Parameter: B

Flux particle size distribution magnitude and slope parameters (parameter names 'A', 'B'):

Particles imaged in each gel at the same magnification were identified, enumerated and measured using an analysis macro created using ImageJ software. Using this macro, images were processed by 1) converting images to greyscale, 2) removing background, 3) adjusting brightness/contrast to a consistent degree, 4) thresholding using the "Intermodes" technique, 5) filling holes, and 6) measuring particles. Particles imaged from the same field of view but different focal planes were grouped together and the equivalent spherical diameter (ESD) of each particle was calculated based on the measured two-dimensional surface area. Particles were divided into 26 base-2, log-spaced size classes ranging from 1 um to 8192 um based on their ESD. Counting error was calculated as the square root of the number of particles counted in each size category. Size classes with 4 or fewer counted particles (>=50% error) were excluded from analysis. The abundance of particles in each size bin was calculated by normalizing the number of particles counted by the size bin width and by the percentage of the gel surface counted. The optimal magnification to calculate the abundance of a particle size category was defined as the magnification where the observed abundance most closely followed a power-law distribution. The abundance of 11-45 um particles was quantified at 63x magnification, the abundance of 45-128 um particles was quantified at 16x magnification, and the abundance of >128 um particles was quantified at 7x magnification. Three samples had slightly different size detection limits at each magnification and required different size ranges to quantify a power law distribution of particle abundance. For the 200-m sample collected in August, optimal particle size ranges were 11-64 um (63x), 64-90 um (16x), and >90 um (7x). For the 500-m samples collected in October and March, the optimal size ranges were 11-45 um (63x), 45-64 um (16x), and >64 um (7x). The particle abundance of all five gel trap process blanks were measured and averaged together, and the average was subtracted from the particle abundance measured in each gel trap sample. Particle number flux was calculated by dividing blank-subtracted particle abundance by the trap deployment time.

The slope of each particle size distribution (B) was calculated by fitting the observations of particle number flux (Num_f) to a differential power law size distribution model (Jackson et al., 1997),

Num_f(ESD) = A(ESDr) x (ESD/ESDr)-B

where A(ESDr) equals the number flux of particles in the reference size category ESDr (here 300 um). B indicates the slope of the power law function; higher values have steeper slopes and a higher proportion of small particles relative to large particles. The "optim" function in R (R. Development Core Team, 2008) was used to find the least-squares, best-fit values of ?(ESDr) and ? describing particle number fluxes measured in each gel trap.