2.1 CloudSat

CloudSat, a sun-synchronous satellite launched in 2006, carries a 94.05 GHz, nadir-looking cloud-profiling radar (CPR) (Stephens et al., 2008). The range resolution is 485 m, while the along- and cross-track resolution is 1.8 and 1.4 km, respectively. As a part of the A-train constellation, the CloudSat CPR has provided collocated products with the Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) aboard the CALIPSO satellite. DARDAR (Delanoë and Hogan, 2010) is a synergetic ice cloud retrieval product combining measurements by these two sensors and is one of the most advanced datasets of clouds to date. Bear in mind that radar attenuation by ice and liquid is neglected in this product, however.

The CloudSat data used in this study are extracted from the DARDAR product. Parameters used are DARDAR IWC, the DARDAR-normalized number concentration parameter ($N_{\mathrm{0}}^{*}$), and CloudSat radar reflectivity. The time frame of selected data is from 3 July to 1 August 2015. Geographically, data are extracted from a rectangular area in the Pacific Ocean placed directly at the Equator. The area is limited in latitude by 20^∘ S and 20^∘ N and in longitude by 170^∘ E and 130^∘ W. The reason for the selected spatial and temporal frame is given in Sect. 3.1.

2.2 GMI

The Global Precipitation Measurement (GPM) Microwave Imager (GMI) is a conically scanning radiometer with 13 channels in total (Hou et al., 2014). The frequencies of this sensor range from 10.65 to 183.31 GHz, with both h and v polarization at certain frequencies. The channels from 89 to 183.31 GHz have footprint sizes of roughly 6×6 km. GMI is mounted on the GPM satellite, which serves as the core satellite of the GPM constellation. The satellite has a non-sun-synchronous orbit with a 65^∘ inclination, which allows for collocated measurements with other satellites in the GPM constellation. GMI can therefore provide inter-sensor calibration for the GPM constellation satellites for the purpose of improved consistency among precipitation products. This study makes use of the vertically polarized measurements at 186.31 and 191.31 GHz. Data are selected within the same spatial and temporal frame as for the DARDAR data, as described in Sect. 2.1.

2.3 ICI

The Ice Cloud Imager (ICI) is an upcoming conically scanning radiometer that will fly on the second-generation meteorological operational satellite (MetOp-SG B) operated by the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) and scheduled for launch in 2023. Its main goal is to provide global measurements of ice hydrometeors, and it will fly in a polar sun-synchronous orbit. ICI has 13 channels from 183.31 to 664 GHz. Channels placed at 243 and 664 GHz measure both vertical and horizontal polarization, while the other channels measure vertical polarization only. ICI scans with a 53^∘ incidence angle and has a footprint of 15 km. Forward simulations were performed for ICI channels at 328.65, 334.65, and 668.2 GHz.

2.4 ERA-Interim

ERA-Interim is a global atmospheric reanalysis provided by the ECMWF. The parameters used here are pressure, surface, atmospheric temperature, humidity, and cloud liquid water content (CWC). The humidity and CWC fields are not used without modification; they are adjusted in order to be more realistic and agreeable with merged CloudSat data. These modifications are described in detail in Sect. 3.1.

2.5 ARTS

The Atmospheric Radiative Transfer Simulator (ARTS) is an open-source software package that focuses on simulating longwave RT (Buehler et al., 2018). It is intended to describe radiation using the full Stokes vector notation in the most general manner possible, allowing for a large amount of user input flexibility. In itself ARTS behaves as a scripting language on its own. It is oriented towards accuracy and treats particle scattering in a rigorous manner, making it ideal for usage in this study. Several scattering algorithms are available and have been used, including Monte Carlo (Rydberg et al., 2009), RT4 (Fox et al., 2019), and DOIT (Brath et al., 2018). Also available is the DISORT (Discrete Ordinates Radiative Transfer Program for a Multi-Layered Plane-Parallel Medium) algorithm, which is limited to unpolarized radiation. This study only considers totally randomly oriented scattering particles, so this limitation is not a major concern. Furthermore, the method is easy to use, insensitive to settings, and stable. Hence, DISORT was selected as the scattering solver to be used in this study.

