A new approach has been proposed to derive the expressions for three-dimensional radiation stress using solutions of the pressure and velocity distributions and the coordinate transformation function that are derived from a Lagrangian description wherein the pressure is zero (relative to the atmospheric pressure) at the sea surface. Using this approach, analytical expressions of horizontal and vertical depth-dependent radiation stress are derived at a uniform depth and for a sloping bottom, respectively. The results of the depth integration of the expressions agree well with the theory of Longuet-Higgins and Stewart. In the case involving a sloping bottom, the radiation stress expressions from this study provide a better balance of the net momentum compared to those from previous studies.

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We report simultaneous global monitoring of a patch of ionization and in situ observation of ion upflow at the center of the polar cap region during a geomagnetic storm. Our observations indicate strong fluxes of upwelling O+ ions originating from frictional heating produced by rapid antisunward flow of the plasma patch. The statistical results from the crossings of the central polar cap region by Defense Meteorological Satellite Program F16–F18 from 2010 to 2013 confirm that the field‐aligned flow can turn upward when rapid antisunward flows appear, with consequent significant frictional heating of the ions, which overcomes the gravity effect. We suggest that such rapidly moving patches can provide an important source of upwelling ions in a region where downward flows are usually expected. These observations give new insight into the processes of ionosphere‐magnetosphere coupling.