Geostrophic Scatter Diagrams and Potential Vorticity Dynamics

Abstract

Abstract A scatter diagram may be constructed by choosing an appropriate closed or open horizontal curve in physical space and plotting the value of any scalr quantity q against the geostrophic streamfunction ψ for each data point on the curve. The area enclosed on the scatter diagram is equal to the net geostrophic advective flux of q across the chosen curve in physical space. When q is the (quasi-geostrophic) potential vorticity Q, and suitable normalizations are adopted, this result may he exploited to derive measures of departure from free-mode form Q)= Q(ψ) along the curve in physical space. For a certain class of open space curves, an appropriate measure is the width-to-length ratio of the circuit in (ψ, Q) space. Most scatter diagrams that have appeared in the literature included the (ψ, Q) points corresponding to all the data or grid points within a given horizontal domain. The significance of the area enclosed on these diagrams is less clear, but the spread about some curve Q) = Q(ψ) is evidently...