Understanding effective diameter and its application to terrestrial radiation in ice clouds
Abstract. The cloud property known as "effective diameter" or "effective radius", which in essence is the cloud particle size distribution (PSD) volume at bulk density divided by its projected area, is used extensively in atmospheric radiation transfer, climate modeling and remote sensing. This derives from the assumption that PSD optical properties can be uniquely described in terms of their effective diameter, De, and their cloud water content (CWC), henceforth referred to as the De-CWC assumption. This study challenges this assumption, showing that while the De-CWC assumption appears generally valid for liquid water clouds, it appears less valid for ice clouds in regions where (1) absorption is not primarily a function of either the PSD ice water content (IWC) or the PSD projected area, and (2) where wave resonance (i.e. photon tunneling) contributes significantly to absorption. These two regions often strongly coincide at terrestrial wavelengths when De<~60 μm, which is where this De-CWC assumption appears poorest. Treating optical properties solely in terms of De and IWC may lead to errors up to 24%, 26% and 20% for terrestrial radiation in the window region regarding the absorption and extinction coefficients and the single scattering albedo, respectively. Outside the window region, errors may reach 33% and 42% regarding absorption and extinction. The magnitude and sign of these errors can change rapidly with wavelength, which may produce significant errors in climate modeling, remote sensing and other applications concerned with the wavelength dependence of radiation.
Where the De-CWC assumption breaks down, ice cloud optical properties appear to depend on De, IWC and the PSD shape. Optical property parameterizations in climate models and remote sensing algorithms based on historical PSD measurements may exhibit errors due to previously unknown PSD errors (i.e. the presence of ice artifacts due to the shattering of larger ice particles on the probe inlet tube during sampling). More recently developed cloud probes are designed to mitigate this shattering problem. Using realistic PSD shapes for a given temperature (and/or IWC) and cloud type may minimize errors associated with PSD shape in ice optics parameterizations and remote sensing algorithms.
While this topic was investigated using two ice optics schemes (the Yang et al., 2005 database and the modified anomalous diffraction approximation, or MADA), a physical understanding of the limitations of the De-IWC assumption was made possible by using MADA. MADA allows one to approximate the contribution of photon tunneling to absorption relative to other optical processes, which reveals that part of the error regarding the De-IWC assumption can be associated with tunneling. By relating the remaining error to the radiation penetration depth in bulk ice (ΔL) due to absorption, the domain where the De-IWC assumption is weakest was described in terms of De and ΔL.