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.