SUPERPOSING SEMI-GEOSTROPHIC POTENTIAL-VORTICITY ANOMALIES

A numerical method for inversion of the semi-geostrophic potential-vor ticity equation is described. It is used to examine the validity of a strictly linear superposition principle when applied to this high-orde r balance model. These results are important when aiming to extend rig orously the value of recent 'attribution' ideas. Experiments conclude that the nonlinear components of the inversion have only a very short- range effect, with a magnitude which increases with the magnitude of t he potential-vorticity anomalies. For balance of higher-order than qua si-geostrophic these results show that, whilst flow and temperature of an anomaly are nonlinear functions of potential-vorticity magnitude, spatially separated anomalies are quasi-linearly superposable.