Potential spicity (pi) is redefined, which contours are orthogonal to potential density (sigma) contours in the least square sense. Water masses can be viewed in the sigma-pi diagram, instead of the traditional T-S diagram. Due to the or thogonality, distance between water masses in sigma-pi diagram can be rigorously defined. The concept of the distance in water mass analysis proves a new tool in our understanding of the physics of the oceanic circulation.
For a collection of data points, the radius of signal can be defined by the root-mean square distance to the center of water masses. For the world oceans or a regional ocean, the state of oceanic circulation can be evaluated in terms of the radius of the state which is similarly defined. The radius of state proves a powerful index for evaluation of the oceanic state.
The radius of signal can be used to quantify the degree of success in separating climate signals identified from climate data. As an example, this concept is applied to the isopycnal analysis for the oceanic data.