Basic concepts -- Climate variability diagnosed in spherical coordinates -- Climate variability diagnosed in z-coordinate -- External/internal modes in meridional/zonal directions -- Adiabatic signals in the upper ocean -- The regulation of MOC (MHF) by wind stress and buoyancy anomaly -- Adiabatic Heaving signals in the deep ocean -- Heaving, stretching, spicing and isopycnal analysis -- Heaving, stretching and spicing modes -- Potential Spicity -- Sigma-pi diagram and its application -- Isopycnal analysis -- Heaving modes in the world oceans -- Heaving induced by wind stress anomaly -- Heaving induced by anomalous freshwater forcing -- Heaving induced by anomalous wind, freshening and warming -- Heaving induced by convection generated gravity anomaly -- Heaving induced by deep convection generated volume loss -- ENSO events and heaving modes -- Heaving signals in the isopycnal coordinate -- Introduction -- Coordinate transformation by the casting method -- Coordinate transformation by the projecting method -- Difference between the casting method and the projecting method -- Isopycnal layer analysis for the world oceans -- Isopycnal layer analysis based on -- Heaving signals for the shallow water in the Pacific-Indian basin -- Heaving signal propagation through the equatorial sections -- Heaving signals in the isothermal coordinate -- Introduction -- Casting method -- Casting method applied to the GODAS data -- Projecting method -- Signal of layer depth and zonal velocity in the Pacific basin -- Z-theta diagram and its application to climate variability analysis -- Climate signals in the salinity coordinates -- Introduction -- Casting method -- Separating the signals into external and internal modes -- Analysis based on the GODAS data -- Shallow salty water sphere in the Atlantic Ocean.