3.2. Optical Thickness Profiles from Combined CRS and CPL Measurements
The vertical profile of the cloud water content can have significant influence on outgoing IR radiances, even for optically thick clouds. A thick convective cloud with a low ice water content at the top will produce a different IR temperature than one having a dense top (e.g., [
44]). A multilayered ice-over-liquid cloud will yield a different IR temperature than a single-layered ice cloud having the same cumulative optical depth. Thus, it is important to use a realistic vertical profile of the water content or optical depth in the simulations.
The CRS measurements are primarily used to obtain vertical cloud τ profiles at a resolution of 15 m. Three cloud phases, ice, liquid, and mixed phase, are considered here. The vertical profiles are separated into three layers, ice (top layer), mixed-phase (middle layer), and liquid (bottom layer) clouds. The layer with temperatures less than −20 °C is defined as ice cloud, the layer with temperature exceeding 0 °C is a liquid cloud. The layer between −20 °C to 0 °C is the mixed-phase cloud [
45]. In the bottom layer, the liquid cloud water content (
LWC) is computed as follows,
where
LWC is in g·m
−3 and
Ze is in mm
6·m
−3 [
46]. In the ice cloud, the ice water content (
IWC) is
where
IWC and
Ze are in the same units as those for
Ze−
LWC [
47].
For the mixed-phase layer,
LWC is assumed to decrease to 0 linearly with increasing altitude from the freezing level to the bottom of the ice cloud layer. Conversely,
IWC is assumed to increase linearly from 0 g·m
−3 following
Equation (2). On the basis of these assumptions, an ice fraction
IceFra is defined to separate the two parts of CRS reflectivity,
IceFra = −(
T −
T0)/(
T0 −
TTra), where
T is atmospheric temperature in degree,
T0 is the temperature at the freezing level, and
TTra is the transition temperature from mixed-phase to ice cloud. In the present study, 0 °C is used for
T0, so
IceFra =
T/TTra. A phase transition temperature of −20 °C (altitude is ∼8.3 km) is used. Therefore, the two parts of the CRS reflectivity due to cloud ice
and liquid water
, are obtained from
and
, respectively.
IWC and
LWC are then obtained by applying
and
to
Equations (1) and
(2), respectively. Because of difficulties in separating the surface radar return from the hydrometeors within the first 500 m above the surface, CRS reflectivity below 500 m is assumed to be that at the level of 500 m [
48,
49].
While the CRS retrieval algorithm assumes the ice fraction varies as indicated above, the Rosemount icing probes detected no liquid water at temperatures up to −3 °C for this flight segment. Thus, to provide a more realistic variation of cloud water structure, a second profile was constructed assuming no liquid water for temperatures less than 0 °C. Thus, in the 0 to −20 °C transition zone used above, IceFra is set equal to 1.0 for a second set of calculations. Both results are used to determine the sensitivity of the calculations to the assumptions about supercooled liquid water in the clouds.
The CPL measurements are used to compensate for the optically thin cirrus part missed by the CRS measurements [
35].
Figure 7 shows the vertical structure of the cloud system as seen from the CRS and CPL measurements and the 15-m resolution τ profiles constructed from the CRS and CPL data for the pure ice layer. The total optical thicknesses, those from the CPL and those missed by the CRS along the flight track over the cloud system, are also shown in
Figure 7. Visible τ from the CRS shown in
Figure 7(c) is derived from the empirical relationships, τ = 0.065·
IWP0.84 for cloud ice and τ = 3.0/20.0·
LWP for cloud liquid (assuming water clouds with
De = 20 μm and an extinction efficiency,
Qe = 2.0), respectively [
50]. The water paths for each layer are the products of the water content and the 15-m thickness for each layer. The minimum detectable reflectance from the CRS is used to isolate the CPL-measured cloud areas missed by the CRS measurements: overlapping is denoted where the CRS gray region is visible under the CPL color region in
Figure 7(a). The cloudy area missed by the CRS is shown as the gray region in
Figure 7(b).
