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  • View in gallery

    Scatter bidimensional histogram of 37 and 85 GHz for raining pixels in region of 9°–12°S, 60.5°–63.5°W over a 1-yr year (1999) period. Values observed from this particular storm are superimposed in red dots.

  • View in gallery

    The representative hydrometeor profiles including cloud, rain, pristine, snow, graupel, and hail.

  • View in gallery

    (a) TMI observed 37v Tb and (b) 85v Tb over a 3° × 3° scene. The 1° × 1° box enclosed by the dashed line is the focused area for this study.

  • View in gallery

    (a) Simulated 37-GHz and (b) 85-GHz Tb for the 1° × 1° study area at 1950 UTC during the decaying stage.

  • View in gallery

    The four clusters for observation with clustering criteria defined by observation Tb scenes.

  • View in gallery

    Physical property comparisons for using four clusters including (a) PR surface rainfall, (b) 85-GHz polarization information, and (c) Tb relationship between 85- and 37-GHz Tb. In (a) and (b), squares represent the mean values and the bars include the range of 1 standard deviation.

  • View in gallery

    VIRS (a) visible and (b) infrared image at 10.8 μm. The cluster 1 contour is overlaid.

  • View in gallery

    Reflectance ratio of the visible vs near-infrared channel on VIRS as a function of the cluster number with standard deviation imposed.

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    Observed PR reflectivity cross section at 10.3°S overlaid by the cluster number of the pixel that is within 5 km of range of 10.3°S.

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    IWP distribution of each cluster calculated from PR 2A25.

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    Simulation clusters at T47 based on the observation cluster criteria.

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    (a)–(d) Mean profile of each hydrometeor species for each simulation cluster.

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    Cloud (blue), aggregates (yellow), and hail (orange) fields at T47 with contour mixing ratios greater than 0.0, 1.0, and 1.0 g kg−1, respectively.

  • View in gallery

    Simulated PR reflectivity of the mean hydrometeor profiles of each cluster.

  • View in gallery

    Tb comparison of cluster 1 at each frequency between observation and simulation in which (a) surface emissivity for each channel is set to 0.93, (b) water vapor profiles are set to saturation for each pixel, (c) all cloud particles are removed, and (d) surface emissivities are updated for each frequency.

  • View in gallery

    The dTb over Tb(85) relationship comparison between the observation and the simulation for (a) cluster 2 in the control run, (b) cluster 2 in the sensitivity test when all the supercooled water is removed, (c) cluster 3 in the control run, (d) cluster 3 in the sensitivity test when all the supercooled water is removed, (e) cluster 4 in the control run, and (f) cluster 4 in the sensitivity test when the intercept of hail PSD is increased. Squares stand for the observed values, overlaid by its linear regression; grayscale contours stand for the simulated values.

  • View in gallery

    The relationship of dTb over Tb(85) as a function of (a) hydrometeor species, (b) hydrometeor combination, and (c) hail PSD. Squares denote the cases with the same hail IWP.

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    (a) Mie extinction efficiency as a function of x for particles with different refractive indexes. (b) The Tbs of 37, 85, and 37–85 GHz as a function of particle size for rain and hail particles.

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    The dTb over Tb(85) slope comparisons for cluster 4. (a) Control run with hail shape parameter set to 2. (b) Sensitivity run with hail shape parameter set to 5.

  • View in gallery

    (a)–(n) Comparisons of the mean density and number concentration Nt of cluster 4 for each hydrometeor species (note that the scale for Nt is different for each species); (o) comparison of the mean hail Dm of cluster 4; (p) comparison of the hail mean Dm comparison for the simulation with υ = 2, 5, and 10 individually.

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A Clustering Approach to Compare Cloud Model Simulations to Satellite Observations

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  • 1 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
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Abstract

Cloud-resolving models (CRMs) offer an important pathway to interpret satellite observations of microphysical properties of storms. High-frequency microwave brightness temperatures (Tbs) respond to precipitating-sized ice particles and can therefore be compared with simulated Tbs at the same frequencies. By clustering the Tb vectors at these frequencies, the scene can be classified into distinct microphysical regimes (in other words, cloud types). A convective storm over the Amazon observed by the Tropical Rainfall Measuring Mission (TRMM) is simulated using the Regional Atmospheric Modeling System (RAMS) in a semi-ideal setting, and four regimes are defined within the scene using cluster analysis: the “clear sky/thin cirrus” cluster, the “cloudy” cluster, the “stratiform anvil” cluster, and the “convective” cluster. Cluster-by-cluster comparisons between the observations and the simulations disclose biases in the model that are consistent with an overproduction of supercooled water and an excess of large hail particles. While other problems cannot be completely ruled out, the method does provide some guidance to assess microphysical fidelity within each cluster or cloud type. Guided by the apparent model/observational discrepancies in the convective cloud cluster, the hail size parameter was adjusted in order to produce a greater number of smaller hail particles consistent with the observations. While the work cannot define microphysical errors in an unambiguously fashion, the cluster analysis is seen as useful to isolate individual microphysical inconsistencies that can then be addressed within each cluster of cloud type.

Corresponding author address: Fang Wang, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523. E-mail: fwang@atmos.colostate.edu

Abstract

Cloud-resolving models (CRMs) offer an important pathway to interpret satellite observations of microphysical properties of storms. High-frequency microwave brightness temperatures (Tbs) respond to precipitating-sized ice particles and can therefore be compared with simulated Tbs at the same frequencies. By clustering the Tb vectors at these frequencies, the scene can be classified into distinct microphysical regimes (in other words, cloud types). A convective storm over the Amazon observed by the Tropical Rainfall Measuring Mission (TRMM) is simulated using the Regional Atmospheric Modeling System (RAMS) in a semi-ideal setting, and four regimes are defined within the scene using cluster analysis: the “clear sky/thin cirrus” cluster, the “cloudy” cluster, the “stratiform anvil” cluster, and the “convective” cluster. Cluster-by-cluster comparisons between the observations and the simulations disclose biases in the model that are consistent with an overproduction of supercooled water and an excess of large hail particles. While other problems cannot be completely ruled out, the method does provide some guidance to assess microphysical fidelity within each cluster or cloud type. Guided by the apparent model/observational discrepancies in the convective cloud cluster, the hail size parameter was adjusted in order to produce a greater number of smaller hail particles consistent with the observations. While the work cannot define microphysical errors in an unambiguously fashion, the cluster analysis is seen as useful to isolate individual microphysical inconsistencies that can then be addressed within each cluster of cloud type.

