Climate signals in the world oceans are dominated by adiabatic heaving modes intimately linked to adjustment of the thermocline in response to wind stress perturbations; these signals propagate in forms of Rossby waves and Kelvin waves. Climate variability can be explored in terms of a simple reduced gravity model. For example, the effect of diabatic cooling in the subpolar basin can be examined in terms of an adiabatic model based on the concept of the reduced gravity model.Climate changes signals can be view in terms of heaving modes, which are defined in terms of isopycnal coordinates. Heaving signals can be defined in terms of the movement of isopycnal layers, and they can be separated into the external and internal modes. The extended isopycnal analysis provides a rigorous way to diagnose climate variability and sheds light on physical processes driven the climate variability.