Ice water path-optical depth relationships for cirrus and deep stratiform ice cloud layers

Particle size distribution (PSD) and particle shape information collected during Lagrangian spiral descents and balloon ascents through 13 midlatitude and 6 tropical ice clouds are analyzed to investigate the relationship between cloud optical depth in visible wavelengths (τ_v) and the ice water path (IWP). Although this sample size is small, it is far larger than the number of samples used in earlier studies and has the added benefit that it contains data from the top to the bottom of cloud layers, averaging 3 km in geometrical thickness. Furthermore, the observed particle shape and habit information are used directly in the investigation, rather than assuming that the habits are one of a number of pristine types. These observations apply to midlatitude clouds in the temperature range from -65° to -20°C, with τ_v between 0.5 and 7, and estimated radar reflectivities primarily in the range from -20 to 5 dBZ_e (at a frequency of 35 GHz), with some observations extending down to -45 dBZ_e. The tropical observations apply to clouds in the temperature range from -50° to 0°C, with τ_v in the range 20-30, and radar reflectivities primarily between -5 and 25 dBZ_e (at a frequency of 35 GHz). Quantitative relationships between τ_v and IWP that depend on the cloud thickness, midcloud temperature, slope of the particle size distribution, median mass diameter, and effective radius are explored and developed. The underlying basis of these relationships is the correlation between the slope of the particle size distribution and cloud temperature or thickness. The slope of the particle size distribution tends to decrease with increasing cloud thickness (beginning from cloud top) and temperature. This tendency toward a flatter spectral slope, with increasing penetration into the cloud layer, leads to a monotonic decrease in the extinction coefficient relative to the ice water content downward from the cloud top to base. Relationships between τ_v and IWP as a function of the effective radius (r_e) and the median mass diameter (D_m) are found from these observations, and are compared with those found in earlier studies. Given a value of the IWP and a known value of r_e, the earlier studies provide estimates of the τ_v that are comparable to the results of this study. Several means of estimating r_e and D_m indirectly, to circumvent the need to know the values of these variables directly from measurements, are developed. First, relationships are developed between r_e and IWP. Second, relationships are developed to retrieve these variables front vertically pointing Doppler radar observations.