2.6 Single scattering data

The ice particle single scattering properties to be evaluated in this study are provided in the publicly available database by Eriksson et al. (2018), referred to as the ARTS scattering database, as it covers the scope of this study in terms of frequencies and the selection of particle models. It provides scattering data for a total of 34 particle models, 34 frequencies between 1 and 886.4 GHz, and three temperatures at 190, 230, and 270 K.

The particle models, or habits as they are also commonly called, selected for evaluation in this study are outlined in Table 1. A fundamental difference between the particle types is how the particle mass is related to the size as they grow. Traditionally, this relationship is described by a power law:

where m is the particle mass, D_max the maximum diameter, and a and b the coefficients that are specific to the particle model. Table 1 lists values of a and b for each particle model, calculated by fitting a line to the mass–size relationship in logarithmic space; instances of D_max below 200 µm are not included the calculations. Here, D_max is defined as the diameter of the minimum circumsphere of the particle. Because some of the particle types do not cover broad enough size spans, there are also particle mixes available. Particle mixtures consist of pristine crystals at lower sizes and more complex particles like aggregates at larger sizes. There is a gradual shift in particle and scattering properties in a transition region in order to avoid discontinuities. The width and placement of the transition region differs between particle models but is roughly between 100 and 400 µm. Since the reported a and b values are calculated for particle mixtures, they differ somewhat to values reported in Eriksson et al. (2018). The database also includes scattering data for liquid spheres, calculated using Mie code, which will be used to describe scattering by rain.

A soft-spheroid particle is also included, whose scattering properties are calculated using T-matrix code by Mishchenko (2000). The particle is designed to mimic the settings applied in the DARDAR v2.1 product. In short, the spheroids are oblate with an aspect ratio (ratio of the minor to the major axis) of 0.6 and follow the mass–size relationship given in Delanoë et al. (2014, Eqs. 13–15). The refractive index of the particles is calculated using the Maxwell–Garnett mixing formula (Garnett, 1904) assuming an air-in-ice mixture. Eriksson et al. (2015) evaluated mixing rules in the context of soft-spheroid approximations and found that this mixing formula performs relatively good compared to discrete dipole approximation (DDA) data.

While D_max is commonly used to characterize the size of particles, the volume-equivalent diameter D_veq will be used throughout in this study. It is equivalent to the particle mass, which is more related to IWC and is generally more connected to the microwave particle scattering properties than D_max (Ekelund and Eriksson, 2019).

Table 1Summary of the particle models used. Given sizes are in millimetres and refer to the largest particle size of each model. Further details are found in the text.

Download Print Version | Download XLSX

In order to assist the evaluation of the impact of assumed particle type on resulting simulations presented later, an overview of the scattering properties of the included particle types is presented in Fig. 1, displaying the backscattering at 94.1 GHz and extinction at 190.31 and 668.2 GHz as a function of D_veq for all particle types used in panels (a), (b), and (c), respectively. Backscattering and extinction are given as cross section ratios in decibels using the 8-column aggregate as the reference. The 8-column aggregate therefore shows up as a horizontal line in all of the panels.

Figure 1Backscattering ratio at 94.1 GHz (a) and extinction ratio at 190.31 GHz (b) and 668.2 GHz (c) as a function of volume-equivalent diameter D_veq. Legends are common to all panels. The ratios are calculated as the cross section of a given particle model divided by the cross section of the 8-column aggregate and are given in decibels. That is, −3 dB means that the backscattering or extinction cross section is half of the Hong aggregate cross section. All data assume totally random particle orientation.

Download

The ICON cloud ice, 8-column aggregate, and sector snowflake are found to be relatively efficient backscatterers, while the Evans snow aggregate, large column aggregate, and especially the DARDAR spheroid are relatively inefficient. The spread in backscattering is also enhanced as particle size increases. In Fig. 1b, the ordering of particle models in extinction is similar. For instance, the 8-column aggregate is a very efficient scatterer at both 94.1 and 190.31 GHz. However, the spread between the particles is lower in comparison to panel (a). At sizes above 1 mm the lines converge and the 8-column aggregate is gradually replaced by other particles as more efficient scatterers. At 668.2 GHz, the relative spread between particles is even more compact. Above 500 µm, most of the particles, except the DARDAR spheroid and the 8-column aggregate, have aggregated to a cluster of lines with a spread of approximately 2 dB.

