Fig. 4. Description of Eularian and Lagrange methods for capturing the dynamics of variables that are driven by processes occurring over small spatial scales or time periods. In GCM, we used the Lagrange approach to reduce computational costs, allowing decadal-scale simulations. The Eularian approach involves computing the change in the state of all parcels of water (represented by the grid cells) over successive time periods. The Lagrange approach can be used to reduce computational costs by computing changes over time in a representative spatial parcel of water (the gray cells) as it moves downstream through the space-time field (the gray points represent the Eularian grid) in a sample track (the black arrows).