Computational aspects of methods used to simulate the transport of water vapour in a global atmospheric general circulation model are examined. A set of properties useful in characterizing numerical methods for modelling atmospheric transport are identified. Spectral and semi-Lagrangian methods, which are very different in terms of these desired properties are compared. The extent to which the schemes do not satisfy certain properties of the continuous equations provides a measure of one component of the error of the solution. For the spectral scheme, negative specific humidities q indicate such an error component. Conventional semi-Lagrangian schemes are also susceptible to generating negative values. In addition, they are not inherently conservative. Shape-preserving semi-Lagrangian methods do not generate negative values, but still are non-conservative. The degree to which the advection process does not conserve mass provides a measure of another error associated with the numerical solution. The negative error is shown to be large for the spectral transport scheme, measured either locally or globally. Measured globally, the semi-Lagrangian transport schemes' conservation errors are equally large. Locally, the correction of this error can be made very much smaller, relative to physical processes in the model. The study highlights the computational problems which still exist within the better numerical methods used to simulate the transport of water vapour, and demonstrates the care with which one must apply computational constraints to the solution. The spectral and semi-Lagrangian transport schemes produce very different climatologies in model simulations. A comparison of these climatologies will appear elsewhere.
