Robust and less robust features in the tangential geostrophy core flows

P>A number of core surface flow models have been inferred from geomagnetic field models by applying the frozen-flux induction equation. It is well known, however, that the flow is not fully resolvable. Because of theoretical and observational setbacks, the model space of the flow involves a null-space. Elements of the effective null-space can be considered as flows generating geomagnetic secular variation (SV) not sufficiently large compared with the variance of SV models. In the flow inversion, spurious flows belonging to such an effective null-space, thereby practically free from the direct constraint from the SV, may possibly emerge in resulting flow models and disguise the true core flow image. In this paper, we investigate the typical manifestation of the effective null-space in the model flow space, to discuss which part of estimated flow models is subject to the ambiguity due to the false imaging. From existing flow models built with the tangential geostrophy (TG) assumption, we extract a part belonging to the effective null-space. The extraction is performed in the spherical harmonic domain, analyzing the observation equation matrix associating truncated spherical harmonic coefficients of SV and TG flow. This approach is applied to typical TG flow models, epoch by epoch, over the time-span 1842.5-1987.5. The extracted flows are prominent in the azimuthal direction particularly around the equatorial region and vary vigorously in time. They are largely responsible for the zonal toroidal component of the examined models at mid- and low latitudes, whereas not at the polar regions. It is shown, nevertheless, that this poorly robust flow part does not so seriously affect the prediction of the decadal length-of-day variations.