Therefore, the estimate of the particle age (the buy Idelalisib average time for the coastal hit) is apparently underestimated for areas with a low probability of coastal hits. The cell-wise probabilities of coastal hits Pi,j(k) and particle age Ai,j(k) are calculated for each time window k (out of a total of N = 170 time windows) in a straightforward way as the average of the relevant values pmkij, amkij over all M particles released into a particular cell (i , j ): equation(1) Pi,j(k)=1M∑m=1Mpmkij,Ai,j(k)=1M∑m=1Mamkij.Here pmkij and amkij are the values of the counters showing, respectively, whether the m-th particle released into grid cell (i, j) at the beginning of the k-th time window has reached the coast during
this window and the particle age either at the Selleckchem SGI-1776 instant of the first coastal hit or, alternatively, the duration of this time window if the particle remains offshore. This procedure leads to two sets of 2D maps (with a spatial resolution equal to that of the circulation model) of the cell-wise probability of particles released into a particular cell hitting the coast (below referred to as ‘probability’) and the mean time (particle age) for coastal hits for particles from this
cell. The first quantity is a variation of the measure of the probability of coastal hits used by Soomere et al. (2010) to identify the equiprobability line for coastal hits in the Gulf of Finland. The two variables obviously mirror each other to some extent. For example, the minimum of probability evidently occurs more or less where the particle age reaches a maximum. Consequently, the optimum fairways found on the basis of these fields should be located close to each other. The difference between them can be interpreted as a measure of the uncertainty of the entire approach (Soomere et al. 2010). Note that particle age is really much more informative. For example, it is easy to convert particle age to probability (if the age of a particle is less than the duration of the time window, a coastal hit has occurred) but it is impossible to convert the probability PIK3C2G to age. We start the analysis of the similarities and differences
of the results for different model resolutions by comparing the average values of the probability P(k)=〈Pi,j(k)〉 and particle age A(k)=〈Ai,j(k)〉 over all particles released into the entire Gulf of Finland for a particular time window k . Here, the angled brackets signify the operation of taking the arithmetic mean over all L sea points in the calculation area (L = 2270 for the 2 nm model, L = 8810 for the 1 nm model and L = 31838 for the 0.5 nm model ( Andrejev et al. 2010)). Another pair of important quantities are the cumulative average probability P¯(n) for the coastal hit and the cumulative average age A¯(n) of all particles over the entire calculation area and for the first n time windows. They are defined in the classical way: equation(2) P¯(n)=1n∑k=1nP(k),A¯(n)=1n∑k=1nA(k).