2.7 Particle size distributions

The particle size distribution (PSD) describes, as its name suggests, how the particle sizes are distributed within a volume element. By integrating over all sizes, the particle number concentration is attained, while the particle mass density is attained by weighting with the particle mass. IWC is given by

where N describes the PSD and m is the mass of individual particles (in this study given by Eq. 1). Three different PSDs were selected for this study: two of them are commonly used by the passive community and the last one by the radar community. The first PSD by McFarquhar and Heymsfield (1997), denoted as MH97, has been used predominantly in studies related to limb microwave measurements (Davis et al., 2005; Wu et al., 2006; Eriksson et al., 2007; Rydberg et al., 2009). In situ data were collected from the Central Equatorial Pacific Experiment (CEPEX). They should mainly be considered valid for anvil cirrus in the tropics. Consequently, MH97 places relatively low weight on large particles and is therefore less suitable for snow, for instance. In contrast to many other PSD parameterizations, MH97 makes use of the volume-equivalent (mass-equivalent) diameter D_veq as the size descriptor. The MH97 PSD is therefore mass-conserving; i.e. the PSD-integrated mass does not depend on the mass–size relationship of the particle model.

The second PSD used here was developed by Field et al. (2007) and is denoted as F07. F07 and its predecessors have arguably seen more widespread use compared to MH97 (Kulie et al., 2010; Geer and Baordo, 2014; Fox et al., 2019). F07 is a single-moment PSD parameterization based on in situ PSD data compiled from multiple measurement campaigns. As input it requires the temperature and the mass–size relationship (Eq. 1) of the employed particle model, and it also has two different settings for mid-latitude and tropical conditions. Here, only the tropical setting is used, denoted as F07T. It uses D_max as the size descriptor and is therefore not mass-conserving with respect to the assumed particle model.

The PSD used by the DARDAR v2.1 product is employed as well in order to provide insight into this specific product. It is described in Delanoë et al. (2014) and is referred to as D14. It is a modified gamma distribution fitted to in situ data. As such, the same α_F and β_F coefficients used in DARDAR version 2 are used for this study (Cazenave et al., 2019) (${\mathit{\alpha }}_{\mathrm{F}}=-\mathrm{2}$ and β_F=4). As is the case for MH97, this PSD takes D_veq as input and is mass-conserving. Also, the PSD requires two moments as input, the normalized number concentration parameter $N_{\mathrm{0}}^{*}$ and the mean volume-weighted diameter D_m. Any of these parameters can be interchanged with IWC through conversion, so only IWC and $N_{\mathrm{0}}^{*}$ are used in this study. Since the radar inversion algorithm, described later in Sect. 3.2, only retrieves IWC and not $N_{\mathrm{0}}^{*}$, an a priori parameterization of $N_{\mathrm{0}}^{*}$ is used instead. The parameterization, described in Delanoë et al. (2014), takes temperature as input and is defined as

where $k=-\mathrm{0.076586}$ and a=17.948 are coefficients fitted to aircraft in situ measurements, and T is the temperature given in degrees Celsius.

For describing rain, the PSD by Wang et al. (2016) was selected. It is described by a gamma function based on aircraft in situ measurements of multiple convective cores in North Dakota, USA.

The impact of the assumed PSD will be investigated later, and an overview of the PSDs used is therefore given in Fig. 2. The panels show the PSD-weighted extinction cross section of the ICON cloud ice particle using the PSDs of MH97, F07T, and D14, in panels (a), (b), and (c), respectively. Different values of IWC are assumed in the coloured lines, and the distributions have been normalized to have an area equal to 10⁻³. Generally, the PSDs produce mostly small particles, with diameters of roughly 10 µm. However, Fig. 2 shows that in terms of scattering impact, intermediately sized particles (300 to 1000 µm) dominate. Of the investigated PSDs, MH97 puts the highest emphasis on small particles, with two modes being clearly visible for an IWC of 10 mg m⁻³. There is little change as IWC increases, apart from the first mode becoming less pronounced. F07T and D14 are fairly similar to each other, both resulting in a stronger emphasis on larger particles compared to MH97 at increasing values of IWC.

