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CART(Constituent-oriented age and residence time theory) and PTM(Particle-tracking method) are two widely used numerical methods to calculate water age. These two methods are essentially equivalent in theory but their results may be different in practice. The difference of the two methods was evaluated by applying them to calculate water age in an idealized one-dimensional domain. The model results by the two methods are consistent with each other in the case with either spatially uniform flow field or spatially uniform diffusion coefficient. If we allow the spatial variation in horizontal diffusion, a term called pseudo displacement arising from the spatial variation of diffusion coefficient likely plays an important role for the PTM to obtain accurate water age. In particular, if the water particle is released at a place where the diffusion is not the weakest, the water age calculated by the PTM without pseudo displacement is much larger than that by the CART. This suggests that the pseudo displacement cannot be neglected in the PTM to calculate water age in a realistic ocean. As an example, we present its potential importance in the Bohai Sea where the diffusion coefficient varies spatially and greatly.
CART (Constituent-oriented age and residence time theory) and PTM (Particle-tracking method) are two widely used numerical methods to calculate water age. The two of them are essentially equivalent in theory but their results may be different in practice. The difference of the two methods was evaluated by applying them to calculate water age in an idealized one-dimensional domain. The model results by the two methods are consistent with each other in the case with either spatially uniform flow field or spatially uniform diffusion coefficient. If we allow the spatial variation in horizontal diffusion, a term called pseudo displacement arising from the spatial variation of diffusion coefficient likely plays an important role for the PTM to obtain accurate water age. In particular, if the water particle is released at a place where the diffusion is not the weakest, the water age calculated by the PTM without pseudo displacement is much larger than that by the CART. This suggests that the as an example, we present its potential importance in the Bohai Sea where the diffusion coefficient varies spatially and greatly.