Corresponding author address: Fang Wang, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523. E-mail: fwang@atmos.colostate.edu

1. Introduction

Precipitation over land is important in a vast range of applications. Despite its importance, global rain gauge networks remain sparse, while the low penetrating capabilities of operational infrared and visible sensors (Kidder and Vonder Haar 1995) make those measurements reliable only in a statistical sense. Over many parts of the world, passive microwave satellite sensors offer the best hope for quantitative rainfall estimates. Microwave radiation is able to penetrate clouds and interact directly with precipitation-sized hydrometeors. Large ice particles will cause noticeable Tb depressions over land at frequencies greater than 30 GHz. The relationships between ice scattering represented by indicators such as Tb depressions and surface rain rate form the basis for current rainfall retrieval algorithms over land (Spencer et al. 1983; Grody 1991; Ferraro and Marks 1995; Conner and Petty 1998; Grecu and Anagnostou 2001; McCollum and Ferraro 2003). However, these scattering algorithms implicitly accept a relationship between ice aloft and surface rainfall that is known to vary by storm as well as region (Kummerow et al. 1996; Kidd 1998). The variations in location, storm type, and microphysical mechanisms will cause variations in the scattering–rainfall relationship of or even within the storm. These variations therefore need to be accounted for. Cloud-resolving models (CRMs), through their explicit descriptions of cloud microphysical properties, offer a convenient tool to interpret remotely sensed data. In particular, they can offer important additional information when the remotely sensed data contain insufficient information to fully constrain a solution. In this context, CRMs can provide the dynamical connection between ice aloft and precipitation at the surface. A requirement, however, is that the CRM properly represents the ice microphysics of the scene in question.

CRMs employing the nonhydrostatic governing equations may be used to explicitly resolve cloud-scale circulations and an individual cloud element’s microphysical processes at grid spacing of less than a few kilometers. Despite significant advances in cloud physics, many issues still exist in microphysical cloud modeling (Khain et al. 2000), especially in CRM bulk microphysical parameterizations, in which all microphysical processes are described in terms of integral parameters such as mass contents and/or number concentrations of a few types of cloud and precipitation particles. These parameterizations are known to be imperfect and have limitations. In particular, cloud models tend to produce excessive high-density ice particles (Bauer 2001; Biggerstaff et al. 2006; McFarquhar et al. 2006), and the excessive ice in many simulations was found to be problematic even for oceanic rainfall retrievals that relied on CRM simulations as described by Smith et al. (1992), Mugnai et al. (1993), Kummerow et al. (1996), Panegrossi et al. (1998), and Biggerstaff et al. (2006). Kummerow et al. (2006) quantitatively evaluated the retrieval errors associated with the databases built from CRMs in a Bayesian framework. It was stressed that the simulated Tb–rain rate relations are sensitive to the sophistication of the models’ microphysical parameterizations, which could affect the simulated Tb manifold and thus cause sensitivity to the latent heating and hydrometeor profile retrievals (Smith et al. 1992; Panegrossi et al. 1998; Biggerstaff et al. 2006). There is no universally correct cloud microphysical scheme and different cloud types within a storm may possess different dynamical and microphysical properties such that they contain diverse ice and rainfall relationships. Therefore, it is informative and imperative to evaluate the simulated microphysical properties of each cloud type to examine whether the CRM simulation is appropriate for retrieving a given storm. To improve retrieval accuracy over land, the potential biases in the CRM microphysical properties need to be identified and corrected to build more realistic and representative databases of precipitating clouds. Panegrossi et al. (1998) emphasized that similar characteristics between the observation- and simulation-generated databases are desired to provide numerical stability in rainfall retrievals. If suitable, the scattering database built from the simulation is also expected to evolve along with the storm development so that more realistic and reliable microphysical scenes can be reproduced from the observations.

Qualitative discrepancies in storm properties such as location, morphology, intensity, and time evolution are evaluated in some observation and simulation comparison studies (Chaboureau et al. 2002). In this study, it is not expected that CRM simulations match the satellite observations in space and time, especially in a semi-ideal setting wherein these discrepancies may originate from model initialization, boundary conditions, and/or large-scale forcing. Furthermore, satellite sensors can easily detect the location of the storms. The goal of this work is thus not to produce a perfect model simulation, but instead to quantitatively evaluate the microphysical properties of different cloud types to ensure realistic and unbiased microphysics in each cloud regime including the convective core and the stratiform anvil regime. Therefore, in this study, the criteria of defining a good simulation are based not on storm location, morphology, or intensity, but rather on unbiased statistical microphysical properties for each cloud type.

In this paper, cluster analysis of microwave Tbs is used to quantitatively define cloud regimes. A numerical simulation of a convective case over the Amazon is compared with contemporary satellite observations cluster by cluster to quantitatively understand the microphysics discrepancies. This helps clarify the direction of improvement for the cloud model. The satellite observation and CRM simulation of this convective storm are described in section 2. Section 3 describes the cluster analysis while section 4 provides the analysis of individual cloud clusters. Section 5 offers some conclusions.

2. Satellite observation and RAMS simulation of a convective event over LBA region

Based on the low-level wind direction, convection observed during the Tropical Rainfall Measuring Mission–Large-scale Biosphere–Atmosphere experiment in the Amazon (TRMM-LBA) fell into two distinct regimes: a westerly regime wherein convection was weaker, less organized, more widespread, and propagated slowly from the west and an easterly regime wherein more intense, electrified, organized convective systems propagated from the east (Halverson et al. 2002; Rickenbach et al. 2002). A tropical squall line event on 23 February 1999 was observed during the TRMM-LBA field campaign. This convective case belongs to the westerly regime and its convection was only weakly organized as the environmental winds were light (Lang et al. 2007). Widespread convection broke out as a result of daytime heating and gradually formed into lines parallel to the deep tropospheric wind shear. Scattered weak convective cells in the late morning around 1400 UTC [1000 local time (LT)] initiated the convection; the cells became widespread and were loosely organized into southeast–northwest bands by early afternoon around 1700 UTC (1300 LT). The convection was only weakly organized with light environmental winds. A relatively long, thin convective line developed by 2000 UTC but did not persist for long. The convection died out and completely dissipated from the LBA domain by the evening at 0000 UTC 24 February (Lang et al. 2007). The TRMM satellite took a snapshot of this squall line at 2100 UTC during its decaying stage.

Figure 1 shows a scatter bidimensional histogram of 37 and 85 GHz for raining pixels in this region over a 1-yr (1999) period. Values observed from this particular storm are superimposed in red dots. The storm, while not an exact manifestation of mean conditions, can be seen to be generally representative of the convective systems in this region of Amazon.

Fig. 1.
Fig. 1.

Scatter bidimensional histogram of 37 and 85 GHz for raining pixels in region of 9°–12°S, 60.5°–63.5°W over a 1-yr year (1999) period. Values observed from this particular storm are superimposed in red dots.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

a. TRMM observations

The TRMM satellite (Kummerow et al. 1998) was launched in November 1997. It is the first mission dedicated to measure tropical and subtropical rainfall to help better understand rainfall and latent heating distributions. The orbit is inclined at 35° to maximize observations in the tropics. Of primary interest to this study are TRMM’s Microwave Imager (TMI), the precipitation radar (PR), and the visible and infrared scanner (VIRS).