Figure 2Normalized extinction as a function of volume-equivalent diameter D_veq for different combinations of particle size distribution and IWC. Frequency is 190.31 GHz, temperature 255 K, and the assumed particle model is the ICON cloud ice. Each extinction curve is normalized to have an area equal to 10⁻³. (b) Extinction calculated using the 8-column aggregate is included, indicated by dashed lines, for comparison.

Download

As a final comment, the F07 PSD requires the mass–size relationship coefficients as input (a and b in Table 1). For comparison, the 8-column aggregate is included, indicated by dashed lines, in panel (b). This particle model has a value of b=3, resulting in a shift of the distributions towards higher values of D_veq. Hence, comparisons between F07 and other PSDs are generally not straightforward but depend on the assumed particle model.

3.1 Generating synthetic scenes

The synthetic scenes are defined on two-dimensional grids in latitude and pressure, using CloudSat measurements as a reference. Extracted data are restricted to a rectangular geographic area in the Pacific Ocean, within 20^∘ S to 20^∘ N and 170^∘ E to 130^∘ W. The pressure grid is defined up to 42 hPa, and the latitude grid is resolved in steps of roughly 0.01^∘. The time frame of the scenes was selected with the purpose of getting the best possible match between CloudSat measurements and GMI measurements. CloudSat passes the Equator in the Pacific Ocean during daytime at roughly 13:30. Since GPM has a non-sun-synchronous orbit, a day in 2015 when GPM passes the Equator at roughly the same time could be identified and selected as the reference day. A time frame of 30 d centred around this reference day was then set, from which 59 CloudSat overpasses could be identified within the geographic area and selected as references for the synthetic scenes. From this time frame, all available GMI data within the defined geographical area were extracted for comparison to the forward simulations. While the extracted CloudSat and GMI data are not collocated, they are extracted from the same geographic area in the same month and were collected at roughly the same time of the day (within ±4 h). As a consequence, a much larger dataset can be considered than if only collocations were to be considered.

As mentioned in the previous section, the synthetic scenes are composites of data collected form several sources. Atmospheric fields of temperature, humidity, CWC, surface temperature, and elevation are collected from ERA-Interim (see Sect. 2.4). In the IWC-based mode, IWC fields from DARDAR are employed as an input, while in the dBZ-based mode CloudSat retrievals (described in Sect. 3.2) are set as the input, which are converted to IWC fields using microphysical assumptions consistent with the forward simulations (see Fig. 3). Rainwater content (RWC) fields are retrieved from CloudSat reflectivities for both modelling systems, since RWC is not provided by DARDAR. All fields are interpolated onto the aforementioned pressure and latitude grid.

Some modifications to the data provided by ERA-Interim are performed. Relative humidity is set to 0.9 at locations with water content above 50 µg m⁻³ in order to ensure that humidity is not artificially too low or high at locations with clouds or precipitation. Liquid water content is also adjusted. It is set to zero at altitudes higher than 10 km and at temperatures lower than 243 K. Furthermore, for pixels at which IWC or RWC is zero, CWC is set to zero as well. This ensures that ERA-Interim does not place liquid water outside clouds and precipitation detected by CloudSat.

3.2 Radar inversions

A brief description of the radar inversions is given here. First of all, for a given particle and PSD combination the effective radar reflectivity Z_e at frequency ν is given as

