Gamma Distribution Fits of the Fog Droplet Size Spectrum – Impacts on Integrated Quantities.

The droplet size distribution (DSD) varies in shape depending on the fog type and evolves throughout a single fog event. Droplet size distributions govern integrated quantities, like the extinction coefficient, and are generally difficult to model but have significant importance to remote sensing applications. The extinction coefficient from the horizontal propagation of two electromagnetic waves can provide a path-averaged DSD if the shape of the DSD can be constrained. To help quantify the shape of the DSD we fit a Gamma distribution to the measured DSD and use the three coefficients that govern the shape of the Gamma distribution to understand how the resulting DSD evolves. We look at several fog events during the Fatima (Fog and Turbulence Interactions in the Marine Atmosphere) Grand Banks campaign on Sable Island and the Fatima Yellow Sea campaign. Both campaigns primarily consisted of marine advection fog, so we contrast these campaigns with fog events from the C-FOG campaign in Ferryland, Newfoundland, and the CFACT (Cold Fog Amongst Complex Terrain) campaign in Heber, Utah which contained a mix of radiation and mixing/advection fog. We find that coefficients of the Gamma distribution separate into two regimes. The coefficients from the two strictly marine fog campaigns followed one regime whereas the coefficients of the other campaigns followed a separate regime, indicating that there is a difference in the shape of the DSD between fog types. We hypothesize that these two different regimes are due to differences in fog formation mechanisms (e.g. radiation vs advection) alongside influences from collision coalescence and other microphysical processes throughout the lifecycle of the fog event.

We present the measured DSDs for several fog events with the associated fit from the Gamma distribution. We further show how the coefficients for the Gamma distribution change throughout the life cycle of the fog events. We illustrate the variability and uncertainty in the coefficients through the probability density functions of the coefficients. Finally, we explore these coefficients' impact on the DSD's integrated quantities (e.g., visibility, extinction coefficient, liquid water content, and effective radius). We explore whether the extinction coefficient at two unique wavelengths (near-infrared and microwave) can be used to determine the Gamma distribution coefficients and recreate a path-averaged DSD. Since the resulting DSD is based on horizontally integrated measurements it could provide a valuable link between traditional point measurements of visibility and the larger scales associated with numerical weather prediction models.