Plz solve the PDE questionat least questionciSolutionThe AD

Plz solve the PDE question(at least question(c:i))

Solution

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 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 reasonable ranges to maximize the skill between the AD model and HB06 FIB data. Skill is defined as: Skill ¼ 1 meanðCobs CmodÞ 2 meanðCobs CobsÞ 2 ð4Þ where Cobs are log FIB concentration data, Cmod are log AD model outputs, and Cobs 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. Initial patch sizes that maximized alongshore and cross-shore station skill were used to initialize a ‘‘best-fit’’ AD model for subsequent comparisons between modeled and observed FIB concentrations and decay rates. The robustness of the model to alternative initial patch shapes is discussed briefly below (for)