Numerical Integration and Interpolation in Marine Pollutant Transport Modelling

Abstract

Transport modelling of oil and other chemicals in the ocean relies on information on curret velocity as a function of position and time, v(x, t). These data will in many cases be supplied from an ocean circulation model, which produces a velocity field with vectors given at discrete points on a four-dimensional grid. If we consider for simplicity a passive tracer that moves with the water velocity at its position, then calculating the trajectory of the tracer, x(t), starting from a position x_0 when t = 0, can be done by numerically integrating the differential equation x = v(x, t), with the initial condition x(t = 0) = x0.