On Ocean Transport Diagnostics: The Idealized Age Tracer and the Age Spectrum

Abstract The idealized age tracer is commonly used to diagnose transport in ocean models and to help interpret ocean measurements. In most studies only the steady-state distribution, the result of many centuries of model integration, has been presented and analyzed. However, in principle the transient solution provides more information about the transport. Here it is shown that this information can be readily interpreted in terms of the ventilation histories of water masses. A simple relationship is derived, valid for stationary transport, between the transient evolution, τid(r, t), of the idealized age tracer and the “age spectrum,” G(r, t), the distribution of times t since a water mass was last ventilated. Namely, G(r, t) = −∂ttτid(r, t). Implications of the relationship are discussed, and the relationship is illustrated with an idealized model.