where σ_b is the backscattering cross section and K=0.75 the dielectric factor; it is set to the value used by CloudSat (Stephens et al., 2008). Following convention, the reflectivity is shown in decibels relative to the equivalent reflectivity (dBZ), i.e. 10log ₁₀(Z_e). For all microphysical combinations, reflectivities are calculated on an IWC grid and stored in IWC–dBZ tables. At temperatures above 0^∘, the same formula is applied assuming rain instead, for which a separate RWC–dBZ table is constructed. Radar inversions are then performed for each microphysical combination. An onion-peeling concept is used, implying that the atmosphere is divided into layers. The IWC value of the top layer is extracted from the IWC–dBZ table given the measured CloudSat reflectivity at that layer. The two-way radar attenuation of this layer is then calculated, taking the updated IWC (or RWC) value into account. The CloudSat reflectivity of the layer below is then updated to account for the radar attenuation. The maximum correction in decibels is set to 3 in order to account for reflectivity enhancement due to multiple scattering (Battaglia and Simmer, 2008). The IWC and RWC grids are thus calculated iteratively by taking the radar attenuation of above layers into account. Absorption by gases and liquid clouds is considered in the same manner as in the forward simulations, as described in the next section.

3.3 ARTS setup

This section describes the forward simulations and the ARTS settings used. The RT simulations are two-dimensional but approximated using the independent beam approximation; i.e. one-dimensional calculations are performed along the line of sight of the simulated sensors. Polarization effects are neglected, since randomly oriented single scattering will not have a strong effect on polarization. Hence, only the first Stokes element is simulated. All simulations are performed at an earth surface incidence angle of 53^∘, close to the angles used by ICI and the GMI channels mimicked in this study. The simulated frequencies are 166, 186.31, 190.31, 328.65, 334.65, and 668.2 GHz. As this study is of a demonstrative nature, the lower GMI channels are omitted, since these are less sensitive to cloud ice. We also limit the number of covered ICI channels. The antenna pattern of GMI and ICI is approximated post-simulation by averaging over multiple pencil beams assuming a Gaussian footprint pattern with a full width at half maximum of 6 (166, 186.31, and 190.31 GHz) and 15 km (328.65, 334.65, and 668.2 GHz), respectively. Oxygen and water vapour absorption are calculated using the PWR-98 model by Rosenkranz (1998) and nitrogen absorption using the standard profile by Liebe et al. (1993). Furthermore, liquid clouds are treated using the absorption model by Ellison (2007) (scattering by liquid clouds is omitted).

Figure 4Radar reflectivity and IWC relationships at 255 K. The coloured curves are the relationships obtained by combining the particle models in Table 1 with the particle size distributions of MH97 (a), F07T (b), and D14 (c). The black lines represent the IWC–dBZ relationship taken from Protat et al. (2016).

Download

4.1 CloudSat inversions

This section gives an overview of the CloudSat radar inversions. The radar IWC tables are first presented, then retrieved ice water path (IWP) for an example scene is shown. Finally, IWC and IWP across all scenes are overviewed statistically.

4.1.1 IWC–dBZ relationships

Figure 4 overviews calculated relationships between radar reflectivity and IWC, which are used for the CloudSat inversions described in Sect. 3.2. Panel (a) uses the MH97 PSD, panel (b) F07T, and panel (c) D14. For MH97, the spread of the lines is relatively small, roughly a factor of 2, since the PSD puts high emphasis on smaller particles for which the spread in backscattering is less significant (see Fig. 1a). Conversely, F07T results in a large spread of the lines, almost a full order of magnitude. In other words, F07T results in a higher uncertainty in IWC for a given reflectivity value with respect to the assumed particle type. In contrast to MH97 and F07T, D14 displays a more gradual increase in spread. At low reflectivity values, the spread is fairly small, while for large values the spread is comparable to that of F07T. As shown in Fig. 2, D14 emphasizes smaller particles at low values of IWC, similar to MH97. At higher IWC values, the PSD behaves more like F07T, explaining the gradual increase in spread.

Figure 5Example scene with a deep convective core and some medium- to high-altitude ice clouds. (a) DARDAR IWC field and temperature contour lines, going from 270 to 200 K, in steps of 10 K. (b) Ice water path. The black line represents the DARDAR product IWP, while the coloured lines are from radar inversions assuming different particle types, as indicated by the line colour. See the legends in Fig. 6 for a full description of the lines. F07T is the assumed PSD for all the coloured lines in this figure.

