Time-dependency of tangentially geostrophic core surface motions

We present new models of core surface motions for the period 1840-1990. The models are derived under the frozen flux and tangentially geostrophic approximations which neglect, firstly, the contribution of magnetic diffusion to the observed secular variation, and secondly, the contribution of Lorentz forces in the horizontal force balance at the top of the core. The flows are constructed on a temporal basis of B-splines, erected over the 150-year period 1840-1990, and on a spatial basis of toroidal and poloidal vectors in a spectral spherical harmonic expansion. Our parametrisation uses 12 348 parameters in total, but the use of the B-spline basis allows us to solve the resulting linear system using less than 10 MWords of storage. The time-dependent flows are derived so as to be the simplest in a precisely defined spatial and temporal sense which remain compatible with the available data. Of particular interest is the time-dependency of the flows: we expect the flows to be unsteady because changes in the length-of-day on a decade timescale are believed to indicate changes of angular momentum of the core. We show that, despite minimising temporal variations in the flow, such variations are necessary in order for the flows to be able to fit observatory data to an acceptable level; this is seen by comparing the data directly with the observatory time series, and the fit is also quantified globally. Additionally, the root mean square radial secular variation averaged over the earth's surface exhibits two maxima in 1914 and 1978, and the root mean square flow speed averaged over the core surface exhibits two similar peaks at the same times which are a direct consequence of this. We confirm and extend the results of earlier studies showing the probable connection between the surface motions and the changes in the length-of-day. Some 'oscillatory' behaviour can be seen, although the time-period studied is too short to be definitely indicative of truly periodic phenomena. (C) 1997 Elsevier Science B.V.