Correlation-dimension analysis is often used to quantify the dynamics of the obscure attractor from the measured time series. Specifically, the method of sliding-window correlation-dimension is used to detect the temporal changes of the number of controlling parameters in a dynamical process, for example, geomagnetic fluctuation through time. By means of sliding-window correlation-dimension analyses of total-field fluctuations at three geomagnetic ground stations in Taiwan, a decrease in correlation dimension during storms has been confirmed in this paper. Such a decrease in the correlation dimension strongly indicates shrinking of phase space in the geomagnetic dynamical system, while the hidden, degenerated state variable remains inconclusive and more work is needed to address this issue.