TMI is a descendent of the Special Sensor Microwave Imager (SSM/I) and it measures radiance at a viewing angle of approximately 53° over a swath width of 760 km for nine polarized channels at five frequencies: 10.65, 19.35, 21.3, 37.0, and 85.5 GHz. Hereafter, the channels will be referred to 10v, 10h, 19v, 19h, 21v, 37v, 37h, 85v, and 85h (the letter v represents vertical polarization and the h represents horizontal polarization) to identify the measurement frequency and polarization in a simple fashion. The spatial resolution ranges from 63 km × 37 km at 10.65 GHz to 7 km × 5 km at 85.5 GHz.

PR operates at 13.8 GHz and has a horizontal resolution of approximately 4.3 km, a vertical resolution of 250 m, and a swath width of 217 km. TRMM PR data product 2A25 (Iguchi et al. 2000) is used in this study to provide the retrieved surface rain rate, liquid and ice water paths, and cloud type classification. VIRS senses upwelling radiation over a swath width of 720 km in five spectral regions ranging from visible to infrared with central wavelengths residing at 0.63, 1.60, 3.75, 10.8, and 12 μm. Cloud-top properties and cloud phase can be inferred from the measured Tbs at a horizontal resolution of 2.1 km at nadir.

TMI’s 37 and 85 GHz are sensitive to precipitating-size ice particles due to Mie scattering of snow, graupel, and/or hail. The Tb depressions at these frequencies can therefore be used to detect convection that is producing large ice particles. The two frequencies respond to somewhat different ice particle properties. To demonstrate the physical relationship between microwave Tb depressions and hydrometeors more intuitively, sensitivity experiments are performed using a set of hydrometeor profiles containing large graupel and hail concentration intended to represent deep convection situations over land. The hydrometeor species consist of cloud water, rain, pristine ice, snow, graupel, and hail, as shown in Fig. 2.

Fig. 2.
Fig. 2.

The representative hydrometeor profiles including cloud, rain, pristine, snow, graupel, and hail.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

The same two-stream radiative transfer model as in Kummerow et al. (2001) is used. The difference between this two-stream model and an eight-stream discrete ordinate solution for the realistic and multilayered cloud hydrometeor profiles did not exceed 3 K for the microwave range between 6.6 to 183 GHz (Kummerow 1993). In the calculations, all particles are assumed spherical. The densities for mixed particles are prescribed and held constant: 0.4 kg m−3 for graupel and 0.1 kg m−3 for snow. The Maxwell-Garnett mixing rule (Maxwel1-Garnett 1904) is used to calculate their dielectric constants. Exponential distributions are assumed for precipitating particles in this experiment. To eliminate sensitivity from nonmicrophysical factors, the surface temperature is set to 294.3 K and surface emissivity to 1. The surface is assumed Lambertian. The tests are documented in Table 1 and Tb sensitivities of four frequencies (19, 22, 37, and 85 GHz) to hydrometeors are shown in Table 2. Hereafter in this paper, lower frequencies refer to 19 and 22 GHz and higher frequencies refer to 37 and 85 GHz. Here, 10 GHz is not used because it depends heavily on the surface. The Tbs calculated from hydrometeors shown in Fig. 2 serve as the control run, and six sensitivity experiments and results are described below. In test 1, high-density graupel particles are converted to low-density snow particles. All frequencies experience a Tb increase with higher frequencies gaining larger increases. In test 2, all hail is converted to snow. Results are the same as in test 1 except with larger magnitude. The particle density is a critical parameter that determines the heterogeneous particle’s dielectric properties. The density of hail is larger than that of graupel, which is larger than that of snow. Larger density ice particles have larger scattering efficiencies. Higher frequencies correspond to larger size parameters, which further raises the efficiency. As a consequence, higher-density particles produce stronger scattering signal at higher frequencies. Meirold-Mautner et al. (2007) explored the impact of snow density on simulated microwave Tbs and provided similar results. This will be examined in more detail in section 4c. In test 3, the supercooled water content is increased. Lower frequencies experience some decrease in Tbs due to lower emission temperature at elevated weighting function peaks, while higher-frequency Tbs experience increases for this convective profile. The effect of supercooled cloud water at reducing the minima in Tb at high frequencies had been identified by Adler et al. (1991) and was found to be associated with lowering of the single scattering albedo when liquid is mixed with ice particles. Biggerstaff et al. (2006) also reported an average warming of 15 K in Tb at 85 GHz over the convective region in one of their simulations. However, for nonconvective profiles, cooling at higher frequencies may take place due to the lower emission temperature from the cold cloud together with the absence of the scattering by ice particles. In test 4, hail particles are broken into much smaller sizes keeping the same ice water content. All frequencies undergo some increase due to decreased scattering. However, the increase for 37 GHz is larger than for 85 GHz, again due to relative changes in the size parameters. The decrease in the particle size causes larger reduction in the volume scattering extinction at 37 GHz, which will also be further explored in section 4c. In test 5, the hail concentration is doubled. All frequencies have some degree of Tb decrease due to increased ice scattering. Higher frequencies experience more scattering. However, in test 6, when the hail content is doubled again, 85-GHz Tb experience a smaller decrease than those at 37 GHz. This is consistent with the findings of Kodama et al. (2007), who stated that in the presence of intense amounts of hail particles, 85 GHz tends to saturate and thus allows 37 GHz to exhibit a stronger sensitivity and serve as a better proxy for ice scattering in this situation. The 85-GHz Tb is more sensitive to relatively small precipitation-size ice particles in the upper part of clouds, while 37-GHz Tb is more sensitive to supercooled or large frozen hydrometeors, such as large graupel, and large aggregated snowflakes right above the melting layer (Cecil and Zipser 2002; Kodama et al. 2007). Both 37 and 85 GHz are adopted to detect and classify ice microphysics fields in this convective storm.

Table 1.

Documentation of the control simulation and six sensitivity tests.

Table 1.
Table 2.

Simulated dTbs at 19 to 85 GHz for the sensitivity tests.

Table 2.

TRMM passed over the LBA convective scene at 2100 UTC. Figure 3 shows the observed TMI Tbs at 37v and 85v. The enclosed box, measuring approximately 100 km × 100 km, is the focus of this study. The convective core shows up as Tb depression centers in both frequencies. The 85-GHz Tb depression is much deeper than the 37 GHz, which is consistent with results in Table 2.

Fig. 3.
Fig. 3.

