Sigma coordinate pressure gradient errors: Evaluation and reduction by an inverse method

Sigma coordinate models currently suffer from the difficulty encountered in specifying the horizontal pressure gradient. Most of me efforts to reduce this truncation error lead to the loss of at least one integral constraint in the pressure gradient scheme (energy, tracer balance, etc.). Starting fr om a usual Arakawa-based scheme, it is shown that judicious adjustment of t he sigma surfaces together with control of the bottom topography slope para meter and an "optimal modification" of the measured initial pressure held l ead to a drastic reduction in the truncation errors. The first experiment i s based on a coastal academic domain in order to compare the results of the proposed inverse method with published data. A few experiments are then co nducted on the eastern pan of the Gulf of Lions in the Mediterranean using data from the Suiviolion experiment.