Figure 8(a) shows examples of the constructed vertical profiles for 15-m layer ice and liquid cloud τ. One profile is from an anvil cloud measured at 13:56:34 UTC, and the other is taken from a convective core measured at 14:06:10 UTC. The CPL cumulative ice cloud τ missed by the CRS measurements along the flight path are detailed in
Figure 8(b). The τ value most frequently missed by the CRS but detected by the CPL is ∼0.20. Overall, the average τ missed by the CRS is 0.28 ± 0.17, which is consistent with the values (0.15–0.45) deduced by [
35].
3.3. Cloud Bulk Scattering Properties during the Flight Track
Cloud bulk scattering properties are commonly used to simulate IR radiances emanating from clouds [
51–
55]. Ice cloud bulk scattering properties are computed by averaging ice particle single scattering properties (
i.e., single scattering albedo, absorption and scattering efficiency, asymmetric factor, and scattering phase function) over ice cloud habit and particle size distributions.
Accurate measurements of ice cloud particle size and habit distributions are crucial for ice cloud bulk scattering properties. In this study, ice cloud particle size distributions from the 2D-S, CIP and PIP measurements are combined to construct the particle size distributions with a minimum size bin of 5–15 μm. To minimize the effects of large-crystal shattering on number densities of small ice particles, the particle size distributions from the 2D-S for small ice particles are combined with those from the CIP and PIP for large ice particles. To be consistent with the CIP and PIP data that have been averaged over 5 s or about 1.0 km horizontal path, the 2D-S data are averaged in the same way.
Figure 9 shows the combined ice particle size distributions over an anvil ice cloud and convective core from the 2D-S, CIP, and PIP measurements along the flight track over the deep convective cloud system (
Figure 2). High concentrations of small particles are seen in both the anvil at 13:57:09 UTC (
Figure 9(a)) and core at 14:02:07 UTC (
Figure 9(b)). And both cloud types have a second peak concentrated at a maximum dimension
D of 200–300 μm. All of the ice particle size distributions along the DC-8 flight track (
Figure 7(a)) are derived and shown in
Figure 10. The averaged particle size distribution is used for computing ice cloud bulk scattering properties. Besides the measured particle size distributions, the Gamma particle size distribution (e.g., [
56]) is also used for investigating the effects of
De on the IR radiances from this cloud. The Gamma particle size distribution varies with its parameters, dispersion μ and slope κ. Those used by Hong [
56] are adopted here as
where
N0 is the intercept and
D0 is the median of the distribution.
Also taken from the DC-8, the CPI data were used to resolve the ice cloud particle habits simultaneously with ice particle size distributions during TC
4. Using an automatic crystal habit classification program, ice particle shapes measured by the CPI were placed into categories including sphere, column, plate, rosette, budding rosette, and irregular for ice particles with
D < 50 μm and >50 μm.
Figure 11 shows the ice particle habits detected by the CPI along the flight track. It was found that spherical and irregular particles comprise almost all of the habits when
D < 50 μm, while the particles with irregular and column habits are most common when
D > 50 μm. The averaged habit mixing ratios along the flight track are used for computing ice cloud bulk scattering properties. When
D < 50 μm, the habit distribution consists of 55% spheres, 37% irregular particles, and 8% columns. When
D > 50 μm, the habit distribution consists of 73% irregular particles, 19% columns, 6% rosettes including rosettes and budding rosettes, 1% spheres, and 1% plates. Single-scattering properties of ice particles with various habits including column, hollow, bullet rosette, plate, aggregate, and droxtal have been investigated extensively (e.g., [
53,
55,
57] and references therein). The single-scattering properties of droxtal, column, plate, rosette, and aggregate particles are used respectively for the sphere, column, plate, rosette, and irregular habits determined from the CPI data.