(a) TMI observed 37v Tb and (b) 85v Tb over a 3° × 3° scene. The 1° × 1° box enclosed by the dashed line is the focused area for this study.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

b. Regional Atmospheric Modeling System simulation

1) RAMS

The Regional Atmospheric Modeling System (RAMS) model (Cotton et al. 2003) is a CRM developed at Colorado State University (CSU) by merging a nonhydrostatic cloud model (Tripoli and Cotton 1982) and two hydrostatic-mesoscale models (Tremback et al. 1985; Mahrer and Pielke 1977). RAMS is built upon a full set of compressible atmospheric dynamic and thermodynamic equations using an Arakawa C grid and σz terrain-following coordinate system with variable vertical grid spacing to increase resolution near ground and in the boundary layer. The “time-split” time differencing schemes are adopted to damp the propagation of the fast wave modes and several parameterizations are implemented to describe different physical processes.

2) RAMS microphysics parameterization

The bulk microphysical schemes in RAMS (Walko et al. 1995; Meyers et al. 1997) define seven hydrometeor categories including cloud water, rain, pristine ice crystals, snow, aggregates, graupel, and hail. Within a grid, the hydrometeor size distributions are represented using a generalized gamma distribution function for each class:
e1
where the number density n is a function of the diameter D. Here, Nt is the total number concentration, Γ is the gamma function, υ is the shape parameter of the gamma distribution, and Dn is the characteristic diameter. The mass m of a particle with diameter D is expressed in the power-law formula
e2
where and are coefficients that are constant for each species. Using the integral property of gamma distribution, the mean mass diameter can be calculated by
e3
Hydrometeor density is given by
e4
For cloud, rain, graupel, and hail that are assumed spherical in the model, ; therefore, their densities are held constant at 1000, 1000, 300, and 900 kg m−3, respectively. For pristine ice, snow, and aggregates, their densities vary with diameter. The mass mixing ratio of the hydrometeor category is given by
e5
Options of the parameterization include a one-moment scheme in which either r or Nt is prognosed and Dn is diagnosed from Eq. (5), and a two-moment scheme in which both r and Nt are prognosed given a prescribed υ of the distribution. The two-moment scheme is adopted in this simulation.

3) Simulation of the storm

A semi-ideal simulation starting at 1200 UTC 23 February was run for 12 h at 1-km horizontal resolution using RAMS to reproduce the characteristics of the LBA storm shown in Fig. 3. Vertical coordinate includes 40 levels with 37-m resolution near the surface so that the boundary processes can be well captured. The vertical extent is increased by a factor of 1.14 in each successive layer above the surface to a maximum depth of 1028 m and the model top extends to approximately 23 km. The model is initialized with Rebio Jaru station’s 1200 UTC sounding with topography provided by the global U.S. Geological Survey (USGS) surface data (approximately 1-km resolution). Adopted parameterizations include Klemp–Wilhelmson lateral boundary conditions with 20 m s−1 phase speed and the Harrington radiation scheme for both shortwave and longwave radiation. The two-moment microphysics scheme is adopted and the shape parameter υ of the size distribution for each hydrometeor is preassigned (3, 2, 2, 2, 2, and 2 for cloud, pristine ice, snow, aggregates, graupel, and hail, respectively). The surface fluxes are nudged as surface forcing to help stimulate convection along thermodynamically unstable regions. Latent and sensible heat fluxes measurements collected at Abracos Hill and Ji Parana (Lang et al. 2007) are used to construct the flux time series expressed by cosine functions whose amplitudes and periods are determined from the observation data. The simulation of the storm is divided into two areas and the inner and outer areas are forced with both latent and sensible heat fluxes time series whose functions have different magnitudes but equal 11-h periods. The Rebio Jaru sounding and details of the surface forcing used in this study can be found in Lang et al. (2007). Convection first kicks off at the boundary between these two areas where the forcing gradient is the largest and therefore the most unstable.

The first five hours of the simulation are considered model spinup time when clouds start to form. At around 1730 UTC, the domain averaged surface rainfall is found to increase sharply during the next 1.5 h and reach its peak at 1910 UTC. Rainfall starts to decrease afterward as the storm decays. Simulation results are output every 10 min. Time step 47 (hereafter referred to as T47), for instance, corresponds to 1950 UTC when the storm is experiencing the early stage of the decaying process. Model outputs include thermodynamic properties and hydrometeor profiles, from which the optical properties including extinction coefficients, scattering coefficients, and asymmetry parameters can be calculated to serve as inputs to simulate the Tbs at TMI frequencies. The same two-stream radiative transfer model (Kummerow 1993) with Eddington approximation described in section 2a and an independent pixel plane-parallel assumption is used in this work as the observational operator. Compared to the uncertainties from the microphysical profiles generated by the CRM, this model is accurate enough for the current purpose although it provides only an approximate 3D effect and no polarization information of nonspherical particles (Kummerow 1993). Surface emissivity is initially fixed at 0.93 for all channels in the calculation. This value is based on the 2006 annual mean surface emissivity retrieved from Advanced Microwave Scanning Radiometer for EOS (AMSR-E) that carries similar frequencies as TMI (Bytheway and Kummerow 2010). The size distributions [Eq. (1)] and hydrometeor densities [Eq. (4)] for RAMS are used in the Tb simulations. The Tbs are then averaged from the model resolution to TMI resolutions using a 2D Gaussian filter with the full width at half maximum (FWHM) set to each frequency’s respective footprints (Kummerow et al. 1998). Cyclic boundary conditions are applied in the averaging.

The simulated Tb scenes for 37 and 85 GHz at TMI resolutions are displayed in Fig. 4. When compared with the observed scenes presented in Fig. 3, the discrepancies are obvious. The simulated convective core is dislocated from the observed one by about half a degree (50 km) in the southeast direction, and there also exists a separate weaker core to the northwest of the main core. Besides the differences in location and morphology, the convection generated in the simulation is also more intense than the observation with Tb at 85 GHz around 100 K versus the observed value of 180 K. This indicates that either the model is overproducing large ice particles or T47 is early in the decaying process with the convection still too strong when compared to the observation snapshot.

Fig. 4.
Fig. 4.

(a) Simulated 37-GHz and (b) 85-GHz Tb for the 1° × 1° study area at 1950 UTC during the decaying stage.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

3. Cluster analysis

Different cloud regimes within the same storm system bear different microphysical properties. For example, the convective core contains hail and graupel particles produced in the strong updraft, while stratiform anvil clouds are mostly composed of low-density particles including pristine ice, snow, and aggregates. It is crucial for cloud models to produce correct microphysical properties for each cloud type so that realistic scattering/rainfall relations are established by the simulations for improved rainfall retrievals over land. To define cloud regimes in the scenes, k-means cluster analysis is employed to group pixels or grids with coherent physical properties.

a. Description of analysis

Cluster analysis is a classification method that groups data with similar properties together into self-similar categories. First of all, centroids are chosen and the Euclidean distance from each data point to each centroid is computed. The data point is then assigned to the closest centroid. The center of each resulting cluster is recalculated and the distances are computed again to the new centroid and the clusters are redefined. The iterative process continues until the clusters are stable. The clustering analysis follows the work of Boccippio et al. (2005) and Finn (2006). The specific clustering technique used in this study is the k-means technique described by Anderberg (1973). Using cluster analysis, the storm scene can be classified into several cloud types, in which each cluster is expected to possess diverse microphysics properties.

