e., following the tidal excursion). Neglecting cross-shore advection (including PD-0332991 chemical structure rips, etc.) will generally lead to conservative estimates of the contribution of physical dilution to FIB decay. In the AD model, FIB particles are advected alongshore by 20 min average currents (u), that vary in the cross-shore (y). FIB particles diffuse along- and cross-shore by horizontal diffusion (κh). For a particle starting at (xt, yt), its position at (xt+Δt, yt+Δt) is: equation(2) xt+Δt=xt+∂κh(yt)∂yΔt+R2κhryt+12∂κh∂yΔtΔt+uΔt equation(3) yt+Δt=yt+∂κh(yt)∂yΔt+R2κhryt+12∂κh∂yΔtΔtwhere R is a random
number with zero mean and variance r. For this model, r = 1/3, giving R a uniform distribution with range [−1 1] ( Ross and Sharples, 2004 and Tanaka and Franks, 2008). The time step was Δt = 1 s for all model runs. A reflecting boundary condition was used at the shoreline; otherwise particles could move anywhere in the domain. The AD model was initialized at
t0 = 0650 h (the earliest FIB sampling time) with 80,000 bacterial particles distributed uniformly within a rectangular (x, y) patch. Each particle represents a number of FIB (concentration C); the actual number of FIB per particle can be scaled to match the data, provided the same scaling is applied to every particle. Our scaling constants were determined such that the space–time mean of AD modeled FIB equaled Selleckchem INCB024360 the space–time mean of measured FIB (E. coli or Enterococcus). Initial patch boundaries (along and cross-shore) were identified by varying patch boundary locations over Niclosamide reasonable ranges to maximize the skill between the AD model and HB06 FIB data. Skill is defined as: equation(4) Skill=1-mean(Cobs-Cmod)2mean(Cobs-C¯obs)2where Cobs are log FIB concentration
data, Cmod are log AD model outputs, and C¯obs is the space–time mean of log(Cobs) for all stations and times ( Krause et al., 2005). Here, skill is a measure of how much better (or worse) the model explains fluctuations in the data than the data mean. A value of 0 indicates that the model performs the same as the data mean. A value of 1 indicates that the model explains all the variance after removing the mean, and a negative value indicates that the model performs worse than the data mean. Depending on the context, the numerator for skill was calculated for individual stations, groups of stations, or all stations together; the denominator was always the same (all stations). HB06 FIB observations showed the offshore FIB patch edge to be ∼140–300 m from the shoreline. The effect of this range of possible offshore patch edges was explored in the model. The northernmost patch edge was varied from 0 to 2000 m north of the sampling region, and the southernmost patch edge was varied from 0 to 2000 m south of the sampling region. The initial patch always included the 1 km-long sampling region.