Superposing semi‐geostrophic potential‐vorticity anomalies

A numerical method for inversion of the semi‐geostrophic potential‐vorticity equation is described. It is used to examine the validity of a strictly linear superposition principle when applied to this high‐order balance model. These results are important when aiming to extend rigorously 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 the potential‐vorticity anomalies. For balance of higher‐order than quasi‐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.