First Ever Satellite Remote Sensing of Small Ice Crystals in Cirrus Clouds:
Theory and Methods

How Photon Tunneling Can be Used to Remotely Detect
Small Ice Crystals in Cirrus

Photon Tunneling is the process by which radiation beyond the physical cross-section of a particle is either absorbed or scattered outside the forward diffraction peak. Tunneling is strongest when:

1. Effective size and wavelength are comparable
2. Particle shape is spherical or quasi-spherical
3. The real refractive index is relatively large

Therefore tunneling contributions at thermal infrared wavelengths are greatest for smallest (D < 60 μm) ice crystals. To detect the tunneling signal is to detect small ice crystals.

Ice particle size distribution (PSD) scheme for evaluating potential tunneling contributions
(scheme in red; green and blue = observed mean PSD)

Based on 22 flight missions in synoptic mid-latitude cirrus, PSD measured by the FSSP, CPI and 2DC probes were averaged over temperature intervals of 5 °C and are shown in blue and green. Red curves are predicted by the PSD scheme developed from these measurements, based on the temperature and ice water content of the observed PSD.

Decomposition of the two modes of the PSD

Shown above are the predicted complete PSD (blue + green) and the PSD for the large mode only (green) at the indicated temperatures. The effective diameter or D_e for both PSD are given. When only the large mode is used, 12-11 μm emissivity differences are near zero. By incrementing the small mode, so also these emissivity differences increase. In this way this PSD scheme is used to retrieve the concentration of small ice crystals, along with D_e.

Only the large mode of the size distribution is used to calculate the above absorption efficiencies from two different methods: finite difference time domain (FDTD) and the modified anomalous diffraction approximation or MADA (Mitchell 2000, 2002; Mitchell et al. 2006). Photon tunneling is explicitly represented in MADA, and is set to zero here. The close agreement between MADA and FDTD indicate that tunneling contributions are negligible when only the large mode is considered.

Absorption efficiencies (Q_abs) for a bimodal size distribution (solid curve) comprised of quasi-spheres (droxtals) in the small mode and bullet rosettes in the large mode. Dashed curve is for the large mode, rosettes only. Q_abs for wavelengths > 11 μm are greater for the complete PSD due to tunneling. Tunneling depends strongly on the real index of refraction, n_r. The reason Q_abs is greater at 12 μm than 11 μm when the full PSD is used is because n_r has a minimum near 11 μm but is substantial at 12 μm. Since tunneling is a measure of the small mode, and the 11 – 12 μm Q_abs difference is only from tunneling, this difference serves as a measure of the small mode of the PSD. These calculations are based on the optical property database given in Yang et al. (Appl. Opt. 2005).

Theoretical curves of effective emissivity difference vs. effective emissivity, based on the above PSD scheme. Dashed curves are based on the large mode only while solid curves are based on the complete PSD (small mode + large mode) for different temperatures. The higher the small mode ice mass content (or ice crystal number concentration, N_sm), the higher the "arches" are. This principle is used to determine N_sm by matching theory with observations, as described alongside this figure.

1. Begin with satellite retrievals of cloud temperature and cloud emissivity (ε) at 11 and 12 μm wavelength channels.
2. Use retrieved temperature to estimate PSD mean size D and dispersion (ν) for large and small mode. Difference between the solid and dashed curves results primarily from differences in contribution of small PSD mode to the ice water content (IWC). This also determines the effective diameter D_e. Dispersion parameter v has little influence on the emissivities or emissivity differences.
3. Locate retrieved ∆ε (y-axis) and the 11 μm ε by (1) incrementing the modeled ice water path (IWP) to increase ε(11 μm) and (2) incrementing the small mode contribution to the cloud IWC, which elevates the curve.
4. If all IWC is in small mode and retrieved ∆ε and ε(11 μm) are still not located, then decrease small mode D to locate them.
5. If retrieved point lies below the “large mode only” curve (e.g. a dashed curve), then systematically decrease D for large mode until a match is obtained. Negative ∆ε values correspond to maximum allowed D values.
6. This method retrieves IWP, D_e, and the small-to-large mode ice crystal concentration ratio. For a given IWC, it also estimates the ice particle number concentration and the complete PSD, even when it is bimodal.