Download

Also included is the radar reflectivity relationship developed by Protat et al. (2016, Eqs. 3–5), which is based on collocated airborne radar and in situ measurements of deep convective systems in the northern part of Australia. Calculated relationships cover the Protat line fairly well, though MH97 tends to underestimate reflectivity values in comparison. However, this is expected; since the relationship by Protat is empirical, it is to some degree influenced by azimuthally oriented particles. Azimuthal alignment enhances nadir or zenith backscattering (Hogan et al., 2012); hence, it is expected that the calculated reflectivities are underestimated by a few decibels in comparison to Protat. Also note that the slopes of the MH97 and Protat radar relationships are almost the same.

Figure 6Mean IWC as a function of altitude. Assumed PSD is MH97 (a), F07T (b), and D14 (c).

Download

4.2 Simulated GMI observations

This section overviews the simulated measurements of TB. First, bulk extinction coefficients are overviewed, which is useful for the interpretation of simulated TBs. TBs are then shown for the same example scene as presented in Sect. 4.1.2. Finally, simulated TBs are analysed statistically, including the results from all simulated scenes.

4.2.1 Bulk extinction

Bulk extinction is shown in Fig. 7 as a function of either IWC (panel a) or radar reflectivity (panels b and c). Extinction is shown in terms of extinction coefficient ratios, i.e. γ_ext of given particle divided by γ_ext of a reference particle: in this case the 8-column aggregate. The extinction coefficient is given by

Figure 7Ratios of the extinction coefficient γ_ext as a function of IWC (a) and radar reflectivity (b, c). The ratios are calculated by dividing γ_ext of given particle model by γ_ext of the 8-column aggregate. Hence, the 8-column aggregate appears as a straight line. The frequencies are 190.31 GHz (a, b) and 668.2 GHz (c). PSD is F07T, and temperature is 255 K.

Download

$$\begin{array}{}\text{(5)}& {\mathit{\gamma }}_{\mathrm{ext}}=\underset{\mathrm{0}}{\overset{\mathrm{\infty }}{\int }}{\mathit{\sigma }}_{\mathrm{e}}\left(D_{\mathrm{veq}}\right)N\left(D_{\mathrm{veq}}\right)\mathrm{d}{D}_{\mathrm{veq}},\end{array}$$

where σ_e is the extinction cross section. The frequency is 190.31 GHz in panels (a) and (b), and it is 668.2 GHz in panel (c). PSD is F07T in all panels, and the assumed temperature is 255 K. The spread between particle models in panel (a) is large, over 10 dB, implying that simulated TBs are indeed highly dependant upon the assumed particle model (in the IWC retrieval). On the other hand, there is a clear reduction in spread in panel (b), where extinction is expressed in terms of radar reflectivity. This will partly explain the results shown in the next sections. In panel (c), the frequency is 668.2 GHz instead. The spread is slightly larger, with the 8-column aggregate, ICON cloud ice, and DARDAR spheroid particles standing out. The extinction coefficient γ_ext as a function of IWC at 668.2 GHz (not shown here) behaves fairly similar compared to the lines in panel (a).

4.2.2 Example scene

Simulated TBs are presented here for the example scene shown in Fig. 5. In Fig. 8, simulations at 190.31 GHz for different combinations of PSD, particle type, and modelling mode (IWC-based versus dBZ-based) are presented. See the figure caption for details on how the data are displayed.

Figure 8a assumes F07T as a PSD and makes use of the IWC-based mode. The uncertainty in TB due to the particle type assumption is the highest for this combination. For instance, the spread of lines at the peak at 9.2^∘ is almost 60 K. The uncertainty is significantly reduced in panel (c), where the dBZ-based mode is used instead. The effect is similar in panel (b), where the PSD has been switched to MH97 (but still using the IWC-based mode). In both cases the uncertainty is reduced by a factor of roughly 3. There is also a noticeable shift towards lower TB depressions when MH97 is used due to the greater emphasis on smaller particles of this PSD. The lowest spread overall is attained in panel (d), where PSD is MH97 and the dBZ-based mode is employed. The spread is reduced by roughly a factor of 6 in comparison to panel (a). The tendencies discussed here largely hold for the other frequencies as well but are not shown here.