Because of high surface emissivity over land, precipitation is generally retrieved through the scattering signals from large precipitating ice particles in the passive microwave methods. Targeted at improving land precipitation, the criteria for clustering in this study are based on ice microphysics. The Tbs at high microwave frequencies are good proxies of ice microphysics, as was examined in the previous sensitivity experiments. For each pixel, the Tb vector consisting of 37v, 37h, 85v, and 85h was clustered into self-similar vectors. Because the range of Tb at 85 GHz is significantly larger than at 37 GHz, scaling to both observations and model Tb is applied first, as follows:
e6
where max(Tb) and min(Tb) refer to the observed Tbs.

Two clusters correspond to convective and nonconvective pixels, which is too coarse. Three clusters separate well in Tb space but clusters have a category of light to moderate rain that is difficult to assign physical meaning to. Compared to four clusters, five clusters add in an intermediate cluster with very small surface rain rate. This makes this cluster less interesting to this work whose focus is more on the microphysics of raining scenes. Six clusters start to overlap the classes. Therefore, four clusters were chosen as a compromise between mathematical similarity and physical interpretation.

b. The observed clusters

Figure 5 displays the four clusters of the observation. Observed TMI Tbs, PR retrieved rainfall/water paths, and VIRS retrieved cloud properties can be used to infer physical properties of the underlying clouds within TMI 85-GHz footprints (Rapp et al. 2005). The PR surface rain rate, 85-GHz polarization, and 37- and 85-GHz Tb relationship are examined together, as shown in Fig. 6.

Fig. 5.
Fig. 5.

The four clusters for observation with clustering criteria defined by observation Tb scenes.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Fig. 6.
Fig. 6.

Physical property comparisons for using four clusters including (a) PR surface rainfall, (b) 85-GHz polarization information, and (c) Tb relationship between 85- and 37-GHz Tb. In (a) and (b), squares represent the mean values and the bars include the range of 1 standard deviation.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Figure 7 shows the VIRS visible and infrared image of this storm with the contour of cluster 1 overlaid. The visible image shows that cluster 1 compares well to the darker region of the visible image that is associated with the relatively lower reflectance (mean value for this cluster is 0.53). Cluster 1, therefore, can be associated with either clear sky or thin cirrus. The existence of thin cirrus is further confirmed by the silk-like morphology in the visible image and also the low cloud-top temperature inferred from the infrared image. Together with the fact that this cluster includes little rain as shown in Fig. 6, cluster 1 is called the “clear sky/thin cirrus” cluster.

Fig. 7.
Fig. 7.

VIRS (a) visible and (b) infrared image at 10.8 μm. The cluster 1 contour is overlaid.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

It is clear from the infrared image that the whole area of interest is mostly covered with clouds. The reflectance ratio of 0.6 μm/1.6 μm has been used in the Moderate Resolution Imaging Spectroradiometer (MODIS) cloud mask algorithms to identify the cloud phase (King et al. 1996). The absorption efficiency for both water and ice is small but similar around 0.6 μm, while the absorption for ice is larger than that for water at around 1.6 μm (Warren 1984; Hale and Querry 1973) such that the reflectance at 1.6 μm is smaller for ice than for water. The ratio is thus larger for ice than for water. For each TMI pixel that is assigned a cluster number, reflectance ratios are calculated for all the VIRS pixels included within the TMI footprint. Figure 8 shows the mean and standard deviation of the reflectance ratio for each cluster. While the standard deviation is seen to be fairly large within each cluster, this is expected as only the microwave Tbs that respond to large hydrometeors are used in the clustering algorithm. The reflectance ratio, which is a measure of the ice-to-liquid ratio at the top of the cloud, increases with each cluster, suggesting that the higher cluster values contain more ice than liquid at cloud top. Cluster 2, therefore, contains a higher percentage of water phase at the cloud top compared to clusters 3 and 4. Together with the cirrus cover as shown in the infrared image of Fig. 7, cluster 2 is most likely associated with multilayer clouds with lower level water clouds covered by cirrus. Figure 6 shows that this cluster produces small rain rates and this cluster is termed the “cloudy” regime.

Fig. 8.
Fig. 8.

Reflectance ratio of the visible vs near-infrared channel on VIRS as a function of the cluster number with standard deviation imposed.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Figure 6 shows that cluster 3 contains intermediate rain rates and has the strongest 85-GHz polarization signal, defined as Tb(85v) − Tb(85h). The mean polarization in this cluster approaches 4 K, as seen in this figure. Large polarization signals such as these are caused by horizontally oriented ice particles such as snow and aggregates that exist in stratiform regions of the storm (Heymsfield and Fulton 1994; Anagnostou and Kummerow 1997; Prabhakara et al. 2001). The spatial location of cluster 3, surrounding the deep scattering denoted by cluster 4, provides evidence that cluster 3 corresponds to the storm’s stratiform anvil region. Figure 9 shows the cross section of the radar reflectivity at 10.3°S overlaid by the cluster number of the pixel that is within 5 km of 10.3°S. The selected latitude passes through all four clusters. It is clear that the stratiform anvil lies adjacent to the convective core that corresponds to the high reflectivity region. Cluster 3 is defined as the “stratiform anvil” cluster.

Fig. 9.
Fig. 9.

Observed PR reflectivity cross section at 10.3°S overlaid by the cluster number of the pixel that is within 5 km of range of 10.3°S.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Figure 6 shows that cluster 4 is associated with larger rainfall and more intense Tb depressions that are produced by strong scattering of large precipitating particles representative of the convective core. Resemblance of cluster 4 to the Tb depression areas in Fig. 3 together with the higher reflectivity in Fig. 9 further verify the convective properties of this cluster. Cluster 4, therefore, is defined as the “convective” cluster.

Ice water path (IWP) and liquid water path (LWP) can be calculated from PR 2A25 products using the linearly interpolated precipitation water parameter coefficients from the five nodes (Iguchi et al. 2000). The mean IWP for each cluster is 0.01, 0.07, 0.19, and 0.72 kg m−2, and the mean LWP for each cluster is 0.02, 0.12, 0.59, and 0.76 kg m−2. The distribution of IWP for each cluster is shown in Fig. 10. These values are consistent with the properties of the defined cloud types.

Fig. 10.
Fig. 10.

