AMPR Tb in 40 140–superpixel KWAJEX wet dataset.

  • Fig. 5.

    TMI synthesis optimization diagrams plotted as correlation coefficient with respect to AMPR–TMI overpass time difference. (bottom right) The 85.5-GHz synthesis requires a slope optimization analysis to identify optimum time difference window.

  • Fig. 6.

    The 3–4-km-layer ARMAR to PR distribution (top) median and (second from top) mean matchup number (plotted in number × 10−1) sensitivity to observation time difference, and 3–4-km-layer (third from top) PR and (bottom) ARMAR matched distribution histograms.

  • Fig. 7.

    (top left) The GV-radar convective–stratiform mapping plotted by CSI vs superpixel number, (top right) variation of convective superpixel fraction with changes in CSI as calculated from distribution of GV-radar-derived convective–stratiform–weak echo superpixels shown in top left panel, (bottom left) GV-radar convective–stratiform mapping plotted in ES space, and (bottom right) ES space separation of convective and stratiform superpixels using convective fraction values > 0.5 = convective (or CSI > 0.31 = convective).

  • Fig. 8.

    (top left) The 2a12 (solid) and GV-radar (dashed) rain rates at matched HQ GV-radar superpixels are compared [HQ indicates high-resolution range (range < 78 km) and best interpolation quality (interpolation quality = 8)]. (top right) The corresponding scatter diagram of 2a12 and GV-radar rain rates. (bottom) The individual histograms.

  • Fig. 9.

    Comparisons involving 2a25 rain rates with respect to (top left) GV radar and (bottom left) 2a12. (right) The corresponding scatter diagrams.

  • Fig. 10.

    (top left) Rain rate and (top right) liquid water content intercomparisons for synthesized 2a25-derived vs Convair-derived values in 2–3-km layer. Convair rain rates and LWCs are recalculated from particle size spectra after conversion of ice artifacts to liquid water spheres. Synthesized 2a25 LWCs are calculated from rain rates assuming M–P distribution. (bottom six) The scatter diagram and histogram comparisons of reflectivity calculated from aircraft particle spectra vs ARMAR, displayed for (left) ARMAR vs Convair in the 2–3-km layer and (right) ARMAR vs Citation in the 6–7-km layer.

  • Fig. 11.

    (top) The ES diagram of all merged–matched aircraft priority-leg microphysical measurements. (bottom) The ES diagram of only those superpixels in which Convair observations match up with one or both of the other aircraft observations; these points are used to produce total-column microphysical profiles. Lighter shaded symbols indicate points with a 37.1-GHz depression but no saturation at 19.1 GHz. Darker symbols are predominately those points with no 19.1-GHz saturation or 37.1-GHz depression. Squares indicate data from the Convair, circles are from the Citation, and plus signs are from the DC-8.

  • Fig. 12.

    (left and right) The observed minus assumed column-averaged microphysical parameter differences vs GV-radar minus 2a12 rain-rate differences with respect to liquid and ice. (center) Scatter diagram of 2a12 vs GV-radar rain rate, highlighting 23 points with the greatest rain-rate differences used for outside diagrams. Black lines in the outside diagrams are linear least squares fit lines to indicate a general trend with respect to increasing rain-rate difference.

  • Fig. 13.

    (top) Three-dimensional depictions of KWAJEX rain-rate surfaces derived from GV radar, synthesized 2a25, and synthesized 2a12. Surfaces are smoothed using an 11 × 11 averaging filter. White enclosed areas in low-emission/low-scattering regions of each surface indicate the approximate area of matched-up aircraft microphysical data (i.e., in ES coordinate space). (bottom) Three-dimensional illustration of how convective fraction specification to (middle) 2a12 algorithm changes (left) original unmodified rain-rate profiles to (right) final modified profiles at high-emission/high-scattering points. Surfaces are smoothed using 11 × 11 averaging filter. Lower color-coded rain-rate scale applies to lower-left panel only. Top color-coded rain-rate scale applies to all three top panels and lower-right panel.

  • Fig. 14.

    (top left) The observed minus assumed LWC difference vs GV-radar minus 2a12 rain-rate difference at the E and S index > 0.5. (bottom left) The same for E index > 0.5 and S index < 0.5. (right) Assumed (2a12 derived) vs observed (2a25 derived) LWCs at same points and same ES regions as shown on the left.

  • Fig. 15.

    (top) Composite profile of matched KWAJEX aircraft and 2a12 IWC data with cubic-spline-smoothed average curve fits (black/gray lines). (middle) The same for LWC. (bottom) Composite-averaged altitude vs liquid and ice water content profiles of aircraft- and 2a12-derived LWC and IWC. Profiles are equivalent to those shown in top two panels except for individual data points being removed and abscissa scales being reduced.

  • Fig. 16.

    (top) Averaged IWC profiles composited over all superpixel-matched microphysical A/C measurements for four ice habits (graupel, aggregates, needle/columns, and indeterminate ice particles). Note that the needle/column profile lies very close to the altitude axis. (bottom) Similar profiles, except in terms of the fraction of total ice water content.

  • Fig. A1. Idealized curves of brightness temperature vs rain rate and decision trees for (top) E index and (bottom) S index calculations. (left) Plot locations of the brightness temperature thresholds (TB10MIN, TB19MIN, TB37MAX, etc.) that are referenced in (right) the decision trees. Curves of idealized brightness temperature vs rain rate are closely related to those from Spencer et al. (1989).

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