Figure 8Simulated TBs for the same scene as in Fig. 5. The simulations in each panel assume a different PSD and model system mode. The frequency is 190.31 GHz in all panels. Employed modes are IWC-based (a, b) and dBZ-based (c, d). The PSDs are MH97 (a, c) and F07T (b, d).

Download

Figure 9 is similar to Fig. 8, but the model system used and PSD are kept constant for all panels. Instead, different frequencies are displayed in each panel. PSD is F07T and the dBZ-based mode is used; hence, the panels can be compared with Fig. 8c, wherein the frequency is 190.31 GHz. Panel (a) illustrates TBs at 186.31 GHz and displays similar tendencies as 190.31 GHz but with lower TB depression overall. This is a consequence of 186.31 GHz being closer to the centre of a water vapour absorption line; i.e. the TB depressions are masked by the stronger water vapour absorption at higher altitudes. The simulations at 328.65 and 334.65 GHz shown in panels (b) and (c), respectively, show similar tendencies. At 328.65 GHz, the TB depressions are lower compared to 334.65 GHz, especially at the peak at 9.2^∘. As for 190.31 GHz, this is a consequence of proximity to a water vapour absorption line. Relative to the channels close to 180 GHz, the 300 GHz channels show higher TB depression for thinner clouds, as evident by the peaks at 9.2 and 10.5^∘. However, the uncertainty is fairly similar in magnitude if one excludes the DARDAR-spheroid particle shown by the dashed green line. The DARDAR spheroid is a clear outlier at the higher sub-millimetre frequencies.

In Fig. 9d, simulations are shown for 668.2 GHz. This channel shows the highest TB depressions among all the channels for high-altitude thin clouds, as evident by the peaks at 10.5^∘ and higher. There also seems to be a more distinct separation between different particle types. As for the 300 GHz channels, the DARDAR spheroid results in relatively low TB depressions. Furthermore, the 8-column aggregate and the ICON cloud ice are also distinguished, having clustered into a group of intermediate values of TB. The remaining particle types have clustered into a large group with high TB depressions.

Figure 9As in Fig. 8, but all panels use PSD F07T and the dBZ-based mode. The frequency is different in each panel. Frequencies are 186.31 GHz (a), 328.65 GHz (b), 334.65 GHz (c), and 668.2 GHz (d).

Download

4.2.3 TB distributions

This section gives a statistical overview of simulated TBs. Figure 10 displays TB occurrence frequencies for different combinations of particle types, PSDs, and model systems. Simulations using the D14 PSD are omitted here, since they produce fairly similar results compared to MH97. Black lines represent GMI data (see Sect. 2.2) at 190.31 GHz for comparison. The peak at around 270 K corresponds to simulations of clear-sky cases, which is the most frequent scenario. Lower TB values correspond to increasingly high-altitude and thick clouds. The lowest TB values are typically associated with deep convective cores, as seen in Fig. 8 for example. This was verified by partitioning the cold-simulated observations by the CloudSat classification product, revealing that around 70 % of TBs below 200 K are categorized as deep convection.

Figure 10a, which uses F07T and the IWC-based mode, shows the largest spread in lines. On the other hand, the lines cover the GMI measurements shown by the black line fairly well. In panel (b), PSD is switched to MH97, showing a clear reduction in uncertainty (as in Fig. 8). However, for MH97 there is a tendency to underestimate TB in comparison to GMI.

In Fig. 10c and d, the dBZ-based mode is used instead, showing a clear decrease in uncertainty for both PSDs. Both PSDs agree well with GMI above 170 K, showing no significant bias. It is difficult to visually distinguish which particle models agree best with GMI, the exception being the DARDAR spheroid in panel (c). However, the forward simulations tend to produce a relatively large amount of very low TBs. Only the large column aggregate agrees with GMI at these cold TBs for F07T, MH97, and D14. As already mentioned, the simulated distributions using the D14 PSD (not shown here) are similar to MH97 when the dBZ-based mode is used.

By visual inspection, agreement with GMI (channels explored) is good, indicating the robustness of the forward simulations at these frequencies. However, there is a mismatch close to the peak of the distributions, indicating that clear-sky observations do not matching perfect. The fact that for most particle and PSD combinations, distributions predict significantly colder temperatures than GMI indicates that simulated observations of deep convection do not match GMI perfectly. Simulated distributions at 166 and 186.31 GHz (not shown here) behave very similarly in comparison to the simulations at 190.31 GHz.