IWP distribution of each cluster calculated from PR 2A25.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

4. Analysis and discussion

a. Assigning simulation pixels to clusters

The simulation produces significantly different Tbs from the observations as evidenced by a comparison of Figs. 3 and 4. Here, each simulation pixel is assigned to a corresponding observation cluster based on the pixel’s closeness to the clusters’ centroid Tb vectors to ensure that the two sets of clusters are based on the same criteria. For example, Fig. 11 shows the simulation clusters for T47. The convective cluster is consistent with the Tb depressions in Fig. 4 and the stratiform portion of the simulated storm also lies adjacent to the convective core as in Fig. 5. The Tb values of the centroids corresponding to each of the four clusters are given in Table 3 for reference.

Fig. 11.
Fig. 11.

Simulation clusters at T47 based on the observation cluster criteria.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Table 3.

The Tb of the centroids corresponding to each of the four clusters.

Table 3.

b. Analysis by cluster

The CRM simulation for this convective cloud is semi-ideal and it has the “cold start” procedure for model spinup before meaningful cloud and precipitation are predicted. However, the microphysical properties of a specific cloud type should be consistent regardless of the developing stages of the storm. Thus, T35, T47, and T59 at 2-h intervals that cover the cumulus, mature, and decaying stages of the storm ensemble are combined together for analysis instead of deciding upon the closest (e.g., Wiedner et al. 2004) or the most appropriate (e.g., Lang et al. 2007) time step in the simulation for the comparisons.

Figure 12 shows the mean microphysical profiles for each simulation cluster. The profiles are averaged to TMI’s 85-GHz resolution applying the same Gaussian filter that is used in calculating the Tbs. Cluster 1 includes mostly clouds, as shown in Fig. 12a, which is caused by the overproduction of clouds in the model. Figure 13 shows the overwhelming cloud fields at the mature stage (T47) of the storm. This is most likely caused by the sounding used for the initialization, which is saturated around 600 mb. The production of snow and graupel is small in this simulation. The absence of graupel particles is due to the adopted binned riming scheme (Saleeby and Cotton 2008) in which the arbitrary wetting condition moves the rimed wetting particles to hail instead of graupel. For clusters 2 to 4, pristine ice, aggregates, and rain amounts increase with the cluster number. Hail becomes abundant in cluster 4, which can also be seen from the hail mixing ratio contour in Fig. 13. The distribution of hail is consistent with the convective cluster in Fig. 11. Figure 14 is the simulated PR reflectivity for the mean hydrometeor profiles in Fig. 12 of each cluster. Compared with Fig. 9, the simulated reflectivity profile has comparable magnitude but extends significantly higher. Given that the model reflectivities correspond to the mean reflectivity profiles of the cluster while the observations correspond to a single time realization, there are of course differences.

Fig. 12.
Fig. 12.

(a)–(d) Mean profile of each hydrometeor species for each simulation cluster.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Fig. 13.
Fig. 13.

Cloud (blue), aggregates (yellow), and hail (orange) fields at T47 with contour mixing ratios greater than 0.0, 1.0, and 1.0 g kg−1, respectively.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Fig. 14.
Fig. 14.

Simulated PR reflectivity of the mean hydrometeor profiles of each cluster.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

1) Tb comparisons for cluster 1

Figure 15a shows the comparison of the observed and simulated Tbs for cluster 1 when the surface emissivity is fixed at 0.93 for each frequency. Values shown correspond to the mean value and standard deviation for both observed and modeled brightness temperatures. The comparison shows that the simulated Tb ranges at all channels are lower than the observed ones, and the discrepancies reach 5 K in some frequencies. Lower Tbs may be caused by too little emission, too much extinction, or an insufficient signal from the surface. To test the sensitivity of the Tb discrepancies to potential errors in the column water vapor, all the water vapor profiles in this cluster are tuned to saturation. Figure 15b shows that Tbs increase slightly, but the impact on reducing the discrepancies is negligible. The sensitivity to excessive extinction is examined by removing all the cloud particles. Figure 15c shows that the removal of cloud produces a negligible impact for the lower frequencies, while having an excessive impact over higher frequencies. Another potential bias source for the Tb simulation of this cluster is the presumed surface emissivities ε. The observed Tbs can be used to find the correct ε to be used in the model because thin cirrus is present in the observation cluster but it is basically invisible to the microwave frequencies. As such, the observations mostly reflect the surface properties. An average ε was obtained for each frequency from this cloud free cluster. The method follows Bytheway and Kummerow (2010). The calculated emissivities of 10, 19, 21, 37, and 85 GHz, are 0.943, 0.956, 0.945, 0.927, and 0.935, respectively. Given that the values of 0.93 corresponds to a global mean value as described in Bytheway and Kummerow (2010), small departures in the emissivity (−0.003 to 0.026) are not unexpected for the specific region considered here. Figure 15d shows the improved agreement between the observation and simulation. The new emissivities are employed for the rest of clusters.

Fig. 15.
Fig. 15.

Tb comparison of cluster 1 at each frequency between observation and simulation in which (a) surface emissivity for each channel is set to 0.93, (b) water vapor profiles are set to saturation for each pixel, (c) all cloud particles are removed, and (d) surface emissivities are updated for each frequency.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

2) Tb comparisons for cluster 2

The gray shades shown in Fig. 16, while representing the frequency of occurrence of Tb combinations in the model, must be interpreted carefully. In particular, heavy shades represent generally clear scenes or scenes with little cloud water. The colder Tb values generally represent more hydrometeors and thus are more sensitive to the adjustments made in the model. With different weighting functions, Tbs at 37 GHz [shortened as Tb(37) hereafter] and at 85 GHz [Tb(85) hereafter] exhibit different degrees of sensitivity to the microphysical properties, as manifested in Table 2. Figure 16a shows the Tb difference between 37v and 85v (shortened as dTb hereafter) as a function of Tb(85) between the observed scene and the simulated storms for cluster 2. A linear regression corresponding to the observed relationship (open squares) is plotted to highlight the differences with the simulated values (in grayscale). For this cluster, the simulation at Tb(85) is somewhat colder than the observation. It also produces smaller dTbs at the same Tb(85).

Fig. 16.
Fig. 16.

The dTb over Tb(85) relationship comparison between the observation and the simulation for (a) cluster 2 in the control run, (b) cluster 2 in the sensitivity test when all the supercooled water is removed, (c) cluster 3 in the control run, (d) cluster 3 in the sensitivity test when all the supercooled water is removed, (e) cluster 4 in the control run, and (f) cluster 4 in the sensitivity test when the intercept of hail PSD is increased. Squares stand for the observed values, overlaid by its linear regression; grayscale contours stand for the simulated values.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

To obtain a better match between the observation and the simulation, static adjustments of the simulated microphysics are performed. The mean freezing level in the simulation is approximately 4.63 km, and Fig. 12b indicates the existence of large amounts of supercooled water in this cluster that is related to the initialization sounding. When the supercooled water is completely removed, the Tb(85) range increases and the dTb also increases at the same Tb(85) as shown in Fig. 16b. After the adjustment, the observation pixels are mostly included within the simulation for cluster 2. In this nonconvective scene, the supercooled water can depress Tbs by elevating the weighting functions to lower temperatures. This liquid also decreases the dTbs. Therefore, the removal of the supercooled water brings the dTbs over Tb(85) relationship closer to that of the observation for this cluster. The physical reason will be further explored in section 4c.

