The derivation of a numerical diagnostic model for the forcing of the geopotential

Simply applying the divergence operator to the horizontal velocity equation in spherical‐isobaric coordinates yields a more solvable linear geopotential equation (than the geopotential tendency and the omega equations) for diagnosing the geopotential and its anomalies responsible for global floods and droughts. This geopotential model is freed from the zero‐denominator problem caused by the observed neutral stability which affects the geopotential tendency and omega equations. The geopotential equation's forcing terms 2–5 (the direct operation results of the horizontal advection term in the velocity equation) can identify the synoptic signals mixed up by the classical divergence equation's quadratic and Jacobian terms (the manipulated results of the above terms 2–5). Solving this geopotential equation with the successive‐over‐relaxation method and the neutral stability as calculated from the reanalysis data produces reasonably good reconstructions of the global and local geopotential fields. The additional advantages of the present geopotential model over the geopotential tendency, omega and divergence models are that the geopotential model reveals and explains the following mechanisms which received less attention in previous studies. (1) The saddle patterns favour the high systems. (2) The equatorial easterlies favour the low systems. (3) The contributions of ageostrophic processes associated with jets and saddle flows to the transitions of weather patterns might be overlooked by the geopotential tendency model in which neutral stability and static instability in cold domes as well as jet‐induced inertial instability are smoothed out artificially. Copyright © 2008 Royal Meteorological Society