Figure 10Occurrence frequencies of TBs at 190.31 GHz assuming various particle models. Curves are normalized to have unit area. The different coloured lines represent the particle type used in the forward simulation. The black line is derived from GMI measurements. The modes used are IWC-based (a, b) and dBZ-based (c, d). The PSDs are MH97 (a, c) and F07T (b, d).

Download

At higher simulated frequencies, there are currently no measurements available for comparison. At 328.65 and 334.65 GHz (not shown here) the spread of the lines is slightly higher in comparison to 190.31 GHz for all PSD and model mode combinations. The exception is the DARDAR spheroid, which for some combinations produces a significantly lower amount of cold TBs.

At 668.2 GHz, the picture is somewhat different. Figure 11 overviews simulated TBs at 668.2 GHz. The layout is similar to Fig. 10, but simulations using the IWC-based mode are omitted, and MH97 is switched out for D14 in panel (b). In contrast to the dBZ-based simulations at 190.31 GHz, a clear spread between particle models is observed at intermediate TB values. In essence, the simulations at 668.2 GHz demonstrate higher sensitivity to the particle type assumption than at 190.31 GHz, with some exceptions. The DARDAR spheroid is the most significant outlier, generally resulting in very warm distributions compared to the other particles.

Figure 11As in Fig.10c and d, but for 668.2 GHz and with D14 PSD used in panel (b).

Download

4.2.4 Overview of performance

In order to provide an overview of the performance of the particle models and PSDs, differences between simulated and GMI-observed mean TBs are calculated. Because collocated passive and active observations were not used in this study, it is not possible to perform a quantitative error analysis. Hence, we are limited to comparing statistics for the simulations and GMI observations.

The mean TBs are derived as

$$\begin{array}{}\text{(6)}& {\stackrel{\mathrm{‾}}{T}}_{\mathrm{b}}={\displaystyle \frac{{\int }_{\mathrm{0}}^{\mathrm{240}}{T}_{\mathrm{b}}N\left(T_{\mathrm{b}}\right)\mathrm{d}{T}_{\mathrm{b}}}{{\int }_{\mathrm{0}}^{\mathrm{240}}N\left(T_{\mathrm{b}}\right)\mathrm{d}{T}_{\mathrm{b}}}},\end{array}$$

where N is the distribution of TBs. Clear-sky cases are removed by only considering TBs below a threshold of 240 K. The difference in mean TBs is then

$$\begin{array}{}\text{(7)}& \mathrm{\Delta }{\stackrel{\mathrm{‾}}{T}}_{\mathrm{b}}={\stackrel{\mathrm{‾}}{T}}_{\mathrm{b}}-{\stackrel{\mathrm{‾}}{T}}_{\mathrm{b},\mathrm{GMI}}.\end{array}$$

Table 2 shows $\mathrm{\Delta }{\stackrel{\mathrm{‾}}{T}}_{\mathrm{b}}$ for each GMI frequency, particle model, and PSD combination. The particle and PSD combinations generally result in negative TB differences larger than 10 K for at least one channel. One exception is the DARDAR spheroid, which tends toward positive differences and surprisingly results in fairly low TB differences when combined with MH97. The large column aggregate typically results in the lowest TB differences for all PSD and frequency combinations. The Evans snow aggregate combined with MH97 yields the lowest TB differences by a small margin, but it does not perform well with the other PSDs. Focusing on the PSDs, F07T yields the largest TB differences for most frequencies and particle models, while MH97 typically yields the smallest. As previously explained, F07T puts emphasis on larger particles, explaining the stronger TB depressions compared to MH97. In summary, the large column aggregate and the Evans snow aggregate, combined with MH97, result in the lowest TB differences.

Table 2Differences between the means of simulated and GMI-observed TBs (see Eq. 7) in units of Kelvin. Only TBs below 240 K are considered, essentially filtering out clear-sky cases.

Download Print Version | Download XLSX