Abstract
In this chapter we shall extend the ideas from the previous chapters to the three-dimensional problem. We consider the case that we need to interpolate to a departure point in three dimensions. We shall introduce some different vertical coordinate systems that are used in operational numerical weather prediction systems, as well as in ocean modeling. We shall consider finite difference, finite element, and finite volume approaches, all as an extension of the flux-form from the last chapter for chemical transport. We revisit the assumptions of only needing two iterations to find the departure point, as well as being inconsistent in the order of the velocity interpolation compared to the fields' interpolation to the departure point.
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