The discrepancy in this cluster is shared by Varble et al. (2011), who found the overestimation of stratiform area in cloud-resolving models because of a preponderance of very low rain rates. A simulation with reduced humidity was performed to assess if the amount of supercooled water could be attributed to excessive moisture at midlevels. For this experiment, the relative humidity in the initialization profile from 400 to 750 mb was adjusted to 50% and then 20%. With these adjustments, the supercooled water above the freezing level was reduced significantly but at the expense of convection. The model was unable to generate any deep convection with this sounding, indicating that the solution here is more complex than simply reducing the humidity at midlevels.

3) Tb comparisons for cluster 3

Figure 12c shows that cluster 3 is dominated by clouds, pristine ice, and aggregates. The existence of these cloud species is consistent with not only the cluster’s name of stratiform, but with the PR’s identification of stratiform precipitation in this region of the storm. The simulated cluster produces higher Tb(85) range and smaller dTb at the same Tb(85), shown in Fig. 16c. As in cluster 2, removing all the supercooled water increases the dTb and seems to fix the discrepancies quite well as shown in Fig. 16d. Besides removing all the supercooled water, the match can be improved further by increasing the aggregates amounts while increasing the PSD’s intercept to produce more but smaller aggregate particles.

4) Tb comparisons for cluster 4

Figure 12d shows that all hydrometeor species are further increased in cluster 4, especially the hail particles that are generally associated with strong convections. Figure 16e shows that the simulated dTbs are lower than those in the observations and the underestimation is especially obvious in the low Tb(85) regime, which is depressed by the large precipitating-sized ice particles (hail in this case). A few pixels in this cluster contain higher Tb(85)s that extend into the lower cluster regimes. These outliers are found to be associated with relatively larger LWPs and lower Tb(37). These lower Tb(37)s will cause the pixels to be assigned to a higher cluster number even with relatively warmer Tb(85)s. To facilitate our understanding, simplifications are made in this section including that the particle densities for all species are held constant and υ, the shape parameter defined in Eq. (1), is assumed to be 1 for the size distribution of the precipitating particles. Figure 16f shows that when the intercept of the hail PSD is increased, the simulated slope gets closer to that of the observation although there is still lack of agreement. A larger intercept with the same hail IWP produces more but smaller hail particles. This modification produces warmer Tb(85) and larger dTb, as was demonstrated from test 4 in Table 2.

c. General relationships

The sensitivity of Tb to changes in hydrometeor concentrations and properties are shown in Fig. 17. These tests use the basic hydrometeor profiles shown in Fig. 2, but scale each liquid and ice water content from 0.01 to 10 times the value shown in Fig. 2 in order to get a broad range of hydrometeor contents used to create Fig. 17. In Fig. 17a, only hydrometeors of the indicated species are considered while the other hydrometeors are set to zero. The “rain” line, for instance, represents the general shape of the rain profile shown in Fig. 2, but scaled such as the left end of the curve represents very high rainwater contents. Figure 17b does the same but shows differences when only hail is retained compared to when both hail and rainwater contents are retained. Figure 17c considers only the hail profile with the three lines representing three different intercept parameters and thus three different hail size distributions. Figure 17a shows that liquid species (cloud and rain) alone cannot produce very low Tb(85) or very large dTb. Maximum values for dTb appear to be below 10 K. Ice species can produce much lower Tb(85) and much larger dTb. Hail can produce larger dTb than graupel or aggregates. When rain is added to hail, as shown in Fig. 17b, dTb is lowered for all brightness temperatures. This is due to the rain’s large absorption cross section that overwhelms the scattering properties of the hail. Figure 17c shows the impact of changing the intercept parameter on the dTb versus Tb(85) fit. It is revealed that hail particle size distribution (PSD) with larger can produce larger dTb at the same Tb(85).

Fig. 17.
Fig. 17.

The relationship of dTb over Tb(85) as a function of (a) hydrometeor species, (b) hydrometeor combination, and (c) hail PSD. Squares denote the cases with the same hail IWP.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Mie theory is applied here to understand the above results. The size parameter x is defined as , where r is the particle radius and λ is the wavelength. As the λ of 85 GHz is approximately 2.3 times smaller than that of 37 GHz, the x of 85 GHz is roughly 2.3 times larger than that of 37 GHz for a particle with the same size.

Figure 18a shows the Mie extinction efficiency Qext as a function of x for three particles with different dielectric properties. Their refractive indexes are 1.77 + 1.0i, 1.77 + 0.0001i, and 1.33 + 0.0001i, which roughly represent properties of rain, hail, and graupel, respectively. The real part of a refractive index represents the scattering characteristics while the imaginary part represents the absorption characteristics of the particle. For all three cases, the difference in Qext between 37 and 85 GHz increases until x for 85 GHz reaches the Qext peak, after which the difference decreases. For rain, the peak x is approximately 2, which is equivalent to a radius of 1.1 mm at 85 GHz. Therefore, liquid drops cannot produce very large dTb since larger drops reduce the dTb value. Furthermore, adding liquid to ice will weaken the ability to produce large dTb at the same 85 GHz. Liquid particles have large imaginary refractive indices, so that they are both efficient absorbers and emitters. Therefore, liquid drops cannot produce very low Tb(85) values. Aggregates, graupel, and hail particles are all regarded as an ice matrix with air inclusions in the calculation of their dielectric constants (Maxwell-Garnett 1904). The density of hail is larger than that of graupel, which is larger than the density of aggregates. These densities will determine the fraction of air inclusion and thus the refractive index of the mixture. As hail has a larger real part in the refractive index than graupel, its slope before the Qext peak is steeper, as shown in Fig. 18a, and therefore the dQext difference is larger. This produces a larger dTb. The decrease of dTb after the peak of the curves in Fig. 17 is caused by the decrease of 85-GHz Qext after its peak in Fig. 18a. This explains the phenomenon that in the extremely intense convective storms, Tb(85) saturates while Tb(37) has a larger sensitivity on the storm intensity (Kodama et al. 2007).

Fig. 18.
Fig. 18.