Following Yang
et al., the single-scattering properties of ice particles are then averaged over the habit distributions and particle size distributions to obtain ice cloud bulk scattering properties, which are functions of wavelength, and
De, which is defined by:
where
f(
D) is the particle habit distribution and the summation of
f(
D) over
N equals 1.0,
i is the index for
N ice particle habits at
D, and
V and
A are the particle volume and projected area, respectively [
53]. The liquid cloud is assumed to be composed of spherical water droplets. An effective radius
re of 10 μm with a gamma particle size distribution following Mishchenko and Travis [
50] is used for the water cloud bulk scattering properties. For mixed-phase cloud portions (
Figure 8(a)), a water-phase mixing ratio γ is defined by
LWC/(
IWC +
LWC) first, then the bulk scattering properties of mixed-phase clouds are derived by combining those of the ice and water clouds [
58–
61].
3.4. Effects of Optical Thickness and Particle Size on IR Radiances over Deep Convective Cloud
Simulations and observations of the brightness temperatures at 3.7, 6.7, 7.3, 8.5, 10.8, and 12.0 μm (BT03, BT06, BT07, BT08, BT11, and BT12) over the cloud system are compared to examine the effects of τ and De on the IR brightness temperatures.
The correlated
k-distribution routines developed by Kratz [
62] and Kratz and Rose [
63] for the MODIS bands are used to compute the absorption optical depth for each layer in a clear-sky atmosphere. The atmospheric profiles of temperature and humidity (
Figure 3), as well as ozone, are used in the correlated
k-distribution calculations for each band. The surface emissivity is assumed to be 1.00 for the IR bands. The spectral brightness temperatures over the clouds are then computed with the discrete ordinates radiative transfer model [
64] using the constructed cloud τ profiles (Section 3.2), the computed bulk scattering properties, and various
De in the range of 10–150 μm.
Figure 12 shows the simulated and observed BT values over the subject cloud system as a function of ice cloud τ using the profile in
Figure 3(b). Results are similar for most channels. Differences are discussed in Section 4. The mean particle size distribution (
De = 95 μm) along the flight track is used for the simulations. Since the measured BT
03 values include reflected solar radiation while the simulations only include the emitted radiance, the measurements of BT
03 are omitted in
Figure 12(a). The other simulated values generally agree with the corresponding observations. In particular, for optically thick ice clouds with τ > 20, the simulated values are essentially the same as the observations. For optically thin ice clouds (τ < 1), the simulated BT
08, BT
11, and BT
12 are greater than the observations, while the simulated BT
06, BT
07, BT
08, BT
11, and BT
12 are less than the observations for ice clouds having 5 < τ < 10 (anvil clouds). These differences are most likely due to the uncertainties in derived ice cloud τ from the CRS (or/and CPL), which can be distinctly different because of the uncertainties in
Ze−
LWC relationship [
44,
65]. The underlying water clouds tend to decrease the BT
03, BT
08, BT
11, and BT
12 values for non-opaque ice clouds, but have negligible effect on the water vapor channels’ brightness temperatures. The simulations and observations both reveal that all six BTs are sensitive to ice cloud optical depth for τ up to 20. Furthermore, these sensitivities are essentially monotonic,
i.e., these brightness temperatures monotonically decrease with increasing ice cloud optical thickness up to τ = 20. When τ is above 20, the brightness temperatures vary widely although a weak decreasing trend with increasing ice cloud τ is apparent.
The sensitivity of the radiances to phase transition temperature is illustrated in
Figure 13, where the 3.7 and 6.7-μm simulations used the −20 °C transition temperature (red) and 0° transition (blue, same as blue in
Figure 12). The results are similar for the other channels (not shown). Negligible change is seen in the radiances, but the entire set of radiances is shifted to the right. Thus, the simulated radiances correspond to greater optical depths if it is assumed that the hydrometeors are entirely in the ice phase for T < 0°, as indicated by the
in situ data rather than assuming that the layer between 0° and −20 °C is a mixture of ice and water as formulated in Section 3.2 above. This result is encouraging because the phase of clouds in that temperature range is often uncertain.