(a) Mie extinction efficiency as a function of x for particles with different refractive indexes. (b) The Tbs of 37, 85, and 37–85 GHz as a function of particle size for rain and hail particles.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Figure 18b shows the Tbs of 37, 85, and 37–85 GHz as a function of particle size for rain and hail particles by assuming monodispersed distributions. With increasing particle size, Tb at 85 GHz decreases faster than Tb at 37 GHz because of a larger size parameter. Therefore, the dTb increases until Qext hits its peak at 85 GHz. Taking the hail particle as an example, dTb reaches maximum at 1 mm that corresponds to x = 2 at 85 GHz. Rain particles do not produce very low Tb and very large dTb. These are consistent with Fig. 18a.

With an exponential PSD, while the mass is conserved, there will be more but smaller hail particles when the intercept gets larger. Squares in Fig. 17c correspond to the cases that share the same hail IWP at different PSD. By increasing the PSD intercept, more but smaller hail particles produce larger dTb at the same Tb(85). The dTb over Tb(85) relationship depends on the microphysical properties within the cluster and can therefore help identify errors in the model microphysical representations.

d. Dynamic adjustments

The adjustments in section 4b demonstrate that static modification of the simulated microphysics can produce improved agreement with the observation. However, these static adjustments ignore the pertinent microphysical processes. Changing the hail PSD intercept will change not only the hail sizes, but also the mean terminal fall velocity that modulates the collection and coalescence process and the evaporation and melting processes that impact the strength of the downdraft and the intensity of the cold pool (van Den Heever and Cotton 2004). To this end, a dynamic adjustment provides a more consistent and physical picture. Taking cluster 4 as the example, the goal of this section is to perform a dynamic adjustment that leads to more abundant but smaller hail particles compared with the control run.

Keeping all the settings identical to the control run, a sensitivity experiment is carried out by increasing the hail PSD υ from 2 to 5. This experiment is named HAILGNU5. The PSD and particle densities follow the same ones as in RAMS for the Tb simulation in this section. Comparison of Figs. 19a and 19b shows that the dTb over Tb(85) relationship in HAILGNU5 gets significantly closer to that of the observation than in the control run. It is noteworthy again that compared with the improvement in Fig. 16f, this adjustment in HAILGNU5 is physically and microphysically consistent. Figure 20 shows the comparisons of the mean density and number concentration Nt of cluster 4 for each species and also the comparison of the mean Dm for hail. Figures 20n and 20o reveal that HAILGNU5 is capable of generating more abundant (larger Nt) but smaller (smaller Dm) hail particles.

Fig. 19.
Fig. 19.

The dTb over Tb(85) slope comparisons for cluster 4. (a) Control run with hail shape parameter set to 2. (b) Sensitivity run with hail shape parameter set to 5.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Fig. 20.
Fig. 20.

(a)–(n) Comparisons of the mean density and number concentration Nt of cluster 4 for each hydrometeor species (note that the scale for Nt is different for each species); (o) comparison of the mean hail Dm of cluster 4; (p) comparison of the hail mean Dm comparison for the simulation with υ = 2, 5, and 10 individually.

Citation: Journal of Climate 25, 22; 10.1175/JCLI-D-11-00472.1

Figure 20 illustrates the model behavior. With a fixed Dm, the distribution gets narrower when ν is increased [refer to Fig. 1 in Walko et al. (1995)] and Dn decreases in value. In RAMS, smaller Dn values result in reduced bulk collection rates for hail owing to the reduced terminal velocity associated with smaller Dn; the riming efficiency of hail in the binned riming scheme is dependent on particle sizes and therefore is also impacted (Loftus 2012). These changes, on the other hand, will augment the vapor deposition on pristine ice to form snow, and also the aggregation process. This appears to cause the mean density and Nt for pristine ice, snow, and aggregates to all increase as seen in Fig. 20. The melting of these ice particles produces more rain drops and the increased rain droplets in turn collect more low-density ice particles if these rain drops are able to rise above the freezing level (i.e., in updraft) to produce the resultant more abundant but smaller hail particles compared with the control run. Figure 20(p) shows that the Dm of hail is further decreased when υ is increased to 10. This verifies that the change of hail properties from increasing hail υ can be reproduced.

5. Conclusions

Limited by the computation efficiency and current knowledge, CRM microphysics parameterizations still require significant assumptions. Biases in the CRM microphysics need to be identified and corrected. This work develops a method to use remote sensing observations to diagnose the model microphysical deficiencies in different cloud types so that improvement of the simulations of each cloud type can be made separately. The work focuses on illustrating the methodology instead of exploring the exhaustive solutions of the improvement, which will depend on the specific cloud model and simulation.

A convective storm is captured by TRMM at its decaying stage over the TRMM LBA region. Frequencies at 37 and 85 GHz are sensitive to ice scattering and can be used as proxies of ice microphysics in the convective storms. Cluster analysis of the Tbs at 37 and 85 GHz of TMI is performed and four clusters are found to be the optimal choice for representing the distinct microphysics over the selected storm scene. Using the matched retrieval properties from PR and VIRS, the four associated cloud types are labeled as clear/thin cirrus, cloudy, stratiform anvil, and convective. The relationship of dTb versus Tb(85) is found to contain relevant information of the microphysical properties including hydrometeor species and size distributions. It is found that the semi-ideal simulation produced an overwhelmingly cloudy background, and proper surface ε values in the RTM are essential to provide a consistent clear-sky background. To improve the simulated relationships of the cloudy and stratiform anvil clusters, the large amounts of supercooled water need to be removed. Keeping the same hail content but fixing the hail size distribution generally fixes the Tb for the convective cluster. Physically consistent microphysical pictures instead of static adjustment of the microphysical scenes are desired. To demonstrate the dynamic adjustment with the goal of improving the microphysics of the convective cluster, a sensitivity simulation is carried out by increasing the hail PSD gamma exponent value. Compared with the control run, the new simulation is capable of producing more but smaller hail particles and, therefore, generating a closer relationship to that of the observation. While these are perhaps not the only adjustments that can lead to better agreement between model and observed Tb, the method demonstrates how different process parameters in the model can be evaluated with this method.

When field experiments are not easily available, the specification of the engineering parameters in the parameterizations that need to be prescribed by the model users are uncertain and should ideally depend on the types of clouds being simulated. This work provides a procedure of using satellite observations to guide the choice of these adjustable parameters. In the long term, this work also reveals the potential of constraining these parameters using data assimilation techniques.

The improved microphysics, especially of the ice species, can help build improved microphysics–radiation databases for the microwave physical rainfall retrieval algorithms over land. The improved microphysics in the CRMs can also provide improved precipitation products at higher temporal and spatial resolutions, which is demanded by the hydrological communities. The method can also be applied to other types of satellite observations that may contain sensitivity to different microphysical properties.

Acknowledgments

The authors are very grateful to two anonymous reviewers for valuable suggestions that greatly helped to improve the paper. We thank Drs. A. Loftus, S. Saleeby, N. Guy, and K. Suzuki for helpful discussions, and Dr. G. Carrió for provision of the RAMS model. This work was supported by NASA under Contract NNX08AT04A.

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