Figure 14 shows the simulated and observed BTDs among the 3.7, 6.7, 7.3, 8.5, 10.8, and 12.0-μm bands over the cloud system as a function of ice cloud τ. As in
Figure 12(a), the BTD(3.7–11) (BTD between 6.7 and 10.8-μm bands and others are similarly defined) measurements are not shown in
Figure 14(a). In general, the simulated values of BTD(6.7–11), BTD(8.5–11), BTD(11–12), and BTD(6.7–7.3) are consistent with their respective observations. They are differentially impacted by the presence of low clouds when the ice clouds are optically thin. The water vapor bands at 6.7 and 7.3 μm are affected by upper and middle tropospheric water vapor and above, respectively when the ice clouds are optically thin. This is clearly shown in
Figure 14(f), which shows that the simulated BTD(6.7–7.3) values differ significantly from the observations when τ < 3, but dramatically decrease as τ increases. Both the simulated and observed BTDs show strong sensitivities to τ of up to 10. Weak sensitivities to τ up to 20 are also found for BTD(3.7–11), BTD(6.7–11), BTD(3.7–6.7) and BTD(6.7–7.3).
Brightness temperatures for the six bands and their BTDs are commonly used to estimate ice cloud
De. As noted earlier, previous studies of infrared cloud retrievals have been limited mainly to non-opaque ice clouds having τ < ∼5. Here, the effects of ice particle size
De on the BTDs and the potential of estimating
De for optically thick ice clouds are investigated by performing simulations with
De in the range of 10–150 μm.
Figure 15 shows simulated BTDs for various 3.7, 6.7, 7.3, 8.5, 10.8, and 12.0-μm pairs over the subject cloud system as functions of τ and
De. For these simulations, only ice clouds are involved. The observed BTDs, except for those for the 3.7-μm band with its reflected solar radiances, are also shown together with these simulations. Consistent with previous studies, BTD(3.7–11), BTD(8.5–11), BTD(11–12), and BTD(3.7–6.7) show strong sensitivity to ice cloud
De when the ice clouds are non-opaque [
10,
14,
19,
66]. With τ increasing above ∼3, the differences in BTD(3.7–11), BTD(8.5–11), BTD(11–12), and BTD(3.7–6.7) as a function of
De decrease eventually. BTD(6.7–11) is essentially insensitive to
De, which indicates that it could provide a good estimation of τ, since it increases asymptotically toward zero at τ > 20 in the present simulations. BTD(6.7–7.3) only shows differences for
De < 30 μm. When the opaque ice cloud τ increases, the sensitivity of these BTDs to
De decreases dramatically. BTD(8.5–11) and BTD(11–12) are only sensitive to small
De while BTD(3.7–11) and BTD(3.7–6.7) still show weak sensitivity to large values of
De.
Although BTD(3.7–11), BTD(8.5–11), BTD(11–12), and BTD(3.7–6.7) show significant variability over the deep convective clouds (τ > 20), the general feature of decreasing BTDs with increasing
De is still apparent. In order to investigate the potential for estimating
De, the BTDs for each
De are averaged for ice clouds having τ in the range of 20–100.
Figure 16 shows the BTD(3.7–11), BTD(8.5–11), BTD(11–12), and BTD(3.7–6.7) over the tropical deep convective clouds (20 < τ < 100) as a function of
De. It is evident that BTD(3.7–11) and BTD(3.7–6.7) are sensitive to
De, especially for
De > 50. BTD(8.5–11) is only sensitive to
De values smaller than 50–70 μm and BTD(11–12) is only sensitive to the smallest
De values. This feature reveals the potential for estimating small
De using those two BTDs for tropical deep convective clouds during nighttime. The dependencies of BTD(3.7–11) and BTD(3.7–6.7) are likely too small to be useful for a retrieval of
De for τ > 20 for two reasons. At the low temperatures associated with these thick clouds, the noise at ∼3.7 μm can be as high as 3.5 K [
67] and the uncertainty in the water vapor in and around the cloud top can cause errors of ∼1 K (shown later), which cover the range of the signal in
Figure 16.